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import argparse
import numpy as np
import os
import pprint
import yaml
# HACK: Get logger to print to stdout
import sys
sys.ps1 = '>>> ' # Make it "interactive"
import tensorflow as tf
from multiprocessing import Queue
from lib.config import cfg_from_file, cfg_from_list, cfg
from lib.data_process import make_data_processes, kill_processes
from lib.solver import Solver
from lib.solver_encoder import TextEncoderSolver, TextEncoderCosDistSolver, LBASolver
from lib.solver_gan import End2EndGANDebugSolver
from lib.solver_classifier import ClassifierSolver
from lib.cwgan import CWGAN
from lib.lba import LBA
from lib.classifier import Classifier
import lib.utils as utils
import models
del sys.ps1 # HACK: Get logger to print to stdout
def parse_args():
"""Parse the arguments.
"""
parser = argparse.ArgumentParser(
description='Main text2voxel train/test file.')
parser.add_argument('--cfg',
dest='cfg_files',
action='append',
help='optional config file',
default=None,
type=str)
parser.add_argument('--dont_save_voxels', dest='dont_save_voxels', action='store_true')
parser.add_argument('--lba_only', dest='lba_only', action='store_true')
parser.add_argument('--metric_learning_only', dest='metric_learning_only', action='store_true')
parser.add_argument('--non_inverted_loss', dest='non_inverted_loss', action='store_true')
parser.add_argument('--synth_embedding', dest='synth_embedding', action='store_true')
parser.add_argument('--all_tuples', dest='all_tuples', action='store_true')
parser.add_argument('--reed_classifier', dest='reed_classifier', action='store_true')
parser.add_argument('--val_split',
dest='split',
help='data split for validation/testing (train, val, test)',
default=None,
type=str)
parser.add_argument('--queue_capacity',
dest='queue_capacity',
help='size of queue',
default=None,
type=int)
parser.add_argument('--n_minibatch_test',
dest='n_minibatch_test',
help='number of minibatches to use for test phase',
default=None,
type=int)
parser.add_argument('--dataset', dest='dataset',
help='dataset',
default=None,
type=str)
parser.add_argument('--improved_wgan', dest='improved_wgan', action='store_true')
parser.add_argument('--debug', dest='is_debug', action='store_true')
parser.add_argument('--rand', dest='randomize',
help='randomize (do not use a fixed seed)',
action='store_true')
parser.add_argument('--tiny_dataset', dest='tiny_dataset',
help='use a tiny dataset (~5 examples)',
action='store_true')
parser.add_argument('--model',
dest='model',
help='name of the network model',
default=None,
type=str)
parser.add_argument('--text_encoder', dest='text_encoder',
help='train/test on text encoder',
action='store_true')
parser.add_argument('--classifier', dest='classifier',
help='train/test on classifier',
action='store_true')
parser.add_argument('--end2end', dest='end2end',
help='train/test using end2end model such as End2EndLBACWGAN',
action='store_true')
parser.add_argument('--shapenet_ct_classifier', dest='shapenet_ct_classifier',
help='chair/table classifier (sets up for classification)',
action='store_true')
parser.add_argument('--noise_size',
dest='noise_size',
help='dimension of the noise',
default=None,
type=int)
parser.add_argument('--noise_dist', dest='noise_dist',
help='noise distribution (uniform, gaussian)',
default=None,
type=str)
parser.add_argument('--validation', dest='validation',
help='run validation while training',
action='store_true')
parser.add_argument('--test', dest='test',
help='test mode',
action='store_true')
parser.add_argument('--test_npy', dest='test_npy',
help='test mode using npy files',
action='store_true')
parser.add_argument('--save_outputs', dest='save_outputs',
help='save the outputs to a file',
action='store_true')
parser.add_argument('--summary_freq',
dest='summary_freq',
help='summary frequency',
default=None,
type=int)
parser.add_argument('--optimizer',
dest='optimizer',
help='name of the optimizer',
default=None,
type=str)
parser.add_argument('--critic_optimizer',
dest='critic_optimizer',
help='name of the critic optimizer',
default=None,
type=str)
parser.add_argument('--batch_size',
dest='batch_size',
help='batch size',
default=None,
type=int)
parser.add_argument('--lba_mode',
dest='lba_mode',
help='LBA mode type (TST, STS, MM)',
default=None,
type=str)
parser.add_argument('--lba_test_mode',
dest='lba_test_mode',
help='LBA test mode (shape, text) - what to input during forward pass',
default=None,
type=str)
parser.add_argument('--visit_weight',
dest='visit_weight',
help='visit weight for lba models',
default=None,
type=float)
parser.add_argument('--lba_unnormalize', dest='lba_unnormalize', action='store_true')
parser.add_argument('--num_critic_steps',
dest='num_critic_steps',
help='number of critic steps per train step',
default=None,
type=int)
parser.add_argument('--intense_training_freq',
dest='intense_training_freq',
help='frequency of intense critic training',
default=None,
type=int)
parser.add_argument('--uniform_max',
dest='uniform_max',
help='absolute max for uniform distribution',
default=None,
type=float)
parser.add_argument('--match_loss_coeff',
dest='match_loss_coeff',
help='coefficient for real match loss',
default=None,
type=float)
parser.add_argument('--fake_match_loss_coeff',
dest='fake_match_loss_coeff',
help='coefficient for fake match loss',
default=None,
type=float)
parser.add_argument('--fake_mismatch_loss_coeff',
dest='fake_mismatch_loss_coeff',
help='coefficient for fake mismatch loss',
default=None,
type=float)
parser.add_argument('--gp_weight',
dest='gp_weight',
help='coefficient for gradient penalty',
default=None,
type=float)
parser.add_argument('--text2text_weight',
dest='text2text_weight',
help='coefficient for text2text loss',
default=None,
type=float)
parser.add_argument('--shape2shape_weight',
dest='shape2shape_weight',
help='coefficient for shape2shape loss',
default=None,
type=float)
parser.add_argument('--learning_rate',
dest='learning_rate',
help='learning rate',
default=None,
type=float)
parser.add_argument('--critic_lr_multiplier',
dest='critic_lr_multiplier',
help='critic learning rate multiplier',
default=None,
type=float)
parser.add_argument('--decay_steps',
dest='decay_steps',
help='decay steps',
default=None,
type=int)
parser.add_argument('--num_epochs',
dest='num_epochs',
help='number of epochs',
default=None,
type=int)
parser.add_argument('--augment_max',
dest='augment_max',
help='maximum augmentation perturbation out of 255',
default=None,
type=int)
parser.add_argument('--set',
dest='set_cfgs',
help='set config keys',
default=None,
nargs=argparse.REMAINDER)
parser.add_argument('--ckpt_path', dest='ckpt_path',
help='Initialize network from checkpoint',
default=None)
parser.add_argument('--lba_ckpt_path', dest='lba_ckpt_path',
help='Initialize LBA component of end2endlbawgan network from checkpoint',
default=None)
parser.add_argument('--val_ckpt_path', dest='val_ckpt_path',
help='Initialize validation network from checkpoint',
default=None)
parser.add_argument('--log_path', dest='log_path', help='set log path',
default=None)
args = parser.parse_args()
return args
def modify_args(args):
"""Modify the default config based on the command line arguments.
"""
# modify default config if requested
if args.cfg_files is not None:
for cfg_file in args.cfg_files:
cfg_from_file(cfg_file)
randomize = args.randomize
if args.test: # Always randomize in test phase
randomize = True
if not randomize:
np.random.seed(cfg.CONST.RNG_SEED)
# NOTE: Unfortunately order matters here
if args.lba_only is True:
cfg_from_list(['LBA.COSINE_DIST', False])
if args.metric_learning_only is True:
cfg_from_list(['LBA.NO_LBA', True])
if args.non_inverted_loss is True:
cfg_from_list(['LBA.INVERTED_LOSS', False])
if args.dataset is not None:
cfg_from_list(['CONST.DATASET', args.dataset])
if args.lba_mode is not None:
cfg_from_list(['LBA.MODEL_TYPE', args.lba_mode])
if args.lba_test_mode is not None:
cfg_from_list(['LBA.TEST_MODE', args.lba_test_mode])
# cfg_from_list(['LBA.N_CAPTIONS_PER_MODEL', 1]) # NOTE: Important!
if args.shapenet_ct_classifier is True:
cfg_from_list(['CONST.SHAPENET_CT_CLASSIFIER', args.shapenet_ct_classifier])
if args.visit_weight is not None:
cfg_from_list(['LBA.VISIT_WEIGHT', args.visit_weight])
if args.lba_unnormalize is True:
cfg_from_list(['LBA.NORMALIZE', False])
if args.improved_wgan is True:
cfg_from_list(['CONST.IMPROVED_WGAN', args.improved_wgan])
if args.synth_embedding is True:
cfg_from_list(['CONST.SYNTH_EMBEDDING', args.synth_embedding])
if args.all_tuples is True:
cfg_from_list(['CONST.TEST_ALL_TUPLES', args.all_tuples])
if args.reed_classifier is True:
cfg_from_list(['CONST.REED_CLASSIFIER', args.reed_classifier])
if args.noise_dist is not None:
cfg_from_list(['GAN.NOISE_DIST', args.noise_dist])
if args.uniform_max is not None:
cfg_from_list(['GAN.NOISE_UNIF_ABS_MAX', args.uniform_max])
if args.num_critic_steps is not None:
cfg_from_list(['WGAN.NUM_CRITIC_STEPS', args.num_critic_steps])
if args.intense_training_freq is not None:
cfg_from_list(['WGAN.INTENSE_TRAINING_FREQ', args.intense_training_freq])
if args.match_loss_coeff is not None:
cfg_from_list(['WGAN.MATCH_LOSS_COEFF', args.match_loss_coeff])
if args.fake_match_loss_coeff is not None:
cfg_from_list(['WGAN.FAKE_MATCH_LOSS_COEFF', args.fake_match_loss_coeff])
if args.fake_mismatch_loss_coeff is not None:
cfg_from_list(['WGAN.FAKE_MISMATCH_LOSS_COEFF', args.fake_mismatch_loss_coeff])
if args.gp_weight is not None:
cfg_from_list(['WGAN.GP_COEFF', args.gp_weight])
if args.text2text_weight is not None:
cfg_from_list(['WGAN.TEXT2TEXT_WEIGHT', args.text2text_weight])
if args.shape2shape_weight is not None:
cfg_from_list(['WGAN.SHAPE2SHAPE_WEIGHT', args.shape2shape_weight])
if args.learning_rate is not None:
cfg_from_list(['TRAIN.LEARNING_RATE', args.learning_rate])
if args.critic_lr_multiplier is not None:
cfg_from_list(['GAN.D_LEARNING_RATE_MULTIPLIER', args.critic_lr_multiplier])
if args.decay_steps is not None:
cfg_from_list(['TRAIN.DECAY_STEPS', args.decay_steps])
if args.queue_capacity is not None:
cfg_from_list(['CONST.QUEUE_CAPACITY', args.queue_capacity])
if args.n_minibatch_test is not None:
cfg_from_list(['CONST.N_MINIBATCH_TEST', args.n_minibatch_test])
if args.noise_size is not None:
cfg_from_list(['GAN.NOISE_SIZE', args.noise_size])
if args.batch_size is not None:
cfg_from_list(['CONST.BATCH_SIZE', args.batch_size])
if args.summary_freq is not None:
cfg_from_list(['TRAIN.SUMMARY_FREQ', args.summary_freq])
if args.num_epochs is not None:
cfg_from_list(['TRAIN.NUM_EPOCHS', args.num_epochs])
if args.model is not None:
cfg_from_list(['NETWORK', args.model])
if args.optimizer is not None:
cfg_from_list(['TRAIN.OPTIMIZER', args.optimizer])
if args.critic_optimizer is not None:
cfg_from_list(['GAN.D_OPTIMIZER', args.critic_optimizer])
if args.ckpt_path is not None:
cfg_from_list(['DIR.CKPT_PATH', args.ckpt_path])
if args.lba_ckpt_path is not None:
cfg_from_list(['END2END.LBA_CKPT_PATH', args.lba_ckpt_path])
if args.val_ckpt_path is not None:
cfg_from_list(['DIR.VAL_CKPT_PATH', args.val_ckpt_path])
if args.log_path is not None:
cfg_from_list(['DIR.LOG_PATH', args.log_path])
if args.augment_max is not None:
cfg_from_list(['TRAIN.AUGMENT_MAX', args.augment_max])
if args.test:
cfg_from_list(['TRAIN.AUGMENT_MAX', 0])
cfg_from_list(['CONST.BATCH_SIZE', 1])
cfg_from_list(['LBA.N_CAPTIONS_PER_MODEL', 1]) # NOTE: Important!
cfg_from_list(['LBA.N_PRIMITIVE_SHAPES_PER_CATEGORY', 1]) # NOTE: Important!
if args.test_npy:
cfg_from_list(['CONST.BATCH_SIZE', 1])
# To overwrite default variables, put the set_cfgs after all argument initializations
if args.set_cfgs is not None:
cfg_from_list(args.set_cfgs)
def get_inputs_dict(args):
"""Gets the input dict for the current model and dataset.
"""
if cfg.CONST.DATASET == 'shapenet':
if (args.text_encoder is True) or (args.end2end is True) or (args.classifier is True):
inputs_dict = utils.open_pickle(cfg.DIR.TRAIN_DATA_PATH)
val_inputs_dict = utils.open_pickle(cfg.DIR.VAL_DATA_PATH)
test_inputs_dict = utils.open_pickle(cfg.DIR.TEST_DATA_PATH)
else: # Learned embeddings
inputs_dict = utils.open_pickle(cfg.DIR.SHAPENET_METRIC_EMBEDDINGS_TRAIN)
val_inputs_dict = utils.open_pickle(cfg.DIR.SHAPENET_METRIC_EMBEDDINGS_VAL)
test_inputs_dict = utils.open_pickle(cfg.DIR.SHAPENET_METRIC_EMBEDDINGS_TEST)
elif cfg.CONST.DATASET == 'primitives':
if ((cfg.CONST.SYNTH_EMBEDDING is True) or (args.text_encoder is True) or
(args.classifier is True)):
if args.classifier and not cfg.CONST.REED_CLASSIFIER: # Train on all splits for classifier
tf.logging.info('Using all (train/val/test) splits for training')
inputs_dict = utils.open_pickle(cfg.DIR.PRIMITIVES_ALL_SPLITS_DATA_PATH)
else:
tf.logging.info('Using train split only for training')
inputs_dict = utils.open_pickle(cfg.DIR.PRIMITIVES_TRAIN_DATA_PATH)
val_inputs_dict = utils.open_pickle(cfg.DIR.PRIMITIVES_VAL_DATA_PATH)
test_inputs_dict = utils.open_pickle(cfg.DIR.PRIMITIVES_TEST_DATA_PATH)
else: # Learned embeddings
inputs_dict = utils.open_pickle(cfg.DIR.PRIMITIVES_METRIC_EMBEDDINGS_TRAIN)
val_inputs_dict = utils.open_pickle(cfg.DIR.PRIMITIVES_METRIC_EMBEDDINGS_VAL)
test_inputs_dict = utils.open_pickle(cfg.DIR.PRIMITIVES_METRIC_EMBEDDINGS_TEST)
else:
raise ValueError('Please use a valid dataset (shapenet, primitives).')
if args.tiny_dataset is True:
if ((cfg.CONST.DATASET == 'primitives' and cfg.CONST.SYNTH_EMBEDDING is True)
or (args.text_encoder is True)):
raise NotImplementedError('Tiny dataset not supported for synthetic embeddings.')
ds = 5 # New dataset size
if cfg.CONST.BATCH_SIZE > ds:
raise ValueError('Please use a smaller batch size than {}.'.format(ds))
inputs_dict = utils.change_dataset_size(inputs_dict, new_dataset_size=ds)
val_inputs_dict = utils.change_dataset_size(val_inputs_dict, new_dataset_size=ds)
test_inputs_dict = utils.change_dataset_size(test_inputs_dict, new_dataset_size=ds)
# Select the validation/test split
if args.split == 'train':
split_str = 'train'
val_inputs_dict = inputs_dict
elif (args.split == 'val') or (args.split is None):
split_str = 'val'
val_inputs_dict = val_inputs_dict
elif args.split == 'test':
split_str = 'test'
val_inputs_dict = test_inputs_dict
else:
raise ValueError('Please select a valid split (train, val, test).')
print('Validation/testing on {} split.'.format(split_str))
if (cfg.CONST.DATASET == 'shapenet') and (cfg.CONST.SHAPENET_CT_CLASSIFIER is True):
category_model_list, class_labels = Classifier.set_up_classification(inputs_dict)
val_category_model_list, val_class_labels = Classifier.set_up_classification(val_inputs_dict)
assert class_labels == val_class_labels
# Update inputs dicts
inputs_dict['category_model_list'] = category_model_list
inputs_dict['class_labels'] = class_labels
val_inputs_dict['category_model_list'] = val_category_model_list
val_inputs_dict['class_labels'] = val_class_labels
return inputs_dict, val_inputs_dict
def get_solver(g, net, args, is_training):
if isinstance(net, LBA):
solver = LBASolver(net, g, is_training)
elif args.text_encoder:
solver = TextEncoderSolver(net, g, is_training)
elif isinstance(net, Classifier):
solver = ClassifierSolver(net, g, is_training)
elif isinstance(net, CWGAN):
solver = End2EndGANDebugSolver(net, g, is_training)
else:
raise ValueError('Invalid network.')
return solver
def main():
"""Main text2voxel function.
"""
args = parse_args()
print('Called with args:')
print(args)
if args.save_outputs is True and args.test is False:
raise ValueError('Can only save outputs when testing, not training.')
if args.validation:
assert not args.test
if args.test:
assert args.ckpt_path is not None
modify_args(args)
print('----------------- CONFIG -------------------')
pprint.pprint(cfg)
# Save yaml
os.makedirs(cfg.DIR.LOG_PATH, exist_ok=True)
with open(os.path.join(cfg.DIR.LOG_PATH, 'run_cfg.yaml'), 'w') as out_yaml:
yaml.dump(cfg, out_yaml, default_flow_style=False)
# set up logger
tf.logging.set_verbosity(tf.logging.INFO)
try:
with tf.Graph().as_default() as g: # create graph
# Load data
inputs_dict, val_inputs_dict = get_inputs_dict(args)
# Build network
is_training = not args.test
print('------------ BUILDING NETWORK -------------')
network_class = models.load_model(cfg.NETWORK)
net = network_class(inputs_dict, is_training)
# Prefetching data processes
#
# Create worker and data queue for data processing. For training data, use
# multiple processes to speed up the loading. For validation data, use 1
# since the queue will be popped every TRAIN.NUM_VALIDATION_ITERATIONS.
# set up data queue and start enqueue
np.random.seed(123)
data_process_class = models.get_data_process_pairs(cfg.NETWORK, is_training)
val_data_process_class = models.get_data_process_pairs(cfg.NETWORK, is_training=False)
if is_training:
global train_queue, train_processes
train_queue = Queue(cfg.CONST.QUEUE_CAPACITY)
train_processes = make_data_processes(data_process_class, train_queue, inputs_dict,
cfg.CONST.NUM_WORKERS, repeat=True)
if args.validation:
global val_queue, val_processes
val_queue = Queue(cfg.CONST.QUEUE_CAPACITY)
val_processes = make_data_processes(val_data_process_class, val_queue,
val_inputs_dict, 1, repeat=True)
else:
global test_queue, test_processes
test_inputs_dict = val_inputs_dict
test_queue = Queue(cfg.CONST.QUEUE_CAPACITY)
test_processes = make_data_processes(val_data_process_class, test_queue,
test_inputs_dict, 1, repeat=False)
# Create solver
solver = get_solver(g, net, args, is_training)
# Run solver
if is_training:
if args.validation:
if cfg.DIR.VAL_CKPT_PATH is not None:
assert train_processes[0].iters_per_epoch != 0
assert val_processes[0].iters_per_epoch != 0
solver.train(train_processes[0].iters_per_epoch, train_queue,
val_processes[0].iters_per_epoch, val_queue=val_queue,
val_inputs_dict=val_inputs_dict)
else:
if isinstance(net, LBA):
assert cfg.LBA.TEST_MODE is not None
assert cfg.LBA.TEST_MODE == 'shape'
assert train_processes[0].iters_per_epoch != 0
assert val_processes[0].iters_per_epoch != 0
solver.train(train_processes[0].iters_per_epoch, train_queue,
val_processes[0].iters_per_epoch, val_queue=val_queue,
val_inputs_dict=val_inputs_dict)
else:
assert train_processes[0].iters_per_epoch != 0
assert val_processes[0].iters_per_epoch != 0
solver.train(train_processes[0].iters_per_epoch, train_queue,
val_processes[0].iters_per_epoch, val_queue=val_queue)
else:
solver.train(train_processes[0].iters_per_epoch, train_queue)
else:
solver.test(test_processes[0], test_queue,
num_minibatches=cfg.CONST.N_MINIBATCH_TEST,
save_outputs=args.save_outputs)
finally:
# Clean up the processes and queues
if is_training:
kill_processes(train_queue, train_processes)
if args.validation:
kill_processes(val_queue, val_processes)
else:
kill_processes(test_queue, test_processes)
if __name__ == '__main__':
main()
|
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|
[STATEMENT]
lemma infnorm_Max:
fixes x :: "'a::euclidean_space"
shows "infnorm x = Max ((\<lambda>i. \<bar>x \<bullet> i\<bar>) ` Basis)"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
1. infnorm x = (MAX i\<in>Basis. \<bar>x \<bullet> i\<bar>)
[PROOF STEP]
by (simp add: infnorm_def infnorm_set_image cSup_eq_Max)
|
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|
#!/usr/bin/python
# -*- coding:utf-8 -*-
import cv2
import numpy as np
import matplotlib.pyplot as plt
#Numpy：(a+b)%255
#OpenCV：Math.min(a+b,255)
def add(img1,img2):
result = cv2.add(img1, img2)
cv2.imshow("add", result)
cv2.waitKey(0)
#融合
def addWeighted(img1, alpha, img2, beta, gamma):
result = cv2.addWeighted(img1,alpha,img2,beta,gamma)
cv2.imshow("addWeighted", result)
cv2.waitKey(0)
#减法
def subtract(img1, img2):
result = cv2.subtract(img1, img2)
cv2.imshow("subtract", result)
cv2.waitKey(0)
if __name__ == '__main__':
img1 = cv2.imread("images/Forest_500X280.jpg")
print(img1.shape)
img2 = cv2.imread("images/Forest1_500X280.jpg")
print(img2.shape)
#add(img1, img2)
#addWeighted(img1, 0.2, img2, 0.8, 0)
addWeighted(img1, 0.3, img2, 1.0, 0)
#subtract(img1,img2)
|
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|
# nodenet/tester/fctest.py
# Description:
# "fctest.py" provide fullyconnected neuralnet testing.
# Copyright 2018 NOOXY. All Rights Reserved.
import numpy as np
import nodenet.neuralnets as nn
import nodenet.layers as layers
import nodenet.functions as f
import nodenet.trainingsessions as sessions
import nodenet.interface.graph as graph
import nodenet.utilities as util
import nodenet.interface.console as console
import nodenet.io as nnio
import nodenet.variables as var
console.logo()
# Graphing test 1
fig = graph.Figure((2, 1))
datasets = util.get_sin_1x1_datasets(2000, noise=0.1)
datasets = util.cut_dataset_by_ratio_ramdom([datasets[0], datasets[1]])
console.log('tester', 'graphing test 1...', msg_color='Green')
fig.plot_2D(datasets[0].flatten(), datasets[1].flatten(), 0, 'graph of sin(x) and training result')
console.log('tester', 'graphing 1 passed.', msg_color='Red')
# NeuralNet test
console.log('tester', 'fullyconnectednet test...', msg_color='Green')
neuralnet = nn.SimpleContainer()
layers = [
layers.Nodes1D(1, f.linear),
layers.FullyConnected1D(1, 16),
layers.Nodes1D(16, f.tanh),
layers.FullyConnected1D(16, 16),
layers.Nodes1D(16, f.tanh),
layers.FullyConnected1D(16, 1),
layers.Nodes1D(1, f.linear),
]
neuralnet.setup(layers, name='tester neuralnet')
console.log('tester', str(neuralnet))
console.log('tester', 'fullyconnectednet passed.', msg_color='Red')
# Training test
console.log('tester', 'fullyconnectednet training test...', msg_color='Green')
batch_training = sessions.MiniBatchSession()
forward_config = var.forward_training_config
backward_config = var.backward_training_config
# forward_config = var.forward_dropout_training_config
# backward_config = var.backward_dropout_training_config
batch_training.setup(neuralnet, datasets, target_loss=0.00001, mini_batch_size=500, max_epoch=10000, forward_config=forward_config, backward_config=backward_config, verbose_interval=1000)
loss = batch_training.startTraining()
fig.plot_traing_loss(loss, 1)
console.log('tester', 'fullyconnectednet training test passed.', msg_color='Red')
# Graphing test 2
console.log('tester', 'graphing test 2...', msg_color='Green')
inputx = np.linspace(-10, 10, 100)
outputy = []
for x in inputx:
outputy.append(neuralnet.forward(np.array([x]))[0])
fig.plot_2D(inputx, outputy, 0, 'training')
console.log('tester', 'graphing test 2 passed.', msg_color='Red')
# IO test
console.log('tester', 'io test...', msg_color='Green')
nnio.save_neuralnet(neuralnet, 'tester')
newneuralnet = nnio.load_neuralnet('tester')
console.log('tester', str(neuralnet))
console.log('tester', 'io test passed.', msg_color='Red')
console.log('tester', 'test passed. Press any key to escape.')
input()
|
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|
\documentclass{mcmthesis}
\mcmsetup{CTeX = false,
tcn = 0000000, problem = A,
sheet = true, titleinsheet = true, keywordsinsheet = true, titlepage = false, abstract = false}
\usepackage{newtxtext}%\usepackage{palatino}
\usepackage{lipsum}
\usepackage{diagbox}
\usepackage{setspace}
\usepackage[nottoc]{tocbibind}
\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
\newtheorem{definition}{Definition}[section]
\usepackage{titlesec}
\setcounter{secnumdepth}{4}
\titleformat{\paragraph}
{\normalfont\normalsize\bfseries}{\theparagraph}{1em}{}
\titlespacing*{\paragraph}{0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}
\title{Title}
\begin{document}
\begin{abstract}
\lipsum[1]
\begin{keywords}
no; keyword;
\end{keywords}
\end{abstract}
\maketitle
\tableofcontents
\newpage
\section{Introduction}
\subsection{Background}
\lipsum[2]
\begin{figure}[htbp]
\minipage{0.5\textwidth}
\includegraphics[width=\linewidth]{/img/Fungus_in_a_Wood.jpg}
\caption{Fungus in a wood}\label{fig:fungus1}
\endminipage\hfill
\minipage{0.45\textwidth}
\includegraphics[width=\linewidth]{/img/960px-Armillaria_gallica_57632.jpg}
\caption{Armillaria Gallic}\label{fig:fungus2}
\endminipage\hfill
\end{figure}
\lipsum[3]
\subsection{Problem Restatement}
\lipsum[4]
\subsection{Our Approach}
\lipsum[5]
\section{Assumptions}
\lipsum[6]
\section{Notations}
\lipsum[7]
\section{The Data}
\lipsum[8]
\section{model 1}
\lipsum[9]
\subsection{Inspiration}
\lipsum[1]
\subsubsection{section 1}
\paragraph{P 2}
\paragraph{P 1}
\lipsum[2]
\subsection{Model}
\lipsum[3]
\section{model 2}
\lipsum[1]
\subsection{Inspiration}
\lipsum[2]
\subsection{Model}
\lipsum[4]
\section{Conclusions}
\subsection{Summary of Results}
\subsubsection{Result of Problem 1}
\lipsum[2]
\subsubsection{Result of Problem 2}
\lipsum[2]
\subsubsection{Result of Problem 3}
\lipsum[2]
\subsubsection{Result of Problem 4}
\lipsum[2]
\subsubsection{Result of Problem 5}
\lipsum[2]
\subsection{Possible Improvements}
\lipsum[1]
\bibliographystyle{unsrt}
\bibliography{references}
\newpage
\section*{\centerline{Letter title}}
\lipsum[1]
\newpage
\begin{appendices}
\section{Tools and Software}
\hspace{1.25em} Paper written and generated via \LaTeX, free distribution.
Dataset filtered by Python.
Graph generated and calculation using MATLAB R2019b for academic use on Mac.
Calculation of linear regression using EViews 8
\section{The Codes}
Here are simulation programmes we used in our model as follow.
%\subsection{Code 1}
%\lstinputlisting[language=Matlab]{./code/modelling8.m}
%
%
%\subsection{Code 2}
%\lstinputlisting[language=Python]{./code/DataProcess.py}
\end{appendices}
\end{document}
|
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|
from winning.std_calibration import centered_std_density
from winning.lattice_calibration import dividend_implied_ability
import numpy as np
import matplotlib.pyplot as plt
from winning.lattice_plot import densitiesPlot
from winning.lattice import skew_normal_density
# Illustrates the basic calibration
# Exactly the same but now we plot the densities
if __name__ =='__main__':
# Choose the length of the lattice, which is 2*L+1
L = 600
# Choose the unit of discretization
unit = 0.01
# The unit is used to create an approximation of a density, here N(0,1) for simplicity
density = centered_std_density(L=L, unit=unit)
# Step 2. We set winning probabilities, most commonly represented in racing as inverse probabilities ('dividends')
dividends = [2,6,np.nan, 3]
# Step 3. The algorithm implies relative ability (i.e. how much to translate the performance distributions)
# Missing values will be assigned odds of 1999:1 ... or you can leave them out.
abilities = dividend_implied_ability(dividends=dividends,density=density, nan_value=2000, unit=unit)
densities = [skew_normal_density(L=L, unit=unit, loc=a, a=0, scale=1.0) for a in abilities]
legend = [ str(d) for d in dividends ]
densitiesPlot(densities=densities, unit=unit, legend=legend)
plt.show()
|
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|
import gym
import time
import random
import numpy as np
from collections import deque
import os
os.environ['TF_CPP_MIN_LOG_LEVEL']='2'
os.system('export CUDA_VISIBLE_DEVICES=""')
import tensorflow as tf
import keras.backend.tensorflow_backend as KTF
def get_session(gpu_fraction=0.7):
'''Assume that you have 6GB of GPU memory and want to allocate ~2GB'''
num_threads = os.environ.get('OMP_NUM_THREADS')
gpu_options = tf.GPUOptions(per_process_gpu_memory_fraction=gpu_fraction)
if num_threads:
return tf.Session(config=tf.ConfigProto(
gpu_options=gpu_options, intra_op_parallelism_threads=num_threads))
else:
print( "ok" )
return tf.Session(config=tf.ConfigProto(gpu_options=gpu_options))
def run_on_cpu():
config = tf.ConfigProto(
device_count = {'GPU': 0}
)
return tf.Session(config=config)
KTF.set_session(get_session())
#KTF.set_session( run_on_cpu() )
env = gym.make( 'BreakoutDeterministic-v4')
# Preprocess observation
# Crop image - do not keep score
# Grayscale image - reduce the rgb space to grayscale, save space
import cv2
import matplotlib.pyplot as plt
#get_ipython().magic('matplotlib inline')
def to_grayscale( observation ):
r, g, b = observation[:,:,0], observation[:,:,1], observation[:,:,2]
ret = 0.299 * r + 0.587 * g + 0.114 * b
return ( np.array( ret, dtype=np.uint8 ) )
def preprocess_observation( observation ):
res = cv2.resize( observation, (84,110) )
crop = res[18:110-8:,:,:]
grayscale = to_grayscale( crop )#cv2.cvtColor( crop, cv2.COLOR_BGR2GRAY )
return ( grayscale )
"""
def preprocess_observation( observation ):
res = cv2.resize( observation, (84,110) )#resize to 110x84
crop = res[18:110-8,:,:]#crop image
grayscale = to_grayscale( crop )
thresh, bn = cv2.threshold( grayscale, 80, 255, cv2.THRESH_BINARY )
#grayscale=cv2.cvtColor( crop, cv2.COLOR_BGR2GRAY )#apply grayscale
#grayscale = grayscale.astype( float ) / 255.0#normalize image
return ( np.array( bn / np.max(bn), dtype=np.uint8 ) )
"""
from keras.models import Sequential
from keras.layers import Dense, Flatten, Activation, Lambda
from keras.layers.convolutional import Conv2D
from keras.optimizers import RMSprop, Adam
from keras import initializers
# Build model
model = Sequential()
init_distr = initializers.RandomNormal(mean=0.0, stddev=0.05, seed=None)
#32 filters of kernel(3,3), stride=4, input shape must be in format row, col, channels
#init='uniform',
model.add( Lambda(lambda x: x / 255.0, dtype='float32', input_shape=(84,84,4)) )
model.add( Conv2D(32, (8,8), strides=(4,4), padding='same' ) )#deep mind
#model.add( Conv2D(16, (8,8), strides=(2,2), kernel_initializer=initializers.random_normal(stddev=0.01), padding='same', input_shape=(84,84,4) ) )
model.add( Activation( 'relu' ) )
model.add(Conv2D(64, (4,4), strides=(2,2), padding='same' ) )#deep min
#model.add(Conv2D(32, (4,4), strides=(2,2), kernel_initializer=initializers.random_normal(stddev=0.01), padding='same' ) )
model.add( Activation( 'relu' ) )
model.add(Conv2D(64, (3,3), strides=(1,1), kernel_initializer=initializers.random_normal(stddev=0.01), padding='same' ) )
model.add( Activation( 'relu' ) )
model.add(Flatten())
model.add(Dense(512, kernel_initializer=init_distr, activation='relu'))
model.add(Dense(256, kernel_initializer=init_distr, activation='relu'))
model.add(Dense(128, kernel_initializer=init_distr, activation='relu'))
model.add( Dense( env.action_space.n, kernel_initializer=init_distr, activation='linear' ) )
#model.compile(RMSprop(), 'MSE')
#model.compile(loss='mse', optimizer='adam', metrics=['accuracy'])
learning_rate = 0.001#025
model.compile(loss='mse', optimizer=Adam(lr=learning_rate), metrics=['accuracy'] )
model.summary()
init_state = preprocess_observation( env.reset() )
recent_frames = deque(maxlen=4)
for i in range( 4 ):
recent_frames.append( init_state )
import time
gamma = 0.99
alpha = 1#0.999999#00025
max_reward = 0.0
epoch = 0
start_episode = 1
epsilon = 1
epsilon_min = 0.1
exploration_steps = 500000#1000000
epsilon_discount = ( epsilon - epsilon_min ) / exploration_steps
MAX_SIZE = 40000#capacity of deque
MIN_MIN_SIZE = 20000#min size for replay
D = deque( maxlen=MAX_SIZE )#[]
frames = 0
def load_deque():
global D
pkl_file = open( 'mydeque.pkl', 'rb')
D = pickle.load( pkl_file )
pkl_file.close()
def save_deque():
output = open( 'mydeque.pkl', 'wb' )
pickle.dump( D, output )
output.close()
def load_dqn_model():
global model
from keras.models import model_from_json
# load json and create model
json_file = open('model_background.json', 'r')
loaded_model_json = json_file.read()
json_file.close()
model = model_from_json(loaded_model_json)
# load weights into new model
model.load_weights("model_background.h5")
print("Loaded model from disk")
#model.compile(loss='mse', optimizer='adam', metrics=['accuracy'])
model.compile(loss='mse', optimizer=Adam(lr=learning_rate), metrics=['accuracy'] )
import pandas as pd
import pickle
episodes = []
rewards = []
epsilons = []
total_frames = []
def save_train():
global episodes, rewards, epsilons, total_frames
#save [episodes, rewards, epsilons ] to csv file
d = {'episode': episodes, 'reward': rewards, 'epsilon': epsilons, 'total_frames': total_frames}
df = pd.DataFrame(data=d, index=None)
if not os.path.isfile('filename.csv'):
df.to_csv('filename.csv',header ='column_names', index=None)
else: # else it exists so append without writing the header
df.to_csv('filename.csv',mode = 'a',header=False, index=None)
episodes = []
rewards = []
epsilons = []
total_frames = []
#save model to disk
# serialize model to JSON
model_json = model.to_json()
with open("model_background.json", "w") as json_file:
json_file.write(model_json)
# serialize weights to HDF5
model.save_weights("model_background.h5")
print("Saved model to disk")
#save deque to disk
#save_deque()
def load_train():
global start_episode, epsilon, frames
#get last episode and epsilon
if not os.path.isfile('filename.csv'):
start_episode, epsilon = 1, 1
else: # else it exists so append without writing the header
df = pd.read_csv( 'filename.csv')
if len(df) == 0:
start_episode, epsilon, frames = 1, 1, 0
else:
epsilon = list( df['epsilon'].tail(1) )[0]
start_episode = list( df['episode'].tail(1) )[0] + 1
frames = list( df['total_frames'].tail(1) )[0]
if os.path.isfile('model_background.json'):
load_dqn_model()
#if os.path.isfile('mydeque.pkl'):
#load_deque()
load_train()
#print( start_episode, epsilon )
#print( type( start_episode ) )
#print( type( epsilon ) )
#print( model.summary() )
#print( D )
total_observe = 12000#total_episodes
MIN_SIZE = 32
observe_frame = 0
def must_observe():
return ( observe_frame < MIN_MIN_SIZE )
def replay( ):
if len( D ) < MIN_MIN_SIZE:
return
#print( "sample" )
samples = random.sample( D, MIN_SIZE )
all_x = []
all_y = []
for sample in samples:
observation, reward, done, new_observation, action = sample
y = model.predict( observation.reshape( ( 1, 84, 84, 4) ) )
Q_next = model.predict( new_observation.reshape( ( 1, 84, 84, 4) ) )
reward = np.clip( reward, -1, 1 )
if done:
y[0,action] = reward
else:
y[0,action] = reward + gamma * ( np.max( Q_next[0] ) )
#print( y )
neural_network_observation = observation.reshape( ( 1, 84, 84, 4) )
all_x.append( neural_network_observation )
all_y.append( y )
#model.fit( neural_network_observation, y, epochs=1, verbose=0 )
#model.train_on_batch( neural_network_observation, y )
all_x = np.array( all_x ).reshape( (MIN_SIZE,84,84,4) )
all_y = np.array( all_y ).reshape( (MIN_SIZE,4) )
#model.train_on_batch( all_x, all_y )
model.fit(all_x, all_y, epochs=1, batch_size=MIN_SIZE, verbose=0)
del all_x, all_y
start = time.time()
episode = start_episode
while episode <= total_observe:#3600*5):
observation = env.reset()
observation = preprocess_observation( observation )
recent_frames = deque(maxlen=4)
for i in range( 4 ):
recent_frames.append( observation )
total_reward = 0
#print( episode )
cur_lives = 5
step = 0
action = 0
steps = 0
while True:
#env.render()
stack_observation = np.stack(recent_frames,axis=0)
if must_observe():
observe_frame += 1
if must_observe() == False:
steps += 1
#if step % 4 == 0:
if random.uniform(0,1) < epsilon:
action = env.action_space.sample()
else:
Q = model.predict( stack_observation.reshape( ( 1, 84, 84, 4) ) )[0]
action = np.argmax( Q )
#step = 0
new_observation, reward, done, info = env.step( action )
new_observation = preprocess_observation( new_observation )#apply preprocess
#plt.imshow( new_observation )
#plt.show(block=False)
#plt.pause(0.5)#.sleep(3)
#plt.close()
next_recent_frames = recent_frames.copy()
next_recent_frames.append( new_observation )
next_new_observation = np.stack(next_recent_frames,axis=0)
memory_reward = reward
if info['ale.lives'] < cur_lives:
cur_lives = info['ale.lives']
memory_reward = -1
D.append( ( stack_observation, memory_reward, done, next_new_observation, action ) )
total_reward += reward
replay()
if done:
#print( str(episode) + "Game over!", end= ' ' ),
#replay()]]]
if must_observe() == False:
episodes.append( episode )
rewards.append( total_reward )
epsilons.append( epsilon )
D.append( ( stack_observation, -1, done, next_new_observation, action ) )
break
observation = new_observation
recent_frames.append( observation )
if must_observe() == False:
epsilon = max( epsilon_min, epsilon - epsilon_discount )
if must_observe() == False:
frames += steps
total_frames.append( frames )
print( "Episode " + str(episode) + " | total reward := " + str(total_reward) + " | steps := " + str(steps) + " total frames := " + str(frames) )
else:
print( "Observe total frames := " + str(observe_frame) )
if episode % 10 == 0 and episode > 1:
if must_observe() == False:
save_train()
if must_observe() == False:
episode += 1
end = time.time()
print("total time is " + str( end - start ) )
|
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|
function tSeries = rmBlurGrayTSeries(view,tSeries,iterlambda)
% rmBlurGrayTSeries - smooth raw time series across cortical surface
%
% tSeries = rmBlurGrayTSeries(view,tSeries,iterlambda);
%
% result^{i+1}[x] = c2[x] s^i[x] data missing
% = c1[x] (input[x] + lambda s^i[x]) otherwise
%
% c_1[x] = 1/(1 + numNeighbors)
% c_2[x] = 1/numNeighbors
% s[x] = sumNeighbors
% 2007/02 SOD: adapted from regularizeGray.
if ~exist('view','var') || isempty(view),
error('Need view struct.');
else
if ~strcmpi(view.viewType,'gray'),
error('Need gray viewType.');
end;
end;
if ~exist('tSeries','var') || isempty(tSeries),
error('Need tSeries');
end;
% these defaults approximate a FWHM of 5mm at 1mm3 resolution
if ~exist('iterlambda','var') || isempty(iterlambda),
iter = 5;
lambda = 1;
else
iter = iterlambda(1);
lambda = iterlambda(2);
end;
% sanity check
if iter==0 || lambda==0,
return;
end;
% works only on double format (for now):
tSeries = double(tSeries);
warning('off','MATLAB:divideByZero');
% Get numNeighbors and compute c1 and c2
edges = double(view.edges);
numNeighbors = double(view.nodes(4,:));
edgeOffsets = double(view.nodes(5,:));
% Initialize iterations
fprintf(1,'[%s]:Smoothing data:',mfilename);drawnow;tic;
for ii = 1:iter,
% Get indices for missing data, we assume that data is missing for
% entire time for a particular location.
nanSummary = sum(tSeries,1);
NaNs = isnan(nanSummary);
notNaNs = ~isnan(nanSummary);
withData = double(notNaNs);
% compute weights
denom = sumOfNeighbors(withData,edges,edgeOffsets,numNeighbors)';
% compute data that can be estimated (more than one valid data point
% in the neighborhood)
estdata = denom>0.5;
% now restrict NaNs and notNaNs to estdata
NaNs = NaNs(:) & estdata(:);
notNaNs = notNaNs(:) & estdata(:);
% new data
newt = NaN(1,size(tSeries,2));
for n=1:size(tSeries,1)
% input fill nans with zeros
tmp = tSeries(n,:);
tmp(NaNs) = 0;
% Compute sumNeighbors
sumNeighbors = sumOfNeighbors(tmp,edges,edgeOffsets,numNeighbors)';
% Compute new values
newt(NaNs) = sumNeighbors(NaNs) ./ denom(NaNs);
newt(notNaNs) = (tmp(notNaNs) + lambda.*sumNeighbors(notNaNs))./...
(denom(notNaNs)+1);
% store
tSeries(n,:)=newt;
end;
fprintf(1,'.');drawnow;
end;
fprintf(1,'Done[%.1fmin].\n',toc./60);drawnow;
return;
|
{"author": "vistalab", "repo": "vistasoft", "sha": "7f0102c696c091c858233340cc7e1ab02f064d4c", "save_path": "github-repos/MATLAB/vistalab-vistasoft", "path": "github-repos/MATLAB/vistalab-vistasoft/vistasoft-7f0102c696c091c858233340cc7e1ab02f064d4c/mrBOLD/Analysis/retinotopyModel/rmBlurGrayTSeries.m"}
|
import json
import sys
from collections import defaultdict
from math import sqrt
import numpy as np
import theano.tensor as T
import utils
from rbm import CFRBM
from experiments import read_experiment
from utils import revert_expected_value, expand, iteration_str
from dataset import load_dataset
def run(name, dataset, config, all_users, all_movies, tests, initial_v, sep):
config_name = config['name']
number_hidden = config['number_hidden']
epochs = config['epochs']
ks = config['ks']
momentums = config['momentums']
l_w = config['l_w']
l_v = config['l_v']
l_h = config['l_h']
decay = config['decay']
config_result = config.copy()
config_result['results'] = []
vis = T.matrix()
vmasks = T.matrix()
rbm = CFRBM(len(all_users) * 5, number_hidden)
profiles = defaultdict(list)
with open(dataset, 'rt') as data:
for i, line in enumerate(data):
uid, mid, rat, timstamp = line.strip().split(sep)
profiles[mid].append((uid, float(rat)))
print("Users and ratings loaded")
for j in range(epochs):
def get_index(col):
if j/(epochs/len(col)) < len(col):
return j/(epochs/len(col))
else:
return -1
index = get_index(ks)
mindex = get_index(momentums)
icurrent_l_w = get_index(l_w)
icurrent_l_v = get_index(l_v)
icurrent_l_h = get_index(l_h)
k = ks[index]
momentum = momentums[mindex]
current_l_w = l_w[icurrent_l_w]
current_l_v = l_v[icurrent_l_v]
current_l_h = l_h[icurrent_l_h]
train = rbm.cdk_fun(vis,
vmasks,
k=k,
w_lr=current_l_w,
v_lr=current_l_v,
h_lr=current_l_h,
decay=decay,
momentum=momentum)
predict = rbm.predict(vis)
batch_size = 10
for batch_i, batch in enumerate(utils.chunker(profiles.keys(),
batch_size)):
size = min(len(batch), batch_size)
# create needed binary vectors
bin_profiles = {}
masks = {}
for movieid in batch:
movie_profile = [0.] * len(all_users)
mask = [0] * (len(all_users) * 5)
for user_id, rat in profiles[movieid]:
movie_profile[all_users.index(user_id)] = rat
for _i in range(5):
mask[5 * all_users.index(user_id) + _i] = 1
example = expand(np.array([movie_profile])).astype('float32')
bin_profiles[movieid] = example
masks[movieid] = mask
movies_batch = [bin_profiles[id] for id in batch]
masks_batch = [masks[id] for id in batch]
train_batch = np.array(movies_batch).reshape(size,
len(all_users) * 5)
train_masks = np.array(masks_batch).reshape(size,
len(all_users) * 5)
train_masks = train_masks.astype('float32')
train(train_batch, train_masks)
sys.stdout.write('.')
sys.stdout.flush()
batch_size = 10
ratings = []
predictions = []
for batch in utils.chunker(tests.keys(), batch_size):
size = min(len(batch), batch_size)
# create needed binary vectors
bin_profiles = {}
masks = {}
for movieid in batch:
movie_profile = [0.] * len(all_users)
mask = [0] * (len(all_users) * 5)
for userid, rat in profiles[movieid]:
movie_profile[all_users.index(userid)] = rat
for _i in range(5):
mask[5 * all_users.index(userid) + _i] = 1
example = expand(np.array([movie_profile])).astype('float32')
bin_profiles[movieid] = example
masks[movieid] = mask
positions = {movie_id: pos for pos, movie_id in enumerate(batch)}
movies_batch = [bin_profiles[el] for el in batch]
test_batch = np.array(movies_batch).reshape(size,
len(all_users) * 5)
movie_predictions = revert_expected_value(predict(test_batch))
for movie_id in batch:
test_users = tests[movie_id]
try:
for user, rating in test_users:
current_movie = movie_predictions[positions[movie_id]]
predicted = current_movie[all_users.index(user)]
rating = float(rating)
ratings.append(rating)
predictions.append(predicted)
except Exception:
pass
vabs = np.vectorize(abs)
distances = np.array(ratings) - np.array(predictions)
mae = vabs(distances).mean()
rmse = sqrt((distances ** 2).mean())
iteration_result = {
'iteration': j,
'k': k,
'momentum': momentum,
'mae': mae,
'rmse': rmse,
'lrate': current_l_w
}
config_result['results'].append(iteration_result)
print(iteration_str.format(j, k, current_l_w, momentum, mae, rmse))
with open('{}_{}.json'.format(config_name, name), 'wt') as res_output:
res_output.write(json.dumps(config_result, indent=4))
if __name__ == "__main__":
experiment = read_experiment(sys.argv[1])
name = experiment['name']
train_path = experiment['train_path']
test_path = experiment['test_path']
sep = experiment['sep']
all_users, all_movies, tests = load_dataset(train_path, test_path, sep,
user_based=False)
for config in experiment['configs']:
run(name, train_path, config, all_users, all_movies, tests, None, sep)
|
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|
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import pandas as pd
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import matplotlib as mpl
import matplotlib.ticker as mtick
#from brokenaxes import brokenaxes
from matplotlib import gridspec
from matplotlib.pyplot import MultipleLocator
fig = plt.figure(figsize=(18, 6))
gs = gridspec.GridSpec(1, 2, width_ratios=[6, 1])
# 建立子图
ax1 = fig.add_subplot(gs[0]) # 2*1
# 第一个图为
plt.rcParams.update({'font.size': 30})
x = np.arange(8)
bar_width = 0.23
tick_label = ["Cyc","Epi","Gen","Soy","Vid","IR","FP","WC"]
df1 = pd.read_csv('MasterSP.csv')
df2 = pd.read_csv('WorkerSP.csv')
y_2 = list(df1['schedule_overhead'])
y_3 = list(df2['schedule_overhead'])
for index in range(len(y_2)):
y_2[index] = np.log10(y_2[index])+3
for index in range(len(y_3)):
y_3[index] = np.log10(y_3[index])+3
#ax1.bar(x-1.5*bar_width, y_1, bar_width, color="#76180E", align="center", label="HyperFlow-serverless solo-run",edgecolor='black',linewidth=2)
ax1.bar(x-0.5*bar_width, y_2, bar_width, color="#74a9cf", align="center", label="MasterSP (HyperFlow-serverless)",edgecolor='black',linewidth=2)
ax1.bar(x+0.5*bar_width, y_3, bar_width, color="#9bbb59", align="center", label="WorkerSP (FaaSFlow)",edgecolor='black',linewidth=2)
#ax1.bar(x+1.5*bar_width, y_4, bar_width, color="#FFFED5", align="center", label="FaaSFlow-FaaStore co-run",edgecolor='black',linewidth=2)
#F7903D#59A95A#4D85BD
ax1.set_ylim(0,4.4)
ax1.tick_params(labelsize=32)
ax1.set_xticklabels(tick_label, fontsize=32)
ax1.set_ylabel('The scheduling overhead\n in the e2e latency(s) ', fontsize=32)
plt.yticks([0, 1, 2,3,4], ["0.001","0.01" , "0.1", "1","10"],fontsize=32)
plt.xticks(x, tick_label,rotation=0)
ax1.axhline(y=1, color='tab:grey', linestyle='--')
ax1.axhline(y=2, color='tab:grey', linestyle='--')
ax1.axhline(y=3, color='tab:grey', linestyle='--')
ax1.axhline(y=4, color='tab:grey', linestyle='--')
ax1.legend(ncol=1,loc='upper right',fontsize=26)
# 设置子图之间的间距，默认值为1.08
plt.tight_layout(pad=0)
fig.savefig("schedule_overhead.pdf", bbox_inches='tight')
plt.show()
|
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|
import sys
import time
import numpy as np
import matplotlib.pyplot as plt
from multiprocessing import Pool
# if len(sys.argv) < 3:
# print('ERROR Args number. Needed: \n[1]In Path(with file.npy) -- prepros file \n[2]Out Path(with .json)')
# sys.exit()
#
#
# in_path = str(sys.argv[1])
# out_path = str(sys.argv[2])
in_path = '/Users/Juan/django_projects/adaptive-boxes/data_binary/squares.binary'
out_path = ''
data_matrix = np.loadtxt(in_path, delimiter=",")
data_matrix[:,0] = 1
# Plot
fig = plt.figure(figsize=(6, 3.2))
ax = fig.add_subplot(111)
plt.imshow(data_matrix)
ax.set_aspect('equal')
# Flatten Matrix
data_matrix_f = data_matrix.flatten()
# Kernel Data
dim3_block_x = data_matrix.shape[1]
dim3_block_y = data_matrix.shape[0]
block_dim_y = dim3_block_y
block_dim_x = dim3_block_x
# KERNEL
# Kernel non-editable - they go in for-loop
block_idx_x = 0
block_idx_y = 0
thread_idx_x = 0
thread_idx_y = 0
# Kernel editable
# Params
distances = np.zeros(shape=[data_matrix_f.shape[0]]) # Could be stored in Cache- Shared Memory
idx_i = 7 # y rand point
idx_j = 13 # x rand point
plt.scatter(idx_j, idx_i, c='r')
m = data_matrix.shape[0]
n = data_matrix.shape[1]
# br ----
for i in range(idx_i, m):
temp_value = data_matrix_f[i * n + idx_j]
if temp_value == 0:
i = i - 1
break
else:
plt.scatter(idx_j, i, c='g', marker='x')
d0 = i
for j in range(idx_j + 1, n):
for i in range(idx_i, d0 + 1):
# print(str(j) + ' ' + str(i))
temp_value = data_matrix_f[i * n + j]
if temp_value == 0:
i = i - 1
break
else:
plt.scatter(j, i, c='b', marker='x')
if i < d0:
j = j - 1
break
# bl ----
for i in range(idx_i, m):
temp_value = data_matrix_f[i * n + idx_j]
if temp_value == 0:
i = i - 1
break
else:
plt.scatter(idx_j, i, c='g', marker='x')
d0 = i
for j in range(idx_j - 1, -1, -1):
for i in range(idx_i, d0 + 1):
# print(str(j) + ' ' + str(i))
temp_value = data_matrix_f[i * n + j]
if temp_value == 0:
i = i - 1
break
else:
plt.scatter(j, i, c='b', marker='x')
if i < d0:
j = j + 1
break
# tl ----
for i in range(idx_i, -1, -1):
temp_value = data_matrix_f[i * n + idx_j]
if temp_value == 0:
i = i + 1
break
else:
plt.scatter(idx_j, i, c='g', marker='x')
d0 = i
for j in range(idx_j - 1, -1, -1):
for i in range(idx_i, d0 - 1, -1):
# print(str(j) + ' ' + str(i))
temp_value = data_matrix_f[i * n + j]
if temp_value == 0:
i = i + 1
break
else:
plt.scatter(j, i, c='b', marker='x')
if i > d0:
j = j + 1
break
# tr ----
for i in range(idx_i, -1, -1):
temp_value = data_matrix_f[i * n + idx_j]
if temp_value == 0:
i = i + 1
break
else:
plt.scatter(idx_j, i, c='g', marker='x')
d0 = i
for j in range(idx_j + 1, n):
for i in range(idx_i, d0 -1, - 1):
# print(str(j) + ' ' + str(i))
temp_value = data_matrix_f[i * n + j]
if temp_value == 0:
i = i + 1
break
else:
plt.scatter(j, i, c='b', marker='x')
if i > d0:
j = j - 1
break
# plt.scatter(j, idx_i_arg, c='g', marker='x')
# plt.scatter(j, idx_i_arg + first_step_i - 1, c='g', marker='x')
# Run Kernel
for thread_idx_y in range(block_dim_y):
for thread_idx_x in range(block_dim_x):
# print('running threadId.x: ' + str(thread_idx_x) + ' threadId.y: ' + str(thread_idx_y))
i = thread_idx_y
j = thread_idx_x
g_i = block_dim_y * block_idx_y + i
g_j = block_dim_x * block_idx_x + j
m = block_dim_y
n = block_dim_x
plt.scatter(j, i, c='b', marker='x')
val_in_b = data_matrix_f[n * i + j]
val_in_a = data_matrix_f[n * i + idx_j]
distance_j = (j - idx_j) * val_in_b * val_in_a
distance_i = (i - idx_i) * val_in_b * val_in_a
print('i: ' + str(i) + ' j: ' + str(j) + ' distance ' + str(distance_j))
# if distance_j > 0:
distances[i * n + j] = distance_j
# distances[i * n + j] = distance_j
# if j == idx_j:
# distances[i * n + j] = distance_j + distance_i
print(distances.reshape([m, n]))
distances_matrix = distances.reshape([m, n])
# Break
# Get min distance in left - Atomic can be used(In this case: min() function)
distances_matrix = distances.reshape([m, n])
idx_d = 1
distances_matrix[idx_d, :].max()
distances_matrix[idx_d, :].min()
for thread_idx_y in range(block_dim_y):
for thread_idx_x in range(block_dim_x):
# print('running threadId.x: ' + str(thread_idx_x) + ' threadId.y: ' + str(thread_idx_y))
i = thread_idx_y
j = thread_idx_x
g_i = block_dim_y * block_idx_y + i
g_j = block_dim_x * block_idx_x + j
m = block_dim_y
n = block_dim_x
if (j == 0):
distances[i * n + 0: i * n + m]
def get_right_bottom_rectangle(idx_i_arg, idx_j_arg):
step_j = 0
first_step_i = 0
while True:
i = idx_i_arg
j = idx_j_arg + step_j
if j == n:
break
temp_val = data_matrix[i, j]
if temp_val == 0:
break
step_i = 0
while True:
i = idx_i_arg + step_i
if i == m:
break
# print(i)
temp_val = data_matrix[i, j]
# print(temp_val)
# plt.scatter(j, i, c='g', marker='x')
if temp_val == 0:
break
step_i += 1
if step_j == 0:
first_step_i = step_i
else:
if step_i < first_step_i:
break
plt.scatter(j, idx_i_arg, c='g', marker='x')
plt.scatter(j, idx_i_arg + first_step_i - 1, c='g', marker='x')
x1_val = idx_j_arg
y1_val = idx_i_arg
x2_val = idx_j_arg + step_j - 1
y2_val = idx_i_arg + first_step_i - 1
return x1_val, x2_val, y1_val, y2_val
def get_left_bottom_rectangle(idx_i_arg, idx_j_arg):
step_j = 0
first_step_i = 0
while True:
i = idx_i_arg
j = idx_j_arg - step_j
if j == -1:
break
temp_val = data_matrix[i, j]
if temp_val == 0:
break
step_i = 0
while True:
i = idx_i_arg + step_i
if i == m:
break
# print(i)
temp_val = data_matrix[i, j]
# print(temp_val)
# plt.scatter(j, i, c='g', marker='x')
if temp_val == 0:
break
step_i += 1
if step_j == 0:
first_step_i = step_i
else:
if step_i < first_step_i:
break
plt.scatter(j, idx_i_arg, c='g', marker='x')
plt.scatter(j, idx_i_arg + first_step_i - 1, c='b', marker='x')
step_j += 1
x1_val = idx_j_arg
y1_val = idx_i_arg
x2_val = idx_j_arg - step_j + 1
y2_val = idx_i_arg + first_step_i - 1
return x1_val, x2_val, y1_val, y2_val
def get_left_top_rectangle(idx_i_arg, idx_j_arg):
step_j = 0
first_step_i = 0
while True:
i = idx_i_arg
j = idx_j_arg - step_j
if j == -1:
break
temp_val = data_matrix[i, j]
if temp_val == 0:
break
step_i = 0
while True:
i = idx_i_arg - step_i
if i == -1:
break
# print(i)
temp_val = data_matrix[i, j]
# print(temp_val)
# plt.scatter(j, i, c='g', marker='x')
if temp_val == 0:
break
step_i += 1
if step_j == 0:
first_step_i = step_i
else:
if step_i < first_step_i:
break
plt.scatter(j, idx_i_arg, c='g', marker='x')
plt.scatter(j, idx_i_arg - first_step_i + 1, c='b', marker='x')
step_j += 1
x1_val = idx_j_arg
y1_val = idx_i_arg
x2_val = idx_j_arg - step_j + 1
y2_val = idx_i_arg - first_step_i + 1
return x1_val, x2_val, y1_val, y2_val
def get_right_top_rectangle(idx_i_arg, idx_j_arg):
step_j = 0
first_step_i = 0
while True:
i = idx_i_arg
j = idx_j_arg + step_j
if j == n:
break
temp_val = data_matrix[i, j]
if temp_val == 0:
break
step_i = 0
while True:
i = idx_i_arg - step_i
if i == -1:
break
# print(i)
temp_val = data_matrix[i, j]
# print(temp_val)
# plt.scatter(j, i, c='g', marker='x')
if temp_val == 0:
break
step_i += 1
if step_j == 0:
first_step_i = step_i
else:
if step_i < first_step_i:
break
plt.scatter(j, idx_i_arg, c='g', marker='x')
plt.scatter(j, idx_i_arg - first_step_i + 1, c='g', marker='x')
step_j += 1
x1_val = idx_j_arg
y1_val = idx_i_arg
x2_val = idx_j_arg + step_j - 1
y2_val = idx_i_arg - first_step_i + 1
return x1_val, x2_val, y1_val, y2_val
# Plot
fig = plt.figure(figsize=(6, 3.2))
ax = fig.add_subplot(111)
plt.imshow(data_matrix)
ax.set_aspect('equal')
m = data_matrix.shape[0] # for i
n = data_matrix.shape[1] # for j
for i_n in range(m):
for j_n in range(n):
if data_matrix[i_n, j_n] == 1:
plt.scatter(j_n, i_n, c='w', marker='.')
idx_i = 10 # y rand point
idx_j = 1 # x rand point
plt.scatter(idx_j, idx_i, c='r')
coords = np.zeros(shape=[4, 4]) # 4 threads: [right-bottom right_top , left-bt, left-tp], 4 coords: [x1 x2 y1 y2]
x1, x2, y1, y2 = get_right_bottom_rectangle(idx_i, idx_j)
coords[0, :] = np.array([x1, x2, y1, y2])
p1 = np.array([x1, y1])
p2 = np.array([x1, y2])
p3 = np.array([x2, y1])
p4 = np.array([x2, y2])
ps = np.array([p1, p2, p4, p3, p1])
plt.plot(ps[:, 0], ps[:, 1], c='w')
x1, x2, y1, y2 = get_right_top_rectangle(idx_i, idx_j)
coords[1, :] = np.array([x1, x2, y1, y2])
p1 = np.array([x1, y1])
p2 = np.array([x1, y2])
p3 = np.array([x2, y1])
p4 = np.array([x2, y2])
ps = np.array([p1, p2, p4, p3, p1])
plt.plot(ps[:, 0], ps[:, 1], c='w')
x1, x2, y1, y2 = get_left_bottom_rectangle(idx_i, idx_j)
coords[2, :] = np.array([x1, x2, y1, y2])
p1 = np.array([x1, y1])
p2 = np.array([x1, y2])
p3 = np.array([x2, y1])
p4 = np.array([x2, y2])
ps = np.array([p1, p2, p4, p3, p1])
plt.plot(ps[:, 0], ps[:, 1], c='w')
x1, x2, y1, y2 = get_left_top_rectangle(idx_i, idx_j)
coords[3, :] = np.array([x1, x2, y1, y2])
p1 = np.array([x1, y1])
p2 = np.array([x1, y2])
p3 = np.array([x2, y1])
p4 = np.array([x2, y2])
ps = np.array([p1, p2, p4, p3, p1])
plt.plot(ps[:, 0], ps[:, 1], c='w')
# coords[]
pr = coords[[0, 1], 1].min()
pl = coords[[2, 3], 1].max()
pb = coords[[0, 2], 3].min()
pt = coords[[1, 3], 3].max()
# final x1x2 and y1y2
x1 = pl
x2 = pr
y1 = pt
y2 = pb
plt.scatter(x1, y1, c='r')
plt.scatter(x2, y2, c='b')
p1 = np.array([x1, y1])
p2 = np.array([x1, y2])
p3 = np.array([x2, y1])
p4 = np.array([x2, y2])
ps = np.array([p1, p2, p4, p3, p1])
plt.plot(ps[:, 0], ps[:, 1], c='r')
data_matrix[y1:y2 + 1, x1:x2 + 1] = 0
|
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|
import pickle
import os
import numpy as np
import argparse
from matplotlib import pyplot as plt
import matplotlib
import glob
import pandas as pd
from PIL import Image
from tqdm import tqdm
parser = argparse.ArgumentParser(description='read two annotations files')
parser.add_argument('--aff_wild2_pkl', type=str, default = '/media/Samsung/Aff-wild2-Challenge/annotations/annotations.pkl')
parser.add_argument('--VA_pkl', type=str, default = '/media/Samsung/AFEW_VA/annotations.pkl')
parser.add_argument('--save_path', type=str, default='/media/Samsung/Aff-wild2-Challenge/exps/create_new_training_set_VA/create_annotation_file/mixed_VA_annotations.pkl')
args = parser.parse_args()
VA_list = ['valence', 'arousal']
def read_aff_wild2():
total_data = pickle.load(open(args.aff_wild2_pkl, 'rb'))
# training set
train_data = total_data['VA_Set']['Training_Set']
paths = []
labels = []
for video in train_data.keys():
data = train_data[video]
labels.append(np.stack([data['valence'], data['arousal']], axis=1))
paths.append(data['path'].values)
paths = np.concatenate(paths, axis=0)
labels = np.concatenate(labels, axis=0)
train_data = {'label': labels, 'path': paths}
# validation set
val_data = total_data['VA_Set']['Validation_Set']
paths = []
labels = []
for video in val_data.keys():
data = val_data[video]
labels.append(np.stack([data['valence'], data['arousal']], axis=1))
paths.append(data['path'].values)
paths = np.concatenate(paths, axis=0)
labels = np.concatenate(labels, axis=0)
val_data = {'label':labels, 'path':paths}
return train_data, val_data
def merge_two_datasets():
data_aff_wild2, data_aff_wild2_val = read_aff_wild2()
# downsample x 5 the training set in aff_wild training set
aff_wild_train_labels = data_aff_wild2['label']
aff_wild_train_paths = data_aff_wild2['path']
length = len(aff_wild_train_labels)
index = [True if i%5 ==0 else False for i in range(length)]
aff_wild_train_labels = aff_wild_train_labels[index]
aff_wild_train_paths = aff_wild_train_paths[index]
data_aff_wild2 = {'label':aff_wild_train_labels, 'path':aff_wild_train_paths}
# downsample x 5 the training set in aff_wild
data_VA = pickle.load(open(args.VA_pkl, 'rb'))
data_VA = {**data_VA['Training_Set'], **data_VA['Validation_Set']}
labels =[]
paths = []
for video in data_VA.keys():
data = data_VA[video]
labels.append(np.stack([data['valence'], data['arousal']], axis=1))
paths.append(data['path'])
paths = np.concatenate(paths, axis=0)
labels = np.concatenate(labels, axis=0)
data_VA = {'label':labels, 'path':paths}
data_merged = {'label': np.concatenate((data_aff_wild2['label'], data_VA['label']), axis=0),
'path': list(data_aff_wild2['path']) + list(data_VA['path'])}
print("Aff-wild2 :{}".format(len(data_aff_wild2['label'])))
print("AFEW_VA:{}".format(len(data_VA['label'])))
return {'Training_Set': data_merged, 'Validation_Set': data_aff_wild2_val}
def plot_distribution(data):
all_samples = data['label']
plt.hist2d(all_samples[:, 0] , all_samples[:, 1] , bins=(20, 20), cmap=plt.cm.jet)
plt.xlabel("Valence")
plt.ylabel('Arousal')
plt.colorbar()
plt.show()
if __name__== '__main__':
data_file = merge_two_datasets()
pickle.dump(data_file, open(args.save_path, 'wb'))
plot_distribution(data_file['Training_Set'])
|
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|
%% DEMO 18: Arbitrary axis of rotation
%
%
%
% Some modenr CT geometires are starting to be a bit more complex, one of
% the common things being arbitrary axis of rotation i.e. the detector and the
% source can move not in a circular path, but in a "spherical" path.
%
% In TIGRE this has been implemented by defining the rotation with 3
% angles, specifically the ZYZ configuration of Euler angles.
%
% This demo shows how to use it.
%
%--------------------------------------------------------------------------
%--------------------------------------------------------------------------
% This file is part of the TIGRE Toolbox
% % Copyright (c) 2015, University of Bath and
% CERN-European Organization for Nuclear Research
% All rights reserved.
%
% License: Open Source under BSD.
% See the full license at
% https://github.com/CERN/TIGRE/blob/master/LICENSE
%
% Contact: tigre.toolbox@gmail.com
% Codes: https://github.com/CERN/TIGRE/
% Coded by: Ander Biguri
%--------------------------------------------------------------------------
%% Initialize
clear;
close all;
%% Define Geometry
%
% VARIABLE DESCRIPTION UNITS
%-------------------------------------------------------------------------------------
geo.DSD = 1536; % Distance Source Detector (mm)
geo.DSO = 1000; % Distance Source Origin (mm)
% Detector parameters
geo.nDetector=[512; 512]; % number of pixels (px)
geo.dDetector=[0.8; 0.8]; % size of each pixel (mm)
geo.sDetector=geo.nDetector.*geo.dDetector; % total size of the detector (mm)
% Image parameters
geo.nVoxel=[128;128;128]; % number of voxels (vx)
% a bit smaller than usual because the demo includes a very big detector
% angle for showcase
geo.sVoxel=[256;256;256]/1.5; % total size of the image (mm)
geo.dVoxel=geo.sVoxel./geo.nVoxel; % size of each voxel (mm)
% Offsets
geo.offOrigin =[0;0;0]; % Offset of image from origin (mm)
geo.offDetector=[0; 0]; % Offset of Detector (mm)
% Auxiliary
geo.accuracy=0.5; % Accuracy of FWD proj (vx/sample)
geo.mode='cone';
%% Define angles
numProjs = 100;
anglesY=linspace(0,2*pi,numProjs);
anglesZ2=anglesY;
anglesZ1=pi*sin(linspace(0,2*pi,numProjs));
angles=[anglesZ1;anglesY;anglesZ2];
%% Get Image
head=headPhantom(geo.nVoxel);
%% Project
projections=Ax(head,geo,angles);
plotProj(projections,(1:100)*pi/180); % angle information not right in the title
%% Reconstruct:
% Note, FDK will not work.
imgSIRT = SIRT(projections,geo, angles,50);
imgCGLS = CGLS(projections,geo, angles,10);
plotImg([head imgCGLS imgSIRT] ,'dim',3)
|
{"author": "CERN", "repo": "TIGRE", "sha": "8df632662228d1b1c52afd95c90d0f7a9f8dc4b3", "save_path": "github-repos/MATLAB/CERN-TIGRE", "path": "github-repos/MATLAB/CERN-TIGRE/TIGRE-8df632662228d1b1c52afd95c90d0f7a9f8dc4b3/MATLAB/Demos/d18_ArbitraryAxisOfRotation.m"}
|
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import animation
import matplotlib.patches as patches
#my imports
import cv2
from LucasKanade import LucasKanade
# write your script here, we recommend the above libraries for making your animation
frames = np.load('../data/carseq.npy')
H, W, T = frames.shape
rect0 = np.array([59, 116, 145, 151]).astype('float').T
rect = rect0.copy()
rect_lk = rect0.copy()
p0 = np.zeros(2).astype('float')
carseqrects = np.zeros((T, 4))
carseqrects[0, :] = rect
fig=plt.figure(figsize=(5, 1))
columns = 5
rows = 1
index = 1
for i in range(1, T):
p_lk = LucasKanade(frames[:, :, i-1], frames[:, :, i], rect_lk)
rect_lk += np.array([p_lk[1], p_lk[0], p_lk[1], p_lk[0]]).T
rect_prev = rect.copy()
p = LucasKanade(frames[:, :, i-1], frames[:, :, i], rect)
rect += np.array([p[1], p[0], p[1], p[0]]).T
p0 = np.array([rect[1]-rect0[1], rect[0]-rect0[0]]).T
p_star = LucasKanade(frames[:, :, 0], frames[:, :, i], rect0, p0)
p_star[1] = p_star[1] - (rect_prev[0] - rect0[0])
p_star[0] = p_star[0] - (rect_prev[1] - rect0[1])
if np.linalg.norm(p_star-p)<= 2.5:
p = p_star
rect = rect_prev + np.array([p[1], p[0], p[1], p[0]]).T
carseqrects[i, :] = rect
frame = frames[:, :, i].copy()
cv2.rectangle(frame, (int(rect[0]),int(rect[1])), (int(rect[2]),int(rect[3])),(255), 1)
if i in [2, 100, 200, 300, 400]:
#cv2.imwrite('frame_'+str(i) + '.jpg', frame.astype('uint8'))
rect_patch = patches.Rectangle((rect[0],rect[1]),
rect[2]-rect[0],
rect[3]-rect[1],
linewidth=1,edgecolor='y',facecolor='none')
rect_lk_patch = patches.Rectangle((rect_lk[0],rect_lk[1]),
rect_lk[2]-rect_lk[0],
rect_lk[3]-rect_lk[1],
linewidth=1,edgecolor='g',facecolor='none')
ax = fig.add_subplot(rows, columns, index)
ax.add_patch(rect_patch)
ax.add_patch(rect_lk_patch)
ax.imshow(frames[:, :, i], cmap='gray')
ax.get_yaxis().set_visible(False)
ax.get_xaxis().set_visible(False)
index+=1
cv2.imshow('input', frame)
print('frame: ', i)
if cv2.waitKey(10) == ord('q'):
break
np.save('carseqrects-wcrt.npy', carseqrects)
cv2.destroyAllWindows()
plt.show()
|
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|
export TemperatureSensor, getTemperatureSensors, getTemperatureSensor, numChannels, getTemperatures, getTemperature
abstract type TemperatureSensor <: Device end
include("DummyTemperatureSensor.jl")
include("ArduinoTemperatureSensor.jl")
#include("FOTemp.jl")
Base.close(t::TemperatureSensor) = nothing
@mustimplement numChannels(sensor::TemperatureSensor)
@mustimplement getTemperatures(sensor::TemperatureSensor)
@mustimplement getTemperature(sensor::TemperatureSensor, channel::Int)
getTemperatureSensors(scanner::MPIScanner) = getDevices(scanner, TemperatureSensor)
getTemperatureSensor(scanner::MPIScanner) = getDevice(scanner, TemperatureSensor)
|
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|
# Import the used packages.
import numpy as np
import numpy.random as rd
# Define the static methods used in the Game class.
def move_column(column, max=3, length=4):
"""
Moves the elements of the column from left to right as in 2048.
Modifies the given array.
Parameters
----------
column : numpy array
A numpy array of length 4 (not necessarily).
max : int, optional
The first position to check, between 0 and 3 included (default is 3).
For example, 3 to check every value,
2 to ommit the last one in the vector, ...
length : int, optional
The length of the column (default is 4).
Returns
-------
boolean
A boolean indicating if changes occurred.
"""
modif = False
i = max - 1
while 0 <= i < max:
if column[i] != 0:
j = i
while i < length - 1 and column[i + 1] == 0:
i += 1
if j != i:
column[i] = column[j]
column[j] = 0
modif = True
i -= 1
return modif
def combine_column(column, length=4, move=True):
"""
Combines the number in the column as in the 2048 rules.
Modifies the given array.
Parameters
----------
column : numpy array
The numpy array of length 4 (not necessarily) to combine.
Must be processed by `move_column()`.
length : int, optional
The length of the column (default is 4).
move: bool, optional
Weither to apply `move_column()` at the start (default is True).
Returns
-------
boolean
A boolean indicating if changes occurred.
"""
modif = False
if move:
modif = move_column(column=column, max=length - 1, length=length)
for i in range(length - 1, 0, -1):
if column[i] != 0 and column[i] == column[i - 1]:
column[i] *= 2
column[i - 1] = 0
modif = True
move_column(column=column, max=i, length=length)
return modif
|
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|
C
C $Id$
C
LOGICAL FUNCTION CSSWPTST (N1,N2,N3,N4,X,Y,Z)
INTEGER N1, N2, N3, N4
DOUBLE PRECISION X(*), Y(*), Z(*)
C
C***********************************************************
C
C From STRIPACK
C Robert J. Renka
C Dept. of Computer Science
C Univ. of North Texas
C renka@cs.unt.edu
C 03/29/91
C
C This function decides whether or not to replace a
C diagonal arc in a quadrilateral with the other diagonal.
C The decision will be to swap (CSSWPTST = TRUE) if and only
C if N4 lies above the plane (in the half-space not contain-
C ing the origin) defined by (N1,N2,N3), or equivalently, if
C the projection of N4 onto this plane is interior to the
C circumcircle of (N1,N2,N3). The decision will be for no
C swap if the quadrilateral is not strictly convex.
C
C
C On input:
C
C N1,N2,N3,N4 = Indexes of the four nodes defining the
C quadrilateral with N1 adjacent to N2,
C and (N1,N2,N3) in counterclockwise
C order. The arc connecting N1 to N2
C should be replaced by an arc connec-
C ting N3 to N4 if CSSWPTST = TRUE. Refer
C to Subroutine CSSWAP.
C
C X,Y,Z = Arrays of length N containing the Cartesian
C coordinates of the nodes. (X(I),Y(I),Z(I))
C define node I for I = N1, N2, N3, and N4.
C
C Input parameters are not altered by this routine.
C
C On output:
C
C CSSWPTST = TRUE if and only if the arc connecting N1
C and N2 should be swapped for an arc con-
C necting N3 and N4.
C
C Modules required by CSSWPTST: None
C
C***********************************************************
C
DOUBLE PRECISION DX1, DX2, DX3, DY1, DY2, DY3, DZ1,
. DZ2, DZ3, X4, Y4, Z4
C
C Local parameters:
C
C DX1,DY1,DZ1 = Coordinates of N4->N1
C DX2,DY2,DZ2 = Coordinates of N4->N2
C DX3,DY3,DZ3 = Coordinates of N4->N3
C X4,Y4,Z4 = Coordinates of N4
C
X4 = X(N4)
Y4 = Y(N4)
Z4 = Z(N4)
DX1 = X(N1) - X4
DX2 = X(N2) - X4
DX3 = X(N3) - X4
DY1 = Y(N1) - Y4
DY2 = Y(N2) - Y4
DY3 = Y(N3) - Y4
DZ1 = Z(N1) - Z4
DZ2 = Z(N2) - Z4
DZ3 = Z(N3) - Z4
C
C N4 lies above the plane of (N1,N2,N3) iff N3 lies above
C the plane of (N2,N1,N4) iff Det(N3-N4,N2-N4,N1-N4) =
C (N3-N4,N2-N4 X N1-N4) > 0.
C
CSSWPTST = DX3*(DY2*DZ1 - DY1*DZ2)
. -DY3*(DX2*DZ1 - DX1*DZ2)
. +DZ3*(DX2*DY1 - DX1*DY2) .GT. 0.D0
RETURN
END
|
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|
from jax import grad, jit, vmap, value_and_grad
import jax.numpy as jnp
import jax.scipy as jsp
import numpy as np
import jax
from jax import random
from functools import partial
from jax.example_libraries import optimizers
from scipy.optimize import nnls
jax.config.update("jax_platform_name", "cpu")
class UBVI:
def __init__(
self,
target_log_pdf,
component_dist,
n_samples=100,
n_logfg_samples=100,
**kwargs
):
self.target_log_pdf = target_log_pdf
self.n_samples = n_samples
self.n_logfg_samples = n_logfg_samples
self.Z = jnp.empty((0, 0))
self._logfg = jnp.empty(0)
self._logfgsum = -jnp.inf
def _compute_weights(self):
Znew = jnp.exp(
self.component_dist.log_sqrt_pair_integral(self.params[-1, :], self.params)
)
Zold = self.Z
self.Z = jnp.zeros((self.params.shape[0], self.params.shape[0]))
self.Z[:-1, :-1] = Zold
self.Z[-1, :] = Znew
self.Z[:, -1] = Znew
logfg_old = self._logfg
self._logfg = jnp.zeros(self.params.shape[0])
self._logfg[:-1] = logfg_old
self._logfg[-1] = self._logfg_est(self.params[-1, :])
if self.params.shape[0] == 1:
w = jnp.array([1.0])
else:
print(self.Z)
Linv = jnp.invert(jnp.linalg.cholesky(self.Z))
d = jnp.exp(self._logfg - self._logfg.max())
b = nnls(np.array(Linv), -np.einsum("ij,j->i", Linc, d))[0]
lbd = np.einsum("ij,j->i", Linv, b + d)
w = np.max(
np.zeros(1),
np.einsum("ij,j->i", Linv.T, lbd / np.sqrt(((lbd**2).sum()))),
)
self._logfgsum = np.logsumexp(
np.concatenate(
(-np.array(np.inf)[None], self._logfg[w > 0] + torch.log(w[w > 0])),
0,
),
0,
)
return w
def _hellsq_estimate(self):
samples = self._sample_g(self.n_samples)
lf = 0.5 * self.target_log_pdf(samples)
lg = self._logg(samples)
ln = torch.log(torch.tensor(self.n_samples, dtype=torch.float32))
return 1.0 - torch.exp(
torch.logsumexp(lf - lg - ln, 0)
- 0.5 * torch.logsumexp(2 * lf - 2 * lg - ln, 0)
)
if __name__ == "__main__":
from distributions import Gaussian
cauchy = lambda x: -jnp.log(1 + (x**2).sum(axis=-1))
test = UBVI(
cauchy,
Gaussian(1),
num_opt_steps=1000,
n_samples=100,
n_init=100,
init_inflation=100,
n_logfg_samples=100,
)
|
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|
#!/usr/bin/env python2
# -*- coding: utf-8 -*-
"""
Created on Thu Sep 26 16:02:16 2019
@author: justin
"""
import tensorflow as tf
import numpy as np
import tensorflow.contrib.slim as slim
import sys
sys.path.append('../')
import layers
def lrelu(x):
return tf.maximum(x*0.2,x)
def relu(x):
return tf.nn.relu(x)
def upsample_to(x1, x2, output_channels, in_channels, scope,reuse=False):
with tf.variable_scope(scope,reuse=reuse):
pool_size = 2
deconv_filter = tf.get_variable(shape= [pool_size, pool_size, output_channels, in_channels],initializer=tf.truncated_normal_initializer(stddev=0.001),name='dcf')
deconv = tf.nn.conv2d_transpose(x1, deconv_filter, tf.shape(x2) , strides=[1, pool_size, pool_size, 1] )
return deconv
def upsample_and_concat_c(x1, x2, output_channels, in_channels, scope,reuse=False):
with tf.variable_scope(scope,reuse=reuse):
pool_size = 2
deconv_filter = tf.get_variable(shape= [pool_size, pool_size, output_channels, in_channels],initializer=tf.truncated_normal_initializer(stddev=0.001),name='dcf')
deconv = tf.nn.conv2d_transpose(x1, deconv_filter, tf.shape(x2) , strides=[1, pool_size, pool_size, 1] )
deconv_output = tf.concat([deconv, x2],3)
# deconv_output.set_shape([None, None, None, output_channels*2])
return deconv_output
def est_structure(x,size,sigma):
## x is a single channel tensor
def _tf_fspecial_gauss(size, sigma):
x_data, y_data = np.mgrid[-size//2 - 1:size//2 + 1, -size//2 - 1:size//2 + 1]
x_data = np.expand_dims(x_data, axis=-1)
x_data = np.expand_dims(x_data, axis=-1)
y_data = np.expand_dims(y_data, axis=-1)
y_data = np.expand_dims(y_data, axis=-1)
x = tf.constant(x_data, dtype=tf.float32)
y = tf.constant(y_data, dtype=tf.float32)
g = tf.exp(-((x**2.0 + y**2.0)/(2.0*sigma**2.0)))
return g / tf.reduce_sum(g)
window = _tf_fspecial_gauss(size, sigma)
final = tf.nn.conv2d(x, window, strides=[1,1,1,1], padding='SAME')
return final
def pad(x,p=1):
p = int(p)
return tf.pad(x,[[0,0],[p,p],[p,p],[0,0]],'REFLECT')
def pad_4(x,p=1):
p=int(p)
return tf.pad(x,[[0,0],[p,p],[p,p],[0,0],[0,0]],'REFLECT')
def Conv_block(input,num_conv=1,num_out=3,rate=[1]*10,fil_s=3,chan=32,act=lrelu,name=None,reuse=False):
with tf.variable_scope(name,reuse=reuse):
current = input
for i in range(num_conv):
current=slim.conv2d(pad(current,rate[i]*(fil_s-1)/2),chan,[fil_s,fil_s],
rate=rate[i], activation_fn=act,padding='VALID',scope='g_conv%d'%(i),reuse=reuse)
out = slim.conv2d(pad(current,rate[i]*(fil_s-1)/2),num_out,[fil_s,fil_s],
rate=rate[i], activation_fn=act,padding='VALID',scope='g_conv_out',reuse=reuse)
return out
def Conv_block1(input,num_conv=1,num_out=3,rate=[1]*10,fil_s=3,chan=32,act=lrelu,name=None,reuse=False):
with tf.variable_scope(name,reuse=reuse):
current = input
for i in range(num_conv-1):
current=slim.conv2d(pad(current,rate[i]*(fil_s-1)/2),chan,[fil_s,fil_s],
rate=rate[i], activation_fn=act,padding='VALID',scope='g_conv%d'%(i),reuse=reuse)
out = slim.conv2d(pad(current,(fil_s-1)/2),num_out,[fil_s,fil_s],
activation_fn=act,padding='VALID',scope='g_conv_out',reuse=reuse)
return out
def Conv_block_residual(input,num_block=1,rate=[1]*10,fil_s=3,chan=32,act=lrelu,name=None,reuse=False):
with tf.variable_scope(name,reuse=reuse):
current = slim.conv2d(pad(input,(fil_s-1)/2),chan,[fil_s,fil_s], activation_fn=act,padding='VALID',scope='g_conv',reuse=reuse)
for i in range(num_block):
add = current
current=slim.conv2d(pad(current,rate[i]*(fil_s-1)/2),chan,[fil_s,fil_s],
rate=rate[i], activation_fn=act,padding='VALID',scope='g_conv01%d'%(i),reuse=reuse)
current=slim.conv2d(pad(current,rate[i]*(fil_s-1)/2),chan,[fil_s,fil_s],
rate=rate[i], activation_fn=None,padding='VALID',scope='g_conv02%d'%(i),reuse=reuse)
current = act(add + current)
out = current
return out
def U_net22(input,num_down=4,num_block=1,num_conv=1,num_out=3,multis=False,rate=[1]*10,fil_s=3,w_init=None,b_init=None,is_residual=False,start_chan=32,act=lrelu,is_global=False,name=None,reuse=False):
## parameters
conv_ = []
chan_ = []
if w_init is None:
w_init = tf.contrib.slim.xavier_initializer()
if b_init is None:
b_init = tf.constant_initializer(value=0.0)
for i in range(num_down+1):
chan_.append(start_chan*(2**(i)))
with tf.variable_scope(name,reuse=reuse):
current = input
with tf.variable_scope('contracting_ops',reuse=reuse):
for i in range(num_down):
current = slim.conv2d(pad(current,(fil_s-1)/2),chan_[i],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,
activation_fn=act,scope='g_conv%d'%(i),padding='VALID',reuse=reuse)
for ii in range(num_block):
adding = current
for j in range(num_conv):
current=slim.conv2d(pad(current,rate[i]*(fil_s-1)/2),chan_[i],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,rate=rate[i], activation_fn=act,padding='VALID',scope='g_conv%d_block%d_%d'%(i,ii,j),reuse=reuse)
current=slim.conv2d(pad(current,(fil_s-1)/2),chan_[i],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, activation_fn=None,padding='VALID',scope='g_conv%d_block%d'%(i,ii),reuse=reuse)
if is_residual is True:
current = act(current + adding)
else:
current = act(current)
#pool=slim.conv2d(current,chan_[i],[fil_s,fil_s], stride=2,
# weights_initializer=w_init,biases_initializer=b_init, activation_fn=act,padding='SAME',scope='pool%d'%(i),reuse=reuse)
pool=slim.max_pool2d(current, [2, 2], padding='SAME',scope='pool%d'%(i))
conv_.append(current)
current = pool
current=slim.conv2d(pad(current,(fil_s-1)/2),chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, activation_fn=act,padding='VALID',scope='g_conv%d'%(num_down),reuse=reuse)
contract_temp = current
##
with tf.variable_scope('local_ops',reuse=reuse):
current = contract_temp
for ii in range(num_block):
adding = current
for j in range(num_conv):
current = slim.conv2d(pad(current,rate[num_down]*(fil_s-1)/2),chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, rate=rate[num_down],activation_fn=act,padding='VALID',scope='g_conv_block%d_%d'%(ii,j),reuse=reuse)
current = slim.conv2d(pad(current,(fil_s-1)/2),chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,activation_fn=None,padding='VALID',scope='g_conv_block%d'%(ii),reuse=reuse)
if is_residual is True:
current = act(current + adding)
else:
current = act(current)
restore_temp = current
if is_global is True:
with tf.variable_scope('global_ops',reuse=reuse):
current = contract_temp
'''
for i in range(3):
current = slim.conv2d(current,chan_[num_down],[fil_s,fil_s],activation_fn=act,scope='global%d'%(i),reuse=reuse)
current = slim.max_pool2d(current, [2, 2], padding='SAME',scope='global_pool%d'%(i))
'''
global_feature = tf.reduce_mean(current,[1,2],keepdims=False)
current = slim.fully_connected(global_feature,chan_[num_down]*2,activation_fn=lrelu,scope='fully_enhan00',reuse=reuse)
current = slim.fully_connected(current,chan_[num_down]*2,activation_fn=None,scope='fully_enhan01',reuse=reuse)
global_feature = tf.reshape(current,[-1,1,1,chan_[num_down]*2])
restore_temp = act(restore_temp*global_feature[:,:,:,0:chan_[num_down]] + global_feature[:,:,:,chan_[num_down]:])
multis_list = []
with tf.variable_scope('expanding_ops',reuse=reuse):
current = restore_temp
for i in range(num_down):
index_current = num_down-1-i
current = upsample_and_concat_c( current, conv_[index_current], chan_[index_current], chan_[index_current+1], scope='uac%d'%(i),reuse=reuse )
current = slim.conv2d(pad(current,(fil_s-1)/2),chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, padding='VALID',activation_fn=act,scope='g_dconv%d'%(i),reuse=reuse)
for ii in range(num_block):
adding = current
for j in range(num_conv):
current=slim.conv2d(pad(current,rate[index_current]*(fil_s-1)/2), chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,rate=rate[index_current], padding='VALID',activation_fn=act,scope='g_dconv_block%d%d_%d'%(i,ii,j),reuse=reuse)
current=slim.conv2d(pad(current,(fil_s-1)/2), chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, padding='VALID',activation_fn=None,scope='g_dconv_block%d%d'%(i,ii),reuse=reuse)
if i == num_down-1 and ii == num_block-1:
if is_residual is True:
current = current + adding
else:
current = current
else:
if is_residual is True:
current = act(current + adding)
else:
current = act(current)
'''
if multis is True:
multis_list.append(slim.conv2d(current, num_out,[1,1], weights_initializer=w_init,biases_initializer=b_init, activation_fn=tf.nn.tanh,scope='final',reuse=reuse))
'''
final = slim.conv2d(current, num_out,[1,1], weights_initializer=w_init,biases_initializer=b_init, activation_fn=None,scope='final',reuse=reuse)
return final
def U_net222(input,num_down=4,num_block=1,num_conv=1,num_out=3,rate=[1]*10,fil_s=3,w_init=None,b_init=None,is_residual=False,start_chan=32,act=lrelu,is_global=False,name=None,reuse=False):
## parameters
conv_ = []
chan_ = []
if w_init is None:
w_init = tf.contrib.slim.xavier_initializer()
if b_init is None:
b_init = tf.constant_initializer(value=0.0)
for i in range(num_down+1):
chan_.append(start_chan*(2**(i)))
with tf.variable_scope(name,reuse=reuse):
current = input
with tf.variable_scope('contracting_ops',reuse=reuse):
for i in range(num_down):
current = slim.conv2d(current,chan_[i],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,
activation_fn=act,scope='g_conv%d'%(i),padding='SAME',reuse=reuse)
for ii in range(num_block):
adding = current
for j in range(num_conv):
current=slim.conv2d(current,chan_[i],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,rate=rate[i], activation_fn=act,padding='SAME',scope='g_conv%d_block%d_%d'%(i,ii,j),reuse=reuse)
current=slim.conv2d(current,chan_[i],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, activation_fn=None,padding='SAME',scope='g_conv%d_block%d'%(i,ii),reuse=reuse)
if is_residual is True:
current = act(current + adding)
else:
current = act(current)
pool=slim.conv2d(current,chan_[i],[fil_s,fil_s], stride=2,
weights_initializer=w_init,biases_initializer=b_init, activation_fn=act,padding='SAME',scope='pool%d'%(i),reuse=reuse)
#pool=slim.max_pool2d(current, [2, 2], padding='SAME',scope='pool%d'%(i))
conv_.append(current)
current = pool
current=slim.conv2d(pad(current,(fil_s-1)/2),chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, activation_fn=act,padding='VALID',scope='g_conv%d'%(num_down),reuse=reuse)
contract_temp = current
##
with tf.variable_scope('local_ops',reuse=reuse):
current = contract_temp
for ii in range(num_block):
adding = current
for j in range(num_conv):
current = slim.conv2d(current,chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, rate=rate[num_down],activation_fn=act,padding='SAME',scope='g_conv_block%d_%d'%(ii,j),reuse=reuse)
current = slim.conv2d(current,chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,activation_fn=None,padding='SAME',scope='g_conv_block%d'%(ii),reuse=reuse)
if is_residual is True:
current = act(current + adding)
else:
current = act(current)
restore_temp = current
if is_global is True:
with tf.variable_scope('global_ops',reuse=reuse):
current = contract_temp
'''
for i in range(3):
current = slim.conv2d(current,chan_[num_down],[fil_s,fil_s],activation_fn=act,scope='global%d'%(i),reuse=reuse)
current = slim.max_pool2d(current, [2, 2], padding='SAME',scope='global_pool%d'%(i))
'''
global_feature = tf.reduce_mean(current,[1,2],keepdims=False)
current = slim.fully_connected(global_feature,chan_[num_down]*2,activation_fn=lrelu,scope='fully_enhan00',reuse=reuse)
current = slim.fully_connected(current,chan_[num_down]*2,activation_fn=None,scope='fully_enhan01',reuse=reuse)
global_feature = tf.reshape(current,[-1,1,1,chan_[num_down]*2])
restore_temp = act(restore_temp*global_feature[:,:,:,0:chan_[num_down]] + global_feature[:,:,:,chan_[num_down]:])
multis_list = []
with tf.variable_scope('expanding_ops',reuse=reuse):
current = restore_temp
for i in range(num_down):
index_current = num_down-1-i
current = upsample_and_concat_c( current, conv_[index_current], chan_[index_current], chan_[index_current+1], scope='uac%d'%(i),reuse=reuse )
current = slim.conv2d(current,chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, padding='SAME',activation_fn=act,scope='g_dconv%d'%(i),reuse=reuse)
for ii in range(num_block):
adding = current
for j in range(num_conv):
current=slim.conv2d(current, chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,rate=rate[index_current], padding='SAME',activation_fn=act,scope='g_dconv_block%d%d_%d'%(i,ii,j),reuse=reuse)
current=slim.conv2d(current, chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, padding='SAME',activation_fn=None,scope='g_dconv_block%d%d'%(i,ii),reuse=reuse)
if is_residual is True:
current = act(current + adding)
else:
current = act(current)
if i is not (num_down-1):
multis_list.append(slim.conv2d(current, num_out,[1,1], weights_initializer=w_init,biases_initializer=b_init, activation_fn=tf.nn.tanh,scope='super%d'%(i),reuse=reuse))
final = slim.conv2d(current, num_out,[1,1], weights_initializer=w_init,biases_initializer=b_init, activation_fn=tf.nn.tanh,scope='final',reuse=reuse)
return final,multis_list
def BilateralNet(input,spatial_bin=128,intensity_bin=8,is_glob_pool=True,net_input_size=512,coef=12,last_chan=96,reuse=False):
## Preprocessing
act = lrelu
with tf.variable_scope('Enhancement',reuse=reuse):
shape = tf.shape(input)
if is_glob_pool==True:
H,W = tf.cast(tf.round(shape[1]/6),tf.int32),tf.cast(tf.round(shape[2]/6),tf.int32)
else:
H,W = 512,512
start = tf.image.resize_images(input,[H,W])
with tf.variable_scope('splat',reuse=reuse):
n_ds_layers = int(np.log2(net_input_size/spatial_bin))
current = start
for i in range(n_ds_layers):
chan = 32*(2**(i))
current = slim.conv2d(current,chan,[3,3], stride=1, activation_fn=act,scope='conv_%d'%(i),reuse=reuse)
current = slim.conv2d(current,chan,[3,3], stride=2, activation_fn=act,scope='conv%d'%(i),reuse=reuse)
splat_out = current
with tf.variable_scope('global',reuse=reuse):
current = splat_out
for i in range(2):
current = slim.conv2d(current,64,[3,3], stride=2, activation_fn=act,scope='conv%d'%(i),reuse=reuse)
_, lh, lw, lc = current.get_shape().as_list()
if is_glob_pool == False:
current = tf.reshape(current, [-1, lh*lw*lc]) # flattening
else:
current = tf.reduce_mean(current,[1,2],keepdims=False)
current = slim.fully_connected(current,256,normalizer_fn=None,activation_fn=act,scope='fully_rest00',reuse=reuse)
current = slim.fully_connected(current,128,normalizer_fn=None,activation_fn=act,scope='fully_rest01',reuse=reuse)
current = slim.fully_connected(current,last_chan,normalizer_fn=None,activation_fn=act,scope='fully_rest02',reuse=reuse)
current = tf.reshape(current,[-1,1,1,last_chan])
global_out = current
with tf.variable_scope('local',reuse=reuse):
for i in range(2):
current = slim.conv2d(current,last_chan,[3,3], stride=1, activation_fn=act,scope='conv%d'%(i),reuse=reuse)
local_out = current
with tf.variable_scope('fusion',reuse=reuse):
grid_chan_size = intensity_bin*coef
current = act(local_out + global_out)
A = slim.conv2d(current,grid_chan_size,[3,3], stride=1, activation_fn=None,scope='conv',reuse=reuse)
with tf.variable_scope('guide_curve'):
npts = 15
nchans = 3
idtity = np.identity(nchans, dtype=np.float32) + np.random.randn(1).astype(np.float32)*1e-4
ccm = tf.get_variable('ccm', dtype=tf.float32, initializer=idtity) # initializer could be np array
ccm_bias = tf.get_variable('ccm_bias', shape=[nchans,], dtype=tf.float32, initializer=tf.constant_initializer(0.0))
guidemap = tf.matmul(tf.reshape(input, [-1, nchans]), ccm) #input_tensor shap should be (1,hei,wid,nchans),or will be faulty
guidemap = tf.nn.bias_add(guidemap, ccm_bias, name='ccm_bias_add') #bias: A 1-D Tensor with size matching the last dimension of value.
guidemap = tf.reshape(guidemap, tf.shape(input))
shifts_ = np.linspace(0, 1, npts, endpoint=False, dtype=np.float32)
shifts_ = shifts_[np.newaxis, np.newaxis, np.newaxis, np.newaxis,:]
shifts_ = np.tile(shifts_, (1, 1, 1, nchans, 1))
guidemap = tf.expand_dims(input, 4) # 5
shifts = tf.get_variable('shifts', dtype=tf.float32, initializer=shifts_)
slopes_ = np.zeros([1, 1, 1, nchans, npts], dtype=np.float32)
slopes_[:, :, :, :, 0] = 1.0
slopes = tf.get_variable('slopes', dtype=tf.float32, initializer=slopes_)
guidemap = tf.reduce_sum(slopes*tf.nn.relu(guidemap-shifts), reduction_indices=[4])
guidemap = slim.conv2d(inputs=guidemap,num_outputs=1, kernel_size=1, weights_initializer=tf.constant_initializer(1.0/nchans),
biases_initializer=tf.constant_initializer(0),activation_fn=None, reuse=reuse,scope='channel_mixing')
guidemap = tf.clip_by_value(guidemap, 0, 1)
with tf.variable_scope('guided_upsample'):
out = []
input_aug = tf.concat([input,tf.ones_like(input[:,:,:,0:1],dtype=tf.float32)],3)
shape = tf.shape(A)
A = tf.reshape(A,[shape[0],shape[1],shape[2],intensity_bin,coef])
Au = layers.guided_upsampling(A,guidemap)
for i in range(3):
out.append(tf.reduce_sum(input_aug*Au[:,:,:,i*4:(i+1)*4],3,keepdims=True))
final = tf.concat(out,3)
return final
def df_kpn(input_rgbs,noise,filt_s=5,reuse=False):
def get_pixel_value(img,x,y,z): # img B,H,W,F,3
shape = tf.shape(x) # x,y,z: B,H,W,Sam
batch_size = shape[0]
hei,wid,sam = shape[1],shape[2],shape[3] # B,H,W,Sam
batch_idx = tf.range(0,batch_size)
batch_idx = tf.reshape(batch_idx,[batch_size,1,1,1])
b = tf.tile(batch_idx,[1,hei,wid,sam])
indices = tf.stack([b,y,x,z],4)
return tf.gather_nd(img,indices)
input_rgbs = tf.transpose(input_rgbs,[0,1,2,4,3]) # B H W F C
input_lums = tf.reduce_mean(input_rgbs,4,keepdims=False) # B H W F 1
shape = tf.shape(input_lums)
num_samples = 3*filt_s*filt_s
## Offset net
with tf.variable_scope('Offset_N'):
offsets = U_net22(input_lums,num_down=3,num_block=1,num_conv=1,num_out=3*num_samples,rate=[1]*10,fil_s=filt_s,is_residual=False,
start_chan=32,act=relu,is_global=False,name='Offset_N',reuse=reuse)
offsets_shape = tf.shape(offsets)
offsets_r = tf.reshape(offsets,[offsets_shape[0],offsets_shape[1],offsets_shape[2],3,num_samples]) # B,H,W,F,Sam
with tf.variable_scope('Sampler'):
## Sampler
offsets_x = offsets_r[:,:,:,0,:]
offsets_y = offsets_r[:,:,:,1,:]
offsets_z = offsets_r[:,:,:,2,:]
x = tf.linspace(-1.0,1.0,shape[2])
y = tf.linspace(-1.0,1.0,shape[1])
x,y = tf.meshgrid(x,y)
x,y = tf.reshape(x,[-1,shape[1],shape[2],1]),tf.reshape(y,[-1,shape[1],shape[2],1])
x,y = tf.tile(x,[1,1,1,num_samples]),tf.tile(y,[1,1,1,num_samples])
x_t,y_t = x+offsets_x,y+offsets_y
z_t = offsets_z
max_x,max_y,max_z = shape[2]-1,shape[1]-1,shape[3]-1 # int
zero = tf.zeros([],tf.int32) # int
x_t_sc = (x_t+1.0)*0.5*tf.cast(max_x,tf.float32) #float
y_t_sc = (y_t+1.0)*0.5*tf.cast(max_y,tf.float32)
z_t_sc = (z_t+1.0)*0.5*tf.cast(max_z,tf.float32)
x0 = tf.cast(tf.floor(x_t_sc),tf.int32) # int
x1 = x0 + 1
y0 = tf.cast(tf.floor(y_t_sc),tf.int32)
y1 = y0 + 1
z0 = tf.cast(tf.floor(z_t_sc),tf.int32)
z1 = z0 + 1
x0,x1 = tf.clip_by_value(x0,zero,max_x),tf.clip_by_value(x1,zero,max_x) #int
y0,y1 = tf.clip_by_value(y0,zero,max_y),tf.clip_by_value(y1,zero,max_y)
z0,z1 = tf.clip_by_value(z0,zero,max_z),tf.clip_by_value(z1,zero,max_z)
I000 = get_pixel_value(input_rgbs,x0,y0,z0) # float
I001 = get_pixel_value(input_rgbs,x0,y0,z1)
I010 = get_pixel_value(input_rgbs,x0,y1,z0)
I011 = get_pixel_value(input_rgbs,x0,y1,z1)
I100 = get_pixel_value(input_rgbs,x1,y0,z0)
I101 = get_pixel_value(input_rgbs,x1,y0,z1)
I110 = get_pixel_value(input_rgbs,x1,y1,z0)
I111 = get_pixel_value(input_rgbs,x1,y1,z1)
w000 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w001 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w010 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w011 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w100 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w101 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w110 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w111 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w000,w001,w010,w011 = tf.expand_dims(w000,4),tf.expand_dims(w001,4),tf.expand_dims(w010,4),tf.expand_dims(w011,4)
w100,w101,w110,w111 = tf.expand_dims(w100,4),tf.expand_dims(w101,4),tf.expand_dims(w110,4),tf.expand_dims(w111,4)
align_out = tf.add_n([w000*I000,w001*I001,w010*I010,w011*I011,w100*I100,w101*I101,w110*I110,w111*I111])
## kpn
with tf.variable_scope('KPN'):
shape_input_rgbs = tf.shape(input_rgbs)
input_rgbs_m = tf.reshape(input_rgbs,[shape_input_rgbs[0],shape_input_rgbs[1],shape_input_rgbs[2],
shape_input_rgbs[3]*shape_input_rgbs[4]])
shape_align_out = tf.shape(align_out)
align_out_m = tf.reshape(align_out,[shape_align_out[0],shape_align_out[1],shape_align_out[2],
shape_align_out[3]*shape_align_out[4]])
input_kpn = tf.concat([input_rgbs_m,noise,offsets,align_out_m],3)
kernels = Conv_block(input_kpn,num_conv=3,num_out=num_samples,rate=[1]*10,fil_s=5,chan=64,act=relu,name='KPN',reuse=reuse)
#kernels = U_net22(input_kpn,num_down=3,num_block=1,num_conv=1,num_out=filt_s*filt_s*3,rate=[1]*10,fil_s=filt_s,
# is_residual=False,start_chan=32,act=lrelu,is_global=False,name='KPN',reuse=reuse)
kernels = tf.expand_dims(kernels,4)
rgb_filter = kernels*align_out
axu_out = []
for i in range(3):
axu_out.append(3.0*tf.reduce_sum(rgb_filter[:,:,:,i*9:i*9+9,:],3,keepdims=False))
rgb_out = tf.reduce_sum(rgb_filter,3,keepdims=False)
return rgb_out,axu_out
def df_kpn_enhan(input_rgbs,noise,filt_s=5,reuse=False):
def get_pixel_value(img,x,y,z): # img B,H,W,F,3
shape = tf.shape(x) # x,y,z: B,H,W,Sam
batch_size = shape[0]
hei,wid,sam = shape[1],shape[2],shape[3] # B,H,W,Sam
batch_idx = tf.range(0,batch_size)
batch_idx = tf.reshape(batch_idx,[batch_size,1,1,1])
b = tf.tile(batch_idx,[1,hei,wid,sam])
indices = tf.stack([b,y,x,z],4)
return tf.gather_nd(img,indices) # B,H,W,Sam,C
input_rgbs = tf.transpose(input_rgbs,[0,1,2,4,3]) # B H W F C
input_lums = tf.reduce_mean(input_rgbs,4,keepdims=False) # B H W F 1
shape = tf.shape(input_lums)
num_samples = 3*filt_s*filt_s
## Offset net
with tf.variable_scope('Offset_N'):
w_init = tf.constant_initializer(0.0)
b_init = tf.constant_initializer(0.0)
offsets = U_net22(input_lums,num_down=3,num_block=1,num_conv=1,w_init=w_init,b_init=b_init,num_out=3*num_samples,rate=[1]*10,fil_s=filt_s,is_residual=False,
start_chan=32,act=lrelu,is_global=False,name='Offset_N',reuse=reuse)
offsets_shape = tf.shape(offsets)
offsets_r = tf.reshape(offsets,[offsets_shape[0],offsets_shape[1],offsets_shape[2],3,num_samples]) # B,H,W,F,Sam
with tf.variable_scope('Sampler'):
## Sampler
offsets_x = offsets_r[:,:,:,0,:]
offsets_y = offsets_r[:,:,:,1,:]
offsets_z = offsets_r[:,:,:,2,:]
x = tf.linspace(-1.0,1.0,shape[2])
y = tf.linspace(-1.0,1.0,shape[1])
x,y = tf.meshgrid(x,y)
x,y = tf.reshape(x,[-1,shape[1],shape[2],1]),tf.reshape(y,[-1,shape[1],shape[2],1])
x,y = tf.tile(x,[1,1,1,num_samples]),tf.tile(y,[1,1,1,num_samples])
x_t,y_t = x+offsets_x,y+offsets_y
z_t = offsets_z
max_x,max_y,max_z = shape[2]-1,shape[1]-1,shape[3]-1 # int
zero = tf.zeros([],tf.int32) # int
x_t_sc = (x_t+1.0)*0.5*tf.cast(max_x,tf.float32) #float
y_t_sc = (y_t+1.0)*0.5*tf.cast(max_y,tf.float32)
z_t_sc = (z_t+1.0)*0.5*tf.cast(max_z,tf.float32)
x0 = tf.cast(tf.floor(x_t_sc),tf.int32) # int
x1 = x0 + 1
y0 = tf.cast(tf.floor(y_t_sc),tf.int32)
y1 = y0 + 1
z0 = tf.cast(tf.floor(z_t_sc),tf.int32)
z1 = z0 + 1
x0,x1 = tf.clip_by_value(x0,zero,max_x),tf.clip_by_value(x1,zero,max_x) #int
y0,y1 = tf.clip_by_value(y0,zero,max_y),tf.clip_by_value(y1,zero,max_y)
z0,z1 = tf.clip_by_value(z0,zero,max_z),tf.clip_by_value(z1,zero,max_z)
I000 = get_pixel_value(input_rgbs,x0,y0,z0) # float
I001 = get_pixel_value(input_rgbs,x0,y0,z1)
I010 = get_pixel_value(input_rgbs,x0,y1,z0)
I011 = get_pixel_value(input_rgbs,x0,y1,z1)
I100 = get_pixel_value(input_rgbs,x1,y0,z0)
I101 = get_pixel_value(input_rgbs,x1,y0,z1)
I110 = get_pixel_value(input_rgbs,x1,y1,z0)
I111 = get_pixel_value(input_rgbs,x1,y1,z1)
w000 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w001 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w010 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w011 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w100 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w101 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w110 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w111 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w000,w001,w010,w011 = tf.expand_dims(w000,4),tf.expand_dims(w001,4),tf.expand_dims(w010,4),tf.expand_dims(w011,4)
w100,w101,w110,w111 = tf.expand_dims(w100,4),tf.expand_dims(w101,4),tf.expand_dims(w110,4),tf.expand_dims(w111,4)
align_out = tf.add_n([w000*I000,w001*I001,w010*I010,w011*I011,w100*I100,w101*I101,w110*I110,w111*I111])
## kpn
with tf.variable_scope('KPN'):
shape_input_rgbs = tf.shape(input_rgbs)
input_rgbs_m = tf.reshape(input_rgbs,[shape_input_rgbs[0],shape_input_rgbs[1],shape_input_rgbs[2],
shape_input_rgbs[3]*shape_input_rgbs[4]])
shape_align_out = tf.shape(align_out)
align_out_m = tf.reshape(align_out,[shape_align_out[0],shape_align_out[1],shape_align_out[2],
shape_align_out[3]*shape_align_out[4]])
input_kpn = tf.concat([input_rgbs_m,noise,offsets,align_out_m],3)
#kernels = Conv_block(input_kpn,num_conv=3,num_out=num_samples,rate=[1]*10,fil_s=5,chan=64,act=relu,name='KPN',reuse=reuse)
kernels = U_net22(input_kpn,num_down=3,num_block=1,num_conv=1,num_out=filt_s*filt_s*3,rate=[1]*10,fil_s=filt_s,
is_residual=False,start_chan=32,act=lrelu,is_global=True,name='KPN',reuse=reuse)
kernels = tf.expand_dims(kernels,4)
rgb_filter = kernels*align_out
axu_out = []
for i in range(3):
axu_out.append(3.0*tf.reduce_sum(rgb_filter[:,:,:,i*9:i*9+9,:],3,keepdims=False))
rgb_out = tf.reduce_sum(rgb_filter,3,keepdims=False)
return rgb_out,axu_out
def df_kpn_enhan_1(input_rgbs,noise,num_fr=5,filt_s=3,reuse=False):
## different anealing loss
def get_pixel_value(img,x,y): # img B,H,W,3
shape = tf.shape(x) # x,y: B,H,W,1
batch_size = shape[0]
hei,wid = shape[1],shape[2] # B,H,W,1
batch_idx = tf.range(0,batch_size)
batch_idx = tf.reshape(batch_idx,[batch_size,1,1,1])
b = tf.tile(batch_idx,[1,hei,wid,1])
indices = tf.concat([b,y,x],3)
return tf.gather_nd(img,indices) # B,H,W,C
input_rgbs = tf.transpose(input_rgbs,[0,1,2,4,3]) # B H W F C
input_lums = tf.reduce_mean(input_rgbs,4,keepdims=False) # B H W F 1
shape = tf.shape(input_lums)
B,H,W,F = shape[0],shape[1],shape[2],shape[3]
num_samples = filt_s*filt_s
## Offset net
with tf.variable_scope('Offset_N'):
w_init = tf.constant_initializer(0.0)
b_init = tf.constant_initializer(0.0)
offsets = U_net22(input_lums,num_down=3,num_block=1,num_conv=1,w_init=w_init,b_init=b_init,num_out=2*num_fr,
rate=[1]*10,fil_s=filt_s,is_residual=False,start_chan=32,act=lrelu,is_global=False,name='Offset_N',reuse=reuse)
offsets_shape = tf.shape(offsets)
offsets_r = tf.reshape(offsets,[offsets_shape[0],offsets_shape[1],offsets_shape[2],2,num_fr]) # B,H,W,2,F
with tf.variable_scope('Sampler'):
## generate initail grid with initial filter kernel locations
x = tf.linspace(0.0,1.0,W)
y = tf.linspace(0.0,1.0,H)
x,y = tf.meshgrid(x,y)
x,y = tf.reshape(x,[-1,H,W,1]),tf.reshape(y,[-1,H,W,1])
x,y = tf.tile(x,[1,1,1,num_fr]),tf.tile(y,[1,1,1,num_fr]) # B,H,W,F
## adding offsets for each frame
aligned_list = []
for i in range(num_fr):
offsets_x_current = offsets_r[:,:,:,0,i:i+1] # B,H,W,1
offsets_y_current = offsets_r[:,:,:,1,i:i+1] # B,H,W,1
x_current,y_current = x[:,:,:,i:i+1],y[:,:,:,i:i+1]
x_new, y_new = x_current + offsets_x_current, y_current + offsets_y_current
x_new = tf.clip_by_value(x_new,0.0,1.0)
y_new = tf.clip_by_value(y_new,0.0,1.0)
x_t_sc = x_new*(tf.cast(W,tf.float32)-1.0)
y_t_sc = y_new*(tf.cast(H,tf.float32)-1.0)
x0 = tf.cast(tf.floor(x_t_sc),tf.int32) # # B,H,W,1
x1 = tf.clip_by_value(x0 + 1,0,W-1)
y0 = tf.cast(tf.floor(y_t_sc),tf.int32)
y1 = tf.clip_by_value(y0 + 1,0,H-1)
I00 = get_pixel_value(input_rgbs[:,:,:,i,:],x0,y0) # float
I01 = get_pixel_value(input_rgbs[:,:,:,i,:],x0,y1)
I10 = get_pixel_value(input_rgbs[:,:,:,i,:],x1,y0)
I11 = get_pixel_value(input_rgbs[:,:,:,i,:],x1,y1) # I=B,H,W,C
w00 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)
w01 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)
w10 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)
w11 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)
align_out = tf.add_n([w00*I00,w01*I01,w10*I10,w11*I11])
aligned_list.append(align_out)
aligned_imgs = tf.stack(align_out,3) # B,H,W,F,3
## kpn
with tf.variable_scope('KPN'):
shape_input_rgbs = tf.shape(input_rgbs)
input_rgbs_m = tf.reshape(input_rgbs,[shape_input_rgbs[0],shape_input_rgbs[1],shape_input_rgbs[2],
shape_input_rgbs[3]*shape_input_rgbs[4]])
shape_align_out = tf.shape(aligned_imgs)
align_out_m = tf.reshape(aligned_imgs,[shape_align_out[0],shape_align_out[1],shape_align_out[2],
shape_align_out[3]*shape_align_out[4]])
input_kpn = tf.concat([input_rgbs_m,noise,offsets,align_out_m],3)
#kernels = Conv_block(input_kpn,num_conv=3,num_out=num_samples,rate=[1]*10,fil_s=5,chan=64,act=relu,name='KPN',reuse=reuse)
kernels = U_net22(input_kpn,num_down=3,num_block=1,num_conv=1,num_out=filt_s*filt_s*3,rate=[1]*10,fil_s=filt_s,
is_residual=False,start_chan=32,act=lrelu,is_global=True,name='KPN',reuse=reuse)
kernels = tf.expand_dims(kernels,4)
rgb_filter = kernels*align_out
axu_out = []
for i in range(3):
axu_out.append(3.0*tf.reduce_sum(rgb_filter[:,:,:,i*9:i*9+9,:],3,keepdims=False))
rgb_out = tf.reduce_sum(rgb_filter,3,keepdims=False)
return rgb_out,axu_out
def EDVR(input_rgbs,fra_s=5,num_fea=32,reuse = False):
def dcn(fea,offset,group=8,fil_s=3,name=None,reuse=False):
def grid_fil(x,y):
case = [[-1.0,-1.0],[-1.0,0.0],[-1.0,1.0],[0.0,-1.0],[0.0,0.0],[0.0,1.0],[1.0,-1.0],[1.0,0.0],[1.0,1.0]]
offset_x,offset_y = [],[]
shape = tf.shape(x)
for i in case:
case_x,case_y = 2.0*i[0]/tf.cast(shape[2],tf.float32),2.0*i[1]/tf.cast(shape[1],tf.float32)
offset_x.append(tf.reshape(case_x,[1,1,1,1]))
offset_y.append(tf.reshape(case_y,[1,1,1,1]))
offset_x_,offset_y_ = tf.concat(offset_x,3),tf.concat(offset_y,3)
x_new,y_new = x+offset_x_,y+offset_y_
return x_new,y_new
def get_pixel_value(img,x,y): # img B,H,W,8
shape = tf.shape(x) # x,y,z: B,H,W,9
batch_size = shape[0]
hei,wid,sam = shape[1],shape[2],shape[3] # B,H,W,Sam
batch_idx = tf.range(0,batch_size)
batch_idx = tf.reshape(batch_idx,[batch_size,1,1,1])
b = tf.tile(batch_idx,[1,hei,wid,sam])
indices = tf.stack([b,y,x],4)
return tf.gather_nd(img,indices)
with tf.variable_scope(name,reuse=reuse):
offset = Conv_block1(offset,num_conv=1,num_out=group*2*fil_s*fil_s,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='ali',reuse=reuse)
offset_x,offset_y = offset[:,:,:,0:group*fil_s*fil_s],offset[:,:,:,group*fil_s*fil_s:group*fil_s*fil_s*2]
#mask = tf.sigmoid(mask)
shape = tf.shape(offset_x)
collect = []
for i in range(group):
num_c = int(num_fea/group)
#mask_current = tf.expand_dims(mask[:,:,:,i*fil_s*fil_s:(i+1)*fil_s*fil_s],4)
fea_current = fea[:,:,:,i*num_c:(i+1)*num_c]
x = tf.linspace(-1.0,1.0,shape[2])
y = tf.linspace(-1.0,1.0,shape[1])
x,y = tf.meshgrid(x,y)
x,y = tf.reshape(x,[-1,shape[1],shape[2],1]),tf.reshape(y,[-1,shape[1],shape[2],1])
x,y = tf.tile(x,[1,1,1,fil_s*fil_s]),tf.tile(y,[1,1,1,fil_s*fil_s])
x,y = grid_fil(x,y)
x_t,y_t = x+offset_x[:,:,:,i*fil_s*fil_s:(i+1)*fil_s*fil_s],y+offset_y[:,:,:,i*fil_s*fil_s:(i+1)*fil_s*fil_s]
max_x,max_y = shape[2]-1,shape[1]-1 # int
zero = tf.zeros([],tf.int32) # int
x_t_sc = (x_t+1.0)*0.5*tf.cast(max_x,tf.float32) #float
y_t_sc = (y_t+1.0)*0.5*tf.cast(max_y,tf.float32)
x0 = tf.cast(tf.floor(x_t_sc),tf.int32) # int
x1 = x0 + 1
y0 = tf.cast(tf.floor(y_t_sc),tf.int32)
y1 = y0 + 1
x0,x1 = tf.clip_by_value(x0,zero,max_x+1),tf.clip_by_value(x1,zero,max_x+1) #int
y0,y1 = tf.clip_by_value(y0,zero,max_y+1),tf.clip_by_value(y1,zero,max_y+1)
padd = [[0,0],[0,1],[0,1],[0,0]]
I00 = get_pixel_value(tf.pad(fea_current,padd,'SYMMETRIC'),x0,y0) # float
I01 = get_pixel_value(tf.pad(fea_current,padd,'SYMMETRIC'),x0,y1)
I10 = get_pixel_value(tf.pad(fea_current,padd,'SYMMETRIC'),x1,y0)
I11 = get_pixel_value(tf.pad(fea_current,padd,'SYMMETRIC'),x1,y1)
w00 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)
w01 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)
w10 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)
w11 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)
w00,w01,w10,w11 = tf.expand_dims(w00,4),tf.expand_dims(w01,4),tf.expand_dims(w10,4),tf.expand_dims(w11,4)
align_out = tf.add_n([w00*I00,w01*I01,w10*I10,w11*I11])
align_out = align_out#*mask_current
align_out = tf.reshape(align_out,[shape[0],shape[1],shape[2],-1]) # B,H,W,8*9
collect.append(align_out)
collect_ = tf.concat(collect,3)
out = Conv_block1(collect_,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=1,chan=num_fea,act=lrelu,name='out',reuse=reuse)
return out
def PCD_align(nalign,ref,name,reuse=False): # nalign is B,H,W,C
with tf.variable_scope(name,reuse=reuse):
group = 4
L3_offset = tf.concat([nalign[2],ref[2]],3)
L3_offset = Conv_block1(L3_offset,num_conv=2,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea3',reuse=reuse)
L3_fea = dcn(nalign[2],L3_offset,group=group,fil_s=3,name='dcn3',reuse=reuse)
L2_offset = tf.concat([nalign[1],ref[1]],3)
L2_offset = Conv_block1(L2_offset,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea2',reuse=reuse)*2.0
L2_offset = upsample_and_concat_c(L3_offset,L2_offset,num_fea, num_fea, 'ou_and_c3',reuse=reuse)
L2_offset = Conv_block1(L2_offset,num_conv=2,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea21',reuse=reuse)
L2_fea = dcn(nalign[1],L2_offset,group=group,fil_s=3,name='dcn2',reuse=reuse)
L2_fea = upsample_and_concat_c(L3_fea,L2_fea,num_fea, num_fea, 'fu_and_c3',reuse=reuse)
L2_fea = Conv_block1(L2_fea,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea22',reuse=reuse)
L1_offset = tf.concat([nalign[0],ref[0]],3)
L1_offset = Conv_block1(L1_offset,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea1',reuse=reuse)*2.0
L1_offset = upsample_and_concat_c(L2_offset,L1_offset,num_fea, num_fea, 'ou_and_c2',reuse=reuse)
L1_offset = Conv_block1(L1_offset,num_conv=2,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea11',reuse=reuse)
L1_fea = dcn(nalign[0],L1_offset,group=group,fil_s=3,name='dcn1',reuse=reuse)
L1_fea = upsample_and_concat_c(L2_fea,L1_fea,num_fea, num_fea, 'fu_and_c2',reuse=reuse)
L1_fea = Conv_block1(L1_fea,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea12',reuse=reuse)
offset = tf.concat([L1_fea,ref[0]],3)
offset = Conv_block1(offset,num_conv=2,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea0',reuse=reuse)
L1_fea = dcn(L1_fea,offset,group=group,fil_s=3,name='dcn0',reuse=reuse)
return L1_fea # B H W 64
input_rgbs = tf.transpose(input_rgbs,[0,4,1,2,3]) # B F H W C
in_shape = tf.shape(input_rgbs) # B F H W C
B, F, H, W, C = in_shape[0],in_shape[1],in_shape[2],in_shape[3],in_shape[4]
center = int((fra_s+1)/2-1)
with tf.variable_scope('Fea_extr'):
current = input_rgbs # B F,H W C
current = tf.reshape(input_rgbs,[-1, H, W, C])
current = Conv_block1(current,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='pre_fea0',reuse=reuse)
current = Conv_block_residual(current,num_block=2,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,
name='pre_fea1',reuse=reuse)
Fea_extr = current
with tf.variable_scope('Align'):
current = Fea_extr
L1_fea = Conv_block1(current,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea00',reuse=reuse)
L1_fea = Conv_block1(L1_fea,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea01',reuse=reuse)
L2_fea = Conv_block1(L1_fea,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea10',reuse=reuse)
L2_fea = Conv_block1(L2_fea,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea11',reuse=reuse)
L2_fea=slim.conv2d(L2_fea,num_fea,[3,3], stride=2, activation_fn=lrelu,padding='SAME',scope='fea13',reuse=reuse)
#L2_fea=slim.max_pool2d(L2_fea, [3, 3], padding='SAME',scope='fea13')
L3_fea = Conv_block1(L2_fea,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea20',reuse=reuse)
L3_fea = Conv_block1(L3_fea,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fea21',reuse=reuse)
L3_fea = slim.conv2d(L3_fea,num_fea,[3,3], stride=2, activation_fn=lrelu,padding='SAME',scope='fea22',reuse=reuse)
#L3_fea=slim.max_pool2d(L3_fea, [3, 3], padding='SAME',scope='fea22')
L1_fea = tf.reshape(L1_fea,[B,F, H, W, -1])
L2_fea = tf.reshape(L2_fea,[B,F, H//2, W//2, -1])
L3_fea = tf.reshape(L3_fea,[B,F, H//4, W//4, -1])
L1_center,L2_center,L3_center = L1_fea[:,center:center+1,:,:,:],L2_fea[:,center:center+1,:,:,:],L3_fea[:,center:center+1,:,:,:] ## center:B,H,W,64
L1_center,L2_center,L3_center = tf.tile(L1_center,[1,F,1,1,1]),tf.tile(L2_center,[1,F,1,1,1]),tf.tile(L3_center,[1,F,1,1,1])
L1_center = tf.reshape(L1_center,[B*F,H,W,-1])
L2_center = tf.reshape(L2_center,[B*F,H//2,W//2,-1])
L3_center = tf.reshape(L3_center,[B*F,H//4,W//4,-1])
L1_fea = tf.reshape(L1_fea,[B*F,H,W,-1])
L2_fea = tf.reshape(L2_fea,[B*F,H//2,W//2,-1])
L3_fea = tf.reshape(L3_fea,[B*F,H//4,W//4,-1])
nalign,refs = [L1_fea,L2_fea,L3_fea],[L1_center,L2_center,L3_center]
PCD_out_ = PCD_align(nalign,refs,'pcd',reuse=reuse)
#print(PCD_out_.shape)
#PCD_out_ = Conv_block1(PCD_out_,num_conv=1,num_out=3,rate=[1]*10,fil_s=1,chan=32,act=relu,name='fuse',reuse=reuse)
PCD_out_ = tf.reshape(PCD_out_,[B,F,H,W,num_fea])
#PCD_out_ = tf.transpose(PCD_out_,[0,2,3,4,1])
with tf.variable_scope('TSA'):
aligned_fea = PCD_out_
emb_ref = Conv_block1(aligned_fea[:,center,:,:,:],num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=64,act=lrelu,name='emb_ref',reuse=reuse)
emb_in = tf.reshape(aligned_fea,[-1,H, W,num_fea])
emb = Conv_block1(emb_in,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='emb',reuse=reuse)
emb = tf.reshape(emb,[B,F,H,W,num_fea])
col_l = []
for i in range(fra_s):
emb_cur = emb[:,i,:,:,:]
color_temp = tf.reduce_sum(emb_cur*emb_ref,3,keepdims=False) # B,H,W
col_l.append(color_temp)
col_prob = tf.sigmoid(tf.stack(col_l,1)) # B,N,H,W
col_prob = tf.tile(tf.expand_dims(col_prob,4),[1,1,1,1,num_fea])
aligned_fea = aligned_fea*col_prob # B,N,H,W,64
aligned_fea = tf.reshape(tf.transpose(aligned_fea,[0,2,3,1,4]),[B,H,W,-1])
tfuse_fea = Conv_block1(aligned_fea,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='fuse',reuse=reuse) # B,H,W,64
# Spatial attention
att = Conv_block1(aligned_fea,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='spa0',reuse=reuse)
add0 = att
att_max = slim.max_pool2d(att, [3, 3], padding='SAME',scope='spa0max')
att_aver = slim.avg_pool2d(att, [3, 3], padding='SAME',scope='spa0aver')
con = tf.concat([att_max,att_aver],3)
att = Conv_block1(con,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='spa0a',reuse=reuse) # B,H,W,64
add1 = att
att = Conv_block1(att,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='spa1',reuse=reuse) # B,H,W,64
att_max = slim.max_pool2d(att, [3, 3], padding='SAME',scope='spa1max')
att_aver = slim.avg_pool2d(att, [3, 3], padding='SAME',scope='spa1aver')
con = tf.concat([att_max,att_aver],3)
att = Conv_block1(con,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='spa1a',reuse=reuse) # B,H,W,64
att = Conv_block1(att,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='spa1af',reuse=reuse) # B,H,W,64
att = upsample_to(att,add1,num_fea,num_fea,scope='uac0',reuse=reuse)
att = Conv_block1(att,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='spa2af',reuse=reuse) # B,H,W,64
att = att + add1
att = Conv_block1(att,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='spa3af',reuse=reuse) # B,H,W,64
att = upsample_to(att,add0,num_fea,num_fea,scope='uac1',reuse=reuse)
att_add = Conv_block1(att,num_conv=1,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='spa4af',reuse=reuse) # B,H,W,64
att_mul = Conv_block1(att_add,num_conv=2,num_out=num_fea,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='spa5af',reuse=reuse) # B,H,W,64
att_mul = tf.sigmoid(att_mul)
fea = tfuse_fea*att_mul*2.0+att_add
fea = Conv_block_residual(fea,num_block=4,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='out_residual',reuse=reuse)
out = Conv_block1(fea,num_conv=2,num_out=3,rate=[1]*10,fil_s=3,chan=num_fea,act=lrelu,name='out_conv',reuse=reuse) # B,H,W,64
return out
def pack_fea(x,num_fr=5): #B,F,H,W,C
shape = tf.shape(x)
B,F,H,W,C = shape[0],shape[1],shape[2],shape[3],shape[4]
center = int((num_fr+1)/2)
ref = x[:,center-1:center,:,:,:] #B,1,H,W,C
inds = np.concatenate([np.arange(0,center-1),np.arange(center,num_fr)],0)
lis = [x[:,i:i+1,:,:,:] for i in inds]
others = tf.concat(lis,1) #B,F-1,H,W,C
ref_tile = tf.tile(ref,[1,num_fr-1,1,1,1]) #B,F-1,H,W,C
ref_tile_r = tf.reshape(ref_tile,[B*(F-1),H,W,C]) #B*(F-1),H,W,C
others_r = tf.reshape(others,[B*(F-1),H,W,C]) #B*(F-1),H,W,C
in_feas =tf.concat([others_r,ref_tile_r],3)
return in_feas,ref,others #B*(F-1),H,W,C*2, #B,1,H,W,C #B,F-1,H,W,C
def get_pixel_value(img,x,y): # img B,H,W,C
shape = tf.shape(x) # x,y,z: B,H,W
batch_size = shape[0]
hei,wid = shape[1],shape[2] # B,H,W
batch_idx = tf.range(0,batch_size)
batch_idx = tf.reshape(batch_idx,[batch_size,1,1])
b = tf.tile(batch_idx,[1,hei,wid])
indices = tf.stack([b,y,x],3)
return tf.gather_nd(img,indices) # B,H,W,C
def get_pixel_value_3D(img,x,y,z): # img B,H,W,F,C
shape = tf.shape(x) # x,y,z: B,H,W
batch_size = shape[0]
hei,wid = shape[1],shape[2] # B,H,W
batch_idx = tf.range(0,batch_size)
batch_idx = tf.reshape(batch_idx,[batch_size,1,1])
b = tf.tile(batch_idx,[1,hei,wid])
indices = tf.stack([b,y,x,z],3)
return tf.gather_nd(img,indices) # B,H,W,C
def U_Net_align_spy(img,num_fr=5,num_down=4,reuse = False): # img:B,H,W,C,F noise:B,H,W,1
def image_warp(images, flow, name='image_warp'):
with tf.name_scope(name):
shape = tf.shape(images)
batch_size = shape[0]
height = shape[1]
width = shape[2]
channels = shape[3]
#images = tf.reshape(images,[-1,height,width,channels])
#flow = tf.reshape(flow,[-1,height,width,2])
x = tf.linspace(0.0,1.0,width)
y = tf.linspace(0.0,1.0,height)
grid_x, grid_y = tf.meshgrid(x, y)
grid_x, grid_y = tf.cast(grid_x,flow.dtype),tf.cast(grid_y,flow.dtype)
grid_x, grid_y = tf.expand_dims(tf.expand_dims(grid_x,0),3),tf.expand_dims(tf.expand_dims(grid_y,0),3)
grid_y = (grid_y + flow[:,:,:,0:1])*tf.cast(height-1,flow.dtype)
grid_x = (grid_x + flow[:,:,:,1:2])*tf.cast(width-1,flow.dtype)
grid = tf.concat([grid_y, grid_x], 3) # B,H,W,2
coords = tf.reshape(grid,[batch_size, height * width, 2]) # B,H*W,2
coords = tf.stack([tf.minimum(tf.maximum(0.0, coords[:, :, 0]), tf.cast(height, flow.dtype) - 1.0),
tf.minimum(tf.maximum(0.0, coords[:, :, 1]), tf.cast(width, flow.dtype) - 1.0)], axis=2)
floors = tf.cast(tf.floor(coords), tf.int32)
ceils = floors + 1 ## the ceils and floors are not clipped
alphas = tf.cast(coords - tf.cast(floors, flow.dtype), images.dtype)
alphas = tf.reshape(tf.minimum(tf.maximum(0.0, alphas), 1.0), shape=[batch_size, height, width, 1, 2])
images_flattened = tf.reshape(images, [-1, channels])
batch_offsets = tf.expand_dims(tf.range(batch_size) * height * width, axis=1)
def gather(y_coords, x_coords):
linear_coordinates = batch_offsets + y_coords * width + x_coords
gathered_values = tf.gather(images_flattened, linear_coordinates)
return tf.reshape(gathered_values, shape)
top_left = gather(floors[:, :, 0], floors[:, :, 1]) # B,H,W,C
top_right = gather(floors[:, :, 0], ceils[:, :, 1])
bottom_left = gather(ceils[:, :, 0], floors[:, :, 1])
bottom_right = gather(ceils[:, :, 0], ceils[:, :, 1])
interp_top = alphas[:, :, :, :, 1] * (top_right - top_left) + top_left
interp_bottom = alphas[:, :, :, :, 1] * (bottom_right - bottom_left) + bottom_left
interpolated = alphas[:, :, :, :, 0] * (interp_bottom - interp_top) + interp_top
return interpolated
def pack_fea(x,num_fr=5): #B,F,H,W,C
shape = tf.shape(x)
B,F,H,W,C = shape[0],shape[1],shape[2],shape[3],shape[4]
center = int((num_fr+1)/2)
ref = x[:,center-1:center,:,:,:] #B,1,H,W,C
inds = np.concatenate([np.arange(0,center-1),np.arange(center,num_fr)],0)
lis = [x[:,i:i+1,:,:,:] for i in inds]
others = tf.concat(lis,1) #B,F-1,H,W,C
ref_tile = tf.tile(ref,[1,num_fr-1,1,1,1]) #B,F-1,H,W,C
ref_tile_r = tf.reshape(ref_tile,[B*(F-1),H,W,C]) #B*(F-1),H,W,C
others_r = tf.reshape(others,[B*(F-1),H,W,C]) #B*(F-1),H,W,C
in_feas =tf.concat([others_r,ref_tile_r],3)
return in_feas,ref,others #B*(F-1),H,W,C*2, #B,1,H,W,C #B,F-1,H,W,C
def U_net2222(inputlist,num_down=4,num_conv=1,num_out=3,rate=[1]*10,fil_s=3,w_init=None,b_init=None,start_chan=32,act=lrelu,name=None,reuse=False):
## parameters
conv_ = []
chan_ = []
if w_init is None:
w_init = tf.contrib.slim.xavier_initializer()
if b_init is None:
b_init = tf.constant_initializer(value=0.0)
for i in range(num_down+1):
chan_.append(start_chan*(2**(i)))
##
multis_list = []
with tf.variable_scope('local_ops',reuse=reuse):
current = inputlist[num_down]
for j in range(num_conv):
current = slim.conv2d(current,chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, rate=1,activation_fn=act,padding='SAME',scope='g_conv_block_%d'%(j),reuse=reuse)
fine_flow = slim.conv2d(current,2,[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,activation_fn=tf.nn.tanh,padding='SAME',scope='g_conv_block',reuse=reuse)
current_imgs = inputlist[num_down]
other_img,ref_img = current_imgs[:,:,:,0:3],current_imgs[:,:,:,3:]
multis_list.append(image_warp(other_img,fine_flow,'fine_wapring%d'%(num_down)))
restore_temp = fine_flow
with tf.variable_scope('expanding_ops',reuse=reuse):
init_flow = restore_temp
for i in range(num_down):
index_current = num_down-1-i
current_imgs = inputlist[index_current]
other_img,ref_img = current_imgs[:,:,:,0:3],current_imgs[:,:,:,3:]
up_flow = slim.conv2d_transpose(init_flow,2,3,(2,2),padding='SAME',scope='up%d'%(i),reuse=reuse)
other_img_warped = image_warp(other_img,up_flow,'init_wapring%d'%(i))
fea = tf.concat([other_img_warped,ref_img,up_flow],3)
#current = upsample_and_concat_c( current, conv_[index_current], chan_[index_current], chan_[index_current+1], scope='uac%d'%(i),reuse=reuse )
current = slim.conv2d(fea,chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, padding='SAME',activation_fn=act,scope='g_dconv%d'%(i),reuse=reuse)
for j in range(num_conv):
current=slim.conv2d(current, chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,rate=1, padding='SAME',activation_fn=act,scope='g_dconv_block%d_%d'%(i,j),reuse=reuse)
fine_flow = up_flow + slim.conv2d(current,2,[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, padding='SAME',activation_fn=tf.nn.tanh,scope='g_dconv_block%d'%(i),reuse=reuse)
multis_list.append(image_warp(other_img,fine_flow,'fine_wapring%d'%(i)))
init_flow = fine_flow
return multis_list
img = tf.transpose(img,[0,4,1,2,3])
shape = tf.shape(img)
B,F,H,W,C = shape[0],shape[1],shape[2],shape[3],shape[4]
with tf.variable_scope('Stage1',reuse=reuse):
current = img
in_imgs_dn,ref_img_dn,other_imgs_dn = pack_fea(current,num_fr=num_fr) #B*(F-1),H,W,C*2, #B,1,H,W,C #B,F-1,H,W,C
in_imgs_dn = tf.clip_by_value(in_imgs_dn,0.0,1.0)
w_init = tf.constant_initializer(0.0)
b_init = tf.constant_initializer(0.0)
rate = [1,2,2,4,4,8]
inlist = []
for i in range(num_down+1):
size = [tf.cast(H/(2**i),tf.int32),tf.cast(W/(2**i),tf.int32)]
inlist.append(tf.image.resize_bilinear(in_imgs_dn,size))
warped_imgs_list = U_net2222(inlist,num_down=num_down,num_conv=6,num_out=2,rate=rate,fil_s=5,w_init=None,b_init=None,
start_chan=32,act=lrelu,name='Alignment',reuse=reuse) # B*(F-1),H,W,2
for i in range(len(warped_imgs_list)):
current = warped_imgs_list[i]
shape = tf.shape(current)
H_c,W_c,C_c = shape[1],shape[2],shape[3]
warped_imgs_list[i] = tf.transpose(tf.reshape(current,[B,F-1,H_c,W_c,C_c]),[0,2,3,4,1])
warped_imgs_list.reverse()
return warped_imgs_list
def LiangNN(img,noise,num_fr=5,reuse = False): # img:B,H,W,C,F noise:B,H,W,1
img = tf.transpose(img,[0,4,1,2,3])
center = int((num_fr+1)/2-1)
shape = tf.shape(img)
B,F,H,W,C = shape[0],shape[1],shape[2],shape[3],shape[4]
## Single frame denoising
with tf.variable_scope('Stage0',reuse=reuse):
current = tf.reshape(img,[B*F,H,W,C])
noise_exp = tf.tile(noise,[B*F,1,1,1])
current = tf.concat([current,noise_exp],3)
single_dn_out = U_net22(current,num_down=3,num_block=1,num_conv=1,num_out=3,rate=[1]*10,fil_s=3,w_init=None,b_init=None,is_residual=False,
start_chan=32,act=lrelu,is_global=False,name='SingleDN',reuse=reuse)
single_dn_out = tf.reshape(single_dn_out,[B,F,H,W,C]) # B,F,H,W,C
ref_img_dn = single_dn_out[:,center:center+1,:,:,:]
single_dn_out_final = tf.transpose(single_dn_out,[0,2,3,4,1])
### Alignment
current = (tf.clip_by_value(single_dn_out_final,0.0,1.0)+1e-4)**(1.0/2.2)
warped_imgs_list = U_Net_align_spy(current,num_fr=num_fr,num_down=4,reuse=reuse)
warped_img = warped_imgs_list[0]
warped_img_out = (tf.clip_by_value(warped_img,0.0,1.0)+1e-4)**2.2
warped_img = tf.transpose(warped_img_out,[0,4,1,2,3])
### Fusion
with tf.variable_scope('Stage2',reuse=reuse):
chan = 32
bs = 15
#current0 = tf.concat([align_out[:,0:center,:,:,:],ref_img,align_out[:,center:,:,:,:]],1) # B,F,H,W,C
current = tf.concat([warped_img[:,0:center,:,:,:],ref_img_dn,warped_img[:,center:,:,:,:]],1) # B,F,H,W,C
#current = tf.concat([current0,current1],4) # B,F,H,W,C*2
#current = tf.concat([current,tf.tile(ref_img_dn,[1,F,1,1,1])],4) # B,F,H,W,C*3
current = tf.reshape(current,[B*F,H,W,C]) # B*F,H,W,C*2
#current = tf.concat([current,noise_exp],3) # B*F,H,W,C*3+1
feas = Conv_block_residual(current,num_block=4,rate=[1]*10,fil_s=3,chan=chan,act=lrelu,name='out_residual',reuse=reuse)
feas = tf.reshape(feas,[B,F,H,W,chan])
ref_fea = feas[:,center,:,:,:] # B,H,W,chan
other_feas = tf.concat([feas[:,:center,:,:,:],feas[:,center+1:,:,:,:]],1) # B,F-1,H,W,chan
alphas = tf.Variable(np.ones(shape=[1,1,1,chan],dtype=np.float32),dtype=tf.float32)
out_list1 = []
for i in range(num_fr-1):
other_fea_cur = other_feas[:,i,:,:,:]
ref_fea_p = pad(ref_fea,p=(bs-1)/2)
other_fea_cur_p = pad(other_fea_cur,p=(bs-1)/2)
residual = tf.abs(ref_fea_p-other_fea_cur_p)
weight = slim.separable_conv2d(residual,num_outputs=None,kernel_size=bs,padding='VALID',
weights_initializer=tf.constant_initializer(value=1.0/(bs*bs)),
biases_initializer=None,scope='we%d'%(i),reuse=reuse)
weight = tf.exp(-alphas*weight)
out_list1.append(weight*other_fea_cur+(1.0-weight)*ref_fea)
out = tf.reduce_mean(tf.stack(out_list1,1),1)
out_final = Conv_block1(out,num_conv=4,num_out=3,rate=[1]*10,fil_s=1,chan=3,act=lrelu,name='out_conv',reuse=reuse) # B,H,W,3
return single_dn_out_final,warped_img_out,out_final
def U_Net_align(img,num_fr=5,reuse = False): # img:B,H,W,C,F noise:B,H,W,1
def U_net2222(input,num_down=4,num_conv=1,num_out=3,rate=[1]*10,fil_s=3,w_init=None,b_init=None,start_chan=32,act=lrelu,name=None,reuse=False):
## parameters
conv_ = []
chan_ = []
if w_init is None:
w_init = tf.contrib.slim.xavier_initializer()
if b_init is None:
b_init = tf.constant_initializer(value=0.0)
for i in range(num_down+1):
chan_.append(start_chan*(2**(i)))
with tf.variable_scope(name,reuse=reuse):
current = input
with tf.variable_scope('contracting_ops',reuse=reuse):
for i in range(num_down):
current = slim.conv2d(current,chan_[i],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,
activation_fn=act,scope='g_conv%d'%(i),padding='SAME',reuse=reuse)
for j in range(num_conv):
current=slim.conv2d(current,chan_[i],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,rate=rate[i], activation_fn=act,padding='SAME',scope='g_conv%d_block_%d'%(i,j),reuse=reuse)
current=slim.conv2d(current,chan_[i],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, activation_fn=act,padding='SAME',scope='g_conv%d_block'%(i),reuse=reuse)
pool=slim.conv2d(current,chan_[i],[fil_s,fil_s], stride=2,
weights_initializer=w_init,biases_initializer=b_init, activation_fn=act,padding='SAME',scope='pool%d'%(i),reuse=reuse)
#pool=slim.max_pool2d(current, [2, 2], padding='SAME',scope='pool%d'%(i))
conv_.append(current)
current = pool
current=slim.conv2d(pad(current,(fil_s-1)/2),chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, activation_fn=act,padding='VALID',scope='g_conv%d'%(num_down),reuse=reuse)
contract_temp = current
##
with tf.variable_scope('local_ops',reuse=reuse):
current = contract_temp
for j in range(num_conv):
current = slim.conv2d(current,chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, rate=rate[num_down],activation_fn=act,padding='SAME',scope='g_conv_block_%d'%(j),reuse=reuse)
current = slim.conv2d(current,chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,activation_fn=act,padding='SAME',scope='g_conv_block',reuse=reuse)
restore_temp = current
multis_list = []
with tf.variable_scope('expanding_ops',reuse=reuse):
current = restore_temp
for i in range(num_down):
index_current = num_down-1-i
current = upsample_and_concat_c( current, conv_[index_current], chan_[index_current], chan_[index_current+1], scope='uac%d'%(i),reuse=reuse )
current = slim.conv2d(current,chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, padding='SAME',activation_fn=act,scope='g_dconv%d'%(i),reuse=reuse)
for j in range(num_conv):
current=slim.conv2d(current, chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,rate=rate[index_current], padding='SAME',activation_fn=act,scope='g_dconv_block%d_%d'%(i,j),reuse=reuse)
current=slim.conv2d(current, chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, padding='SAME',activation_fn=tf.nn.tanh,scope='g_dconv_block%d'%(i),reuse=reuse)
if i is not (num_down-1):
multis_list.append(slim.conv2d(current, num_out,[1,1], weights_initializer=w_init,biases_initializer=b_init, activation_fn=tf.nn.tanh,scope='super%d'%(i),reuse=reuse))
final = slim.conv2d(current, num_out,[1,1], weights_initializer=w_init,biases_initializer=b_init, activation_fn=tf.nn.tanh,scope='final',reuse=reuse)
return final,multis_list
def image_warp(images, flow, name='image_warp'):
with tf.name_scope(name):
shape = tf.shape(images)
batch_size = shape[1]
height = shape[2]
width = shape[3]
frame_s = shape[1]
channels = shape[4]
images = tf.reshape(images,[-1,height,width,channels])
flow = tf.reshape(flow,[-1,height,width,2])
x = tf.linspace(0.0,1.0,width)
y = tf.linspace(0.0,1.0,height)
grid_x, grid_y = tf.meshgrid(x, y)
grid_x, grid_y = tf.cast(grid_x,flow.dtype),tf.cast(grid_y,flow.dtype)
grid_x, grid_y = tf.expand_dims(tf.expand_dims(grid_x,0),3),tf.expand_dims(tf.expand_dims(grid_y,0),3)
grid_y = (grid_y + flow[:,:,:,0:1])*tf.cast(height-1,flow.dtype)
grid_x = (grid_x + flow[:,:,:,1:2])*tf.cast(width-1,flow.dtype)
grid = tf.concat([grid_y, grid_x], 3) # B,H,W,2
coords = tf.reshape(grid,[batch_size, height * width, 2]) # B,H*W,2
coords = tf.stack([tf.minimum(tf.maximum(0.0, coords[:, :, 0]), tf.cast(height, flow.dtype) - 1.0),
tf.minimum(tf.maximum(0.0, coords[:, :, 1]), tf.cast(width, flow.dtype) - 1.0)], axis=2)
floors = tf.cast(tf.floor(coords), tf.int32)
ceils = floors + 1 ## the ceils and floors are not clipped
alphas = tf.cast(coords - tf.cast(floors, flow.dtype), images.dtype)
alphas = tf.reshape(tf.minimum(tf.maximum(0.0, alphas), 1.0), shape=[batch_size, height, width, 1, 2])
images_flattened = tf.reshape(images, [-1, channels])
batch_offsets = tf.expand_dims(tf.range(batch_size) * height * width, axis=1)
def gather(y_coords, x_coords):
linear_coordinates = batch_offsets + y_coords * width + x_coords
gathered_values = tf.gather(images_flattened, linear_coordinates)
return tf.reshape(gathered_values, shape)
top_left = gather(floors[:, :, 0], floors[:, :, 1]) # B,H,W,C
top_right = gather(floors[:, :, 0], ceils[:, :, 1])
bottom_left = gather(ceils[:, :, 0], floors[:, :, 1])
bottom_right = gather(ceils[:, :, 0], ceils[:, :, 1])
interp_top = alphas[:, :, :, :, 1] * (top_right - top_left) + top_left
interp_bottom = alphas[:, :, :, :, 1] * (bottom_right - bottom_left) + bottom_left
interpolated = alphas[:, :, :, :, 0] * (interp_bottom - interp_top) + interp_top
interpolated = tf.reshape(interpolated, [1,frame_s,height,width,channels]) # this should be right
interpolated = tf.transpose(interpolated,[0,2,3,4,1]) # B,H,W,C,F-1
return interpolated
img = tf.transpose(img,[0,4,1,2,3])
shape = tf.shape(img)
B,F,H,W,C = shape[0],shape[1],shape[2],shape[3],shape[4]
with tf.variable_scope('Stage1',reuse=reuse):
current = img
in_imgs_dn,ref_img_dn,other_imgs_dn = pack_fea(current,num_fr=num_fr) #B*(F-1),H,W,C*2, #B,1,H,W,C #B,F-1,H,W,C
in_imgs_dn = tf.clip_by_value(in_imgs_dn,0.0,1.0)
w_init = tf.constant_initializer(0.0)
b_init = tf.constant_initializer(0.0)
rate = [1,2,2,4,4,8]
offsets, offsets_list = U_net2222(in_imgs_dn,num_down=4,num_conv=1,num_out=2,rate=rate,fil_s=3,w_init=None,b_init=None,
start_chan=32,act=lrelu,name='Alignment',reuse=reuse) # B*(F-1),H,W,2
offsets = tf.reshape(offsets,[B,F-1,H,W,2])
other_imgs_dn_suplist = []
for i in range(len(offsets_list)):
current = offsets_list[i] # B*(F-1),?,?,2
current_shape = tf.shape(current)
H_,W_ = current_shape[1],current_shape[2]
current_other_imgs_dn = tf.image.resize_bilinear(tf.reshape(other_imgs_dn,[B*(F-1),H,W,C]),[H_,W_])
current_other_imgs_dn = tf.reshape(current_other_imgs_dn,[B,F-1,H_,W_,C])
other_imgs_dn_suplist.append(current_other_imgs_dn)
offsets_list[i] = tf.reshape(current,[B,F-1,H_,W_,2])
warped_img = image_warp(other_imgs_dn,offsets)
warped_imglist = [image_warp(other_imgs_dn_suplist[i],offsets_list[i]) for i in range(len(offsets_list))]
return warped_img,warped_imglist
def cost_volume(c1, warp, search_range, name,reuse):
with tf.variable_scope(name,reuse=reuse):
padded_lvl = tf.pad(warp, [[0, 0], [search_range, search_range], [search_range, search_range], [0, 0]])
_, h, w, _ = tf.unstack(tf.shape(c1))
max_offset = search_range * 2 + 1
cost_vol = []
for y in range(0, max_offset):
for x in range(0, max_offset):
slice = tf.slice(padded_lvl, [0, y, x, 0], [-1, h, w, -1])
cost = tf.reduce_mean(c1 * slice, axis=3, keepdims=True)
cost_vol.append(cost)
cost_vol = tf.concat(cost_vol, axis=3)
cost_vol = lrelu(cost_vol)
return cost_vol
def image_warp_3D_bil(images, flow, num_fr=5,name='image_warp'):
## Flow: B,H,W,3*(F-1) images: B,H,W,C*(F-1)
with tf.name_scope(name):
shape = tf.shape(images)
batch_size = shape[0]
height = shape[1]
width = shape[2]
images = tf.transpose(tf.reshape(images,[batch_size,height,width,3,num_fr-1]),[0,1,2,4,3]) # B,H,W,F-1,C
flow = tf.reshape(flow,[batch_size,height,width,3,num_fr-1]) # B,H,W,3,F-1
offset_x = flow[:,:,:,0,:] # B,H,W,F-1
offset_y = flow[:,:,:,1,:]
offset_z = flow[:,:,:,2,:]
x = tf.linspace(-1.0,1.0,width)
y = tf.linspace(-1.0,1.0,height)
x,y = tf.meshgrid(x,y)
x,y = tf.reshape(x,[1,height,width,1]),tf.reshape(y,[1,height,width,1])
x_t, y_t = x + offset_x, y + offset_y # B,H,W,F-1
z_t = offset_z # float
max_x,max_y,max_z = width,height,num_fr-1 # int
zero = tf.zeros([],tf.int32) # int
x_t_sc = 0.5*(x_t+1.0)*tf.cast(width-1,tf.float32) #float
y_t_sc = 0.5*(y_t+1.0)*tf.cast(height-1,tf.float32)
z_t_sc = 0.5*(z_t+1.0)*tf.cast(num_fr-2,tf.float32) #float
x0 = tf.cast(tf.floor(x_t_sc),tf.int32) # int
x1 = x0 + 1
y0 = tf.cast(tf.floor(y_t_sc),tf.int32)
y1 = y0 + 1
z0 = tf.cast(tf.floor(z_t_sc),tf.int32)
z1 = z0 + 1
x0,x1 = tf.clip_by_value(x0,zero,max_x),tf.clip_by_value(x1,zero,max_x) #int
y0,y1 = tf.clip_by_value(y0,zero,max_y),tf.clip_by_value(y1,zero,max_y)
z0,z1 = tf.clip_by_value(z0,zero,max_z),tf.clip_by_value(z1,zero,max_z)
def get_pixel_value_3D(img,x,y,z): # img B,H,W,F-1,C
shape = tf.shape(x) # x,y,z: B,H,W,F-1
batch = shape[0]
hei,wid,fr = shape[1],shape[2],shape[3]
batch_idx = tf.range(0,batch)
batch_idx = tf.reshape(batch_idx,[batch,1,1,1])
b = tf.tile(batch_idx,[1,hei,wid,fr]) # b: B,H,W,F-1
indices = tf.stack([b,y,x,z],4)
return tf.gather_nd(img,indices) # B,H,W,F-1,C
paddings = tf.constant([[0,0],[0,1],[0,1],[0,1],[0,0]])
I000 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x0,y0,z0) # float
I001 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x0,y0,z1)
I010 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x0,y1,z0)
I011 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x0,y1,z1) # B,H,W,C
I100 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x1,y0,z0) # B,H,W,C
I101 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x1,y0,z1) # B,H,W,C
I110 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x1,y1,z0) # B,H,W,C
I111 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x1,y1,z1) # B,H,W,C
x0,y0,z0 = tf.cast(x0,tf.float32),tf.cast(y0,tf.float32),tf.cast(z0,tf.float32)
x1,y1,z1 = tf.cast(x1,tf.float32),tf.cast(y1,tf.float32),tf.cast(z1,tf.float32)
w000 = tf.maximum(1.0-tf.abs(x0-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y0-y_t_sc),0.0)* \
tf.maximum(1.0-tf.abs(z0-z_t_sc),0.0)
w001 = tf.maximum(1.0-tf.abs(x0-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y0-y_t_sc),0.0)* \
tf.maximum(1.0-tf.abs(z1-z_t_sc),0.0)
w010 = tf.maximum(1.0-tf.abs(x0-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y1-y_t_sc),0.0)* \
tf.maximum(1.0-tf.abs(z0-z_t_sc),0.0)
w011 = tf.maximum(1.0-tf.abs(x0-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y1-y_t_sc),0.0)* \
tf.maximum(1.0-tf.abs(z1-z_t_sc),0.0)
w100 = tf.maximum(1.0-tf.abs(x1-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y0-y_t_sc),0.0)* \
tf.maximum(1.0-tf.abs(z0-z_t_sc),0.0)
w101 = tf.maximum(1.0-tf.abs(x1-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y0-y_t_sc),0.0)* \
tf.maximum(1.0-tf.abs(z1-z_t_sc),0.0)
w110 = tf.maximum(1.0-tf.abs(x1-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y1-y_t_sc),0.0)* \
tf.maximum(1.0-tf.abs(z0-z_t_sc),0.0)
w111 = tf.maximum(1.0-tf.abs(x1-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y1-y_t_sc),0.0)* \
tf.maximum(1.0-tf.abs(z1-z_t_sc),0.0)
w000,w001,w010,w011 = tf.expand_dims(w000,4),tf.expand_dims(w001,4),tf.expand_dims(w010,4),tf.expand_dims(w011,4)
w100,w101,w110,w111 = tf.expand_dims(w100,4),tf.expand_dims(w101,4),tf.expand_dims(w110,4),tf.expand_dims(w111,4)
aligned_img = tf.add_n([w000*I000,w001*I001,w010*I010,w011*I011,w100*I100,w101*I101,w110*I110,w111*I111]) #B,H,W,F-1,C
aligned_img = tf.transpose(aligned_img,[0,1,2,4,3]) #B,H,W,C,F-1
aligned_img = tf.reshape(aligned_img,[batch_size,height,width,3*(num_fr-1)])
return aligned_img #B,H,W,C*(F-1)
def U_Net_align_spy_3D(img,num_fr=5,num_down=4,reuse = False): # img:B,H,W,C,F noise:B,H,W,1
def pack_fea(x,num_fr=5): #B,F,H,W,C
shape = tf.shape(x)
B,H,W,C,F = shape[0],shape[1],shape[2],shape[3],shape[4]
center = int((num_fr+1)/2)
ref_img = x[:,:,:,:,center-1] #B,H,W,C
inds = np.concatenate([np.arange(0,center-1),np.arange(center,num_fr)],0)
others_list = [x[:,:,:,:,i] for i in inds]
other_imgs = tf.stack(others_list,4) ## B,H,W,C,F-1
other_imgs = tf.reshape(other_imgs,[B,H,W,C*(F-1)]) ## B,H,W,(C*F-1)
in_imgs = tf.concat([x[:,:,:,:,i] for i in range(num_fr)],3)
return in_imgs,ref_img,other_imgs
# in_imgs: B,H,W,C*F ref_img: B,H,W,C other_imgs: B,H,W,(C*F-1)
def image_warp_3D(images, flow, name='image_warp'):
## Flow: B,H,W,3*(F-1) images: B,H,W,C*(F-1)
with tf.name_scope(name):
shape = tf.shape(images)
batch_size = shape[0]
height = shape[1]
width = shape[2]
images = tf.transpose(tf.reshape(images,[batch_size,height,width,3,num_fr-1]),[0,1,2,4,3]) # B,H,W,F-1,C
flow = tf.reshape(flow,[batch_size,height,width,3,num_fr-1]) # B,H,W,3,F-1
offset_x = flow[:,:,:,0,:] # B,H,W,F-1
offset_y = flow[:,:,:,1,:]
offset_z = flow[:,:,:,2,:]
x = tf.linspace(-1.0,1.0,width)
y = tf.linspace(-1.0,1.0,height)
x,y = tf.meshgrid(x,y)
x,y = tf.reshape(x,[1,height,width,1]),tf.reshape(y,[1,height,width,1])
x_t, y_t = x + offset_x, y + offset_y # B,H,W,F-1
z_t = offset_z # float
max_x,max_y,max_z = width,height,num_fr-2 # int
zero = tf.zeros([],tf.int32) # int
x_t_sc = 0.5*(x_t+1.0)*tf.cast(width-1,tf.float32) #float
y_t_sc = 0.5*(y_t+1.0)*tf.cast(height-1,tf.float32)
z_t_sc = 0.5*(z_t+1.0)*tf.cast(num_fr-2,tf.float32) #float
x0 = tf.cast(tf.floor(x_t_sc),tf.int32) # int
x1 = x0 + 1
y0 = tf.cast(tf.floor(y_t_sc),tf.int32)
y1 = y0 + 1
z0 = tf.cast(tf.round(z_t_sc),tf.int32)
x0,x1 = tf.clip_by_value(x0,zero,max_x),tf.clip_by_value(x1,zero,max_x) #int
y0,y1 = tf.clip_by_value(y0,zero,max_y),tf.clip_by_value(y1,zero,max_y)
z0 = tf.clip_by_value(z0,zero,max_z)
def get_pixel_value_3D(img,x,y,z): # img B,H,W,F-1,C
shape = tf.shape(x) # x,y,z: B,H,W,F-1
batch = shape[0]
hei,wid,fr = shape[1],shape[2],shape[3]
batch_idx = tf.range(0,batch)
batch_idx = tf.reshape(batch_idx,[batch,1,1,1])
b = tf.tile(batch_idx,[1,hei,wid,fr]) # b: B,H,W,F-1
indices = tf.stack([b,y,x,z],4)
return tf.gather_nd(img,indices) # B,H,W,F-1,C
paddings = tf.constant([[0,0],[0,1],[0,1],[0,0],[0,0]])
I00 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x0,y0,z0) # float
I01 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x0,y1,z0)
I10 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x1,y0,z0)
I11 = get_pixel_value_3D(tf.pad(images,paddings,"SYMMETRIC"),x1,y1,z0) # B,H,W,C
x0,y0,z0 = tf.cast(x0,tf.float32),tf.cast(y0,tf.float32),tf.cast(z0,tf.float32)
x1,y1 = tf.cast(x1,tf.float32),tf.cast(y1,tf.float32)
w00 = tf.maximum(1.0-tf.abs(x0-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y0-y_t_sc),0.0)
w01 = tf.maximum(1.0-tf.abs(x0-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y1-y_t_sc),0.0)
w10 = tf.maximum(1.0-tf.abs(x1-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y0-y_t_sc),0.0)
w11 = tf.maximum(1.0-tf.abs(x1-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(y1-y_t_sc),0.0)
w00,w01,w10,w11 = tf.expand_dims(w00,4),tf.expand_dims(w01,4),tf.expand_dims(w10,4),tf.expand_dims(w11,4)
aligned_img = tf.add_n([w00*I00,w01*I01,w10*I10,w11*I11]) #B,H,W,F-1,C
aligned_img = tf.transpose(aligned_img,[0,1,2,4,3]) #B,H,W,C,F-1
aligned_img = tf.reshape(aligned_img,[batch_size,height,width,3*(num_fr-1)])
return aligned_img #B,H,W,C*(F-1)
def U_net2222(inputlist,other_list,ref_img_list,num_down=4,num_conv=1,num_out=3,rate=[1]*10,fil_s=3,w_init=None,b_init=None,start_chan=32,act=lrelu,name=None,reuse=False):
## parameters
# inputlist: B,H,W,C*F other_list: B,H,W,C*(F-1) ref_img_list: B,H,W,C
chan_ = []
if w_init is None:
w_init = tf.contrib.slim.xavier_initializer()
if b_init is None:
b_init = tf.constant_initializer(value=0.0)
for i in range(num_down+1):
chan_.append(start_chan*(2**(i)))
##
warping_func = image_warp_3D
multis_list = []
temporal_list = []
with tf.variable_scope('local_ops',reuse=reuse):
current = inputlist[num_down]
for j in range(num_conv):
current = slim.conv2d(current,chan_[num_down],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, rate=1,activation_fn=act,padding='SAME',scope='g_conv_block_%d'%(j),reuse=reuse)
fine_flow = slim.conv2d(current,3*(num_fr-1),[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,activation_fn=tf.nn.tanh,padding='SAME',scope='g_conv_block',reuse=reuse)
# B,H,W,F-1
temporal_list.append(tf.reshape(fine_flow,[fine_flow.shape[0],fine_flow.shape[1],fine_flow.shape[2],3,num_fr-1]))
other_imgs = other_list[num_down]
'''
shape_cur = tf.shape(fine_flow)
B_c,H_c,W_c = shape_cur[0],shape_cur[1],shape_cur[2]
fine_flow0 = tf.zeros_like(fine_flow[:,:,:,0:num_fr-1],dtype=tf.float32)
fine_flow1 = tf.zeros_like(fine_flow[:,:,:,0:num_fr-1],dtype=tf.float32)
fine_flow2 = tf.ones_like(fine_flow[:,:,:,0:num_fr-1],dtype=tf.float32)*tf.reshape(tf.constant([-1.0,-0.8,0.8,1.0]),[1,1,1,4])
fine_flow = tf.stack([fine_flow0,fine_flow1,fine_flow2],3)
fine_flow = tf.reshape(fine_flow,[B_c,H_c,W_c,-1])
'''
multis_list.append(warping_func(other_imgs,fine_flow,name='fine_wapring%d'%(num_down)))
restore_temp = fine_flow
with tf.variable_scope('expanding_ops',reuse=reuse):
init_flow = restore_temp
for i in range(num_down):
index_current = num_down-1-i
other_imgs,ref_img = other_list[index_current],ref_img_list[index_current]
up_flow = slim.conv2d_transpose(init_flow,3*(num_fr-1),3,(2,2),padding='SAME',scope='up%d'%(i),reuse=reuse)
other_img_warped = image_warp_3D_bil(other_imgs,up_flow,name='init_wapring%d'%(i))
fea = tf.concat([other_img_warped,ref_img,up_flow],3)
#current = upsample_and_concat_c( current, conv_[index_current], chan_[index_current], chan_[index_current+1], scope='uac%d'%(i),reuse=reuse )
current = slim.conv2d(fea,chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, padding='SAME',activation_fn=act,scope='g_dconv%d'%(i),reuse=reuse)
for j in range(num_conv):
current=slim.conv2d(current, chan_[index_current],[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init,rate=1, padding='SAME',activation_fn=act,scope='g_dconv_block%d_%d'%(i,j),reuse=reuse)
fine_flow = up_flow + slim.conv2d(current,3*(num_fr-1),[fil_s,fil_s],
weights_initializer=w_init,biases_initializer=b_init, padding='SAME',activation_fn=tf.nn.tanh,scope='g_dconv_block%d'%(i),reuse=reuse)
temporal_list.append(tf.reshape(fine_flow,[fine_flow.shape[0],fine_flow.shape[1],fine_flow.shape[2],3,num_fr-1]))
multis_list.append(warping_func(other_imgs,fine_flow,name='fine_wapring%d'%(i)))
init_flow = fine_flow
return multis_list,temporal_list
shape = tf.shape(img)
B,H,W,C,F = shape[0],shape[1],shape[2],shape[3],shape[4]
with tf.variable_scope('Stage1',reuse=reuse):
current = img
in_imgs,ref_img,other_imgs = pack_fea(current,num_fr=num_fr) #B*(F-1),H,W,C*2, #B,1,H,W,C #B,F-1,H,W,C
in_imgs = tf.clip_by_value(in_imgs,0.0,1.0)
inlist = []
ref_img_list = []
other_list = []
for i in range(num_down+1):
size = [tf.cast(H/(2**i),tf.int32),tf.cast(W/(2**i),tf.int32)]
inlist.append(tf.image.resize_bilinear(in_imgs,size))
other_list.append(tf.image.resize_bilinear(other_imgs,size))
ref_img_list.append(tf.image.resize_bilinear(ref_img,size))
warped_imgs_list,temporal_list = U_net2222(inlist,other_list,ref_img_list,num_down=num_down,num_conv=6,num_out=2,fil_s=5,w_init=None,b_init=None,
start_chan=32,act=lrelu,name='Alignment',reuse=reuse) # B*(F-1),H,W,2
for i in range(len(warped_imgs_list)):
current = warped_imgs_list[i]
shape = tf.shape(current)
H_c,W_c,C_c = shape[1],shape[2],shape[3]
warped_imgs_list[i] = tf.reshape(current,[B,H_c,W_c,3,F-1])
warped_imgs_list.reverse()
temporal_list.reverse()
return warped_imgs_list,temporal_list
'''
img = tf.zeros(shape=[1,512,512,3,7])
out = EDVR(img,fra_s=7,num_fea=32,reuse = False)
'''
'''
img = tf.zeros(shape=[1,512,512,3,7])
noise = tf.zeros(shape=[1,512,512,1])
out = LiangNN(img,noise,num_fr=7,reuse = False)
img = tf.ones(shape=[1,512,512,3*7])
w_init = tf.constant_initializer(0.0)
b_init = tf.constant_initializer(0.0)
offsets = U_net22(img,num_down=4,num_block=1,num_conv=1,num_out=3,rate=[1]*10,fil_s=3,w_init=w_init,b_init=b_init,is_residual=False,
start_chan=32,act=lrelu,is_global=True,name='Alignment',reuse=False) # B,H,W,3
out = tf.reduce_mean(offsets)
sess = tf.Session()
sess.run(tf.global_variables_initializer())
out_ = sess.run(out)
print(out_)
'''
def STTN(img,noise,num_fr=5,reuse = False): # img:B,H,W,C,F noise:B,H,W,1
shape = tf.shape(img)
B,H,W,C,F = shape[0],shape[1],shape[2],shape[3],shape[4]
img_in = tf.reshape(img,[B,H,W,C*F]) #B,H,W,C*F
### Alignment
with tf.variable_scope('STTN',reuse=reuse):
current = img_in
current = (tf.clip_by_value(current,0.0,1.0)+1e-4)**(1.0/2.2)
w_init = None#tf.constant_initializer(0.0)
b_init = None#tf.constant_initializer(0.0)
offsets = U_net22(current,num_down=4,num_block=1,num_conv=1,num_out=3,rate=[1]*10,fil_s=3,w_init=w_init,b_init=b_init,is_residual=False,
start_chan=32,act=lrelu,is_global=True,name='Alignment',reuse=reuse) # B,H,W,3
img_to_align = tf.transpose(img,[0,1,2,4,3]) # img:B,H,W,F,C
offset_x = offsets[:,:,:,0] # B,H,W
offset_y = offsets[:,:,:,1]
offset_z = offsets[:,:,:,2]
x = tf.linspace(-1.0,1.0,W)
y = tf.linspace(-1.0,1.0,H)
x,y = tf.meshgrid(x,y)
x,y = tf.reshape(x,[-1,H,W]),tf.reshape(y,[-1,H,W])
x_t, y_t = x + offset_x, y + offset_y
z_t = offset_z
max_x,max_y,max_z = W-1,H-1,F-1 # int
zero = tf.zeros([],tf.int32) # int
x_t_sc = 0.5*(x_t+1.0)*tf.cast(max_x,tf.float32) #float
y_t_sc = 0.5*(y_t+1.0)*tf.cast(max_y,tf.float32)
z_t_sc = 0.5*(z_t+1.0)*tf.cast(max_z,tf.float32) #float
x0 = tf.cast(tf.floor(x_t_sc),tf.int32) # int
x1 = x0 + 1
y0 = tf.cast(tf.floor(y_t_sc),tf.int32)
y1 = y0 + 1
z0 = tf.cast(tf.floor(z_t_sc),tf.int32)
z1 = z0 + 1
x0,x1 = tf.clip_by_value(x0,zero,max_x),tf.clip_by_value(x1,zero,max_x) #int
y0,y1 = tf.clip_by_value(y0,zero,max_y),tf.clip_by_value(y1,zero,max_y)
z0,z1 = tf.clip_by_value(z0,zero,max_z),tf.clip_by_value(z1,zero,max_z)
I000 = get_pixel_value_3D(img_to_align,x0,y0,z0) # float
I001 = get_pixel_value_3D(img_to_align,x0,y0,z1)
I010 = get_pixel_value_3D(img_to_align,x0,y1,z0)
I011 = get_pixel_value_3D(img_to_align,x0,y1,z1) # B,H,W,C
I100 = get_pixel_value_3D(img_to_align,x1,y0,z0) # B,H,W,C
I101 = get_pixel_value_3D(img_to_align,x1,y0,z1) # B,H,W,C
I110 = get_pixel_value_3D(img_to_align,x1,y1,z0) # B,H,W,C
I111 = get_pixel_value_3D(img_to_align,x1,y1,z1) # B,H,W,C
w000 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w001 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w010 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w011 = tf.maximum(1.0-tf.abs(tf.cast(x0,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w100 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w101 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y0,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w110 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z0,tf.float32)-z_t_sc),0.0)
w111 = tf.maximum(1.0-tf.abs(tf.cast(x1,tf.float32)-x_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(y1,tf.float32)-y_t_sc),0.0)*tf.maximum(1.0-tf.abs(tf.cast(z1,tf.float32)-z_t_sc),0.0)
w000,w001,w010,w011 = tf.expand_dims(w000,3),tf.expand_dims(w001,3),tf.expand_dims(w010,3),tf.expand_dims(w011,3)
w100,w101,w110,w111 = tf.expand_dims(w100,3),tf.expand_dims(w101,3),tf.expand_dims(w110,3),tf.expand_dims(w111,3)
aligned_img = tf.add_n([w000*I000,w001*I001,w010*I010,w011*I011,w100*I100,w101*I101,w110*I110,w111*I111])
### Fusion
with tf.variable_scope('ImageProcessing',reuse=reuse):
current = tf.concat([aligned_img,noise],3)
out_final = U_net22(current,num_down=4,num_block=1,num_conv=1,num_out=3,rate=[1]*10,fil_s=3,w_init=None,b_init=None,is_residual=False,
start_chan=32,act=lrelu,is_global=True,name='IP',reuse=reuse) # B,H,W,3
return aligned_img,out_final
|
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|
import numpy as np
import torch
import argparse
import os
import gym
gym.logger.set_level(40)
import time
import json
import dmc2gym
import utils
from logger import Logger
from video import VideoRecorder
from dynode import DyNODESacAgent
def parse_args():
parser = argparse.ArgumentParser()
# environment
parser.add_argument('--domain_name', default='cartpole')
parser.add_argument('--task_name', default='swingup')
# replay buffer
parser.add_argument('--replay_buffer_capacity', default=100000, type=int)
# train
parser.add_argument('--agent', default='DyNODE-SAC', type=str)
parser.add_argument('--init_steps', default=1000, type=int)
parser.add_argument('--num_train_steps', default=100001, type=int)
parser.add_argument('--batch_size', default=128, type=int)
parser.add_argument('--hidden_dim', default=256, type=int)
# eval
parser.add_argument('--eval_freq', default=5000, type=int)
parser.add_argument('--num_eval_episodes', default=10, type=int)
# critic
parser.add_argument('--critic_lr', default=1e-3, type=float)
parser.add_argument('--critic_beta', default=0.9, type=float)
parser.add_argument('--critic_tau', default=0.01, type=float)
parser.add_argument('--critic_target_update_freq', default=1, type=int)
# actor
parser.add_argument('--actor_lr', default=1e-3, type=float)
parser.add_argument('--actor_beta', default=0.9, type=float)
parser.add_argument('--actor_log_std_min', default=-10, type=float)
parser.add_argument('--actor_log_std_max', default=2, type=float)
# model
parser.add_argument('--model_lr', default=1e-3, type=float)
parser.add_argument('--kind', default='D', type=str, help= "options D or P") # Deterministic or Probalilistic
parser.add_argument('--model_num_updates', default=1, type=int)
parser.add_argument('--model_warm_up', default=1000, type=int)
parser.add_argument('--k_step', default=10, type=int)
# sac
parser.add_argument('--discount', default=0.99, type=float)
parser.add_argument('--init_temperature', default=0.1, type=float)
parser.add_argument('--alpha_lr', default=1e-4, type=float)
parser.add_argument('--alpha_beta', default=0.5, type=float)
# misc
parser.add_argument('--seed', default=-1, type=int)
parser.add_argument('--work_dir', default='./logdir', type=str)
parser.add_argument('--save_tb', default=False, action='store_true')
parser.add_argument('--save_video', default=True, action='store_true')
parser.add_argument('--save_model', default=False, action='store_true')
parser.add_argument('--log_interval', default=100, type=int)
args = parser.parse_args()
return args
def evaluate(env, agent, video, num_episodes, L, step, args):
all_ep_rewards = []
def run_eval_loop(sample_stochastically=True):
start_time = time.time()
prefix = 'stochastic_' if sample_stochastically else ''
for i in range(num_episodes):
obs = env.reset()
video.init(enabled=(i == 0))
done = False
episode_reward = 0
while not done:
with utils.eval_mode(agent):
if sample_stochastically:
action = agent.sample_action(obs)
else:
action = agent.select_action(obs)
obs, reward, done, _ = env.step(action)
video.record(env)
episode_reward += reward
video.save('%d.mp4' % step)
L.log('eval/' + prefix + 'episode_reward', episode_reward, step)
all_ep_rewards.append(episode_reward)
L.log('eval/' + prefix + 'eval_time', time.time()-start_time , step)
mean_ep_reward = np.mean(all_ep_rewards)
best_ep_reward = np.max(all_ep_rewards)
L.log('eval/' + prefix + 'mean_episode_reward', mean_ep_reward, step)
L.log('eval/' + prefix + 'best_episode_reward', best_ep_reward, step)
run_eval_loop(sample_stochastically=False)
L.dump(step)
def main():
args = parse_args()
if args.seed == -1:
args.__dict__["seed"] = np.random.randint(1,1000000)
utils.set_seed_everywhere(args.seed)
env = dmc2gym.make(domain_name=args.domain_name, task_name=args.task_name, seed=args.seed)
env.seed(args.seed)
method = args.agent + " (H="+ str(args.k_step) +")"
model_kind = "dynode_model" if args.agent == "DyNODE-SAC" else "nn_model"
# make directory
env_name = args.domain_name + '-' + args.task_name
args.work_dir = args.work_dir + '/' + env_name + '/' + method + '/' + str(args.seed)
utils.make_dir(args.work_dir)
video_dir = utils.make_dir(os.path.join(args.work_dir, 'video'))
model_dir = utils.make_dir(os.path.join(args.work_dir, 'model'))
video = VideoRecorder(video_dir if args.save_video else None)
with open(os.path.join(args.work_dir, 'args.json'), 'w+') as f:
json.dump(vars(args), f, sort_keys=True, indent=4)
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
action_shape = env.action_space.shape
obs_shape = env.observation_space.shape
replay_buffer = utils.ReplayBuffer(obs_shape=obs_shape, action_shape=action_shape,
capacity=args.replay_buffer_capacity, batch_size=args.batch_size, device=device)
agent = DyNODESacAgent(obs_shape=obs_shape, action_shape=action_shape, device=device, model_kind = model_kind,
kind=args.kind, step_MVE = args.k_step, hidden_dim=args.hidden_dim, discount=args.discount,
init_temperature=args.init_temperature, alpha_lr=args.alpha_lr,
alpha_beta=args.alpha_beta, actor_lr=args.actor_lr, actor_beta=args.actor_beta,
actor_log_std_min=args.actor_log_std_min, actor_log_std_max=args.actor_log_std_max,
critic_lr=args.critic_lr, critic_beta=args.critic_beta,
critic_tau=args.critic_tau, critic_target_update_freq=args.critic_target_update_freq,
model_lr=args.model_lr, log_interval=args.log_interval)
L = Logger(args.work_dir, use_tb=args.save_tb)
episode, episode_reward, done = 0, 0, True
start_time = time.time()
for step in range(args.num_train_steps):
# evaluate agent periodically
if step % args.eval_freq == 0:
L.log('eval/episode', episode, step)
evaluate(env, agent, video, args.num_eval_episodes, L, step, args)
if args.save_model:
agent.save_model(model_dir, step)
if done:
if step > 0:
if step % args.log_interval == 0:
L.log('train/duration', time.time() - start_time, step)
L.dump(step)
start_time = time.time()
if step % args.log_interval == 0:
L.log('train/episode_reward', episode_reward, step)
obs = env.reset()
done = False
episode_reward = 0
episode_step = 0
episode += 1
if step % args.log_interval == 0:
L.log('train/episode', episode, step)
# sample action for data collection
if step < args.init_steps:
action = env.action_space.sample()
else:
with utils.eval_mode(agent):
action = agent.sample_action(obs)
if step >= args.model_warm_up:
for _ in range(args.model_num_updates):
agent.update_model(replay_buffer, L, step)
# run training update
if step >= args.init_steps:
for _ in range(2):
agent.update(replay_buffer, L, step)
next_obs, reward, done, _ = env.step(action)
# allow infinit bootstrap
done_bool = 0 if episode_step + 1 == env._max_episode_steps else float(done)
episode_reward += reward
replay_buffer.add(obs, action, reward, next_obs, done_bool, done)
obs = next_obs
episode_step += 1
if __name__ == '__main__':
torch.multiprocessing.set_start_method('spawn')
main()
|
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|
//
// Copyright Markus Rickert 2008
//
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//
#include <algorithm>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/bindings/blas/blas.hpp>
#include <boost/numeric/bindings/traits/ublas_matrix.hpp>
#include <boost/numeric/bindings/traits/ublas_vector.hpp>
#include <boost/numeric/bindings/traits/ublas_vector2.hpp>
int
main(int argc, char** argv)
{
// a * b' = C ; a' * b = d
{
boost::numeric::ublas::vector<double> a(3);
for (std::size_t i = 0; i < a.size(); ++i) a(i) = i;
std::cout << "a=" << a << std::endl;
boost::numeric::ublas::vector<double> b(3);
for (std::size_t i = 0; i < b.size(); ++i) b(i) = i;
std::cout << "b=" << b << std::endl;
boost::numeric::ublas::matrix<double, boost::numeric::ublas::column_major> c(3, 3);
boost::numeric::bindings::blas::gemm(
boost::numeric::bindings::traits::NO_TRANSPOSE,
boost::numeric::bindings::traits::TRANSPOSE,
1.0, a, b, 0.0, c
);
std::cout << "C=" << c << std::endl;
boost::numeric::ublas::vector<double> d(1);
boost::numeric::bindings::blas::gemm(
boost::numeric::bindings::traits::TRANSPOSE,
boost::numeric::bindings::traits::NO_TRANSPOSE,
1.0, a, b, 0.0, d
);
std::cout << "d=" << d << std::endl;
}
std::cout << std::endl;
// a * b' = C ; a' * b = d
{
boost::numeric::ublas::bounded_vector<double, 3> a;
for (std::size_t i = 0; i < a.size(); ++i) a(i) = i;
std::cout << "a=" << a << std::endl;
boost::numeric::ublas::bounded_vector<double, 3> b;
for (std::size_t i = 0; i < b.size(); ++i) b(i) = i;
std::cout << "b=" << b << std::endl;
boost::numeric::ublas::bounded_matrix<double, 3, 3, boost::numeric::ublas::column_major> c;
boost::numeric::bindings::blas::gemm(
boost::numeric::bindings::traits::NO_TRANSPOSE,
boost::numeric::bindings::traits::TRANSPOSE,
1.0, a, b, 0.0, c
);
std::cout << "C=" << c << std::endl;
boost::numeric::ublas::bounded_vector<double, 1> d;
boost::numeric::bindings::blas::gemm(
boost::numeric::bindings::traits::TRANSPOSE,
boost::numeric::bindings::traits::NO_TRANSPOSE,
1.0, a, b, 0.0, d
);
std::cout << "d=" << d << std::endl;
}
std::cout << std::endl;
// A * B = C
{
boost::numeric::ublas::bounded_matrix<double, 4, 3, boost::numeric::ublas::column_major> a;
for (std::size_t i = 0; i < a.size1(); ++i) for (std::size_t j = 0; j < a.size2(); ++j) a(i, j) = i * a.size2() + j;
std::cout << "A=" << a << std::endl;
boost::numeric::ublas::bounded_matrix<double, 3, 4, boost::numeric::ublas::column_major> b;
for (std::size_t i = 0; i < b.size1(); ++i) for (std::size_t j = 0; j < b.size2(); ++j) b(i, j) = i * b.size2() + j;
std::cout << "B=" << b << std::endl;
boost::numeric::ublas::bounded_matrix<double, 4, 4, boost::numeric::ublas::column_major> c;
boost::numeric::bindings::blas::gemm(a, b, c);
std::cout << "C=" << c << std::endl;
}
std::cout << std::endl;
// A[0:3;0:2] * B[0:2;0:3] = C
{
boost::numeric::ublas::bounded_matrix<double, 4, 3, boost::numeric::ublas::column_major> a;
for (std::size_t i = 0; i < a.size1(); ++i) for (std::size_t j = 0; j < a.size2(); ++j) a(i, j) = i * a.size2() + j;
std::cout << "A=" << a << std::endl;
boost::numeric::ublas::matrix_range<
boost::numeric::ublas::bounded_matrix<double, 4, 3, boost::numeric::ublas::column_major>
> a2 = boost::numeric::ublas::subrange(a, 0, 3, 0, 2);
std::cout << "A2=" << a2 << std::endl;
boost::numeric::ublas::bounded_matrix<double, 3, 4, boost::numeric::ublas::column_major> b;
for (std::size_t i = 0; i < b.size1(); ++i) for (std::size_t j = 0; j < b.size2(); ++j) b(i, j) = i * b.size2() + j;
std::cout << "B=" << b << std::endl;
boost::numeric::ublas::matrix_range<
boost::numeric::ublas::bounded_matrix<double, 3, 4, boost::numeric::ublas::column_major>
> b2 = boost::numeric::ublas::subrange(b, 0, 2, 0, 3);
std::cout << "B2=" << b2 << std::endl;
boost::numeric::ublas::bounded_matrix<double, 4, 4, boost::numeric::ublas::column_major> c;
std::fill(c.data().begin(), c.data().end(), 0.0);
boost::numeric::ublas::matrix_range<
boost::numeric::ublas::bounded_matrix<double, 4, 4, boost::numeric::ublas::column_major>
> c2 = boost::numeric::ublas::subrange(c, 0, 3, 0, 3);
boost::numeric::bindings::blas::gemm(a2, b2, c2);
std::cout << "C2=" << c2 << std::endl;
std::cout << "C=" << c << std::endl;
}
std::cout << std::endl;
// a + b = b ; b - a = b
{
boost::numeric::ublas::bounded_vector<double, 3> a;
for (std::size_t i = 0; i < a.size(); ++i) a(i) = i;
std::cout << "a=" << a << std::endl;
boost::numeric::ublas::bounded_vector<double, 3> b;
for (std::size_t i = 0; i < b.size(); ++i) b(i) = i;
std::cout << "b=" << b << std::endl;
boost::numeric::bindings::blas::axpy(1.0, a, b);
std::cout << "b=" << b << std::endl;
boost::numeric::bindings::blas::axpy(-1.0, a, b);
std::cout << "b=" << b << std::endl;
}
std::cout << std::endl;
// b + c = c ; c - b = c
{
boost::numeric::ublas::matrix<double, boost::numeric::ublas::column_major> a(5, 5);
for (std::size_t i = 0; i < a.size1(); ++i) for (std::size_t j = 0; j < a.size2(); ++j) a(i, j) = i * a.size2() + j;
std::cout << "A=" << a << std::endl;
boost::numeric::ublas::matrix_vector_range<
boost::numeric::ublas::matrix<double, boost::numeric::ublas::column_major>
> b(a, boost::numeric::ublas::range(1, 4), boost::numeric::ublas::range(0, 3));
std::cout << "b=" << b << std::endl;
boost::numeric::ublas::matrix_vector_slice<
boost::numeric::ublas::matrix<double, boost::numeric::ublas::column_major>
> c(a, boost::numeric::ublas::slice(0, 1, 3), boost::numeric::ublas::slice(3, 0, 3));
std::cout << "c=" << c << std::endl;
boost::numeric::bindings::blas::axpy(1.0, b, c);
std::cout << "c=" << c << std::endl;
boost::numeric::bindings::blas::axpy(-1.0, b, c);
std::cout << "c=" << c << std::endl;
}
std::cout << std::endl;
// b + c = c ; c - b = c
{
boost::numeric::ublas::bounded_matrix<double, 5, 5, boost::numeric::ublas::column_major> a;
for (std::size_t i = 0; i < a.size1(); ++i) for (std::size_t j = 0; j < a.size2(); ++j) a(i, j) = i * a.size2() + j;
std::cout << "A=" << a << std::endl;
boost::numeric::ublas::matrix_vector_range<
boost::numeric::ublas::bounded_matrix<double, 5, 5, boost::numeric::ublas::column_major>
> b(a, boost::numeric::ublas::range(1, 4), boost::numeric::ublas::range(0, 3));
std::cout << "b=" << b << std::endl;
boost::numeric::ublas::matrix_vector_slice<
boost::numeric::ublas::bounded_matrix<double, 5, 5, boost::numeric::ublas::column_major>
> c(a, boost::numeric::ublas::slice(0, 1, 3), boost::numeric::ublas::slice(3, 0, 3));
std::cout << "c=" << c << std::endl;
boost::numeric::bindings::blas::axpy(1.0, b, c);
std::cout << "c=" << c << std::endl;
boost::numeric::bindings::blas::axpy(-1.0, b, c);
std::cout << "c=" << c << std::endl;
}
return 0;
}
|
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|
import matplotlib.pyplot as plt
from envs.gridworld import AGENT_SIZES, RGB_COLORS
import numpy as np
import os
from envs.key_door import *
from envs.gridworld import *
from utils.gen_utils import *
from model import get_discrete_representation
from torchvision.utils import save_image
def visualize_representations(env, model):
# 1. visualize clustering if number of agents is 1 or 2
# 2. visualize factorization with histogram
# 3. visualize hamming distance graphs
figs = None
if env.name == 'gridworld':
if env.n_agents == 1:
figs = visualize_clusters_online_single(env, model)
elif env.n_agents == 2:
figs = visualize_clusters_online_double(env, model)
if env.name == 'key-wall' or env.name == 'key-corridor':
figs = visualize_single_agent_and_key(env, model)
return figs
def visualize_clusters_online_single(env, model):
assert env.n_agents == 1
num_factors = model.num_onehots
rows = np.arange(0, env.grid_n, env.grid_n//16)
cols = np.arange(0, env.grid_n, env.grid_n//16)
cluster_map = []
for c in cols:
batch_pos = np.transpose(np.stack((np.repeat(c, len(rows)), rows)), (1,0))
im_torch = np_to_var(position_to_image(batch_pos, env.n_agents, env.grid_n)).permute(0,3,1,2)
zs = model.encode(im_torch, vis=True).cpu().numpy()
z_labels = np.sum(np.array([zs[:, i] * model.z_dim ** (num_factors - i - 1) for i in range(num_factors)]),
axis=0, dtype=int)
cluster_map.append(z_labels)
cluster_map = np.array(cluster_map)
print("cluster map")
print(cluster_map)
fig = plt.figure()
plt.imshow(cluster_map, cmap = 'gist_rainbow')
return fig
def visualize_clusters_online_double_fix_one_agent(model, n_agents, grid_n, fixed_agent=0):
fig = plt.figure()
rows = np.arange(0, grid_n, grid_n // 16)
cols = np.arange(0, grid_n, grid_n // 16)
fixed_poses = np.arange(0, grid_n, grid_n // 4)
n_subplots = 4
plot_idx = 1
num_factors = model.num_onehots
onehots_0 = []
onehots_1 = []
for idx, fixed_row in enumerate(fixed_poses):
for fixed_col in fixed_poses:
fixed_pos = np.tile(np.array((fixed_row, fixed_col)), (len(cols), 1))
cluster_map = []
oh0_map = []
oh1_map = []
for c in cols:
batch_pos = np.transpose(np.stack((np.repeat(c, len(rows)), rows)), (1, 0))
batch_pos = np.hstack((batch_pos, fixed_pos)) if fixed_agent == 0 else np.hstack((fixed_pos, batch_pos))
im_torch = np_to_var(position_to_image(batch_pos, n_agents, grid_n)).permute(0, 3, 1, 2)
zs = model.encode(im_torch, vis=True).cpu().numpy()
oh0_map.append(zs[:,0])
oh1_map.append(zs[:,1])
z_labels = np.sum(
np.array([zs[:, i] * model.z_dim ** (num_factors - i - 1) for i in range(num_factors)]),
axis=0, dtype=int)
cluster_map.append(z_labels)
cluster_map = np.array(cluster_map)
ax = fig.add_subplot(n_subplots, n_subplots, plot_idx)
ax.tick_params(axis='both', which='both', bottom=False, top=False, left=False, labelbottom=False,
labelleft=False)
print("cluster map %d fixing agent %d" % (idx, fixed_agent))
print(cluster_map)
plt.imshow(cluster_map, cmap='gist_rainbow')
onehots_0.append(np.array(oh0_map))
onehots_1.append(np.array(oh1_map))
plot_idx += 1
onehot_0_fig = plot_one_onehot_2agents(onehots_0, n_subplots**2)
onehot_1_fig = plot_one_onehot_2agents(onehots_1, n_subplots**2)
return fig, onehot_0_fig, onehot_1_fig
def visualize_clusters_online_double(env, model):
plot_0, onehot_0_fig_0, onehot_1_fig_0 = visualize_clusters_online_double_fix_one_agent(model, env.n_agents, env.grid_n, fixed_agent=0)
plot_1, onehot_0_fig_1, onehot_1_fig_1 = visualize_clusters_online_double_fix_one_agent(model, env.n_agents, env.grid_n, fixed_agent=1)
return plot_0, onehot_0_fig_0, onehot_1_fig_0, plot_1, onehot_0_fig_1, onehot_1_fig_1
def position_to_image(positions, n_agents, grid_n):
'''
Converts batch of agent xy positions to batch of rgb images
:param positions: batch of agent positions
:param n_agents: # agents
:param grid_n: grid size
:return: [sample_size, grid_n, grid_n, n_agents] images
'''
if grid_n not in [16,64]:
raise NotImplementedError("Grid size not supported: %d" % grid_n)
n_samples = positions.shape[0]
ims = np.zeros((n_samples, grid_n, grid_n, 3))
for i in range(n_agents):
agent_dim = AGENT_SIZES[i]
x_cur, y_cur = positions[:, 2*i], positions[:, 2*i+1]
if grid_n in [16, 64]:
for x in range(agent_dim[0]):
for y in range(agent_dim[1]):
ims[np.arange(n_samples),
(x_cur+x) % grid_n,
(y_cur+y) % grid_n] += np.tile(np.array(list(RGB_COLORS.values())[i]), (n_samples,1))
return ims
def visualize_attn_map(amaps): # amap: B X 1 X W X H
fig = plt.figure()
n_subplots = len(amaps) # should be 16
assert n_subplots == 16, "number of attention map samples should be 16"
for i in range(len(amaps)):
activations = amaps[i][0].cpu().detach().numpy()
ax = fig.add_subplot(4, 4, i+1)
ax.tick_params(axis='both', which='both', bottom=False, top=False, left=False, labelbottom=False,
labelleft=False)
plt.imshow(activations, cmap='Greys')
return fig
def plot_one_onehot_2agents(onehot_labels, n):
fig = plt.figure()
plot_idx = 1
n_subplots = 4
for labels in onehot_labels:
grid = labels.reshape(n,n)
ax = fig.add_subplot(n_subplots, n_subplots, plot_idx)
ax.tick_params(axis='both', which='both', bottom=False, top=False, left=False, labelbottom=False,
labelleft=False)
plt.imshow(grid, cmap='gist_rainbow')
plot_idx+=1
return fig
def sample_trajectory(env, len_traj=400, choose_agent_i=0):
'''
Samples 1 trajectory length len_traj, moving agent choose_agent_i, fixing all other agents
:param n_agents: total # agents
:param n: grid width
:param n_samples: number of trajectories to samples
:param choose_agent_i: agent to move
:return: np array of positions along trajectory [len_traj, 2*n_agents]
'''
actions = np.eye(env.n_agents*2)
actions = np.concatenate((actions, -1 * actions))
actions = np.concatenate((actions[choose_agent_i*2: choose_agent_i*2+2],
actions[env.n_agents*2+choose_agent_i*2: env.n_agents*2+choose_agent_i*2+2]))
os = []
for i in range(len_traj):
action = actions[np.random.randint(len(actions))]
env.step(action)
os.append(env.get_obs())
os = np.array(os).astype('int')
return os
def get_factorization_hist(env, model, len_traj=600, n_traj=10):
if env.name == 'gridworld':
return test_factorization_fix_agents(env, model, len_traj, n_traj)
elif env.name == 'key-wall' or env.name == 'key-corridor':
return test_factorization_single_agent_key(env, model)
def test_factorization_fix_agents(env, model, len_traj=600, n_traj=10):
'''
Samples random trajectories moving one agent at a time, returns two lists of histograms of hamming distances and onehot changes
by moving each agent. Histogram lists should be written to tensorboard
:param model: CPC model
:param n_agents: # agents
:param grid_n: grid width
:param len_traj: length of trajectories to sample
:param n_traj: number of trajectories to sample
:return: tuple of two lists of histogram figs (plt.fig), each length n_agents
1. list of histograms of hamming distances
2. list of histograms of onehot changes, moving one agent at a time
'''
hamming_hist_lst = []
onehot_hist_lst = []
for i in range(env.n_agents):
dist_onehots = []
for n in range(n_traj):
dist_onehots = []
x = sample_trajectory(env, len_traj=len_traj, choose_agent_i=i)
# y = position_to_image(x, env.n_agents, env.grid_n)
zs = get_discrete_representation(model, x)
dist_hamming = np.sum(zs[1:] - zs[:-1] != 0, axis=1)
prev_z = zs[0]
for zlabel in zs[1:]:
for k in range(model.num_onehots):
if zlabel[k] != prev_z[k]:
dist_onehots.append(k)
prev_z = zlabel
hammings_hist = plt.figure()
plt.hist(dist_hamming)
plt.ylabel("hamming distance distribution moving only agent %d" % i)
hamming_hist_lst.append(hammings_hist)
onehots_hist = plt.figure()
print("dist_onehots", dist_onehots)
plt.hist(dist_onehots, bins=np.arange(model.num_onehots + 1))
plt.ylabel("onehot changes only moving agent %d" % i)
onehot_hist_lst.append(onehots_hist)
return hamming_hist_lst, onehot_hist_lst
def save_plots(savepath, losses, est_lbs):
plt.plot(losses)
plt.ylabel('C_loss')
loss_path = os.path.join(savepath, "loss.png")
plt.savefig(loss_path)
plt.plot(est_lbs)
plt.ylabel('estimated lowerbound')
lb_path = os.path.join(savepath, "est_lowerbounds.png")
plt.savefig(lb_path)
plt.close('all')
def visualize_node(node, all_labels, dataset, grid_n, savepath):
# visualize some samples
idx = np.where(all_labels == node)[0]
anchors = dataset[0][::8]
node_samples = anchors[idx][:64]
np.random.shuffle(node_samples)
node_samples = np.concatenate((node_samples, np.zeros((len(node_samples), grid_n, grid_n, 1))), axis=3)
samples_tensor = np_to_var(node_samples).permute(0,3,1,2)
save_image(samples_tensor, os.path.join(savepath, "node_%d_samples.png" % node), padding=16)
def get_2agents_density(node, labels, dataset):
idx = np.where(labels == node)[0]
anchors = dataset[0][::8][idx]
sum_positions = anchors.sum(axis=0)
agent_0_pos, agent_1_pos = sum_positions[:,:, 0], sum_positions[:,:,1]
return agent_0_pos/agent_0_pos.max(), agent_1_pos/agent_1_pos.max()
def visualize_density_failed_2agents(cur_pos, cur_node, node_to_go, labels, dataset, savepath, epoch):
# visualize where execute_plan fails
agent_0_dist, agent_1_dist = get_2agents_density(cur_node, labels, dataset)
agent_0_dist_next, agent_1_dist_next = get_2agents_density(node_to_go, labels, dataset)
agent_0_cur_pos = np.zeros(agent_0_dist.shape)
agent_0_cur_pos[cur_pos[0], cur_pos[1]] = 1
agent_1_cur_pos = np.zeros(agent_1_dist.shape)
agent_1_cur_pos[cur_pos[2], cur_pos[3]] = 1
fig = plt.figure()
ax = fig.add_subplot(1, 2, 1)
im0 = np.stack([agent_0_dist, agent_0_dist_next, agent_0_cur_pos], axis=2)
plt.imshow(im0)
ax = fig.add_subplot(1, 2, 2)
im1 = np.stack([agent_1_dist, agent_1_dist_next, agent_1_cur_pos], axis=2)
plt.imshow(im1)
fname = "epoch_%d_failed_to_leave_node_%d" % (epoch, cur_node)
plt.savefig(os.path.join(savepath, fname))
def test_factorization_single_agent_key(env, model, n_traj=10, len_traj=200):
'''
move agent with and with key, count onehot changes for
1. Any agent movement with or without key, not changing key state within trajectory
2. Fixing agent position, placing/taking away key
'''
onehot_hist_lst = []
# 1. -------------- test factorization of agent
dist_onehots_a = []
for traj in range(n_traj):
env.reset()
traj_with_key = env.sample_random_trajectory(len_traj, interact_with_key=False)
zs = get_discrete_representation(model, traj_with_key)
prev_z = zs[0]
for zlabel in zs[1:]:
for k in range(model.num_onehots):
if zlabel[k] != prev_z[k]:
dist_onehots_a.append(k)
prev_z = zlabel
env.remove_all_keys()
traj_no_key = env.sample_random_trajectory(len_traj, interact_with_key=False)
zs = get_discrete_representation(model, traj_no_key)
prev_z = zs[0]
for zlabel in zs[1:]:
for k in range(model.num_onehots):
if zlabel[k] != prev_z[k]:
dist_onehots_a.append(k)
prev_z = zlabel
onehots_hist = plt.figure()
print("dist_onehots for moving agent", dist_onehots_a)
plt.hist(dist_onehots_a, bins=np.arange(model.num_onehots + 1))
plt.ylabel("onehot changes only moving agent")
onehot_hist_lst.append(onehots_hist)
# 2. ----------------- test factorization of key(s)
for key_idx in range(env.n_keys):
dist_onehots_k = []
for i in range(len_traj):
env.reset()
z_key = get_discrete_representation(model, env.get_obs(), single=True)
env.remove_key(key_idx, 0)
z_no_key = get_discrete_representation(model, env.get_obs(), single=True)
for k in range(model.num_onehots):
if z_no_key[k] != z_key[k]:
dist_onehots_k.append(k)
onehots_hist = plt.figure()
print("dist_onehots for changing key %d" % key_idx, dist_onehots_k)
plt.hist(dist_onehots_k, bins=np.arange(model.num_onehots + 1))
plt.ylabel("onehot changes only placing/removing key %d (fixing agent)" % key_idx)
onehot_hist_lst.append(onehots_hist)
return onehot_hist_lst
def visualize_single_agent_and_key(env, model):
# try to place agent at each position, with and without key on the grid
assert isinstance(env, KeyWall) or isinstance(env, KeyCorridor)
map_key = np.full((GRID_N, GRID_N), -1)
map_no_key = np.full((GRID_N, GRID_N), -1)
env.reset()
for x in range(GRID_N):
for y in range(GRID_N):
pos = (x,y)
obs = env.get_obs()
if env.try_place_agent(pos):
if model.encoder_form == 'cswm-key-gt':
z = model.encode((np_to_var(obs).unsqueeze(0).permute(0, 3, 1, 2), 1), vis=True)
else:
z = model.encode(np_to_var(obs).unsqueeze(0).permute(0, 3, 1, 2), vis=True)
z_label = tensor_to_label(z[0], model.num_onehots, model.z_dim)
map_key[pos] = z_label
env.remove_all_keys()
for x in range(GRID_N):
for y in range(GRID_N):
for y in range(GRID_N):
pos = (x, y)
obs = env.get_obs()
if env.try_place_agent(pos):
if model.encoder_form == 'cswm-key-gt':
z = model.encode((np_to_var(obs).unsqueeze(0).permute(0, 3, 1, 2), 0), vis=True)
else:
z = model.encode(np_to_var(obs).unsqueeze(0).permute(0, 3, 1, 2), vis=True)
z_label = tensor_to_label(z[0], model.num_onehots, model.z_dim)
map_no_key[pos] = z_label
print("map with key")
print(map_key)
print()
print("map no key")
print(map_no_key)
fig0 = plt.figure()
plt.imshow(map_key, cmap='gist_rainbow')
fig1 = plt.figure()
plt.imshow(map_no_key, cmap='gist_rainbow')
return fig0, fig1
|
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|
import numpy as np
import sklearn as sk
def get_class_weights(total_counts, class_positive_counts, multiply, use_class_balancing, class_mode="multiclass"):
"""
Calculate class_weight used in training
Arguments:
total_counts - int
class_positive_counts - dict of int, ex: {"Effusion": 300, "Infiltration": 500 ...}
multiply - int, positve weighting multiply
use_class_balancing - boolean
Returns:
class_weight - dict of dict, ex: {"Effusion": { 0: 0.01, 1: 0.99 }, ... }
"""
def get_single_class_weight(pos_counts):
denominator = (total_counts - pos_counts) * multiply + pos_counts
# print(f"Total counts = {total_counts}, Positive counts = {pos_counts}")
return {
0: pos_counts / denominator,
1: (denominator - pos_counts) / denominator,
}
def balancing(class_weights, label_counts, multiply=10):
"""
Normalize the class_weights so that each class has the same impact to backprop
ex: label_counts: [1, 2, 3] -> factor: [1, 1/2, 1/3] * len(label_counts) / (1+1/2+1/3)
"""
balanced = {}
# compute factor
reciprocal = np.reciprocal(label_counts.astype(float))
factor = reciprocal * len(label_counts) * multiply / np.sum(reciprocal)
# multiply by factor
i = 0
for c, w in class_weights.items():
balanced[c] = {
0: w[0] * factor[i],
1: w[1] * factor[i],
}
i += 1
return balanced
if class_mode == "multiclass":
class_id = range(len(class_names))
class_weights = sk.utils.class_weight.compute_class_weight('balanced')
return dict(zip(class_id, class_weights))
elif class_mode == "multibinary":
class_names = list(class_positive_counts.keys())
label_counts = np.array(list(class_positive_counts.values()))
class_weights = {}
for i, class_name in enumerate(class_names):
class_weights[class_name] = get_single_class_weight(label_counts[i])
if use_class_balancing:
class_weights = balancing(class_weights, label_counts)
return class_weights
|
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|
import numpy as np
import pylab as plt
from transitionControl import transitionControl
alpha=0.1
epsilon=0.1 # exploration policy
num_iters=1e2
gamma=0.95
allstates=np.zeros([6,9]) # Change the size of the maze.
num_step_taken=np.zeros(int(num_iters))
# action 0 is right,left is 1, up is 2,down is 3.
qvalues=np.zeros([54,4])
for hi in range (int(num_iters)):
num_tries=0
curstate=[2,0]
csi=np.ravel_multi_index(curstate,allstates.shape) # initialize the current state to start state [3,1]
qvisit=np.zeros([54,4])
while (1): #until terminal state
num_tries=num_tries+1
#print(curstate)
np.ravel_multi_index(curstate,allstates.shape) #convert to index # convert state to index
if(np.random.rand(1)>epsilon): # greedy action
action=np.argmax(qvalues[csi,:])
qvisit[csi,action]=1
else:
temp=np.random.permutation(4) # exploring action
action=temp[0]
qvisit[csi,action]=1
nextstate,signal,reward= transitionControl(curstate,action)
nsi=np.ravel_multi_index(nextstate,allstates.shape)
if signal==1 : # we have now reached a terminal state
qvalues[csi,action]=qvalues[csi,action]+ alpha*(reward- qvalues[csi,action])
qvisit[csi,action]=1
break
q_next=np.argmax(qvalues[nsi,:])
qvalues[csi,action]=qvalues[csi,action]+ alpha*(reward +qvalues[nsi,q_next]- qvalues[csi,action])
curstate=nextstate
csi=nsi
print('Henry has completed the task in',int(num_tries))
num_step_taken[hi]=num_tries
#now we shall plot everthing
plt.plot(range(int(num_iters)),num_step_taken,'k')
plt.xlabel('Number of iterations')
plt.ylabel('Number of moves taken to solve')
plt.title('Agent on Maze Task')
plt.show()
# Simulate the maze
|
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|
# Copyright 2022 Google LLC.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Core Sparse MoE utils using pjit.
Many thanks to Parker Schuh and Sudip Roy, for helping with the einsum
implementation, and to Jonathan Heek for helping writing the lift transform.
The following abbreviations are sometimes used to name the size of different
axes in the arrays.
G = num_groups. It must be a multiple of num_experts.
S = group_size.
E = num_experts.
C = capacity.
K = num_selected_experts. It must be <= num_experts.
"""
import abc
import math
from typing import Any, Callable, Dict, Mapping, Optional, Tuple
import flax.core.lift
import flax.linen.partitioning
import flax.linen.transforms
import flax.struct
import jax
from jax.experimental import pjit
import jax.numpy as jnp
import vmoe.partitioning
Array = jnp.ndarray
PartitionSpec = pjit.PartitionSpec
with_sharding_constraint = vmoe.partitioning.with_sharding_constraint
_add_axis_to_metadata = flax.linen.partitioning._add_axis_to_metadata # pylint: disable=protected-access
class BaseDispatcher(abc.ABC):
"""Base class for different dispatcher implementations.
Dispatchers are in charge of preparing the data to be dispatched to the
different experts, and then combining the outputs of each expert for each
item. There are different ways of doing so with different memory / flops /
runtime implications when running on actual hardware.
In all cases, when dispatching data, they take an array of shape (G, S, ...).
The groups (G) are dispatched independently of each other. The items in each
group (S) will take place in the buffer (of capacity C) of items to be
processed by each expert (E). The output is an array of shape (E, G * C, ...)
with the elements to be processed by each expert.
When combining data, they take an array of shape (E, G * C, ...) and output
an array of shape (G, S, ...). Notice that the trailing dimensions (...) at
combine might not be the same as the ones at dispatch (e.g. if the expert
changes the shape of the data).
"""
@abc.abstractmethod
def dispatch(self, data: Array) -> Array:
"""Dispatches data to experts.
Args:
data: (G, S, ...) array with the data to dispatch to the experts.
Returns:
(E, G * C, ...) array with the data to be processed by each expert.
"""
@abc.abstractmethod
def combine(self, data: Array) -> Array:
"""Combines outputs from multiple experts.
Args:
data: (E, G * C, ...) array with the output data from each expert.
Returns:
(G, S, ...) array with the combined outputs from each expert.
"""
@flax.struct.dataclass
class EinsumDispatcher(BaseDispatcher):
"""Dispatcher using Einsum.
Attributes:
combine_weights: (G, S, E, C) array with the combine weights for each item
(G, S) for each expert (E) and buffer position (C).
dispatch_weights: Optional. (G, S, E, C) array with the dispatch weights of
each item (G, S) for each expert (E) and buffer position (C).
partition_spec: Optional. PartitionSpec used to constrain the sharding of
the data arrays. By default (None), no sharding constraint is specified.
einsum_precision: Optional. Precision used in all the einsums (e.g.
combining the outputs of different experts).
"""
combine_weights: Array
dispatch_weights: Optional[Array] = None
partition_spec: Optional[PartitionSpec] = flax.struct.field(
pytree_node=False, default=None)
einsum_precision: jax.lax.Precision = flax.struct.field(
pytree_node=False, default=jax.lax.Precision.DEFAULT)
def dispatch(self, data: Array) -> Array:
dispatch_weights = (
self.combine_weights > 0
if self.dispatch_weights is None else self.dispatch_weights)
data = jnp.einsum("GSEC,GS...->GEC...", dispatch_weights, data,
precision=self.einsum_precision)
return _dispatch(data, self.partition_spec)
def combine(self, data: Array) -> Array:
"""Combines data from experts according to combine_weights."""
num_groups, _, _, _ = self.combine_weights.shape
data = _receive(data, num_groups, self.partition_spec)
return jnp.einsum("GSEC,GEC...->GS...", self.combine_weights, data,
precision=self.einsum_precision)
@flax.struct.dataclass
class ExpertIndicesDispatcher(BaseDispatcher):
"""Dispatcher using scatter/gather with (expert, buffer) indices.
Attributes:
indices: (G, S, K, 2) integer array with the (expert, buffer) indices of
each item (G, S) and their K-selected experts. The tuple (expert, buffer)
for each item is represented in the last dimension (of size 2).
combine_weights: (G, S, K) array with the combine weights of each item
(G, S) and their K-selected experts.
num_experts: Number of experts.
capacity: Capacity of each expert's buffer per group.
partition_spec: Optional. PartitionSpec used to constrain the sharding of
the data arrays. By default (None), no sharding constraint is specified.
einsum_precision: Optional. Precision used in all the einsums (e.g.
combining the outputs of different experts).
"""
indices: Array # (G, S, K, 2).
combine_weights: Array # (G, S, K).
num_experts: int = flax.struct.field(pytree_node=False)
capacity: int = flax.struct.field(pytree_node=False)
partition_spec: Optional[PartitionSpec] = flax.struct.field(
pytree_node=False, default=None)
einsum_precision: jax.lax.Precision = flax.struct.field(
pytree_node=False, default=jax.lax.Precision.DEFAULT)
def dispatch(self, data: Array) -> Array:
num_groups, _, num_selected_experts, _ = self.indices.shape
_, _, *item_shape = data.shape
data = jnp.repeat(data, num_selected_experts, axis=1)
indices = self.indices.reshape(num_groups, -1, 2)
shape = (self.num_experts, self.capacity, *item_shape)
data = jax.vmap(lambda x, i: _scatter_nd(i, x, shape))(data, indices)
return _dispatch(data, self.partition_spec)
def combine(self, data: Array) -> Array:
num_groups, _, _ = self.combine_weights.shape
data = _receive(data, num_groups, self.partition_spec)
data = jax.vmap(lambda x, i: x[i[:, :, 0], i[:, :, 1]])(data, self.indices)
# Mask invalid gathered data.
mask = jnp.logical_and(self.indices[..., 0] < self.num_experts,
self.indices[..., 1] < self.capacity)
data = data * mask.reshape(mask.shape + (1,) * (data.ndim - 3))
# Weighted sum of the outputs of the K-selected experts for each item.
return jnp.einsum("GSK...,GSK->GS...", data, self.combine_weights,
precision=jax.lax.Precision.HIGHEST)
@flax.struct.dataclass
class Bfloat16Dispatcher(BaseDispatcher):
"""Dispatcher wrapper converting data to bfloat16 to save bandwidth."""
dispatcher: BaseDispatcher
def dispatch(self, data: Array) -> Array:
dtype = data.dtype
data = _cast_to_bfloat16(data)
data = self.dispatcher.dispatch(data)
return data.astype(dtype)
def combine(self, data: Array) -> Array:
dtype = data.dtype
data = _cast_to_bfloat16(data)
data = self.dispatcher.combine(data)
return data.astype(dtype)
def get_top_experts_per_item_dispatcher(gates: Array, name: str,
num_selected_experts: int,
batch_priority: bool,
capacity: Optional[int] = None,
capacity_factor: Optional[float] = None,
**dispatcher_kwargs) -> BaseDispatcher:
"""Returns a dispatcher implementing Top-Experts-Per-Item routing.
For each item, the `num_selected_experts` experts with the largest gating
score are selected in a greedy fashion. However, because each expert has a
fixed `capacity`, if more items than `capacity` select a given expert some of
the assignments will be ignored. All top-1 choices have priority over top-2
choices and so on. In addition, the choices that are ignored also depend on
`batch_priority`. If it is False, the "Vanilla" algorithm is used, meaning
that items in earlier positions of the array have priority. If it is True, the
"Batch Priority Routing" algorithm (see https://arxiv.org/abs/2106.05974) is
used, which gives more priority to the items whose largest score is greater.
Args:
gates: (S, E) array with the gating values for each (item, expert).
These values will also be used as combine_weights for the selected pairs.
name: String with the type of dispatcher to use (supported values are
"einsum" and "indices").
num_selected_experts: Maximum number of experts to select per each item (K).
batch_priority: Whether to use batch priority routing or not.
capacity: If given, maximum number of items processed by each expert.
Either this or `capacity_factor` must be given.
capacity_factor: If given, sets the `capacity` to this factor of S * K / E.
Either this or `capacity` must be given.
**dispatcher_kwargs: Additional arguments for the dispatcher object.
Returns:
A dispatcher.
"""
if (capacity is None) == (capacity_factor is None):
raise ValueError(
"You must specify either 'capacity' or 'capacity_factor', and not both."
f" Current values are capacity = {capacity!r}, "
f"capacity_factor = {capacity_factor!r}")
if not capacity:
group_size, num_experts = gates.shape
capacity = _compute_capacity(
# Target number of tokens to split among the `num_experts` experts.
num_tokens=group_size * num_selected_experts,
num_experts=num_experts,
capacity_factor=capacity_factor)
fn_map = {
"einsum": _get_top_experts_per_item_einsum_dispatcher,
"indices": _get_top_experts_per_item_expert_indices_dispatcher,
}
if name not in fn_map:
raise ValueError(f"Unknown dispatcher type: {name!r}")
return fn_map[name](gates, num_selected_experts, capacity, batch_priority,
**dispatcher_kwargs)
def sparse_moe_spmd(target: flax.linen.transforms.Target,
variable_axes: Mapping[flax.core.lift.CollectionFilter,
flax.core.lift.InOutAxis],
split_rngs: Mapping[flax.core.lift.PRNGSequenceFilter,
bool],
has_aux: bool = False,
methods=None):
"""Lift transformation that wraps a target with a Sparse MoE using SPMD.
SPMD stands for "Single Program, Multiple Data", meaning that all experts
actually implement the same function (program), but use different data
(inputs and parameters). Thus, a single target to "expertify" is given.
When an instance of a Linen module wrapped with this transformation is called,
it expects one additional argument at the beginning, a "dispatcher"
(see `BaseDispatcher`). This "dispatcher" is used to prepare the arguments to
be processed by each "expert". The "target" is wrapped with vmap and applied
to different sets of parameters and inputs. Finally, the "dispatcher" combines
the outputs of all experts applied to each given item.
If the target has any auxiliary outputs (e.g. metrics) that should not be
combined, these can be returned by using "has_aux = True".
Args:
target: A target to wrap with a Sparse MoE (e.g. a flax.linen.Module) with
methods passed via the `methods` argument.
variable_axes: Mapping indicating the axis along each variable collection is
"expertified". Typically, this is something like {"params": 0}.
split_rngs: Mapping indicating whether to split each of the PRNGKeys passed
to the experts.
has_aux: If the target returns any auxiliary output that should not be
combined, set this to True.
methods: Methods from the target to wrap with a Sparse MoE. By default,
the "__call__" method will be wrapped.
Returns:
A transformed target.
"""
def wrapper(expert_fn: Callable[..., Any]):
def transformed(scopes, dispatcher, *inputs):
# Prepare inputs to be processed by each expert.
inputs = jax.tree_map(dispatcher.dispatch, inputs)
# Wrap the target with vmap, to pass different parameters and inputs to
# each expert.
outputs = flax.core.lift.vmap(
expert_fn,
in_axes=0,
out_axes=0,
variable_axes=variable_axes,
split_rngs=split_rngs)(scopes, *inputs)
# Combine outputs.
if has_aux:
outputs, aux = outputs
outputs = jax.tree_map(dispatcher.combine, outputs)
return (outputs, aux) if has_aux else outputs
return transformed
return flax.linen.transforms.lift_transform(wrapper, target, methods=methods)
def sparse_moe_spmd_with_axes(
target: flax.linen.transforms.Target,
variable_axes: Mapping[flax.core.lift.CollectionFilter,
flax.core.lift.InOutAxis],
split_rngs: Mapping[flax.core.lift.PRNGSequenceFilter, bool],
partitioning_axis_names: Mapping[str, str],
has_aux: bool = False,
methods=None):
"""Lift transformation similar to sparse_moe_spmd with partitioned named axes."""
variable_axes = dict(variable_axes)
for name in partitioning_axis_names:
variable_axes[f"{name}_axes"] = None
lifted = sparse_moe_spmd(target, variable_axes, split_rngs, has_aux, methods)
for collection_name, axis in variable_axes.items():
if collection_name in partitioning_axis_names:
lifted = _add_axis_to_metadata(
lifted,
axis_pos=axis,
axis_name=partitioning_axis_names[collection_name],
axis_col=f"{collection_name}_axes")
return lifted
def _cast_to_bfloat16(x: Array) -> Array:
return x.astype(jnp.bfloat16) if jnp.issubdtype(x.dtype, jnp.floating) else x
def _compute_capacity(num_tokens, num_experts, capacity_factor):
capacity = int(math.ceil(num_tokens * capacity_factor / num_experts))
if capacity < 1:
raise ValueError(f"The values num_tokens = f{num_tokens}, num_experts = "
f"{num_experts} and capacity_factor = {capacity_factor} "
f"lead to capacity = {capacity}, but it must be greater "
"than or equal to 1.")
# Make capacity multiple of 4 to try to avoid padding.
capacity += (-capacity) % 4
return capacity
def _convert_partition_spec(spec):
if spec is not None and not isinstance(spec, PartitionSpec):
spec = (spec,) if isinstance(spec, str) else tuple(spec)
spec = PartitionSpec(*spec)
return spec
def _dispatch(data: Array, partition_spec: Optional[PartitionSpec]) -> Array:
"""Dispatches data to experts using all_to_all."""
partition_spec = _convert_partition_spec(partition_spec)
num_groups, num_experts, capacity, *item_shape = data.shape
data = with_sharding_constraint(data, partition_spec)
data = data.reshape(num_experts, -1, num_experts, capacity, *item_shape)
data = jnp.swapaxes(data, 0, 2)
data = data.reshape(-1, *item_shape)
data = with_sharding_constraint(data, partition_spec)
return data.reshape(num_experts, num_groups * capacity, *item_shape)
def _receive(data: Array, num_groups: int,
partition_spec: Optional[PartitionSpec]) -> Array:
"""Receives data from experts using all_to_all."""
partition_spec = _convert_partition_spec(partition_spec)
num_experts, num_groups_time_capacity, *item_shape = data.shape
capacity = num_groups_time_capacity // num_groups
data = data.reshape(num_experts * num_groups, capacity, *item_shape)
data = with_sharding_constraint(data, partition_spec)
data = data.reshape(num_experts, -1, num_experts, capacity, *item_shape)
data = jnp.swapaxes(data, 0, 2)
data = data.reshape(num_groups, num_experts, capacity, *item_shape)
data = with_sharding_constraint(data, partition_spec)
return data
def _scatter_nd(indices, updates, shape):
"""Jax implementation of tf.scatter_nd.
Notes:
- The updates are cumulative, ie. if multiple indices point to the
same position, the output value at this position is accumulated.
- We rely on the fact that out-of-range indices will be quietly ignored and
don't raise any error. This breaks what JAX index ops specify
(https://jax.readthedocs.io/en/latest/jax.ops.html), but makes the code
easier.
Args:
indices: An int matrix of (i, j, ...) indices with shape [B, ndim].
updates: An array of data points with shape [B, ...].
shape: An int vector with the dimensions of the output array of size [ndim].
Returns:
An array of shape `shape` with updated values at given indices.
"""
# See: https://www.tensorflow.org/api_docs/python/tf/scatter_nd.
zeros = jnp.zeros(shape, updates.dtype)
key = tuple(jnp.moveaxis(indices, -1, 0))
return zeros.at[key].add(updates)
def _get_top_experts_per_item_common(
gates: Array, num_selected_experts: int,
batch_priority: bool) -> Tuple[Array, Array, Array]:
"""Returns common arrays used by Top-Experts-Per-Item routing.
Args:
gates: (S, E) array with the gating values for each (item, expert).
These values will also be used as combine_weights for the selected pairs.
num_selected_experts: Maximum number of experts to select per item.
batch_priority: Whether to use batch priority routing or not.
Returns:
- `combine_weights`, with shape (S, K) with the weights used to
combine the outputs of the K-selected experts for each item.
- `expert_index`, with shape (S, K) containing the expert_index for each of
the K-selected experts for each item.
- `buffer_index`, with shape (S, K, E) containing the buffer index for each
item and selected expert.
"""
group_size, num_experts = gates.shape
combine_weights, expert_index = jax.lax.top_k(gates, num_selected_experts)
if batch_priority:
# Sort items according to their maximum routing weight. The permutation will
# be reversed later, so no need to permute combine_weights here.
perm = jnp.argsort(-combine_weights[:, 0])
expert_index = expert_index[perm]
# (K * S,). Make K the leading axis to ensure that top-1 choices have priority
# over top-2 choices and so on. Flatten array for cumsum.
expert_index = jnp.swapaxes(expert_index, 0, 1).ravel()
# (K * S, E). Convert expert indices to a one-hot array.
expert_one_hot = jax.nn.one_hot(expert_index, num_experts, dtype=jnp.int32)
# (K * S, E) -> (K, S, E) -> (S, K, E). Use cumsum to compute the buffer idx
# within each experts' buffer.
buffer_index = jnp.cumsum(expert_one_hot, axis=0) * expert_one_hot - 1
buffer_index = buffer_index.reshape(-1, group_size, num_experts)
buffer_index = jnp.swapaxes(buffer_index, 0, 1)
# (K, S) -> (S, K). Revert expert_index to the original shape.
expert_index = jnp.swapaxes(expert_index.reshape(-1, group_size), 0, 1)
if batch_priority:
# Permute the items to their original order.
inv_perm = jnp.argsort(perm)
expert_index = expert_index[inv_perm]
buffer_index = buffer_index[inv_perm]
return combine_weights, expert_index, buffer_index
def _get_top_experts_per_item_einsum_dispatcher(
gates: Array, num_selected_experts: int, capacity: int,
batch_priority: bool, **dispatcher_kwargs) -> EinsumDispatcher:
"""Returns an EinsumDispatcher performing Top-Experts-Per-Item routing.
Args:
gates: (S, E) array with the gating values for each (item, expert).
These values will also be used as combine_weights for the selected pairs.
num_selected_experts: Maximum number of experts to select per each item.
capacity: Maximum number of items processed by each expert.
batch_priority: Whether to use batch priority routing or not.
**dispatcher_kwargs: Additional arguments for the EinsumDispatcher.
Returns:
An EinsumDispatcher object.
"""
_, _, buffer_idx = _get_top_experts_per_item_common(
gates, num_selected_experts, batch_priority)
# (S, K, E) -> (S, E). Select the only buffer index for each (item, expert).
buffer_idx = jnp.max(buffer_idx, axis=1)
# (S, E, C). Convert the buffer indices to a one-hot matrix. We rely on the
# fact that indices < 0 or >= capacity will be ignored by the dispatcher.
dispatch_weights = jax.nn.one_hot(buffer_idx, capacity, dtype=jnp.bool_)
einsum_precision = dispatcher_kwargs.get("einsum_precision",
jax.lax.Precision.DEFAULT)
combine_weights = jnp.einsum(
"SE,SEC->SEC", gates, dispatch_weights, precision=einsum_precision)
return EinsumDispatcher(
combine_weights=combine_weights,
dispatch_weights=dispatch_weights,
**dispatcher_kwargs)
def _get_top_experts_per_item_expert_indices_dispatcher(
gates: Array, num_selected_experts: int, capacity: int,
batch_priority: bool, **dispatcher_kwargs) -> ExpertIndicesDispatcher:
"""Returns an ExpertIndicesDispatcher performing Top-Experts-Per-Item routing.
Args:
gates: (S, E) array with the gating values for each (item, expert).
These values will also be used as combine_weights for the selected pairs.
num_selected_experts: Maximum number of experts to select per each item.
capacity: Maximum number of items processed by each expert.
batch_priority: Whether to use batch priority routing or not.
**dispatcher_kwargs: Additional arguments for the ExpertIndicesDispatcher.
Returns:
An ExpertIndicesDispatcher object.
"""
_, num_experts = gates.shape
combine_weights, expert_idx, buffer_idx = _get_top_experts_per_item_common(
gates, num_selected_experts, batch_priority)
# (S, K, E) -> (S, K). Select the only buffer index for each (item, k_choice).
buffer_idx = jnp.max(buffer_idx, axis=2)
return ExpertIndicesDispatcher(
indices=jnp.stack([expert_idx, buffer_idx], axis=-1),
combine_weights=combine_weights,
num_experts=num_experts,
capacity=capacity,
**dispatcher_kwargs)
|
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|
"""Collection of functions to run simulation studies and plot results"""
from time import time
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D # noqa:F401
import src.functions_to_approximate as functions
import src.interpolate as interpolators
from src.auxiliary import get_grid
from src.auxiliary import get_interpolation_points
from src.auxiliary import rmse as root_mean_squared_error
def execute_study(study_params, interpolation_params):
"""Run the simulation study with parameters *study_params*.
...
Parameters
----------
study_params: dict
...
interpolation_params: dict
...
Returns
-------
results: dict
...
"""
# load parameters
interpolation_method = study_params["controls"]["interpolation method"]
func_name = study_params["controls"]["function to approximate"]
func_name_short = func_name[: func_name.find("_")]
interpolator_name = study_params[interpolation_method]["interpolator"]
grid_density = study_params["controls"]["grid density"]
grid_method = study_params["controls"]["grid method"]
iterations = study_params["controls"]["iterations"]
n_interpolation_points = study_params["controls"][
"number of points for accuracy check"
]
accuracy_check_seed = study_params["controls"]["seed for accuracy check"]
# set grid parameters
grid_params = {}
grid_params["orders"] = study_params["grid"]["orders"][grid_density]
grid_params["lower bounds"] = study_params["grid"]["lower bounds"][func_name_short]
grid_params["upper bounds"] = study_params["grid"]["upper bounds"][func_name_short]
# set functionals for function to approximate and interpolator
func = getattr(functions, func_name)
interpolator = getattr(interpolators, interpolator_name)
# initiate dict to store results
results = {"rmse": {}, "runtime": {}, "gridpoints": {}}
for dims in study_params["controls"]["dims"]:
# generate grid
grid, index = get_grid(grid_params, dims)
# get interpolation points
interpolation_points = get_interpolation_points(
n_interpolation_points, grid, accuracy_check_seed,
)
# get results on interpolation points
results_calc = func(interpolation_points)
# initiate objects to store results
rmse_tmp = []
runtime_tmp = []
n_gridpoints_effective_tmp = []
# iterate over settings
for iteration in range(iterations):
# print(f"dimension: {dims}; iteration: {iteration + 1}")
# adjust interpolation parameters
interpolation_params[interpolation_method]["grid method"] = grid_method
interpolation_params[interpolation_method][
"evaluate off-grid"
] = study_params["controls"]["evaluate off-grid"]
if interpolation_method == "linear":
interpolation_params["linear"]["sparse grid level"] = study_params[
"linear"
]["sparse grid levels"][iteration]
interpolation_params["linear"]["interpolation points"] = study_params[
"linear"
]["interpolation points"][iteration]
elif interpolation_method == "spline":
interpolation_params["spline"]["interpolation points"] = study_params[
"spline"
]["interpolation points"][iteration]
elif interpolation_method == "smolyak":
interpolation_params["smolyak"]["sparse grid level"] = study_params[
"smolyak"
]["sparse grid levels"][iteration]
elif interpolation_method == "sparse":
interpolation_params["sparse"]["sparse grid level"] = study_params[
"sparse"
]["sparse grid levels"][iteration]
# interpolate and capture computation time
start = time()
results_interp, n_gridpoints_effective = interpolator(
interpolation_points, grid, func, interpolation_params
)
stop = time()
# assess interpolation accuracy
rmse_iter = root_mean_squared_error(results_interp, results_calc)
# store results
rmse_tmp.append(rmse_iter)
runtime_tmp.append(stop - start)
n_gridpoints_effective_tmp.append(n_gridpoints_effective)
results["rmse"][dims] = np.array(object=rmse_tmp)
results["runtime"][dims] = np.array(object=runtime_tmp)
results["gridpoints"][dims] = np.array(object=n_gridpoints_effective_tmp)
return results
def plot_results(results, study_params):
"""Plot results for a single simulation study.
...
Parameters
----------
results: dict
...
study_params: dict
...
Returns
-------
None
"""
plot_legend = []
plot_x = []
plot_y = []
for dim in study_params["controls"]["dims"]:
plot_legend.append("# vars: " + str(dim))
plot_x.append(results["gridpoints"][dim])
plot_y.append(results["rmse"][dim])
for idx in range(len(study_params["controls"]["dims"])):
plt.plot(plot_x[idx], plot_y[idx])
plt.xscale("log")
plt.yscale("log")
plt.xlabel("number of interpolation points (log axis)")
plt.ylabel("root mean squared error (log axis)")
plt.legend(plot_legend)
plt.title(
"Interpolation accuracy (" + study_params["controls"]["grid density"] + " grid)"
)
plt.show()
return
def compare_fit_2d_iter(study_params, interpolation_params, iteration):
"""Plot fit for 2D function with givel level of accuracy.
...
Parameters
----------
study_params: dict
...
iteration: int
...
Returns
-------
None
"""
# set interpolation parameters
dims = 2
interpolation_method = study_params["controls"]["interpolation method"]
func_name = study_params["controls"]["function to approximate"]
func_name_short = func_name[: func_name.find("_")]
interpolator_name = study_params[interpolation_method]["interpolator"]
grid_density = study_params["controls"]["grid density"]
grid_method = study_params["controls"]["grid method"]
n_interpolation_points = study_params["controls"][
"number of points for accuracy check"
]
accuracy_check_seed = study_params["controls"]["seed for accuracy check"]
# set grid parameters
grid_params = {}
grid_params["orders"] = study_params["grid"]["orders"][grid_density]
grid_params["lower bounds"] = study_params["grid"]["lower bounds"][func_name_short]
grid_params["upper bounds"] = study_params["grid"]["upper bounds"][func_name_short]
# set functionals for function to approximate and interpolator
func = getattr(functions, func_name)
interpolator = getattr(interpolators, interpolator_name)
# generate grid / state space
grid, index = get_grid(grid_params, dims)
# generate grid for plotting
n_plot_x = n_plot_y = 100
n_plot = n_plot_x * n_plot_y
x = np.linspace(
grid_params["lower bounds"][0], grid_params["upper bounds"][0], n_plot_x
)
y = np.linspace(
grid_params["lower bounds"][1], grid_params["upper bounds"][1], n_plot_y
)
X, Y = np.meshgrid(x, y)
plot_grid = np.asarray([X.reshape(n_plot), Y.reshape(n_plot)]).T
func_on_plot_grid_actual = func(plot_grid)
func_on_plot_grid_actual = np.asarray(func_on_plot_grid_actual).reshape(
(n_plot_x, n_plot_y)
)
# adjust interpolation parameters
interpolation_params[interpolation_method]["grid method"] = grid_method
interpolation_params[interpolation_method]["evaluate off-grid"] = study_params[
"controls"
]["evaluate off-grid"]
if interpolation_method == "linear":
interpolation_params["linear"]["sparse grid level"] = study_params["linear"][
"sparse grid levels"
][iteration]
interpolation_params["linear"]["interpolation points"] = study_params["linear"][
"interpolation points"
][iteration]
elif interpolation_method == "spline":
interpolation_params["spline"]["interpolation points"] = study_params["spline"][
"interpolation points"
][iteration]
elif interpolation_method == "smolyak":
interpolation_params["smolyak"]["sparse grid level"] = study_params["smolyak"][
"sparse grid levels"
][iteration]
elif interpolation_method == "sparse":
interpolation_params["sparse"]["sparse grid level"] = study_params["sparse"][
"sparse grid levels"
][iteration]
# interpolate and capture computation time
start = time()
func_on_plot_grid_interpolated, n_gridpoints_effective = interpolator(
plot_grid, grid, func, interpolation_params
)
stop = time()
runtime = stop - start
func_on_plot_grid_interpolated = np.asarray(func_on_plot_grid_interpolated).reshape(
(n_plot_x, n_plot_y)
)
# calculate approximation error
interpolation_points = get_interpolation_points(
n_interpolation_points, grid, accuracy_check_seed,
)
results_interp, n_gridpoints_effective = interpolator(
interpolation_points, grid, func, interpolation_params
)
results_calc = func(interpolation_points)
rmse = root_mean_squared_error(results_interp, results_calc)
# plot results
print(f"grid method: {grid_method}")
print(f"total number of interpolation points: {n_gridpoints_effective}")
print(f"runtime for interpolation: {runtime}")
print(f"root mean squared error: {rmse}")
fig = plt.figure(figsize=(16, 6))
ax = fig.add_subplot(
131, projection="3d", title=f"{func_name_short} function, dim=2 (calculated)"
)
ax.plot_surface(
X, Y, func_on_plot_grid_actual, rstride=1, cstride=1, cmap=plt.cm.magma
)
ax = fig.add_subplot(
132, projection="3d", title=f"{func_name_short} function, dim=2 (interpolated)"
)
ax.plot_surface(
X, Y, func_on_plot_grid_interpolated, rstride=1, cstride=1, cmap=plt.cm.magma
)
ax = fig.add_subplot(
133, projection="3d", title=f"{func_name_short} function, dim=2 (error)"
)
ax.plot_surface(
X,
Y,
func_on_plot_grid_actual - func_on_plot_grid_interpolated,
rstride=1,
cstride=1,
cmap=plt.cm.magma,
)
# ax.set_zlim(0.0, ax.get_zlim()[1] * 2)
plt.show()
print("-------------------------------------------------------------------")
return
def compare_results(results_1, results_2, study_params_1, study_params_2):
"""Plot results for a two simulation studies for comparison.
...
Parameters
----------
results_1: dict
...
study_params_1: dict
...
results_2: dict
...
study_params_2: dict
...
Returns
-------
None
"""
plot_legend = []
plot_colors = ["b", "g", "r", "c", "m", "y", "k", "b"]
dims = list(
set(study_params_1["controls"]["dims"]).intersection(
study_params_2["controls"]["dims"]
)
)
# pdb.set_trace()
for dim in dims:
plt.plot(
results_1["gridpoints"][dim],
results_1["rmse"][dim],
str(plot_colors[dim] + "-"),
results_2["gridpoints"][dim],
results_2["rmse"][dim],
str(plot_colors[dim] + ":"),
)
plot_legend.append(str(dim) + " vars (setting 1)")
plot_legend.append(str(dim) + " vars (setting 2)")
plt.xscale("log")
plt.yscale("log")
plt.xlabel("number of interpolation points (log axis)")
plt.ylabel("root mean squared error (log axis)")
plt.legend(plot_legend)
plt.title("Interpolation accuracy")
plt.show()
return
|
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|
import numpy as np
import numpy.random as npr
import flymc as ff
from util import nd, nd_bounds
import unittest
from model_setup import *
npr.seed(1)
class DerivativesTest(object):
PLACES = 4
NUM_TRIALS = 10
N = 30
D = 4
K = 3
def test_prior(self):
for model, th, z in self.random_setup():
LB, UB = nd_bounds(model._logPrior, th)
AD = model._D_logPrior(th)
self.check_ordered(LB, AD, UB)
def test_likelihood(self):
for model, th, z in self.random_setup():
LB, UB = nd_bounds(lambda th: np.sum(model._logL(th, z.bright)), th)
AD = np.sum(model._D_logL(th, z.bright), axis=0)
self.check_ordered(LB, AD, UB)
def test_bound(self):
for model, th, z in self.random_setup():
LB, UB = nd_bounds(lambda th:
np.sum(model._logB(th, z.bright)), th)
AD = np.sum(model._D_logB(th, z.bright), axis=0)
self.check_ordered(LB, AD, UB)
def test_LB_gap(self):
for model, th, z in self.random_setup():
LB, UB = nd_bounds(lambda th:
np.sum(model._LBgap(th, z.bright)), th)
AD = np.sum(model._D_LBgap(th, z.bright), axis=0)
self.check_ordered(LB, AD, UB)
def test_bound_product(self):
for model, th, z in self.random_setup():
LB, UB = nd_bounds(lambda th: model._logBProduct(th), th)
AD = model._D_logBProduct(th)
self.check_ordered(LB, AD, UB)
def test_marg_likelihood(self):
for model, th, z in self.random_setup():
LB, UB = nd_bounds(lambda th: model.log_p_marg(th), th)
AD = model.D_log_p_marg(th)
self.check_ordered(LB, AD, UB)
def test_pseudo_likelihood(self):
for model, th, z in self.random_setup():
LB, UB = nd_bounds(lambda th: np.sum(model.log_pseudo_lik(th, z.bright)), th)
AD = np.sum(model._D_log_pseudo_lik(th, z.bright), axis=0)
self.check_ordered(LB, AD, UB)
def test_joint_posterior(self):
for model, th, z in self.random_setup():
LB, UB = nd_bounds(lambda th: model.log_p_joint(th, z), th)
AD = model.D_log_p_joint(th, z)
self.check_ordered(LB, AD, UB)
def check_ordered(self, A, B, C):
# Check that A < B < C
for a, b, c in zip(A.ravel(), B.ravel(), C.ravel()):
self.assertLess(a, b)
self.assertLess(b, c)
def check_close(self, A, B):
rel_error = np.abs(A-B)/np.abs(A)
self.assertEqual(A.shape, B.shape)
self.assertAlmostEqual(np.max(rel_error), 0, places=self.PLACES)
class LogisticModelTest(LogisticModelSetup, DerivativesTest, unittest.TestCase):
pass
class MulticlassLogisticModelTest(MulticlassLogisticModelSetup, DerivativesTest, unittest.TestCase):
pass
class RobustRegressionModelTest(RobustRegressionModelSetup, DerivativesTest, unittest.TestCase):
pass
|
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|
!AceGenModule rmodel
!nstatv: 58
!ElasticType: NeoHookean
!IsoHardType: TwoIsoHard
!KinHardType: BC_D07mod
!DistHardType: rmodel
!
!Material parameters (16):
!G (Shear modulus)
!K (Bulk modulus)
!Y0 (Initial yield limit)
!k1 (Isotropic hardening constant 1)
!Rinf1 (Isotropic saturation 1)
!k2 (Isotropic hardening constant 2)
!Rinf2 (Isotropic saturation 2)
!delta (amount of AF vs BC)
!Hkin1
!Binf1
!Hkin2
!Binf2
!cL (Evolution parameter for CL)
!bL (Amount of latent hardening)
!Hr (hardening modulus for r)
!rinf (saturation value of r)
module acegen_mod
implicit none
contains
subroutine model_size(nparam,nstatv,nvar)
implicit none
integer nparam, nstatv, nvar
nparam = 16
nstatv = 58
nvar = 16
end subroutine model_size
!**************************************************************
!* AceGen 6.702 Windows (4 May 16) *
!* Co. J. Korelc 2013 16 Nov 19 17:49:23 *
!**************************************************************
! User : Full professional version
! Notebook : MainFile
! Evaluation time : 53 s Mode : Optimal
! Number of formulae : 715 Method: Automatic
! Subroutine : elastic size: 15988
! Total size of Mathematica code : 15988 subexpressions
! Total size of Fortran code : 36673 bytes
!******************* S U B R O U T I N E **********************
SUBROUTINE elastic(mpar,statev,Fnew,sigma,ddsdde,yielding,xguess)
USE SMSUtility
IMPLICIT NONE
INTEGER i01,i02
DOUBLE PRECISION v(1008),mpar(16),statev(58),Fnew(9),sigma(6),ddsdde(6,6),yielding,xguess(16)
v(991)=statev(38)*statev(39)+statev(42)*statev(43)+statev(45)*statev(46)
v(990)=statev(37)*statev(39)+statev(41)*statev(43)+statev(44)*statev(46)
v(989)=statev(37)*statev(38)+statev(41)*statev(42)+statev(44)*statev(45)
v(986)=statev(47)**2
v(985)=statev(48)**2
v(983)=statev(49)**2
v(982)=mpar(14)**2
v(984)=2d0*v(982)
v(954)=(2d0/3d0)+mpar(14)*statev(29)
v(953)=(-1d0/3d0)+mpar(14)*statev(35)
v(952)=(-1d0/3d0)+mpar(14)*statev(36)
v(951)=(-1d0/3d0)+mpar(14)*statev(40)
v(950)=(2d0/3d0)+mpar(14)*statev(30)
v(949)=(2d0/3d0)+mpar(14)*statev(31)
v(948)=2d0*mpar(14)
v(947)=0.5d0+mpar(14)*statev(32)
v(946)=0.5d0+mpar(14)*statev(33)
v(945)=0.5d0+mpar(14)*statev(34)
v(944)=statev(54)*statev(55)
v(943)=-(statev(54)*statev(58))
v(942)=-(statev(55)*statev(56))
v(941)=statev(56)*statev(58)
v(940)=1d0+statev(52)
v(939)=statev(57)*statev(58)
v(938)=-(statev(53)*statev(57))
v(937)=statev(53)*statev(54)
v(936)=1d0+statev(51)
v(935)=statev(56)*statev(57)
v(934)=statev(53)*statev(55)
v(933)=1d0+statev(50)
v(932)=statev(7)*statev(9)
v(931)=-(statev(6)*statev(7))
v(930)=statev(5)*statev(6)
v(929)=-(statev(5)*statev(9))
v(928)=1d0+statev(3)
v(927)=statev(4)*statev(5)
v(926)=-(statev(4)*statev(8))
v(925)=statev(8)*statev(9)
v(924)=1d0+statev(2)
v(923)=statev(4)*statev(6)
v(922)=statev(7)*statev(8)
v(921)=1d0+statev(1)
v(920)=statev(24)*statev(25)
v(919)=-(statev(25)*statev(26))
v(918)=statev(26)*statev(28)
v(917)=-(statev(24)*statev(28))
v(916)=1d0+statev(22)
v(915)=statev(27)*statev(28)
v(914)=-(statev(23)*statev(27))
v(913)=statev(23)*statev(24)
v(912)=1d0+statev(21)
v(911)=statev(23)*statev(25)
v(910)=statev(26)*statev(27)
v(909)=1d0+statev(20)
v(908)=statev(15)*statev(16)
v(907)=-(statev(16)*statev(17))
v(906)=statev(17)*statev(19)
v(905)=-(statev(15)*statev(19))
v(904)=1d0+statev(13)
v(903)=statev(18)*statev(19)
v(902)=-(statev(14)*statev(18))
v(901)=statev(14)*statev(15)
v(900)=1d0+statev(12)
v(899)=statev(14)*statev(16)
v(898)=statev(17)*statev(18)
v(897)=1d0+statev(11)
v(896)=statev(46)**2
v(895)=statev(45)**2
v(894)=statev(44)**2
v(893)=statev(43)**2
v(892)=statev(42)**2
v(891)=statev(41)**2
v(890)=statev(39)**2
v(889)=statev(38)**2
v(888)=statev(37)**2
v(887)=1d0/(Fnew(6)*(Fnew(4)*Fnew(5)-Fnew(2)*Fnew(7))+Fnew(3)*(Fnew(1)*Fnew(2)-Fnew(4)*Fnew(8))+(-(Fnew(1)*Fnew(5))&
&+Fnew(7)*Fnew(8))*Fnew(9))
v(996)=2d0*v(887)
v(199)=-(statev(15)*v(897))+v(898)
v(190)=-(statev(19)*v(897))+v(899)
v(198)=-(statev(17)*v(900))+v(901)
v(197)=v(897)*v(900)+v(902)
v(191)=-(statev(16)*v(900))+v(903)
v(195)=v(900)*v(904)+v(905)
v(194)=-(statev(14)*v(904))+v(906)
v(193)=v(897)*v(904)+v(907)
v(192)=-(statev(18)*v(904))+v(908)
v(222)=-(statev(24)*v(909))+v(910)
v(213)=-(statev(28)*v(909))+v(911)
v(221)=-(statev(26)*v(912))+v(913)
v(220)=v(909)*v(912)+v(914)
v(214)=-(statev(25)*v(912))+v(915)
v(218)=v(912)*v(916)+v(917)
v(217)=-(statev(23)*v(916))+v(918)
v(216)=v(909)*v(916)+v(919)
v(215)=-(statev(27)*v(916))+v(920)
v(104)=-(statev(5)*v(921))+v(922)
v(100)=-(statev(9)*v(921))+v(923)
v(108)=-(statev(6)*v(924))+v(925)
v(106)=v(921)*v(924)+v(926)
v(105)=-(statev(7)*v(924))+v(927)
v(110)=v(924)*v(928)+v(929)
v(109)=-(statev(8)*v(928))+v(930)
v(102)=v(921)*v(928)+v(931)
v(101)=-(statev(4)*v(928))+v(932)
v(260)=-(statev(58)*v(933))+v(934)
v(255)=-(statev(54)*v(933))+v(935)
v(257)=-(statev(56)*v(936))+v(937)
v(254)=v(933)*v(936)+v(938)
v(253)=-(statev(55)*v(936))+v(939)
v(262)=-(statev(53)*v(940))+v(941)
v(261)=v(933)*v(940)+v(942)
v(258)=v(936)*v(940)+v(943)
v(256)=-(statev(57)*v(940))+v(944)
v(289)=v(945)*v(948)
v(287)=v(946)*v(948)
v(284)=v(947)*v(948)
v(292)=(v(951)*v(951))
v(291)=(v(952)*v(952))
v(278)=(v(953)*v(953))
v(96)=1d0/(statev(9)*v(104)+statev(6)*v(105)+v(106)*v(928))
v(332)=v(104)*v(96)
v(331)=v(105)*v(96)
v(330)=v(106)*v(96)
v(329)=v(101)*v(96)
v(328)=v(100)*v(96)
v(327)=v(102)*v(96)
v(326)=v(108)*v(96)
v(325)=v(109)*v(96)
v(324)=v(110)*v(96)
v(97)=(Fnew(7)*v(108)+Fnew(4)*v(109)+Fnew(1)*v(110))*v(96)
v(992)=(v(97)*v(97))
v(955)=2d0*v(97)
v(339)=v(326)*v(955)
v(348)=-v(339)/3d0
v(336)=v(325)*v(955)
v(345)=-v(336)/3d0
v(333)=v(324)*v(955)
v(342)=-v(333)/3d0
v(98)=(Fnew(5)*v(100)+Fnew(8)*v(101)+Fnew(2)*v(102))*v(96)
v(956)=2d0*v(98)
v(358)=v(329)*v(956)
v(367)=-v(358)/3d0
v(355)=v(328)*v(956)
v(364)=-v(355)/3d0
v(352)=v(327)*v(956)
v(361)=-v(352)/3d0
v(99)=(Fnew(9)*v(104)+Fnew(6)*v(105)+Fnew(3)*v(106))*v(96)
v(957)=2d0*v(99)
v(377)=v(332)*v(957)
v(386)=-v(377)/3d0
v(374)=v(331)*v(957)
v(383)=-v(374)/3d0
v(371)=v(330)*v(957)
v(380)=-v(371)/3d0
v(103)=(Fnew(7)*v(100)+Fnew(1)*v(101)+Fnew(4)*v(102))*v(96)
v(993)=(v(103)*v(103))
v(958)=2d0*v(103)
v(393)=v(103)*v(326)+v(328)*v(97)
v(390)=v(103)*v(325)+v(327)*v(97)
v(387)=v(103)*v(324)+v(329)*v(97)
v(357)=v(328)*v(958)
v(366)=-v(357)/3d0
v(354)=v(327)*v(958)
v(363)=-v(354)/3d0
v(351)=v(329)*v(958)
v(360)=-v(351)/3d0
v(107)=(Fnew(2)*v(104)+Fnew(8)*v(105)+Fnew(5)*v(106))*v(96)
v(959)=2d0*v(107)
v(421)=v(107)*v(329)+v(331)*v(98)
v(418)=v(107)*v(328)+v(330)*v(98)
v(415)=v(107)*v(327)+v(332)*v(98)
v(376)=v(331)*v(959)
v(385)=-v(376)/3d0
v(373)=v(330)*v(959)
v(382)=-v(373)/3d0
v(370)=v(332)*v(959)
v(379)=-v(370)/3d0
v(111)=(Fnew(3)*v(108)+Fnew(9)*v(109)+Fnew(6)*v(110))*v(96)
v(960)=2d0*v(111)
v(449)=v(111)*v(332)+v(325)*v(99)
v(446)=v(111)*v(331)+v(324)*v(99)
v(443)=v(111)*v(330)+v(326)*v(99)
v(341)=v(325)*v(960)
v(350)=-v(341)/3d0
v(338)=v(324)*v(960)
v(347)=-v(338)/3d0
v(335)=v(326)*v(960)
v(344)=-v(335)/3d0
v(112)=(Fnew(4)*v(104)+Fnew(1)*v(105)+Fnew(7)*v(106))*v(96)
v(995)=v(112)*v(958)
v(994)=(v(112)*v(112))
v(961)=2d0*v(112)
v(447)=v(112)*v(326)+v(330)*v(97)
v(444)=v(112)*v(325)+v(332)*v(97)
v(441)=v(112)*v(324)+v(331)*v(97)
v(420)=v(112)*v(328)+v(103)*v(330)
v(417)=v(112)*v(327)+v(103)*v(332)
v(414)=v(112)*v(329)+v(103)*v(331)
v(375)=v(330)*v(961)
v(384)=-v(375)/3d0
v(372)=v(332)*v(961)
v(381)=-v(372)/3d0
v(369)=v(331)*v(961)
v(378)=-v(369)/3d0
v(113)=(Fnew(5)*v(108)+Fnew(2)*v(109)+Fnew(8)*v(110))*v(96)
v(962)=2d0*v(113)
v(448)=v(107)*v(324)+v(113)*v(331)
v(445)=v(107)*v(326)+v(113)*v(330)
v(442)=v(107)*v(325)+v(113)*v(332)
v(394)=v(113)*v(329)+v(324)*v(98)
v(391)=v(113)*v(328)+v(326)*v(98)
v(388)=v(113)*v(327)+v(325)*v(98)
v(340)=v(324)*v(962)
v(349)=-v(340)/3d0
v(337)=v(326)*v(962)
v(346)=-v(337)/3d0
v(334)=v(325)*v(962)
v(343)=-v(334)/3d0
v(114)=(Fnew(3)*v(100)+Fnew(6)*v(101)+Fnew(9)*v(102))*v(96)
v(963)=2d0*v(114)
v(422)=v(114)*v(332)+v(327)*v(99)
v(419)=v(114)*v(331)+v(329)*v(99)
v(416)=v(114)*v(330)+v(328)*v(99)
v(395)=v(114)*v(325)+v(111)*v(327)
v(392)=v(114)*v(324)+v(111)*v(329)
v(389)=v(114)*v(326)+v(111)*v(328)
v(359)=v(327)*v(963)
v(368)=-v(359)/3d0
v(356)=v(329)*v(963)
v(365)=-v(356)/3d0
v(353)=v(328)*v(963)
v(362)=-v(353)/3d0
v(115)=(v(111)*v(111))+(v(113)*v(113))+v(992)
v(135)=-v(115)/3d0
v(116)=(v(114)*v(114))+(v(98)*v(98))+v(993)
v(136)=-v(116)/3d0
v(117)=(v(107)*v(107))+v(994)+(v(99)*v(99))
v(538)=(2d0/3d0)*v(117)+v(135)+v(136)
v(128)=-v(117)/3d0
v(548)=(2d0/3d0)*v(116)+v(128)+v(135)
v(528)=(2d0/3d0)*v(115)+v(128)+v(136)
v(118)=v(111)*v(114)+v(103)*v(97)+v(113)*v(98)
v(964)=2d0*v(118)
v(404)=v(395)*v(964)
v(413)=v(116)*v(341)+v(115)*v(359)-v(404)
v(403)=v(394)*v(964)
v(412)=v(116)*v(340)+v(115)*v(358)-v(403)
v(402)=v(393)*v(964)
v(411)=v(116)*v(339)+v(115)*v(357)-v(402)
v(401)=v(392)*v(964)
v(410)=v(116)*v(338)+v(115)*v(356)-v(401)
v(400)=v(391)*v(964)
v(409)=v(116)*v(337)+v(115)*v(355)-v(400)
v(399)=v(390)*v(964)
v(408)=v(116)*v(336)+v(115)*v(354)-v(399)
v(398)=v(389)*v(964)
v(407)=v(116)*v(335)+v(115)*v(353)-v(398)
v(397)=v(388)*v(964)
v(406)=v(116)*v(334)+v(115)*v(352)-v(397)
v(396)=v(387)*v(964)
v(405)=v(116)*v(333)+v(115)*v(351)-v(396)
v(134)=(v(118)*v(118))
v(150)=v(115)*v(116)-v(134)
v(119)=v(103)*v(112)+v(107)*v(98)+v(114)*v(99)
v(965)=2d0*v(119)
v(498)=v(119)*v(964)
v(431)=v(422)*v(965)
v(440)=v(117)*v(359)+v(116)*v(377)-v(431)
v(430)=v(421)*v(965)
v(439)=v(117)*v(358)+v(116)*v(376)-v(430)
v(429)=v(420)*v(965)
v(438)=v(117)*v(357)+v(116)*v(375)-v(429)
v(428)=v(419)*v(965)
v(437)=v(117)*v(356)+v(116)*v(374)-v(428)
v(427)=v(418)*v(965)
v(436)=v(117)*v(355)+v(116)*v(373)-v(427)
v(426)=v(417)*v(965)
v(435)=v(117)*v(354)+v(116)*v(372)-v(426)
v(425)=v(416)*v(965)
v(434)=v(117)*v(353)+v(116)*v(371)-v(425)
v(424)=v(415)*v(965)
v(433)=v(117)*v(352)+v(116)*v(370)-v(424)
v(423)=v(414)*v(965)
v(432)=v(117)*v(351)+v(116)*v(369)-v(423)
v(122)=(v(119)*v(119))
v(139)=v(116)*v(117)-v(122)
v(120)=v(107)*v(113)+v(112)*v(97)+v(111)*v(99)
v(966)=2d0*v(120)
v(497)=v(120)*v(964)
v(495)=v(120)*v(965)
v(485)=v(449)*v(966)
v(494)=v(117)*v(341)+v(115)*v(377)-v(485)
v(484)=v(448)*v(966)
v(493)=v(117)*v(340)+v(115)*v(376)-v(484)
v(483)=v(447)*v(966)
v(492)=v(117)*v(339)+v(115)*v(375)-v(483)
v(482)=v(446)*v(966)
v(491)=v(117)*v(338)+v(115)*v(374)-v(482)
v(481)=v(445)*v(966)
v(490)=v(117)*v(337)+v(115)*v(373)-v(481)
v(480)=v(444)*v(966)
v(489)=v(117)*v(336)+v(115)*v(372)-v(480)
v(479)=v(443)*v(966)
v(488)=v(117)*v(335)+v(115)*v(371)-v(479)
v(478)=v(442)*v(966)
v(487)=v(117)*v(334)+v(115)*v(370)-v(478)
v(477)=v(441)*v(966)
v(486)=v(117)*v(333)+v(115)*v(369)-v(477)
v(476)=-(v(118)*v(377))-v(117)*v(395)+v(120)*v(422)+v(119)*v(449)
v(475)=-(v(118)*v(376))-v(117)*v(394)+v(120)*v(421)+v(119)*v(448)
v(474)=-(v(118)*v(375))-v(117)*v(393)+v(120)*v(420)+v(119)*v(447)
v(473)=-(v(118)*v(374))-v(117)*v(392)+v(120)*v(419)+v(119)*v(446)
v(472)=-(v(118)*v(373))-v(117)*v(391)+v(120)*v(418)+v(119)*v(445)
v(471)=-(v(118)*v(372))-v(117)*v(390)+v(120)*v(417)+v(119)*v(444)
v(470)=-(v(118)*v(371))-v(117)*v(389)+v(120)*v(416)+v(119)*v(443)
v(469)=-(v(118)*v(370))-v(117)*v(388)+v(120)*v(415)+v(119)*v(442)
v(468)=-(v(118)*v(369))-v(117)*v(387)+v(120)*v(414)+v(119)*v(441)
v(467)=-(v(119)*v(341))+v(120)*v(395)-v(115)*v(422)+v(118)*v(449)
v(466)=-(v(119)*v(340))+v(120)*v(394)-v(115)*v(421)+v(118)*v(448)
v(465)=-(v(119)*v(339))+v(120)*v(393)-v(115)*v(420)+v(118)*v(447)
v(464)=-(v(119)*v(338))+v(120)*v(392)-v(115)*v(419)+v(118)*v(446)
v(463)=-(v(119)*v(337))+v(120)*v(391)-v(115)*v(418)+v(118)*v(445)
v(462)=-(v(119)*v(336))+v(120)*v(390)-v(115)*v(417)+v(118)*v(444)
v(461)=-(v(119)*v(335))+v(120)*v(389)-v(115)*v(416)+v(118)*v(443)
v(460)=-(v(119)*v(334))+v(120)*v(388)-v(115)*v(415)+v(118)*v(442)
v(459)=-(v(119)*v(333))+v(120)*v(387)-v(115)*v(414)+v(118)*v(441)
v(458)=-(v(120)*v(359))+v(119)*v(395)+v(118)*v(422)-v(116)*v(449)
v(457)=-(v(120)*v(358))+v(119)*v(394)+v(118)*v(421)-v(116)*v(448)
v(456)=-(v(120)*v(357))+v(119)*v(393)+v(118)*v(420)-v(116)*v(447)
v(455)=-(v(120)*v(356))+v(119)*v(392)+v(118)*v(419)-v(116)*v(446)
v(454)=-(v(120)*v(355))+v(119)*v(391)+v(118)*v(418)-v(116)*v(445)
v(453)=-(v(120)*v(354))+v(119)*v(390)+v(118)*v(417)-v(116)*v(444)
v(452)=-(v(120)*v(353))+v(119)*v(389)+v(118)*v(416)-v(116)*v(443)
v(451)=-(v(120)*v(352))+v(119)*v(388)+v(118)*v(415)-v(116)*v(442)
v(450)=-(v(120)*v(351))+v(119)*v(387)+v(118)*v(414)-v(116)*v(441)
v(151)=v(118)*v(119)-v(116)*v(120)
v(146)=-(v(115)*v(119))+v(118)*v(120)
v(141)=-(v(117)*v(118))+v(119)*v(120)
v(126)=(v(120)*v(120))
v(506)=-(v(122)*v(341))-v(126)*v(359)+v(150)*v(377)+v(117)*v(413)-v(115)*v(431)-v(116)*v(485)+v(395)*v(495)+v(422)*v&
&(497)+v(449)*v(498)
v(505)=-(v(122)*v(340))-v(126)*v(358)+v(150)*v(376)+v(117)*v(412)-v(115)*v(430)-v(116)*v(484)+v(394)*v(495)+v(421)*v&
&(497)+v(448)*v(498)
v(504)=-(v(122)*v(339))-v(126)*v(357)+v(150)*v(375)+v(117)*v(411)-v(115)*v(429)-v(116)*v(483)+v(393)*v(495)+v(420)*v&
&(497)+v(447)*v(498)
v(503)=-(v(122)*v(338))-v(126)*v(356)+v(150)*v(374)+v(117)*v(410)-v(115)*v(428)-v(116)*v(482)+v(392)*v(495)+v(419)*v&
&(497)+v(446)*v(498)
v(502)=-(v(122)*v(337))-v(126)*v(355)+v(150)*v(373)+v(117)*v(409)-v(115)*v(427)-v(116)*v(481)+v(391)*v(495)+v(418)*v&
&(497)+v(445)*v(498)
v(501)=-(v(122)*v(336))-v(126)*v(354)+v(150)*v(372)+v(117)*v(408)-v(115)*v(426)-v(116)*v(480)+v(390)*v(495)+v(417)*v&
&(497)+v(444)*v(498)
v(500)=-(v(122)*v(335))-v(126)*v(353)+v(150)*v(371)+v(117)*v(407)-v(115)*v(425)-v(116)*v(479)+v(389)*v(495)+v(416)*v&
&(497)+v(443)*v(498)
v(499)=-(v(122)*v(334))-v(126)*v(352)+v(150)*v(370)+v(117)*v(406)-v(115)*v(424)-v(116)*v(478)+v(388)*v(495)+v(415)*v&
&(497)+v(442)*v(498)
v(496)=-(v(122)*v(333))-v(126)*v(351)+v(150)*v(369)+v(117)*v(405)-v(115)*v(423)-v(116)*v(477)+v(387)*v(495)+v(414)*v&
&(497)+v(441)*v(498)
v(145)=v(115)*v(117)-v(126)
v(123)=-(v(115)*v(122))-v(116)*v(126)+v(117)*v(150)+v(118)*v(495)
v(975)=v(141)/v(123)
v(569)=1d0/v(123)**0.23333333333333334d1
v(967)=(-4d0/3d0)*v(569)
v(577)=v(506)*v(967)
v(576)=v(505)*v(967)
v(575)=v(504)*v(967)
v(574)=v(503)*v(967)
v(573)=v(502)*v(967)
v(572)=v(501)*v(967)
v(571)=v(500)*v(967)
v(570)=v(499)*v(967)
v(568)=v(496)*v(967)
v(559)=1d0/v(123)**2
v(567)=-(v(506)*v(559))
v(566)=-(v(505)*v(559))
v(565)=-(v(504)*v(559))
v(564)=-(v(503)*v(559))
v(563)=-(v(502)*v(559))
v(562)=-(v(501)*v(559))
v(561)=-(v(500)*v(559))
v(560)=-(v(499)*v(559))
v(558)=-(v(496)*v(559))
v(518)=1d0/v(123)**0.13333333333333333d1
v(971)=mpar(1)*v(518)
v(968)=-v(518)/3d0
v(527)=v(506)*v(968)
v(526)=v(505)*v(968)
v(525)=v(504)*v(968)
v(524)=v(503)*v(968)
v(523)=v(502)*v(968)
v(522)=v(501)*v(968)
v(521)=v(500)*v(968)
v(520)=v(499)*v(968)
v(519)=v(496)*v(968)
v(507)=sqrt(v(123))
v(969)=mpar(2)*(1d0-1d0/(2d0*v(507)))
v(517)=v(506)*v(969)
v(516)=v(505)*v(969)
v(515)=v(504)*v(969)
v(514)=v(503)*v(969)
v(513)=v(502)*v(969)
v(512)=v(501)*v(969)
v(511)=v(500)*v(969)
v(510)=v(499)*v(969)
v(508)=v(496)*v(969)
v(130)=mpar(2)*(v(123)-v(507))
v(129)=1d0/v(123)**0.3333333333333333d0
v(970)=mpar(1)*v(129)
v(557)=v(517)+mpar(1)*(v(129)*(v(350)+(2d0/3d0)*v(359)+v(386))+v(527)*v(548))
v(556)=v(516)+mpar(1)*(v(129)*(v(349)+(2d0/3d0)*v(358)+v(385))+v(526)*v(548))
v(555)=v(515)+mpar(1)*(v(129)*(v(348)+(2d0/3d0)*v(357)+v(384))+v(525)*v(548))
v(554)=v(514)+mpar(1)*(v(129)*(v(347)+(2d0/3d0)*v(356)+v(383))+v(524)*v(548))
v(553)=v(513)+mpar(1)*(v(129)*(v(346)+(2d0/3d0)*v(355)+v(382))+v(523)*v(548))
v(552)=v(512)+mpar(1)*(v(129)*(v(345)+(2d0/3d0)*v(354)+v(381))+v(522)*v(548))
v(551)=v(511)+mpar(1)*(v(129)*(v(344)+(2d0/3d0)*v(353)+v(380))+v(521)*v(548))
v(550)=v(510)+mpar(1)*(v(129)*(v(343)+(2d0/3d0)*v(352)+v(379))+v(520)*v(548))
v(549)=v(508)+mpar(1)*(v(129)*(v(342)+(2d0/3d0)*v(351)+v(378))+v(519)*v(548))
v(547)=v(517)+mpar(1)*(v(129)*(v(350)+v(368)+(2d0/3d0)*v(377))+v(527)*v(538))
v(546)=v(516)+mpar(1)*(v(129)*(v(349)+v(367)+(2d0/3d0)*v(376))+v(526)*v(538))
v(545)=v(515)+mpar(1)*(v(129)*(v(348)+v(366)+(2d0/3d0)*v(375))+v(525)*v(538))
v(544)=v(514)+mpar(1)*(v(129)*(v(347)+v(365)+(2d0/3d0)*v(374))+v(524)*v(538))
v(543)=v(513)+mpar(1)*(v(129)*(v(346)+v(364)+(2d0/3d0)*v(373))+v(523)*v(538))
v(542)=v(512)+mpar(1)*(v(129)*(v(345)+v(363)+(2d0/3d0)*v(372))+v(522)*v(538))
v(541)=v(511)+mpar(1)*(v(129)*(v(344)+v(362)+(2d0/3d0)*v(371))+v(521)*v(538))
v(540)=v(510)+mpar(1)*(v(129)*(v(343)+v(361)+(2d0/3d0)*v(370))+v(520)*v(538))
v(539)=v(508)+mpar(1)*(v(129)*(v(342)+v(360)+(2d0/3d0)*v(369))+v(519)*v(538))
v(537)=v(517)+mpar(1)*(v(129)*((2d0/3d0)*v(341)+v(368)+v(386))+v(527)*v(528))
v(536)=v(516)+mpar(1)*(v(129)*((2d0/3d0)*v(340)+v(367)+v(385))+v(526)*v(528))
v(535)=v(515)+mpar(1)*(v(129)*((2d0/3d0)*v(339)+v(366)+v(384))+v(525)*v(528))
v(534)=v(514)+mpar(1)*(v(129)*((2d0/3d0)*v(338)+v(365)+v(383))+v(524)*v(528))
v(533)=v(513)+mpar(1)*(v(129)*((2d0/3d0)*v(337)+v(364)+v(382))+v(523)*v(528))
v(532)=v(512)+mpar(1)*(v(129)*((2d0/3d0)*v(336)+v(363)+v(381))+v(522)*v(528))
v(531)=v(511)+mpar(1)*(v(129)*((2d0/3d0)*v(335)+v(362)+v(380))+v(521)*v(528))
v(530)=v(510)+mpar(1)*(v(129)*((2d0/3d0)*v(334)+v(361)+v(379))+v(520)*v(528))
v(529)=v(508)+mpar(1)*(v(129)*((2d0/3d0)*v(333)+v(360)+v(378))+v(519)*v(528))
v(152)=v(130)+v(528)*v(970)
v(977)=v(139)*v(152)
v(974)=v(151)*v(152)
v(147)=v(130)+v(538)*v(970)
v(973)=v(147)*v(150)
v(972)=v(146)*v(147)
v(142)=v(130)+v(548)*v(970)
v(976)=v(142)*v(145)
v(613)=mpar(1)*(v(395)*v(518)+v(118)*v(577))
v(612)=mpar(1)*(v(394)*v(518)+v(118)*v(576))
v(611)=mpar(1)*(v(393)*v(518)+v(118)*v(575))
v(610)=mpar(1)*(v(392)*v(518)+v(118)*v(574))
v(609)=mpar(1)*(v(391)*v(518)+v(118)*v(573))
v(608)=mpar(1)*(v(390)*v(518)+v(118)*v(572))
v(607)=mpar(1)*(v(389)*v(518)+v(118)*v(571))
v(606)=mpar(1)*(v(388)*v(518)+v(118)*v(570))
v(605)=mpar(1)*(v(387)*v(518)+v(118)*v(568))
v(604)=mpar(1)*(v(458)*v(518)+v(151)*v(577))
v(603)=mpar(1)*(v(457)*v(518)+v(151)*v(576))
v(602)=mpar(1)*(v(456)*v(518)+v(151)*v(575))
v(601)=mpar(1)*(v(455)*v(518)+v(151)*v(574))
v(600)=mpar(1)*(v(454)*v(518)+v(151)*v(573))
v(599)=mpar(1)*(v(453)*v(518)+v(151)*v(572))
v(598)=mpar(1)*(v(452)*v(518)+v(151)*v(571))
v(597)=mpar(1)*(v(451)*v(518)+v(151)*v(570))
v(596)=mpar(1)*(v(450)*v(518)+v(151)*v(568))
v(595)=mpar(1)*(v(422)*v(518)+v(119)*v(577))
v(594)=mpar(1)*(v(421)*v(518)+v(119)*v(576))
v(593)=mpar(1)*(v(420)*v(518)+v(119)*v(575))
v(592)=mpar(1)*(v(419)*v(518)+v(119)*v(574))
v(591)=mpar(1)*(v(418)*v(518)+v(119)*v(573))
v(590)=mpar(1)*(v(417)*v(518)+v(119)*v(572))
v(589)=mpar(1)*(v(416)*v(518)+v(119)*v(571))
v(588)=mpar(1)*(v(415)*v(518)+v(119)*v(570))
v(587)=mpar(1)*(v(414)*v(518)+v(119)*v(568))
v(586)=mpar(1)*(v(449)*v(518)+v(120)*v(577))
v(585)=mpar(1)*(v(448)*v(518)+v(120)*v(576))
v(584)=mpar(1)*(v(447)*v(518)+v(120)*v(575))
v(583)=mpar(1)*(v(446)*v(518)+v(120)*v(574))
v(582)=mpar(1)*(v(445)*v(518)+v(120)*v(573))
v(581)=mpar(1)*(v(444)*v(518)+v(120)*v(572))
v(580)=mpar(1)*(v(443)*v(518)+v(120)*v(571))
v(579)=mpar(1)*(v(442)*v(518)+v(120)*v(570))
v(578)=mpar(1)*(v(441)*v(518)+v(120)*v(568))
v(149)=v(120)*v(971)
v(144)=v(119)*v(971)
v(685)=v(149)*v(476)+v(144)*v(494)+(v(147)*v(467)+v(146)*v(547))/v(123)+v(141)*v(586)+v(145)*v(595)+v(567)*v(972)
v(684)=v(149)*v(475)+v(144)*v(493)+(v(147)*v(466)+v(146)*v(546))/v(123)+v(141)*v(585)+v(145)*v(594)+v(566)*v(972)
v(683)=v(149)*v(474)+v(144)*v(492)+(v(147)*v(465)+v(146)*v(545))/v(123)+v(141)*v(584)+v(145)*v(593)+v(565)*v(972)
v(682)=v(149)*v(473)+v(144)*v(491)+(v(147)*v(464)+v(146)*v(544))/v(123)+v(141)*v(583)+v(145)*v(592)+v(564)*v(972)
v(681)=v(149)*v(472)+v(144)*v(490)+(v(147)*v(463)+v(146)*v(543))/v(123)+v(141)*v(582)+v(145)*v(591)+v(563)*v(972)
v(680)=v(149)*v(471)+v(144)*v(489)+(v(147)*v(462)+v(146)*v(542))/v(123)+v(141)*v(581)+v(145)*v(590)+v(562)*v(972)
v(679)=v(149)*v(470)+v(144)*v(488)+(v(147)*v(461)+v(146)*v(541))/v(123)+v(141)*v(580)+v(145)*v(589)+v(561)*v(972)
v(678)=v(149)*v(469)+v(144)*v(487)+(v(147)*v(460)+v(146)*v(540))/v(123)+v(141)*v(579)+v(145)*v(588)+v(560)*v(972)
v(677)=v(149)*v(468)+v(144)*v(486)+(v(147)*v(459)+v(146)*v(539))/v(123)+v(141)*v(578)+v(145)*v(587)+v(558)*v(972)
v(622)=v(144)*v(467)+v(146)*v(595)
v(621)=v(144)*v(466)+v(146)*v(594)
v(620)=v(144)*v(465)+v(146)*v(593)
v(619)=v(144)*v(464)+v(146)*v(592)
v(618)=v(144)*v(463)+v(146)*v(591)
v(617)=v(144)*v(462)+v(146)*v(590)
v(616)=v(144)*v(461)+v(146)*v(589)
v(615)=v(144)*v(460)+v(146)*v(588)
v(614)=v(144)*v(459)+v(146)*v(587)
v(140)=v(151)*v(971)
v(631)=v(140)*v(449)+v(120)*v(604)
v(667)=(v(147)*v(413)+v(150)*v(547))/v(123)+v(622)+v(631)+v(567)*v(973)
v(630)=v(140)*v(448)+v(120)*v(603)
v(666)=(v(147)*v(412)+v(150)*v(546))/v(123)+v(621)+v(630)+v(566)*v(973)
v(629)=v(140)*v(447)+v(120)*v(602)
v(665)=(v(147)*v(411)+v(150)*v(545))/v(123)+v(620)+v(629)+v(565)*v(973)
v(628)=v(140)*v(446)+v(120)*v(601)
v(664)=(v(147)*v(410)+v(150)*v(544))/v(123)+v(619)+v(628)+v(564)*v(973)
v(627)=v(140)*v(445)+v(120)*v(600)
v(663)=(v(147)*v(409)+v(150)*v(543))/v(123)+v(618)+v(627)+v(563)*v(973)
v(626)=v(140)*v(444)+v(120)*v(599)
v(662)=(v(147)*v(408)+v(150)*v(542))/v(123)+v(617)+v(626)+v(562)*v(973)
v(625)=v(140)*v(443)+v(120)*v(598)
v(661)=(v(147)*v(407)+v(150)*v(541))/v(123)+v(616)+v(625)+v(561)*v(973)
v(624)=v(140)*v(442)+v(120)*v(597)
v(660)=(v(147)*v(406)+v(150)*v(540))/v(123)+v(615)+v(624)+v(560)*v(973)
v(623)=v(140)*v(441)+v(120)*v(596)
v(659)=(v(147)*v(405)+v(150)*v(539))/v(123)+v(614)+v(623)+v(558)*v(973)
v(138)=v(118)*v(971)
v(724)=v(149)*v(413)+v(138)*v(467)+(v(152)*v(458)+v(151)*v(537))/v(123)+v(150)*v(586)+v(146)*v(613)+v(567)*v(974)
v(723)=v(149)*v(412)+v(138)*v(466)+(v(152)*v(457)+v(151)*v(536))/v(123)+v(150)*v(585)+v(146)*v(612)+v(566)*v(974)
v(722)=v(149)*v(411)+v(138)*v(465)+(v(152)*v(456)+v(151)*v(535))/v(123)+v(150)*v(584)+v(146)*v(611)+v(565)*v(974)
v(721)=v(149)*v(410)+v(138)*v(464)+(v(152)*v(455)+v(151)*v(534))/v(123)+v(150)*v(583)+v(146)*v(610)+v(564)*v(974)
v(720)=v(149)*v(409)+v(138)*v(463)+(v(152)*v(454)+v(151)*v(533))/v(123)+v(150)*v(582)+v(146)*v(609)+v(563)*v(974)
v(719)=v(149)*v(408)+v(138)*v(462)+(v(152)*v(453)+v(151)*v(532))/v(123)+v(150)*v(581)+v(146)*v(608)+v(562)*v(974)
v(718)=v(149)*v(407)+v(138)*v(461)+(v(152)*v(452)+v(151)*v(531))/v(123)+v(150)*v(580)+v(146)*v(607)+v(561)*v(974)
v(717)=v(149)*v(406)+v(138)*v(460)+(v(152)*v(451)+v(151)*v(530))/v(123)+v(150)*v(579)+v(146)*v(606)+v(560)*v(974)
v(716)=v(149)*v(405)+v(138)*v(459)+(v(152)*v(450)+v(151)*v(529))/v(123)+v(150)*v(578)+v(146)*v(605)+v(558)*v(974)
v(676)=v(140)*v(422)+v(138)*v(440)+v(142)*(v(476)/v(123)+v(141)*v(567))+v(119)*v(604)+v(139)*v(613)+v(557)*v(975)
v(675)=v(140)*v(421)+v(138)*v(439)+v(142)*(v(475)/v(123)+v(141)*v(566))+v(119)*v(603)+v(139)*v(612)+v(556)*v(975)
v(674)=v(140)*v(420)+v(138)*v(438)+v(142)*(v(474)/v(123)+v(141)*v(565))+v(119)*v(602)+v(139)*v(611)+v(555)*v(975)
v(673)=v(140)*v(419)+v(138)*v(437)+v(142)*(v(473)/v(123)+v(141)*v(564))+v(119)*v(601)+v(139)*v(610)+v(554)*v(975)
v(672)=v(140)*v(418)+v(138)*v(436)+v(142)*(v(472)/v(123)+v(141)*v(563))+v(119)*v(600)+v(139)*v(609)+v(553)*v(975)
v(671)=v(140)*v(417)+v(138)*v(435)+v(142)*(v(471)/v(123)+v(141)*v(562))+v(119)*v(599)+v(139)*v(608)+v(552)*v(975)
v(670)=v(140)*v(416)+v(138)*v(434)+v(142)*(v(470)/v(123)+v(141)*v(561))+v(119)*v(598)+v(139)*v(607)+v(551)*v(975)
v(669)=v(140)*v(415)+v(138)*v(433)+v(142)*(v(469)/v(123)+v(141)*v(560))+v(119)*v(597)+v(139)*v(606)+v(550)*v(975)
v(668)=v(140)*v(414)+v(138)*v(432)+v(142)*(v(468)/v(123)+v(141)*v(558))+v(119)*v(596)+v(139)*v(605)+v(549)*v(975)
v(640)=v(138)*v(476)+v(141)*v(613)
v(658)=(v(142)*v(494)+v(145)*v(557))/v(123)+v(622)+v(640)+v(567)*v(976)
v(649)=(v(152)*v(440)+v(139)*v(537))/v(123)+v(631)+v(640)+v(567)*v(977)
v(639)=v(138)*v(475)+v(141)*v(612)
v(657)=(v(142)*v(493)+v(145)*v(556))/v(123)+v(621)+v(639)+v(566)*v(976)
v(648)=(v(152)*v(439)+v(139)*v(536))/v(123)+v(630)+v(639)+v(566)*v(977)
v(638)=v(138)*v(474)+v(141)*v(611)
v(656)=(v(142)*v(492)+v(145)*v(555))/v(123)+v(620)+v(638)+v(565)*v(976)
v(647)=(v(152)*v(438)+v(139)*v(535))/v(123)+v(629)+v(638)+v(565)*v(977)
v(637)=v(138)*v(473)+v(141)*v(610)
v(655)=(v(142)*v(491)+v(145)*v(554))/v(123)+v(619)+v(637)+v(564)*v(976)
v(646)=(v(152)*v(437)+v(139)*v(534))/v(123)+v(628)+v(637)+v(564)*v(977)
v(636)=v(138)*v(472)+v(141)*v(609)
v(654)=(v(142)*v(490)+v(145)*v(553))/v(123)+v(618)+v(636)+v(563)*v(976)
v(645)=(v(152)*v(436)+v(139)*v(533))/v(123)+v(627)+v(636)+v(563)*v(977)
v(635)=v(138)*v(471)+v(141)*v(608)
v(653)=(v(142)*v(489)+v(145)*v(552))/v(123)+v(617)+v(635)+v(562)*v(976)
v(644)=(v(152)*v(435)+v(139)*v(532))/v(123)+v(626)+v(635)+v(562)*v(977)
v(634)=v(138)*v(470)+v(141)*v(607)
v(652)=(v(142)*v(488)+v(145)*v(551))/v(123)+v(616)+v(634)+v(561)*v(976)
v(643)=(v(152)*v(434)+v(139)*v(531))/v(123)+v(625)+v(634)+v(561)*v(977)
v(633)=v(138)*v(469)+v(141)*v(606)
v(651)=(v(142)*v(487)+v(145)*v(550))/v(123)+v(615)+v(633)+v(560)*v(976)
v(642)=(v(152)*v(433)+v(139)*v(530))/v(123)+v(624)+v(633)+v(560)*v(977)
v(632)=v(138)*v(468)+v(141)*v(605)
v(650)=(v(142)*v(486)+v(145)*v(549))/v(123)+v(614)+v(632)+v(558)*v(976)
v(641)=(v(152)*v(432)+v(139)*v(529))/v(123)+v(623)+v(632)+v(558)*v(977)
v(133)=v(144)*v(146)
v(132)=v(120)*v(140)
v(125)=v(138)*v(141)
v(124)=v(125)+v(132)+v(977)/v(123)
v(131)=v(125)+v(133)+v(976)/v(123)
v(137)=v(132)+v(133)+v(973)/v(123)
v(143)=v(138)*v(139)+v(119)*v(140)+v(142)*v(975)
v(148)=v(144)*v(145)+v(141)*v(149)+v(972)/v(123)
v(705)=v(143)*v(325)+v(131)*v(327)+v(148)*v(332)
v(708)=v(113)*v(669)+v(107)*v(678)+v(705)+v(651)*v(98)
v(701)=v(143)*v(324)+v(131)*v(329)+v(148)*v(331)
v(714)=v(113)*v(675)+v(107)*v(684)+v(701)+v(657)*v(98)
v(697)=v(143)*v(326)+v(131)*v(328)+v(148)*v(330)
v(711)=v(113)*v(672)+v(107)*v(681)+v(697)+v(654)*v(98)
v(692)=v(103)*v(656)+v(112)*v(683)+v(697)+v(674)*v(97)
v(689)=v(103)*v(653)+v(112)*v(680)+v(705)+v(671)*v(97)
v(686)=v(103)*v(650)+v(112)*v(677)+v(701)+v(668)*v(97)
v(168)=v(103)*v(131)+v(112)*v(148)+v(143)*v(97)
v(164)=v(114)*v(131)+v(111)*v(143)+v(148)*v(99)
v(160)=v(113)*v(143)+v(107)*v(148)+v(131)*v(98)
v(153)=v(138)*v(146)+v(149)*v(150)+v(974)/v(123)
v(765)=v(124)*v(325)+v(143)*v(327)+v(153)*v(332)
v(777)=v(113)*v(642)+v(107)*v(717)+v(765)+v(669)*v(98)
v(761)=v(124)*v(324)+v(143)*v(329)+v(153)*v(331)
v(783)=v(113)*v(648)+v(107)*v(723)+v(761)+v(675)*v(98)
v(757)=v(124)*v(326)+v(143)*v(328)+v(153)*v(330)
v(780)=v(113)*v(645)+v(107)*v(720)+v(757)+v(672)*v(98)
v(753)=v(153)*v(325)+v(148)*v(327)+v(137)*v(332)
v(768)=v(107)*v(660)+v(113)*v(717)+v(753)+v(678)*v(98)
v(749)=v(153)*v(324)+v(148)*v(329)+v(137)*v(331)
v(774)=v(107)*v(666)+v(113)*v(723)+v(749)+v(684)*v(98)
v(745)=v(153)*v(326)+v(148)*v(328)+v(137)*v(330)
v(771)=v(107)*v(663)+v(113)*v(720)+v(745)+v(681)*v(98)
v(740)=v(112)*v(665)+v(103)*v(683)+v(745)+v(722)*v(97)
v(737)=v(112)*v(662)+v(103)*v(680)+v(753)+v(719)*v(97)
v(734)=v(112)*v(659)+v(103)*v(677)+v(749)+v(716)*v(97)
v(731)=v(103)*v(674)+v(112)*v(722)+v(757)+v(647)*v(97)
v(728)=v(103)*v(671)+v(112)*v(719)+v(765)+v(644)*v(97)
v(725)=v(103)*v(668)+v(112)*v(716)+v(761)+v(641)*v(97)
v(170)=v(103)*v(143)+v(112)*v(153)+v(124)*v(97)
v(169)=v(112)*v(137)+v(103)*v(148)+v(153)*v(97)
v(166)=v(114)*v(148)+v(111)*v(153)+v(137)*v(99)
v(165)=v(111)*v(124)+v(114)*v(143)+v(153)*v(99)
v(162)=v(107)*v(137)+v(113)*v(153)+v(148)*v(98)
v(161)=v(113)*v(124)+v(107)*v(153)+v(143)*v(98)
v(833)=v(161)*v(324)+v(160)*v(329)+v(162)*v(331)
v(828)=v(161)*v(326)+v(160)*v(328)+v(162)*v(330)
v(806)=v(161)*v(325)+v(160)*v(327)+v(162)*v(332)
v(163)=v(103)*v(160)+v(112)*v(162)+v(161)*v(97)
v(997)=v(163)*v(887)
v(167)=v(113)*v(165)+v(107)*v(166)+v(164)*v(98)
v(999)=v(167)*v(887)
v(171)=v(114)*v(168)+v(111)*v(170)+v(169)*v(99)
v(998)=v(171)*v(887)
v(179)=1d0/(statev(16)*v(198)+statev(19)*v(199)+v(197)*v(904))**2
v(186)=-(v(179)*((v(197)*v(197))+(v(198)*v(198))+(v(199)*v(199))))
v(184)=1d0/v(179)**0.3333333333333333d0
v(980)=-(mpar(9)*v(184))
v(981)=v(179)*v(980)
v(183)=v(179)*((v(191)*v(191))+(v(192)*v(192))+(v(195)*v(195)))
v(188)=-v(183)/3d0
v(182)=-(v(179)*((v(190)*v(190))+(v(193)*v(193))+(v(194)*v(194))))
v(187)=v(182)/3d0
v(181)=v(186)/3d0
v(202)=1d0/(statev(25)*v(221)+statev(28)*v(222)+v(220)*v(916))**2
v(209)=-(v(202)*((v(220)*v(220))+(v(221)*v(221))+(v(222)*v(222))))
v(207)=1d0/v(202)**0.3333333333333333d0
v(978)=mpar(11)*v(207)
v(979)=v(202)*v(978)
v(206)=v(202)*((v(214)*v(214))+(v(215)*v(215))+(v(218)*v(218)))
v(211)=-v(206)/3d0
v(205)=-(v(202)*((v(213)*v(213))+(v(216)*v(216))+(v(217)*v(217))))
v(210)=v(205)/3d0
v(204)=v(209)/3d0
v(203)=(v(204)+(2d0/3d0)*v(206)+v(210))*v(978)
v(208)=(v(204)+(-2d0/3d0)*v(205)+v(211))*v(978)
v(219)=(v(213)*v(214)+v(215)*v(216)+v(217)*v(218))*v(979)
v(223)=(v(213)*v(220)+v(217)*v(221)+v(216)*v(222))*v(979)
v(224)=(v(214)*v(220)+v(218)*v(221)+v(215)*v(222))*v(979)
v(225)=v(152)-v(203)+(v(181)+(2d0/3d0)*v(183)+v(187))*v(980)
v(234)=-v(225)/3d0
v(226)=v(142)-v(208)+(v(181)+(-2d0/3d0)*v(182)+v(188))*v(980)
v(235)=-v(226)/3d0
v(227)=v(147)+((2d0/3d0)*v(209)-v(210)-v(211))*v(978)+((-2d0/3d0)*v(186)+v(187)+v(188))*v(980)
v(232)=-v(227)/3d0
v(228)=v(118)*v(131)+v(115)*v(143)+v(120)*v(148)-v(219)+(v(190)*v(191)+v(192)*v(193)+v(194)*v(195))*v(981)
v(1000)=2d0*v(228)
v(229)=v(119)*v(137)+v(116)*v(148)+v(118)*v(153)-v(223)+(v(190)*v(197)+v(194)*v(198)+v(193)*v(199))*v(981)
v(1001)=2d0*v(229)
v(230)=v(120)*v(124)+v(119)*v(143)+v(117)*v(153)-v(224)+(v(191)*v(197)+v(195)*v(198)+v(192)*v(199))*v(981)
v(1002)=2d0*v(230)
v(231)=(2d0/3d0)*v(225)+v(232)+v(235)
v(233)=(2d0/3d0)*v(226)+v(232)+v(234)
v(236)=(2d0/3d0)*v(227)+v(234)+v(235)
v(238)=1d0/sqrt(0.1d-19+2d0*v(228)**2+2d0*v(229)**2+2d0*v(230)**2+v(231)**2+v(233)**2+v(236)**2)
v(319)=v(983)*v(984)
v(318)=v(984)*v(985)
v(313)=statev(48)*v(984)
v(310)=v(984)*v(986)
v(304)=statev(49)*v(984)
v(296)=statev(46)*v(984)
v(295)=statev(47)*v(984)
v(286)=statev(41)*v(984)
v(283)=statev(43)*v(984)
v(282)=statev(42)*v(984)
v(271)=statev(39)*v(984)
v(270)=statev(38)*v(984)
v(269)=statev(37)*v(984)
v(245)=1d0/(statev(58)*v(255)+statev(55)*v(257)+v(254)*v(940))**2
v(880)=v(245)*(v(254)*v(260)+v(255)*v(261)+v(257)*v(262))
v(878)=v(245)*(v(253)*v(260)+v(256)*v(261)+v(258)*v(262))
v(252)=-(v(245)*((v(254)*v(254))+(v(255)*v(255))+(v(257)*v(257))))
v(250)=-(v(245)*((v(260)*v(260))+(v(261)*v(261))+(v(262)*v(262))))
v(246)=v(252)/3d0
v(247)=v(250)/3d0
v(248)=v(245)*((v(253)*v(253))+(v(256)*v(256))+(v(258)*v(258)))
v(249)=1d0/v(245)**0.3333333333333333d0
v(987)=mpar(15)*v(249)
v(875)=(v(246)+v(247)+(2d0/3d0)*v(248))*v(987)
v(251)=-v(248)/3d0
v(877)=(v(247)+v(251)+(-2d0/3d0)*v(252))*v(987)
v(876)=(v(246)+(-2d0/3d0)*v(250)+v(251))*v(987)
v(259)=(-2d0)*v(987)
v(267)=1d0+v(238)*(-(v(231)*v(875))-v(233)*v(876)-v(236)*v(877)+v(259)*(v(230)*v(245)*(v(253)*v(254)+v(255)*v(256)+v&
&(257)*v(258))+v(228)*v(878)+v(229)*v(880)))
v(1003)=3d0*v(267)
v(988)=0.15d1*v(267)
v(268)=(statev(41)*v(269)+statev(42)*v(270)+statev(43)*v(271)+v(951)*v(952)+v(953)*(v(950)+v(954)))*v(988)
v(273)=(statev(44)*v(269)+statev(45)*v(270)+statev(46)*v(271)+v(951)*v(953)+v(952)*(v(949)+v(954)))*v(988)
v(274)=(statev(47)*v(270)+statev(48)*v(271)+statev(37)*v(284)+mpar(14)*(statev(44)*v(952)+statev(41)*v(953)+statev(37&
&)*v(954)))*v(988)
v(275)=(statev(47)*v(269)+statev(49)*v(271)+statev(38)*v(287)+mpar(14)*(statev(45)*v(952)+statev(42)*v(953)+statev(38&
&)*v(954)))*v(988)
v(276)=(statev(48)*v(269)+statev(49)*v(270)+statev(39)*v(289)+mpar(14)*(statev(46)*v(952)+statev(43)*v(953)+statev(39&
&)*v(954)))*v(988)
v(281)=(statev(45)*v(282)+statev(46)*v(283)+statev(44)*v(286)+(v(949)+v(950))*v(951)+v(952)*v(953))*v(988)
v(285)=(statev(47)*v(282)+statev(48)*v(283)+statev(41)*v(284)+mpar(14)*(statev(41)*v(950)+statev(44)*v(951)+statev(37&
&)*v(953)))*v(988)
v(288)=(statev(49)*v(283)+statev(47)*v(286)+statev(42)*v(287)+mpar(14)*(statev(42)*v(950)+statev(45)*v(951)+statev(38&
&)*v(953)))*v(988)
v(290)=(statev(49)*v(282)+statev(48)*v(286)+statev(43)*v(289)+mpar(14)*(statev(43)*v(950)+statev(46)*v(951)+statev(39&
&)*v(953)))*v(988)
v(294)=(statev(44)*v(284)+statev(45)*v(295)+statev(48)*v(296)+mpar(14)*(statev(44)*v(949)+statev(41)*v(951)+statev(37&
&)*v(952)))*v(988)
v(297)=(statev(45)*v(287)+statev(44)*v(295)+statev(49)*v(296)+mpar(14)*(statev(45)*v(949)+statev(42)*v(951)+statev(38&
&)*v(952)))*v(988)
v(298)=(statev(46)*v(289)+statev(45)*v(304)+statev(44)*v(313)+mpar(14)*(statev(46)*v(949)+statev(43)*v(951)+statev(39&
&)*v(952)))*v(988)
v(305)=v(988)*(statev(47)*(v(284)+v(287))+statev(48)*v(304)+v(982)*v(989))
v(306)=v(988)*(statev(48)*(v(284)+v(289))+statev(49)*v(295)+v(982)*v(990))
v(314)=v(988)*(statev(49)*(v(287)+v(289))+statev(47)*v(313)+v(982)*v(991))
v(791)=(v(103)*v(669)+v(112)*v(717))*v(955)+v(642)*v(992)+v(651)*v(993)+v(660)*v(994)+v(678)*v(995)
v(797)=(v(103)*v(670)+v(112)*v(718))*v(955)+v(643)*v(992)+v(652)*v(993)+v(661)*v(994)+v(679)*v(995)
v(810)=(v(103)*v(672)+v(112)*v(720))*v(955)+v(645)*v(992)+v(654)*v(993)+v(663)*v(994)+v(681)*v(995)
v(817)=(v(103)*v(673)+v(112)*v(721))*v(955)+v(646)*v(992)+v(655)*v(993)+v(664)*v(994)+v(682)*v(995)
v(873)=(Fnew(8)*(v(833)+v(103)*(v(113)*v(668)+v(107)*v(677)+v(650)*v(98))+v(97)*(v(113)*v(641)+v(107)*v(716)+v(668)*v&
&(98))+v(112)*(v(107)*v(659)+v(113)*v(716)+v(677)*v(98)))+Fnew(2)*(v(806)+v(103)*(v(113)*v(671)+v(107)*v(680)+v(653)*v&
&(98))+v(97)*(v(113)*v(644)+v(107)*v(719)+v(671)*v(98))+v(112)*(v(107)*v(662)+v(113)*v(719)+v(680)*v(98)))+Fnew(5)*(v&
&(828)+v(103)*(v(113)*v(674)+v(107)*v(683)+v(656)*v(98))+v(97)*(v(113)*v(647)+v(107)*v(722)+v(674)*v(98))+v(112)*(v(107&
&)*v(665)+v(113)*v(722)+v(683)*v(98))))*v(996)
v(872)=(Fnew(6)*(v(114)*v(686)+v(111)*v(725)+v(734)*v(99))+Fnew(9)*(v(114)*v(689)+v(111)*v(728)+v(737)*v(99))+Fnew(3)*&
&(v(114)*v(692)+v(111)*v(731)+v(740)*v(99)))*v(996)
v(832)=(v(103)*v(675)+v(112)*v(723))*v(955)+v(648)*v(992)+v(657)*v(993)+v(666)*v(994)+v(684)*v(995)
v(868)=(Fnew(4)*(v(103)*v(708)+v(112)*v(768)+v(777)*v(97))+Fnew(7)*(v(103)*v(711)+v(112)*v(771)+v(780)*v(97))+Fnew(1)*&
&(v(103)*v(714)+v(112)*v(774)+v(783)*v(97)))*v(996)
v(840)=(v(103)*v(676)+v(112)*v(724))*v(955)+v(649)*v(992)+v(658)*v(993)+v(667)*v(994)+v(685)*v(995)
v(851)=(Fnew(4)*v(791)+Fnew(7)*v(810)+Fnew(1)*v(832))*v(996)
v(852)=-v(851)/4d0
v(853)=(Fnew(7)*v(797)+Fnew(1)*v(817)+Fnew(4)*v(840))*v(996)
v(854)=-v(853)/4d0
v(855)=(Fnew(9)*v(791)+Fnew(3)*v(810)+Fnew(6)*v(832))*v(996)
v(860)=-v(855)/4d0
sigma(1)=v(887)*(v(103)*v(168)+v(112)*v(169)+v(170)*v(97))
sigma(2)=v(887)*(v(113)*v(161)+v(107)*v(162)+v(160)*v(98))
sigma(3)=v(887)*(v(114)*v(164)+v(111)*v(165)+v(166)*v(99))
sigma(4)=v(997)
sigma(5)=v(998)
sigma(6)=v(999)
ddsdde(1,1)=v(887)*(Fnew(1)*(v(170)*v(324)+v(168)*v(329)+v(169)*v(331)+v(103)*v(686)+v(112)*v(734)+v(725)*v(97))+Fnew(4&
&)*(v(170)*v(325)+v(168)*v(327)+v(169)*v(332)+v(103)*v(689)+v(112)*v(737)+v(728)*v(97))+Fnew(7)*(v(170)*v(326)+v(168)*v&
&(328)+v(169)*v(330)+v(103)*v(692)+v(112)*v(740)+v(731)*v(97)))
ddsdde(1,2)=(Fnew(2)*v(791)+Fnew(5)*v(810)+Fnew(8)*v(832))*v(887)
ddsdde(1,3)=(Fnew(3)*v(797)+Fnew(6)*v(817)+Fnew(9)*v(840))*v(887)
ddsdde(1,4)=v(852)
ddsdde(1,5)=v(854)
ddsdde(1,6)=v(855)/2d0
ddsdde(2,2)=v(887)*(Fnew(2)*(v(107)*v(768)+v(113)*v(777)+v(806)+v(708)*v(98))+Fnew(5)*(v(107)*v(771)+v(113)*v(780)+v&
&(828)+v(711)*v(98))+Fnew(8)*(v(107)*v(774)+v(113)*v(783)+v(833)+v(714)*v(98)))
ddsdde(2,3)=v(887)*(Fnew(3)*(v(98)*(v(113)*v(670)+v(107)*v(679)+v(652)*v(98))+v(113)*(v(113)*v(643)+v(107)*v(718)+v(670&
&)*v(98))+v(107)*(v(107)*v(661)+v(113)*v(718)+v(679)*v(98)))+Fnew(6)*(v(98)*(v(113)*v(673)+v(107)*v(682)+v(655)*v(98))+v&
&(113)*(v(113)*v(646)+v(107)*v(721)+v(673)*v(98))+v(107)*(v(107)*v(664)+v(113)*v(721)+v(682)*v(98)))+Fnew(9)*(v(98)*(v&
&(113)*v(676)+v(107)*v(685)+v(658)*v(98))+v(113)*(v(113)*v(649)+v(107)*v(724)+v(676)*v(98))+v(107)*(v(107)*v(667)+v(113&
&)*v(724)+v(685)*v(98))))
ddsdde(2,4)=v(852)
ddsdde(2,5)=v(853)/2d0
ddsdde(2,6)=v(860)
ddsdde(3,3)=v(887)*(Fnew(3)*(v(165)*v(326)+v(164)*v(328)+v(166)*v(330)+v(99)*(v(114)*v(679)+v(111)*v(718)+v(745)+v(661&
&)*v(99))+v(114)*(v(114)*v(652)+v(111)*v(670)+v(697)+v(679)*v(99))+v(111)*(v(111)*v(643)+v(114)*v(670)+v(757)+v(718)*v&
&(99)))+Fnew(6)*(v(165)*v(324)+v(164)*v(329)+v(166)*v(331)+v(99)*(v(114)*v(682)+v(111)*v(721)+v(749)+v(664)*v(99))+v(114&
&)*(v(114)*v(655)+v(111)*v(673)+v(701)+v(682)*v(99))+v(111)*(v(111)*v(646)+v(114)*v(673)+v(761)+v(721)*v(99)))+Fnew(9)*&
&(v(165)*v(325)+v(164)*v(327)+v(166)*v(332)+v(99)*(v(114)*v(685)+v(111)*v(724)+v(753)+v(667)*v(99))+v(114)*(v(114)*v(658&
&)+v(111)*v(676)+v(705)+v(685)*v(99))+v(111)*(v(111)*v(649)+v(114)*v(676)+v(765)+v(724)*v(99))))
ddsdde(3,4)=v(851)/2d0
ddsdde(3,5)=v(854)
ddsdde(3,6)=v(860)
ddsdde(4,4)=(v(868)+v(873))/4d0
ddsdde(4,5)=v(999)/2d0
ddsdde(4,6)=v(998)/2d0
ddsdde(5,5)=(v(868)+v(872))/4d0
ddsdde(5,6)=v(997)/2d0
ddsdde(6,6)=(v(872)+v(873))/4d0
DO i01=2,6
DO i02=1,i01-1
ddsdde(i01,i02)=ddsdde(i02,i01)
ENDDO
ENDDO
yielding=-mpar(3)-mpar(5)*(1d0-dexp(-(mpar(4)*statev(10))))-mpar(7)*(1d0-dexp(-(mpar(6)*statev(10))))+sqrt(v(1000)*(v&
&(225)*v(274)+v(226)*v(285)+v(227)*v(294)+v(1001)*v(305)+v(1002)*v(306)+v(1003)*v(228)*(v(310)+v(318)+2d0*v(947)**2+(v&
&(888)+v(891)+v(894))*v(982)))+v(1001)*(v(225)*v(275)+v(226)*v(288)+v(227)*v(297)+v(1000)*v(305)+v(1002)*v(314)+v(1003&
&)*v(229)*(v(310)+v(319)+2d0*v(946)**2+(v(889)+v(892)+v(895))*v(982)))+v(1002)*(v(225)*v(276)+v(226)*v(290)+v(227)*v(298&
&)+v(1000)*v(306)+v(1001)*v(314)+v(1003)*v(230)*(v(318)+v(319)+2d0*v(945)**2+(v(890)+v(893)+v(896))*v(982)))+v(225)*(v&
&(226)*v(268)+v(227)*v(273)+v(1000)*v(274)+v(1001)*v(275)+v(1002)*v(276)+v(225)*(v(278)+v(291)+v(954)**2+2d0*(v(888)+v&
&(889)+v(890))*v(982))*v(988))+v(226)*(v(225)*v(268)+v(227)*v(281)+v(1000)*v(285)+v(1001)*v(288)+v(1002)*v(290)+v(226)*&
&(v(278)+v(292)+v(950)**2+2d0*(v(891)+v(892)+v(893))*v(982))*v(988))+v(227)*(v(225)*v(273)+v(226)*v(281)+v(1000)*v(294)&
&+v(1001)*v(297)+v(1002)*v(298)+v(227)*(v(291)+v(292)+v(949)**2+2d0*(v(894)+v(895)+v(896))*v(982))*v(988)))
xguess(1)=0d0
xguess(2)=v(231)
xguess(3)=v(233)
xguess(4)=v(228)
xguess(5)=v(230)
xguess(6)=v(229)
xguess(7)=v(203)
xguess(8)=v(208)
xguess(9)=v(219)
xguess(10)=v(224)
xguess(11)=v(223)
xguess(12)=v(875)
xguess(13)=v(876)
xguess(14)=v(877)
xguess(15)=v(878)*v(987)
xguess(16)=v(880)*v(987)
END SUBROUTINE
!**************************************************************
!* AceGen 6.702 Windows (4 May 16) *
!* Co. J. Korelc 2013 4 Dec 19 21:34:42 *
!**************************************************************
! User : Full professional version
! Notebook : MainFile
! Evaluation time : 82 s Mode : Optimal
! Number of formulae : 688 Method: Automatic
! Subroutine : residual size: 12652
! Total size of Mathematica code : 12652 subexpressions
! Total size of Fortran code : 30351 bytes
!******************* S U B R O U T I N E **********************
SUBROUTINE residual(x,mpar,statev,Fnew,R)
USE SMSUtility
IMPLICIT NONE
DOUBLE PRECISION v(852),x(16),mpar(16),statev(58),Fnew(9),R(16)
v(830)=1d0/mpar(16)
v(829)=v(830)*x(12)
v(789)=1d0/mpar(12)
v(788)=1d0/mpar(10)
v(756)=4d0*x(5)
v(755)=4d0*x(6)
v(754)=4d0*x(4)
v(753)=2d0*x(3)
v(749)=2d0*x(2)
v(748)=2d0*x(5)
v(747)=2d0*x(6)
v(746)=2d0*x(4)
v(743)=x(5)**2
v(742)=x(6)**2
v(741)=8d0*x(6)
v(740)=x(4)**2
v(737)=mpar(14)**2
v(738)=2d0*v(737)
v(732)=2d0*mpar(14)
v(727)=-x(12)-x(13)
v(726)=-x(7)-x(8)
v(725)=2d0*v(742)
v(724)=2d0*v(743)
v(723)=2d0*v(740)
v(722)=x(3)**2
v(721)=x(2)**2
v(720)=-x(2)-x(3)
v(764)=2d0*v(720)
v(745)=(v(720)*v(720))
v(744)=4d0*v(720)
v(719)=dabs(x(1))
v(718)=1d0+statev(52)
v(717)=1d0+statev(51)
v(716)=1d0+statev(50)
v(715)=1d0+statev(3)
v(714)=1d0+statev(2)
v(713)=1d0+statev(1)
v(712)=1d0+statev(22)
v(711)=1d0+statev(21)
v(710)=1d0+statev(20)
v(709)=1d0+statev(13)
v(708)=1d0+statev(12)
v(707)=1d0+statev(11)
v(706)=1d0-mpar(8)
v(216)=v(721)+v(722)+v(723)+v(724)+v(725)+v(745)
v(225)=1d0/sqrt(v(216))
v(118)=1d0/sqrt(0.1d-19+v(216))
v(116)=statev(10)+v(719)
v(117)=v(118)*x(2)
v(728)=(-4d0)*v(117)
v(217)=-(v(117)*x(12))
v(119)=v(118)*x(3)
v(729)=(-4d0)*v(119)
v(218)=-(v(119)*x(13))
v(137)=(-1d0/3d0)-v(117)*v(119)
v(127)=(2d0/3d0)-(v(119)*v(119))
v(120)=v(118)*v(720)
v(730)=(-4d0)*v(120)
v(219)=-(v(120)*v(727))
v(144)=(-1d0/3d0)-v(119)*v(120)
v(139)=(-1d0/3d0)-v(117)*v(120)
v(129)=(2d0/3d0)-(v(120)*v(120))
v(121)=v(118)*x(4)
v(731)=(-8d0)*v(121)
v(220)=(-2d0)*v(121)*x(14)
v(131)=0.5d0-(v(121)*v(121))
v(122)=v(118)*x(6)
v(221)=(-2d0)*v(122)*x(16)
v(133)=0.5d0-(v(122)*v(122))
v(123)=v(118)*x(5)
v(222)=(-2d0)*v(123)*x(15)
v(226)=-v(217)-v(218)-v(219)-v(220)-v(221)-v(222)
v(157)=1d0+v(217)+v(218)+v(219)+v(220)+v(221)+v(222)
v(739)=0.15d1*v(157)
v(135)=0.5d0-(v(123)*v(123))
v(124)=(2d0/3d0)-(v(117)*v(117))
v(126)=((((2d0/3d0)+statev(29))*v(124)+((2d0/3d0)+statev(30))*v(127)+((2d0/3d0)+statev(31))*v(129)+4d0*(0.5d0+statev(32&
&))*v(131)+4d0*(0.5d0+statev(33))*v(133)+4d0*(0.5d0+statev(34))*v(135)+2d0*((-1d0/3d0)+statev(35))*v(137)+2d0*((-1d0/3d0&
&)+statev(36))*v(139)+2d0*((-1d0/3d0)+statev(40))*v(144)+v(121)*(statev(37)*v(728)+statev(41)*v(729)+statev(44)*v(730))&
&+v(122)*(statev(38)*v(728)+statev(42)*v(729)+statev(45)*v(730)+statev(47)*v(731))+v(123)*((-8d0)*statev(49)*v(122)&
&+statev(39)*v(728)+statev(43)*v(729)+statev(46)*v(730)+statev(48)*v(731)))*((-1d0)+dexp((-7d0)*mpar(13)*v(719))))/7d0
v(736)=-(v(121)*v(126))
v(735)=-(v(120)*v(126))
v(734)=-(v(119)*v(126))
v(733)=-(v(117)*v(126))
v(158)=(2d0/3d0)+mpar(14)*(statev(29)+v(124)*v(126))
v(170)=(2d0/3d0)+mpar(14)*(statev(30)+v(126)*v(127))
v(173)=(2d0/3d0)+mpar(14)*(statev(31)+v(126)*v(129))
v(192)=0.5d0+mpar(14)*(statev(32)+v(126)*v(131))
v(175)=v(192)*v(732)
v(200)=0.5d0+mpar(14)*(statev(33)+v(126)*v(133))
v(179)=v(200)*v(732)
v(208)=0.5d0+mpar(14)*(statev(34)+v(126)*v(135))
v(182)=v(208)*v(732)
v(159)=(-1d0/3d0)+mpar(14)*(statev(35)+v(126)*v(137))
v(171)=(v(159)*v(159))
v(160)=(-1d0/3d0)+mpar(14)*(statev(36)+v(126)*v(139))
v(184)=(v(160)*v(160))
v(141)=statev(37)+v(121)*v(733)
v(193)=(v(141)*v(141))
v(142)=statev(38)+v(122)*v(733)
v(201)=(v(142)*v(142))
v(143)=statev(39)+v(123)*v(733)
v(209)=(v(143)*v(143))
v(162)=(-1d0/3d0)+mpar(14)*(statev(40)+v(126)*v(144))
v(185)=(v(162)*v(162))
v(146)=statev(41)+v(121)*v(734)
v(194)=(v(146)*v(146))
v(147)=statev(42)+v(122)*v(734)
v(202)=(v(147)*v(147))
v(148)=statev(43)+v(123)*v(734)
v(210)=(v(148)*v(148))
v(149)=statev(44)+v(121)*v(735)
v(195)=(v(149)*v(149))
v(150)=statev(45)+v(122)*v(735)
v(203)=(v(150)*v(150))
v(151)=statev(46)+v(123)*v(735)
v(211)=(v(151)*v(151))
v(152)=statev(47)+v(122)*v(736)
v(153)=statev(48)+v(123)*v(736)
v(154)=statev(49)-v(122)*v(123)*v(126)
v(213)=(v(154)*v(154))*v(738)
v(212)=(v(153)*v(153))*v(738)
v(206)=v(153)*v(738)
v(204)=(v(152)*v(152))*v(738)
v(197)=v(154)*v(738)
v(189)=v(151)*v(738)
v(188)=v(152)*v(738)
v(180)=v(146)*v(738)
v(177)=v(148)*v(738)
v(176)=v(147)*v(738)
v(165)=v(143)*v(738)
v(164)=v(142)*v(738)
v(163)=v(141)*v(738)
v(156)=((v(158)*v(158))+v(171)+v(184)+2d0*(v(193)+v(201)+v(209))*v(737))*v(739)
v(161)=(v(160)*v(162)+v(146)*v(163)+v(147)*v(164)+v(148)*v(165)+v(159)*(v(158)+v(170)))*v(739)
v(750)=v(161)*x(3)
v(166)=(v(159)*v(162)+v(149)*v(163)+v(150)*v(164)+v(151)*v(165)+v(160)*(v(158)+v(173)))*v(739)
v(751)=v(166)*v(720)
v(167)=(mpar(14)*(v(141)*v(158)+v(146)*v(159)+v(149)*v(160))+v(152)*v(164)+v(153)*v(165)+v(141)*v(175))*v(739)
v(168)=(mpar(14)*(v(142)*v(158)+v(147)*v(159)+v(150)*v(160))+v(152)*v(163)+v(154)*v(165)+v(142)*v(179))*v(739)
v(169)=(mpar(14)*(v(143)*v(158)+v(148)*v(159)+v(151)*v(160))+v(153)*v(163)+v(154)*v(164)+v(143)*v(182))*v(739)
v(172)=((v(170)*v(170))+v(171)+v(185)+2d0*(v(194)+v(202)+v(210))*v(737))*v(739)
v(174)=(v(159)*v(160)+v(162)*(v(170)+v(173))+v(150)*v(176)+v(151)*v(177)+v(149)*v(180))*v(739)
v(758)=v(174)*v(720)
v(178)=(mpar(14)*(v(141)*v(159)+v(149)*v(162)+v(146)*v(170))+v(146)*v(175)+v(152)*v(176)+v(153)*v(177))*v(739)
v(181)=(mpar(14)*(v(142)*v(159)+v(150)*v(162)+v(147)*v(170))+v(154)*v(177)+v(147)*v(179)+v(152)*v(180))*v(739)
v(183)=(mpar(14)*(v(143)*v(159)+v(151)*v(162)+v(148)*v(170))+v(154)*v(176)+v(153)*v(180)+v(148)*v(182))*v(739)
v(186)=((v(173)*v(173))+v(184)+v(185)+2d0*(v(195)+v(203)+v(211))*v(737))*v(739)
v(187)=(mpar(14)*(v(141)*v(160)+v(146)*v(162)+v(149)*v(173))+v(149)*v(175)+v(150)*v(188)+v(153)*v(189))*v(739)
v(759)=v(187)*x(4)
v(190)=(mpar(14)*(v(142)*v(160)+v(147)*v(162)+v(150)*v(173))+v(150)*v(179)+v(149)*v(188)+v(154)*v(189))*v(739)
v(760)=v(190)*x(6)
v(191)=(mpar(14)*(v(143)*v(160)+v(148)*v(162)+v(151)*v(173))+v(151)*v(182)+v(150)*v(197)+v(149)*v(206))*v(739)
v(761)=v(191)*x(5)
v(196)=(2d0*(v(192)*v(192))+v(204)+v(212)+(v(193)+v(194)+v(195))*v(737))*v(739)
v(762)=4d0*v(196)
v(198)=(v(152)*(v(175)+v(179))+v(153)*v(197)+(v(141)*v(142)+v(146)*v(147)+v(149)*v(150))*v(737))*v(739)
v(765)=v(198)*x(4)
v(199)=(v(153)*(v(175)+v(182))+v(154)*v(188)+(v(141)*v(143)+v(146)*v(148)+v(149)*v(151))*v(737))*v(739)
v(763)=v(199)*x(5)
v(205)=(2d0*(v(200)*v(200))+v(204)+v(213)+(v(201)+v(202)+v(203))*v(737))*v(739)
v(766)=4d0*v(205)
v(207)=(v(154)*(v(179)+v(182))+v(152)*v(206)+(v(142)*v(143)+v(147)*v(148)+v(150)*v(151))*v(737))*v(739)
v(767)=v(207)*x(5)
v(214)=(2d0*(v(208)*v(208))+v(212)+v(213)+(v(209)+v(210)+v(211))*v(737))*v(739)
v(768)=4d0*v(214)
v(215)=v(156)*v(721)+v(172)*v(722)+v(186)*v(745)+v(749)*(v(167)*v(746)+v(168)*v(747)+v(169)*v(748)+v(750)+v(751))+v(753&
&)*(v(178)*v(746)+v(181)*v(747)+v(183)*v(748)+v(758))+v(744)*v(759)+v(744)*v(760)+v(744)*v(761)+v(740)*v(762)+v(741)*v&
&(765)+v(742)*v(766)+v(741)*v(767)+v(743)*v(768)+8d0*v(763)*x(4)
v(757)=-(v(215)*v(225))
v(224)=1d0/sqrt(v(215))
v(752)=v(224)/2d0
v(223)=v(752)*(v(156)*v(749)+2d0*v(750)+2d0*v(751)+v(167)*v(754)+v(168)*v(755)+v(169)*v(756)+v(757)*(-(v(117)*v(226))+x&
&(12)))
v(771)=v(223)*v(719)
v(369)=(v(223)*v(223))
v(227)=v(752)*(v(161)*v(749)+v(172)*v(753)+v(178)*v(754)+v(181)*v(755)+v(183)*v(756)+2d0*v(758)+v(757)*(-(v(119)*v(226)&
&)+x(13)))
v(774)=v(227)*v(719)
v(370)=(v(227)*v(227))
v(228)=v(752)*(v(166)*v(749)+v(174)*v(753)+(-(v(120)*v(226))+v(727))*v(757)+4d0*v(759)+4d0*v(760)+4d0*v(761)+v(186)*v&
&(764))
v(777)=v(228)*v(719)
v(371)=(v(228)*v(228))
v(229)=v(752)*(v(167)*v(749)+v(178)*v(753)+v(198)*v(755)+4d0*v(763)+v(187)*v(764)+v(757)*(-(v(121)*v(226))+x(14))+v(762&
&)*x(4))
v(785)=2d0*v(229)
v(770)=v(229)*v(719)
v(372)=(v(229)*v(229))
v(230)=v(752)*(v(168)*v(749)+v(181)*v(753)+v(190)*v(764)+4d0*v(765)+4d0*v(767)+v(757)*(-(v(122)*v(226))+x(16))+v(766)*x&
&(6))
v(786)=2d0*v(230)
v(773)=v(230)*v(719)
v(373)=(v(230)*v(230))
v(231)=v(752)*(v(169)*v(749)+v(183)*v(753)+v(199)*v(754)+v(207)*v(755)+v(191)*v(764)+v(757)*(-(v(123)*v(226))+x(15))+v&
&(768)*x(5))
v(787)=2d0*v(231)
v(769)=v(231)*v(719)
v(374)=(v(231)*v(231))
v(232)=(v(719)*v(719))
v(268)=v(232)*v(374)
v(267)=v(232)*v(373)
v(255)=((v(227)+v(228))*v(230)+v(229)*v(231))*v(232)
v(271)=v(255)*v(773)
v(250)=v(232)*v(372)
v(236)=((v(223)+v(227))*v(229)+v(230)*v(231))*v(232)
v(252)=v(236)*v(770)
v(235)=(v(229)*v(230)+(v(223)+v(228))*v(231))*v(232)
v(270)=v(235)*v(769)
v(233)=v(250)+v(268)+v(232)*v(369)
v(239)=(v(231)*v(233)+v(228)*v(235)+v(230)*v(236))*v(719)
v(274)=v(239)*v(769)
v(238)=(v(229)*v(233)+v(230)*v(235)+v(227)*v(236))*v(719)
v(254)=v(238)*v(770)
v(234)=v(252)+v(270)+v(233)*v(771)
v(242)=(v(229)*v(234)+v(227)*v(238)+v(230)*v(239))*v(719)
v(258)=v(242)*v(770)
v(241)=(v(231)*v(234)+v(230)*v(238)+v(228)*v(239))*v(719)
v(276)=v(241)*v(769)
v(237)=v(254)+v(274)+v(234)*v(771)
v(245)=(v(231)*v(237)+v(228)*v(241)+v(230)*v(242))*v(719)
v(280)=v(245)*v(769)
v(244)=(v(229)*v(237)+v(230)*v(241)+v(227)*v(242))*v(719)
v(260)=v(244)*v(770)
v(240)=v(258)+v(276)+v(237)*v(771)
v(243)=v(260)+v(280)+v(240)*v(771)
v(772)=5040d0+v(243)
v(246)=(v(231)*v(240)+v(230)*v(244)+v(228)*v(245))*v(719)
v(282)=v(246)*v(769)
v(247)=(v(229)*v(240)+v(227)*v(244)+v(230)*v(245))*v(719)
v(285)=(7d0*(360d0*v(235)+120d0*v(239)+30d0*v(241)+6d0*v(245)+v(246))+v(719)*(v(228)*v(246)+v(230)*v(247)+v(231)*v(772)&
&))/5040d0
v(265)=v(247)*v(770)
v(775)=5040d0+v(265)
v(287)=(2520d0*v(233)+840d0*v(234)+210d0*v(237)+42d0*v(240)+7d0*v(243)+v(282)+v(771)*v(772)+v(775))/5040d0
v(249)=(7d0*(360d0*v(236)+120d0*v(238)+30d0*v(242)+6d0*v(244)+v(247))+v(719)*(v(230)*v(246)+v(227)*v(247)+v(229)*v(772)&
&))/5040d0
v(248)=statev(8)*v(249)+statev(6)*v(285)+v(287)*v(713)
v(251)=v(250)+v(267)+v(232)*v(370)
v(257)=(v(231)*v(236)+v(230)*v(251)+v(228)*v(255))*v(719)
v(273)=v(257)*v(773)
v(253)=v(252)+v(271)+v(251)*v(774)
v(261)=(v(231)*v(238)+v(230)*v(253)+v(228)*v(257))*v(719)
v(277)=v(261)*v(773)
v(256)=v(254)+v(273)+v(253)*v(774)
v(263)=(v(231)*v(242)+v(230)*v(256)+v(228)*v(261))*v(719)
v(279)=v(263)*v(773)
v(259)=v(258)+v(277)+v(256)*v(774)
v(262)=v(260)+v(279)+v(259)*v(774)
v(776)=5040d0+v(262)
v(264)=(v(231)*v(244)+v(230)*v(259)+v(228)*v(263))*v(719)
v(284)=(7d0*(360d0*v(255)+120d0*v(257)+30d0*v(261)+6d0*v(263)+v(264))+v(719)*(v(231)*v(247)+v(228)*v(264)+v(230)*v(776)&
&))/5040d0
v(283)=v(264)*v(773)
v(289)=(2520d0*v(251)+840d0*v(253)+210d0*v(256)+42d0*v(259)+7d0*v(262)+v(283)+v(775)+v(774)*v(776))/5040d0
v(266)=statev(4)*v(249)+statev(9)*v(284)+v(289)*v(714)
v(269)=v(267)+v(268)+v(232)*v(371)
v(272)=v(270)+v(271)+v(269)*v(777)
v(275)=v(273)+v(274)+v(272)*v(777)
v(278)=v(276)+v(277)+v(275)*v(777)
v(281)=v(279)+v(280)+v(278)*v(777)
v(291)=(5040d0+2520d0*v(269)+840d0*v(272)+210d0*v(275)+42d0*v(278)+7d0*v(281)+v(282)+v(283)+(5040d0+v(281))*v(777))&
&/5040d0
v(286)=statev(5)*v(284)+statev(7)*v(285)+v(291)*v(715)
v(288)=statev(9)*v(285)+statev(4)*v(287)+v(249)*v(714)
v(290)=statev(7)*v(249)+statev(5)*v(289)+v(284)*v(715)
v(292)=statev(8)*v(284)+statev(6)*v(291)+v(285)*v(713)
v(293)=statev(5)*v(249)+statev(7)*v(287)+v(285)*v(715)
v(304)=v(288)*v(290)-v(266)*v(293)
v(300)=v(248)*v(286)-v(292)*v(293)
v(294)=statev(6)*v(284)+statev(8)*v(289)+v(249)*v(713)
v(308)=v(290)*v(292)-v(286)*v(294)
v(306)=-(v(248)*v(290))+v(293)*v(294)
v(305)=v(248)*v(266)-v(288)*v(294)
v(295)=statev(4)*v(285)+statev(9)*v(291)+v(284)*v(714)
v(310)=-(v(266)*v(292))+v(294)*v(295)
v(309)=v(266)*v(286)-v(290)*v(295)
v(302)=-(v(286)*v(288))+v(293)*v(295)
v(301)=v(288)*v(292)-v(248)*v(295)
v(296)=1d0/(v(292)*v(304)+v(286)*v(305)+v(295)*v(306))
v(297)=v(296)*(Fnew(4)*v(308)+Fnew(1)*v(309)+Fnew(7)*v(310))
v(298)=v(296)*(Fnew(2)*v(300)+Fnew(5)*v(301)+Fnew(8)*v(302))
v(299)=v(296)*(Fnew(6)*v(304)+Fnew(3)*v(305)+Fnew(9)*v(306))
v(303)=v(296)*(Fnew(4)*v(300)+Fnew(7)*v(301)+Fnew(1)*v(302))
v(307)=v(296)*(Fnew(8)*v(304)+Fnew(5)*v(305)+Fnew(2)*v(306))
v(311)=v(296)*(Fnew(9)*v(308)+Fnew(6)*v(309)+Fnew(3)*v(310))
v(312)=v(296)*(Fnew(1)*v(304)+Fnew(7)*v(305)+Fnew(4)*v(306))
v(313)=v(296)*(Fnew(2)*v(308)+Fnew(8)*v(309)+Fnew(5)*v(310))
v(314)=v(296)*(Fnew(9)*v(300)+Fnew(3)*v(301)+Fnew(6)*v(302))
v(315)=(v(297)*v(297))+(v(311)*v(311))+(v(313)*v(313))
v(335)=-v(315)/3d0
v(316)=(v(298)*v(298))+(v(303)*v(303))+(v(314)*v(314))
v(336)=-v(316)/3d0
v(317)=(v(299)*v(299))+(v(307)*v(307))+(v(312)*v(312))
v(328)=-v(317)/3d0
v(318)=v(297)*v(303)+v(298)*v(313)+v(311)*v(314)
v(334)=(v(318)*v(318))
v(350)=v(315)*v(316)-v(334)
v(319)=v(298)*v(307)+v(303)*v(312)+v(299)*v(314)
v(322)=(v(319)*v(319))
v(339)=v(316)*v(317)-v(322)
v(320)=v(299)*v(311)+v(297)*v(312)+v(307)*v(313)
v(778)=v(319)*v(320)
v(351)=v(318)*v(319)-v(316)*v(320)
v(346)=-(v(315)*v(319))+v(318)*v(320)
v(341)=-(v(317)*v(318))+v(778)
v(326)=(v(320)*v(320))
v(345)=v(315)*v(317)-v(326)
v(323)=-(v(315)*v(322))-v(316)*v(326)+v(317)*v(350)+2d0*v(318)*v(778)
v(330)=mpar(2)*(v(323)-sqrt(v(323)))
v(329)=1d0/v(323)**0.3333333333333333d0
v(779)=mpar(1)*v(329)
v(352)=v(330)+((2d0/3d0)*v(315)+v(328)+v(336))*v(779)
v(783)=v(352)/v(323)
v(666)=-v(352)/3d0
v(360)=v(352)-x(2)-x(7)
v(364)=-v(360)/3d0
v(347)=v(330)+((2d0/3d0)*v(317)+v(335)+v(336))*v(779)
v(782)=v(347)/v(323)
v(663)=-v(347)/3d0
v(363)=-v(347)+v(720)+v(726)
v(359)=v(363)/3d0
v(342)=v(330)+((2d0/3d0)*v(316)+v(328)+v(335))*v(779)
v(781)=v(342)/v(323)
v(665)=-v(342)/3d0
v(358)=-v(342)+x(3)+x(8)
v(362)=v(358)/3d0
v(321)=1d0/v(323)**0.13333333333333333d1
v(780)=mpar(1)*v(321)
v(349)=v(320)*v(780)
v(344)=v(319)*v(780)
v(340)=v(351)*v(780)
v(338)=v(318)*v(780)
v(333)=v(344)*v(346)
v(332)=v(320)*v(340)
v(325)=v(338)*v(341)
v(343)=v(338)*v(339)+v(319)*v(340)+v(341)*v(781)
v(348)=v(344)*v(345)+v(341)*v(349)+v(346)*v(782)
v(353)=v(338)*v(346)+v(349)*v(350)+v(351)*v(783)
v(354)=v(315)*v(343)+v(320)*v(348)+v(318)*(v(325)+v(333)+v(345)*v(781))
v(355)=v(316)*v(348)+v(318)*v(353)+v(319)*(v(332)+v(333)+v(350)*v(782))
v(356)=v(319)*v(343)+v(317)*v(353)+v(320)*(v(325)+v(332)+v(339)*v(783))
v(357)=v(359)+(2d0/3d0)*v(360)+v(362)
v(361)=(-2d0/3d0)*v(358)+v(359)+v(364)
v(365)=v(362)+(-2d0/3d0)*v(363)+v(364)
v(366)=v(354)-x(4)-x(9)
v(367)=v(355)-x(11)-x(6)
v(368)=v(356)-x(10)-x(5)
v(375)=sqrt(v(369)+v(370)+v(371)+2d0*v(372)+2d0*v(373)+2d0*v(374))
v(784)=v(706)/v(375)
v(387)=v(784)*(v(228)*v(726)+v(787)*x(10)+v(786)*x(11)+v(223)*x(7)+v(227)*x(8)+v(785)*x(9))
v(378)=v(784)*(v(223)*v(357)+v(227)*v(361)+v(228)*v(365)+v(366)*v(785)+v(367)*v(786)+v(368)*v(787))
v(377)=0.15d1*mpar(8)*v(375)
v(376)=-v(223)+(v(357)*v(377)+v(223)*v(378))*v(788)
v(792)=v(376)*v(719)
v(379)=-v(227)+(v(361)*v(377)+v(227)*v(378))*v(788)
v(795)=v(379)*v(719)
v(380)=-v(228)+(v(365)*v(377)+v(228)*v(378))*v(788)
v(798)=v(380)*v(719)
v(381)=-v(229)+(v(366)*v(377)+v(229)*v(378))*v(788)
v(791)=v(381)*v(719)
v(410)=v(232)*(v(381)*v(381))
v(382)=-v(230)+(v(367)*v(377)+v(230)*v(378))*v(788)
v(794)=v(382)*v(719)
v(427)=v(232)*(v(382)*v(382))
v(383)=-v(231)+(v(368)*v(377)+v(231)*v(378))*v(788)
v(790)=v(383)*v(719)
v(428)=v(232)*(v(383)*v(383))
v(415)=v(232)*((v(379)+v(380))*v(382)+v(381)*v(383))
v(431)=v(415)*v(794)
v(396)=v(232)*((v(376)+v(379))*v(381)+v(382)*v(383))
v(412)=v(396)*v(791)
v(395)=v(232)*(v(381)*v(382)+(v(376)+v(380))*v(383))
v(430)=v(395)*v(790)
v(386)=-v(223)+v(789)*(v(223)*v(387)+v(377)*x(7))
v(806)=v(386)*v(719)
v(388)=-v(227)+v(789)*(v(227)*v(387)+v(377)*x(8))
v(809)=v(388)*v(719)
v(389)=-v(228)+(v(228)*v(387)+v(377)*v(726))*v(789)
v(812)=v(389)*v(719)
v(390)=-v(229)+v(789)*(v(229)*v(387)+v(377)*x(9))
v(805)=v(390)*v(719)
v(473)=v(232)*(v(390)*v(390))
v(391)=-v(230)+v(789)*(v(230)*v(387)+v(377)*x(11))
v(808)=v(391)*v(719)
v(490)=v(232)*(v(391)*v(391))
v(392)=-v(231)+v(789)*(v(231)*v(387)+v(377)*x(10))
v(804)=v(392)*v(719)
v(491)=v(232)*(v(392)*v(392))
v(478)=v(232)*((v(388)+v(389))*v(391)+v(390)*v(392))
v(494)=v(478)*v(808)
v(459)=v(232)*((v(386)+v(388))*v(390)+v(391)*v(392))
v(475)=v(459)*v(805)
v(458)=v(232)*(v(390)*v(391)+(v(386)+v(389))*v(392))
v(493)=v(458)*v(804)
v(393)=v(232)*(v(376)*v(376))+v(410)+v(428)
v(399)=(v(383)*v(393)+v(380)*v(395)+v(382)*v(396))*v(719)
v(434)=v(399)*v(790)
v(398)=(v(381)*v(393)+v(382)*v(395)+v(379)*v(396))*v(719)
v(414)=v(398)*v(791)
v(394)=v(412)+v(430)+v(393)*v(792)
v(402)=(v(381)*v(394)+v(379)*v(398)+v(382)*v(399))*v(719)
v(418)=v(402)*v(791)
v(401)=(v(383)*v(394)+v(382)*v(398)+v(380)*v(399))*v(719)
v(436)=v(401)*v(790)
v(397)=v(414)+v(434)+v(394)*v(792)
v(405)=(v(383)*v(397)+v(380)*v(401)+v(382)*v(402))*v(719)
v(440)=v(405)*v(790)
v(404)=(v(381)*v(397)+v(382)*v(401)+v(379)*v(402))*v(719)
v(420)=v(404)*v(791)
v(400)=v(418)+v(436)+v(397)*v(792)
v(403)=v(420)+v(440)+v(400)*v(792)
v(793)=5040d0+v(403)
v(406)=(v(383)*v(400)+v(382)*v(404)+v(380)*v(405))*v(719)
v(442)=v(406)*v(790)
v(407)=(v(381)*v(400)+v(379)*v(404)+v(382)*v(405))*v(719)
v(445)=(7d0*(360d0*v(395)+120d0*v(399)+30d0*v(401)+6d0*v(405)+v(406))+v(719)*(v(380)*v(406)+v(382)*v(407)+v(383)*v(793)&
&))/5040d0
v(425)=v(407)*v(791)
v(796)=5040d0+v(425)
v(447)=(2520d0*v(393)+840d0*v(394)+210d0*v(397)+42d0*v(400)+7d0*v(403)+v(442)+v(792)*v(793)+v(796))/5040d0
v(409)=(7d0*(360d0*v(396)+120d0*v(398)+30d0*v(402)+6d0*v(404)+v(407))+v(719)*(v(382)*v(406)+v(379)*v(407)+v(381)*v(793)&
&))/5040d0
v(408)=statev(18)*v(409)+statev(16)*v(445)+v(447)*v(707)
v(411)=v(232)*(v(379)*v(379))+v(410)+v(427)
v(417)=(v(383)*v(396)+v(382)*v(411)+v(380)*v(415))*v(719)
v(433)=v(417)*v(794)
v(413)=v(412)+v(431)+v(411)*v(795)
v(421)=(v(383)*v(398)+v(382)*v(413)+v(380)*v(417))*v(719)
v(437)=v(421)*v(794)
v(416)=v(414)+v(433)+v(413)*v(795)
v(423)=(v(383)*v(402)+v(382)*v(416)+v(380)*v(421))*v(719)
v(439)=v(423)*v(794)
v(419)=v(418)+v(437)+v(416)*v(795)
v(422)=v(420)+v(439)+v(419)*v(795)
v(797)=5040d0+v(422)
v(424)=(v(383)*v(404)+v(382)*v(419)+v(380)*v(423))*v(719)
v(444)=(7d0*(360d0*v(415)+120d0*v(417)+30d0*v(421)+6d0*v(423)+v(424))+v(719)*(v(383)*v(407)+v(380)*v(424)+v(382)*v(797)&
&))/5040d0
v(443)=v(424)*v(794)
v(449)=(2520d0*v(411)+840d0*v(413)+210d0*v(416)+42d0*v(419)+7d0*v(422)+v(443)+v(796)+v(795)*v(797))/5040d0
v(426)=statev(14)*v(409)+statev(19)*v(444)+v(449)*v(708)
v(429)=v(232)*(v(380)*v(380))+v(427)+v(428)
v(432)=v(430)+v(431)+v(429)*v(798)
v(435)=v(433)+v(434)+v(432)*v(798)
v(438)=v(436)+v(437)+v(435)*v(798)
v(441)=v(439)+v(440)+v(438)*v(798)
v(451)=(5040d0+2520d0*v(429)+840d0*v(432)+210d0*v(435)+42d0*v(438)+7d0*v(441)+v(442)+v(443)+(5040d0+v(441))*v(798))&
&/5040d0
v(446)=statev(15)*v(444)+statev(17)*v(445)+v(451)*v(709)
v(813)=(-2d0)*v(446)
v(448)=statev(19)*v(445)+statev(14)*v(447)+v(409)*v(708)
v(820)=v(426)*v(448)
v(818)=v(408)*v(448)
v(450)=statev(17)*v(409)+statev(15)*v(449)+v(444)*v(709)
v(817)=v(448)*v(450)
v(799)=v(446)*v(450)
v(542)=v(408)*v(799)
v(536)=v(448)*v(799)
v(452)=statev(18)*v(444)+statev(16)*v(451)+v(445)*v(707)
v(825)=v(408)*v(452)
v(453)=statev(15)*v(409)+statev(17)*v(447)+v(445)*v(709)
v(814)=-(v(450)*v(453))
v(566)=-(v(426)*v(453))+v(817)
v(557)=v(408)*v(446)-v(452)*v(453)
v(454)=statev(16)*v(444)+statev(18)*v(449)+v(409)*v(707)
v(819)=v(408)*v(454)
v(801)=v(448)*v(454)
v(800)=v(453)*v(454)
v(565)=v(408)*v(426)-v(801)
v(564)=-(v(408)*v(450))+v(800)
v(826)=(v(564)*v(564))+(v(565)*v(565))+(v(566)*v(566))
v(558)=v(450)*v(452)-v(446)*v(454)
v(541)=v(452)*v(800)
v(539)=v(452)*v(801)
v(455)=statev(14)*v(445)+statev(19)*v(451)+v(444)*v(708)
v(824)=v(448)*v(455)
v(803)=v(453)*v(455)
v(802)=v(408)*v(455)
v(562)=-(v(426)*v(452))+v(454)*v(455)
v(561)=v(448)*v(452)-v(802)
v(560)=-(v(446)*v(448))+v(803)
v(559)=v(426)*v(446)-v(450)*v(455)
v(538)=v(426)*v(802)
v(535)=v(426)*v(803)
v(530)=(-2d0)*v(452)*v(455)
v(456)=v(232)*(v(386)*v(386))+v(473)+v(491)
v(462)=(v(392)*v(456)+v(389)*v(458)+v(391)*v(459))*v(719)
v(497)=v(462)*v(804)
v(461)=(v(390)*v(456)+v(391)*v(458)+v(388)*v(459))*v(719)
v(477)=v(461)*v(805)
v(457)=v(475)+v(493)+v(456)*v(806)
v(465)=(v(390)*v(457)+v(388)*v(461)+v(391)*v(462))*v(719)
v(481)=v(465)*v(805)
v(464)=(v(392)*v(457)+v(391)*v(461)+v(389)*v(462))*v(719)
v(499)=v(464)*v(804)
v(460)=v(477)+v(497)+v(457)*v(806)
v(468)=(v(392)*v(460)+v(389)*v(464)+v(391)*v(465))*v(719)
v(503)=v(468)*v(804)
v(467)=(v(390)*v(460)+v(391)*v(464)+v(388)*v(465))*v(719)
v(483)=v(467)*v(805)
v(463)=v(481)+v(499)+v(460)*v(806)
v(466)=v(483)+v(503)+v(463)*v(806)
v(807)=5040d0+v(466)
v(469)=(v(392)*v(463)+v(391)*v(467)+v(389)*v(468))*v(719)
v(505)=v(469)*v(804)
v(470)=(v(390)*v(463)+v(388)*v(467)+v(391)*v(468))*v(719)
v(508)=(7d0*(360d0*v(458)+120d0*v(462)+30d0*v(464)+6d0*v(468)+v(469))+v(719)*(v(389)*v(469)+v(391)*v(470)+v(392)*v(807)&
&))/5040d0
v(488)=v(470)*v(805)
v(810)=5040d0+v(488)
v(510)=(2520d0*v(456)+840d0*v(457)+210d0*v(460)+42d0*v(463)+7d0*v(466)+v(505)+v(806)*v(807)+v(810))/5040d0
v(472)=(7d0*(360d0*v(459)+120d0*v(461)+30d0*v(465)+6d0*v(467)+v(470))+v(719)*(v(391)*v(469)+v(388)*v(470)+v(390)*v(807)&
&))/5040d0
v(471)=statev(27)*v(472)+statev(25)*v(508)+v(510)*v(710)
v(474)=v(232)*(v(388)*v(388))+v(473)+v(490)
v(480)=(v(392)*v(459)+v(391)*v(474)+v(389)*v(478))*v(719)
v(496)=v(480)*v(808)
v(476)=v(475)+v(494)+v(474)*v(809)
v(484)=(v(392)*v(461)+v(391)*v(476)+v(389)*v(480))*v(719)
v(500)=v(484)*v(808)
v(479)=v(477)+v(496)+v(476)*v(809)
v(486)=(v(392)*v(465)+v(391)*v(479)+v(389)*v(484))*v(719)
v(502)=v(486)*v(808)
v(482)=v(481)+v(500)+v(479)*v(809)
v(485)=v(483)+v(502)+v(482)*v(809)
v(811)=5040d0+v(485)
v(487)=(v(392)*v(467)+v(391)*v(482)+v(389)*v(486))*v(719)
v(507)=(7d0*(360d0*v(478)+120d0*v(480)+30d0*v(484)+6d0*v(486)+v(487))+v(719)*(v(392)*v(470)+v(389)*v(487)+v(391)*v(811)&
&))/5040d0
v(506)=v(487)*v(808)
v(512)=(2520d0*v(474)+840d0*v(476)+210d0*v(479)+42d0*v(482)+7d0*v(485)+v(506)+v(810)+v(809)*v(811))/5040d0
v(489)=statev(23)*v(472)+statev(28)*v(507)+v(512)*v(711)
v(492)=v(232)*(v(389)*v(389))+v(490)+v(491)
v(495)=v(493)+v(494)+v(492)*v(812)
v(498)=v(496)+v(497)+v(495)*v(812)
v(501)=v(499)+v(500)+v(498)*v(812)
v(504)=v(502)+v(503)+v(501)*v(812)
v(514)=(5040d0+2520d0*v(492)+840d0*v(495)+210d0*v(498)+42d0*v(501)+7d0*v(504)+v(505)+v(506)+(5040d0+v(504))*v(812))&
&/5040d0
v(509)=statev(24)*v(507)+statev(26)*v(508)+v(514)*v(712)
v(511)=statev(28)*v(508)+statev(23)*v(510)+v(472)*v(711)
v(513)=statev(26)*v(472)+statev(24)*v(512)+v(507)*v(712)
v(515)=statev(27)*v(507)+statev(25)*v(514)+v(508)*v(710)
v(516)=statev(24)*v(472)+statev(26)*v(510)+v(508)*v(712)
v(589)=v(511)*v(513)-v(489)*v(516)
v(580)=v(471)*v(509)-v(515)*v(516)
v(517)=statev(25)*v(507)+statev(27)*v(512)+v(472)*v(710)
v(588)=v(471)*v(489)-v(511)*v(517)
v(587)=-(v(471)*v(513))+v(516)*v(517)
v(581)=v(513)*v(515)-v(509)*v(517)
v(518)=statev(23)*v(508)+statev(28)*v(514)+v(507)*v(711)
v(585)=-(v(489)*v(515))+v(517)*v(518)
v(584)=v(511)*v(515)-v(471)*v(518)
v(583)=-(v(509)*v(511))+v(516)*v(518)
v(582)=v(489)*v(509)-v(513)*v(518)
v(519)=v(455)*v(564)+v(446)*v(565)+v(452)*v(566)
v(520)=(v(408)*v(408))
v(521)=(v(446)*v(446))
v(522)=(v(448)*v(448))
v(823)=v(520)+v(522)
v(523)=(v(452)*v(452))
v(815)=v(521)+v(523)
v(524)=v(453)*v(813)
v(525)=(v(453)*v(453))
v(822)=v(520)+v(525)
v(821)=v(522)+v(525)
v(526)=(v(455)*v(455))
v(816)=v(521)+v(526)
v(527)=v(530)*v(818)+v(523)*v(821)+v(526)*v(822)+v(521)*v(823)+v(524)*(v(824)+v(825))
v(528)=(v(426)*v(426))
v(529)=(v(450)*v(450))
v(531)=v(450)*v(813)
v(532)=(v(454)*v(454))
v(533)=(v(523)+v(526))*v(529)+v(426)*v(454)*v(530)+(v(452)*v(454)+v(426)*v(455))*v(531)+v(528)*v(815)+v(532)*v(816)
v(534)=v(446)*v(535)+v(455)*v(536)+v(452)*v(538)+v(455)*v(539)+v(446)*v(541)+v(452)*v(542)+v(523)*v(814)+v(526)*v(814)&
&-v(816)*v(819)-v(815)*v(820)
v(537)=v(453)*v(817)
v(540)=v(454)*v(818)
v(543)=v(453)*v(819)
v(544)=v(452)*(v(408)*(-v(814)+v(820))-v(454)*v(821))+v(455)*(v(537)+v(540)-v(426)*v(822))+v(446)*(v(543)+v(453)*v(820)&
&-v(450)*v(823))
v(545)=-(v(446)*v(453)*(v(528)+v(532)))+v(450)*v(535)+v(426)*v(536)+v(454)*v(538)+v(426)*v(539)+v(450)*v(541)+v(454)*v&
&(542)-v(529)*v(824)-v(532)*v(824)+(-v(528)-v(529))*v(825)
v(548)=1d0/((v(545)*(v(534)*v(544)-v(527)*v(545))-v(544)*(v(533)*v(544)-v(534)*v(545))+(v(527)*v(533)-(v(534)*v(534))&
&)*v(826))/v(519)**6)**0.3333333333333333d0
v(840)=-(mpar(9)*v(548))
v(546)=1d0/v(519)**2
v(842)=-(mpar(9)*v(546)*v(548))
v(841)=v(546)*v(840)
v(553)=-(v(546)*v(826))
v(551)=v(533)*v(546)
v(555)=-v(551)/3d0
v(550)=-(v(527)*v(546))
v(554)=v(550)/3d0
v(549)=v(553)/3d0
v(569)=1d0/(v(518)*v(587)+v(509)*v(588)+v(515)*v(589))**2
v(576)=-(v(569)*((v(587)*v(587))+(v(588)*v(588))+(v(589)*v(589))))
v(574)=1d0/v(569)**0.3333333333333333d0
v(827)=mpar(11)*v(574)
v(828)=v(569)*v(827)
v(573)=v(569)*((v(581)*v(581))+(v(582)*v(582))+(v(585)*v(585)))
v(578)=-v(573)/3d0
v(572)=-(v(569)*((v(580)*v(580))+(v(583)*v(583))+(v(584)*v(584))))
v(577)=v(572)/3d0
v(571)=v(576)/3d0
v(570)=(v(571)+(2d0/3d0)*v(573)+v(577))*v(827)
v(575)=(v(571)+(-2d0/3d0)*v(572)+v(578))*v(827)
v(586)=(v(580)*v(581)+v(582)*v(583)+v(584)*v(585))*v(828)
v(590)=(v(580)*v(587)+v(584)*v(588)+v(583)*v(589))*v(828)
v(591)=(v(581)*v(587)+v(585)*v(588)+v(582)*v(589))*v(828)
v(592)=-v(117)+v(829)
v(833)=v(592)*v(719)
v(593)=-v(119)+v(830)*x(13)
v(836)=v(593)*v(719)
v(594)=-v(120)+v(727)*v(830)
v(839)=v(594)*v(719)
v(595)=-v(121)+v(830)*x(14)
v(832)=v(595)*v(719)
v(615)=v(232)*(v(595)*v(595))
v(596)=-v(122)+v(830)*x(16)
v(835)=v(596)*v(719)
v(632)=v(232)*(v(596)*v(596))
v(597)=-v(123)+v(830)*x(15)
v(831)=v(597)*v(719)
v(633)=v(232)*(v(597)*v(597))
v(620)=v(232)*(-(v(592)*v(596))+v(595)*v(597))
v(636)=v(620)*v(835)
v(601)=v(232)*(-(v(594)*v(595))+v(596)*v(597))
v(617)=v(601)*v(832)
v(600)=v(232)*(v(595)*v(596)-v(593)*v(597))
v(635)=v(600)*v(831)
v(598)=v(232)*(v(592)*v(592))+v(615)+v(633)
v(604)=(v(597)*v(598)+v(594)*v(600)+v(596)*v(601))*v(719)
v(639)=v(604)*v(831)
v(603)=(v(595)*v(598)+v(596)*v(600)+v(593)*v(601))*v(719)
v(619)=v(603)*v(832)
v(599)=v(617)+v(635)+v(598)*v(833)
v(607)=(v(595)*v(599)+v(593)*v(603)+v(596)*v(604))*v(719)
v(623)=v(607)*v(832)
v(606)=(v(597)*v(599)+v(596)*v(603)+v(594)*v(604))*v(719)
v(641)=v(606)*v(831)
v(602)=v(619)+v(639)+v(599)*v(833)
v(610)=(v(597)*v(602)+v(594)*v(606)+v(596)*v(607))*v(719)
v(645)=v(610)*v(831)
v(609)=(v(595)*v(602)+v(596)*v(606)+v(593)*v(607))*v(719)
v(625)=v(609)*v(832)
v(605)=v(623)+v(641)+v(602)*v(833)
v(608)=v(625)+v(645)+v(605)*v(833)
v(834)=5040d0+v(608)
v(611)=(v(597)*v(605)+v(596)*v(609)+v(594)*v(610))*v(719)
v(647)=v(611)*v(831)
v(612)=(v(595)*v(605)+v(593)*v(609)+v(596)*v(610))*v(719)
v(650)=(7d0*(360d0*v(600)+120d0*v(604)+30d0*v(606)+6d0*v(610)+v(611))+v(719)*(v(594)*v(611)+v(596)*v(612)+v(597)*v(834)&
&))/5040d0
v(630)=v(612)*v(832)
v(837)=5040d0+v(630)
v(652)=(2520d0*v(598)+840d0*v(599)+210d0*v(602)+42d0*v(605)+7d0*v(608)+v(647)+v(833)*v(834)+v(837))/5040d0
v(614)=(7d0*(360d0*v(601)+120d0*v(603)+30d0*v(607)+6d0*v(609)+v(612))+v(719)*(v(596)*v(611)+v(593)*v(612)+v(595)*v(834)&
&))/5040d0
v(613)=statev(57)*v(614)+statev(55)*v(650)+v(652)*v(716)
v(616)=v(232)*(v(593)*v(593))+v(615)+v(632)
v(622)=(v(597)*v(601)+v(596)*v(616)+v(594)*v(620))*v(719)
v(638)=v(622)*v(835)
v(618)=v(617)+v(636)+v(616)*v(836)
v(626)=(v(597)*v(603)+v(596)*v(618)+v(594)*v(622))*v(719)
v(642)=v(626)*v(835)
v(621)=v(619)+v(638)+v(618)*v(836)
v(628)=(v(597)*v(607)+v(596)*v(621)+v(594)*v(626))*v(719)
v(644)=v(628)*v(835)
v(624)=v(623)+v(642)+v(621)*v(836)
v(627)=v(625)+v(644)+v(624)*v(836)
v(838)=5040d0+v(627)
v(629)=(v(597)*v(609)+v(596)*v(624)+v(594)*v(628))*v(719)
v(649)=(7d0*(360d0*v(620)+120d0*v(622)+30d0*v(626)+6d0*v(628)+v(629))+v(719)*(v(597)*v(612)+v(594)*v(629)+v(596)*v(838)&
&))/5040d0
v(648)=v(629)*v(835)
v(654)=(2520d0*v(616)+840d0*v(618)+210d0*v(621)+42d0*v(624)+7d0*v(627)+v(648)+v(837)+v(836)*v(838))/5040d0
v(631)=statev(53)*v(614)+statev(58)*v(649)+v(654)*v(717)
v(634)=v(232)*(v(594)*v(594))+v(632)+v(633)
v(637)=v(635)+v(636)+v(634)*v(839)
v(640)=v(638)+v(639)+v(637)*v(839)
v(643)=v(641)+v(642)+v(640)*v(839)
v(646)=v(644)+v(645)+v(643)*v(839)
v(656)=(5040d0+2520d0*v(634)+840d0*v(637)+210d0*v(640)+42d0*v(643)+7d0*v(646)+v(647)+v(648)+(5040d0+v(646))*v(839))&
&/5040d0
v(651)=statev(54)*v(649)+statev(56)*v(650)+v(656)*v(718)
v(653)=statev(58)*v(650)+statev(53)*v(652)+v(614)*v(717)
v(655)=statev(56)*v(614)+statev(54)*v(654)+v(649)*v(718)
v(657)=statev(57)*v(649)+statev(55)*v(656)+v(650)*v(716)
v(658)=statev(54)*v(614)+statev(56)*v(652)+v(650)*v(718)
v(701)=v(653)*v(655)-v(631)*v(658)
v(693)=v(613)*v(651)-v(657)*v(658)
v(659)=statev(55)*v(649)+statev(57)*v(654)+v(614)*v(716)
v(702)=v(613)*v(631)-v(653)*v(659)
v(700)=-(v(613)*v(655))+v(658)*v(659)
v(694)=v(655)*v(657)-v(651)*v(659)
v(660)=statev(53)*v(650)+statev(58)*v(656)+v(649)*v(717)
v(698)=-(v(631)*v(657))+v(659)*v(660)
v(697)=v(653)*v(657)-v(613)*v(660)
v(696)=-(v(651)*v(653))+v(658)*v(660)
v(695)=v(631)*v(651)-v(655)*v(660)
v(662)=(2d0/3d0)*v(352)-v(570)+v(663)+v(665)+(v(549)+(2d0/3d0)*v(551)+v(554))*v(840)
v(664)=(2d0/3d0)*v(342)-v(575)+v(663)+v(666)+(v(549)+(-2d0/3d0)*v(550)+v(555))*v(840)
v(667)=(2d0/3d0)*v(347)+v(665)+v(666)+((2d0/3d0)*v(576)-v(577)-v(578))*v(827)+((-2d0/3d0)*v(553)+v(554)+v(555))*v(840)
v(668)=v(354)-v(586)+v(534)*v(841)
v(843)=2d0*v(668)
v(669)=v(355)-v(590)+(v(557)*v(564)+v(561)*v(565)+v(560)*v(566))*v(842)
v(844)=2d0*v(669)
v(670)=v(356)-mpar(9)*v(546)*v(548)*(v(558)*v(564)+v(562)*v(565)+v(559)*v(566))-v(591)
v(845)=2d0*v(670)
v(683)=1d0/(v(660)*v(700)+v(657)*v(701)+v(651)*v(702))**2
v(690)=-(v(683)*((v(694)*v(694))+(v(695)*v(695))+(v(698)*v(698))))
v(689)=-(v(683)*((v(693)*v(693))+(v(696)*v(696))+(v(697)*v(697))))
v(687)=1d0/v(683)**0.3333333333333333d0
v(846)=-(mpar(15)*v(687))
v(847)=v(683)*v(846)
v(688)=-(v(683)*((v(700)*v(700))+(v(701)*v(701))+(v(702)*v(702))))/3d0
R(1)=-mpar(3)-mpar(5)*(1d0-dexp(-(mpar(4)*v(116))))-mpar(7)*(1d0-dexp(-(mpar(6)*v(116))))+sqrt(v(662)*(v(156)*v(662)+v&
&(161)*v(664)+v(166)*v(667)+v(167)*v(843)+v(168)*v(844)+v(169)*v(845))+v(664)*(v(161)*v(662)+v(172)*v(664)+v(174)*v(667)&
&+v(178)*v(843)+v(181)*v(844)+v(183)*v(845))+v(667)*(v(166)*v(662)+v(174)*v(664)+v(186)*v(667)+v(187)*v(843)+v(190)*v&
&(844)+v(191)*v(845))+v(843)*(v(167)*v(662)+v(178)*v(664)+v(187)*v(667)+v(196)*v(843)+v(198)*v(844)+v(199)*v(845))+v(844&
&)*(v(168)*v(662)+v(181)*v(664)+v(190)*v(667)+v(198)*v(843)+v(205)*v(844)+v(207)*v(845))+v(845)*(v(169)*v(662)+v(183)*v&
&(664)+v(191)*v(667)+v(199)*v(843)+v(207)*v(844)+v(214)*v(845)))
R(2)=-v(662)+x(2)
R(3)=-v(664)+x(3)
R(4)=-v(668)+x(4)
R(5)=-v(670)+x(5)
R(6)=-v(669)+x(6)
R(7)=-v(570)+x(7)
R(8)=-v(575)+x(8)
R(9)=-v(586)+x(9)
R(10)=-v(591)+x(10)
R(11)=-v(590)+x(11)
R(12)=(v(688)+v(689)/3d0+(-2d0/3d0)*v(690))*v(846)+x(12)
R(13)=(v(688)+(-2d0/3d0)*v(689)+v(690)/3d0)*v(846)+x(13)
R(14)=(v(693)*v(694)+v(695)*v(696)+v(697)*v(698))*v(847)+x(14)
R(15)=(v(694)*v(700)+v(695)*v(701)+v(698)*v(702))*v(847)+x(15)
R(16)=(v(693)*v(700)+v(696)*v(701)+v(697)*v(702))*v(847)+x(16)
END SUBROUTINE
!**************************************************************
!* AceGen 6.702 Windows (4 May 16) *
!* Co. J. Korelc 2013 16 Nov 19 16:43:05 *
!**************************************************************
! User : Full professional version
! Notebook : MainFile
! Evaluation time : 1521 s Mode : Optimal
! Number of formulae : 7595 Method: Automatic
! Subroutine : jacobian size: 212632
! Total size of Mathematica code : 212632 subexpressions
! Total size of Fortran code : 514647 bytes
!******************* S U B R O U T I N E **********************
SUBROUTINE jacobian(x,mpar,statev,Fnew,dRdX)
USE SMSUtility
IMPLICIT NONE
DOUBLE PRECISION v(8244),x(16),mpar(16),statev(58),Fnew(9),dRdX(16,16)
v(7996)=1d0/mpar(10)
v(7994)=1d0/mpar(12)
v(7993)=2d0*x(10)
v(7992)=2d0*x(11)
v(7991)=2d0*x(9)
v(7790)=0.15d1*mpar(8)
v(7702)=8d0*x(5)*x(6)
v(7692)=8d0*x(4)
v(7704)=v(7692)*x(6)
v(7703)=v(7692)*x(5)
v(7689)=2d0*x(5)
v(7688)=2d0*x(4)
v(7686)=x(5)**2
v(7696)=4d0*v(7686)
v(7684)=x(6)**2
v(7694)=4d0*v(7684)
v(7682)=x(4)**2
v(7691)=4d0*v(7682)
v(7665)=2d0*x(6)
v(7646)=mpar(14)**2
v(7655)=4d0*v(7646)
v(7654)=2d0*v(7646)
v(7585)=2d0*mpar(14)
v(7555)=(-8d0)*statev(48)
v(7549)=(-8d0)*statev(47)
v(7535)=2d0*x(15)
v(7534)=2d0*x(16)
v(7533)=2d0*x(14)
v(7532)=-x(12)-x(13)
v(7531)=-x(7)-x(8)
v(7530)=2d0*v(7684)
v(7529)=2d0*v(7686)
v(7528)=2d0*v(7682)
v(7527)=x(3)**2
v(7526)=x(2)**2
v(7525)=2d0*x(2)
v(7524)=2d0*x(3)
v(7523)=-x(2)-x(3)
v(7687)=(v(7523)*v(7523))
v(7522)=dabs(x(1))
v(8118)=2d0*v(7522)
v(7521)=4d0*x(6)
v(7716)=v(7521)*x(3)
v(7698)=v(7521)*v(7523)
v(7520)=4d0*x(5)
v(7712)=v(7520)*x(3)
v(7697)=v(7520)*v(7523)
v(7519)=4d0*x(4)
v(7717)=v(7519)*x(3)
v(7699)=v(7519)*v(7523)
v(7518)=dsign(1.d0,x(1))
v(7517)=1d0+statev(52)
v(7516)=1d0+statev(51)
v(7515)=1d0+statev(50)
v(7514)=1d0+statev(3)
v(7513)=1d0+statev(2)
v(7512)=1d0+statev(1)
v(7511)=1d0+statev(22)
v(7510)=1d0+statev(21)
v(7509)=1d0+statev(20)
v(7508)=1d0+statev(13)
v(7507)=1d0+statev(12)
v(7506)=1d0+statev(11)
v(7505)=(-1d0/3d0)+statev(40)
v(7561)=2d0*v(7505)
v(7504)=(-1d0/3d0)+statev(36)
v(7560)=2d0*v(7504)
v(7503)=(-1d0/3d0)+statev(35)
v(7559)=2d0*v(7503)
v(7502)=0.5d0+statev(34)
v(7558)=4d0*v(7502)
v(7501)=0.5d0+statev(33)
v(7557)=4d0*v(7501)
v(7500)=0.5d0+statev(32)
v(7556)=4d0*v(7500)
v(7499)=(2d0/3d0)+statev(31)
v(7498)=(2d0/3d0)+statev(30)
v(7497)=(2d0/3d0)+statev(29)
v(7496)=1d0/mpar(16)
v(7495)=1d0-mpar(8)
v(6592)=v(7496)*v(7522)
v(8164)=5040d0*v(6592)
v(1738)=v(7518)*v(8118)
v(821)=dexp((-7d0)*mpar(13)*v(7522))
v(824)=(-1d0)+v(821)
v(7551)=v(824)/7d0
v(680)=(-2d0)*v(7523)
v(7715)=-(v(680)*x(3))
v(681)=v(680)+v(7524)
v(679)=v(680)+v(7525)
v(216)=v(7526)+v(7527)+v(7528)+v(7529)+v(7530)+v(7687)
v(693)=0.1d-19+v(216)
v(692)=1d0/sqrt(v(693))
v(695)=-v(692)/(2d0*v(693))
v(699)=v(695)*v(7521)
v(768)=v(699)*x(4)
v(6768)=-(v(7522)*v(768))
v(891)=v(7549)*v(768)
v(737)=v(699)*v(7523)
v(714)=v(699)*x(3)
v(704)=v(699)*x(2)
v(698)=v(695)*v(7520)
v(782)=v(698)*x(6)
v(6771)=-(v(7522)*v(782))
v(8169)=720d0*v(6771)
v(767)=v(698)*x(4)
v(7562)=2d0*v(767)
v(6604)=-(v(7522)*v(767))
v(880)=v(7555)*v(767)
v(736)=v(698)*v(7523)
v(713)=v(698)*x(3)
v(703)=v(698)*x(2)
v(697)=v(695)*v(7519)
v(735)=v(697)*v(7523)
v(712)=v(697)*x(3)
v(702)=v(697)*x(2)
v(696)=v(681)*v(695)
v(796)=v(696)*x(5)
v(781)=v(696)*x(6)
v(765)=v(696)*x(4)
v(701)=v(696)*x(2)
v(694)=v(679)*v(695)
v(795)=v(694)*x(5)
v(780)=v(694)*x(6)
v(764)=v(694)*x(4)
v(710)=v(694)*x(3)
v(685)=1d0/sqrt(v(216))
v(687)=-v(685)/(2d0*v(216))
v(691)=v(687)*v(7521)
v(690)=v(687)*v(7520)
v(689)=v(687)*v(7519)
v(688)=v(681)*v(687)
v(686)=v(679)*v(687)
v(797)=v(692)+v(698)*x(5)
v(783)=v(692)+v(699)*x(6)
v(766)=v(692)+v(697)*x(4)
v(734)=-v(692)+v(696)*v(7523)
v(733)=-v(692)+v(694)*v(7523)
v(711)=v(692)+v(696)*x(3)
v(700)=v(692)+v(694)*x(2)
v(808)=v(737)*v(7532)+v(7533)*v(768)+v(7535)*v(782)+v(7534)*v(783)+v(704)*x(12)+v(714)*x(13)
v(807)=v(736)*v(7532)+v(7533)*v(767)+v(7534)*v(782)+v(7535)*v(797)+v(703)*x(12)+v(713)*x(13)
v(806)=v(735)*v(7532)+v(7533)*v(766)+v(7535)*v(767)+v(7534)*v(768)+v(702)*x(12)+v(712)*x(13)
v(805)=v(734)*v(7532)+v(7533)*v(765)+v(7534)*v(781)+v(7535)*v(796)+v(701)*x(12)+v(711)*x(13)
v(804)=v(733)*v(7532)+v(7533)*v(764)+v(7534)*v(780)+v(7535)*v(795)+v(700)*x(12)+v(710)*x(13)
v(116)=statev(10)+v(7522)
v(117)=v(692)*x(2)
v(7537)=(-2d0)*v(117)
v(7536)=(-4d0)*v(117)
v(893)=statev(38)*v(7536)
v(881)=statev(39)*v(7536)
v(869)=statev(37)*v(7536)
v(820)=v(704)*v(7537)
v(819)=v(703)*v(7537)
v(818)=v(702)*v(7537)
v(817)=v(701)*v(7537)
v(816)=v(700)*v(7537)
v(217)=-(v(117)*x(12))
v(119)=v(692)*x(3)
v(7539)=(-2d0)*v(119)
v(7538)=(-4d0)*v(119)
v(894)=statev(42)*v(7538)
v(882)=statev(43)*v(7538)
v(870)=statev(41)*v(7538)
v(732)=v(714)*v(7539)
v(731)=v(713)*v(7539)
v(730)=v(712)*v(7539)
v(729)=v(711)*v(7539)
v(728)=v(710)*v(7539)
v(727)=v(704)*v(7539)
v(725)=v(703)*v(7539)
v(723)=v(702)*v(7539)
v(721)=-(v(119)*v(701))-v(117)*v(711)
v(720)=-(v(119)*v(700))-v(117)*v(710)
v(218)=-(v(119)*x(13))
v(137)=(-1d0/3d0)-v(117)*v(119)
v(127)=(2d0/3d0)-(v(119)*v(119))
v(120)=v(692)*v(7523)
v(7541)=(-2d0)*v(120)
v(7540)=(-4d0)*v(120)
v(861)=statev(46)*v(7540)
v(7572)=v(861)+v(882)
v(859)=statev(45)*v(7540)
v(7573)=v(859)+v(894)
v(856)=statev(44)*v(7540)
v(7570)=v(856)+v(870)
v(810)=v(119)-v(120)
v(809)=v(117)-v(120)
v(763)=v(737)*v(7541)
v(762)=v(736)*v(7541)
v(761)=v(735)*v(7541)
v(760)=v(734)*v(7541)
v(759)=v(733)*v(7541)
v(758)=v(704)*v(7541)
v(756)=v(703)*v(7541)
v(754)=v(702)*v(7541)
v(752)=-(v(120)*v(701))-v(117)*v(734)
v(751)=-(v(120)*v(700))-v(117)*v(733)
v(750)=v(714)*v(7541)
v(748)=v(713)*v(7541)
v(746)=v(712)*v(7541)
v(744)=-(v(120)*v(711))-v(119)*v(734)
v(743)=-(v(120)*v(710))-v(119)*v(733)
v(219)=-(v(120)*v(7532))
v(144)=(-1d0/3d0)-v(119)*v(120)
v(139)=(-1d0/3d0)-v(117)*v(120)
v(129)=(2d0/3d0)-(v(120)*v(120))
v(121)=v(692)*x(4)
v(7543)=(-2d0)*v(121)
v(7542)=(-4d0)*v(121)
v(836)=statev(44)*v(7542)
v(7554)=2d0*v(836)
v(828)=statev(41)*v(7542)
v(7553)=2d0*v(828)
v(825)=statev(37)*v(7542)
v(7552)=2d0*v(825)
v(779)=v(7543)*v(768)
v(778)=v(7543)*v(767)
v(777)=v(7543)*v(766)
v(776)=v(7543)*v(765)
v(775)=v(7543)*v(764)
v(220)=v(7543)*x(14)
v(131)=0.5d0-(v(121)*v(121))
v(122)=v(692)*x(6)
v(7546)=(-2d0)*v(122)
v(7545)=(-4d0)*v(122)
v(7544)=(-8d0)*v(122)
v(883)=statev(49)*v(7544)
v(842)=statev(47)*v(7544)
v(837)=statev(45)*v(7545)
v(7567)=2d0*v(837)
v(830)=statev(42)*v(7545)
v(7565)=2d0*v(830)
v(826)=statev(38)*v(7545)
v(7563)=2d0*v(826)
v(794)=v(7546)*v(783)
v(793)=v(7546)*v(782)
v(792)=v(7546)*v(768)
v(791)=v(7546)*v(781)
v(790)=v(7546)*v(780)
v(221)=v(7546)*x(16)
v(133)=0.5d0-(v(122)*v(122))
v(123)=v(692)*x(5)
v(7550)=(-2d0)*v(123)
v(7548)=(-4d0)*v(123)
v(7547)=(-8d0)*v(123)
v(847)=statev(49)*v(7547)
v(7577)=2d0*v(847)
v(844)=statev(48)*v(7547)
v(7580)=v(842)+v(844)
v(7571)=2d0*v(844)
v(7576)=v(7571)+2d0*v(842)
v(838)=statev(46)*v(7548)
v(7575)=v(836)+v(837)+v(838)
v(7568)=2d0*v(838)
v(832)=statev(43)*v(7548)
v(7579)=v(828)+v(830)+v(832)
v(7566)=2d0*v(832)
v(7574)=v(7565)+v(7566)
v(827)=statev(39)*v(7548)
v(7578)=v(825)+v(826)+v(827)
v(7564)=2d0*v(827)
v(7569)=v(7563)+v(7564)
v(815)=v(7550)*v(782)
v(895)=v(7551)*(v(732)*v(7498)+v(727)*v(7559)+v(750)*v(7561)+v(7560)*v(758)+v(7499)*v(763)+v(7571)*v(768)+v(7556)*v(779&
&)+v(7557)*v(794)+v(7558)*v(815)+v(7497)*v(820)+v(704)*(v(7552)+v(7564)+v(826))+v(714)*(v(7553)+v(7566)+v(830))+v(737)*&
&(v(7554)+v(7568)+v(837))+v(782)*v(883)+v(122)*v(891)+v(783)*(v(121)*v(7549)+v(7573)+v(847)+v(893)))
v(7624)=v(117)*v(895)
v(7613)=v(119)*v(895)
v(7600)=v(120)*v(895)
v(7591)=v(121)*v(895)
v(814)=v(7550)*v(797)
v(884)=v(7551)*(v(731)*v(7498)+v(725)*v(7559)+v(756)*v(7560)+v(748)*v(7561)+v(7499)*v(762)+v(7556)*v(778)+v(7557)*v(793&
&)+v(7558)*v(814)+v(7497)*v(819)+v(703)*(v(7552)+v(7563)+v(827))+v(713)*(v(7553)+v(7565)+v(832))+v(736)*(v(7554)+v(7567)&
&+v(838))+v(7562)*v(842)+v(782)*v(847)+v(123)*v(880)+v(797)*(v(121)*v(7555)+v(7572)+v(881)+v(883)))
v(7625)=v(117)*v(884)
v(7614)=v(119)*v(884)
v(7601)=v(120)*v(884)
v(7593)=v(121)*v(884)
v(813)=-(v(123)*v(7562))
v(872)=v(7551)*(v(730)*v(7498)+v(723)*v(7559)+v(754)*v(7560)+v(746)*v(7561)+v(7499)*v(761)+v(7556)*v(777)+v(7557)*v(792&
&)+v(7558)*v(813)+v(7497)*v(818)+v(702)*(v(7569)+v(825))+v(712)*(v(7574)+v(828))+v(735)*(v(7567)+v(7568)+v(836))+v(766)*&
&(v(7570)+v(7580)+v(869))+v(7562)*v(883)+v(121)*(v(880)+v(891)))
v(7632)=v(117)*v(872)
v(7621)=v(119)*v(872)
v(7610)=v(120)*v(872)
v(7606)=-(v(122)*v(872))
v(812)=v(7550)*v(796)
v(862)=v(7551)*(v(729)*v(7498)+v(721)*v(7559)+v(752)*v(7560)+v(744)*v(7561)+v(701)*(v(7552)+v(7569))+v(734)*v(7575)+v&
&(711)*v(7579)+v(7499)*v(760)+(v(7570)+v(7576))*v(765)+v(7556)*v(776)+(v(7573)+v(7577))*v(781)+v(7557)*v(791)+v(7572)*v&
&(796)+v(7558)*v(812)+v(7497)*v(817))
v(811)=v(7550)*v(795)
v(852)=v(7551)*(v(728)*v(7498)+v(720)*v(7559)+v(751)*v(7560)+v(743)*v(7561)+v(710)*(v(7553)+v(7574))+v(733)*v(7575)+v&
&(700)*v(7578)+v(7499)*v(759)+v(7556)*v(775)+v(7557)*v(790)+v(7558)*v(811)+v(7497)*v(816)+v(764)*(v(7576)+v(856)+v(869))&
&+v(795)*(v(861)+v(881))+v(780)*(v(7577)+v(859)+v(893)))
v(222)=v(7550)*x(15)
v(226)=-v(217)-v(218)-v(219)-v(220)-v(221)-v(222)
v(1715)=-(v(226)*v(782))
v(1711)=-(v(226)*v(767))
v(1702)=-(v(123)*v(226))+x(15)
v(7736)=-(v(1702)*v(685))
v(1679)=-(v(226)*v(768))
v(1670)=-(v(122)*v(226))+x(16)
v(7741)=-(v(1670)*v(685))
v(1642)=-(v(121)*v(226))+x(14)
v(7746)=-(v(1642)*v(685))
v(1616)=-(v(120)*v(226))+v(7532)
v(7751)=-(v(1616)*v(685))
v(1589)=-(v(119)*v(226))+x(13)
v(7754)=-(v(1589)*v(685))
v(1563)=-(v(117)*v(226))+x(12)
v(7766)=-(v(1563)*v(685))
v(157)=1d0+v(217)+v(218)+v(219)+v(220)+v(221)+v(222)
v(7648)=0.15d1*v(157)
v(135)=0.5d0-(v(123)*v(123))
v(124)=(2d0/3d0)-(v(117)*v(117))
v(822)=v(124)*v(7497)+v(127)*v(7498)+v(129)*v(7499)+v(131)*v(7556)+v(133)*v(7557)+v(135)*v(7558)+v(137)*v(7559)+v(139&
&)*v(7560)+v(144)*v(7561)+v(120)*v(7575)+v(117)*v(7578)+v(119)*v(7579)+v(121)*v(7580)+v(122)*v(847)
v(823)=-(mpar(13)*v(7518)*v(821)*v(822))
v(7584)=mpar(14)*v(823)
v(7583)=-(v(121)*v(823))
v(7582)=-(v(122)*v(823))
v(7581)=-(v(123)*v(823))
v(1180)=v(122)*v(7581)
v(1172)=v(121)*v(7581)
v(1163)=v(121)*v(7582)
v(1151)=v(120)*v(7581)
v(1138)=v(120)*v(7582)
v(1124)=v(120)*v(7583)
v(1111)=v(119)*v(7581)
v(1097)=v(119)*v(7582)
v(1082)=v(119)*v(7583)
v(1065)=v(144)*v(7584)
v(1051)=v(117)*v(7581)
v(1037)=v(117)*v(7582)
v(1022)=v(117)*v(7583)
v(1005)=v(139)*v(7584)
v(987)=v(137)*v(7584)
v(969)=v(135)*v(7584)
v(980)=v(7585)*v(969)
v(951)=v(133)*v(7584)
v(962)=v(7585)*v(951)
v(933)=v(131)*v(7584)
v(944)=v(7585)*v(933)
v(921)=v(129)*v(7584)
v(909)=v(127)*v(7584)
v(897)=v(124)*v(7584)
v(126)=v(7551)*v(822)
v(7645)=-(v(121)*v(126))
v(7629)=v(126)*v(704)
v(7628)=v(126)*v(700)+v(117)*v(852)
v(7623)=v(126)*v(703)
v(7622)=-(v(117)*v(126))
v(7618)=v(126)*v(714)
v(7616)=v(126)*v(711)+v(119)*v(862)
v(7612)=v(126)*v(713)
v(7611)=-(v(119)*v(126))
v(7609)=v(126)*v(766)
v(7605)=v(126)*v(737)
v(7604)=v(126)*v(733)+v(120)*v(852)
v(7603)=v(126)*v(734)+v(120)*v(862)
v(7599)=v(126)*v(736)
v(7598)=-(v(120)*v(126))
v(7595)=v(7609)+v(121)*v(872)
v(7594)=v(126)*v(768)
v(7590)=-(v(126)*v(783))
v(7589)=v(126)*v(767)
v(7588)=-(v(126)*v(797))
v(7587)=(-2d0)*v(126)
v(7627)=v(701)*v(7587)-v(117)*v(862)
v(7617)=v(710)*v(7587)-v(119)*v(852)
v(7597)=v(7587)*v(764)-v(121)*v(852)
v(7596)=v(7587)*v(765)-v(121)*v(862)
v(7586)=v(126)*v(782)
v(1187)=v(123)*v(7590)-v(122)*(v(7586)+v(123)*v(895))
v(1186)=v(122)*v(7588)-v(123)*(v(7586)+v(122)*v(884))
v(1184)=v(123)*(v(7587)*v(781)-v(122)*v(862))
v(1182)=v(123)*(v(7587)*v(780)-v(122)*v(852))
v(1178)=v(121)*v(7588)-v(123)*(v(7589)+v(7593))
v(1177)=-(v(121)*v(7589))-v(123)*v(7595)
v(1176)=v(123)*v(7596)
v(1174)=v(123)*v(7597)
v(1171)=v(121)*v(7590)-v(122)*(v(7591)+v(7594))
v(1169)=-(v(122)*v(7589))
v(7592)=2d0*v(1169)
v(1185)=v(7592)+v(123)*v(7606)
v(1179)=-(v(123)*v(7591))+v(7592)
v(1170)=v(7592)-v(122)*v(7593)
v(1168)=-(v(121)*v(7594))-v(122)*v(7595)
v(1167)=v(122)*v(7596)
v(1165)=v(122)*v(7597)
v(1155)=v(120)*v(7588)-v(123)*(v(7599)+v(7601))
v(1153)=-(v(123)*v(7603))+v(7598)*v(796)
v(1152)=-(v(123)*v(7604))+v(7598)*v(795)
v(1144)=v(120)*v(7590)-v(122)*(v(7600)+v(7605))
v(1142)=-(v(122)*v(7599))
v(7602)=2d0*v(1142)
v(1156)=-(v(123)*v(7600))+v(7602)
v(1143)=-(v(122)*v(7601))+v(7602)
v(1140)=-(v(122)*v(7603))+v(7598)*v(781)
v(1139)=-(v(122)*v(7604))+v(7598)*v(780)
v(1130)=-(v(121)*v(7605))
v(7607)=2d0*v(1130)
v(1141)=v(120)*v(7606)+v(7607)
v(1131)=-(v(120)*v(7591))+v(7607)
v(1128)=-(v(121)*v(7599))
v(7608)=2d0*v(1128)
v(1154)=v(7608)-v(123)*v(7610)
v(1129)=-(v(120)*v(7593))+v(7608)
v(1127)=-(v(120)*v(7609))-v(121)*(v(126)*v(735)+v(7610))
v(1126)=-(v(121)*v(7603))+v(7598)*v(765)
v(1125)=-(v(121)*v(7604))+v(7598)*v(764)
v(1116)=v(119)*v(7588)-v(123)*(v(7612)+v(7614))
v(1114)=-(v(123)*v(7616))+v(7611)*v(796)
v(1113)=v(123)*v(7617)
v(1104)=-(v(122)*(v(7613)+v(7618)))+v(7611)*v(783)
v(1102)=-(v(122)*v(7612))
v(7615)=2d0*v(1102)
v(1117)=-(v(123)*v(7613))+v(7615)
v(1103)=-(v(122)*v(7614))+v(7615)
v(1100)=-(v(122)*v(7616))+v(7611)*v(781)
v(1099)=v(122)*v(7617)
v(1089)=-(v(121)*v(7618))
v(7619)=2d0*v(1089)
v(1101)=v(119)*v(7606)+v(7619)
v(1090)=-(v(119)*v(7591))+v(7619)
v(1087)=-(v(121)*v(7612))
v(7620)=2d0*v(1087)
v(1115)=v(7620)-v(123)*v(7621)
v(1088)=-(v(119)*v(7593))+v(7620)
v(1086)=-(v(119)*v(7609))-v(121)*(v(126)*v(712)+v(7621))
v(1085)=-(v(121)*v(7616))+v(7611)*v(765)
v(1084)=v(121)*v(7617)
v(1075)=mpar(14)*(v(126)*v(750)+v(144)*v(895))
v(1073)=mpar(14)*(v(126)*v(748)+v(144)*v(884))
v(1071)=mpar(14)*(v(126)*v(746)+v(144)*v(872))
v(1069)=mpar(14)*(v(126)*v(744)+v(144)*v(862))
v(1067)=mpar(14)*(v(126)*v(743)+v(144)*v(852))
v(1056)=v(117)*v(7588)-v(123)*(v(7623)+v(7625))
v(1054)=v(123)*v(7627)
v(1052)=-(v(123)*v(7628))+v(7622)*v(795)
v(1044)=-(v(122)*(v(7624)+v(7629)))+v(7622)*v(783)
v(1042)=-(v(122)*v(7623))
v(7626)=2d0*v(1042)
v(1057)=-(v(123)*v(7624))+v(7626)
v(1043)=-(v(122)*v(7625))+v(7626)
v(1040)=v(122)*v(7627)
v(1038)=-(v(122)*v(7628))+v(7622)*v(780)
v(1029)=-(v(121)*v(7629))
v(7630)=2d0*v(1029)
v(1041)=v(117)*v(7606)+v(7630)
v(1030)=-(v(117)*v(7591))+v(7630)
v(1027)=-(v(121)*v(7623))
v(7631)=2d0*v(1027)
v(1055)=v(7631)-v(123)*v(7632)
v(1028)=-(v(117)*v(7593))+v(7631)
v(1026)=-(v(117)*v(7609))-v(121)*(v(126)*v(702)+v(7632))
v(1025)=v(121)*v(7627)
v(1023)=-(v(121)*v(7628))+v(7622)*v(764)
v(1015)=mpar(14)*(v(126)*v(758)+v(139)*v(895))
v(1013)=mpar(14)*(v(126)*v(756)+v(139)*v(884))
v(1011)=mpar(14)*(v(126)*v(754)+v(139)*v(872))
v(1009)=mpar(14)*(v(126)*v(752)+v(139)*v(862))
v(1007)=mpar(14)*(v(126)*v(751)+v(139)*v(852))
v(997)=mpar(14)*(v(126)*v(727)+v(137)*v(895))
v(995)=mpar(14)*(v(126)*v(725)+v(137)*v(884))
v(993)=mpar(14)*(v(126)*v(723)+v(137)*v(872))
v(991)=mpar(14)*(v(126)*v(721)+v(137)*v(862))
v(989)=mpar(14)*(v(126)*v(720)+v(137)*v(852))
v(979)=mpar(14)*(v(126)*v(815)+v(135)*v(895))
v(985)=v(7585)*v(979)
v(977)=mpar(14)*(v(126)*v(814)+v(135)*v(884))
v(984)=v(7585)*v(977)
v(975)=mpar(14)*(v(126)*v(813)+v(135)*v(872))
v(983)=v(7585)*v(975)
v(973)=mpar(14)*(v(126)*v(812)+v(135)*v(862))
v(982)=v(7585)*v(973)
v(971)=mpar(14)*(v(126)*v(811)+v(135)*v(852))
v(981)=v(7585)*v(971)
v(961)=mpar(14)*(v(126)*v(794)+v(133)*v(895))
v(967)=v(7585)*v(961)
v(959)=mpar(14)*(v(126)*v(793)+v(133)*v(884))
v(966)=v(7585)*v(959)
v(957)=mpar(14)*(v(126)*v(792)+v(133)*v(872))
v(965)=v(7585)*v(957)
v(955)=mpar(14)*(v(126)*v(791)+v(133)*v(862))
v(964)=v(7585)*v(955)
v(953)=mpar(14)*(v(126)*v(790)+v(133)*v(852))
v(963)=v(7585)*v(953)
v(943)=mpar(14)*(v(126)*v(779)+v(131)*v(895))
v(949)=v(7585)*v(943)
v(941)=mpar(14)*(v(126)*v(778)+v(131)*v(884))
v(948)=v(7585)*v(941)
v(939)=mpar(14)*(v(126)*v(777)+v(131)*v(872))
v(947)=v(7585)*v(939)
v(937)=mpar(14)*(v(126)*v(776)+v(131)*v(862))
v(946)=v(7585)*v(937)
v(935)=mpar(14)*(v(126)*v(775)+v(131)*v(852))
v(945)=v(7585)*v(935)
v(931)=mpar(14)*(v(126)*v(763)+v(129)*v(895))
v(929)=mpar(14)*(v(126)*v(762)+v(129)*v(884))
v(927)=mpar(14)*(v(126)*v(761)+v(129)*v(872))
v(925)=mpar(14)*(v(126)*v(760)+v(129)*v(862))
v(923)=mpar(14)*(v(126)*v(759)+v(129)*v(852))
v(919)=mpar(14)*(v(126)*v(732)+v(127)*v(895))
v(917)=mpar(14)*(v(126)*v(731)+v(127)*v(884))
v(915)=mpar(14)*(v(126)*v(730)+v(127)*v(872))
v(913)=mpar(14)*(v(126)*v(729)+v(127)*v(862))
v(911)=mpar(14)*(v(126)*v(728)+v(127)*v(852))
v(907)=mpar(14)*(v(126)*v(820)+v(124)*v(895))
v(905)=mpar(14)*(v(126)*v(819)+v(124)*v(884))
v(903)=mpar(14)*(v(126)*v(818)+v(124)*v(872))
v(901)=mpar(14)*(v(126)*v(817)+v(124)*v(862))
v(899)=mpar(14)*(v(126)*v(816)+v(124)*v(852))
v(158)=(2d0/3d0)+mpar(14)*(statev(29)+v(124)*v(126))
v(7653)=2d0*v(158)
v(170)=(2d0/3d0)+mpar(14)*(statev(30)+v(126)*v(127))
v(7705)=v(158)+v(170)
v(7651)=2d0*v(170)
v(173)=(2d0/3d0)+mpar(14)*(statev(31)+v(126)*v(129))
v(7681)=v(158)+v(173)
v(7676)=v(170)+v(173)
v(7649)=2d0*v(173)
v(192)=0.5d0+mpar(14)*(statev(32)+v(126)*v(131))
v(7663)=4d0*v(192)
v(175)=v(192)*v(7585)
v(200)=0.5d0+mpar(14)*(statev(33)+v(126)*v(133))
v(7661)=4d0*v(200)
v(179)=v(200)*v(7585)
v(7666)=v(175)+v(179)
v(208)=0.5d0+mpar(14)*(statev(34)+v(126)*v(135))
v(7657)=4d0*v(208)
v(182)=v(208)*v(7585)
v(7669)=v(175)+v(182)
v(7659)=v(179)+v(182)
v(159)=(-1d0/3d0)+mpar(14)*(statev(35)+v(126)*v(137))
v(7633)=2d0*v(159)
v(1003)=v(7633)*v(997)
v(1002)=v(7633)*v(995)
v(1001)=v(7633)*v(993)
v(1000)=v(7633)*v(991)
v(999)=v(7633)*v(989)
v(998)=v(7633)*v(987)
v(171)=(v(159)*v(159))
v(160)=(-1d0/3d0)+mpar(14)*(statev(36)+v(126)*v(139))
v(7634)=2d0*v(160)
v(1021)=v(1015)*v(7634)
v(1020)=v(1013)*v(7634)
v(1019)=v(1011)*v(7634)
v(1018)=v(1009)*v(7634)
v(1017)=v(1007)*v(7634)
v(1016)=v(1005)*v(7634)
v(184)=(v(160)*v(160))
v(141)=statev(37)+v(121)*v(7622)
v(7635)=2d0*v(141)
v(1036)=v(1030)*v(7635)
v(1035)=v(1028)*v(7635)
v(1034)=v(1026)*v(7635)
v(1033)=v(1025)*v(7635)
v(1032)=v(1023)*v(7635)
v(1031)=v(1022)*v(7635)
v(193)=(v(141)*v(141))
v(142)=statev(38)+v(122)*v(7622)
v(7636)=2d0*v(142)
v(1050)=v(1044)*v(7636)
v(1049)=v(1043)*v(7636)
v(1048)=v(1041)*v(7636)
v(1047)=v(1040)*v(7636)
v(1046)=v(1038)*v(7636)
v(1045)=v(1037)*v(7636)
v(201)=(v(142)*v(142))
v(143)=statev(39)+v(123)*v(7622)
v(7637)=2d0*v(143)
v(1063)=v(1057)*v(7637)
v(1062)=v(1056)*v(7637)
v(1061)=v(1055)*v(7637)
v(1060)=v(1054)*v(7637)
v(1059)=v(1052)*v(7637)
v(1058)=v(1051)*v(7637)
v(209)=(v(143)*v(143))
v(162)=(-1d0/3d0)+mpar(14)*(statev(40)+v(126)*v(144))
v(7638)=2d0*v(162)
v(1081)=v(1075)*v(7638)
v(1080)=v(1073)*v(7638)
v(1079)=v(1071)*v(7638)
v(1078)=v(1069)*v(7638)
v(1077)=v(1067)*v(7638)
v(1076)=v(1065)*v(7638)
v(185)=(v(162)*v(162))
v(146)=statev(41)+v(121)*v(7611)
v(7639)=2d0*v(146)
v(1096)=v(1090)*v(7639)
v(1095)=v(1088)*v(7639)
v(1094)=v(1086)*v(7639)
v(1093)=v(1085)*v(7639)
v(1092)=v(1084)*v(7639)
v(1091)=v(1082)*v(7639)
v(194)=(v(146)*v(146))
v(147)=statev(42)+v(122)*v(7611)
v(7640)=2d0*v(147)
v(1110)=v(1104)*v(7640)
v(1109)=v(1103)*v(7640)
v(1108)=v(1101)*v(7640)
v(1107)=v(1100)*v(7640)
v(1106)=v(1099)*v(7640)
v(1105)=v(1097)*v(7640)
v(202)=(v(147)*v(147))
v(148)=statev(43)+v(123)*v(7611)
v(7641)=2d0*v(148)
v(1123)=v(1117)*v(7641)
v(1122)=v(1116)*v(7641)
v(1121)=v(1115)*v(7641)
v(1120)=v(1114)*v(7641)
v(1119)=v(1113)*v(7641)
v(1118)=v(1111)*v(7641)
v(210)=(v(148)*v(148))
v(149)=statev(44)+v(121)*v(7598)
v(7642)=2d0*v(149)
v(1137)=v(1131)*v(7642)
v(1136)=v(1129)*v(7642)
v(1135)=v(1127)*v(7642)
v(1134)=v(1126)*v(7642)
v(1133)=v(1125)*v(7642)
v(1132)=v(1124)*v(7642)
v(195)=(v(149)*v(149))
v(150)=statev(45)+v(122)*v(7598)
v(7643)=2d0*v(150)
v(1150)=v(1144)*v(7643)
v(1149)=v(1143)*v(7643)
v(1148)=v(1141)*v(7643)
v(1147)=v(1140)*v(7643)
v(1146)=v(1139)*v(7643)
v(1145)=v(1138)*v(7643)
v(203)=(v(150)*v(150))
v(151)=statev(46)+v(123)*v(7598)
v(7644)=2d0*v(151)
v(1162)=v(1156)*v(7644)
v(1161)=v(1155)*v(7644)
v(1160)=v(1154)*v(7644)
v(1159)=v(1153)*v(7644)
v(1158)=v(1152)*v(7644)
v(1157)=v(1151)*v(7644)
v(211)=(v(151)*v(151))
v(152)=statev(47)+v(122)*v(7645)
v(153)=statev(48)+v(123)*v(7645)
v(154)=statev(49)-v(122)*v(123)*v(126)
v(1402)=(v(173)*v(173))+v(184)+v(185)+2d0*(v(195)+v(203)+v(211))*v(7646)
v(7647)=0.15d1*v(1402)
v(1412)=v(7546)*v(7647)
v(1411)=v(7550)*v(7647)
v(1410)=v(7543)*v(7647)
v(1409)=-(v(7647)*v(810))
v(1408)=-(v(7647)*v(809))
v(1407)=-(v(7647)*v(808))+v(7648)*(v(1021)+v(1081)+2d0*(v(1137)+v(1150)+v(1162))*v(7646)+v(7649)*v(931))
v(1406)=-(v(7647)*v(807))+v(7648)*(v(1020)+v(1080)+2d0*(v(1136)+v(1149)+v(1161))*v(7646)+v(7649)*v(929))
v(1405)=-(v(7647)*v(806))+v(7648)*(v(1019)+v(1079)+2d0*(v(1135)+v(1148)+v(1160))*v(7646)+v(7649)*v(927))
v(1404)=-(v(7647)*v(805))+v(7648)*(v(1018)+v(1078)+2d0*(v(1134)+v(1147)+v(1159))*v(7646)+v(7649)*v(925))
v(1403)=-(v(7647)*v(804))+v(7648)*(v(1017)+v(1077)+2d0*(v(1133)+v(1146)+v(1158))*v(7646)+v(7649)*v(923))
v(1401)=v(7648)*(v(1016)+v(1076)+2d0*(v(1132)+v(1145)+v(1157))*v(7646)+v(7649)*v(921))
v(1342)=(v(170)*v(170))+v(171)+v(185)+2d0*(v(194)+v(202)+v(210))*v(7646)
v(7650)=0.15d1*v(1342)
v(1352)=v(7546)*v(7650)
v(1351)=v(7550)*v(7650)
v(1350)=v(7543)*v(7650)
v(1349)=-(v(7650)*v(810))
v(1348)=-(v(7650)*v(809))
v(1347)=-(v(7650)*v(808))+v(7648)*(v(1003)+v(1081)+2d0*(v(1096)+v(1110)+v(1123))*v(7646)+v(7651)*v(919))
v(1346)=-(v(7650)*v(807))+v(7648)*(v(1002)+v(1080)+2d0*(v(1095)+v(1109)+v(1122))*v(7646)+v(7651)*v(917))
v(1345)=-(v(7650)*v(806))+v(7648)*(v(1001)+v(1079)+2d0*(v(1094)+v(1108)+v(1121))*v(7646)+v(7651)*v(915))
v(1344)=-(v(7650)*v(805))+v(7648)*(v(1000)+v(1078)+2d0*(v(1093)+v(1107)+v(1120))*v(7646)+v(7651)*v(913))
v(1343)=-(v(7650)*v(804))+v(7648)*(v(1077)+2d0*(v(1092)+v(1106)+v(1119))*v(7646)+v(7651)*v(911)+v(999))
v(1341)=v(7648)*(v(1076)+2d0*(v(1091)+v(1105)+v(1118))*v(7646)+v(7651)*v(909)+v(998))
v(1270)=(v(158)*v(158))+v(171)+v(184)+2d0*(v(193)+v(201)+v(209))*v(7646)
v(7652)=0.15d1*v(1270)
v(1280)=v(7546)*v(7652)
v(1279)=v(7550)*v(7652)
v(1278)=v(7543)*v(7652)
v(1277)=-(v(7652)*v(810))
v(1276)=-(v(7652)*v(809))
v(1275)=-(v(7652)*v(808))+v(7648)*(v(1003)+v(1021)+2d0*(v(1036)+v(1050)+v(1063))*v(7646)+v(7653)*v(907))
v(1274)=-(v(7652)*v(807))+v(7648)*(v(1002)+v(1020)+2d0*(v(1035)+v(1049)+v(1062))*v(7646)+v(7653)*v(905))
v(1273)=-(v(7652)*v(806))+v(7648)*(v(1001)+v(1019)+2d0*(v(1034)+v(1048)+v(1061))*v(7646)+v(7653)*v(903))
v(1272)=-(v(7652)*v(805))+v(7648)*(v(1000)+v(1018)+2d0*(v(1033)+v(1047)+v(1060))*v(7646)+v(7653)*v(901))
v(1271)=-(v(7652)*v(804))+v(7648)*(v(1017)+2d0*(v(1032)+v(1046)+v(1059))*v(7646)+v(7653)*v(899)+v(999))
v(1269)=v(7648)*(v(1016)+2d0*(v(1031)+v(1045)+v(1058))*v(7646)+v(7653)*v(897)+v(998))
v(1268)=v(1030)*v(7654)
v(1267)=v(1028)*v(7654)
v(1266)=v(1026)*v(7654)
v(1265)=v(1025)*v(7654)
v(1264)=v(1023)*v(7654)
v(1263)=v(1022)*v(7654)
v(1262)=v(1044)*v(7654)
v(1261)=v(1043)*v(7654)
v(1260)=v(1041)*v(7654)
v(1259)=v(1040)*v(7654)
v(1258)=v(1038)*v(7654)
v(1257)=v(1037)*v(7654)
v(1256)=v(1057)*v(7654)
v(1255)=v(1056)*v(7654)
v(1254)=v(1055)*v(7654)
v(1253)=v(1054)*v(7654)
v(1252)=v(1052)*v(7654)
v(1251)=v(1051)*v(7654)
v(1250)=v(1104)*v(7654)
v(1249)=v(1103)*v(7654)
v(1248)=v(1101)*v(7654)
v(1247)=v(1100)*v(7654)
v(1246)=v(1099)*v(7654)
v(1245)=v(1097)*v(7654)
v(1244)=v(1117)*v(7654)
v(1243)=v(1116)*v(7654)
v(1242)=v(1115)*v(7654)
v(1241)=v(1114)*v(7654)
v(1240)=v(1113)*v(7654)
v(1239)=v(1111)*v(7654)
v(1238)=v(1090)*v(7654)
v(1237)=v(1088)*v(7654)
v(1236)=v(1086)*v(7654)
v(1235)=v(1085)*v(7654)
v(1234)=v(1084)*v(7654)
v(1233)=v(1082)*v(7654)
v(1232)=v(1171)*v(7654)
v(1231)=v(1170)*v(7654)
v(1230)=v(1168)*v(7654)
v(1229)=v(1167)*v(7654)
v(1228)=v(1165)*v(7654)
v(1227)=v(1163)*v(7654)
v(1226)=v(1156)*v(7654)
v(1225)=v(1155)*v(7654)
v(1224)=v(1154)*v(7654)
v(1223)=v(1153)*v(7654)
v(1222)=v(1152)*v(7654)
v(1221)=v(1151)*v(7654)
v(1220)=v(1187)*v(7654)
v(1219)=v(1186)*v(7654)
v(1218)=v(1185)*v(7654)
v(1217)=v(1184)*v(7654)
v(1216)=v(1182)*v(7654)
v(1215)=v(1180)*v(7654)
v(1209)=v(152)*v(7655)
v(1214)=v(1171)*v(1209)
v(1213)=v(1170)*v(1209)
v(1212)=v(1168)*v(1209)
v(1211)=v(1167)*v(1209)
v(1210)=v(1165)*v(1209)
v(1208)=v(1163)*v(1209)
v(1207)=v(1179)*v(7654)
v(1206)=v(1178)*v(7654)
v(1205)=v(1177)*v(7654)
v(1204)=v(1176)*v(7654)
v(1203)=v(1174)*v(7654)
v(1202)=v(1172)*v(7654)
v(1196)=v(153)*v(7655)
v(1201)=v(1179)*v(1196)
v(1200)=v(1178)*v(1196)
v(1199)=v(1177)*v(1196)
v(1198)=v(1176)*v(1196)
v(1197)=v(1174)*v(1196)
v(1195)=v(1172)*v(1196)
v(1449)=v(7648)*(v(1195)+v(1208)+(v(1031)+v(1091)+v(1132))*v(7646)+v(7663)*v(933))
v(1189)=v(154)*v(7655)
v(1194)=v(1187)*v(1189)
v(1193)=v(1186)*v(1189)
v(1192)=v(1185)*v(1189)
v(1191)=v(1184)*v(1189)
v(1190)=v(1182)*v(1189)
v(1188)=v(1180)*v(1189)
v(1509)=v(7648)*(v(1188)+v(1195)+(v(1058)+v(1118)+v(1157))*v(7646)+v(7657)*v(969))
v(1485)=v(7648)*(v(1188)+v(1208)+(v(1045)+v(1105)+v(1145))*v(7646)+v(7661)*v(951))
v(213)=(v(154)*v(154))*v(7654)
v(212)=(v(153)*v(153))*v(7654)
v(1510)=2d0*(v(208)*v(208))+v(212)+v(213)+(v(209)+v(210)+v(211))*v(7646)
v(7656)=0.15d1*v(1510)
v(1520)=v(7546)*v(7656)
v(1519)=v(7550)*v(7656)
v(1518)=v(7543)*v(7656)
v(1517)=-(v(7656)*v(810))
v(1516)=-(v(7656)*v(809))
v(1515)=-(v(7656)*v(808))+v(7648)*(v(1194)+v(1201)+(v(1063)+v(1123)+v(1162))*v(7646)+v(7657)*v(979))
v(1514)=-(v(7656)*v(807))+v(7648)*(v(1193)+v(1200)+(v(1062)+v(1122)+v(1161))*v(7646)+v(7657)*v(977))
v(1513)=-(v(7656)*v(806))+v(7648)*(v(1192)+v(1199)+(v(1061)+v(1121)+v(1160))*v(7646)+v(7657)*v(975))
v(1512)=-(v(7656)*v(805))+v(7648)*(v(1191)+v(1198)+(v(1060)+v(1120)+v(1159))*v(7646)+v(7657)*v(973))
v(1511)=-(v(7656)*v(804))+v(7648)*(v(1190)+v(1197)+(v(1059)+v(1119)+v(1158))*v(7646)+v(7657)*v(971))
v(206)=v(153)*v(7654)
v(1498)=v(152)*v(206)+(v(142)*v(143)+v(147)*v(148)+v(150)*v(151))*v(7646)+v(154)*v(7659)
v(7658)=0.15d1*v(1498)
v(1508)=v(7546)*v(7658)
v(1723)=v(1508)*v(7520)
v(1507)=v(7550)*v(7658)
v(1548)=v(1507)*v(7665)
v(7695)=v(1548)*v(7689)
v(7685)=v(1548)*v(7665)
v(1506)=v(7543)*v(7658)
v(1505)=-(v(7658)*v(810))
v(1504)=-(v(7658)*v(809))
v(1503)=-(v(7658)*v(808))+v(7648)*(v(1207)*v(152)+v(1171)*v(206)+(v(1057)*v(142)+v(1044)*v(143)+v(1117)*v(147)+v(1104&
&)*v(148)+v(1156)*v(150)+v(1144)*v(151))*v(7646)+v(1187)*v(7659)+v(154)*(v(967)+v(985)))
v(1502)=-(v(7658)*v(807))+v(7648)*(v(1206)*v(152)+v(1170)*v(206)+(v(1056)*v(142)+v(1043)*v(143)+v(1116)*v(147)+v(1103&
&)*v(148)+v(1155)*v(150)+v(1143)*v(151))*v(7646)+v(1186)*v(7659)+v(154)*(v(966)+v(984)))
v(1501)=-(v(7658)*v(806))+v(7648)*(v(1205)*v(152)+v(1168)*v(206)+(v(1055)*v(142)+v(1041)*v(143)+v(1115)*v(147)+v(1101&
&)*v(148)+v(1154)*v(150)+v(1141)*v(151))*v(7646)+v(1185)*v(7659)+v(154)*(v(965)+v(983)))
v(1500)=-(v(7658)*v(805))+v(7648)*(v(1204)*v(152)+v(1167)*v(206)+(v(1054)*v(142)+v(1040)*v(143)+v(1114)*v(147)+v(1100&
&)*v(148)+v(1153)*v(150)+v(1140)*v(151))*v(7646)+v(1184)*v(7659)+v(154)*(v(964)+v(982)))
v(1499)=-(v(7658)*v(804))+v(7648)*(v(1203)*v(152)+v(1165)*v(206)+(v(1052)*v(142)+v(1038)*v(143)+v(1113)*v(147)+v(1099&
&)*v(148)+v(1152)*v(150)+v(1139)*v(151))*v(7646)+v(1182)*v(7659)+v(154)*(v(963)+v(981)))
v(1497)=v(7648)*(v(1202)*v(152)+v(1163)*v(206)+(v(1051)*v(142)+v(1037)*v(143)+v(1111)*v(147)+v(1097)*v(148)+v(1151)*v&
&(150)+v(1138)*v(151))*v(7646)+v(1180)*v(7659)+v(154)*(v(962)+v(980)))
v(204)=(v(152)*v(152))*v(7654)
v(1486)=2d0*(v(200)*v(200))+v(204)+v(213)+(v(201)+v(202)+v(203))*v(7646)
v(7660)=0.15d1*v(1486)
v(1496)=v(7546)*v(7660)
v(1495)=v(7550)*v(7660)
v(1494)=v(7543)*v(7660)
v(1493)=-(v(7660)*v(810))
v(1492)=-(v(7660)*v(809))
v(1491)=-(v(7660)*v(808))+v(7648)*(v(1194)+v(1214)+(v(1050)+v(1110)+v(1150))*v(7646)+v(7661)*v(961))
v(1490)=-(v(7660)*v(807))+v(7648)*(v(1193)+v(1213)+(v(1049)+v(1109)+v(1149))*v(7646)+v(7661)*v(959))
v(1489)=-(v(7660)*v(806))+v(7648)*(v(1192)+v(1212)+(v(1048)+v(1108)+v(1148))*v(7646)+v(7661)*v(957))
v(1488)=-(v(7660)*v(805))+v(7648)*(v(1191)+v(1211)+(v(1047)+v(1107)+v(1147))*v(7646)+v(7661)*v(955))
v(1487)=-(v(7660)*v(804))+v(7648)*(v(1190)+v(1210)+(v(1046)+v(1106)+v(1146))*v(7646)+v(7661)*v(953))
v(1450)=2d0*(v(192)*v(192))+v(204)+v(212)+(v(193)+v(194)+v(195))*v(7646)
v(7662)=0.15d1*v(1450)
v(1460)=v(7546)*v(7662)
v(1459)=v(7550)*v(7662)
v(1458)=v(7543)*v(7662)
v(1457)=-(v(7662)*v(810))
v(1456)=-(v(7662)*v(809))
v(1455)=-(v(7662)*v(808))+v(7648)*(v(1201)+v(1214)+(v(1036)+v(1096)+v(1137))*v(7646)+v(7663)*v(943))
v(1454)=-(v(7662)*v(807))+v(7648)*(v(1200)+v(1213)+(v(1035)+v(1095)+v(1136))*v(7646)+v(7663)*v(941))
v(1453)=-(v(7662)*v(806))+v(7648)*(v(1199)+v(1212)+(v(1034)+v(1094)+v(1135))*v(7646)+v(7663)*v(939))
v(1452)=-(v(7662)*v(805))+v(7648)*(v(1198)+v(1211)+(v(1033)+v(1093)+v(1134))*v(7646)+v(7663)*v(937))
v(1451)=-(v(7662)*v(804))+v(7648)*(v(1197)+v(1210)+(v(1032)+v(1092)+v(1133))*v(7646)+v(7663)*v(935))
v(197)=v(154)*v(7654)
v(1462)=v(153)*v(197)+(v(141)*v(142)+v(146)*v(147)+v(149)*v(150))*v(7646)+v(152)*v(7666)
v(7664)=0.15d1*v(1462)
v(1472)=v(7546)*v(7664)
v(1471)=v(7550)*v(7664)
v(1470)=v(7543)*v(7664)
v(1689)=v(1470)*v(7521)
v(1547)=v(1470)*v(7665)
v(7700)=v(1547)*v(7688)
v(7683)=v(1547)*v(7665)
v(1469)=-(v(7664)*v(810))
v(1468)=-(v(7664)*v(809))
v(1467)=-(v(7664)*v(808))+v(7648)*(v(1220)*v(153)+v(1179)*v(197)+(v(1044)*v(141)+v(1030)*v(142)+v(1104)*v(146)+v(1090&
&)*v(147)+v(1144)*v(149)+v(1131)*v(150))*v(7646)+v(1171)*v(7666)+v(152)*(v(949)+v(967)))
v(1466)=-(v(7664)*v(807))+v(7648)*(v(1219)*v(153)+v(1178)*v(197)+(v(1043)*v(141)+v(1028)*v(142)+v(1103)*v(146)+v(1088&
&)*v(147)+v(1143)*v(149)+v(1129)*v(150))*v(7646)+v(1170)*v(7666)+v(152)*(v(948)+v(966)))
v(1465)=-(v(7664)*v(806))+v(7648)*(v(1218)*v(153)+v(1177)*v(197)+(v(1041)*v(141)+v(1026)*v(142)+v(1101)*v(146)+v(1086&
&)*v(147)+v(1141)*v(149)+v(1127)*v(150))*v(7646)+v(1168)*v(7666)+v(152)*(v(947)+v(965)))
v(1464)=-(v(7664)*v(805))+v(7648)*(v(1217)*v(153)+v(1176)*v(197)+(v(1040)*v(141)+v(1025)*v(142)+v(1100)*v(146)+v(1085&
&)*v(147)+v(1140)*v(149)+v(1126)*v(150))*v(7646)+v(1167)*v(7666)+v(152)*(v(946)+v(964)))
v(1463)=-(v(7664)*v(804))+v(7648)*(v(1216)*v(153)+v(1174)*v(197)+(v(1038)*v(141)+v(1023)*v(142)+v(1099)*v(146)+v(1084&
&)*v(147)+v(1139)*v(149)+v(1125)*v(150))*v(7646)+v(1165)*v(7666)+v(152)*(v(945)+v(963)))
v(1461)=v(7648)*(v(1215)*v(153)+v(1172)*v(197)+(v(1037)*v(141)+v(1022)*v(142)+v(1097)*v(146)+v(1082)*v(147)+v(1138)*v&
&(149)+v(1124)*v(150))*v(7646)+v(1163)*v(7666)+v(152)*(v(944)+v(962)))
v(1438)=mpar(14)*(v(143)*v(160)+v(148)*v(162)+v(151)*v(173))+v(151)*v(182)+v(150)*v(197)+v(149)*v(206)
v(7667)=0.15d1*v(1438)
v(1448)=v(7546)*v(7667)
v(1447)=v(7550)*v(7667)
v(1446)=v(7543)*v(7667)
v(1445)=-(v(7667)*v(810))
v(1444)=-(v(7667)*v(809))
v(1443)=-(v(7667)*v(808))+v(7648)*(v(1207)*v(149)+v(1220)*v(150)+v(1156)*v(182)+v(1144)*v(197)+v(1131)*v(206)+mpar(14)*&
&(v(1015)*v(143)+v(1075)*v(148)+v(1057)*v(160)+v(1117)*v(162)+v(1156)*v(173)+v(151)*v(931))+v(151)*v(985))
v(1442)=-(v(7667)*v(807))+v(7648)*(v(1206)*v(149)+v(1219)*v(150)+v(1155)*v(182)+v(1143)*v(197)+v(1129)*v(206)+mpar(14)*&
&(v(1013)*v(143)+v(1073)*v(148)+v(1056)*v(160)+v(1116)*v(162)+v(1155)*v(173)+v(151)*v(929))+v(151)*v(984))
v(7740)=v(1442)*v(7523)
v(1441)=-(v(7667)*v(806))+v(7648)*(v(1205)*v(149)+v(1218)*v(150)+v(1154)*v(182)+v(1141)*v(197)+v(1127)*v(206)+mpar(14)*&
&(v(1011)*v(143)+v(1071)*v(148)+v(1055)*v(160)+v(1115)*v(162)+v(1154)*v(173)+v(151)*v(927))+v(151)*v(983))
v(1440)=-(v(7667)*v(805))+v(7648)*(v(1204)*v(149)+v(1217)*v(150)+v(1153)*v(182)+v(1140)*v(197)+v(1126)*v(206)+mpar(14)*&
&(v(1009)*v(143)+v(1069)*v(148)+v(1054)*v(160)+v(1114)*v(162)+v(1153)*v(173)+v(151)*v(925))+v(151)*v(982))
v(1439)=-(v(7667)*v(804))+v(7648)*(v(1203)*v(149)+v(1216)*v(150)+v(1152)*v(182)+v(1139)*v(197)+v(1125)*v(206)+mpar(14)*&
&(v(1007)*v(143)+v(1067)*v(148)+v(1052)*v(160)+v(1113)*v(162)+v(1152)*v(173)+v(151)*v(923))+v(151)*v(981))
v(1437)=v(7648)*(v(1202)*v(149)+v(1215)*v(150)+v(1151)*v(182)+v(1138)*v(197)+v(1124)*v(206)+mpar(14)*(v(1005)*v(143)+v&
&(1065)*v(148)+v(1051)*v(160)+v(1111)*v(162)+v(1151)*v(173)+v(151)*v(921))+v(151)*v(980))
v(189)=v(7644)*v(7646)
v(188)=v(152)*v(7654)
v(1474)=v(154)*v(188)+(v(141)*v(143)+v(146)*v(148)+v(149)*v(151))*v(7646)+v(153)*v(7669)
v(7668)=0.15d1*v(1474)
v(1484)=v(7546)*v(7668)
v(1483)=v(7550)*v(7668)
v(1482)=v(7543)*v(7668)
v(1722)=v(1482)*v(7520)
v(1545)=v(1482)*v(7689)
v(7701)=v(1545)*v(7688)
v(7693)=v(1545)*v(7689)
v(1481)=-(v(7668)*v(810))
v(1480)=-(v(7668)*v(809))
v(1479)=-(v(7668)*v(808))+v(7648)*(v(1232)*v(154)+v(1187)*v(188)+(v(1057)*v(141)+v(1030)*v(143)+v(1117)*v(146)+v(1090&
&)*v(148)+v(1156)*v(149)+v(1131)*v(151))*v(7646)+v(1179)*v(7669)+v(153)*(v(949)+v(985)))
v(1478)=-(v(7668)*v(807))+v(7648)*(v(1231)*v(154)+v(1186)*v(188)+(v(1056)*v(141)+v(1028)*v(143)+v(1116)*v(146)+v(1088&
&)*v(148)+v(1155)*v(149)+v(1129)*v(151))*v(7646)+v(1178)*v(7669)+v(153)*(v(948)+v(984)))
v(1477)=-(v(7668)*v(806))+v(7648)*(v(1230)*v(154)+v(1185)*v(188)+(v(1055)*v(141)+v(1026)*v(143)+v(1115)*v(146)+v(1086&
&)*v(148)+v(1154)*v(149)+v(1127)*v(151))*v(7646)+v(1177)*v(7669)+v(153)*(v(947)+v(983)))
v(1476)=-(v(7668)*v(805))+v(7648)*(v(1229)*v(154)+v(1184)*v(188)+(v(1054)*v(141)+v(1025)*v(143)+v(1114)*v(146)+v(1085&
&)*v(148)+v(1153)*v(149)+v(1126)*v(151))*v(7646)+v(1176)*v(7669)+v(153)*(v(946)+v(982)))
v(1475)=-(v(7668)*v(804))+v(7648)*(v(1228)*v(154)+v(1182)*v(188)+(v(1052)*v(141)+v(1023)*v(143)+v(1113)*v(146)+v(1084&
&)*v(148)+v(1152)*v(149)+v(1125)*v(151))*v(7646)+v(1174)*v(7669)+v(153)*(v(945)+v(981)))
v(1473)=v(7648)*(v(1227)*v(154)+v(1180)*v(188)+(v(1051)*v(141)+v(1022)*v(143)+v(1111)*v(146)+v(1082)*v(148)+v(1151)*v&
&(149)+v(1124)*v(151))*v(7646)+v(1172)*v(7669)+v(153)*(v(944)+v(980)))
v(1426)=mpar(14)*(v(142)*v(160)+v(147)*v(162)+v(150)*v(173))+v(150)*v(179)+v(149)*v(188)+v(154)*v(189)
v(7670)=0.15d1*v(1426)
v(1436)=v(7546)*v(7670)
v(1435)=v(7550)*v(7670)
v(1434)=v(7543)*v(7670)
v(1433)=-(v(7670)*v(810))
v(1432)=-(v(7670)*v(809))
v(1431)=-(v(7670)*v(808))+v(7648)*(v(1232)*v(149)+v(1226)*v(154)+v(1144)*v(179)+v(1131)*v(188)+v(1187)*v(189)+mpar(14)*&
&(v(1015)*v(142)+v(1075)*v(147)+v(1044)*v(160)+v(1104)*v(162)+v(1144)*v(173)+v(150)*v(931))+v(150)*v(967))
v(7744)=v(1431)*v(7523)
v(1430)=-(v(7670)*v(807))+v(7648)*(v(1231)*v(149)+v(1225)*v(154)+v(1143)*v(179)+v(1129)*v(188)+v(1186)*v(189)+mpar(14)*&
&(v(1013)*v(142)+v(1073)*v(147)+v(1043)*v(160)+v(1103)*v(162)+v(1143)*v(173)+v(150)*v(929))+v(150)*v(966))
v(1429)=-(v(7670)*v(806))+v(7648)*(v(1230)*v(149)+v(1224)*v(154)+v(1141)*v(179)+v(1127)*v(188)+v(1185)*v(189)+mpar(14)*&
&(v(1011)*v(142)+v(1071)*v(147)+v(1041)*v(160)+v(1101)*v(162)+v(1141)*v(173)+v(150)*v(927))+v(150)*v(965))
v(1428)=-(v(7670)*v(805))+v(7648)*(v(1229)*v(149)+v(1223)*v(154)+v(1140)*v(179)+v(1126)*v(188)+v(1184)*v(189)+mpar(14)*&
&(v(1009)*v(142)+v(1069)*v(147)+v(1040)*v(160)+v(1100)*v(162)+v(1140)*v(173)+v(150)*v(925))+v(150)*v(964))
v(1427)=-(v(7670)*v(804))+v(7648)*(v(1228)*v(149)+v(1222)*v(154)+v(1139)*v(179)+v(1125)*v(188)+v(1182)*v(189)+mpar(14)*&
&(v(1007)*v(142)+v(1067)*v(147)+v(1038)*v(160)+v(1099)*v(162)+v(1139)*v(173)+v(150)*v(923))+v(150)*v(963))
v(1425)=v(7648)*(v(1227)*v(149)+v(1221)*v(154)+v(1138)*v(179)+v(1124)*v(188)+v(1180)*v(189)+mpar(14)*(v(1005)*v(142)+v&
&(1065)*v(147)+v(1037)*v(160)+v(1097)*v(162)+v(1138)*v(173)+v(150)*v(921))+v(150)*v(962))
v(1414)=mpar(14)*(v(141)*v(160)+v(146)*v(162)+v(149)*v(173))+v(149)*v(175)+v(150)*v(188)+v(153)*v(189)
v(7671)=0.15d1*v(1414)
v(1424)=v(7546)*v(7671)
v(1423)=v(7550)*v(7671)
v(1422)=v(7543)*v(7671)
v(1421)=-(v(7671)*v(810))
v(1420)=-(v(7671)*v(809))
v(1419)=-(v(7671)*v(808))+v(7648)*(v(1232)*v(150)+v(1226)*v(153)+v(1131)*v(175)+v(1144)*v(188)+v(1179)*v(189)+mpar(14)*&
&(v(1015)*v(141)+v(1075)*v(146)+v(1030)*v(160)+v(1090)*v(162)+v(1131)*v(173)+v(149)*v(931))+v(149)*v(949))
v(1418)=-(v(7671)*v(807))+v(7648)*(v(1231)*v(150)+v(1225)*v(153)+v(1129)*v(175)+v(1143)*v(188)+v(1178)*v(189)+mpar(14)*&
&(v(1013)*v(141)+v(1073)*v(146)+v(1028)*v(160)+v(1088)*v(162)+v(1129)*v(173)+v(149)*v(929))+v(149)*v(948))
v(1417)=-(v(7671)*v(806))+v(7648)*(v(1230)*v(150)+v(1224)*v(153)+v(1127)*v(175)+v(1141)*v(188)+v(1177)*v(189)+mpar(14)*&
&(v(1011)*v(141)+v(1071)*v(146)+v(1026)*v(160)+v(1086)*v(162)+v(1127)*v(173)+v(149)*v(927))+v(149)*v(947))
v(7750)=v(1417)*v(7523)
v(1416)=-(v(7671)*v(805))+v(7648)*(v(1229)*v(150)+v(1223)*v(153)+v(1126)*v(175)+v(1140)*v(188)+v(1176)*v(189)+mpar(14)*&
&(v(1009)*v(141)+v(1069)*v(146)+v(1025)*v(160)+v(1085)*v(162)+v(1126)*v(173)+v(149)*v(925))+v(149)*v(946))
v(1415)=-(v(7671)*v(804))+v(7648)*(v(1228)*v(150)+v(1222)*v(153)+v(1125)*v(175)+v(1139)*v(188)+v(1174)*v(189)+mpar(14)*&
&(v(1007)*v(141)+v(1067)*v(146)+v(1023)*v(160)+v(1084)*v(162)+v(1125)*v(173)+v(149)*v(923))+v(149)*v(945))
v(1413)=v(7648)*(v(1227)*v(150)+v(1221)*v(153)+v(1124)*v(175)+v(1138)*v(188)+v(1172)*v(189)+mpar(14)*(v(1005)*v(141)+v&
&(1065)*v(146)+v(1022)*v(160)+v(1082)*v(162)+v(1124)*v(173)+v(149)*v(921))+v(149)*v(944))
v(180)=v(7639)*v(7646)
v(177)=v(7641)*v(7646)
v(1378)=mpar(14)*(v(142)*v(159)+v(150)*v(162)+v(147)*v(170))+v(154)*v(177)+v(147)*v(179)+v(152)*v(180)
v(7672)=0.15d1*v(1378)
v(1388)=v(7546)*v(7672)
v(1387)=v(7550)*v(7672)
v(1386)=v(7543)*v(7672)
v(1385)=-(v(7672)*v(810))
v(1384)=-(v(7672)*v(809))
v(1383)=-(v(7672)*v(808))+v(7648)*(v(1238)*v(152)+v(1244)*v(154)+v(1187)*v(177)+v(1104)*v(179)+v(1171)*v(180)+v(147)*v&
&(967)+mpar(14)*(v(1075)*v(150)+v(1044)*v(159)+v(1144)*v(162)+v(1104)*v(170)+v(147)*v(919)+v(142)*v(997)))
v(7743)=v(1383)*x(3)
v(1382)=-(v(7672)*v(807))+v(7648)*(v(1237)*v(152)+v(1243)*v(154)+v(1186)*v(177)+v(1103)*v(179)+v(1170)*v(180)+v(147)*v&
&(966)+mpar(14)*(v(1073)*v(150)+v(1043)*v(159)+v(1143)*v(162)+v(1103)*v(170)+v(147)*v(917)+v(142)*v(995)))
v(1381)=-(v(7672)*v(806))+v(7648)*(v(1236)*v(152)+v(1242)*v(154)+v(1185)*v(177)+v(1101)*v(179)+v(1168)*v(180)+v(147)*v&
&(965)+mpar(14)*(v(1071)*v(150)+v(1041)*v(159)+v(1141)*v(162)+v(1101)*v(170)+v(147)*v(915)+v(142)*v(993)))
v(1380)=-(v(7672)*v(805))+v(7648)*(v(1235)*v(152)+v(1241)*v(154)+v(1184)*v(177)+v(1100)*v(179)+v(1167)*v(180)+v(147)*v&
&(964)+mpar(14)*(v(1069)*v(150)+v(1040)*v(159)+v(1140)*v(162)+v(1100)*v(170)+v(147)*v(913)+v(142)*v(991)))
v(1379)=-(v(7672)*v(804))+v(7648)*(v(1234)*v(152)+v(1240)*v(154)+v(1182)*v(177)+v(1099)*v(179)+v(1165)*v(180)+v(147)*v&
&(963)+mpar(14)*(v(1067)*v(150)+v(1038)*v(159)+v(1139)*v(162)+v(1099)*v(170)+v(147)*v(911)+v(142)*v(989)))
v(1377)=v(7648)*(v(1233)*v(152)+v(1239)*v(154)+v(1180)*v(177)+v(1097)*v(179)+v(1163)*v(180)+v(147)*v(962)+mpar(14)*(v&
&(1065)*v(150)+v(1037)*v(159)+v(1138)*v(162)+v(1097)*v(170)+v(147)*v(909)+v(142)*v(987)))
v(176)=v(7640)*v(7646)
v(1390)=mpar(14)*(v(143)*v(159)+v(151)*v(162)+v(148)*v(170))+v(154)*v(176)+v(153)*v(180)+v(148)*v(182)
v(7673)=0.15d1*v(1390)
v(1400)=v(7546)*v(7673)
v(1399)=v(7550)*v(7673)
v(1398)=v(7543)*v(7673)
v(1397)=-(v(7673)*v(810))
v(1396)=-(v(7673)*v(809))
v(1395)=-(v(7673)*v(808))+v(7648)*(v(1238)*v(153)+v(1250)*v(154)+v(1187)*v(176)+v(1179)*v(180)+v(1117)*v(182)+v(148)*v&
&(985)+mpar(14)*(v(1075)*v(151)+v(1057)*v(159)+v(1156)*v(162)+v(1117)*v(170)+v(148)*v(919)+v(143)*v(997)))
v(1394)=-(v(7673)*v(807))+v(7648)*(v(1237)*v(153)+v(1249)*v(154)+v(1186)*v(176)+v(1178)*v(180)+v(1116)*v(182)+v(148)*v&
&(984)+mpar(14)*(v(1073)*v(151)+v(1056)*v(159)+v(1155)*v(162)+v(1116)*v(170)+v(148)*v(917)+v(143)*v(995)))
v(7738)=v(1394)*x(3)
v(1393)=-(v(7673)*v(806))+v(7648)*(v(1236)*v(153)+v(1248)*v(154)+v(1185)*v(176)+v(1177)*v(180)+v(1115)*v(182)+v(148)*v&
&(983)+mpar(14)*(v(1071)*v(151)+v(1055)*v(159)+v(1154)*v(162)+v(1115)*v(170)+v(148)*v(915)+v(143)*v(993)))
v(1392)=-(v(7673)*v(805))+v(7648)*(v(1235)*v(153)+v(1247)*v(154)+v(1184)*v(176)+v(1176)*v(180)+v(1114)*v(182)+v(148)*v&
&(982)+mpar(14)*(v(1069)*v(151)+v(1054)*v(159)+v(1153)*v(162)+v(1114)*v(170)+v(148)*v(913)+v(143)*v(991)))
v(1391)=-(v(7673)*v(804))+v(7648)*(v(1234)*v(153)+v(1246)*v(154)+v(1182)*v(176)+v(1174)*v(180)+v(1113)*v(182)+v(148)*v&
&(981)+mpar(14)*(v(1067)*v(151)+v(1052)*v(159)+v(1152)*v(162)+v(1113)*v(170)+v(148)*v(911)+v(143)*v(989)))
v(1389)=v(7648)*(v(1233)*v(153)+v(1245)*v(154)+v(1180)*v(176)+v(1172)*v(180)+v(1111)*v(182)+v(148)*v(980)+mpar(14)*(v&
&(1065)*v(151)+v(1051)*v(159)+v(1151)*v(162)+v(1111)*v(170)+v(148)*v(909)+v(143)*v(987)))
v(1366)=mpar(14)*(v(141)*v(159)+v(149)*v(162)+v(146)*v(170))+v(146)*v(175)+v(152)*v(176)+v(153)*v(177)
v(7674)=0.15d1*v(1366)
v(1376)=v(7546)*v(7674)
v(1375)=v(7550)*v(7674)
v(1374)=v(7543)*v(7674)
v(1373)=-(v(7674)*v(810))
v(1372)=-(v(7674)*v(809))
v(1371)=-(v(7674)*v(808))+v(7648)*(v(1250)*v(152)+v(1244)*v(153)+v(1090)*v(175)+v(1171)*v(176)+v(1179)*v(177)+v(146)*v&
&(949)+mpar(14)*(v(1075)*v(149)+v(1030)*v(159)+v(1131)*v(162)+v(1090)*v(170)+v(146)*v(919)+v(141)*v(997)))
v(1370)=-(v(7674)*v(807))+v(7648)*(v(1249)*v(152)+v(1243)*v(153)+v(1088)*v(175)+v(1170)*v(176)+v(1178)*v(177)+v(146)*v&
&(948)+mpar(14)*(v(1073)*v(149)+v(1028)*v(159)+v(1129)*v(162)+v(1088)*v(170)+v(146)*v(917)+v(141)*v(995)))
v(1369)=-(v(7674)*v(806))+v(7648)*(v(1248)*v(152)+v(1242)*v(153)+v(1086)*v(175)+v(1168)*v(176)+v(1177)*v(177)+v(146)*v&
&(947)+mpar(14)*(v(1071)*v(149)+v(1026)*v(159)+v(1127)*v(162)+v(1086)*v(170)+v(146)*v(915)+v(141)*v(993)))
v(7749)=v(1369)*x(3)
v(1368)=-(v(7674)*v(805))+v(7648)*(v(1247)*v(152)+v(1241)*v(153)+v(1085)*v(175)+v(1167)*v(176)+v(1176)*v(177)+v(146)*v&
&(946)+mpar(14)*(v(1069)*v(149)+v(1025)*v(159)+v(1126)*v(162)+v(1085)*v(170)+v(146)*v(913)+v(141)*v(991)))
v(1367)=-(v(7674)*v(804))+v(7648)*(v(1246)*v(152)+v(1240)*v(153)+v(1084)*v(175)+v(1165)*v(176)+v(1174)*v(177)+v(146)*v&
&(945)+mpar(14)*(v(1067)*v(149)+v(1023)*v(159)+v(1125)*v(162)+v(1084)*v(170)+v(146)*v(911)+v(141)*v(989)))
v(1365)=v(7648)*(v(1245)*v(152)+v(1239)*v(153)+v(1082)*v(175)+v(1163)*v(176)+v(1172)*v(177)+v(146)*v(944)+mpar(14)*(v&
&(1065)*v(149)+v(1022)*v(159)+v(1124)*v(162)+v(1082)*v(170)+v(146)*v(909)+v(141)*v(987)))
v(1354)=v(159)*v(160)+v(150)*v(176)+v(151)*v(177)+v(149)*v(180)+v(162)*v(7676)
v(7675)=0.15d1*v(1354)
v(1364)=v(7546)*v(7675)
v(7753)=v(1364)*v(7523)
v(1363)=v(7550)*v(7675)
v(7755)=v(1363)*v(7523)
v(1362)=v(7543)*v(7675)
v(7756)=v(1362)*v(7523)
v(1361)=-(v(7675)*v(810))
v(7757)=v(1361)*v(7523)
v(1360)=-(v(7675)*v(809))
v(7758)=v(1360)*v(7523)
v(1359)=-(v(7675)*v(808))+v(7648)*(v(1238)*v(149)+v(1250)*v(150)+v(1244)*v(151)+v(1015)*v(159)+v(1144)*v(176)+v(1156)*v&
&(177)+v(1131)*v(180)+v(1075)*v(7676)+v(162)*(v(919)+v(931))+v(160)*v(997))
v(1358)=-(v(7675)*v(807))+v(7648)*(v(1237)*v(149)+v(1249)*v(150)+v(1243)*v(151)+v(1013)*v(159)+v(1143)*v(176)+v(1155)*v&
&(177)+v(1129)*v(180)+v(1073)*v(7676)+v(162)*(v(917)+v(929))+v(160)*v(995))
v(1357)=-(v(7675)*v(806))+v(7648)*(v(1236)*v(149)+v(1248)*v(150)+v(1242)*v(151)+v(1011)*v(159)+v(1141)*v(176)+v(1154)*v&
&(177)+v(1127)*v(180)+v(1071)*v(7676)+v(162)*(v(915)+v(927))+v(160)*v(993))
v(1356)=-(v(7675)*v(805))+v(7648)*(v(1235)*v(149)+v(1247)*v(150)+v(1241)*v(151)+v(1009)*v(159)+v(1140)*v(176)+v(1153)*v&
&(177)+v(1126)*v(180)+v(1069)*v(7676)+v(162)*(v(913)+v(925))+v(160)*v(991))
v(7760)=-(v(1356)*v(680))+v(1368)*v(7519)+v(1392)*v(7520)+v(1380)*v(7521)
v(1355)=-(v(7675)*v(804))+v(7648)*(v(1234)*v(149)+v(1246)*v(150)+v(1240)*v(151)+v(1007)*v(159)+v(1139)*v(176)+v(1152)*v&
&(177)+v(1125)*v(180)+v(1067)*v(7676)+v(162)*(v(911)+v(923))+v(160)*v(989))
v(7761)=-(v(1355)*v(680))+v(1367)*v(7519)+v(1391)*v(7520)+v(1379)*v(7521)
v(1353)=v(7648)*(v(1233)*v(149)+v(1245)*v(150)+v(1239)*v(151)+v(1005)*v(159)+v(1138)*v(176)+v(1151)*v(177)+v(1124)*v&
&(180)+v(1065)*v(7676)+v(162)*(v(909)+v(921))+v(160)*v(987))
v(7762)=v(1353)*v(7523)
v(165)=v(7637)*v(7646)
v(164)=v(7636)*v(7646)
v(1306)=mpar(14)*(v(141)*v(158)+v(146)*v(159)+v(149)*v(160))+v(152)*v(164)+v(153)*v(165)+v(141)*v(175)
v(7677)=0.15d1*v(1306)
v(1316)=v(7546)*v(7677)
v(1315)=v(7550)*v(7677)
v(1314)=v(7543)*v(7677)
v(1313)=-(v(7677)*v(810))
v(1312)=-(v(7677)*v(809))
v(1311)=-(v(7677)*v(808))+v(7648)*(v(1262)*v(152)+v(1256)*v(153)+v(1171)*v(164)+v(1179)*v(165)+v(1030)*v(175)+v(141)*v&
&(949)+mpar(14)*(v(1015)*v(149)+v(1030)*v(158)+v(1090)*v(159)+v(1131)*v(160)+v(141)*v(907)+v(146)*v(997)))
v(1310)=-(v(7677)*v(807))+v(7648)*(v(1261)*v(152)+v(1255)*v(153)+v(1170)*v(164)+v(1178)*v(165)+v(1028)*v(175)+v(141)*v&
&(948)+mpar(14)*(v(1013)*v(149)+v(1028)*v(158)+v(1088)*v(159)+v(1129)*v(160)+v(141)*v(905)+v(146)*v(995)))
v(1309)=-(v(7677)*v(806))+v(7648)*(v(1260)*v(152)+v(1254)*v(153)+v(1168)*v(164)+v(1177)*v(165)+v(1026)*v(175)+v(141)*v&
&(947)+mpar(14)*(v(1011)*v(149)+v(1026)*v(158)+v(1086)*v(159)+v(1127)*v(160)+v(141)*v(903)+v(146)*v(993)))
v(7748)=v(1309)*x(2)
v(1308)=-(v(7677)*v(805))+v(7648)*(v(1259)*v(152)+v(1253)*v(153)+v(1167)*v(164)+v(1176)*v(165)+v(1025)*v(175)+v(141)*v&
&(946)+mpar(14)*(v(1009)*v(149)+v(1025)*v(158)+v(1085)*v(159)+v(1126)*v(160)+v(141)*v(901)+v(146)*v(991)))
v(1307)=-(v(7677)*v(804))+v(7648)*(v(1258)*v(152)+v(1252)*v(153)+v(1165)*v(164)+v(1174)*v(165)+v(1023)*v(175)+v(141)*v&
&(945)+mpar(14)*(v(1007)*v(149)+v(1023)*v(158)+v(1084)*v(159)+v(1125)*v(160)+v(141)*v(899)+v(146)*v(989)))
v(1305)=v(7648)*(v(1257)*v(152)+v(1251)*v(153)+v(1163)*v(164)+v(1172)*v(165)+v(1022)*v(175)+v(141)*v(944)+mpar(14)*(v&
&(1005)*v(149)+v(1022)*v(158)+v(1082)*v(159)+v(1124)*v(160)+v(141)*v(897)+v(146)*v(987)))
v(163)=v(7635)*v(7646)
v(1330)=mpar(14)*(v(143)*v(158)+v(148)*v(159)+v(151)*v(160))+v(153)*v(163)+v(154)*v(164)+v(143)*v(182)
v(7678)=0.15d1*v(1330)
v(1340)=v(7546)*v(7678)
v(1339)=v(7550)*v(7678)
v(1338)=v(7543)*v(7678)
v(1337)=-(v(7678)*v(810))
v(1336)=-(v(7678)*v(809))
v(1335)=-(v(7678)*v(808))+v(7648)*(v(1268)*v(153)+v(1262)*v(154)+v(1179)*v(163)+v(1187)*v(164)+v(1057)*v(182)+v(143)*v&
&(985)+mpar(14)*(v(1015)*v(151)+v(1057)*v(158)+v(1117)*v(159)+v(1156)*v(160)+v(143)*v(907)+v(148)*v(997)))
v(1334)=-(v(7678)*v(807))+v(7648)*(v(1267)*v(153)+v(1261)*v(154)+v(1178)*v(163)+v(1186)*v(164)+v(1056)*v(182)+v(143)*v&
&(984)+mpar(14)*(v(1013)*v(151)+v(1056)*v(158)+v(1116)*v(159)+v(1155)*v(160)+v(143)*v(905)+v(148)*v(995)))
v(7737)=v(1334)*x(2)
v(1333)=-(v(7678)*v(806))+v(7648)*(v(1266)*v(153)+v(1260)*v(154)+v(1177)*v(163)+v(1185)*v(164)+v(1055)*v(182)+v(143)*v&
&(983)+mpar(14)*(v(1011)*v(151)+v(1055)*v(158)+v(1115)*v(159)+v(1154)*v(160)+v(143)*v(903)+v(148)*v(993)))
v(1332)=-(v(7678)*v(805))+v(7648)*(v(1265)*v(153)+v(1259)*v(154)+v(1176)*v(163)+v(1184)*v(164)+v(1054)*v(182)+v(143)*v&
&(982)+mpar(14)*(v(1009)*v(151)+v(1054)*v(158)+v(1114)*v(159)+v(1153)*v(160)+v(143)*v(901)+v(148)*v(991)))
v(1331)=-(v(7678)*v(804))+v(7648)*(v(1264)*v(153)+v(1258)*v(154)+v(1174)*v(163)+v(1182)*v(164)+v(1052)*v(182)+v(143)*v&
&(981)+mpar(14)*(v(1007)*v(151)+v(1052)*v(158)+v(1113)*v(159)+v(1152)*v(160)+v(143)*v(899)+v(148)*v(989)))
v(1329)=v(7648)*(v(1263)*v(153)+v(1257)*v(154)+v(1172)*v(163)+v(1180)*v(164)+v(1051)*v(182)+v(143)*v(980)+mpar(14)*(v&
&(1005)*v(151)+v(1051)*v(158)+v(1111)*v(159)+v(1151)*v(160)+v(143)*v(897)+v(148)*v(987)))
v(1318)=mpar(14)*(v(142)*v(158)+v(147)*v(159)+v(150)*v(160))+v(152)*v(163)+v(154)*v(165)+v(142)*v(179)
v(7679)=0.15d1*v(1318)
v(1328)=v(7546)*v(7679)
v(1327)=v(7550)*v(7679)
v(1326)=v(7543)*v(7679)
v(1325)=-(v(7679)*v(810))
v(1324)=-(v(7679)*v(809))
v(1323)=-(v(7679)*v(808))+v(7648)*(v(1268)*v(152)+v(1256)*v(154)+v(1171)*v(163)+v(1187)*v(165)+v(1044)*v(179)+v(142)*v&
&(967)+mpar(14)*(v(1015)*v(150)+v(1044)*v(158)+v(1104)*v(159)+v(1144)*v(160)+v(142)*v(907)+v(147)*v(997)))
v(7742)=v(1323)*x(2)
v(1322)=-(v(7679)*v(807))+v(7648)*(v(1267)*v(152)+v(1255)*v(154)+v(1170)*v(163)+v(1186)*v(165)+v(1043)*v(179)+v(142)*v&
&(966)+mpar(14)*(v(1013)*v(150)+v(1043)*v(158)+v(1103)*v(159)+v(1143)*v(160)+v(142)*v(905)+v(147)*v(995)))
v(1321)=-(v(7679)*v(806))+v(7648)*(v(1266)*v(152)+v(1254)*v(154)+v(1168)*v(163)+v(1185)*v(165)+v(1041)*v(179)+v(142)*v&
&(965)+mpar(14)*(v(1011)*v(150)+v(1041)*v(158)+v(1101)*v(159)+v(1141)*v(160)+v(142)*v(903)+v(147)*v(993)))
v(1320)=-(v(7679)*v(805))+v(7648)*(v(1265)*v(152)+v(1253)*v(154)+v(1167)*v(163)+v(1184)*v(165)+v(1040)*v(179)+v(142)*v&
&(964)+mpar(14)*(v(1009)*v(150)+v(1040)*v(158)+v(1100)*v(159)+v(1140)*v(160)+v(142)*v(901)+v(147)*v(991)))
v(1319)=-(v(7679)*v(804))+v(7648)*(v(1264)*v(152)+v(1252)*v(154)+v(1165)*v(163)+v(1182)*v(165)+v(1038)*v(179)+v(142)*v&
&(963)+mpar(14)*(v(1007)*v(150)+v(1038)*v(158)+v(1099)*v(159)+v(1139)*v(160)+v(142)*v(899)+v(147)*v(989)))
v(1317)=v(7648)*(v(1263)*v(152)+v(1251)*v(154)+v(1163)*v(163)+v(1180)*v(165)+v(1037)*v(179)+v(142)*v(962)+mpar(14)*(v&
&(1005)*v(150)+v(1037)*v(158)+v(1097)*v(159)+v(1138)*v(160)+v(142)*v(897)+v(147)*v(987)))
v(1294)=v(159)*v(162)+v(149)*v(163)+v(150)*v(164)+v(151)*v(165)+v(160)*v(7681)
v(7680)=0.15d1*v(1294)
v(1304)=v(7546)*v(7680)
v(7764)=v(1304)*v(7523)
v(1303)=v(7550)*v(7680)
v(7767)=v(1303)*v(7523)
v(1302)=v(7543)*v(7680)
v(7769)=v(1302)*v(7523)
v(1301)=-(v(7680)*v(810))
v(7771)=v(1301)*v(7523)
v(1300)=-(v(7680)*v(809))
v(7773)=v(1300)*v(7523)
v(1299)=-(v(7680)*v(808))+v(7648)*(v(1268)*v(149)+v(1262)*v(150)+v(1256)*v(151)+v(1075)*v(159)+v(1131)*v(163)+v(1144)*v&
&(164)+v(1156)*v(165)+v(1015)*v(7681)+v(160)*(v(907)+v(931))+v(162)*v(997))
v(1298)=-(v(7680)*v(807))+v(7648)*(v(1267)*v(149)+v(1261)*v(150)+v(1255)*v(151)+v(1073)*v(159)+v(1129)*v(163)+v(1143)*v&
&(164)+v(1155)*v(165)+v(1013)*v(7681)+v(160)*(v(905)+v(929))+v(162)*v(995))
v(1297)=-(v(7680)*v(806))+v(7648)*(v(1266)*v(149)+v(1260)*v(150)+v(1254)*v(151)+v(1071)*v(159)+v(1127)*v(163)+v(1141)*v&
&(164)+v(1154)*v(165)+v(1011)*v(7681)+v(160)*(v(903)+v(927))+v(162)*v(993))
v(1296)=-(v(7680)*v(805))+v(7648)*(v(1265)*v(149)+v(1259)*v(150)+v(1253)*v(151)+v(1069)*v(159)+v(1126)*v(163)+v(1140)*v&
&(164)+v(1153)*v(165)+v(1009)*v(7681)+v(160)*(v(901)+v(925))+v(162)*v(991))
v(1295)=-(v(7680)*v(804))+v(7648)*(v(1264)*v(149)+v(1258)*v(150)+v(1252)*v(151)+v(1067)*v(159)+v(1125)*v(163)+v(1139)*v&
&(164)+v(1152)*v(165)+v(1007)*v(7681)+v(160)*(v(899)+v(923))+v(162)*v(989))
v(1293)=v(7648)*(v(1263)*v(149)+v(1257)*v(150)+v(1251)*v(151)+v(1065)*v(159)+v(1124)*v(163)+v(1138)*v(164)+v(1151)*v&
&(165)+v(1005)*v(7681)+v(160)*(v(897)+v(921))+v(162)*v(987))
v(7781)=v(1293)*v(7523)
v(1282)=v(160)*v(162)+v(146)*v(163)+v(147)*v(164)+v(148)*v(165)+v(159)*v(7705)
v(7690)=0.15d1*v(1282)
v(1292)=v(7546)*v(7690)
v(7763)=v(1292)*x(3)
v(1549)=v(1280)*v(7526)+v(1352)*v(7527)+2d0*v(7683)+2d0*v(7685)+v(1412)*v(7687)+v(1460)*v(7691)+v(1496)*v(7694)+v(1520&
&)*v(7696)+v(1448)*v(7697)+v(1436)*v(7698)+v(1424)*v(7699)+v(1484)*v(7703)+v(7524)*(v(1388)*v(7665)+v(1376)*v(7688)+v&
&(1400)*v(7689)+v(7753))+v(7525)*(v(1328)*v(7665)+v(1316)*v(7688)+v(1340)*v(7689)+v(7763)+v(7764))
v(1291)=v(7550)*v(7690)
v(7765)=v(1291)*x(3)
v(1546)=v(1279)*v(7526)+v(1351)*v(7527)+v(1411)*v(7687)+v(1459)*v(7691)+2d0*v(7693)+v(1495)*v(7694)+2d0*v(7695)+v(1519&
&)*v(7696)+v(1447)*v(7697)+v(1435)*v(7698)+v(1423)*v(7699)+v(1471)*v(7704)+v(7524)*(v(1387)*v(7665)+v(1375)*v(7688)+v&
&(1399)*v(7689)+v(7755))+v(7525)*(v(1327)*v(7665)+v(1315)*v(7688)+v(1339)*v(7689)+v(7765)+v(7767))
v(1290)=v(7543)*v(7690)
v(7768)=v(1290)*x(3)
v(1544)=v(1278)*v(7526)+v(1350)*v(7527)+v(1410)*v(7687)+v(1458)*v(7691)+v(1494)*v(7694)+v(1518)*v(7696)+v(1446)*v(7697)&
&+v(1434)*v(7698)+v(1422)*v(7699)+2d0*v(7700)+2d0*v(7701)+v(1506)*v(7702)+v(7524)*(v(1386)*v(7665)+v(1374)*v(7688)+v&
&(1398)*v(7689)+v(7756))+v(7525)*(v(1326)*v(7665)+v(1314)*v(7688)+v(1338)*v(7689)+v(7768)+v(7769))
v(1289)=-(v(7690)*v(810))
v(7770)=v(1289)*x(3)
v(1543)=v(1277)*v(7526)+v(1349)*v(7527)+v(1409)*v(7687)+v(1457)*v(7691)+v(1493)*v(7694)+v(1517)*v(7696)+v(1445)*v(7697)&
&+v(1433)*v(7698)+v(1421)*v(7699)+v(1505)*v(7702)+v(1481)*v(7703)+v(1469)*v(7704)+v(7524)*(v(1385)*v(7665)+v(1373)*v&
&(7688)+v(1397)*v(7689)+v(7757))+v(7525)*(v(1325)*v(7665)+v(1313)*v(7688)+v(1337)*v(7689)+v(7770)+v(7771))
v(1288)=-(v(7690)*v(809))
v(7772)=v(1288)*x(3)
v(1542)=v(1276)*v(7526)+v(1348)*v(7527)+v(1408)*v(7687)+v(1456)*v(7691)+v(1492)*v(7694)+v(1516)*v(7696)+v(1444)*v(7697)&
&+v(1432)*v(7698)+v(1420)*v(7699)+v(1504)*v(7702)+v(1480)*v(7703)+v(1468)*v(7704)+v(7524)*(v(1384)*v(7665)+v(1372)*v&
&(7688)+v(1396)*v(7689)+v(7758))+v(7525)*(v(1324)*v(7665)+v(1312)*v(7688)+v(1336)*v(7689)+v(7772)+v(7773))
v(1287)=-(v(7690)*v(808))+v(7648)*(v(1268)*v(146)+v(1262)*v(147)+v(1256)*v(148)+v(1075)*v(160)+v(1015)*v(162)+v(1090)*v&
&(163)+v(1104)*v(164)+v(1117)*v(165)+v(159)*(v(907)+v(919))+v(7705)*v(997))
v(7774)=-(v(1299)*v(680))+v(1311)*v(7519)+v(1335)*v(7520)+v(1287)*v(7524)
v(1286)=-(v(7690)*v(807))+v(7648)*(v(1267)*v(146)+v(1261)*v(147)+v(1255)*v(148)+v(1073)*v(160)+v(1013)*v(162)+v(1088)*v&
&(163)+v(1103)*v(164)+v(1116)*v(165)+v(159)*(v(905)+v(917))+v(7705)*v(995))
v(7775)=-(v(1298)*v(680))+v(1310)*v(7519)+v(1322)*v(7521)+v(1286)*v(7524)
v(1285)=-(v(7690)*v(806))+v(7648)*(v(1266)*v(146)+v(1260)*v(147)+v(1254)*v(148)+v(1071)*v(160)+v(1011)*v(162)+v(1086)*v&
&(163)+v(1101)*v(164)+v(1115)*v(165)+v(159)*(v(903)+v(915))+v(7705)*v(993))
v(7777)=-(v(1297)*v(680))+v(1333)*v(7520)+v(1321)*v(7521)+v(1285)*v(7524)
v(1284)=-(v(7690)*v(805))+v(7648)*(v(1265)*v(146)+v(1259)*v(147)+v(1253)*v(148)+v(1069)*v(160)+v(1009)*v(162)+v(1085)*v&
&(163)+v(1100)*v(164)+v(1114)*v(165)+v(159)*(v(901)+v(913))+v(7705)*v(991))
v(7778)=-(v(1296)*v(680))+v(1308)*v(7519)+v(1332)*v(7520)+v(1320)*v(7521)+v(1284)*v(7524)
v(1283)=-(v(7690)*v(804))+v(7648)*(v(1264)*v(146)+v(1258)*v(147)+v(1252)*v(148)+v(1067)*v(160)+v(1007)*v(162)+v(1084)*v&
&(163)+v(1099)*v(164)+v(1113)*v(165)+v(159)*(v(899)+v(911))+v(7705)*v(989))
v(7779)=-(v(1295)*v(680))+v(1307)*v(7519)+v(1331)*v(7520)+v(1319)*v(7521)+v(1283)*v(7524)
v(1281)=v(7648)*(v(1263)*v(146)+v(1257)*v(147)+v(1251)*v(148)+v(1065)*v(160)+v(1005)*v(162)+v(1082)*v(163)+v(1097)*v&
&(164)+v(1111)*v(165)+v(159)*(v(897)+v(909))+v(7705)*v(987))
v(7780)=v(1281)*x(3)
v(1521)=v(1269)*v(7526)+v(1341)*v(7527)+v(1401)*v(7687)+v(1449)*v(7691)+v(1485)*v(7694)+v(1509)*v(7696)+v(1437)*v(7697)&
&+v(1425)*v(7698)+v(1413)*v(7699)+v(1497)*v(7702)+v(1473)*v(7703)+v(1461)*v(7704)+v(7524)*(v(1377)*v(7665)+v(1365)*v&
&(7688)+v(1389)*v(7689)+v(7762))+v(7525)*(v(1317)*v(7665)+v(1305)*v(7688)+v(1329)*v(7689)+v(7780)+v(7781))
v(156)=v(157)*v(7652)
v(7733)=v(156)*x(2)
v(161)=v(157)*v(7690)
v(7734)=v(161)*x(3)
v(7730)=v(161)*x(2)
v(1592)=2d0*v(161)
v(166)=v(157)*v(7680)
v(7735)=v(166)*v(7523)
v(1567)=(-2d0)*v(166)
v(1523)=v(166)*x(2)
v(167)=v(157)*v(7677)
v(7729)=v(167)*x(2)
v(1645)=2d0*v(167)
v(168)=v(157)*v(7679)
v(7727)=v(168)*x(2)
v(1673)=2d0*v(168)
v(169)=v(157)*v(7678)
v(7724)=v(169)*x(2)
v(1705)=2d0*v(169)
v(7709)=v(7735)+v(1645)*x(4)+v(1705)*x(5)+v(1673)*x(6)
v(1522)=v(7709)+v(7733)+v(7734)
v(172)=v(157)*v(7650)
v(7731)=v(172)*x(3)
v(174)=v(157)*v(7675)
v(7732)=v(174)*v(7523)
v(1594)=(-2d0)*v(174)
v(1524)=v(174)*x(3)
v(178)=v(157)*v(7674)
v(1648)=2d0*v(178)
v(181)=v(157)*v(7672)
v(1676)=2d0*v(181)
v(183)=v(157)*v(7673)
v(1708)=2d0*v(183)
v(7707)=v(7732)+v(1648)*x(4)+v(1708)*x(5)+v(1676)*x(6)
v(1531)=v(7707)+v(7730)+v(7731)
v(186)=v(157)*v(7647)
v(1620)=(-2d0)*v(186)
v(1525)=v(186)*v(7523)
v(187)=v(157)*v(7671)
v(1646)=2d0*v(187)
v(1526)=v(1646)*x(4)
v(190)=v(157)*v(7670)
v(1674)=2d0*v(190)
v(1527)=v(1674)*x(6)
v(191)=v(157)*v(7667)
v(1706)=2d0*v(191)
v(1528)=v(1706)*x(5)
v(7706)=-v(1525)-v(1526)-v(1527)-v(1528)
v(1530)=-v(1523)-v(1524)+v(7706)
v(7708)=v(1530)+v(7706)
v(1532)=v(1531)+v(1272)*v(7526)+v(1344)*v(7527)+v(1404)*v(7687)+v(1452)*v(7691)+v(1488)*v(7694)+v(1512)*v(7696)+v(1440&
&)*v(7697)+v(1428)*v(7698)+v(1416)*v(7699)+v(1500)*v(7702)+v(1476)*v(7703)+v(1464)*v(7704)+v(7707)+v(7708)+(v(161)-v(166&
&)+v(7778))*x(2)+(v(172)-v(174)+v(7760))*x(3)
v(1529)=v(1522)+v(1271)*v(7526)+v(1343)*v(7527)+v(1403)*v(7687)+v(1451)*v(7691)+v(1487)*v(7694)+v(1511)*v(7696)+v(1439&
&)*v(7697)+v(1427)*v(7698)+v(1415)*v(7699)+v(1499)*v(7702)+v(1475)*v(7703)+v(1463)*v(7704)+v(7708)+v(7709)+(v(156)-v(166&
&)+v(7779))*x(2)+(v(161)-v(174)+v(7761))*x(3)
v(196)=v(157)*v(7662)
v(198)=v(157)*v(7664)
v(1678)=4d0*v(198)
v(1539)=2d0*v(198)
v(7713)=v(1539)*x(4)
v(7711)=v(1539)*x(6)
v(199)=v(157)*v(7668)
v(1710)=4d0*v(199)
v(1536)=2d0*v(199)
v(7718)=v(1536)*x(4)
v(7710)=v(1536)*x(5)
v(7728)=v(1646)*v(7523)+2d0*v(7710)+2d0*v(7711)+v(1648)*x(3)
v(1533)=v(187)*v(7523)+v(196)*v(7688)+v(7710)+v(7711)+v(7729)+v(178)*x(3)
v(7720)=2d0*v(1533)
v(1534)=v(1273)*v(7526)+v(1345)*v(7527)+v(1405)*v(7687)+v(1453)*v(7691)+v(1489)*v(7694)+v(1513)*v(7696)+v(1441)*v(7697)&
&+v(1429)*v(7698)+v(1501)*v(7702)+v(1393)*v(7712)+v(1357)*v(7715)+v(1381)*v(7716)+v(7720)+v(7728)+v(7519)*(v(196)+v(1465&
&)*v(7665)+v(1477)*v(7689)+v(7748)+v(7749)+v(7750))+(v(1645)+v(7777))*x(2)
v(205)=v(157)*v(7660)
v(207)=v(157)*v(7658)
v(1714)=4d0*v(207)
v(1540)=2d0*v(207)
v(7719)=v(1540)*x(6)
v(7723)=v(1706)*v(7523)+2d0*v(7718)+2d0*v(7719)+v(1708)*x(3)
v(7714)=v(1540)*x(5)
v(7726)=v(1674)*v(7523)+2d0*v(7713)+2d0*v(7714)+v(1676)*x(3)
v(1538)=v(190)*v(7523)+v(205)*v(7665)+v(7713)+v(7714)+v(7727)+v(181)*x(3)
v(7722)=2d0*v(1538)
v(1541)=v(1275)*v(7526)+v(1347)*v(7527)+v(1407)*v(7687)+v(1455)*v(7691)+v(1491)*v(7694)+v(1515)*v(7696)+v(1443)*v(7697)&
&+v(1419)*v(7699)+v(1479)*v(7703)+v(1395)*v(7712)+v(1359)*v(7715)+v(1371)*v(7717)+v(7722)+v(7726)+v(7521)*(v(205)+v(1467&
&)*v(7688)+v(1503)*v(7689)+v(7742)+v(7743)+v(7744))+(v(1673)+v(7774))*x(2)
v(214)=v(157)*v(7656)
v(1535)=v(191)*v(7523)+v(214)*v(7689)+v(7718)+v(7719)+v(7724)+v(183)*x(3)
v(7721)=2d0*v(1535)
v(1537)=v(1274)*v(7526)+v(1346)*v(7527)+v(1406)*v(7687)+v(1454)*v(7691)+v(1490)*v(7694)+v(1514)*v(7696)+v(1430)*v(7698)&
&+v(1418)*v(7699)+v(1466)*v(7704)+v(1358)*v(7715)+v(1382)*v(7716)+v(1370)*v(7717)+v(7721)+v(7723)+v(7520)*(v(214)+v(1502&
&)*v(7665)+v(1478)*v(7688)+v(7737)+v(7738)+v(7740))+(v(1705)+v(7775))*x(2)
v(215)=-(v(1530)*v(7523))+v(1522)*x(2)+v(1531)*x(3)+v(7720)*x(4)+v(7721)*x(5)+v(7722)*x(6)
v(7776)=-(v(1563)*v(215))
v(7759)=-(v(1589)*v(215))
v(7752)=-(v(1616)*v(215))
v(7747)=-(v(1642)*v(215))
v(7745)=-(v(1670)*v(215))
v(7739)=-(v(1702)*v(215))
v(7725)=v(215)*v(685)
v(1718)=v(123)*v(7725)
v(1703)=v(214)*v(7520)+v(7723)+2d0*v(7724)-v(1702)*v(7725)
v(1684)=v(122)*v(7725)
v(1725)=-(v(1684)*v(7550))
v(1671)=v(205)*v(7521)-v(1670)*v(7725)+v(7726)+2d0*v(7727)
v(1654)=v(121)*v(7725)
v(1720)=-(v(1654)*v(7550))
v(1686)=-(v(1654)*v(7546))
v(1643)=v(196)*v(7519)-v(1642)*v(7725)+v(7728)+2d0*v(7729)
v(1628)=-(v(120)*v(7725))
v(1617)=2d0*v(1523)+2d0*v(1524)+2d0*v(1525)+v(187)*v(7519)+v(191)*v(7520)+v(190)*v(7521)-v(1616)*v(7725)
v(1601)=v(119)*v(7725)
v(1590)=v(178)*v(7519)+v(183)*v(7520)+v(181)*v(7521)-v(1589)*v(7725)+2d0*v(7730)+2d0*v(7731)+2d0*v(7732)
v(1574)=v(117)*v(7725)
v(1564)=v(167)*v(7519)+v(169)*v(7520)+v(168)*v(7521)-v(1563)*v(7725)+2d0*v(7733)+2d0*v(7734)+2d0*v(7735)
v(1550)=1d0/sqrt(v(215))
v(7782)=v(1550)/2d0
v(1552)=-(v(7782)/v(215))
v(1562)=v(1549)*v(1552)
v(1561)=v(1546)*v(1552)
v(1560)=v(1544)*v(1552)
v(1559)=v(1543)*v(1552)
v(1558)=v(1542)*v(1552)
v(1557)=v(1541)*v(1552)
v(1556)=v(1537)*v(1552)
v(1555)=v(1534)*v(1552)
v(1554)=v(1532)*v(1552)
v(1553)=v(1529)*v(1552)
v(1551)=v(1521)*v(1552)
v(1726)=(v(1562)*v(1703)+v(1550)*(v(1725)-v(1448)*v(680)+v(1484)*v(7519)+v(1520)*v(7520)+v(1508)*v(7521)+v(1400)*v(7524&
&)+v(1340)*v(7525)+v(1549)*v(7736)))/2d0
v(1724)=(v(1561)*v(1703)+v(1550)*(v(1722)+v(1723)-v(1447)*v(680)+v(1519)*v(7520)+v(1399)*v(7524)+v(1339)*v(7525)+((-1d0&
&)-v(123)*v(7550))*v(7725)+v(1546)*v(7736)))/2d0
v(1721)=(v(1560)*v(1703)+v(1550)*(v(1720)-v(1446)*v(680)+v(1482)*v(7519)+v(1518)*v(7520)+v(1506)*v(7521)+v(1398)*v(7524&
&)+v(1338)*v(7525)+v(1544)*v(7736)))/2d0
v(1719)=(v(1559)*v(1703)+v(1550)*(-(v(1445)*v(680))+v(1481)*v(7519)+v(1517)*v(7520)+v(1505)*v(7521)+v(1397)*v(7524)+v&
&(1337)*v(7525)+v(1543)*v(7736)+v(1718)*v(810)))/2d0
v(1717)=(v(1558)*v(1703)+v(1550)*(-(v(1444)*v(680))+v(1480)*v(7519)+v(1516)*v(7520)+v(1504)*v(7521)+v(1396)*v(7524)+v&
&(1336)*v(7525)+v(1542)*v(7736)+v(1718)*v(809)))/2d0
v(1716)=(v(1557)*v(1703)+v(1550)*(v(1714)-v(1443)*v(680)+v(1479)*v(7519)+v(1515)*v(7520)+v(1503)*v(7521)+v(1395)*v(7524&
&)+v(1335)*v(7525)+v(1541)*v(7736)+v(691)*v(7739)+v(7725)*(-v(1715)+v(123)*v(808))))/2d0
v(1713)=(v(1556)*v(1703)+v(1550)*(4d0*v(214)+v(1478)*v(7519)+v(1514)*v(7520)+v(1502)*v(7521)+v(1537)*v(7736)+2d0*v(7737&
&)+2d0*v(7738)+v(690)*v(7739)+2d0*v(7740)+v(7725)*(v(226)*v(797)+v(123)*v(807))))/2d0
v(1712)=(v(1555)*v(1703)+v(1550)*(v(1710)-v(1441)*v(680)+v(1477)*v(7519)+v(1513)*v(7520)+v(1501)*v(7521)+v(1393)*v(7524&
&)+v(1333)*v(7525)+v(1534)*v(7736)+v(689)*v(7739)+v(7725)*(-v(1711)+v(123)*v(806))))/2d0
v(1709)=(v(1554)*v(1703)+v(1550)*(-v(1706)+v(1708)-v(1440)*v(680)+v(1476)*v(7519)+v(1512)*v(7520)+v(1500)*v(7521)+v&
&(1392)*v(7524)+v(1332)*v(7525)+v(1532)*v(7736)+v(688)*v(7739)+v(7725)*(v(226)*v(796)+v(123)*v(805))))/2d0
v(1707)=(v(1553)*v(1703)+v(1550)*(v(1705)-v(1706)-v(1439)*v(680)+v(1475)*v(7519)+v(1511)*v(7520)+v(1499)*v(7521)+v(1391&
&)*v(7524)+v(1331)*v(7525)+v(1529)*v(7736)+v(686)*v(7739)+v(7725)*(v(226)*v(795)+v(123)*v(804))))/2d0
v(1704)=(v(1551)*v(1703)+v(1550)*(-(v(1437)*v(680))+v(1473)*v(7519)+v(1509)*v(7520)+v(1497)*v(7521)+v(1389)*v(7524)+v&
&(1329)*v(7525)+v(1521)*v(7736)))/2d0
v(1690)=(v(1562)*v(1671)+v(1550)*(v(1689)+v(1723)-v(1436)*v(680)+v(1496)*v(7521)+v(1388)*v(7524)+v(1328)*v(7525)+((-1d0&
&)-v(122)*v(7546))*v(7725)+v(1549)*v(7741)))/2d0
v(1688)=(v(1561)*v(1671)+v(1550)*(v(1725)-v(1435)*v(680)+v(1471)*v(7519)+v(1507)*v(7520)+v(1495)*v(7521)+v(1387)*v(7524&
&)+v(1327)*v(7525)+v(1546)*v(7741)))/2d0
v(1687)=(v(1560)*v(1671)+v(1550)*(v(1686)-v(1434)*v(680)+v(1470)*v(7519)+v(1506)*v(7520)+v(1494)*v(7521)+v(1386)*v(7524&
&)+v(1326)*v(7525)+v(1544)*v(7741)))/2d0
v(1685)=(v(1559)*v(1671)+v(1550)*(-(v(1433)*v(680))+v(1469)*v(7519)+v(1505)*v(7520)+v(1493)*v(7521)+v(1385)*v(7524)+v&
&(1325)*v(7525)+v(1543)*v(7741)+v(1684)*v(810)))/2d0
v(1683)=(v(1558)*v(1671)+v(1550)*(-(v(1432)*v(680))+v(1468)*v(7519)+v(1504)*v(7520)+v(1492)*v(7521)+v(1384)*v(7524)+v&
&(1324)*v(7525)+v(1542)*v(7741)+v(1684)*v(809)))/2d0
v(1682)=(v(1557)*v(1671)+v(1550)*(4d0*v(205)+v(1467)*v(7519)+v(1503)*v(7520)+v(1491)*v(7521)+v(1541)*v(7741)+2d0*v(7742&
&)+2d0*v(7743)+2d0*v(7744)+v(691)*v(7745)+v(7725)*(v(226)*v(783)+v(122)*v(808))))/2d0
v(1681)=(v(1556)*v(1671)+v(1550)*(v(1714)-v(1430)*v(680)+v(1466)*v(7519)+v(1502)*v(7520)+v(1490)*v(7521)+v(1382)*v(7524&
&)+v(1322)*v(7525)+v(1537)*v(7741)+v(690)*v(7745)+v(7725)*(-v(1715)+v(122)*v(807))))/2d0
v(1680)=(v(1555)*v(1671)+v(1550)*(v(1678)-v(1429)*v(680)+v(1465)*v(7519)+v(1501)*v(7520)+v(1489)*v(7521)+v(1381)*v(7524&
&)+v(1321)*v(7525)+v(1534)*v(7741)+v(689)*v(7745)+v(7725)*(-v(1679)+v(122)*v(806))))/2d0
v(1677)=(v(1554)*v(1671)+v(1550)*(-v(1674)+v(1676)-v(1428)*v(680)+v(1464)*v(7519)+v(1500)*v(7520)+v(1488)*v(7521)+v&
&(1380)*v(7524)+v(1320)*v(7525)+v(1532)*v(7741)+v(688)*v(7745)+v(7725)*(v(226)*v(781)+v(122)*v(805))))/2d0
v(1675)=(v(1553)*v(1671)+v(1550)*(v(1673)-v(1674)-v(1427)*v(680)+v(1463)*v(7519)+v(1499)*v(7520)+v(1487)*v(7521)+v(1379&
&)*v(7524)+v(1319)*v(7525)+v(1529)*v(7741)+v(686)*v(7745)+v(7725)*(v(226)*v(780)+v(122)*v(804))))/2d0
v(1672)=(v(1551)*v(1671)+v(1550)*(-(v(1425)*v(680))+v(1461)*v(7519)+v(1497)*v(7520)+v(1485)*v(7521)+v(1377)*v(7524)+v&
&(1317)*v(7525)+v(1521)*v(7741)))/2d0
v(1658)=(v(1562)*v(1643)+v(1550)*(v(1686)-v(1424)*v(680)+v(1460)*v(7519)+v(1484)*v(7520)+v(1472)*v(7521)+v(1376)*v(7524&
&)+v(1316)*v(7525)+v(1549)*v(7746)))/2d0
v(1657)=(v(1561)*v(1643)+v(1550)*(v(1720)-v(1423)*v(680)+v(1459)*v(7519)+v(1483)*v(7520)+v(1471)*v(7521)+v(1375)*v(7524&
&)+v(1315)*v(7525)+v(1546)*v(7746)))/2d0
v(1656)=(v(1560)*v(1643)+v(1550)*(v(1689)+v(1722)-v(1422)*v(680)+v(1458)*v(7519)+v(1374)*v(7524)+v(1314)*v(7525)+((-1d0&
&)-v(121)*v(7543))*v(7725)+v(1544)*v(7746)))/2d0
v(1655)=(v(1559)*v(1643)+v(1550)*(-(v(1421)*v(680))+v(1457)*v(7519)+v(1481)*v(7520)+v(1469)*v(7521)+v(1373)*v(7524)+v&
&(1313)*v(7525)+v(1543)*v(7746)+v(1654)*v(810)))/2d0
v(1653)=(v(1558)*v(1643)+v(1550)*(-(v(1420)*v(680))+v(1456)*v(7519)+v(1480)*v(7520)+v(1468)*v(7521)+v(1372)*v(7524)+v&
&(1312)*v(7525)+v(1542)*v(7746)+v(1654)*v(809)))/2d0
v(1652)=(v(1557)*v(1643)+v(1550)*(v(1678)-v(1419)*v(680)+v(1455)*v(7519)+v(1479)*v(7520)+v(1467)*v(7521)+v(1371)*v(7524&
&)+v(1311)*v(7525)+v(1541)*v(7746)+v(691)*v(7747)+v(7725)*(-v(1679)+v(121)*v(808))))/2d0
v(1651)=(v(1556)*v(1643)+v(1550)*(v(1710)-v(1418)*v(680)+v(1454)*v(7519)+v(1478)*v(7520)+v(1466)*v(7521)+v(1370)*v(7524&
&)+v(1310)*v(7525)+v(1537)*v(7746)+v(690)*v(7747)+v(7725)*(-v(1711)+v(121)*v(807))))/2d0
v(1650)=(v(1555)*v(1643)+v(1550)*(4d0*v(196)+v(1453)*v(7519)+v(1477)*v(7520)+v(1465)*v(7521)+v(1534)*v(7746)+v(689)*v&
&(7747)+2d0*v(7748)+2d0*v(7749)+2d0*v(7750)+v(7725)*(v(226)*v(766)+v(121)*v(806))))/2d0
v(1649)=(v(1554)*v(1643)+v(1550)*(-v(1646)+v(1648)-v(1416)*v(680)+v(1452)*v(7519)+v(1476)*v(7520)+v(1464)*v(7521)+v&
&(1368)*v(7524)+v(1308)*v(7525)+v(1532)*v(7746)+v(688)*v(7747)+v(7725)*(v(226)*v(765)+v(121)*v(805))))/2d0
v(1647)=(v(1553)*v(1643)+v(1550)*(v(1645)-v(1646)-v(1415)*v(680)+v(1451)*v(7519)+v(1475)*v(7520)+v(1463)*v(7521)+v(1367&
&)*v(7524)+v(1307)*v(7525)+v(1529)*v(7746)+v(686)*v(7747)+v(7725)*(v(226)*v(764)+v(121)*v(804))))/2d0
v(1644)=(v(1551)*v(1643)+v(1550)*(-(v(1413)*v(680))+v(1449)*v(7519)+v(1473)*v(7520)+v(1461)*v(7521)+v(1365)*v(7524)+v&
&(1305)*v(7525)+v(1521)*v(7746)))/2d0
v(1630)=(v(1562)*v(1617)+v(1550)*(-(v(1412)*v(680))+v(1424)*v(7519)+v(1448)*v(7520)+v(1436)*v(7521)+v(1364)*v(7524)+v&
&(1304)*v(7525)+v(1628)*v(7546)+v(1549)*v(7751)))/2d0
v(1629)=(v(1561)*v(1617)+v(1550)*(-(v(1411)*v(680))+v(1423)*v(7519)+v(1447)*v(7520)+v(1435)*v(7521)+v(1363)*v(7524)+v&
&(1303)*v(7525)+v(1628)*v(7550)+v(1546)*v(7751)))/2d0
v(1627)=(v(1560)*v(1617)+v(1550)*(-(v(1410)*v(680))+v(1422)*v(7519)+v(1446)*v(7520)+v(1434)*v(7521)+v(1362)*v(7524)+v&
&(1302)*v(7525)+v(1628)*v(7543)+v(1544)*v(7751)))/2d0
v(1626)=(v(1559)*v(1617)+v(1550)*(-(v(1409)*v(680))+v(1421)*v(7519)+v(1445)*v(7520)+v(1433)*v(7521)+v(1361)*v(7524)+v&
&(1301)*v(7525)+v(1543)*v(7751)+v(7725)*(1d0+v(120)*v(810))))/2d0
v(1625)=(v(1558)*v(1617)+v(1550)*(-(v(1408)*v(680))+v(1420)*v(7519)+v(1444)*v(7520)+v(1432)*v(7521)+v(1360)*v(7524)+v&
&(1300)*v(7525)+v(1542)*v(7751)+v(7725)*(1d0+v(120)*v(809))))/2d0
v(1624)=(v(1557)*v(1617)+v(1550)*(4d0*v(190)-v(1407)*v(680)+v(1419)*v(7519)+v(1443)*v(7520)+v(1431)*v(7521)+v(1359)*v&
&(7524)+v(1299)*v(7525)+v(1541)*v(7751)+v(691)*v(7752)+v(7725)*(v(226)*v(737)+v(120)*v(808))))/2d0
v(1623)=(v(1556)*v(1617)+v(1550)*(4d0*v(191)-v(1406)*v(680)+v(1418)*v(7519)+v(1442)*v(7520)+v(1430)*v(7521)+v(1358)*v&
&(7524)+v(1298)*v(7525)+v(1537)*v(7751)+v(690)*v(7752)+v(7725)*(v(226)*v(736)+v(120)*v(807))))/2d0
v(1622)=(v(1555)*v(1617)+v(1550)*(4d0*v(187)-v(1405)*v(680)+v(1417)*v(7519)+v(1441)*v(7520)+v(1429)*v(7521)+v(1357)*v&
&(7524)+v(1297)*v(7525)+v(1534)*v(7751)+v(689)*v(7752)+v(7725)*(v(226)*v(735)+v(120)*v(806))))/2d0
v(1621)=(v(1554)*v(1617)+v(1550)*(-v(1594)+v(1620)-v(1404)*v(680)+v(1416)*v(7519)+v(1440)*v(7520)+v(1428)*v(7521)+v&
&(1356)*v(7524)+v(1296)*v(7525)+v(1532)*v(7751)+v(688)*v(7752)+v(7725)*(v(226)*v(734)+v(120)*v(805))))/2d0
v(1619)=(v(1553)*v(1617)+v(1550)*(-v(1567)+v(1620)-v(1403)*v(680)+v(1415)*v(7519)+v(1439)*v(7520)+v(1427)*v(7521)+v&
&(1355)*v(7524)+v(1295)*v(7525)+v(1529)*v(7751)+v(686)*v(7752)+v(7725)*(v(226)*v(733)+v(120)*v(804))))/2d0
v(1618)=(v(1551)*v(1617)+v(1550)*(-(v(1401)*v(680))+v(1413)*v(7519)+v(1437)*v(7520)+v(1425)*v(7521)+v(1353)*v(7524)+v&
&(1293)*v(7525)+v(1521)*v(7751)))/2d0
v(7830)=v(1618)*v(7522)
v(1604)=(v(1562)*v(1590)+v(1550)*(v(1376)*v(7519)+v(1400)*v(7520)+v(1388)*v(7521)+v(1352)*v(7524)+v(1292)*v(7525)-v&
&(1601)*v(7546)+2d0*v(7753)+v(1549)*v(7754)))/2d0
v(1603)=(v(1561)*v(1590)+v(1550)*(v(1375)*v(7519)+v(1399)*v(7520)+v(1387)*v(7521)+v(1351)*v(7524)+v(1291)*v(7525)-v&
&(1601)*v(7550)+v(1546)*v(7754)+2d0*v(7755)))/2d0
v(1602)=(v(1560)*v(1590)+v(1550)*(v(1374)*v(7519)+v(1398)*v(7520)+v(1386)*v(7521)+v(1350)*v(7524)+v(1290)*v(7525)-v&
&(1601)*v(7543)+v(1544)*v(7754)+2d0*v(7756)))/2d0
v(1600)=(v(1559)*v(1590)+v(1550)*(v(1373)*v(7519)+v(1397)*v(7520)+v(1385)*v(7521)+v(1349)*v(7524)+v(1289)*v(7525)+v&
&(1543)*v(7754)+2d0*v(7757)+v(7725)*((-1d0)+v(119)*v(810))))/2d0
v(1599)=(v(1558)*v(1590)+v(1550)*(v(1372)*v(7519)+v(1396)*v(7520)+v(1384)*v(7521)+v(1348)*v(7524)+v(1288)*v(7525)+v&
&(1542)*v(7754)+2d0*v(7758)+v(1601)*v(809)))/2d0
v(1598)=(v(1557)*v(1590)+v(1550)*(4d0*v(181)-v(1359)*v(680)+v(1371)*v(7519)+v(1395)*v(7520)+v(1383)*v(7521)+v(1347)*v&
&(7524)+v(1287)*v(7525)+v(1541)*v(7754)+v(691)*v(7759)+v(7725)*(v(226)*v(714)+v(119)*v(808))))/2d0
v(1597)=(v(1556)*v(1590)+v(1550)*(4d0*v(183)-v(1358)*v(680)+v(1370)*v(7519)+v(1394)*v(7520)+v(1382)*v(7521)+v(1346)*v&
&(7524)+v(1286)*v(7525)+v(1537)*v(7754)+v(690)*v(7759)+v(7725)*(v(226)*v(713)+v(119)*v(807))))/2d0
v(1596)=(v(1555)*v(1590)+v(1550)*(4d0*v(178)-v(1357)*v(680)+v(1369)*v(7519)+v(1393)*v(7520)+v(1381)*v(7521)+v(1345)*v&
&(7524)+v(1285)*v(7525)+v(1534)*v(7754)+v(689)*v(7759)+v(7725)*(v(226)*v(712)+v(119)*v(806))))/2d0
v(1595)=(v(1554)*v(1590)+v(1550)*(v(1594)+2d0*v(172)+v(1344)*v(7524)+v(1284)*v(7525)+v(1532)*v(7754)+v(688)*v(7759)+v&
&(7760)+v(7725)*(v(226)*v(711)+v(119)*v(805))))/2d0
v(1593)=(v(1553)*v(1590)+v(1550)*(v(1592)+v(1594)+v(1343)*v(7524)+v(1283)*v(7525)+v(1529)*v(7754)+v(686)*v(7759)+v(7761&
&)+v(7725)*(v(226)*v(710)+v(119)*v(804))))/2d0
v(1591)=(v(1551)*v(1590)+v(1550)*(v(1365)*v(7519)+v(1389)*v(7520)+v(1377)*v(7521)+v(1341)*v(7524)+v(1281)*v(7525)+v&
&(1521)*v(7754)+2d0*v(7762)))/2d0
v(7824)=v(1591)*v(7522)
v(1577)=(v(1562)*v(1564)+v(1550)*(v(1316)*v(7519)+v(1340)*v(7520)+v(1328)*v(7521)+v(1280)*v(7525)-v(1574)*v(7546)+2d0*v&
&(7763)+2d0*v(7764)+v(1549)*v(7766)))/2d0
v(1576)=(v(1561)*v(1564)+v(1550)*(v(1315)*v(7519)+v(1339)*v(7520)+v(1327)*v(7521)+v(1279)*v(7525)-v(1574)*v(7550)+2d0*v&
&(7765)+v(1546)*v(7766)+2d0*v(7767)))/2d0
v(1575)=(v(1560)*v(1564)+v(1550)*(v(1314)*v(7519)+v(1338)*v(7520)+v(1326)*v(7521)+v(1278)*v(7525)-v(1574)*v(7543)+v&
&(1544)*v(7766)+2d0*v(7768)+2d0*v(7769)))/2d0
v(1573)=(v(1559)*v(1564)+v(1550)*(v(1313)*v(7519)+v(1337)*v(7520)+v(1325)*v(7521)+v(1277)*v(7525)+v(1543)*v(7766)+2d0*v&
&(7770)+2d0*v(7771)+v(1574)*v(810)))/2d0
v(1572)=(v(1558)*v(1564)+v(1550)*(v(1312)*v(7519)+v(1336)*v(7520)+v(1324)*v(7521)+v(1276)*v(7525)+v(1542)*v(7766)+2d0*v&
&(7772)+2d0*v(7773)+v(7725)*((-1d0)+v(117)*v(809))))/2d0
v(1571)=(v(1557)*v(1564)+v(1550)*(4d0*v(168)+v(1323)*v(7521)+v(1275)*v(7525)+v(1541)*v(7766)+v(7774)+v(691)*v(7776)+v&
&(7725)*(v(226)*v(704)+v(117)*v(808))))/2d0
v(1570)=(v(1556)*v(1564)+v(1550)*(4d0*v(169)+v(1334)*v(7520)+v(1274)*v(7525)+v(1537)*v(7766)+v(7775)+v(690)*v(7776)+v&
&(7725)*(v(226)*v(703)+v(117)*v(807))))/2d0
v(1569)=(v(1555)*v(1564)+v(1550)*(4d0*v(167)+v(1309)*v(7519)+v(1273)*v(7525)+v(1534)*v(7766)+v(689)*v(7776)+v(7777)+v&
&(7725)*(v(226)*v(702)+v(117)*v(806))))/2d0
v(1568)=(v(1554)*v(1564)+v(1550)*(v(1567)+v(1592)+v(1272)*v(7525)+v(1532)*v(7766)+v(688)*v(7776)+v(7778)+v(7725)*(v(226&
&)*v(701)+v(117)*v(805))))/2d0
v(1566)=(v(1553)*v(1564)+v(1550)*(2d0*v(156)+v(1567)+v(1271)*v(7525)+v(1529)*v(7766)+v(686)*v(7776)+v(7779)+v(7725)*(v&
&(226)*v(700)+v(117)*v(804))))/2d0
v(1565)=(v(1551)*v(1564)+v(1550)*(v(1305)*v(7519)+v(1329)*v(7520)+v(1317)*v(7521)+v(1269)*v(7525)+v(1521)*v(7766)+2d0*v&
&(7780)+2d0*v(7781)))/2d0
v(7813)=v(1565)*v(7522)
v(223)=v(1564)*v(7782)
v(7805)=v(223)*v(7518)+v(7813)
v(7804)=v(223)*v(7522)
v(7783)=2d0*v(223)
v(1588)=v(1577)*v(7783)
v(1587)=v(1576)*v(7783)
v(1586)=v(1575)*v(7783)
v(1585)=v(1573)*v(7783)
v(1584)=v(1572)*v(7783)
v(1583)=v(1571)*v(7783)
v(1582)=v(1570)*v(7783)
v(1581)=v(1569)*v(7783)
v(1580)=v(1568)*v(7783)
v(1579)=v(1566)*v(7783)
v(1578)=v(1565)*v(7783)
v(369)=(v(223)*v(223))
v(227)=v(1590)*v(7782)
v(7819)=v(227)*v(7518)+v(7824)
v(7818)=v(227)*v(7522)
v(7792)=v(223)+v(227)
v(7784)=2d0*v(227)
v(1615)=v(1604)*v(7784)
v(1614)=v(1603)*v(7784)
v(1613)=v(1602)*v(7784)
v(1612)=v(1600)*v(7784)
v(1611)=v(1599)*v(7784)
v(1610)=v(1598)*v(7784)
v(1609)=v(1597)*v(7784)
v(1608)=v(1596)*v(7784)
v(1607)=v(1595)*v(7784)
v(1606)=v(1593)*v(7784)
v(1605)=v(1591)*v(7784)
v(370)=(v(227)*v(227))
v(228)=v(1617)*v(7782)
v(7828)=v(228)*v(7518)+v(7830)
v(7827)=v(228)*v(7522)
v(7793)=v(227)+v(228)
v(7791)=v(223)+v(228)
v(7785)=2d0*v(228)
v(1641)=v(1630)*v(7785)
v(1640)=v(1629)*v(7785)
v(1639)=v(1627)*v(7785)
v(1638)=v(1626)*v(7785)
v(1637)=v(1625)*v(7785)
v(1636)=v(1624)*v(7785)
v(1635)=v(1623)*v(7785)
v(1634)=v(1622)*v(7785)
v(1633)=v(1621)*v(7785)
v(1632)=v(1619)*v(7785)
v(1631)=v(1618)*v(7785)
v(371)=(v(228)*v(228))
v(229)=v(1643)*v(7782)
v(7803)=v(229)*v(7518)+v(1644)*v(7522)
v(7797)=v(229)*v(7522)
v(7786)=2d0*v(229)
v(1669)=v(1658)*v(7786)
v(1668)=v(1657)*v(7786)
v(1667)=v(1656)*v(7786)
v(1666)=v(1655)*v(7786)
v(1665)=v(1653)*v(7786)
v(1664)=v(1652)*v(7786)
v(1663)=v(1651)*v(7786)
v(1662)=v(1650)*v(7786)
v(1661)=v(1649)*v(7786)
v(1660)=v(1647)*v(7786)
v(1659)=v(1644)*v(7786)
v(372)=(v(229)*v(229))
v(230)=v(1671)*v(7782)
v(7817)=v(230)*v(7518)+v(1672)*v(7522)
v(7795)=v(230)*v(7522)
v(7787)=2d0*v(230)
v(1701)=v(1690)*v(7787)
v(1700)=v(1688)*v(7787)
v(1699)=v(1687)*v(7787)
v(1698)=v(1685)*v(7787)
v(1697)=v(1683)*v(7787)
v(1696)=v(1682)*v(7787)
v(1695)=v(1681)*v(7787)
v(1694)=v(1680)*v(7787)
v(1693)=v(1677)*v(7787)
v(1692)=v(1675)*v(7787)
v(1691)=v(1672)*v(7787)
v(373)=(v(230)*v(230))
v(231)=v(1703)*v(7782)
v(7801)=v(231)*v(7518)+v(1704)*v(7522)
v(7799)=v(231)*v(7522)
v(7798)=v(229)*v(230)+v(231)*v(7791)
v(7796)=v(230)*v(231)+v(229)*v(7792)
v(7794)=v(229)*v(231)+v(230)*v(7793)
v(7788)=2d0*v(231)
v(3217)=v(228)*v(7531)+v(7788)*x(10)+v(7787)*x(11)+v(223)*x(7)+v(227)*x(8)+v(7786)*x(9)
v(1737)=v(1726)*v(7788)
v(1736)=v(1724)*v(7788)
v(1735)=v(1721)*v(7788)
v(1734)=v(1719)*v(7788)
v(1733)=v(1717)*v(7788)
v(1732)=v(1716)*v(7788)
v(1731)=v(1713)*v(7788)
v(1730)=v(1712)*v(7788)
v(1729)=v(1709)*v(7788)
v(1728)=v(1707)*v(7788)
v(1727)=v(1704)*v(7788)
v(374)=(v(231)*v(231))
v(7987)=sqrt(v(369)+v(370)+v(371)+2d0*v(372)+2d0*v(373)+2d0*v(374))
v(3193)=1d0/v(7987)
v(7789)=v(3193)/2d0
v(3204)=(v(1588)+v(1615)+v(1641)+2d0*v(1669)+2d0*v(1701)+2d0*v(1737))*v(7789)
v(3257)=v(3204)*v(7790)
v(3203)=(v(1587)+v(1614)+v(1640)+2d0*v(1668)+2d0*v(1700)+2d0*v(1736))*v(7789)
v(3256)=v(3203)*v(7790)
v(3202)=(v(1586)+v(1613)+v(1639)+2d0*v(1667)+2d0*v(1699)+2d0*v(1735))*v(7789)
v(3255)=v(3202)*v(7790)
v(3201)=(v(1585)+v(1612)+v(1638)+2d0*v(1666)+2d0*v(1698)+2d0*v(1734))*v(7789)
v(3254)=v(3201)*v(7790)
v(3200)=(v(1584)+v(1611)+v(1637)+2d0*v(1665)+2d0*v(1697)+2d0*v(1733))*v(7789)
v(3253)=v(3200)*v(7790)
v(3199)=(v(1583)+v(1610)+v(1636)+2d0*v(1664)+2d0*v(1696)+2d0*v(1732))*v(7789)
v(3252)=v(3199)*v(7790)
v(3198)=(v(1582)+v(1609)+v(1635)+2d0*v(1663)+2d0*v(1695)+2d0*v(1731))*v(7789)
v(3251)=v(3198)*v(7790)
v(3197)=(v(1581)+v(1608)+v(1634)+2d0*v(1662)+2d0*v(1694)+2d0*v(1730))*v(7789)
v(3250)=v(3197)*v(7790)
v(3196)=(v(1580)+v(1607)+v(1633)+2d0*v(1661)+2d0*v(1693)+2d0*v(1729))*v(7789)
v(3249)=v(3196)*v(7790)
v(3195)=(v(1579)+v(1606)+v(1632)+2d0*v(1660)+2d0*v(1692)+2d0*v(1728))*v(7789)
v(3248)=v(3195)*v(7790)
v(3194)=(v(1578)+v(1605)+v(1631)+2d0*v(1659)+2d0*v(1691)+2d0*v(1727))*v(7789)
v(3247)=v(3194)*v(7790)
v(232)=(v(7522)*v(7522))
v(8122)=-(v(232)*v(767))
v(8007)=2d0*v(232)
v(1826)=v(232)*(v(1690)*v(229)+v(1658)*v(230)+(v(1577)+v(1630))*v(231)+v(1726)*v(7791))
v(1825)=v(232)*(v(1688)*v(229)+v(1657)*v(230)+(v(1576)+v(1629))*v(231)+v(1724)*v(7791))
v(1824)=v(232)*(v(1687)*v(229)+v(1656)*v(230)+(v(1575)+v(1627))*v(231)+v(1721)*v(7791))
v(1823)=v(232)*(v(1685)*v(229)+v(1655)*v(230)+(v(1573)+v(1626))*v(231)+v(1719)*v(7791))
v(1822)=v(232)*(v(1683)*v(229)+v(1653)*v(230)+(v(1572)+v(1625))*v(231)+v(1717)*v(7791))
v(1821)=v(232)*(v(1682)*v(229)+v(1652)*v(230)+(v(1571)+v(1624))*v(231)+v(1716)*v(7791))
v(1820)=v(232)*(v(1681)*v(229)+v(1651)*v(230)+(v(1570)+v(1623))*v(231)+v(1713)*v(7791))
v(1819)=v(232)*(v(1680)*v(229)+v(1650)*v(230)+(v(1569)+v(1622))*v(231)+v(1712)*v(7791))
v(1818)=v(232)*(v(1677)*v(229)+v(1649)*v(230)+(v(1568)+v(1621))*v(231)+v(1709)*v(7791))
v(1817)=v(232)*(v(1675)*v(229)+v(1647)*v(230)+(v(1566)+v(1619))*v(231)+v(1707)*v(7791))
v(1816)=v(232)*(v(1672)*v(229)+v(1644)*v(230)+(v(1565)+v(1618))*v(231)+v(1704)*v(7791))+v(1738)*v(7798)
v(1804)=v(232)*((v(1577)+v(1604))*v(229)+v(1726)*v(230)+v(1690)*v(231)+v(1658)*v(7792))
v(1803)=v(232)*((v(1576)+v(1603))*v(229)+v(1724)*v(230)+v(1688)*v(231)+v(1657)*v(7792))
v(1802)=v(232)*((v(1575)+v(1602))*v(229)+v(1721)*v(230)+v(1687)*v(231)+v(1656)*v(7792))
v(1801)=v(232)*((v(1573)+v(1600))*v(229)+v(1719)*v(230)+v(1685)*v(231)+v(1655)*v(7792))
v(1800)=v(232)*((v(1572)+v(1599))*v(229)+v(1717)*v(230)+v(1683)*v(231)+v(1653)*v(7792))
v(1799)=v(232)*((v(1571)+v(1598))*v(229)+v(1716)*v(230)+v(1682)*v(231)+v(1652)*v(7792))
v(1798)=v(232)*((v(1570)+v(1597))*v(229)+v(1713)*v(230)+v(1681)*v(231)+v(1651)*v(7792))
v(1797)=v(232)*((v(1569)+v(1596))*v(229)+v(1712)*v(230)+v(1680)*v(231)+v(1650)*v(7792))
v(1796)=v(232)*((v(1568)+v(1595))*v(229)+v(1709)*v(230)+v(1677)*v(231)+v(1649)*v(7792))
v(1795)=v(232)*((v(1566)+v(1593))*v(229)+v(1707)*v(230)+v(1675)*v(231)+v(1647)*v(7792))
v(1794)=v(232)*((v(1565)+v(1591))*v(229)+v(1704)*v(230)+v(1672)*v(231)+v(1644)*v(7792))+v(1738)*v(7796)
v(1793)=v(1669)*v(232)
v(1792)=v(1668)*v(232)
v(1791)=v(1667)*v(232)
v(1790)=v(1666)*v(232)
v(1789)=v(1665)*v(232)
v(1788)=v(1664)*v(232)
v(1787)=v(1663)*v(232)
v(1786)=v(1662)*v(232)
v(1785)=v(1661)*v(232)
v(1784)=v(1660)*v(232)
v(1783)=v(1659)*v(232)+v(1738)*v(372)
v(1771)=v(232)*(v(1726)*v(229)+(v(1604)+v(1630))*v(230)+v(1658)*v(231)+v(1690)*v(7793))
v(1770)=v(232)*(v(1724)*v(229)+(v(1603)+v(1629))*v(230)+v(1657)*v(231)+v(1688)*v(7793))
v(1769)=v(232)*(v(1721)*v(229)+(v(1602)+v(1627))*v(230)+v(1656)*v(231)+v(1687)*v(7793))
v(1768)=v(232)*(v(1719)*v(229)+(v(1600)+v(1626))*v(230)+v(1655)*v(231)+v(1685)*v(7793))
v(1767)=v(232)*(v(1717)*v(229)+(v(1599)+v(1625))*v(230)+v(1653)*v(231)+v(1683)*v(7793))
v(1766)=v(232)*(v(1716)*v(229)+(v(1598)+v(1624))*v(230)+v(1652)*v(231)+v(1682)*v(7793))
v(1765)=v(232)*(v(1713)*v(229)+(v(1597)+v(1623))*v(230)+v(1651)*v(231)+v(1681)*v(7793))
v(1764)=v(232)*(v(1712)*v(229)+(v(1596)+v(1622))*v(230)+v(1650)*v(231)+v(1680)*v(7793))
v(1763)=v(232)*(v(1709)*v(229)+(v(1595)+v(1621))*v(230)+v(1649)*v(231)+v(1677)*v(7793))
v(1762)=v(232)*(v(1707)*v(229)+(v(1593)+v(1619))*v(230)+v(1647)*v(231)+v(1675)*v(7793))
v(1761)=v(232)*(v(1704)*v(229)+(v(1591)+v(1618))*v(230)+v(1644)*v(231)+v(1672)*v(7793))+v(1738)*v(7794)
v(1760)=v(1701)*v(232)
v(2123)=v(1760)+v(1793)+v(1615)*v(232)
v(1759)=v(1700)*v(232)
v(2122)=v(1759)+v(1792)+v(1614)*v(232)
v(1758)=v(1699)*v(232)
v(2121)=v(1758)+v(1791)+v(1613)*v(232)
v(1757)=v(1698)*v(232)
v(2120)=v(1757)+v(1790)+v(1612)*v(232)
v(1756)=v(1697)*v(232)
v(2119)=v(1756)+v(1789)+v(1611)*v(232)
v(1755)=v(1696)*v(232)
v(2118)=v(1755)+v(1788)+v(1610)*v(232)
v(1754)=v(1695)*v(232)
v(2117)=v(1754)+v(1787)+v(1609)*v(232)
v(1753)=v(1694)*v(232)
v(2116)=v(1753)+v(1786)+v(1608)*v(232)
v(1752)=v(1693)*v(232)
v(2115)=v(1752)+v(1785)+v(1607)*v(232)
v(1751)=v(1692)*v(232)
v(2114)=v(1751)+v(1784)+v(1606)*v(232)
v(1750)=v(1691)*v(232)+v(1738)*v(373)
v(2113)=v(1750)+v(1783)+v(1605)*v(232)+v(1738)*v(370)
v(1749)=v(1737)*v(232)
v(2299)=v(1749)+v(1760)+v(1641)*v(232)
v(1848)=v(1749)+v(1793)+v(1588)*v(232)
v(1748)=v(1736)*v(232)
v(2298)=v(1748)+v(1759)+v(1640)*v(232)
v(1847)=v(1748)+v(1792)+v(1587)*v(232)
v(1747)=v(1735)*v(232)
v(2297)=v(1747)+v(1758)+v(1639)*v(232)
v(1846)=v(1747)+v(1791)+v(1586)*v(232)
v(1746)=v(1734)*v(232)
v(2296)=v(1746)+v(1757)+v(1638)*v(232)
v(1845)=v(1746)+v(1790)+v(1585)*v(232)
v(1745)=v(1733)*v(232)
v(2295)=v(1745)+v(1756)+v(1637)*v(232)
v(1844)=v(1745)+v(1789)+v(1584)*v(232)
v(1744)=v(1732)*v(232)
v(2294)=v(1744)+v(1755)+v(1636)*v(232)
v(1843)=v(1744)+v(1788)+v(1583)*v(232)
v(1743)=v(1731)*v(232)
v(2293)=v(1743)+v(1754)+v(1635)*v(232)
v(1842)=v(1743)+v(1787)+v(1582)*v(232)
v(1742)=v(1730)*v(232)
v(2292)=v(1742)+v(1753)+v(1634)*v(232)
v(1841)=v(1742)+v(1786)+v(1581)*v(232)
v(1741)=v(1729)*v(232)
v(2291)=v(1741)+v(1752)+v(1633)*v(232)
v(1840)=v(1741)+v(1785)+v(1580)*v(232)
v(1740)=v(1728)*v(232)
v(2290)=v(1740)+v(1751)+v(1632)*v(232)
v(1839)=v(1740)+v(1784)+v(1579)*v(232)
v(1739)=v(1727)*v(232)+v(1738)*v(374)
v(2289)=v(1739)+v(1750)+v(1631)*v(232)+v(1738)*v(371)
v(1838)=v(1739)+v(1783)+v(1578)*v(232)+v(1738)*v(369)
v(268)=v(232)*v(374)
v(267)=v(232)*v(373)
v(255)=v(232)*v(7794)
v(1782)=(v(1771)*v(230)+v(1690)*v(255))*v(7522)
v(1781)=(v(1770)*v(230)+v(1688)*v(255))*v(7522)
v(1780)=(v(1769)*v(230)+v(1687)*v(255))*v(7522)
v(1779)=(v(1768)*v(230)+v(1685)*v(255))*v(7522)
v(1778)=(v(1767)*v(230)+v(1683)*v(255))*v(7522)
v(1777)=(v(1766)*v(230)+v(1682)*v(255))*v(7522)
v(1776)=(v(1765)*v(230)+v(1681)*v(255))*v(7522)
v(1775)=(v(1764)*v(230)+v(1680)*v(255))*v(7522)
v(1774)=(v(1763)*v(230)+v(1677)*v(255))*v(7522)
v(1773)=(v(1762)*v(230)+v(1675)*v(255))*v(7522)
v(1772)=v(1761)*v(7795)+v(255)*v(7817)
v(271)=v(255)*v(7795)
v(250)=v(232)*v(372)
v(236)=v(232)*v(7796)
v(1815)=(v(1804)*v(229)+v(1658)*v(236))*v(7522)
v(1814)=(v(1803)*v(229)+v(1657)*v(236))*v(7522)
v(1813)=(v(1802)*v(229)+v(1656)*v(236))*v(7522)
v(1812)=(v(1801)*v(229)+v(1655)*v(236))*v(7522)
v(1811)=(v(1800)*v(229)+v(1653)*v(236))*v(7522)
v(1810)=(v(1799)*v(229)+v(1652)*v(236))*v(7522)
v(1809)=(v(1798)*v(229)+v(1651)*v(236))*v(7522)
v(1808)=(v(1797)*v(229)+v(1650)*v(236))*v(7522)
v(1807)=(v(1796)*v(229)+v(1649)*v(236))*v(7522)
v(1806)=(v(1795)*v(229)+v(1647)*v(236))*v(7522)
v(1805)=v(1794)*v(7797)+v(236)*v(7803)
v(252)=v(236)*v(7797)
v(235)=v(232)*v(7798)
v(1837)=(v(1826)*v(231)+v(1726)*v(235))*v(7522)
v(1836)=(v(1825)*v(231)+v(1724)*v(235))*v(7522)
v(1835)=(v(1824)*v(231)+v(1721)*v(235))*v(7522)
v(1834)=(v(1823)*v(231)+v(1719)*v(235))*v(7522)
v(1833)=(v(1822)*v(231)+v(1717)*v(235))*v(7522)
v(1832)=(v(1821)*v(231)+v(1716)*v(235))*v(7522)
v(1831)=(v(1820)*v(231)+v(1713)*v(235))*v(7522)
v(1830)=(v(1819)*v(231)+v(1712)*v(235))*v(7522)
v(1829)=(v(1818)*v(231)+v(1709)*v(235))*v(7522)
v(1828)=(v(1817)*v(231)+v(1707)*v(235))*v(7522)
v(1827)=v(1816)*v(7799)+v(235)*v(7801)
v(270)=v(235)*v(7799)
v(233)=v(250)+v(268)+v(232)*v(369)
v(7802)=v(229)*v(233)+v(230)*v(235)+v(227)*v(236)
v(7800)=v(231)*v(233)+v(228)*v(235)+v(230)*v(236)
v(1903)=v(1815)+v(1837)+(v(1848)*v(223)+v(1577)*v(233))*v(7522)
v(1902)=v(1814)+v(1836)+(v(1847)*v(223)+v(1576)*v(233))*v(7522)
v(1901)=v(1813)+v(1835)+(v(1846)*v(223)+v(1575)*v(233))*v(7522)
v(1900)=v(1812)+v(1834)+(v(1845)*v(223)+v(1573)*v(233))*v(7522)
v(1899)=v(1811)+v(1833)+(v(1844)*v(223)+v(1572)*v(233))*v(7522)
v(1898)=v(1810)+v(1832)+(v(1843)*v(223)+v(1571)*v(233))*v(7522)
v(1897)=v(1809)+v(1831)+(v(1842)*v(223)+v(1570)*v(233))*v(7522)
v(1896)=v(1808)+v(1830)+(v(1841)*v(223)+v(1569)*v(233))*v(7522)
v(1895)=v(1807)+v(1829)+(v(1840)*v(223)+v(1568)*v(233))*v(7522)
v(1894)=v(1806)+v(1828)+(v(1839)*v(223)+v(1566)*v(233))*v(7522)
v(1893)=v(1805)+v(1827)+v(1838)*v(7804)+v(233)*v(7805)
v(1881)=(v(1804)*v(227)+v(1848)*v(229)+v(1826)*v(230)+v(1658)*v(233)+v(1690)*v(235)+v(1604)*v(236))*v(7522)
v(1880)=(v(1803)*v(227)+v(1847)*v(229)+v(1825)*v(230)+v(1657)*v(233)+v(1688)*v(235)+v(1603)*v(236))*v(7522)
v(1879)=(v(1802)*v(227)+v(1846)*v(229)+v(1824)*v(230)+v(1656)*v(233)+v(1687)*v(235)+v(1602)*v(236))*v(7522)
v(1878)=(v(1801)*v(227)+v(1845)*v(229)+v(1823)*v(230)+v(1655)*v(233)+v(1685)*v(235)+v(1600)*v(236))*v(7522)
v(1877)=(v(1800)*v(227)+v(1844)*v(229)+v(1822)*v(230)+v(1653)*v(233)+v(1683)*v(235)+v(1599)*v(236))*v(7522)
v(1876)=(v(1799)*v(227)+v(1843)*v(229)+v(1821)*v(230)+v(1652)*v(233)+v(1682)*v(235)+v(1598)*v(236))*v(7522)
v(1875)=(v(1798)*v(227)+v(1842)*v(229)+v(1820)*v(230)+v(1651)*v(233)+v(1681)*v(235)+v(1597)*v(236))*v(7522)
v(1874)=(v(1797)*v(227)+v(1841)*v(229)+v(1819)*v(230)+v(1650)*v(233)+v(1680)*v(235)+v(1596)*v(236))*v(7522)
v(1873)=(v(1796)*v(227)+v(1840)*v(229)+v(1818)*v(230)+v(1649)*v(233)+v(1677)*v(235)+v(1595)*v(236))*v(7522)
v(1872)=(v(1795)*v(227)+v(1839)*v(229)+v(1817)*v(230)+v(1647)*v(233)+v(1675)*v(235)+v(1593)*v(236))*v(7522)
v(1871)=(v(1794)*v(227)+v(1838)*v(229)+v(1816)*v(230)+v(1644)*v(233)+v(1672)*v(235)+v(1591)*v(236))*v(7522)+v(7518)*v&
&(7802)
v(1859)=(v(1826)*v(228)+v(1804)*v(230)+v(1848)*v(231)+v(1726)*v(233)+v(1630)*v(235)+v(1690)*v(236))*v(7522)
v(1858)=(v(1825)*v(228)+v(1803)*v(230)+v(1847)*v(231)+v(1724)*v(233)+v(1629)*v(235)+v(1688)*v(236))*v(7522)
v(1857)=(v(1824)*v(228)+v(1802)*v(230)+v(1846)*v(231)+v(1721)*v(233)+v(1627)*v(235)+v(1687)*v(236))*v(7522)
v(1856)=(v(1823)*v(228)+v(1801)*v(230)+v(1845)*v(231)+v(1719)*v(233)+v(1626)*v(235)+v(1685)*v(236))*v(7522)
v(1855)=(v(1822)*v(228)+v(1800)*v(230)+v(1844)*v(231)+v(1717)*v(233)+v(1625)*v(235)+v(1683)*v(236))*v(7522)
v(1854)=(v(1821)*v(228)+v(1799)*v(230)+v(1843)*v(231)+v(1716)*v(233)+v(1624)*v(235)+v(1682)*v(236))*v(7522)
v(1853)=(v(1820)*v(228)+v(1798)*v(230)+v(1842)*v(231)+v(1713)*v(233)+v(1623)*v(235)+v(1681)*v(236))*v(7522)
v(1852)=(v(1819)*v(228)+v(1797)*v(230)+v(1841)*v(231)+v(1712)*v(233)+v(1622)*v(235)+v(1680)*v(236))*v(7522)
v(1851)=(v(1818)*v(228)+v(1796)*v(230)+v(1840)*v(231)+v(1709)*v(233)+v(1621)*v(235)+v(1677)*v(236))*v(7522)
v(1850)=(v(1817)*v(228)+v(1795)*v(230)+v(1839)*v(231)+v(1707)*v(233)+v(1619)*v(235)+v(1675)*v(236))*v(7522)
v(1849)=(v(1816)*v(228)+v(1794)*v(230)+v(1838)*v(231)+v(1704)*v(233)+v(1618)*v(235)+v(1672)*v(236))*v(7522)+v(7518)*v&
&(7800)
v(239)=v(7522)*v(7800)
v(1870)=(v(1859)*v(231)+v(1726)*v(239))*v(7522)
v(1869)=(v(1858)*v(231)+v(1724)*v(239))*v(7522)
v(1868)=(v(1857)*v(231)+v(1721)*v(239))*v(7522)
v(1867)=(v(1856)*v(231)+v(1719)*v(239))*v(7522)
v(1866)=(v(1855)*v(231)+v(1717)*v(239))*v(7522)
v(1865)=(v(1854)*v(231)+v(1716)*v(239))*v(7522)
v(1864)=(v(1853)*v(231)+v(1713)*v(239))*v(7522)
v(1863)=(v(1852)*v(231)+v(1712)*v(239))*v(7522)
v(1862)=(v(1851)*v(231)+v(1709)*v(239))*v(7522)
v(1861)=(v(1850)*v(231)+v(1707)*v(239))*v(7522)
v(1860)=v(1849)*v(7799)+v(239)*v(7801)
v(274)=v(239)*v(7799)
v(238)=v(7522)*v(7802)
v(1892)=(v(1881)*v(229)+v(1658)*v(238))*v(7522)
v(1891)=(v(1880)*v(229)+v(1657)*v(238))*v(7522)
v(1890)=(v(1879)*v(229)+v(1656)*v(238))*v(7522)
v(1889)=(v(1878)*v(229)+v(1655)*v(238))*v(7522)
v(1888)=(v(1877)*v(229)+v(1653)*v(238))*v(7522)
v(1887)=(v(1876)*v(229)+v(1652)*v(238))*v(7522)
v(1886)=(v(1875)*v(229)+v(1651)*v(238))*v(7522)
v(1885)=(v(1874)*v(229)+v(1650)*v(238))*v(7522)
v(1884)=(v(1873)*v(229)+v(1649)*v(238))*v(7522)
v(1883)=(v(1872)*v(229)+v(1647)*v(238))*v(7522)
v(1882)=v(1871)*v(7797)+v(238)*v(7803)
v(254)=v(238)*v(7797)
v(234)=v(252)+v(270)+v(233)*v(7804)
v(7807)=v(231)*v(234)+v(230)*v(238)+v(228)*v(239)
v(7806)=v(229)*v(234)+v(227)*v(238)+v(230)*v(239)
v(1958)=v(1870)+v(1892)+(v(1903)*v(223)+v(1577)*v(234))*v(7522)
v(1957)=v(1869)+v(1891)+(v(1902)*v(223)+v(1576)*v(234))*v(7522)
v(1956)=v(1868)+v(1890)+(v(1901)*v(223)+v(1575)*v(234))*v(7522)
v(1955)=v(1867)+v(1889)+(v(1900)*v(223)+v(1573)*v(234))*v(7522)
v(1954)=v(1866)+v(1888)+(v(1899)*v(223)+v(1572)*v(234))*v(7522)
v(1953)=v(1865)+v(1887)+(v(1898)*v(223)+v(1571)*v(234))*v(7522)
v(1952)=v(1864)+v(1886)+(v(1897)*v(223)+v(1570)*v(234))*v(7522)
v(1951)=v(1863)+v(1885)+(v(1896)*v(223)+v(1569)*v(234))*v(7522)
v(1950)=v(1862)+v(1884)+(v(1895)*v(223)+v(1568)*v(234))*v(7522)
v(1949)=v(1861)+v(1883)+(v(1894)*v(223)+v(1566)*v(234))*v(7522)
v(1948)=v(1860)+v(1882)+v(1893)*v(7804)+v(234)*v(7805)
v(1936)=(v(1859)*v(228)+v(1881)*v(230)+v(1903)*v(231)+v(1726)*v(234)+v(1690)*v(238)+v(1630)*v(239))*v(7522)
v(1935)=(v(1858)*v(228)+v(1880)*v(230)+v(1902)*v(231)+v(1724)*v(234)+v(1688)*v(238)+v(1629)*v(239))*v(7522)
v(1934)=(v(1857)*v(228)+v(1879)*v(230)+v(1901)*v(231)+v(1721)*v(234)+v(1687)*v(238)+v(1627)*v(239))*v(7522)
v(1933)=(v(1856)*v(228)+v(1878)*v(230)+v(1900)*v(231)+v(1719)*v(234)+v(1685)*v(238)+v(1626)*v(239))*v(7522)
v(1932)=(v(1855)*v(228)+v(1877)*v(230)+v(1899)*v(231)+v(1717)*v(234)+v(1683)*v(238)+v(1625)*v(239))*v(7522)
v(1931)=(v(1854)*v(228)+v(1876)*v(230)+v(1898)*v(231)+v(1716)*v(234)+v(1682)*v(238)+v(1624)*v(239))*v(7522)
v(1930)=(v(1853)*v(228)+v(1875)*v(230)+v(1897)*v(231)+v(1713)*v(234)+v(1681)*v(238)+v(1623)*v(239))*v(7522)
v(1929)=(v(1852)*v(228)+v(1874)*v(230)+v(1896)*v(231)+v(1712)*v(234)+v(1680)*v(238)+v(1622)*v(239))*v(7522)
v(1928)=(v(1851)*v(228)+v(1873)*v(230)+v(1895)*v(231)+v(1709)*v(234)+v(1677)*v(238)+v(1621)*v(239))*v(7522)
v(1927)=(v(1850)*v(228)+v(1872)*v(230)+v(1894)*v(231)+v(1707)*v(234)+v(1675)*v(238)+v(1619)*v(239))*v(7522)
v(1926)=(v(1849)*v(228)+v(1871)*v(230)+v(1893)*v(231)+v(1704)*v(234)+v(1672)*v(238)+v(1618)*v(239))*v(7522)+v(7518)*v&
&(7807)
v(1914)=(v(1881)*v(227)+v(1903)*v(229)+v(1859)*v(230)+v(1658)*v(234)+v(1604)*v(238)+v(1690)*v(239))*v(7522)
v(1913)=(v(1880)*v(227)+v(1902)*v(229)+v(1858)*v(230)+v(1657)*v(234)+v(1603)*v(238)+v(1688)*v(239))*v(7522)
v(1912)=(v(1879)*v(227)+v(1901)*v(229)+v(1857)*v(230)+v(1656)*v(234)+v(1602)*v(238)+v(1687)*v(239))*v(7522)
v(1911)=(v(1878)*v(227)+v(1900)*v(229)+v(1856)*v(230)+v(1655)*v(234)+v(1600)*v(238)+v(1685)*v(239))*v(7522)
v(1910)=(v(1877)*v(227)+v(1899)*v(229)+v(1855)*v(230)+v(1653)*v(234)+v(1599)*v(238)+v(1683)*v(239))*v(7522)
v(1909)=(v(1876)*v(227)+v(1898)*v(229)+v(1854)*v(230)+v(1652)*v(234)+v(1598)*v(238)+v(1682)*v(239))*v(7522)
v(1908)=(v(1875)*v(227)+v(1897)*v(229)+v(1853)*v(230)+v(1651)*v(234)+v(1597)*v(238)+v(1681)*v(239))*v(7522)
v(1907)=(v(1874)*v(227)+v(1896)*v(229)+v(1852)*v(230)+v(1650)*v(234)+v(1596)*v(238)+v(1680)*v(239))*v(7522)
v(1906)=(v(1873)*v(227)+v(1895)*v(229)+v(1851)*v(230)+v(1649)*v(234)+v(1595)*v(238)+v(1677)*v(239))*v(7522)
v(1905)=(v(1872)*v(227)+v(1894)*v(229)+v(1850)*v(230)+v(1647)*v(234)+v(1593)*v(238)+v(1675)*v(239))*v(7522)
v(1904)=(v(1871)*v(227)+v(1893)*v(229)+v(1849)*v(230)+v(1644)*v(234)+v(1591)*v(238)+v(1672)*v(239))*v(7522)+v(7518)*v&
&(7806)
v(242)=v(7522)*v(7806)
v(1925)=(v(1914)*v(229)+v(1658)*v(242))*v(7522)
v(1924)=(v(1913)*v(229)+v(1657)*v(242))*v(7522)
v(1923)=(v(1912)*v(229)+v(1656)*v(242))*v(7522)
v(1922)=(v(1911)*v(229)+v(1655)*v(242))*v(7522)
v(1921)=(v(1910)*v(229)+v(1653)*v(242))*v(7522)
v(1920)=(v(1909)*v(229)+v(1652)*v(242))*v(7522)
v(1919)=(v(1908)*v(229)+v(1651)*v(242))*v(7522)
v(1918)=(v(1907)*v(229)+v(1650)*v(242))*v(7522)
v(1917)=(v(1906)*v(229)+v(1649)*v(242))*v(7522)
v(1916)=(v(1905)*v(229)+v(1647)*v(242))*v(7522)
v(1915)=v(1904)*v(7797)+v(242)*v(7803)
v(258)=v(242)*v(7797)
v(241)=v(7522)*v(7807)
v(1947)=(v(1936)*v(231)+v(1726)*v(241))*v(7522)
v(1946)=(v(1935)*v(231)+v(1724)*v(241))*v(7522)
v(1945)=(v(1934)*v(231)+v(1721)*v(241))*v(7522)
v(1944)=(v(1933)*v(231)+v(1719)*v(241))*v(7522)
v(1943)=(v(1932)*v(231)+v(1717)*v(241))*v(7522)
v(1942)=(v(1931)*v(231)+v(1716)*v(241))*v(7522)
v(1941)=(v(1930)*v(231)+v(1713)*v(241))*v(7522)
v(1940)=(v(1929)*v(231)+v(1712)*v(241))*v(7522)
v(1939)=(v(1928)*v(231)+v(1709)*v(241))*v(7522)
v(1938)=(v(1927)*v(231)+v(1707)*v(241))*v(7522)
v(1937)=v(1926)*v(7799)+v(241)*v(7801)
v(276)=v(241)*v(7799)
v(237)=v(254)+v(274)+v(234)*v(7804)
v(7809)=v(229)*v(237)+v(230)*v(241)+v(227)*v(242)
v(7808)=v(231)*v(237)+v(228)*v(241)+v(230)*v(242)
v(2013)=v(1925)+v(1947)+(v(1958)*v(223)+v(1577)*v(237))*v(7522)
v(2012)=v(1924)+v(1946)+(v(1957)*v(223)+v(1576)*v(237))*v(7522)
v(2011)=v(1923)+v(1945)+(v(1956)*v(223)+v(1575)*v(237))*v(7522)
v(2010)=v(1922)+v(1944)+(v(1955)*v(223)+v(1573)*v(237))*v(7522)
v(2009)=v(1921)+v(1943)+(v(1954)*v(223)+v(1572)*v(237))*v(7522)
v(2008)=v(1920)+v(1942)+(v(1953)*v(223)+v(1571)*v(237))*v(7522)
v(2007)=v(1919)+v(1941)+(v(1952)*v(223)+v(1570)*v(237))*v(7522)
v(2006)=v(1918)+v(1940)+(v(1951)*v(223)+v(1569)*v(237))*v(7522)
v(2005)=v(1917)+v(1939)+(v(1950)*v(223)+v(1568)*v(237))*v(7522)
v(2004)=v(1916)+v(1938)+(v(1949)*v(223)+v(1566)*v(237))*v(7522)
v(2003)=v(1915)+v(1937)+v(1948)*v(7804)+v(237)*v(7805)
v(1991)=(v(1914)*v(227)+v(1958)*v(229)+v(1936)*v(230)+v(1658)*v(237)+v(1690)*v(241)+v(1604)*v(242))*v(7522)
v(1990)=(v(1913)*v(227)+v(1957)*v(229)+v(1935)*v(230)+v(1657)*v(237)+v(1688)*v(241)+v(1603)*v(242))*v(7522)
v(1989)=(v(1912)*v(227)+v(1956)*v(229)+v(1934)*v(230)+v(1656)*v(237)+v(1687)*v(241)+v(1602)*v(242))*v(7522)
v(1988)=(v(1911)*v(227)+v(1955)*v(229)+v(1933)*v(230)+v(1655)*v(237)+v(1685)*v(241)+v(1600)*v(242))*v(7522)
v(1987)=(v(1910)*v(227)+v(1954)*v(229)+v(1932)*v(230)+v(1653)*v(237)+v(1683)*v(241)+v(1599)*v(242))*v(7522)
v(1986)=(v(1909)*v(227)+v(1953)*v(229)+v(1931)*v(230)+v(1652)*v(237)+v(1682)*v(241)+v(1598)*v(242))*v(7522)
v(1985)=(v(1908)*v(227)+v(1952)*v(229)+v(1930)*v(230)+v(1651)*v(237)+v(1681)*v(241)+v(1597)*v(242))*v(7522)
v(1984)=(v(1907)*v(227)+v(1951)*v(229)+v(1929)*v(230)+v(1650)*v(237)+v(1680)*v(241)+v(1596)*v(242))*v(7522)
v(1983)=(v(1906)*v(227)+v(1950)*v(229)+v(1928)*v(230)+v(1649)*v(237)+v(1677)*v(241)+v(1595)*v(242))*v(7522)
v(1982)=(v(1905)*v(227)+v(1949)*v(229)+v(1927)*v(230)+v(1647)*v(237)+v(1675)*v(241)+v(1593)*v(242))*v(7522)
v(1981)=(v(1904)*v(227)+v(1948)*v(229)+v(1926)*v(230)+v(1644)*v(237)+v(1672)*v(241)+v(1591)*v(242))*v(7522)+v(7518)*v&
&(7809)
v(1969)=(v(1936)*v(228)+v(1914)*v(230)+v(1958)*v(231)+v(1726)*v(237)+v(1630)*v(241)+v(1690)*v(242))*v(7522)
v(1968)=(v(1935)*v(228)+v(1913)*v(230)+v(1957)*v(231)+v(1724)*v(237)+v(1629)*v(241)+v(1688)*v(242))*v(7522)
v(1967)=(v(1934)*v(228)+v(1912)*v(230)+v(1956)*v(231)+v(1721)*v(237)+v(1627)*v(241)+v(1687)*v(242))*v(7522)
v(1966)=(v(1933)*v(228)+v(1911)*v(230)+v(1955)*v(231)+v(1719)*v(237)+v(1626)*v(241)+v(1685)*v(242))*v(7522)
v(1965)=(v(1932)*v(228)+v(1910)*v(230)+v(1954)*v(231)+v(1717)*v(237)+v(1625)*v(241)+v(1683)*v(242))*v(7522)
v(1964)=(v(1931)*v(228)+v(1909)*v(230)+v(1953)*v(231)+v(1716)*v(237)+v(1624)*v(241)+v(1682)*v(242))*v(7522)
v(1963)=(v(1930)*v(228)+v(1908)*v(230)+v(1952)*v(231)+v(1713)*v(237)+v(1623)*v(241)+v(1681)*v(242))*v(7522)
v(1962)=(v(1929)*v(228)+v(1907)*v(230)+v(1951)*v(231)+v(1712)*v(237)+v(1622)*v(241)+v(1680)*v(242))*v(7522)
v(1961)=(v(1928)*v(228)+v(1906)*v(230)+v(1950)*v(231)+v(1709)*v(237)+v(1621)*v(241)+v(1677)*v(242))*v(7522)
v(1960)=(v(1927)*v(228)+v(1905)*v(230)+v(1949)*v(231)+v(1707)*v(237)+v(1619)*v(241)+v(1675)*v(242))*v(7522)
v(1959)=(v(1926)*v(228)+v(1904)*v(230)+v(1948)*v(231)+v(1704)*v(237)+v(1618)*v(241)+v(1672)*v(242))*v(7522)+v(7518)*v&
&(7808)
v(245)=v(7522)*v(7808)
v(1980)=(v(1969)*v(231)+v(1726)*v(245))*v(7522)
v(1979)=(v(1968)*v(231)+v(1724)*v(245))*v(7522)
v(1978)=(v(1967)*v(231)+v(1721)*v(245))*v(7522)
v(1977)=(v(1966)*v(231)+v(1719)*v(245))*v(7522)
v(1976)=(v(1965)*v(231)+v(1717)*v(245))*v(7522)
v(1975)=(v(1964)*v(231)+v(1716)*v(245))*v(7522)
v(1974)=(v(1963)*v(231)+v(1713)*v(245))*v(7522)
v(1973)=(v(1962)*v(231)+v(1712)*v(245))*v(7522)
v(1972)=(v(1961)*v(231)+v(1709)*v(245))*v(7522)
v(1971)=(v(1960)*v(231)+v(1707)*v(245))*v(7522)
v(1970)=v(1959)*v(7799)+v(245)*v(7801)
v(280)=v(245)*v(7799)
v(244)=v(7522)*v(7809)
v(2002)=(v(1991)*v(229)+v(1658)*v(244))*v(7522)
v(2001)=(v(1990)*v(229)+v(1657)*v(244))*v(7522)
v(2000)=(v(1989)*v(229)+v(1656)*v(244))*v(7522)
v(1999)=(v(1988)*v(229)+v(1655)*v(244))*v(7522)
v(1998)=(v(1987)*v(229)+v(1653)*v(244))*v(7522)
v(1997)=(v(1986)*v(229)+v(1652)*v(244))*v(7522)
v(1996)=(v(1985)*v(229)+v(1651)*v(244))*v(7522)
v(1995)=(v(1984)*v(229)+v(1650)*v(244))*v(7522)
v(1994)=(v(1983)*v(229)+v(1649)*v(244))*v(7522)
v(1993)=(v(1982)*v(229)+v(1647)*v(244))*v(7522)
v(1992)=v(1981)*v(7797)+v(244)*v(7803)
v(260)=v(244)*v(7797)
v(240)=v(258)+v(276)+v(237)*v(7804)
v(7811)=v(229)*v(240)+v(227)*v(244)+v(230)*v(245)
v(7810)=v(231)*v(240)+v(230)*v(244)+v(228)*v(245)
v(2057)=(v(1991)*v(227)+v(2013)*v(229)+v(1969)*v(230)+v(1658)*v(240)+v(1604)*v(244)+v(1690)*v(245))*v(7522)
v(2056)=(v(1990)*v(227)+v(2012)*v(229)+v(1968)*v(230)+v(1657)*v(240)+v(1603)*v(244)+v(1688)*v(245))*v(7522)
v(2055)=(v(1989)*v(227)+v(2011)*v(229)+v(1967)*v(230)+v(1656)*v(240)+v(1602)*v(244)+v(1687)*v(245))*v(7522)
v(2054)=(v(1988)*v(227)+v(2010)*v(229)+v(1966)*v(230)+v(1655)*v(240)+v(1600)*v(244)+v(1685)*v(245))*v(7522)
v(2053)=(v(1987)*v(227)+v(2009)*v(229)+v(1965)*v(230)+v(1653)*v(240)+v(1599)*v(244)+v(1683)*v(245))*v(7522)
v(2052)=(v(1986)*v(227)+v(2008)*v(229)+v(1964)*v(230)+v(1652)*v(240)+v(1598)*v(244)+v(1682)*v(245))*v(7522)
v(2051)=(v(1985)*v(227)+v(2007)*v(229)+v(1963)*v(230)+v(1651)*v(240)+v(1597)*v(244)+v(1681)*v(245))*v(7522)
v(2050)=(v(1984)*v(227)+v(2006)*v(229)+v(1962)*v(230)+v(1650)*v(240)+v(1596)*v(244)+v(1680)*v(245))*v(7522)
v(2049)=(v(1983)*v(227)+v(2005)*v(229)+v(1961)*v(230)+v(1649)*v(240)+v(1595)*v(244)+v(1677)*v(245))*v(7522)
v(2048)=(v(1982)*v(227)+v(2004)*v(229)+v(1960)*v(230)+v(1647)*v(240)+v(1593)*v(244)+v(1675)*v(245))*v(7522)
v(2047)=(v(1981)*v(227)+v(2003)*v(229)+v(1959)*v(230)+v(1644)*v(240)+v(1591)*v(244)+v(1672)*v(245))*v(7522)+v(7518)*v&
&(7811)
v(2035)=(v(1969)*v(228)+v(1991)*v(230)+v(2013)*v(231)+v(1726)*v(240)+v(1690)*v(244)+v(1630)*v(245))*v(7522)
v(2034)=(v(1968)*v(228)+v(1990)*v(230)+v(2012)*v(231)+v(1724)*v(240)+v(1688)*v(244)+v(1629)*v(245))*v(7522)
v(2033)=(v(1967)*v(228)+v(1989)*v(230)+v(2011)*v(231)+v(1721)*v(240)+v(1687)*v(244)+v(1627)*v(245))*v(7522)
v(2032)=(v(1966)*v(228)+v(1988)*v(230)+v(2010)*v(231)+v(1719)*v(240)+v(1685)*v(244)+v(1626)*v(245))*v(7522)
v(2031)=(v(1965)*v(228)+v(1987)*v(230)+v(2009)*v(231)+v(1717)*v(240)+v(1683)*v(244)+v(1625)*v(245))*v(7522)
v(2030)=(v(1964)*v(228)+v(1986)*v(230)+v(2008)*v(231)+v(1716)*v(240)+v(1682)*v(244)+v(1624)*v(245))*v(7522)
v(2029)=(v(1963)*v(228)+v(1985)*v(230)+v(2007)*v(231)+v(1713)*v(240)+v(1681)*v(244)+v(1623)*v(245))*v(7522)
v(2028)=(v(1962)*v(228)+v(1984)*v(230)+v(2006)*v(231)+v(1712)*v(240)+v(1680)*v(244)+v(1622)*v(245))*v(7522)
v(2027)=(v(1961)*v(228)+v(1983)*v(230)+v(2005)*v(231)+v(1709)*v(240)+v(1677)*v(244)+v(1621)*v(245))*v(7522)
v(2026)=(v(1960)*v(228)+v(1982)*v(230)+v(2004)*v(231)+v(1707)*v(240)+v(1675)*v(244)+v(1619)*v(245))*v(7522)
v(2025)=(v(1959)*v(228)+v(1981)*v(230)+v(2003)*v(231)+v(1704)*v(240)+v(1672)*v(244)+v(1618)*v(245))*v(7522)+v(7518)*v&
&(7810)
v(2024)=v(1980)+v(2002)+(v(2013)*v(223)+v(1577)*v(240))*v(7522)
v(2023)=v(1979)+v(2001)+(v(2012)*v(223)+v(1576)*v(240))*v(7522)
v(2022)=v(1978)+v(2000)+(v(2011)*v(223)+v(1575)*v(240))*v(7522)
v(2021)=v(1977)+v(1999)+(v(2010)*v(223)+v(1573)*v(240))*v(7522)
v(2020)=v(1976)+v(1998)+(v(2009)*v(223)+v(1572)*v(240))*v(7522)
v(2019)=v(1975)+v(1997)+(v(2008)*v(223)+v(1571)*v(240))*v(7522)
v(2018)=v(1974)+v(1996)+(v(2007)*v(223)+v(1570)*v(240))*v(7522)
v(2017)=v(1973)+v(1995)+(v(2006)*v(223)+v(1569)*v(240))*v(7522)
v(2016)=v(1972)+v(1994)+(v(2005)*v(223)+v(1568)*v(240))*v(7522)
v(2015)=v(1971)+v(1993)+(v(2004)*v(223)+v(1566)*v(240))*v(7522)
v(2014)=v(1970)+v(1992)+v(2003)*v(7804)+v(240)*v(7805)
v(243)=v(260)+v(280)+v(240)*v(7804)
v(7812)=5040d0+v(243)
v(246)=v(7522)*v(7810)
v(2046)=(v(2035)*v(231)+v(1726)*v(246))*v(7522)
v(2045)=(v(2034)*v(231)+v(1724)*v(246))*v(7522)
v(2044)=(v(2033)*v(231)+v(1721)*v(246))*v(7522)
v(2043)=(v(2032)*v(231)+v(1719)*v(246))*v(7522)
v(2042)=(v(2031)*v(231)+v(1717)*v(246))*v(7522)
v(2041)=(v(2030)*v(231)+v(1716)*v(246))*v(7522)
v(2040)=(v(2029)*v(231)+v(1713)*v(246))*v(7522)
v(2039)=(v(2028)*v(231)+v(1712)*v(246))*v(7522)
v(2038)=(v(2027)*v(231)+v(1709)*v(246))*v(7522)
v(2037)=(v(2026)*v(231)+v(1707)*v(246))*v(7522)
v(2036)=v(2025)*v(7799)+v(246)*v(7801)
v(282)=v(246)*v(7799)
v(247)=v(7522)*v(7811)
v(7815)=v(230)*v(246)+v(227)*v(247)
v(7814)=v(228)*v(246)+v(230)*v(247)
v(2101)=(7d0*(360d0*v(1804)+120d0*v(1881)+30d0*v(1914)+6d0*v(1991)+v(2057))+v(7522)*(v(2057)*v(227)+v(2024)*v(229)+v&
&(2035)*v(230)+v(1690)*v(246)+v(1604)*v(247)+v(1658)*v(7812)))/5040d0
v(2100)=(7d0*(360d0*v(1803)+120d0*v(1880)+30d0*v(1913)+6d0*v(1990)+v(2056))+v(7522)*(v(2056)*v(227)+v(2023)*v(229)+v&
&(2034)*v(230)+v(1688)*v(246)+v(1603)*v(247)+v(1657)*v(7812)))/5040d0
v(2099)=(7d0*(360d0*v(1802)+120d0*v(1879)+30d0*v(1912)+6d0*v(1989)+v(2055))+v(7522)*(v(2055)*v(227)+v(2022)*v(229)+v&
&(2033)*v(230)+v(1687)*v(246)+v(1602)*v(247)+v(1656)*v(7812)))/5040d0
v(2098)=(7d0*(360d0*v(1801)+120d0*v(1878)+30d0*v(1911)+6d0*v(1988)+v(2054))+v(7522)*(v(2054)*v(227)+v(2021)*v(229)+v&
&(2032)*v(230)+v(1685)*v(246)+v(1600)*v(247)+v(1655)*v(7812)))/5040d0
v(2097)=(7d0*(360d0*v(1800)+120d0*v(1877)+30d0*v(1910)+6d0*v(1987)+v(2053))+v(7522)*(v(2053)*v(227)+v(2020)*v(229)+v&
&(2031)*v(230)+v(1683)*v(246)+v(1599)*v(247)+v(1653)*v(7812)))/5040d0
v(2096)=(7d0*(360d0*v(1799)+120d0*v(1876)+30d0*v(1909)+6d0*v(1986)+v(2052))+v(7522)*(v(2052)*v(227)+v(2019)*v(229)+v&
&(2030)*v(230)+v(1682)*v(246)+v(1598)*v(247)+v(1652)*v(7812)))/5040d0
v(2095)=(7d0*(360d0*v(1798)+120d0*v(1875)+30d0*v(1908)+6d0*v(1985)+v(2051))+v(7522)*(v(2051)*v(227)+v(2018)*v(229)+v&
&(2029)*v(230)+v(1681)*v(246)+v(1597)*v(247)+v(1651)*v(7812)))/5040d0
v(2094)=(7d0*(360d0*v(1797)+120d0*v(1874)+30d0*v(1907)+6d0*v(1984)+v(2050))+v(7522)*(v(2050)*v(227)+v(2017)*v(229)+v&
&(2028)*v(230)+v(1680)*v(246)+v(1596)*v(247)+v(1650)*v(7812)))/5040d0
v(2093)=(7d0*(360d0*v(1796)+120d0*v(1873)+30d0*v(1906)+6d0*v(1983)+v(2049))+v(7522)*(v(2049)*v(227)+v(2016)*v(229)+v&
&(2027)*v(230)+v(1677)*v(246)+v(1595)*v(247)+v(1649)*v(7812)))/5040d0
v(2092)=(7d0*(360d0*v(1795)+120d0*v(1872)+30d0*v(1905)+6d0*v(1982)+v(2048))+v(7522)*(v(2048)*v(227)+v(2015)*v(229)+v&
&(2026)*v(230)+v(1675)*v(246)+v(1593)*v(247)+v(1647)*v(7812)))/5040d0
v(2091)=v(1794)/2d0+v(1871)/6d0+v(1904)/24d0+v(1981)/120d0+v(2047)/720d0+v(7803)+((v(2047)*v(227)+v(2014)*v(229)+v(2025&
&)*v(230)+v(1644)*v(243)+v(1672)*v(246)+v(1591)*v(247))*v(7522)+v(7518)*(v(229)*v(243)+v(7815)))/5040d0
v(2079)=(v(2057)*v(229)+v(1658)*v(247))*v(7522)
v(2090)=(2520d0*v(1848)+840d0*v(1903)+210d0*v(1958)+42d0*v(2013)+7d0*v(2024)+v(2046)+v(2079)+v(7522)*(v(2024)*v(223)+v&
&(1577)*v(7812)))/5040d0
v(2078)=(v(2056)*v(229)+v(1657)*v(247))*v(7522)
v(2089)=(2520d0*v(1847)+840d0*v(1902)+210d0*v(1957)+42d0*v(2012)+7d0*v(2023)+v(2045)+v(2078)+v(7522)*(v(2023)*v(223)+v&
&(1576)*v(7812)))/5040d0
v(2077)=(v(2055)*v(229)+v(1656)*v(247))*v(7522)
v(2088)=(2520d0*v(1846)+840d0*v(1901)+210d0*v(1956)+42d0*v(2011)+7d0*v(2022)+v(2044)+v(2077)+v(7522)*(v(2022)*v(223)+v&
&(1575)*v(7812)))/5040d0
v(2076)=(v(2054)*v(229)+v(1655)*v(247))*v(7522)
v(2087)=(2520d0*v(1845)+840d0*v(1900)+210d0*v(1955)+42d0*v(2010)+7d0*v(2021)+v(2043)+v(2076)+v(7522)*(v(2021)*v(223)+v&
&(1573)*v(7812)))/5040d0
v(2075)=(v(2053)*v(229)+v(1653)*v(247))*v(7522)
v(2086)=(2520d0*v(1844)+840d0*v(1899)+210d0*v(1954)+42d0*v(2009)+7d0*v(2020)+v(2042)+v(2075)+v(7522)*(v(2020)*v(223)+v&
&(1572)*v(7812)))/5040d0
v(2074)=(v(2052)*v(229)+v(1652)*v(247))*v(7522)
v(2085)=(2520d0*v(1843)+840d0*v(1898)+210d0*v(1953)+42d0*v(2008)+7d0*v(2019)+v(2041)+v(2074)+v(7522)*(v(2019)*v(223)+v&
&(1571)*v(7812)))/5040d0
v(2073)=(v(2051)*v(229)+v(1651)*v(247))*v(7522)
v(2084)=(2520d0*v(1842)+840d0*v(1897)+210d0*v(1952)+42d0*v(2007)+7d0*v(2018)+v(2040)+v(2073)+v(7522)*(v(2018)*v(223)+v&
&(1570)*v(7812)))/5040d0
v(2072)=(v(2050)*v(229)+v(1650)*v(247))*v(7522)
v(2083)=(2520d0*v(1841)+840d0*v(1896)+210d0*v(1951)+42d0*v(2006)+7d0*v(2017)+v(2039)+v(2072)+v(7522)*(v(2017)*v(223)+v&
&(1569)*v(7812)))/5040d0
v(2071)=(v(2049)*v(229)+v(1649)*v(247))*v(7522)
v(2082)=(2520d0*v(1840)+840d0*v(1895)+210d0*v(1950)+42d0*v(2005)+7d0*v(2016)+v(2038)+v(2071)+v(7522)*(v(2016)*v(223)+v&
&(1568)*v(7812)))/5040d0
v(2070)=(v(2048)*v(229)+v(1647)*v(247))*v(7522)
v(2081)=(2520d0*v(1839)+840d0*v(1894)+210d0*v(1949)+42d0*v(2004)+7d0*v(2015)+v(2037)+v(2070)+v(7522)*(v(2015)*v(223)+v&
&(1566)*v(7812)))/5040d0
v(2069)=v(2047)*v(7797)+v(247)*v(7803)
v(2080)=(2520d0*v(1838)+840d0*v(1893)+210d0*v(1948)+42d0*v(2003)+7d0*v(2014)+v(2036)+v(2069)+v(223)*(v(2014)*v(7522)+v&
&(7518)*v(7812))+v(7812)*v(7813))/5040d0
v(2068)=(7d0*(360d0*v(1826)+120d0*v(1859)+30d0*v(1936)+6d0*v(1969)+v(2035))+(5040d0*v(1726)+v(2035)*v(228)+v(2057)*v&
&(230)+v(2024)*v(231)+v(1726)*v(243)+v(1630)*v(246)+v(1690)*v(247))*v(7522))/5040d0
v(2409)=statev(7)*v(2090)+statev(5)*v(2101)+v(2068)*v(7514)
v(2376)=statev(9)*v(2068)+statev(4)*v(2090)+v(2101)*v(7513)
v(2112)=statev(6)*v(2068)+statev(8)*v(2101)+v(2090)*v(7512)
v(2067)=(7d0*(360d0*v(1825)+120d0*v(1858)+30d0*v(1935)+6d0*v(1968)+v(2034))+(5040d0*v(1724)+v(2034)*v(228)+v(2056)*v&
&(230)+v(2023)*v(231)+v(1724)*v(243)+v(1629)*v(246)+v(1688)*v(247))*v(7522))/5040d0
v(2408)=statev(7)*v(2089)+statev(5)*v(2100)+v(2067)*v(7514)
v(2375)=statev(9)*v(2067)+statev(4)*v(2089)+v(2100)*v(7513)
v(2111)=statev(6)*v(2067)+statev(8)*v(2100)+v(2089)*v(7512)
v(2066)=(7d0*(360d0*v(1824)+120d0*v(1857)+30d0*v(1934)+6d0*v(1967)+v(2033))+(5040d0*v(1721)+v(2033)*v(228)+v(2055)*v&
&(230)+v(2022)*v(231)+v(1721)*v(243)+v(1627)*v(246)+v(1687)*v(247))*v(7522))/5040d0
v(2407)=statev(7)*v(2088)+statev(5)*v(2099)+v(2066)*v(7514)
v(2374)=statev(9)*v(2066)+statev(4)*v(2088)+v(2099)*v(7513)
v(2110)=statev(6)*v(2066)+statev(8)*v(2099)+v(2088)*v(7512)
v(2065)=(7d0*(360d0*v(1823)+120d0*v(1856)+30d0*v(1933)+6d0*v(1966)+v(2032))+(5040d0*v(1719)+v(2032)*v(228)+v(2054)*v&
&(230)+v(2021)*v(231)+v(1719)*v(243)+v(1626)*v(246)+v(1685)*v(247))*v(7522))/5040d0
v(2406)=statev(7)*v(2087)+statev(5)*v(2098)+v(2065)*v(7514)
v(2373)=statev(9)*v(2065)+statev(4)*v(2087)+v(2098)*v(7513)
v(2109)=statev(6)*v(2065)+statev(8)*v(2098)+v(2087)*v(7512)
v(2064)=(7d0*(360d0*v(1822)+120d0*v(1855)+30d0*v(1932)+6d0*v(1965)+v(2031))+(5040d0*v(1717)+v(2031)*v(228)+v(2053)*v&
&(230)+v(2020)*v(231)+v(1717)*v(243)+v(1625)*v(246)+v(1683)*v(247))*v(7522))/5040d0
v(2405)=statev(7)*v(2086)+statev(5)*v(2097)+v(2064)*v(7514)
v(2372)=statev(9)*v(2064)+statev(4)*v(2086)+v(2097)*v(7513)
v(2108)=statev(6)*v(2064)+statev(8)*v(2097)+v(2086)*v(7512)
v(2063)=(7d0*(360d0*v(1821)+120d0*v(1854)+30d0*v(1931)+6d0*v(1964)+v(2030))+(5040d0*v(1716)+v(2030)*v(228)+v(2052)*v&
&(230)+v(2019)*v(231)+v(1716)*v(243)+v(1624)*v(246)+v(1682)*v(247))*v(7522))/5040d0
v(2404)=statev(7)*v(2085)+statev(5)*v(2096)+v(2063)*v(7514)
v(2371)=statev(9)*v(2063)+statev(4)*v(2085)+v(2096)*v(7513)
v(2107)=statev(6)*v(2063)+statev(8)*v(2096)+v(2085)*v(7512)
v(2062)=(7d0*(360d0*v(1820)+120d0*v(1853)+30d0*v(1930)+6d0*v(1963)+v(2029))+(5040d0*v(1713)+v(2029)*v(228)+v(2051)*v&
&(230)+v(2018)*v(231)+v(1713)*v(243)+v(1623)*v(246)+v(1681)*v(247))*v(7522))/5040d0
v(2403)=statev(7)*v(2084)+statev(5)*v(2095)+v(2062)*v(7514)
v(2370)=statev(9)*v(2062)+statev(4)*v(2084)+v(2095)*v(7513)
v(2106)=statev(6)*v(2062)+statev(8)*v(2095)+v(2084)*v(7512)
v(2061)=(7d0*(360d0*v(1819)+120d0*v(1852)+30d0*v(1929)+6d0*v(1962)+v(2028))+(5040d0*v(1712)+v(2028)*v(228)+v(2050)*v&
&(230)+v(2017)*v(231)+v(1712)*v(243)+v(1622)*v(246)+v(1680)*v(247))*v(7522))/5040d0
v(2402)=statev(7)*v(2083)+statev(5)*v(2094)+v(2061)*v(7514)
v(2369)=statev(9)*v(2061)+statev(4)*v(2083)+v(2094)*v(7513)
v(2105)=statev(6)*v(2061)+statev(8)*v(2094)+v(2083)*v(7512)
v(2060)=(7d0*(360d0*v(1818)+120d0*v(1851)+30d0*v(1928)+6d0*v(1961)+v(2027))+(5040d0*v(1709)+v(2027)*v(228)+v(2049)*v&
&(230)+v(2016)*v(231)+v(1709)*v(243)+v(1621)*v(246)+v(1677)*v(247))*v(7522))/5040d0
v(2401)=statev(7)*v(2082)+statev(5)*v(2093)+v(2060)*v(7514)
v(2368)=statev(9)*v(2060)+statev(4)*v(2082)+v(2093)*v(7513)
v(2104)=statev(6)*v(2060)+statev(8)*v(2093)+v(2082)*v(7512)
v(2059)=(7d0*(360d0*v(1817)+120d0*v(1850)+30d0*v(1927)+6d0*v(1960)+v(2026))+(5040d0*v(1707)+v(2026)*v(228)+v(2048)*v&
&(230)+v(2015)*v(231)+v(1707)*v(243)+v(1619)*v(246)+v(1675)*v(247))*v(7522))/5040d0
v(2400)=statev(7)*v(2081)+statev(5)*v(2092)+v(2059)*v(7514)
v(2367)=statev(9)*v(2059)+statev(4)*v(2081)+v(2092)*v(7513)
v(2103)=statev(6)*v(2059)+statev(8)*v(2092)+v(2081)*v(7512)
v(2058)=v(1816)/2d0+v(1849)/6d0+v(1926)/24d0+v(1959)/120d0+v(2025)/720d0+v(7801)+((v(2025)*v(228)+v(2047)*v(230)+v(2014&
&)*v(231)+v(1704)*v(243)+v(1618)*v(246)+v(1672)*v(247))*v(7522)+v(7518)*(v(231)*v(243)+v(7814)))/5040d0
v(2399)=statev(7)*v(2080)+statev(5)*v(2091)+v(2058)*v(7514)
v(2366)=statev(9)*v(2058)+statev(4)*v(2080)+v(2091)*v(7513)
v(2102)=statev(6)*v(2058)+statev(8)*v(2091)+v(2080)*v(7512)
v(285)=(7d0*(360d0*v(235)+120d0*v(239)+30d0*v(241)+6d0*v(245)+v(246))+v(7522)*(v(231)*v(7812)+v(7814)))/5040d0
v(265)=v(247)*v(7797)
v(7826)=5040d0+v(265)
v(287)=(2520d0*v(233)+840d0*v(234)+210d0*v(237)+42d0*v(240)+7d0*v(243)+v(282)+v(7804)*v(7812)+v(7826))/5040d0
v(249)=(7d0*(360d0*v(236)+120d0*v(238)+30d0*v(242)+6d0*v(244)+v(247))+v(7522)*(v(229)*v(7812)+v(7815)))/5040d0
v(248)=statev(8)*v(249)+statev(6)*v(285)+v(287)*v(7512)
v(251)=v(250)+v(267)+v(232)*v(370)
v(7816)=v(231)*v(236)+v(230)*v(251)+v(228)*v(255)
v(2156)=v(1782)+v(1815)+(v(2123)*v(227)+v(1604)*v(251))*v(7522)
v(2155)=v(1781)+v(1814)+(v(2122)*v(227)+v(1603)*v(251))*v(7522)
v(2154)=v(1780)+v(1813)+(v(2121)*v(227)+v(1602)*v(251))*v(7522)
v(2153)=v(1779)+v(1812)+(v(2120)*v(227)+v(1600)*v(251))*v(7522)
v(2152)=v(1778)+v(1811)+(v(2119)*v(227)+v(1599)*v(251))*v(7522)
v(2151)=v(1777)+v(1810)+(v(2118)*v(227)+v(1598)*v(251))*v(7522)
v(2150)=v(1776)+v(1809)+(v(2117)*v(227)+v(1597)*v(251))*v(7522)
v(2149)=v(1775)+v(1808)+(v(2116)*v(227)+v(1596)*v(251))*v(7522)
v(2148)=v(1774)+v(1807)+(v(2115)*v(227)+v(1595)*v(251))*v(7522)
v(2147)=v(1773)+v(1806)+(v(2114)*v(227)+v(1593)*v(251))*v(7522)
v(2146)=v(1772)+v(1805)+v(2113)*v(7818)+v(251)*v(7819)
v(2134)=(v(1771)*v(228)+v(2123)*v(230)+v(1804)*v(231)+v(1726)*v(236)+v(1690)*v(251)+v(1630)*v(255))*v(7522)
v(2133)=(v(1770)*v(228)+v(2122)*v(230)+v(1803)*v(231)+v(1724)*v(236)+v(1688)*v(251)+v(1629)*v(255))*v(7522)
v(2132)=(v(1769)*v(228)+v(2121)*v(230)+v(1802)*v(231)+v(1721)*v(236)+v(1687)*v(251)+v(1627)*v(255))*v(7522)
v(2131)=(v(1768)*v(228)+v(2120)*v(230)+v(1801)*v(231)+v(1719)*v(236)+v(1685)*v(251)+v(1626)*v(255))*v(7522)
v(2130)=(v(1767)*v(228)+v(2119)*v(230)+v(1800)*v(231)+v(1717)*v(236)+v(1683)*v(251)+v(1625)*v(255))*v(7522)
v(2129)=(v(1766)*v(228)+v(2118)*v(230)+v(1799)*v(231)+v(1716)*v(236)+v(1682)*v(251)+v(1624)*v(255))*v(7522)
v(2128)=(v(1765)*v(228)+v(2117)*v(230)+v(1798)*v(231)+v(1713)*v(236)+v(1681)*v(251)+v(1623)*v(255))*v(7522)
v(2127)=(v(1764)*v(228)+v(2116)*v(230)+v(1797)*v(231)+v(1712)*v(236)+v(1680)*v(251)+v(1622)*v(255))*v(7522)
v(2126)=(v(1763)*v(228)+v(2115)*v(230)+v(1796)*v(231)+v(1709)*v(236)+v(1677)*v(251)+v(1621)*v(255))*v(7522)
v(2125)=(v(1762)*v(228)+v(2114)*v(230)+v(1795)*v(231)+v(1707)*v(236)+v(1675)*v(251)+v(1619)*v(255))*v(7522)
v(2124)=(v(1761)*v(228)+v(2113)*v(230)+v(1794)*v(231)+v(1704)*v(236)+v(1672)*v(251)+v(1618)*v(255))*v(7522)+v(7518)*v&
&(7816)
v(257)=v(7522)*v(7816)
v(2145)=(v(2134)*v(230)+v(1690)*v(257))*v(7522)
v(2144)=(v(2133)*v(230)+v(1688)*v(257))*v(7522)
v(2143)=(v(2132)*v(230)+v(1687)*v(257))*v(7522)
v(2142)=(v(2131)*v(230)+v(1685)*v(257))*v(7522)
v(2141)=(v(2130)*v(230)+v(1683)*v(257))*v(7522)
v(2140)=(v(2129)*v(230)+v(1682)*v(257))*v(7522)
v(2139)=(v(2128)*v(230)+v(1681)*v(257))*v(7522)
v(2138)=(v(2127)*v(230)+v(1680)*v(257))*v(7522)
v(2137)=(v(2126)*v(230)+v(1677)*v(257))*v(7522)
v(2136)=(v(2125)*v(230)+v(1675)*v(257))*v(7522)
v(2135)=v(2124)*v(7795)+v(257)*v(7817)
v(273)=v(257)*v(7795)
v(253)=v(252)+v(271)+v(251)*v(7818)
v(7820)=v(231)*v(238)+v(230)*v(253)+v(228)*v(257)
v(2189)=v(1892)+v(2145)+(v(2156)*v(227)+v(1604)*v(253))*v(7522)
v(2188)=v(1891)+v(2144)+(v(2155)*v(227)+v(1603)*v(253))*v(7522)
v(2187)=v(1890)+v(2143)+(v(2154)*v(227)+v(1602)*v(253))*v(7522)
v(2186)=v(1889)+v(2142)+(v(2153)*v(227)+v(1600)*v(253))*v(7522)
v(2185)=v(1888)+v(2141)+(v(2152)*v(227)+v(1599)*v(253))*v(7522)
v(2184)=v(1887)+v(2140)+(v(2151)*v(227)+v(1598)*v(253))*v(7522)
v(2183)=v(1886)+v(2139)+(v(2150)*v(227)+v(1597)*v(253))*v(7522)
v(2182)=v(1885)+v(2138)+(v(2149)*v(227)+v(1596)*v(253))*v(7522)
v(2181)=v(1884)+v(2137)+(v(2148)*v(227)+v(1595)*v(253))*v(7522)
v(2180)=v(1883)+v(2136)+(v(2147)*v(227)+v(1593)*v(253))*v(7522)
v(2179)=v(1882)+v(2135)+v(2146)*v(7818)+v(253)*v(7819)
v(2167)=(v(2134)*v(228)+v(2156)*v(230)+v(1881)*v(231)+v(1726)*v(238)+v(1690)*v(253)+v(1630)*v(257))*v(7522)
v(2166)=(v(2133)*v(228)+v(2155)*v(230)+v(1880)*v(231)+v(1724)*v(238)+v(1688)*v(253)+v(1629)*v(257))*v(7522)
v(2165)=(v(2132)*v(228)+v(2154)*v(230)+v(1879)*v(231)+v(1721)*v(238)+v(1687)*v(253)+v(1627)*v(257))*v(7522)
v(2164)=(v(2131)*v(228)+v(2153)*v(230)+v(1878)*v(231)+v(1719)*v(238)+v(1685)*v(253)+v(1626)*v(257))*v(7522)
v(2163)=(v(2130)*v(228)+v(2152)*v(230)+v(1877)*v(231)+v(1717)*v(238)+v(1683)*v(253)+v(1625)*v(257))*v(7522)
v(2162)=(v(2129)*v(228)+v(2151)*v(230)+v(1876)*v(231)+v(1716)*v(238)+v(1682)*v(253)+v(1624)*v(257))*v(7522)
v(2161)=(v(2128)*v(228)+v(2150)*v(230)+v(1875)*v(231)+v(1713)*v(238)+v(1681)*v(253)+v(1623)*v(257))*v(7522)
v(2160)=(v(2127)*v(228)+v(2149)*v(230)+v(1874)*v(231)+v(1712)*v(238)+v(1680)*v(253)+v(1622)*v(257))*v(7522)
v(2159)=(v(2126)*v(228)+v(2148)*v(230)+v(1873)*v(231)+v(1709)*v(238)+v(1677)*v(253)+v(1621)*v(257))*v(7522)
v(2158)=(v(2125)*v(228)+v(2147)*v(230)+v(1872)*v(231)+v(1707)*v(238)+v(1675)*v(253)+v(1619)*v(257))*v(7522)
v(2157)=(v(2124)*v(228)+v(2146)*v(230)+v(1871)*v(231)+v(1704)*v(238)+v(1672)*v(253)+v(1618)*v(257))*v(7522)+v(7518)*v&
&(7820)
v(261)=v(7522)*v(7820)
v(2178)=(v(2167)*v(230)+v(1690)*v(261))*v(7522)
v(2177)=(v(2166)*v(230)+v(1688)*v(261))*v(7522)
v(2176)=(v(2165)*v(230)+v(1687)*v(261))*v(7522)
v(2175)=(v(2164)*v(230)+v(1685)*v(261))*v(7522)
v(2174)=(v(2163)*v(230)+v(1683)*v(261))*v(7522)
v(2173)=(v(2162)*v(230)+v(1682)*v(261))*v(7522)
v(2172)=(v(2161)*v(230)+v(1681)*v(261))*v(7522)
v(2171)=(v(2160)*v(230)+v(1680)*v(261))*v(7522)
v(2170)=(v(2159)*v(230)+v(1677)*v(261))*v(7522)
v(2169)=(v(2158)*v(230)+v(1675)*v(261))*v(7522)
v(2168)=v(2157)*v(7795)+v(261)*v(7817)
v(277)=v(261)*v(7795)
v(256)=v(254)+v(273)+v(253)*v(7818)
v(7821)=v(231)*v(242)+v(230)*v(256)+v(228)*v(261)
v(2222)=v(1925)+v(2178)+(v(2189)*v(227)+v(1604)*v(256))*v(7522)
v(2221)=v(1924)+v(2177)+(v(2188)*v(227)+v(1603)*v(256))*v(7522)
v(2220)=v(1923)+v(2176)+(v(2187)*v(227)+v(1602)*v(256))*v(7522)
v(2219)=v(1922)+v(2175)+(v(2186)*v(227)+v(1600)*v(256))*v(7522)
v(2218)=v(1921)+v(2174)+(v(2185)*v(227)+v(1599)*v(256))*v(7522)
v(2217)=v(1920)+v(2173)+(v(2184)*v(227)+v(1598)*v(256))*v(7522)
v(2216)=v(1919)+v(2172)+(v(2183)*v(227)+v(1597)*v(256))*v(7522)
v(2215)=v(1918)+v(2171)+(v(2182)*v(227)+v(1596)*v(256))*v(7522)
v(2214)=v(1917)+v(2170)+(v(2181)*v(227)+v(1595)*v(256))*v(7522)
v(2213)=v(1916)+v(2169)+(v(2180)*v(227)+v(1593)*v(256))*v(7522)
v(2212)=v(1915)+v(2168)+v(2179)*v(7818)+v(256)*v(7819)
v(2200)=(v(2167)*v(228)+v(2189)*v(230)+v(1914)*v(231)+v(1726)*v(242)+v(1690)*v(256)+v(1630)*v(261))*v(7522)
v(2199)=(v(2166)*v(228)+v(2188)*v(230)+v(1913)*v(231)+v(1724)*v(242)+v(1688)*v(256)+v(1629)*v(261))*v(7522)
v(2198)=(v(2165)*v(228)+v(2187)*v(230)+v(1912)*v(231)+v(1721)*v(242)+v(1687)*v(256)+v(1627)*v(261))*v(7522)
v(2197)=(v(2164)*v(228)+v(2186)*v(230)+v(1911)*v(231)+v(1719)*v(242)+v(1685)*v(256)+v(1626)*v(261))*v(7522)
v(2196)=(v(2163)*v(228)+v(2185)*v(230)+v(1910)*v(231)+v(1717)*v(242)+v(1683)*v(256)+v(1625)*v(261))*v(7522)
v(2195)=(v(2162)*v(228)+v(2184)*v(230)+v(1909)*v(231)+v(1716)*v(242)+v(1682)*v(256)+v(1624)*v(261))*v(7522)
v(2194)=(v(2161)*v(228)+v(2183)*v(230)+v(1908)*v(231)+v(1713)*v(242)+v(1681)*v(256)+v(1623)*v(261))*v(7522)
v(2193)=(v(2160)*v(228)+v(2182)*v(230)+v(1907)*v(231)+v(1712)*v(242)+v(1680)*v(256)+v(1622)*v(261))*v(7522)
v(2192)=(v(2159)*v(228)+v(2181)*v(230)+v(1906)*v(231)+v(1709)*v(242)+v(1677)*v(256)+v(1621)*v(261))*v(7522)
v(2191)=(v(2158)*v(228)+v(2180)*v(230)+v(1905)*v(231)+v(1707)*v(242)+v(1675)*v(256)+v(1619)*v(261))*v(7522)
v(2190)=(v(2157)*v(228)+v(2179)*v(230)+v(1904)*v(231)+v(1704)*v(242)+v(1672)*v(256)+v(1618)*v(261))*v(7522)+v(7518)*v&
&(7821)
v(263)=v(7522)*v(7821)
v(2211)=(v(2200)*v(230)+v(1690)*v(263))*v(7522)
v(2210)=(v(2199)*v(230)+v(1688)*v(263))*v(7522)
v(2209)=(v(2198)*v(230)+v(1687)*v(263))*v(7522)
v(2208)=(v(2197)*v(230)+v(1685)*v(263))*v(7522)
v(2207)=(v(2196)*v(230)+v(1683)*v(263))*v(7522)
v(2206)=(v(2195)*v(230)+v(1682)*v(263))*v(7522)
v(2205)=(v(2194)*v(230)+v(1681)*v(263))*v(7522)
v(2204)=(v(2193)*v(230)+v(1680)*v(263))*v(7522)
v(2203)=(v(2192)*v(230)+v(1677)*v(263))*v(7522)
v(2202)=(v(2191)*v(230)+v(1675)*v(263))*v(7522)
v(2201)=v(2190)*v(7795)+v(263)*v(7817)
v(279)=v(263)*v(7795)
v(259)=v(258)+v(277)+v(256)*v(7818)
v(7822)=v(231)*v(244)+v(230)*v(259)+v(228)*v(263)
v(2244)=(v(2200)*v(228)+v(2222)*v(230)+v(1991)*v(231)+v(1726)*v(244)+v(1690)*v(259)+v(1630)*v(263))*v(7522)
v(2243)=(v(2199)*v(228)+v(2221)*v(230)+v(1990)*v(231)+v(1724)*v(244)+v(1688)*v(259)+v(1629)*v(263))*v(7522)
v(2242)=(v(2198)*v(228)+v(2220)*v(230)+v(1989)*v(231)+v(1721)*v(244)+v(1687)*v(259)+v(1627)*v(263))*v(7522)
v(2241)=(v(2197)*v(228)+v(2219)*v(230)+v(1988)*v(231)+v(1719)*v(244)+v(1685)*v(259)+v(1626)*v(263))*v(7522)
v(2240)=(v(2196)*v(228)+v(2218)*v(230)+v(1987)*v(231)+v(1717)*v(244)+v(1683)*v(259)+v(1625)*v(263))*v(7522)
v(2239)=(v(2195)*v(228)+v(2217)*v(230)+v(1986)*v(231)+v(1716)*v(244)+v(1682)*v(259)+v(1624)*v(263))*v(7522)
v(2238)=(v(2194)*v(228)+v(2216)*v(230)+v(1985)*v(231)+v(1713)*v(244)+v(1681)*v(259)+v(1623)*v(263))*v(7522)
v(2237)=(v(2193)*v(228)+v(2215)*v(230)+v(1984)*v(231)+v(1712)*v(244)+v(1680)*v(259)+v(1622)*v(263))*v(7522)
v(2236)=(v(2192)*v(228)+v(2214)*v(230)+v(1983)*v(231)+v(1709)*v(244)+v(1677)*v(259)+v(1621)*v(263))*v(7522)
v(2235)=(v(2191)*v(228)+v(2213)*v(230)+v(1982)*v(231)+v(1707)*v(244)+v(1675)*v(259)+v(1619)*v(263))*v(7522)
v(2234)=(v(2190)*v(228)+v(2212)*v(230)+v(1981)*v(231)+v(1704)*v(244)+v(1672)*v(259)+v(1618)*v(263))*v(7522)+v(7518)*v&
&(7822)
v(2233)=v(2002)+v(2211)+(v(2222)*v(227)+v(1604)*v(259))*v(7522)
v(2232)=v(2001)+v(2210)+(v(2221)*v(227)+v(1603)*v(259))*v(7522)
v(2231)=v(2000)+v(2209)+(v(2220)*v(227)+v(1602)*v(259))*v(7522)
v(2230)=v(1999)+v(2208)+(v(2219)*v(227)+v(1600)*v(259))*v(7522)
v(2229)=v(1998)+v(2207)+(v(2218)*v(227)+v(1599)*v(259))*v(7522)
v(2228)=v(1997)+v(2206)+(v(2217)*v(227)+v(1598)*v(259))*v(7522)
v(2227)=v(1996)+v(2205)+(v(2216)*v(227)+v(1597)*v(259))*v(7522)
v(2226)=v(1995)+v(2204)+(v(2215)*v(227)+v(1596)*v(259))*v(7522)
v(2225)=v(1994)+v(2203)+(v(2214)*v(227)+v(1595)*v(259))*v(7522)
v(2224)=v(1993)+v(2202)+(v(2213)*v(227)+v(1593)*v(259))*v(7522)
v(2223)=v(1992)+v(2201)+v(2212)*v(7818)+v(259)*v(7819)
v(262)=v(260)+v(279)+v(259)*v(7818)
v(7823)=5040d0+v(262)
v(264)=v(7522)*v(7822)
v(7825)=v(231)*v(247)+v(228)*v(264)
v(2266)=(v(2244)*v(230)+v(1690)*v(264))*v(7522)
v(2277)=(v(2079)+2520d0*v(2123)+840d0*v(2156)+210d0*v(2189)+42d0*v(2222)+7d0*v(2233)+v(2266)+v(7522)*(v(2233)*v(227)+v&
&(1604)*v(7823)))/5040d0
v(2265)=(v(2243)*v(230)+v(1688)*v(264))*v(7522)
v(2276)=(v(2078)+2520d0*v(2122)+840d0*v(2155)+210d0*v(2188)+42d0*v(2221)+7d0*v(2232)+v(2265)+v(7522)*(v(2232)*v(227)+v&
&(1603)*v(7823)))/5040d0
v(2264)=(v(2242)*v(230)+v(1687)*v(264))*v(7522)
v(2275)=(v(2077)+2520d0*v(2121)+840d0*v(2154)+210d0*v(2187)+42d0*v(2220)+7d0*v(2231)+v(2264)+v(7522)*(v(2231)*v(227)+v&
&(1602)*v(7823)))/5040d0
v(2263)=(v(2241)*v(230)+v(1685)*v(264))*v(7522)
v(2274)=(v(2076)+2520d0*v(2120)+840d0*v(2153)+210d0*v(2186)+42d0*v(2219)+7d0*v(2230)+v(2263)+v(7522)*(v(2230)*v(227)+v&
&(1600)*v(7823)))/5040d0
v(2262)=(v(2240)*v(230)+v(1683)*v(264))*v(7522)
v(2273)=(v(2075)+2520d0*v(2119)+840d0*v(2152)+210d0*v(2185)+42d0*v(2218)+7d0*v(2229)+v(2262)+v(7522)*(v(2229)*v(227)+v&
&(1599)*v(7823)))/5040d0
v(2261)=(v(2239)*v(230)+v(1682)*v(264))*v(7522)
v(2272)=(v(2074)+2520d0*v(2118)+840d0*v(2151)+210d0*v(2184)+42d0*v(2217)+7d0*v(2228)+v(2261)+v(7522)*(v(2228)*v(227)+v&
&(1598)*v(7823)))/5040d0
v(2260)=(v(2238)*v(230)+v(1681)*v(264))*v(7522)
v(2271)=(v(2073)+2520d0*v(2117)+840d0*v(2150)+210d0*v(2183)+42d0*v(2216)+7d0*v(2227)+v(2260)+v(7522)*(v(2227)*v(227)+v&
&(1597)*v(7823)))/5040d0
v(2259)=(v(2237)*v(230)+v(1680)*v(264))*v(7522)
v(2270)=(v(2072)+2520d0*v(2116)+840d0*v(2149)+210d0*v(2182)+42d0*v(2215)+7d0*v(2226)+v(2259)+v(7522)*(v(2226)*v(227)+v&
&(1596)*v(7823)))/5040d0
v(2258)=(v(2236)*v(230)+v(1677)*v(264))*v(7522)
v(2269)=(v(2071)+2520d0*v(2115)+840d0*v(2148)+210d0*v(2181)+42d0*v(2214)+7d0*v(2225)+v(2258)+v(7522)*(v(2225)*v(227)+v&
&(1595)*v(7823)))/5040d0
v(2257)=(v(2235)*v(230)+v(1675)*v(264))*v(7522)
v(2268)=(v(2070)+2520d0*v(2114)+840d0*v(2147)+210d0*v(2180)+42d0*v(2213)+7d0*v(2224)+v(2257)+v(7522)*(v(2224)*v(227)+v&
&(1593)*v(7823)))/5040d0
v(2256)=v(2234)*v(7795)+v(264)*v(7817)
v(2267)=(v(2069)+2520d0*v(2113)+840d0*v(2146)+210d0*v(2179)+42d0*v(2212)+7d0*v(2223)+v(2256)+v(227)*(v(2223)*v(7522)+v&
&(7518)*v(7823))+v(7823)*v(7824))/5040d0
v(2255)=(7d0*(360d0*v(1771)+120d0*v(2134)+30d0*v(2167)+6d0*v(2200)+v(2244))+v(7522)*(v(2244)*v(228)+v(2233)*v(230)+v&
&(2057)*v(231)+v(1726)*v(247)+v(1630)*v(264)+v(1690)*v(7823)))/5040d0
v(2442)=statev(6)*v(2255)+statev(8)*v(2277)+v(2101)*v(7512)
v(2387)=statev(7)*v(2101)+statev(5)*v(2277)+v(2255)*v(7514)
v(2288)=statev(4)*v(2101)+statev(9)*v(2255)+v(2277)*v(7513)
v(2254)=(7d0*(360d0*v(1770)+120d0*v(2133)+30d0*v(2166)+6d0*v(2199)+v(2243))+v(7522)*(v(2243)*v(228)+v(2232)*v(230)+v&
&(2056)*v(231)+v(1724)*v(247)+v(1629)*v(264)+v(1688)*v(7823)))/5040d0
v(2441)=statev(6)*v(2254)+statev(8)*v(2276)+v(2100)*v(7512)
v(2386)=statev(7)*v(2100)+statev(5)*v(2276)+v(2254)*v(7514)
v(2287)=statev(4)*v(2100)+statev(9)*v(2254)+v(2276)*v(7513)
v(2253)=(7d0*(360d0*v(1769)+120d0*v(2132)+30d0*v(2165)+6d0*v(2198)+v(2242))+v(7522)*(v(2242)*v(228)+v(2231)*v(230)+v&
&(2055)*v(231)+v(1721)*v(247)+v(1627)*v(264)+v(1687)*v(7823)))/5040d0
v(2440)=statev(6)*v(2253)+statev(8)*v(2275)+v(2099)*v(7512)
v(2385)=statev(7)*v(2099)+statev(5)*v(2275)+v(2253)*v(7514)
v(2286)=statev(4)*v(2099)+statev(9)*v(2253)+v(2275)*v(7513)
v(2252)=(7d0*(360d0*v(1768)+120d0*v(2131)+30d0*v(2164)+6d0*v(2197)+v(2241))+v(7522)*(v(2241)*v(228)+v(2230)*v(230)+v&
&(2054)*v(231)+v(1719)*v(247)+v(1626)*v(264)+v(1685)*v(7823)))/5040d0
v(2439)=statev(6)*v(2252)+statev(8)*v(2274)+v(2098)*v(7512)
v(2384)=statev(7)*v(2098)+statev(5)*v(2274)+v(2252)*v(7514)
v(2285)=statev(4)*v(2098)+statev(9)*v(2252)+v(2274)*v(7513)
v(2251)=(7d0*(360d0*v(1767)+120d0*v(2130)+30d0*v(2163)+6d0*v(2196)+v(2240))+v(7522)*(v(2240)*v(228)+v(2229)*v(230)+v&
&(2053)*v(231)+v(1717)*v(247)+v(1625)*v(264)+v(1683)*v(7823)))/5040d0
v(2438)=statev(6)*v(2251)+statev(8)*v(2273)+v(2097)*v(7512)
v(2383)=statev(7)*v(2097)+statev(5)*v(2273)+v(2251)*v(7514)
v(2284)=statev(4)*v(2097)+statev(9)*v(2251)+v(2273)*v(7513)
v(2250)=(7d0*(360d0*v(1766)+120d0*v(2129)+30d0*v(2162)+6d0*v(2195)+v(2239))+v(7522)*(v(2239)*v(228)+v(2228)*v(230)+v&
&(2052)*v(231)+v(1716)*v(247)+v(1624)*v(264)+v(1682)*v(7823)))/5040d0
v(2437)=statev(6)*v(2250)+statev(8)*v(2272)+v(2096)*v(7512)
v(2382)=statev(7)*v(2096)+statev(5)*v(2272)+v(2250)*v(7514)
v(2283)=statev(4)*v(2096)+statev(9)*v(2250)+v(2272)*v(7513)
v(2249)=(7d0*(360d0*v(1765)+120d0*v(2128)+30d0*v(2161)+6d0*v(2194)+v(2238))+v(7522)*(v(2238)*v(228)+v(2227)*v(230)+v&
&(2051)*v(231)+v(1713)*v(247)+v(1623)*v(264)+v(1681)*v(7823)))/5040d0
v(2436)=statev(6)*v(2249)+statev(8)*v(2271)+v(2095)*v(7512)
v(2381)=statev(7)*v(2095)+statev(5)*v(2271)+v(2249)*v(7514)
v(2282)=statev(4)*v(2095)+statev(9)*v(2249)+v(2271)*v(7513)
v(2248)=(7d0*(360d0*v(1764)+120d0*v(2127)+30d0*v(2160)+6d0*v(2193)+v(2237))+v(7522)*(v(2237)*v(228)+v(2226)*v(230)+v&
&(2050)*v(231)+v(1712)*v(247)+v(1622)*v(264)+v(1680)*v(7823)))/5040d0
v(2435)=statev(6)*v(2248)+statev(8)*v(2270)+v(2094)*v(7512)
v(2380)=statev(7)*v(2094)+statev(5)*v(2270)+v(2248)*v(7514)
v(2281)=statev(4)*v(2094)+statev(9)*v(2248)+v(2270)*v(7513)
v(2247)=(7d0*(360d0*v(1763)+120d0*v(2126)+30d0*v(2159)+6d0*v(2192)+v(2236))+v(7522)*(v(2236)*v(228)+v(2225)*v(230)+v&
&(2049)*v(231)+v(1709)*v(247)+v(1621)*v(264)+v(1677)*v(7823)))/5040d0
v(2434)=statev(6)*v(2247)+statev(8)*v(2269)+v(2093)*v(7512)
v(2379)=statev(7)*v(2093)+statev(5)*v(2269)+v(2247)*v(7514)
v(2280)=statev(4)*v(2093)+statev(9)*v(2247)+v(2269)*v(7513)
v(2246)=(7d0*(360d0*v(1762)+120d0*v(2125)+30d0*v(2158)+6d0*v(2191)+v(2235))+v(7522)*(v(2235)*v(228)+v(2224)*v(230)+v&
&(2048)*v(231)+v(1707)*v(247)+v(1619)*v(264)+v(1675)*v(7823)))/5040d0
v(2433)=statev(6)*v(2246)+statev(8)*v(2268)+v(2092)*v(7512)
v(2378)=statev(7)*v(2092)+statev(5)*v(2268)+v(2246)*v(7514)
v(2279)=statev(4)*v(2092)+statev(9)*v(2246)+v(2268)*v(7513)
v(2245)=v(1761)/2d0+v(2124)/6d0+v(2157)/24d0+v(2190)/120d0+v(2234)/720d0+v(7817)+((v(2234)*v(228)+v(2223)*v(230)+v(2047&
&)*v(231)+v(1704)*v(247)+v(1672)*v(262)+v(1618)*v(264))*v(7522)+v(7518)*(v(230)*v(262)+v(7825)))/5040d0
v(2432)=statev(6)*v(2245)+statev(8)*v(2267)+v(2091)*v(7512)
v(2377)=statev(7)*v(2091)+statev(5)*v(2267)+v(2245)*v(7514)
v(2278)=statev(4)*v(2091)+statev(9)*v(2245)+v(2267)*v(7513)
v(284)=(7d0*(360d0*v(255)+120d0*v(257)+30d0*v(261)+6d0*v(263)+v(264))+v(7522)*(v(230)*v(7823)+v(7825)))/5040d0
v(283)=v(264)*v(7795)
v(289)=(2520d0*v(251)+840d0*v(253)+210d0*v(256)+42d0*v(259)+7d0*v(262)+v(283)+v(7818)*v(7823)+v(7826))/5040d0
v(266)=statev(4)*v(249)+statev(9)*v(284)+v(289)*v(7513)
v(269)=v(267)+v(268)+v(232)*v(371)
v(2310)=v(1782)+v(1837)+(v(228)*v(2299)+v(1630)*v(269))*v(7522)
v(2309)=v(1781)+v(1836)+(v(228)*v(2298)+v(1629)*v(269))*v(7522)
v(2308)=v(1780)+v(1835)+(v(228)*v(2297)+v(1627)*v(269))*v(7522)
v(2307)=v(1779)+v(1834)+(v(228)*v(2296)+v(1626)*v(269))*v(7522)
v(2306)=v(1778)+v(1833)+(v(228)*v(2295)+v(1625)*v(269))*v(7522)
v(2305)=v(1777)+v(1832)+(v(228)*v(2294)+v(1624)*v(269))*v(7522)
v(2304)=v(1776)+v(1831)+(v(228)*v(2293)+v(1623)*v(269))*v(7522)
v(2303)=v(1775)+v(1830)+(v(228)*v(2292)+v(1622)*v(269))*v(7522)
v(2302)=v(1774)+v(1829)+(v(228)*v(2291)+v(1621)*v(269))*v(7522)
v(2301)=v(1773)+v(1828)+(v(228)*v(2290)+v(1619)*v(269))*v(7522)
v(2300)=v(1772)+v(1827)+v(2289)*v(7827)+v(269)*v(7828)
v(272)=v(270)+v(271)+v(269)*v(7827)
v(2321)=v(1870)+v(2145)+(v(228)*v(2310)+v(1630)*v(272))*v(7522)
v(2320)=v(1869)+v(2144)+(v(228)*v(2309)+v(1629)*v(272))*v(7522)
v(2319)=v(1868)+v(2143)+(v(228)*v(2308)+v(1627)*v(272))*v(7522)
v(2318)=v(1867)+v(2142)+(v(228)*v(2307)+v(1626)*v(272))*v(7522)
v(2317)=v(1866)+v(2141)+(v(228)*v(2306)+v(1625)*v(272))*v(7522)
v(2316)=v(1865)+v(2140)+(v(228)*v(2305)+v(1624)*v(272))*v(7522)
v(2315)=v(1864)+v(2139)+(v(228)*v(2304)+v(1623)*v(272))*v(7522)
v(2314)=v(1863)+v(2138)+(v(228)*v(2303)+v(1622)*v(272))*v(7522)
v(2313)=v(1862)+v(2137)+(v(228)*v(2302)+v(1621)*v(272))*v(7522)
v(2312)=v(1861)+v(2136)+(v(228)*v(2301)+v(1619)*v(272))*v(7522)
v(2311)=v(1860)+v(2135)+v(2300)*v(7827)+v(272)*v(7828)
v(275)=v(273)+v(274)+v(272)*v(7827)
v(2332)=v(1947)+v(2178)+(v(228)*v(2321)+v(1630)*v(275))*v(7522)
v(2331)=v(1946)+v(2177)+(v(228)*v(2320)+v(1629)*v(275))*v(7522)
v(2330)=v(1945)+v(2176)+(v(228)*v(2319)+v(1627)*v(275))*v(7522)
v(2329)=v(1944)+v(2175)+(v(228)*v(2318)+v(1626)*v(275))*v(7522)
v(2328)=v(1943)+v(2174)+(v(228)*v(2317)+v(1625)*v(275))*v(7522)
v(2327)=v(1942)+v(2173)+(v(228)*v(2316)+v(1624)*v(275))*v(7522)
v(2326)=v(1941)+v(2172)+(v(228)*v(2315)+v(1623)*v(275))*v(7522)
v(2325)=v(1940)+v(2171)+(v(228)*v(2314)+v(1622)*v(275))*v(7522)
v(2324)=v(1939)+v(2170)+(v(228)*v(2313)+v(1621)*v(275))*v(7522)
v(2323)=v(1938)+v(2169)+(v(228)*v(2312)+v(1619)*v(275))*v(7522)
v(2322)=v(1937)+v(2168)+v(2311)*v(7827)+v(275)*v(7828)
v(278)=v(276)+v(277)+v(275)*v(7827)
v(2343)=v(1980)+v(2211)+(v(228)*v(2332)+v(1630)*v(278))*v(7522)
v(2342)=v(1979)+v(2210)+(v(228)*v(2331)+v(1629)*v(278))*v(7522)
v(2341)=v(1978)+v(2209)+(v(228)*v(2330)+v(1627)*v(278))*v(7522)
v(2340)=v(1977)+v(2208)+(v(228)*v(2329)+v(1626)*v(278))*v(7522)
v(2339)=v(1976)+v(2207)+(v(228)*v(2328)+v(1625)*v(278))*v(7522)
v(2338)=v(1975)+v(2206)+(v(228)*v(2327)+v(1624)*v(278))*v(7522)
v(2337)=v(1974)+v(2205)+(v(228)*v(2326)+v(1623)*v(278))*v(7522)
v(2336)=v(1973)+v(2204)+(v(228)*v(2325)+v(1622)*v(278))*v(7522)
v(2335)=v(1972)+v(2203)+(v(228)*v(2324)+v(1621)*v(278))*v(7522)
v(2334)=v(1971)+v(2202)+(v(228)*v(2323)+v(1619)*v(278))*v(7522)
v(2333)=v(1970)+v(2201)+v(2322)*v(7827)+v(278)*v(7828)
v(281)=v(279)+v(280)+v(278)*v(7827)
v(7829)=5040d0+v(281)
v(2354)=(v(2046)+v(2266)+2520d0*v(2299)+840d0*v(2310)+210d0*v(2321)+42d0*v(2332)+7d0*v(2343)+v(7522)*(v(228)*v(2343)+v&
&(1630)*v(7829)))/5040d0
v(2486)=statev(4)*v(2068)+statev(9)*v(2354)+v(2255)*v(7513)
v(2398)=statev(8)*v(2255)+statev(6)*v(2354)+v(2068)*v(7512)
v(2365)=statev(7)*v(2068)+statev(5)*v(2255)+v(2354)*v(7514)
v(2353)=(v(2045)+v(2265)+2520d0*v(2298)+840d0*v(2309)+210d0*v(2320)+42d0*v(2331)+7d0*v(2342)+v(7522)*(v(228)*v(2342)+v&
&(1629)*v(7829)))/5040d0
v(2485)=statev(4)*v(2067)+statev(9)*v(2353)+v(2254)*v(7513)
v(2397)=statev(8)*v(2254)+statev(6)*v(2353)+v(2067)*v(7512)
v(2364)=statev(7)*v(2067)+statev(5)*v(2254)+v(2353)*v(7514)
v(2352)=(v(2044)+v(2264)+2520d0*v(2297)+840d0*v(2308)+210d0*v(2319)+42d0*v(2330)+7d0*v(2341)+v(7522)*(v(228)*v(2341)+v&
&(1627)*v(7829)))/5040d0
v(2484)=statev(4)*v(2066)+statev(9)*v(2352)+v(2253)*v(7513)
v(2396)=statev(8)*v(2253)+statev(6)*v(2352)+v(2066)*v(7512)
v(2363)=statev(7)*v(2066)+statev(5)*v(2253)+v(2352)*v(7514)
v(2351)=(v(2043)+v(2263)+2520d0*v(2296)+840d0*v(2307)+210d0*v(2318)+42d0*v(2329)+7d0*v(2340)+v(7522)*(v(228)*v(2340)+v&
&(1626)*v(7829)))/5040d0
v(2483)=statev(4)*v(2065)+statev(9)*v(2351)+v(2252)*v(7513)
v(2395)=statev(8)*v(2252)+statev(6)*v(2351)+v(2065)*v(7512)
v(2362)=statev(7)*v(2065)+statev(5)*v(2252)+v(2351)*v(7514)
v(2350)=(v(2042)+v(2262)+2520d0*v(2295)+840d0*v(2306)+210d0*v(2317)+42d0*v(2328)+7d0*v(2339)+v(7522)*(v(228)*v(2339)+v&
&(1625)*v(7829)))/5040d0
v(2482)=statev(4)*v(2064)+statev(9)*v(2350)+v(2251)*v(7513)
v(2394)=statev(8)*v(2251)+statev(6)*v(2350)+v(2064)*v(7512)
v(2361)=statev(7)*v(2064)+statev(5)*v(2251)+v(2350)*v(7514)
v(2349)=(v(2041)+v(2261)+2520d0*v(2294)+840d0*v(2305)+210d0*v(2316)+42d0*v(2327)+7d0*v(2338)+v(7522)*(v(228)*v(2338)+v&
&(1624)*v(7829)))/5040d0
v(2481)=statev(4)*v(2063)+statev(9)*v(2349)+v(2250)*v(7513)
v(2393)=statev(8)*v(2250)+statev(6)*v(2349)+v(2063)*v(7512)
v(2360)=statev(7)*v(2063)+statev(5)*v(2250)+v(2349)*v(7514)
v(2348)=(v(2040)+v(2260)+2520d0*v(2293)+840d0*v(2304)+210d0*v(2315)+42d0*v(2326)+7d0*v(2337)+v(7522)*(v(228)*v(2337)+v&
&(1623)*v(7829)))/5040d0
v(2480)=statev(4)*v(2062)+statev(9)*v(2348)+v(2249)*v(7513)
v(2392)=statev(8)*v(2249)+statev(6)*v(2348)+v(2062)*v(7512)
v(2359)=statev(7)*v(2062)+statev(5)*v(2249)+v(2348)*v(7514)
v(2347)=(v(2039)+v(2259)+2520d0*v(2292)+840d0*v(2303)+210d0*v(2314)+42d0*v(2325)+7d0*v(2336)+v(7522)*(v(228)*v(2336)+v&
&(1622)*v(7829)))/5040d0
v(2479)=statev(4)*v(2061)+statev(9)*v(2347)+v(2248)*v(7513)
v(2391)=statev(8)*v(2248)+statev(6)*v(2347)+v(2061)*v(7512)
v(2358)=statev(7)*v(2061)+statev(5)*v(2248)+v(2347)*v(7514)
v(2346)=(v(2038)+v(2258)+2520d0*v(2291)+840d0*v(2302)+210d0*v(2313)+42d0*v(2324)+7d0*v(2335)+v(7522)*(v(228)*v(2335)+v&
&(1621)*v(7829)))/5040d0
v(2478)=statev(4)*v(2060)+statev(9)*v(2346)+v(2247)*v(7513)
v(2390)=statev(8)*v(2247)+statev(6)*v(2346)+v(2060)*v(7512)
v(2357)=statev(7)*v(2060)+statev(5)*v(2247)+v(2346)*v(7514)
v(2345)=(v(2037)+v(2257)+2520d0*v(2290)+840d0*v(2301)+210d0*v(2312)+42d0*v(2323)+7d0*v(2334)+v(7522)*(v(228)*v(2334)+v&
&(1619)*v(7829)))/5040d0
v(2477)=statev(4)*v(2059)+statev(9)*v(2345)+v(2246)*v(7513)
v(2389)=statev(8)*v(2246)+statev(6)*v(2345)+v(2059)*v(7512)
v(2356)=statev(7)*v(2059)+statev(5)*v(2246)+v(2345)*v(7514)
v(2344)=(v(2036)+v(2256)+2520d0*v(2289)+840d0*v(2300)+210d0*v(2311)+42d0*v(2322)+7d0*v(2333)+v(228)*(v(2333)*v(7522)+v&
&(7518)*v(7829))+v(7829)*v(7830))/5040d0
v(2476)=statev(4)*v(2058)+statev(9)*v(2344)+v(2245)*v(7513)
v(2388)=statev(8)*v(2245)+statev(6)*v(2344)+v(2058)*v(7512)
v(2355)=statev(7)*v(2058)+statev(5)*v(2245)+v(2344)*v(7514)
v(291)=(5040d0+2520d0*v(269)+840d0*v(272)+210d0*v(275)+42d0*v(278)+7d0*v(281)+v(282)+v(283)+v(7827)*v(7829))/5040d0
v(286)=statev(5)*v(284)+statev(7)*v(285)+v(291)*v(7514)
v(288)=statev(9)*v(285)+statev(4)*v(287)+v(249)*v(7513)
v(290)=statev(7)*v(249)+statev(5)*v(289)+v(284)*v(7514)
v(292)=statev(8)*v(284)+statev(6)*v(291)+v(285)*v(7512)
v(293)=statev(5)*v(249)+statev(7)*v(287)+v(285)*v(7514)
v(2431)=v(2365)*v(248)+v(2112)*v(286)-v(2409)*v(292)-v(2398)*v(293)
v(2430)=v(2364)*v(248)+v(2111)*v(286)-v(2408)*v(292)-v(2397)*v(293)
v(2429)=v(2363)*v(248)+v(2110)*v(286)-v(2407)*v(292)-v(2396)*v(293)
v(2428)=v(2362)*v(248)+v(2109)*v(286)-v(2406)*v(292)-v(2395)*v(293)
v(2427)=v(2361)*v(248)+v(2108)*v(286)-v(2405)*v(292)-v(2394)*v(293)
v(2426)=v(2360)*v(248)+v(2107)*v(286)-v(2404)*v(292)-v(2393)*v(293)
v(2425)=v(2359)*v(248)+v(2106)*v(286)-v(2403)*v(292)-v(2392)*v(293)
v(2424)=v(2358)*v(248)+v(2105)*v(286)-v(2402)*v(292)-v(2391)*v(293)
v(2423)=v(2357)*v(248)+v(2104)*v(286)-v(2401)*v(292)-v(2390)*v(293)
v(2422)=v(2356)*v(248)+v(2103)*v(286)-v(2400)*v(292)-v(2389)*v(293)
v(2421)=v(2355)*v(248)+v(2102)*v(286)-v(2399)*v(292)-v(2388)*v(293)
v(2420)=-(v(2409)*v(266))+v(2387)*v(288)+v(2376)*v(290)-v(2288)*v(293)
v(2419)=-(v(2408)*v(266))+v(2386)*v(288)+v(2375)*v(290)-v(2287)*v(293)
v(2418)=-(v(2407)*v(266))+v(2385)*v(288)+v(2374)*v(290)-v(2286)*v(293)
v(2417)=-(v(2406)*v(266))+v(2384)*v(288)+v(2373)*v(290)-v(2285)*v(293)
v(2416)=-(v(2405)*v(266))+v(2383)*v(288)+v(2372)*v(290)-v(2284)*v(293)
v(2415)=-(v(2404)*v(266))+v(2382)*v(288)+v(2371)*v(290)-v(2283)*v(293)
v(2414)=-(v(2403)*v(266))+v(2381)*v(288)+v(2370)*v(290)-v(2282)*v(293)
v(2413)=-(v(2402)*v(266))+v(2380)*v(288)+v(2369)*v(290)-v(2281)*v(293)
v(2412)=-(v(2401)*v(266))+v(2379)*v(288)+v(2368)*v(290)-v(2280)*v(293)
v(2411)=-(v(2400)*v(266))+v(2378)*v(288)+v(2367)*v(290)-v(2279)*v(293)
v(2410)=-(v(2399)*v(266))+v(2377)*v(288)+v(2366)*v(290)-v(2278)*v(293)
v(304)=v(288)*v(290)-v(266)*v(293)
v(300)=v(248)*v(286)-v(292)*v(293)
v(294)=statev(6)*v(284)+statev(8)*v(289)+v(249)*v(7512)
v(2475)=v(2288)*v(248)+v(2112)*v(266)-v(2442)*v(288)-v(2376)*v(294)
v(2474)=v(2287)*v(248)+v(2111)*v(266)-v(2441)*v(288)-v(2375)*v(294)
v(2473)=v(2286)*v(248)+v(2110)*v(266)-v(2440)*v(288)-v(2374)*v(294)
v(2472)=v(2285)*v(248)+v(2109)*v(266)-v(2439)*v(288)-v(2373)*v(294)
v(2471)=v(2284)*v(248)+v(2108)*v(266)-v(2438)*v(288)-v(2372)*v(294)
v(2470)=v(2283)*v(248)+v(2107)*v(266)-v(2437)*v(288)-v(2371)*v(294)
v(2469)=v(2282)*v(248)+v(2106)*v(266)-v(2436)*v(288)-v(2370)*v(294)
v(2468)=v(2281)*v(248)+v(2105)*v(266)-v(2435)*v(288)-v(2369)*v(294)
v(2467)=v(2280)*v(248)+v(2104)*v(266)-v(2434)*v(288)-v(2368)*v(294)
v(2466)=v(2279)*v(248)+v(2103)*v(266)-v(2433)*v(288)-v(2367)*v(294)
v(2465)=v(2278)*v(248)+v(2102)*v(266)-v(2432)*v(288)-v(2366)*v(294)
v(2464)=-(v(2387)*v(248))-v(2112)*v(290)+v(2442)*v(293)+v(2409)*v(294)
v(2463)=-(v(2386)*v(248))-v(2111)*v(290)+v(2441)*v(293)+v(2408)*v(294)
v(2462)=-(v(2385)*v(248))-v(2110)*v(290)+v(2440)*v(293)+v(2407)*v(294)
v(2461)=-(v(2384)*v(248))-v(2109)*v(290)+v(2439)*v(293)+v(2406)*v(294)
v(2460)=-(v(2383)*v(248))-v(2108)*v(290)+v(2438)*v(293)+v(2405)*v(294)
v(2459)=-(v(2382)*v(248))-v(2107)*v(290)+v(2437)*v(293)+v(2404)*v(294)
v(2458)=-(v(2381)*v(248))-v(2106)*v(290)+v(2436)*v(293)+v(2403)*v(294)
v(2457)=-(v(2380)*v(248))-v(2105)*v(290)+v(2435)*v(293)+v(2402)*v(294)
v(2456)=-(v(2379)*v(248))-v(2104)*v(290)+v(2434)*v(293)+v(2401)*v(294)
v(2455)=-(v(2378)*v(248))-v(2103)*v(290)+v(2433)*v(293)+v(2400)*v(294)
v(2454)=-(v(2377)*v(248))-v(2102)*v(290)+v(2432)*v(293)+v(2399)*v(294)
v(2453)=-(v(2442)*v(286))+v(2398)*v(290)+v(2387)*v(292)-v(2365)*v(294)
v(2452)=-(v(2441)*v(286))+v(2397)*v(290)+v(2386)*v(292)-v(2364)*v(294)
v(2451)=-(v(2440)*v(286))+v(2396)*v(290)+v(2385)*v(292)-v(2363)*v(294)
v(2450)=-(v(2439)*v(286))+v(2395)*v(290)+v(2384)*v(292)-v(2362)*v(294)
v(2449)=-(v(2438)*v(286))+v(2394)*v(290)+v(2383)*v(292)-v(2361)*v(294)
v(2448)=-(v(2437)*v(286))+v(2393)*v(290)+v(2382)*v(292)-v(2360)*v(294)
v(2447)=-(v(2436)*v(286))+v(2392)*v(290)+v(2381)*v(292)-v(2359)*v(294)
v(2446)=-(v(2435)*v(286))+v(2391)*v(290)+v(2380)*v(292)-v(2358)*v(294)
v(2445)=-(v(2434)*v(286))+v(2390)*v(290)+v(2379)*v(292)-v(2357)*v(294)
v(2444)=-(v(2433)*v(286))+v(2389)*v(290)+v(2378)*v(292)-v(2356)*v(294)
v(2443)=-(v(2432)*v(286))+v(2388)*v(290)+v(2377)*v(292)-v(2355)*v(294)
v(308)=v(290)*v(292)-v(286)*v(294)
v(306)=-(v(248)*v(290))+v(293)*v(294)
v(305)=v(248)*v(266)-v(288)*v(294)
v(295)=statev(4)*v(285)+statev(9)*v(291)+v(284)*v(7513)
v(2531)=v(292)*v(304)+v(286)*v(305)+v(295)*v(306)
v(2533)=1d0/v(2531)**2
v(2543)=-(v(2533)*(v(2475)*v(286)+v(2420)*v(292)+v(2464)*v(295)+v(2398)*v(304)+v(2365)*v(305)+v(2486)*v(306)))
v(7831)=v(2531)*v(2543)
v(7908)=v(2431)+v(300)*v(7831)
v(7877)=v(2464)+v(306)*v(7831)
v(7876)=v(2475)+v(305)*v(7831)
v(7875)=v(2420)+v(304)*v(7831)
v(7842)=v(2453)+v(308)*v(7831)
v(2542)=-(v(2533)*(v(2474)*v(286)+v(2419)*v(292)+v(2463)*v(295)+v(2397)*v(304)+v(2364)*v(305)+v(2485)*v(306)))
v(7832)=v(2531)*v(2542)
v(7911)=v(2430)+v(300)*v(7832)
v(7880)=v(2463)+v(306)*v(7832)
v(7879)=v(2474)+v(305)*v(7832)
v(7878)=v(2419)+v(304)*v(7832)
v(7845)=v(2452)+v(308)*v(7832)
v(2541)=-(v(2533)*(v(2473)*v(286)+v(2418)*v(292)+v(2462)*v(295)+v(2396)*v(304)+v(2363)*v(305)+v(2484)*v(306)))
v(7833)=v(2531)*v(2541)
v(7914)=v(2429)+v(300)*v(7833)
v(7883)=v(2462)+v(306)*v(7833)
v(7882)=v(2473)+v(305)*v(7833)
v(7881)=v(2418)+v(304)*v(7833)
v(7848)=v(2451)+v(308)*v(7833)
v(2540)=-(v(2533)*(v(2472)*v(286)+v(2417)*v(292)+v(2461)*v(295)+v(2395)*v(304)+v(2362)*v(305)+v(2483)*v(306)))
v(7834)=v(2531)*v(2540)
v(7917)=v(2428)+v(300)*v(7834)
v(7886)=v(2461)+v(306)*v(7834)
v(7885)=v(2472)+v(305)*v(7834)
v(7884)=v(2417)+v(304)*v(7834)
v(7851)=v(2450)+v(308)*v(7834)
v(2539)=-(v(2533)*(v(2471)*v(286)+v(2416)*v(292)+v(2460)*v(295)+v(2394)*v(304)+v(2361)*v(305)+v(2482)*v(306)))
v(7835)=v(2531)*v(2539)
v(7920)=v(2427)+v(300)*v(7835)
v(7889)=v(2460)+v(306)*v(7835)
v(7888)=v(2471)+v(305)*v(7835)
v(7887)=v(2416)+v(304)*v(7835)
v(7854)=v(2449)+v(308)*v(7835)
v(2538)=-(v(2533)*(v(2470)*v(286)+v(2415)*v(292)+v(2459)*v(295)+v(2393)*v(304)+v(2360)*v(305)+v(2481)*v(306)))
v(7836)=v(2531)*v(2538)
v(7923)=v(2426)+v(300)*v(7836)
v(7892)=v(2459)+v(306)*v(7836)
v(7891)=v(2470)+v(305)*v(7836)
v(7890)=v(2415)+v(304)*v(7836)
v(7857)=v(2448)+v(308)*v(7836)
v(2537)=-(v(2533)*(v(2469)*v(286)+v(2414)*v(292)+v(2458)*v(295)+v(2392)*v(304)+v(2359)*v(305)+v(2480)*v(306)))
v(7837)=v(2531)*v(2537)
v(7926)=v(2425)+v(300)*v(7837)
v(7895)=v(2458)+v(306)*v(7837)
v(7894)=v(2469)+v(305)*v(7837)
v(7893)=v(2414)+v(304)*v(7837)
v(7860)=v(2447)+v(308)*v(7837)
v(2536)=-(v(2533)*(v(2468)*v(286)+v(2413)*v(292)+v(2457)*v(295)+v(2391)*v(304)+v(2358)*v(305)+v(2479)*v(306)))
v(7838)=v(2531)*v(2536)
v(7929)=v(2424)+v(300)*v(7838)
v(7898)=v(2457)+v(306)*v(7838)
v(7897)=v(2468)+v(305)*v(7838)
v(7896)=v(2413)+v(304)*v(7838)
v(7863)=v(2446)+v(308)*v(7838)
v(2535)=-(v(2533)*(v(2467)*v(286)+v(2412)*v(292)+v(2456)*v(295)+v(2390)*v(304)+v(2357)*v(305)+v(2478)*v(306)))
v(7839)=v(2531)*v(2535)
v(7932)=v(2423)+v(300)*v(7839)
v(7901)=v(2456)+v(306)*v(7839)
v(7900)=v(2467)+v(305)*v(7839)
v(7899)=v(2412)+v(304)*v(7839)
v(7866)=v(2445)+v(308)*v(7839)
v(2534)=-(v(2533)*(v(2466)*v(286)+v(2411)*v(292)+v(2455)*v(295)+v(2389)*v(304)+v(2356)*v(305)+v(2477)*v(306)))
v(7840)=v(2531)*v(2534)
v(7935)=v(2422)+v(300)*v(7840)
v(7904)=v(2455)+v(306)*v(7840)
v(7903)=v(2466)+v(305)*v(7840)
v(7902)=v(2411)+v(304)*v(7840)
v(7869)=v(2444)+v(308)*v(7840)
v(2532)=-(v(2533)*(v(2465)*v(286)+v(2410)*v(292)+v(2454)*v(295)+v(2388)*v(304)+v(2355)*v(305)+v(2476)*v(306)))
v(7841)=v(2531)*v(2532)
v(7938)=v(2421)+v(300)*v(7841)
v(7907)=v(2454)+v(306)*v(7841)
v(7906)=v(2465)+v(305)*v(7841)
v(7905)=v(2410)+v(304)*v(7841)
v(7872)=v(2443)+v(308)*v(7841)
v(2530)=-(v(248)*v(2486))+v(2398)*v(288)+v(2376)*v(292)-v(2112)*v(295)
v(2529)=-(v(248)*v(2485))+v(2397)*v(288)+v(2375)*v(292)-v(2111)*v(295)
v(2528)=-(v(248)*v(2484))+v(2396)*v(288)+v(2374)*v(292)-v(2110)*v(295)
v(2527)=-(v(248)*v(2483))+v(2395)*v(288)+v(2373)*v(292)-v(2109)*v(295)
v(2526)=-(v(248)*v(2482))+v(2394)*v(288)+v(2372)*v(292)-v(2108)*v(295)
v(2525)=-(v(248)*v(2481))+v(2393)*v(288)+v(2371)*v(292)-v(2107)*v(295)
v(2524)=-(v(248)*v(2480))+v(2392)*v(288)+v(2370)*v(292)-v(2106)*v(295)
v(2523)=-(v(2479)*v(248))+v(2391)*v(288)+v(2369)*v(292)-v(2105)*v(295)
v(2522)=-(v(2478)*v(248))+v(2390)*v(288)+v(2368)*v(292)-v(2104)*v(295)
v(2521)=-(v(2477)*v(248))+v(2389)*v(288)+v(2367)*v(292)-v(2103)*v(295)
v(2520)=-(v(2476)*v(248))+v(2388)*v(288)+v(2366)*v(292)-v(2102)*v(295)
v(2519)=-(v(2376)*v(286))-v(2365)*v(288)+v(2486)*v(293)+v(2409)*v(295)
v(2518)=-(v(2375)*v(286))-v(2364)*v(288)+v(2485)*v(293)+v(2408)*v(295)
v(2517)=-(v(2374)*v(286))-v(2363)*v(288)+v(2484)*v(293)+v(2407)*v(295)
v(2516)=-(v(2373)*v(286))-v(2362)*v(288)+v(2483)*v(293)+v(2406)*v(295)
v(2515)=-(v(2372)*v(286))-v(2361)*v(288)+v(2482)*v(293)+v(2405)*v(295)
v(2514)=-(v(2371)*v(286))-v(2360)*v(288)+v(2481)*v(293)+v(2404)*v(295)
v(2513)=-(v(2370)*v(286))-v(2359)*v(288)+v(2480)*v(293)+v(2403)*v(295)
v(2512)=-(v(2369)*v(286))-v(2358)*v(288)+v(2479)*v(293)+v(2402)*v(295)
v(2511)=-(v(2368)*v(286))-v(2357)*v(288)+v(2478)*v(293)+v(2401)*v(295)
v(2510)=-(v(2367)*v(286))-v(2356)*v(288)+v(2477)*v(293)+v(2400)*v(295)
v(2509)=-(v(2366)*v(286))-v(2355)*v(288)+v(2476)*v(293)+v(2399)*v(295)
v(2508)=v(2365)*v(266)+v(2288)*v(286)-v(2486)*v(290)-v(2387)*v(295)
v(2507)=v(2364)*v(266)+v(2287)*v(286)-v(2485)*v(290)-v(2386)*v(295)
v(2506)=v(2363)*v(266)+v(2286)*v(286)-v(2484)*v(290)-v(2385)*v(295)
v(2505)=v(2362)*v(266)+v(2285)*v(286)-v(2483)*v(290)-v(2384)*v(295)
v(2504)=v(2361)*v(266)+v(2284)*v(286)-v(2482)*v(290)-v(2383)*v(295)
v(2503)=v(2360)*v(266)+v(2283)*v(286)-v(2481)*v(290)-v(2382)*v(295)
v(2502)=v(2359)*v(266)+v(2282)*v(286)-v(2480)*v(290)-v(2381)*v(295)
v(2501)=v(2358)*v(266)+v(2281)*v(286)-v(2479)*v(290)-v(2380)*v(295)
v(2500)=v(2357)*v(266)+v(2280)*v(286)-v(2478)*v(290)-v(2379)*v(295)
v(2499)=v(2356)*v(266)+v(2279)*v(286)-v(2477)*v(290)-v(2378)*v(295)
v(2498)=v(2355)*v(266)+v(2278)*v(286)-v(2476)*v(290)-v(2377)*v(295)
v(2497)=-(v(2398)*v(266))-v(2288)*v(292)+v(2486)*v(294)+v(2442)*v(295)
v(2496)=-(v(2397)*v(266))-v(2287)*v(292)+v(2485)*v(294)+v(2441)*v(295)
v(2495)=-(v(2396)*v(266))-v(2286)*v(292)+v(2484)*v(294)+v(2440)*v(295)
v(2494)=-(v(2395)*v(266))-v(2285)*v(292)+v(2483)*v(294)+v(2439)*v(295)
v(2493)=-(v(2394)*v(266))-v(2284)*v(292)+v(2482)*v(294)+v(2438)*v(295)
v(2492)=-(v(2393)*v(266))-v(2283)*v(292)+v(2481)*v(294)+v(2437)*v(295)
v(2491)=-(v(2392)*v(266))-v(2282)*v(292)+v(2480)*v(294)+v(2436)*v(295)
v(2490)=-(v(2391)*v(266))-v(2281)*v(292)+v(2479)*v(294)+v(2435)*v(295)
v(2489)=-(v(2390)*v(266))-v(2280)*v(292)+v(2478)*v(294)+v(2434)*v(295)
v(2488)=-(v(2389)*v(266))-v(2279)*v(292)+v(2477)*v(294)+v(2433)*v(295)
v(2487)=-(v(2388)*v(266))-v(2278)*v(292)+v(2476)*v(294)+v(2432)*v(295)
v(310)=-(v(266)*v(292))+v(294)*v(295)
v(7874)=v(2487)+v(310)*v(7841)
v(7871)=v(2488)+v(310)*v(7840)
v(7868)=v(2489)+v(310)*v(7839)
v(7865)=v(2490)+v(310)*v(7838)
v(7862)=v(2491)+v(310)*v(7837)
v(7859)=v(2492)+v(310)*v(7836)
v(7856)=v(2493)+v(310)*v(7835)
v(7853)=v(2494)+v(310)*v(7834)
v(7850)=v(2495)+v(310)*v(7833)
v(7847)=v(2496)+v(310)*v(7832)
v(7844)=v(2497)+v(310)*v(7831)
v(309)=v(266)*v(286)-v(290)*v(295)
v(7873)=v(2498)+v(309)*v(7841)
v(7870)=v(2499)+v(309)*v(7840)
v(7867)=v(2500)+v(309)*v(7839)
v(7864)=v(2501)+v(309)*v(7838)
v(7861)=v(2502)+v(309)*v(7837)
v(7858)=v(2503)+v(309)*v(7836)
v(7855)=v(2504)+v(309)*v(7835)
v(7852)=v(2505)+v(309)*v(7834)
v(7849)=v(2506)+v(309)*v(7833)
v(7846)=v(2507)+v(309)*v(7832)
v(7843)=v(2508)+v(309)*v(7831)
v(302)=-(v(286)*v(288))+v(293)*v(295)
v(7940)=v(2509)+v(302)*v(7841)
v(7937)=v(2510)+v(302)*v(7840)
v(7934)=v(2511)+v(302)*v(7839)
v(7931)=v(2512)+v(302)*v(7838)
v(7928)=v(2513)+v(302)*v(7837)
v(7925)=v(2514)+v(302)*v(7836)
v(7922)=v(2515)+v(302)*v(7835)
v(7919)=v(2516)+v(302)*v(7834)
v(7916)=v(2517)+v(302)*v(7833)
v(7913)=v(2518)+v(302)*v(7832)
v(7910)=v(2519)+v(302)*v(7831)
v(301)=v(288)*v(292)-v(248)*v(295)
v(7939)=v(2520)+v(301)*v(7841)
v(7936)=v(2521)+v(301)*v(7840)
v(7933)=v(2522)+v(301)*v(7839)
v(7930)=v(2523)+v(301)*v(7838)
v(7927)=v(2524)+v(301)*v(7837)
v(7924)=v(2525)+v(301)*v(7836)
v(7921)=v(2526)+v(301)*v(7835)
v(7918)=v(2527)+v(301)*v(7834)
v(7915)=v(2528)+v(301)*v(7833)
v(7912)=v(2529)+v(301)*v(7832)
v(7909)=v(2530)+v(301)*v(7831)
v(2642)=(Fnew(9)*v(7908)+Fnew(3)*v(7909)+Fnew(6)*v(7910))/v(2531)
v(2641)=(Fnew(9)*v(7911)+Fnew(3)*v(7912)+Fnew(6)*v(7913))/v(2531)
v(2640)=(Fnew(9)*v(7914)+Fnew(3)*v(7915)+Fnew(6)*v(7916))/v(2531)
v(2639)=(Fnew(9)*v(7917)+Fnew(3)*v(7918)+Fnew(6)*v(7919))/v(2531)
v(2638)=(Fnew(9)*v(7920)+Fnew(3)*v(7921)+Fnew(6)*v(7922))/v(2531)
v(2637)=(Fnew(9)*v(7923)+Fnew(3)*v(7924)+Fnew(6)*v(7925))/v(2531)
v(2636)=(Fnew(9)*v(7926)+Fnew(3)*v(7927)+Fnew(6)*v(7928))/v(2531)
v(2635)=(Fnew(9)*v(7929)+Fnew(3)*v(7930)+Fnew(6)*v(7931))/v(2531)
v(2634)=(Fnew(9)*v(7932)+Fnew(3)*v(7933)+Fnew(6)*v(7934))/v(2531)
v(2633)=(Fnew(9)*v(7935)+Fnew(3)*v(7936)+Fnew(6)*v(7937))/v(2531)
v(2632)=(Fnew(9)*v(7938)+Fnew(3)*v(7939)+Fnew(6)*v(7940))/v(2531)
v(2631)=(Fnew(2)*v(7842)+Fnew(8)*v(7843)+Fnew(5)*v(7844))/v(2531)
v(2630)=(Fnew(2)*v(7845)+Fnew(8)*v(7846)+Fnew(5)*v(7847))/v(2531)
v(2629)=(Fnew(2)*v(7848)+Fnew(8)*v(7849)+Fnew(5)*v(7850))/v(2531)
v(2628)=(Fnew(2)*v(7851)+Fnew(8)*v(7852)+Fnew(5)*v(7853))/v(2531)
v(2627)=(Fnew(2)*v(7854)+Fnew(8)*v(7855)+Fnew(5)*v(7856))/v(2531)
v(2626)=(Fnew(2)*v(7857)+Fnew(8)*v(7858)+Fnew(5)*v(7859))/v(2531)
v(2625)=(Fnew(2)*v(7860)+Fnew(8)*v(7861)+Fnew(5)*v(7862))/v(2531)
v(2624)=(Fnew(2)*v(7863)+Fnew(8)*v(7864)+Fnew(5)*v(7865))/v(2531)
v(2623)=(Fnew(2)*v(7866)+Fnew(8)*v(7867)+Fnew(5)*v(7868))/v(2531)
v(2622)=(Fnew(2)*v(7869)+Fnew(8)*v(7870)+Fnew(5)*v(7871))/v(2531)
v(2621)=(Fnew(2)*v(7872)+Fnew(8)*v(7873)+Fnew(5)*v(7874))/v(2531)
v(2620)=(Fnew(1)*v(7875)+Fnew(7)*v(7876)+Fnew(4)*v(7877))/v(2531)
v(2619)=(Fnew(1)*v(7878)+Fnew(7)*v(7879)+Fnew(4)*v(7880))/v(2531)
v(2618)=(Fnew(1)*v(7881)+Fnew(7)*v(7882)+Fnew(4)*v(7883))/v(2531)
v(2617)=(Fnew(1)*v(7884)+Fnew(7)*v(7885)+Fnew(4)*v(7886))/v(2531)
v(2616)=(Fnew(1)*v(7887)+Fnew(7)*v(7888)+Fnew(4)*v(7889))/v(2531)
v(2615)=(Fnew(1)*v(7890)+Fnew(7)*v(7891)+Fnew(4)*v(7892))/v(2531)
v(2614)=(Fnew(1)*v(7893)+Fnew(7)*v(7894)+Fnew(4)*v(7895))/v(2531)
v(2613)=(Fnew(1)*v(7896)+Fnew(7)*v(7897)+Fnew(4)*v(7898))/v(2531)
v(2612)=(Fnew(1)*v(7899)+Fnew(7)*v(7900)+Fnew(4)*v(7901))/v(2531)
v(2611)=(Fnew(1)*v(7902)+Fnew(7)*v(7903)+Fnew(4)*v(7904))/v(2531)
v(2610)=(Fnew(1)*v(7905)+Fnew(7)*v(7906)+Fnew(4)*v(7907))/v(2531)
v(2609)=(Fnew(9)*v(7842)+Fnew(6)*v(7843)+Fnew(3)*v(7844))/v(2531)
v(2608)=(Fnew(9)*v(7845)+Fnew(6)*v(7846)+Fnew(3)*v(7847))/v(2531)
v(2607)=(Fnew(9)*v(7848)+Fnew(6)*v(7849)+Fnew(3)*v(7850))/v(2531)
v(2606)=(Fnew(9)*v(7851)+Fnew(6)*v(7852)+Fnew(3)*v(7853))/v(2531)
v(2605)=(Fnew(9)*v(7854)+Fnew(6)*v(7855)+Fnew(3)*v(7856))/v(2531)
v(2604)=(Fnew(9)*v(7857)+Fnew(6)*v(7858)+Fnew(3)*v(7859))/v(2531)
v(2603)=(Fnew(9)*v(7860)+Fnew(6)*v(7861)+Fnew(3)*v(7862))/v(2531)
v(2602)=(Fnew(9)*v(7863)+Fnew(6)*v(7864)+Fnew(3)*v(7865))/v(2531)
v(2601)=(Fnew(9)*v(7866)+Fnew(6)*v(7867)+Fnew(3)*v(7868))/v(2531)
v(2600)=(Fnew(9)*v(7869)+Fnew(6)*v(7870)+Fnew(3)*v(7871))/v(2531)
v(2599)=(Fnew(9)*v(7872)+Fnew(6)*v(7873)+Fnew(3)*v(7874))/v(2531)
v(2598)=(Fnew(8)*v(7875)+Fnew(5)*v(7876)+Fnew(2)*v(7877))/v(2531)
v(2597)=(Fnew(8)*v(7878)+Fnew(5)*v(7879)+Fnew(2)*v(7880))/v(2531)
v(2596)=(Fnew(8)*v(7881)+Fnew(5)*v(7882)+Fnew(2)*v(7883))/v(2531)
v(2595)=(Fnew(8)*v(7884)+Fnew(5)*v(7885)+Fnew(2)*v(7886))/v(2531)
v(2594)=(Fnew(8)*v(7887)+Fnew(5)*v(7888)+Fnew(2)*v(7889))/v(2531)
v(2593)=(Fnew(8)*v(7890)+Fnew(5)*v(7891)+Fnew(2)*v(7892))/v(2531)
v(2592)=(Fnew(8)*v(7893)+Fnew(5)*v(7894)+Fnew(2)*v(7895))/v(2531)
v(2591)=(Fnew(8)*v(7896)+Fnew(5)*v(7897)+Fnew(2)*v(7898))/v(2531)
v(2590)=(Fnew(8)*v(7899)+Fnew(5)*v(7900)+Fnew(2)*v(7901))/v(2531)
v(2589)=(Fnew(8)*v(7902)+Fnew(5)*v(7903)+Fnew(2)*v(7904))/v(2531)
v(2588)=(Fnew(8)*v(7905)+Fnew(5)*v(7906)+Fnew(2)*v(7907))/v(2531)
v(2587)=(Fnew(4)*v(7908)+Fnew(7)*v(7909)+Fnew(1)*v(7910))/v(2531)
v(2586)=(Fnew(4)*v(7911)+Fnew(7)*v(7912)+Fnew(1)*v(7913))/v(2531)
v(2585)=(Fnew(4)*v(7914)+Fnew(7)*v(7915)+Fnew(1)*v(7916))/v(2531)
v(2584)=(Fnew(4)*v(7917)+Fnew(7)*v(7918)+Fnew(1)*v(7919))/v(2531)
v(2583)=(Fnew(4)*v(7920)+Fnew(7)*v(7921)+Fnew(1)*v(7922))/v(2531)
v(2582)=(Fnew(4)*v(7923)+Fnew(7)*v(7924)+Fnew(1)*v(7925))/v(2531)
v(2581)=(Fnew(4)*v(7926)+Fnew(7)*v(7927)+Fnew(1)*v(7928))/v(2531)
v(2580)=(Fnew(4)*v(7929)+Fnew(7)*v(7930)+Fnew(1)*v(7931))/v(2531)
v(2579)=(Fnew(4)*v(7932)+Fnew(7)*v(7933)+Fnew(1)*v(7934))/v(2531)
v(2578)=(Fnew(4)*v(7935)+Fnew(7)*v(7936)+Fnew(1)*v(7937))/v(2531)
v(2577)=(Fnew(4)*v(7938)+Fnew(7)*v(7939)+Fnew(1)*v(7940))/v(2531)
v(2576)=(Fnew(6)*v(7875)+Fnew(3)*v(7876)+Fnew(9)*v(7877))/v(2531)
v(2575)=(Fnew(6)*v(7878)+Fnew(3)*v(7879)+Fnew(9)*v(7880))/v(2531)
v(2574)=(Fnew(6)*v(7881)+Fnew(3)*v(7882)+Fnew(9)*v(7883))/v(2531)
v(2573)=(Fnew(6)*v(7884)+Fnew(3)*v(7885)+Fnew(9)*v(7886))/v(2531)
v(2572)=(Fnew(6)*v(7887)+Fnew(3)*v(7888)+Fnew(9)*v(7889))/v(2531)
v(2571)=(Fnew(6)*v(7890)+Fnew(3)*v(7891)+Fnew(9)*v(7892))/v(2531)
v(2570)=(Fnew(6)*v(7893)+Fnew(3)*v(7894)+Fnew(9)*v(7895))/v(2531)
v(2569)=(Fnew(6)*v(7896)+Fnew(3)*v(7897)+Fnew(9)*v(7898))/v(2531)
v(2568)=(Fnew(6)*v(7899)+Fnew(3)*v(7900)+Fnew(9)*v(7901))/v(2531)
v(2567)=(Fnew(6)*v(7902)+Fnew(3)*v(7903)+Fnew(9)*v(7904))/v(2531)
v(2566)=(Fnew(6)*v(7905)+Fnew(3)*v(7906)+Fnew(9)*v(7907))/v(2531)
v(2565)=(Fnew(2)*v(7908)+Fnew(5)*v(7909)+Fnew(8)*v(7910))/v(2531)
v(2564)=(Fnew(2)*v(7911)+Fnew(5)*v(7912)+Fnew(8)*v(7913))/v(2531)
v(2563)=(Fnew(2)*v(7914)+Fnew(5)*v(7915)+Fnew(8)*v(7916))/v(2531)
v(2562)=(Fnew(2)*v(7917)+Fnew(5)*v(7918)+Fnew(8)*v(7919))/v(2531)
v(2561)=(Fnew(2)*v(7920)+Fnew(5)*v(7921)+Fnew(8)*v(7922))/v(2531)
v(2560)=(Fnew(2)*v(7923)+Fnew(5)*v(7924)+Fnew(8)*v(7925))/v(2531)
v(2559)=(Fnew(2)*v(7926)+Fnew(5)*v(7927)+Fnew(8)*v(7928))/v(2531)
v(2558)=(Fnew(2)*v(7929)+Fnew(5)*v(7930)+Fnew(8)*v(7931))/v(2531)
v(2557)=(Fnew(2)*v(7932)+Fnew(5)*v(7933)+Fnew(8)*v(7934))/v(2531)
v(2556)=(Fnew(2)*v(7935)+Fnew(5)*v(7936)+Fnew(8)*v(7937))/v(2531)
v(2555)=(Fnew(2)*v(7938)+Fnew(5)*v(7939)+Fnew(8)*v(7940))/v(2531)
v(2554)=(Fnew(4)*v(7842)+Fnew(1)*v(7843)+Fnew(7)*v(7844))/v(2531)
v(2553)=(Fnew(4)*v(7845)+Fnew(1)*v(7846)+Fnew(7)*v(7847))/v(2531)
v(2552)=(Fnew(4)*v(7848)+Fnew(1)*v(7849)+Fnew(7)*v(7850))/v(2531)
v(2551)=(Fnew(4)*v(7851)+Fnew(1)*v(7852)+Fnew(7)*v(7853))/v(2531)
v(2550)=(Fnew(4)*v(7854)+Fnew(1)*v(7855)+Fnew(7)*v(7856))/v(2531)
v(2549)=(Fnew(4)*v(7857)+Fnew(1)*v(7858)+Fnew(7)*v(7859))/v(2531)
v(2548)=(Fnew(4)*v(7860)+Fnew(1)*v(7861)+Fnew(7)*v(7862))/v(2531)
v(2547)=(Fnew(4)*v(7863)+Fnew(1)*v(7864)+Fnew(7)*v(7865))/v(2531)
v(2546)=(Fnew(4)*v(7866)+Fnew(1)*v(7867)+Fnew(7)*v(7868))/v(2531)
v(2545)=(Fnew(4)*v(7869)+Fnew(1)*v(7870)+Fnew(7)*v(7871))/v(2531)
v(2544)=(Fnew(4)*v(7872)+Fnew(1)*v(7873)+Fnew(7)*v(7874))/v(2531)
v(297)=(Fnew(4)*v(308)+Fnew(1)*v(309)+Fnew(7)*v(310))/v(2531)
v(298)=(Fnew(2)*v(300)+Fnew(5)*v(301)+Fnew(8)*v(302))/v(2531)
v(299)=(Fnew(6)*v(304)+Fnew(3)*v(305)+Fnew(9)*v(306))/v(2531)
v(303)=(Fnew(4)*v(300)+Fnew(7)*v(301)+Fnew(1)*v(302))/v(2531)
v(307)=(Fnew(8)*v(304)+Fnew(5)*v(305)+Fnew(2)*v(306))/v(2531)
v(311)=(Fnew(9)*v(308)+Fnew(6)*v(309)+Fnew(3)*v(310))/v(2531)
v(312)=(Fnew(1)*v(304)+Fnew(7)*v(305)+Fnew(4)*v(306))/v(2531)
v(2697)=2d0*(v(2576)*v(299)+v(2598)*v(307)+v(2620)*v(312))
v(2708)=-v(2697)/3d0
v(2696)=2d0*(v(2575)*v(299)+v(2597)*v(307)+v(2619)*v(312))
v(2707)=-v(2696)/3d0
v(2695)=2d0*(v(2574)*v(299)+v(2596)*v(307)+v(2618)*v(312))
v(2706)=-v(2695)/3d0
v(2694)=2d0*(v(2573)*v(299)+v(2595)*v(307)+v(2617)*v(312))
v(2705)=-v(2694)/3d0
v(2693)=2d0*(v(2572)*v(299)+v(2594)*v(307)+v(2616)*v(312))
v(2704)=-v(2693)/3d0
v(2692)=2d0*(v(2571)*v(299)+v(2593)*v(307)+v(2615)*v(312))
v(2703)=-v(2692)/3d0
v(2691)=2d0*(v(2570)*v(299)+v(2592)*v(307)+v(2614)*v(312))
v(2702)=-v(2691)/3d0
v(2690)=2d0*(v(2569)*v(299)+v(2591)*v(307)+v(2613)*v(312))
v(2701)=-v(2690)/3d0
v(2689)=2d0*(v(2568)*v(299)+v(2590)*v(307)+v(2612)*v(312))
v(2700)=-v(2689)/3d0
v(2688)=2d0*(v(2567)*v(299)+v(2589)*v(307)+v(2611)*v(312))
v(2699)=-v(2688)/3d0
v(2687)=2d0*(v(2566)*v(299)+v(2588)*v(307)+v(2610)*v(312))
v(2698)=-v(2687)/3d0
v(313)=(Fnew(2)*v(308)+Fnew(8)*v(309)+Fnew(5)*v(310))/v(2531)
v(2785)=v(2620)*v(297)+v(2609)*v(299)+v(2631)*v(307)+v(2576)*v(311)+v(2554)*v(312)+v(2598)*v(313)
v(2784)=v(2619)*v(297)+v(2608)*v(299)+v(2630)*v(307)+v(2575)*v(311)+v(2553)*v(312)+v(2597)*v(313)
v(2783)=v(2618)*v(297)+v(2607)*v(299)+v(2629)*v(307)+v(2574)*v(311)+v(2552)*v(312)+v(2596)*v(313)
v(2782)=v(2617)*v(297)+v(2606)*v(299)+v(2628)*v(307)+v(2573)*v(311)+v(2551)*v(312)+v(2595)*v(313)
v(2781)=v(2616)*v(297)+v(2605)*v(299)+v(2627)*v(307)+v(2572)*v(311)+v(2550)*v(312)+v(2594)*v(313)
v(2780)=v(2615)*v(297)+v(2604)*v(299)+v(2626)*v(307)+v(2571)*v(311)+v(2549)*v(312)+v(2593)*v(313)
v(2779)=v(2614)*v(297)+v(2603)*v(299)+v(2625)*v(307)+v(2570)*v(311)+v(2548)*v(312)+v(2592)*v(313)
v(2778)=v(2613)*v(297)+v(2602)*v(299)+v(2624)*v(307)+v(2569)*v(311)+v(2547)*v(312)+v(2591)*v(313)
v(2777)=v(2612)*v(297)+v(2601)*v(299)+v(2623)*v(307)+v(2568)*v(311)+v(2546)*v(312)+v(2590)*v(313)
v(2776)=v(2611)*v(297)+v(2600)*v(299)+v(2622)*v(307)+v(2567)*v(311)+v(2545)*v(312)+v(2589)*v(313)
v(2775)=v(2610)*v(297)+v(2599)*v(299)+v(2621)*v(307)+v(2566)*v(311)+v(2544)*v(312)+v(2588)*v(313)
v(2653)=2d0*(v(2554)*v(297)+v(2609)*v(311)+v(2631)*v(313))
v(2664)=-v(2653)/3d0
v(2652)=2d0*(v(2553)*v(297)+v(2608)*v(311)+v(2630)*v(313))
v(2663)=-v(2652)/3d0
v(2651)=2d0*(v(2552)*v(297)+v(2607)*v(311)+v(2629)*v(313))
v(2662)=-v(2651)/3d0
v(2650)=2d0*(v(2551)*v(297)+v(2606)*v(311)+v(2628)*v(313))
v(2661)=-v(2650)/3d0
v(2649)=2d0*(v(2550)*v(297)+v(2605)*v(311)+v(2627)*v(313))
v(2660)=-v(2649)/3d0
v(2648)=2d0*(v(2549)*v(297)+v(2604)*v(311)+v(2626)*v(313))
v(2659)=-v(2648)/3d0
v(2647)=2d0*(v(2548)*v(297)+v(2603)*v(311)+v(2625)*v(313))
v(2658)=-v(2647)/3d0
v(2646)=2d0*(v(2547)*v(297)+v(2602)*v(311)+v(2624)*v(313))
v(2657)=-v(2646)/3d0
v(2645)=2d0*(v(2546)*v(297)+v(2601)*v(311)+v(2623)*v(313))
v(2656)=-v(2645)/3d0
v(2644)=2d0*(v(2545)*v(297)+v(2600)*v(311)+v(2622)*v(313))
v(2655)=-v(2644)/3d0
v(2643)=2d0*(v(2544)*v(297)+v(2599)*v(311)+v(2621)*v(313))
v(2654)=-v(2643)/3d0
v(314)=(Fnew(9)*v(300)+Fnew(3)*v(301)+Fnew(6)*v(302))/v(2531)
v(2752)=v(2598)*v(298)+v(2642)*v(299)+v(2620)*v(303)+v(2565)*v(307)+v(2587)*v(312)+v(2576)*v(314)
v(2751)=v(2597)*v(298)+v(2641)*v(299)+v(2619)*v(303)+v(2564)*v(307)+v(2586)*v(312)+v(2575)*v(314)
v(2750)=v(2596)*v(298)+v(2640)*v(299)+v(2618)*v(303)+v(2563)*v(307)+v(2585)*v(312)+v(2574)*v(314)
v(2749)=v(2595)*v(298)+v(2639)*v(299)+v(2617)*v(303)+v(2562)*v(307)+v(2584)*v(312)+v(2573)*v(314)
v(2748)=v(2594)*v(298)+v(2638)*v(299)+v(2616)*v(303)+v(2561)*v(307)+v(2583)*v(312)+v(2572)*v(314)
v(2747)=v(2593)*v(298)+v(2637)*v(299)+v(2615)*v(303)+v(2560)*v(307)+v(2582)*v(312)+v(2571)*v(314)
v(2746)=v(2592)*v(298)+v(2636)*v(299)+v(2614)*v(303)+v(2559)*v(307)+v(2581)*v(312)+v(2570)*v(314)
v(2745)=v(2591)*v(298)+v(2635)*v(299)+v(2613)*v(303)+v(2558)*v(307)+v(2580)*v(312)+v(2569)*v(314)
v(2744)=v(2590)*v(298)+v(2634)*v(299)+v(2612)*v(303)+v(2557)*v(307)+v(2579)*v(312)+v(2568)*v(314)
v(2743)=v(2589)*v(298)+v(2633)*v(299)+v(2611)*v(303)+v(2556)*v(307)+v(2578)*v(312)+v(2567)*v(314)
v(2742)=v(2588)*v(298)+v(2632)*v(299)+v(2610)*v(303)+v(2555)*v(307)+v(2577)*v(312)+v(2566)*v(314)
v(2719)=v(2587)*v(297)+v(2631)*v(298)+v(2554)*v(303)+v(2642)*v(311)+v(2565)*v(313)+v(2609)*v(314)
v(2718)=v(2586)*v(297)+v(2630)*v(298)+v(2553)*v(303)+v(2641)*v(311)+v(2564)*v(313)+v(2608)*v(314)
v(2717)=v(2585)*v(297)+v(2629)*v(298)+v(2552)*v(303)+v(2640)*v(311)+v(2563)*v(313)+v(2607)*v(314)
v(2716)=v(2584)*v(297)+v(2628)*v(298)+v(2551)*v(303)+v(2639)*v(311)+v(2562)*v(313)+v(2606)*v(314)
v(2715)=v(2583)*v(297)+v(2627)*v(298)+v(2550)*v(303)+v(2638)*v(311)+v(2561)*v(313)+v(2605)*v(314)
v(2714)=v(2582)*v(297)+v(2626)*v(298)+v(2549)*v(303)+v(2637)*v(311)+v(2560)*v(313)+v(2604)*v(314)
v(2713)=v(2581)*v(297)+v(2625)*v(298)+v(2548)*v(303)+v(2636)*v(311)+v(2559)*v(313)+v(2603)*v(314)
v(2712)=v(2580)*v(297)+v(2624)*v(298)+v(2547)*v(303)+v(2635)*v(311)+v(2558)*v(313)+v(2602)*v(314)
v(2711)=v(2579)*v(297)+v(2623)*v(298)+v(2546)*v(303)+v(2634)*v(311)+v(2557)*v(313)+v(2601)*v(314)
v(2710)=v(2578)*v(297)+v(2622)*v(298)+v(2545)*v(303)+v(2633)*v(311)+v(2556)*v(313)+v(2600)*v(314)
v(2709)=v(2577)*v(297)+v(2621)*v(298)+v(2544)*v(303)+v(2632)*v(311)+v(2555)*v(313)+v(2599)*v(314)
v(2675)=2d0*(v(2565)*v(298)+v(2587)*v(303)+v(2642)*v(314))
v(2686)=-v(2675)/3d0
v(2674)=2d0*(v(2564)*v(298)+v(2586)*v(303)+v(2641)*v(314))
v(2685)=-v(2674)/3d0
v(2673)=2d0*(v(2563)*v(298)+v(2585)*v(303)+v(2640)*v(314))
v(2684)=-v(2673)/3d0
v(2672)=2d0*(v(2562)*v(298)+v(2584)*v(303)+v(2639)*v(314))
v(2683)=-v(2672)/3d0
v(2671)=2d0*(v(2561)*v(298)+v(2583)*v(303)+v(2638)*v(314))
v(2682)=-v(2671)/3d0
v(2670)=2d0*(v(2560)*v(298)+v(2582)*v(303)+v(2637)*v(314))
v(2681)=-v(2670)/3d0
v(2669)=2d0*(v(2559)*v(298)+v(2581)*v(303)+v(2636)*v(314))
v(2680)=-v(2669)/3d0
v(2668)=2d0*(v(2558)*v(298)+v(2580)*v(303)+v(2635)*v(314))
v(2679)=-v(2668)/3d0
v(2667)=2d0*(v(2557)*v(298)+v(2579)*v(303)+v(2634)*v(314))
v(2678)=-v(2667)/3d0
v(2666)=2d0*(v(2556)*v(298)+v(2578)*v(303)+v(2633)*v(314))
v(2677)=-v(2666)/3d0
v(2665)=2d0*(v(2555)*v(298)+v(2577)*v(303)+v(2632)*v(314))
v(2676)=-v(2665)/3d0
v(315)=(v(297)*v(297))+(v(311)*v(311))+(v(313)*v(313))
v(335)=-v(315)/3d0
v(316)=(v(298)*v(298))+(v(303)*v(303))+(v(314)*v(314))
v(336)=-v(316)/3d0
v(317)=(v(299)*v(299))+(v(307)*v(307))+(v(312)*v(312))
v(2905)=(2d0/3d0)*v(317)+v(335)+v(336)
v(328)=-v(317)/3d0
v(2932)=(2d0/3d0)*v(316)+v(328)+v(335)
v(2880)=(2d0/3d0)*v(315)+v(328)+v(336)
v(318)=v(297)*v(303)+v(298)*v(313)+v(311)*v(314)
v(7941)=2d0*v(318)
v(2730)=v(2719)*v(7941)
v(2741)=-v(2730)+v(2675)*v(315)+v(2653)*v(316)
v(2729)=v(2718)*v(7941)
v(2740)=-v(2729)+v(2674)*v(315)+v(2652)*v(316)
v(2728)=v(2717)*v(7941)
v(2739)=-v(2728)+v(2673)*v(315)+v(2651)*v(316)
v(2727)=v(2716)*v(7941)
v(2738)=-v(2727)+v(2672)*v(315)+v(2650)*v(316)
v(2726)=v(2715)*v(7941)
v(2737)=-v(2726)+v(2671)*v(315)+v(2649)*v(316)
v(2725)=v(2714)*v(7941)
v(2736)=-v(2725)+v(2670)*v(315)+v(2648)*v(316)
v(2724)=v(2713)*v(7941)
v(2735)=-v(2724)+v(2669)*v(315)+v(2647)*v(316)
v(2723)=v(2712)*v(7941)
v(2734)=-v(2723)+v(2668)*v(315)+v(2646)*v(316)
v(2722)=v(2711)*v(7941)
v(2733)=-v(2722)+v(2667)*v(315)+v(2645)*v(316)
v(2721)=v(2710)*v(7941)
v(2732)=-v(2721)+v(2666)*v(315)+v(2644)*v(316)
v(2720)=v(2709)*v(7941)
v(2731)=-v(2720)+v(2665)*v(315)+v(2643)*v(316)
v(334)=(v(318)*v(318))
v(350)=v(315)*v(316)-v(334)
v(319)=v(298)*v(307)+v(303)*v(312)+v(299)*v(314)
v(7942)=2d0*v(319)
v(2844)=v(319)*v(7941)
v(2763)=v(2752)*v(7942)
v(2774)=-v(2763)+v(2697)*v(316)+v(2675)*v(317)
v(2762)=v(2751)*v(7942)
v(2773)=-v(2762)+v(2696)*v(316)+v(2674)*v(317)
v(2761)=v(2750)*v(7942)
v(2772)=-v(2761)+v(2695)*v(316)+v(2673)*v(317)
v(2760)=v(2749)*v(7942)
v(2771)=-v(2760)+v(2694)*v(316)+v(2672)*v(317)
v(2759)=v(2748)*v(7942)
v(2770)=-v(2759)+v(2693)*v(316)+v(2671)*v(317)
v(2758)=v(2747)*v(7942)
v(2769)=-v(2758)+v(2692)*v(316)+v(2670)*v(317)
v(2757)=v(2746)*v(7942)
v(2768)=-v(2757)+v(2691)*v(316)+v(2669)*v(317)
v(2756)=v(2745)*v(7942)
v(2767)=-v(2756)+v(2690)*v(316)+v(2668)*v(317)
v(2755)=v(2744)*v(7942)
v(2766)=-v(2755)+v(2689)*v(316)+v(2667)*v(317)
v(2754)=v(2743)*v(7942)
v(2765)=-v(2754)+v(2688)*v(316)+v(2666)*v(317)
v(2753)=v(2742)*v(7942)
v(2764)=-v(2753)+v(2687)*v(316)+v(2665)*v(317)
v(322)=(v(319)*v(319))
v(339)=v(316)*v(317)-v(322)
v(320)=v(299)*v(311)+v(297)*v(312)+v(307)*v(313)
v(7943)=2d0*v(320)
v(2843)=v(320)*v(7941)
v(2841)=v(320)*v(7942)
v(2829)=v(2785)*v(7943)
v(2840)=-v(2829)+v(2697)*v(315)+v(2653)*v(317)
v(2828)=v(2784)*v(7943)
v(2839)=-v(2828)+v(2696)*v(315)+v(2652)*v(317)
v(2827)=v(2783)*v(7943)
v(2838)=-v(2827)+v(2695)*v(315)+v(2651)*v(317)
v(2826)=v(2782)*v(7943)
v(2837)=-v(2826)+v(2694)*v(315)+v(2650)*v(317)
v(2825)=v(2781)*v(7943)
v(2836)=-v(2825)+v(2693)*v(315)+v(2649)*v(317)
v(2824)=v(2780)*v(7943)
v(2835)=-v(2824)+v(2692)*v(315)+v(2648)*v(317)
v(2823)=v(2779)*v(7943)
v(2834)=-v(2823)+v(2691)*v(315)+v(2647)*v(317)
v(2822)=v(2778)*v(7943)
v(2833)=-v(2822)+v(2690)*v(315)+v(2646)*v(317)
v(2821)=v(2777)*v(7943)
v(2832)=-v(2821)+v(2689)*v(315)+v(2645)*v(317)
v(2820)=v(2776)*v(7943)
v(2831)=-v(2820)+v(2688)*v(315)+v(2644)*v(317)
v(2819)=v(2775)*v(7943)
v(2830)=-v(2819)+v(2687)*v(315)+v(2643)*v(317)
v(2818)=-(v(2719)*v(317))-v(2697)*v(318)+v(2785)*v(319)+v(2752)*v(320)
v(2817)=-(v(2718)*v(317))-v(2696)*v(318)+v(2784)*v(319)+v(2751)*v(320)
v(2816)=-(v(2717)*v(317))-v(2695)*v(318)+v(2783)*v(319)+v(2750)*v(320)
v(2815)=-(v(2716)*v(317))-v(2694)*v(318)+v(2782)*v(319)+v(2749)*v(320)
v(2814)=-(v(2715)*v(317))-v(2693)*v(318)+v(2781)*v(319)+v(2748)*v(320)
v(2813)=-(v(2714)*v(317))-v(2692)*v(318)+v(2780)*v(319)+v(2747)*v(320)
v(2812)=-(v(2713)*v(317))-v(2691)*v(318)+v(2779)*v(319)+v(2746)*v(320)
v(2811)=-(v(2712)*v(317))-v(2690)*v(318)+v(2778)*v(319)+v(2745)*v(320)
v(2810)=-(v(2711)*v(317))-v(2689)*v(318)+v(2777)*v(319)+v(2744)*v(320)
v(2809)=-(v(2710)*v(317))-v(2688)*v(318)+v(2776)*v(319)+v(2743)*v(320)
v(2808)=-(v(2709)*v(317))-v(2687)*v(318)+v(2775)*v(319)+v(2742)*v(320)
v(2807)=-(v(2752)*v(315))+v(2785)*v(318)-v(2653)*v(319)+v(2719)*v(320)
v(2806)=-(v(2751)*v(315))+v(2784)*v(318)-v(2652)*v(319)+v(2718)*v(320)
v(2805)=-(v(2750)*v(315))+v(2783)*v(318)-v(2651)*v(319)+v(2717)*v(320)
v(2804)=-(v(2749)*v(315))+v(2782)*v(318)-v(2650)*v(319)+v(2716)*v(320)
v(2803)=-(v(2748)*v(315))+v(2781)*v(318)-v(2649)*v(319)+v(2715)*v(320)
v(2802)=-(v(2747)*v(315))+v(2780)*v(318)-v(2648)*v(319)+v(2714)*v(320)
v(2801)=-(v(2746)*v(315))+v(2779)*v(318)-v(2647)*v(319)+v(2713)*v(320)
v(2800)=-(v(2745)*v(315))+v(2778)*v(318)-v(2646)*v(319)+v(2712)*v(320)
v(2799)=-(v(2744)*v(315))+v(2777)*v(318)-v(2645)*v(319)+v(2711)*v(320)
v(2798)=-(v(2743)*v(315))+v(2776)*v(318)-v(2644)*v(319)+v(2710)*v(320)
v(2797)=-(v(2742)*v(315))+v(2775)*v(318)-v(2643)*v(319)+v(2709)*v(320)
v(2796)=-(v(2785)*v(316))+v(2752)*v(318)+v(2719)*v(319)-v(2675)*v(320)
v(2795)=-(v(2784)*v(316))+v(2751)*v(318)+v(2718)*v(319)-v(2674)*v(320)
v(2794)=-(v(2783)*v(316))+v(2750)*v(318)+v(2717)*v(319)-v(2673)*v(320)
v(2793)=-(v(2782)*v(316))+v(2749)*v(318)+v(2716)*v(319)-v(2672)*v(320)
v(2792)=-(v(2781)*v(316))+v(2748)*v(318)+v(2715)*v(319)-v(2671)*v(320)
v(2791)=-(v(2780)*v(316))+v(2747)*v(318)+v(2714)*v(319)-v(2670)*v(320)
v(2790)=-(v(2779)*v(316))+v(2746)*v(318)+v(2713)*v(319)-v(2669)*v(320)
v(2789)=-(v(2778)*v(316))+v(2745)*v(318)+v(2712)*v(319)-v(2668)*v(320)
v(2788)=-(v(2777)*v(316))+v(2744)*v(318)+v(2711)*v(319)-v(2667)*v(320)
v(2787)=-(v(2776)*v(316))+v(2743)*v(318)+v(2710)*v(319)-v(2666)*v(320)
v(2786)=-(v(2775)*v(316))+v(2742)*v(318)+v(2709)*v(319)-v(2665)*v(320)
v(351)=v(318)*v(319)-v(316)*v(320)
v(346)=-(v(315)*v(319))+v(318)*v(320)
v(341)=-(v(317)*v(318))+v(319)*v(320)
v(326)=(v(320)*v(320))
v(2854)=v(2719)*v(2841)+v(2752)*v(2843)+v(2785)*v(2844)-v(2763)*v(315)-v(2829)*v(316)+v(2741)*v(317)-v(2653)*v(322)-v&
&(2675)*v(326)+v(2697)*v(350)
v(2853)=v(2718)*v(2841)+v(2751)*v(2843)+v(2784)*v(2844)-v(2762)*v(315)-v(2828)*v(316)+v(2740)*v(317)-v(2652)*v(322)-v&
&(2674)*v(326)+v(2696)*v(350)
v(2852)=v(2717)*v(2841)+v(2750)*v(2843)+v(2783)*v(2844)-v(2761)*v(315)-v(2827)*v(316)+v(2739)*v(317)-v(2651)*v(322)-v&
&(2673)*v(326)+v(2695)*v(350)
v(2851)=v(2716)*v(2841)+v(2749)*v(2843)+v(2782)*v(2844)-v(2760)*v(315)-v(2826)*v(316)+v(2738)*v(317)-v(2650)*v(322)-v&
&(2672)*v(326)+v(2694)*v(350)
v(2850)=v(2715)*v(2841)+v(2748)*v(2843)+v(2781)*v(2844)-v(2759)*v(315)-v(2825)*v(316)+v(2737)*v(317)-v(2649)*v(322)-v&
&(2671)*v(326)+v(2693)*v(350)
v(2849)=v(2714)*v(2841)+v(2747)*v(2843)+v(2780)*v(2844)-v(2758)*v(315)-v(2824)*v(316)+v(2736)*v(317)-v(2648)*v(322)-v&
&(2670)*v(326)+v(2692)*v(350)
v(2848)=v(2713)*v(2841)+v(2746)*v(2843)+v(2779)*v(2844)-v(2757)*v(315)-v(2823)*v(316)+v(2735)*v(317)-v(2647)*v(322)-v&
&(2669)*v(326)+v(2691)*v(350)
v(2847)=v(2712)*v(2841)+v(2745)*v(2843)+v(2778)*v(2844)-v(2756)*v(315)-v(2822)*v(316)+v(2734)*v(317)-v(2646)*v(322)-v&
&(2668)*v(326)+v(2690)*v(350)
v(2846)=v(2711)*v(2841)+v(2744)*v(2843)+v(2777)*v(2844)-v(2755)*v(315)-v(2821)*v(316)+v(2733)*v(317)-v(2645)*v(322)-v&
&(2667)*v(326)+v(2689)*v(350)
v(2845)=v(2710)*v(2841)+v(2743)*v(2843)+v(2776)*v(2844)-v(2754)*v(315)-v(2820)*v(316)+v(2732)*v(317)-v(2644)*v(322)-v&
&(2666)*v(326)+v(2688)*v(350)
v(2842)=v(2709)*v(2841)+v(2742)*v(2843)+v(2775)*v(2844)-v(2753)*v(315)-v(2819)*v(316)+v(2731)*v(317)-v(2643)*v(322)-v&
&(2665)*v(326)+v(2687)*v(350)
v(345)=v(315)*v(317)-v(326)
v(323)=v(2841)*v(318)-v(315)*v(322)-v(316)*v(326)+v(317)*v(350)
v(7980)=v(341)/v(323)
v(2970)=1d0/v(323)**0.23333333333333334d1
v(7944)=(-4d0/3d0)*v(2970)
v(2980)=v(2854)*v(7944)
v(2979)=v(2853)*v(7944)
v(2978)=v(2852)*v(7944)
v(2977)=v(2851)*v(7944)
v(2976)=v(2850)*v(7944)
v(2975)=v(2849)*v(7944)
v(2974)=v(2848)*v(7944)
v(2973)=v(2847)*v(7944)
v(2972)=v(2846)*v(7944)
v(2971)=v(2845)*v(7944)
v(2969)=v(2842)*v(7944)
v(2958)=1d0/v(323)**2
v(2968)=-(v(2854)*v(2958))
v(2967)=-(v(2853)*v(2958))
v(2966)=-(v(2852)*v(2958))
v(2965)=-(v(2851)*v(2958))
v(2964)=-(v(2850)*v(2958))
v(2963)=-(v(2849)*v(2958))
v(2962)=-(v(2848)*v(2958))
v(2961)=-(v(2847)*v(2958))
v(2960)=-(v(2846)*v(2958))
v(2959)=-(v(2845)*v(2958))
v(2957)=-(v(2842)*v(2958))
v(2868)=1d0/v(323)**0.13333333333333333d1
v(7977)=mpar(1)*v(2868)
v(7945)=-v(2868)/3d0
v(2879)=v(2854)*v(7945)
v(2878)=v(2853)*v(7945)
v(2877)=v(2852)*v(7945)
v(2876)=v(2851)*v(7945)
v(2875)=v(2850)*v(7945)
v(2874)=v(2849)*v(7945)
v(2873)=v(2848)*v(7945)
v(2872)=v(2847)*v(7945)
v(2871)=v(2846)*v(7945)
v(2870)=v(2845)*v(7945)
v(2869)=v(2842)*v(7945)
v(2855)=sqrt(v(323))
v(7946)=mpar(2)*(1d0-1d0/(2d0*v(2855)))
v(2867)=v(2854)*v(7946)
v(2866)=v(2853)*v(7946)
v(2865)=v(2852)*v(7946)
v(2864)=v(2851)*v(7946)
v(2863)=v(2850)*v(7946)
v(2862)=v(2849)*v(7946)
v(2861)=v(2848)*v(7946)
v(2860)=v(2847)*v(7946)
v(2859)=v(2846)*v(7946)
v(2858)=v(2845)*v(7946)
v(2856)=v(2842)*v(7946)
v(330)=mpar(2)*(-v(2855)+v(323))
v(329)=1d0/v(323)**0.3333333333333333d0
v(7976)=mpar(1)*v(329)
v(7975)=mpar(1)*(v(2869)*v(2932)+(v(2654)+(2d0/3d0)*v(2665)+v(2698))*v(329))
v(7974)=mpar(1)*(v(2869)*v(2905)+(v(2654)+v(2676)+(2d0/3d0)*v(2687))*v(329))
v(7973)=mpar(1)*(v(2869)*v(2880)+((2d0/3d0)*v(2643)+v(2676)+v(2698))*v(329))
v(7972)=mpar(1)*(v(2870)*v(2932)+(v(2655)+(2d0/3d0)*v(2666)+v(2699))*v(329))
v(7971)=mpar(1)*(v(2871)*v(2880)+((2d0/3d0)*v(2645)+v(2678)+v(2700))*v(329))
v(7970)=mpar(1)*(v(2872)*v(2932)+(v(2657)+(2d0/3d0)*v(2668)+v(2701))*v(329))
v(7969)=mpar(1)*(v(2872)*v(2905)+(v(2657)+v(2679)+(2d0/3d0)*v(2690))*v(329))
v(7968)=mpar(1)*(v(2872)*v(2880)+((2d0/3d0)*v(2646)+v(2679)+v(2701))*v(329))
v(7967)=mpar(1)*(v(2873)*v(2932)+(v(2658)+(2d0/3d0)*v(2669)+v(2702))*v(329))
v(7966)=mpar(1)*(v(2873)*v(2905)+(v(2658)+v(2680)+(2d0/3d0)*v(2691))*v(329))
v(7965)=mpar(1)*(v(2873)*v(2880)+((2d0/3d0)*v(2647)+v(2680)+v(2702))*v(329))
v(7964)=mpar(1)*(v(2874)*v(2932)+(v(2659)+(2d0/3d0)*v(2670)+v(2703))*v(329))
v(7963)=mpar(1)*(v(2874)*v(2905)+(v(2659)+v(2681)+(2d0/3d0)*v(2692))*v(329))
v(7962)=mpar(1)*(v(2874)*v(2880)+((2d0/3d0)*v(2648)+v(2681)+v(2703))*v(329))
v(7961)=mpar(1)*(v(2875)*v(2932)+(v(2660)+(2d0/3d0)*v(2671)+v(2704))*v(329))
v(7960)=mpar(1)*(v(2875)*v(2905)+(v(2660)+v(2682)+(2d0/3d0)*v(2693))*v(329))
v(7959)=mpar(1)*(v(2875)*v(2880)+((2d0/3d0)*v(2649)+v(2682)+v(2704))*v(329))
v(7958)=mpar(1)*(v(2876)*v(2932)+(v(2661)+(2d0/3d0)*v(2672)+v(2705))*v(329))
v(7957)=mpar(1)*(v(2876)*v(2905)+(v(2661)+v(2683)+(2d0/3d0)*v(2694))*v(329))
v(7956)=mpar(1)*(v(2876)*v(2880)+((2d0/3d0)*v(2650)+v(2683)+v(2705))*v(329))
v(7955)=mpar(1)*(v(2877)*v(2932)+(v(2662)+(2d0/3d0)*v(2673)+v(2706))*v(329))
v(7954)=mpar(1)*(v(2877)*v(2905)+(v(2662)+v(2684)+(2d0/3d0)*v(2695))*v(329))
v(7953)=mpar(1)*(v(2877)*v(2880)+((2d0/3d0)*v(2651)+v(2684)+v(2706))*v(329))
v(7952)=mpar(1)*(v(2878)*v(2932)+(v(2663)+(2d0/3d0)*v(2674)+v(2707))*v(329))
v(7951)=mpar(1)*(v(2878)*v(2905)+(v(2663)+v(2685)+(2d0/3d0)*v(2696))*v(329))
v(7950)=mpar(1)*(v(2878)*v(2880)+((2d0/3d0)*v(2652)+v(2685)+v(2707))*v(329))
v(7949)=mpar(1)*(v(2879)*v(2932)+(v(2664)+(2d0/3d0)*v(2675)+v(2708))*v(329))
v(7948)=mpar(1)*(v(2879)*v(2905)+(v(2664)+v(2686)+(2d0/3d0)*v(2697))*v(329))
v(7947)=mpar(1)*(v(2879)*v(2880)+((2d0/3d0)*v(2653)+v(2686)+v(2708))*v(329))
v(2943)=v(2867)+v(7949)
v(2942)=v(2866)+v(7952)
v(2941)=v(2865)+v(7955)
v(2940)=v(2864)+v(7958)
v(2939)=v(2863)+v(7961)
v(2938)=v(2862)+v(7964)
v(2937)=v(2861)+v(7967)
v(2936)=v(2860)+v(7970)
v(2935)=v(2859)+mpar(1)*(v(2871)*v(2932)+(v(2656)+(2d0/3d0)*v(2667)+v(2700))*v(329))
v(2955)=1d0-v(2935)
v(2956)=v(2955)/3d0
v(2946)=-v(2935)/3d0
v(2934)=v(2858)+v(7972)
v(7108)=(2d0/3d0)*v(2934)
v(2945)=-v(2934)/3d0
v(2933)=v(2856)+v(7975)
v(2916)=v(2867)+v(7948)
v(2915)=v(2866)+v(7951)
v(2914)=v(2865)+v(7954)
v(2913)=v(2864)+v(7957)
v(2912)=v(2863)+v(7960)
v(2911)=v(2862)+v(7963)
v(2910)=v(2861)+v(7966)
v(2909)=v(2860)+v(7969)
v(2908)=v(2859)+mpar(1)*(v(2871)*v(2905)+(v(2656)+v(2678)+(2d0/3d0)*v(2689))*v(329))
v(2929)=(-1d0)-v(2908)
v(2931)=v(2929)/3d0
v(2919)=-v(2908)/3d0
v(2907)=v(2858)+mpar(1)*(v(2870)*v(2905)+(v(2655)+v(2677)+(2d0/3d0)*v(2688))*v(329))
v(2928)=(-1d0)-v(2907)
v(2930)=v(2928)/3d0
v(2918)=-v(2907)/3d0
v(2906)=v(2856)+v(7974)
v(2891)=v(2867)+v(7947)
v(2890)=v(2866)+v(7950)
v(2889)=v(2865)+v(7953)
v(2888)=v(2864)+v(7956)
v(2887)=v(2863)+v(7959)
v(2886)=v(2862)+v(7962)
v(2885)=v(2861)+v(7965)
v(2884)=v(2860)+v(7968)
v(2883)=v(2859)+v(7971)
v(7076)=(2d0/3d0)*v(2883)
v(2894)=-v(2883)/3d0
v(3181)=v(2894)+(-2d0/3d0)*v(2929)+v(2956)
v(3170)=v(2894)+v(2931)+(-2d0/3d0)*v(2955)
v(2882)=v(2858)+mpar(1)*(v(2870)*v(2880)+((2d0/3d0)*v(2644)+v(2677)+v(2699))*v(329))
v(2903)=(-1d0)+v(2882)
v(3158)=(2d0/3d0)*v(2903)+v(2930)+v(2945)
v(2904)=-v(2903)/3d0
v(3180)=v(2904)+(-2d0/3d0)*v(2928)+v(2945)
v(2893)=-v(2882)/3d0
v(2881)=v(2856)+v(7973)
v(352)=v(330)+v(2880)*v(7976)
v(7985)=v(339)*v(352)
v(7984)=v(352)/v(323)
v(7979)=v(351)*v(352)
v(639)=-v(352)/3d0
v(360)=v(352)-x(2)-x(7)
v(364)=-v(360)/3d0
v(347)=v(330)+v(2905)*v(7976)
v(7986)=v(347)*v(350)
v(7982)=v(347)/v(323)
v(7978)=v(346)*v(347)
v(636)=-v(347)/3d0
v(363)=-v(347)+v(7523)+v(7531)
v(359)=v(363)/3d0
v(342)=v(330)+v(2932)*v(7976)
v(7983)=v(342)*v(345)
v(7981)=v(342)/v(323)
v(638)=-v(342)/3d0
v(358)=-v(342)+x(3)+x(8)
v(362)=v(358)/3d0
v(3024)=mpar(1)*(v(2719)*v(2868)+v(2980)*v(318))
v(3023)=mpar(1)*(v(2718)*v(2868)+v(2979)*v(318))
v(3022)=mpar(1)*(v(2717)*v(2868)+v(2978)*v(318))
v(3021)=mpar(1)*(v(2716)*v(2868)+v(2977)*v(318))
v(3020)=mpar(1)*(v(2715)*v(2868)+v(2976)*v(318))
v(3019)=mpar(1)*(v(2714)*v(2868)+v(2975)*v(318))
v(3018)=mpar(1)*(v(2713)*v(2868)+v(2974)*v(318))
v(3017)=mpar(1)*(v(2712)*v(2868)+v(2973)*v(318))
v(3016)=mpar(1)*(v(2711)*v(2868)+v(2972)*v(318))
v(3015)=mpar(1)*(v(2710)*v(2868)+v(2971)*v(318))
v(3014)=mpar(1)*(v(2709)*v(2868)+v(2969)*v(318))
v(3013)=mpar(1)*(v(2796)*v(2868)+v(2980)*v(351))
v(3012)=mpar(1)*(v(2795)*v(2868)+v(2979)*v(351))
v(3011)=mpar(1)*(v(2794)*v(2868)+v(2978)*v(351))
v(3010)=mpar(1)*(v(2793)*v(2868)+v(2977)*v(351))
v(3009)=mpar(1)*(v(2792)*v(2868)+v(2976)*v(351))
v(3008)=mpar(1)*(v(2791)*v(2868)+v(2975)*v(351))
v(3007)=mpar(1)*(v(2790)*v(2868)+v(2974)*v(351))
v(3006)=mpar(1)*(v(2789)*v(2868)+v(2973)*v(351))
v(3005)=mpar(1)*(v(2788)*v(2868)+v(2972)*v(351))
v(3004)=mpar(1)*(v(2787)*v(2868)+v(2971)*v(351))
v(3003)=mpar(1)*(v(2786)*v(2868)+v(2969)*v(351))
v(3002)=mpar(1)*(v(2752)*v(2868)+v(2980)*v(319))
v(3001)=mpar(1)*(v(2751)*v(2868)+v(2979)*v(319))
v(3000)=mpar(1)*(v(2750)*v(2868)+v(2978)*v(319))
v(2999)=mpar(1)*(v(2749)*v(2868)+v(2977)*v(319))
v(2998)=mpar(1)*(v(2748)*v(2868)+v(2976)*v(319))
v(2997)=mpar(1)*(v(2747)*v(2868)+v(2975)*v(319))
v(2996)=mpar(1)*(v(2746)*v(2868)+v(2974)*v(319))
v(2995)=mpar(1)*(v(2745)*v(2868)+v(2973)*v(319))
v(2994)=mpar(1)*(v(2744)*v(2868)+v(2972)*v(319))
v(2993)=mpar(1)*(v(2743)*v(2868)+v(2971)*v(319))
v(2992)=mpar(1)*(v(2742)*v(2868)+v(2969)*v(319))
v(2991)=mpar(1)*(v(2785)*v(2868)+v(2980)*v(320))
v(2990)=mpar(1)*(v(2784)*v(2868)+v(2979)*v(320))
v(2989)=mpar(1)*(v(2783)*v(2868)+v(2978)*v(320))
v(2988)=mpar(1)*(v(2782)*v(2868)+v(2977)*v(320))
v(2987)=mpar(1)*(v(2781)*v(2868)+v(2976)*v(320))
v(2986)=mpar(1)*(v(2780)*v(2868)+v(2975)*v(320))
v(2985)=mpar(1)*(v(2779)*v(2868)+v(2974)*v(320))
v(2984)=mpar(1)*(v(2778)*v(2868)+v(2973)*v(320))
v(2983)=mpar(1)*(v(2777)*v(2868)+v(2972)*v(320))
v(2982)=mpar(1)*(v(2776)*v(2868)+v(2971)*v(320))
v(2981)=mpar(1)*(v(2775)*v(2868)+v(2969)*v(320))
v(349)=v(320)*v(7977)
v(344)=v(319)*v(7977)
v(3079)=v(2991)*v(341)+v(2840)*v(344)+v(3002)*v(345)+(v(2916)*v(346)+v(2807)*v(347))/v(323)+v(2818)*v(349)+v(2968)*v&
&(7978)
v(3078)=v(2990)*v(341)+v(2839)*v(344)+v(3001)*v(345)+(v(2915)*v(346)+v(2806)*v(347))/v(323)+v(2817)*v(349)+v(2967)*v&
&(7978)
v(3077)=v(2989)*v(341)+v(2838)*v(344)+v(3000)*v(345)+(v(2914)*v(346)+v(2805)*v(347))/v(323)+v(2816)*v(349)+v(2966)*v&
&(7978)
v(3076)=v(2988)*v(341)+v(2837)*v(344)+v(2999)*v(345)+(v(2913)*v(346)+v(2804)*v(347))/v(323)+v(2815)*v(349)+v(2965)*v&
&(7978)
v(3075)=v(2987)*v(341)+v(2836)*v(344)+v(2998)*v(345)+(v(2912)*v(346)+v(2803)*v(347))/v(323)+v(2814)*v(349)+v(2964)*v&
&(7978)
v(3074)=v(2986)*v(341)+v(2835)*v(344)+v(2997)*v(345)+(v(2911)*v(346)+v(2802)*v(347))/v(323)+v(2813)*v(349)+v(2963)*v&
&(7978)
v(3073)=v(2985)*v(341)+v(2834)*v(344)+v(2996)*v(345)+(v(2910)*v(346)+v(2801)*v(347))/v(323)+v(2812)*v(349)+v(2962)*v&
&(7978)
v(3072)=v(2984)*v(341)+v(2833)*v(344)+v(2995)*v(345)+(v(2909)*v(346)+v(2800)*v(347))/v(323)+v(2811)*v(349)+v(2961)*v&
&(7978)
v(3071)=v(2983)*v(341)+v(2832)*v(344)+v(2994)*v(345)+(v(2908)*v(346)+v(2799)*v(347))/v(323)+v(2810)*v(349)+v(2960)*v&
&(7978)
v(3070)=v(2982)*v(341)+v(2831)*v(344)+v(2993)*v(345)+(v(2907)*v(346)+v(2798)*v(347))/v(323)+v(2809)*v(349)+v(2959)*v&
&(7978)
v(3069)=v(2981)*v(341)+v(2830)*v(344)+v(2992)*v(345)+(v(2906)*v(346)+v(2797)*v(347))/v(323)+v(2808)*v(349)+v(2957)*v&
&(7978)
v(3035)=v(2807)*v(344)+v(3002)*v(346)
v(3034)=v(2806)*v(344)+v(3001)*v(346)
v(3033)=v(2805)*v(344)+v(3000)*v(346)
v(3032)=v(2804)*v(344)+v(2999)*v(346)
v(3031)=v(2803)*v(344)+v(2998)*v(346)
v(3030)=v(2802)*v(344)+v(2997)*v(346)
v(3029)=v(2801)*v(344)+v(2996)*v(346)
v(3028)=v(2800)*v(344)+v(2995)*v(346)
v(3027)=v(2799)*v(344)+v(2994)*v(346)
v(3026)=v(2798)*v(344)+v(2993)*v(346)
v(3025)=v(2797)*v(344)+v(2992)*v(346)
v(340)=v(351)*v(7977)
v(3046)=v(3013)*v(320)+v(2785)*v(340)
v(3045)=v(3012)*v(320)+v(2784)*v(340)
v(3044)=v(3011)*v(320)+v(2783)*v(340)
v(3043)=v(3010)*v(320)+v(2782)*v(340)
v(3042)=v(3009)*v(320)+v(2781)*v(340)
v(3041)=v(3008)*v(320)+v(2780)*v(340)
v(3040)=v(3007)*v(320)+v(2779)*v(340)
v(3039)=v(3006)*v(320)+v(2778)*v(340)
v(3038)=v(3005)*v(320)+v(2777)*v(340)
v(3037)=v(3004)*v(320)+v(2776)*v(340)
v(3036)=v(3003)*v(320)+v(2775)*v(340)
v(338)=v(318)*v(7977)
v(3090)=v(2807)*v(338)+v(3024)*v(346)+v(2741)*v(349)+v(2991)*v(350)+(v(2891)*v(351)+v(2796)*v(352))/v(323)+v(2968)*v&
&(7979)
v(3089)=v(2806)*v(338)+v(3023)*v(346)+v(2740)*v(349)+v(2990)*v(350)+(v(2890)*v(351)+v(2795)*v(352))/v(323)+v(2967)*v&
&(7979)
v(3088)=v(2805)*v(338)+v(3022)*v(346)+v(2739)*v(349)+v(2989)*v(350)+(v(2889)*v(351)+v(2794)*v(352))/v(323)+v(2966)*v&
&(7979)
v(3087)=v(2804)*v(338)+v(3021)*v(346)+v(2738)*v(349)+v(2988)*v(350)+(v(2888)*v(351)+v(2793)*v(352))/v(323)+v(2965)*v&
&(7979)
v(3086)=v(2803)*v(338)+v(3020)*v(346)+v(2737)*v(349)+v(2987)*v(350)+(v(2887)*v(351)+v(2792)*v(352))/v(323)+v(2964)*v&
&(7979)
v(3085)=v(2802)*v(338)+v(3019)*v(346)+v(2736)*v(349)+v(2986)*v(350)+(v(2886)*v(351)+v(2791)*v(352))/v(323)+v(2963)*v&
&(7979)
v(3084)=v(2801)*v(338)+v(3018)*v(346)+v(2735)*v(349)+v(2985)*v(350)+(v(2885)*v(351)+v(2790)*v(352))/v(323)+v(2962)*v&
&(7979)
v(3083)=v(2800)*v(338)+v(3017)*v(346)+v(2734)*v(349)+v(2984)*v(350)+(v(2884)*v(351)+v(2789)*v(352))/v(323)+v(2961)*v&
&(7979)
v(3082)=v(2799)*v(338)+v(3016)*v(346)+v(2733)*v(349)+v(2983)*v(350)+(v(2883)*v(351)+v(2788)*v(352))/v(323)+v(2960)*v&
&(7979)
v(3081)=v(2798)*v(338)+v(3015)*v(346)+v(2732)*v(349)+v(2982)*v(350)+(v(2882)*v(351)+v(2787)*v(352))/v(323)+v(2959)*v&
&(7979)
v(3080)=v(2797)*v(338)+v(3014)*v(346)+v(2731)*v(349)+v(2981)*v(350)+(v(2881)*v(351)+v(2786)*v(352))/v(323)+v(2957)*v&
&(7979)
v(3068)=v(3013)*v(319)+v(2774)*v(338)+v(3024)*v(339)+v(2752)*v(340)+(v(2818)/v(323)+v(2968)*v(341))*v(342)+v(2943)*v&
&(7980)
v(3067)=v(3012)*v(319)+v(2773)*v(338)+v(3023)*v(339)+v(2751)*v(340)+(v(2817)/v(323)+v(2967)*v(341))*v(342)+v(2942)*v&
&(7980)
v(3066)=v(3011)*v(319)+v(2772)*v(338)+v(3022)*v(339)+v(2750)*v(340)+(v(2816)/v(323)+v(2966)*v(341))*v(342)+v(2941)*v&
&(7980)
v(3065)=v(3010)*v(319)+v(2771)*v(338)+v(3021)*v(339)+v(2749)*v(340)+(v(2815)/v(323)+v(2965)*v(341))*v(342)+v(2940)*v&
&(7980)
v(3064)=v(3009)*v(319)+v(2770)*v(338)+v(3020)*v(339)+v(2748)*v(340)+(v(2814)/v(323)+v(2964)*v(341))*v(342)+v(2939)*v&
&(7980)
v(3063)=v(3008)*v(319)+v(2769)*v(338)+v(3019)*v(339)+v(2747)*v(340)+(v(2813)/v(323)+v(2963)*v(341))*v(342)+v(2938)*v&
&(7980)
v(3062)=v(3007)*v(319)+v(2768)*v(338)+v(3018)*v(339)+v(2746)*v(340)+(v(2812)/v(323)+v(2962)*v(341))*v(342)+v(2937)*v&
&(7980)
v(3061)=v(3006)*v(319)+v(2767)*v(338)+v(3017)*v(339)+v(2745)*v(340)+(v(2811)/v(323)+v(2961)*v(341))*v(342)+v(2936)*v&
&(7980)
v(3060)=v(3005)*v(319)+v(2766)*v(338)+v(3016)*v(339)+v(2744)*v(340)+(v(2810)/v(323)+v(2960)*v(341))*v(342)+v(2935)*v&
&(7980)
v(3059)=v(3004)*v(319)+v(2765)*v(338)+v(3015)*v(339)+v(2743)*v(340)+(v(2809)/v(323)+v(2959)*v(341))*v(342)+v(2934)*v&
&(7980)
v(3058)=v(3003)*v(319)+v(2764)*v(338)+v(3014)*v(339)+v(2742)*v(340)+(v(2808)/v(323)+v(2957)*v(341))*v(342)+v(2933)*v&
&(7980)
v(3057)=v(2818)*v(338)+v(3024)*v(341)
v(3056)=v(2817)*v(338)+v(3023)*v(341)
v(3055)=v(2816)*v(338)+v(3022)*v(341)
v(3054)=v(2815)*v(338)+v(3021)*v(341)
v(3053)=v(2814)*v(338)+v(3020)*v(341)
v(3052)=v(2813)*v(338)+v(3019)*v(341)
v(3051)=v(2812)*v(338)+v(3018)*v(341)
v(3050)=v(2811)*v(338)+v(3017)*v(341)
v(3049)=v(2810)*v(338)+v(3016)*v(341)
v(3048)=v(2809)*v(338)+v(3015)*v(341)
v(3047)=v(2808)*v(338)+v(3014)*v(341)
v(333)=v(344)*v(346)
v(332)=v(320)*v(340)
v(325)=v(338)*v(341)
v(324)=v(325)+v(332)+v(339)*v(7984)
v(331)=v(325)+v(333)+v(345)*v(7981)
v(337)=v(332)+v(333)+v(350)*v(7982)
v(343)=v(338)*v(339)+v(319)*v(340)+v(341)*v(7981)
v(348)=v(344)*v(345)+v(341)*v(349)+v(346)*v(7982)
v(3112)=v(3068)*v(315)+v(3079)*v(320)+v(2719)*v(331)+v(2653)*v(343)+v(2785)*v(348)+v(318)*(v(3035)+v(3057)+(v(2840)*v&
&(342)+v(2943)*v(345))/v(323)+v(2968)*v(7983))
v(3110)=v(3067)*v(315)+v(3078)*v(320)+v(2718)*v(331)+v(2652)*v(343)+v(2784)*v(348)+v(318)*(v(3034)+v(3056)+(v(2839)*v&
&(342)+v(2942)*v(345))/v(323)+v(2967)*v(7983))
v(3108)=v(3066)*v(315)+v(3077)*v(320)+v(2717)*v(331)+v(2651)*v(343)+v(2783)*v(348)+v(318)*(v(3033)+v(3055)+(v(2838)*v&
&(342)+v(2941)*v(345))/v(323)+v(2966)*v(7983))
v(3106)=v(3065)*v(315)+v(3076)*v(320)+v(2716)*v(331)+v(2650)*v(343)+v(2782)*v(348)+v(318)*(v(3032)+v(3054)+(v(2837)*v&
&(342)+v(2940)*v(345))/v(323)+v(2965)*v(7983))
v(3104)=v(3064)*v(315)+v(3075)*v(320)+v(2715)*v(331)+v(2649)*v(343)+v(2781)*v(348)+v(318)*(v(3031)+v(3053)+(v(2836)*v&
&(342)+v(2939)*v(345))/v(323)+v(2964)*v(7983))
v(3102)=v(3063)*v(315)+v(3074)*v(320)+v(2714)*v(331)+v(2648)*v(343)+v(2780)*v(348)+v(318)*(v(3030)+v(3052)+(v(2835)*v&
&(342)+v(2938)*v(345))/v(323)+v(2963)*v(7983))
v(3100)=v(3062)*v(315)+v(3073)*v(320)+v(2713)*v(331)+v(2647)*v(343)+v(2779)*v(348)+v(318)*(v(3029)+v(3051)+(v(2834)*v&
&(342)+v(2937)*v(345))/v(323)+v(2962)*v(7983))
v(3098)=v(3061)*v(315)+v(3072)*v(320)+v(2712)*v(331)+v(2646)*v(343)+v(2778)*v(348)+v(318)*(v(3028)+v(3050)+(v(2833)*v&
&(342)+v(2936)*v(345))/v(323)+v(2961)*v(7983))
v(3190)=(-1d0)+v(3098)
v(3096)=v(3060)*v(315)+v(3071)*v(320)+v(2711)*v(331)+v(2645)*v(343)+v(2777)*v(348)+v(318)*(v(3027)+v(3049)+(v(2832)*v&
&(342)+v(2935)*v(345))/v(323)+v(2960)*v(7983))
v(3094)=v(3059)*v(315)+v(3070)*v(320)+v(2710)*v(331)+v(2644)*v(343)+v(2776)*v(348)+v(318)*(v(3026)+v(3048)+(v(2831)*v&
&(342)+v(2934)*v(345))/v(323)+v(2959)*v(7983))
v(3092)=v(3058)*v(315)+v(3069)*v(320)+v(2709)*v(331)+v(2643)*v(343)+v(2775)*v(348)+v(318)*(v(3025)+v(3047)+(v(2830)*v&
&(342)+v(2933)*v(345))/v(323)+v(2957)*v(7983))
v(353)=v(338)*v(346)+v(349)*v(350)+v(351)*v(7984)
v(3156)=v(3090)*v(317)+v(3068)*v(319)+v(2785)*v(324)+v(2752)*v(343)+v(2697)*v(353)+v(320)*(v(3046)+v(3057)+(v(2891)*v&
&(339)+v(2774)*v(352))/v(323)+v(2968)*v(7985))
v(3154)=v(3089)*v(317)+v(3067)*v(319)+v(2784)*v(324)+v(2751)*v(343)+v(2696)*v(353)+v(320)*(v(3045)+v(3056)+(v(2890)*v&
&(339)+v(2773)*v(352))/v(323)+v(2967)*v(7985))
v(3152)=v(3088)*v(317)+v(3066)*v(319)+v(2783)*v(324)+v(2750)*v(343)+v(2695)*v(353)+v(320)*(v(3044)+v(3055)+(v(2889)*v&
&(339)+v(2772)*v(352))/v(323)+v(2966)*v(7985))
v(3150)=v(3087)*v(317)+v(3065)*v(319)+v(2782)*v(324)+v(2749)*v(343)+v(2694)*v(353)+v(320)*(v(3043)+v(3054)+(v(2888)*v&
&(339)+v(2771)*v(352))/v(323)+v(2965)*v(7985))
v(3148)=v(3086)*v(317)+v(3064)*v(319)+v(2781)*v(324)+v(2748)*v(343)+v(2693)*v(353)+v(320)*(v(3042)+v(3053)+(v(2887)*v&
&(339)+v(2770)*v(352))/v(323)+v(2964)*v(7985))
v(3146)=v(3085)*v(317)+v(3063)*v(319)+v(2780)*v(324)+v(2747)*v(343)+v(2692)*v(353)+v(320)*(v(3041)+v(3052)+(v(2886)*v&
&(339)+v(2769)*v(352))/v(323)+v(2963)*v(7985))
v(3144)=v(3084)*v(317)+v(3062)*v(319)+v(2779)*v(324)+v(2746)*v(343)+v(2691)*v(353)+v(320)*(v(3040)+v(3051)+(v(2885)*v&
&(339)+v(2768)*v(352))/v(323)+v(2962)*v(7985))
v(3192)=(-1d0)+v(3144)
v(3142)=v(3083)*v(317)+v(3061)*v(319)+v(2778)*v(324)+v(2745)*v(343)+v(2690)*v(353)+v(320)*(v(3039)+v(3050)+(v(2884)*v&
&(339)+v(2767)*v(352))/v(323)+v(2961)*v(7985))
v(3140)=v(3082)*v(317)+v(3060)*v(319)+v(2777)*v(324)+v(2744)*v(343)+v(2689)*v(353)+v(320)*(v(3038)+v(3049)+(v(2883)*v&
&(339)+v(2766)*v(352))/v(323)+v(2960)*v(7985))
v(3138)=v(3081)*v(317)+v(3059)*v(319)+v(2776)*v(324)+v(2743)*v(343)+v(2688)*v(353)+v(320)*(v(3037)+v(3048)+(v(2882)*v&
&(339)+v(2765)*v(352))/v(323)+v(2959)*v(7985))
v(3136)=v(3080)*v(317)+v(3058)*v(319)+v(2775)*v(324)+v(2742)*v(343)+v(2687)*v(353)+v(320)*(v(3036)+v(3047)+(v(2881)*v&
&(339)+v(2764)*v(352))/v(323)+v(2957)*v(7985))
v(3134)=v(3079)*v(316)+v(3090)*v(318)+v(2752)*v(337)+v(2675)*v(348)+v(2719)*v(353)+v(319)*(v(3035)+v(3046)+(v(2741)*v&
&(347)+v(2916)*v(350))/v(323)+v(2968)*v(7986))
v(3132)=v(3078)*v(316)+v(3089)*v(318)+v(2751)*v(337)+v(2674)*v(348)+v(2718)*v(353)+v(319)*(v(3034)+v(3045)+(v(2740)*v&
&(347)+v(2915)*v(350))/v(323)+v(2967)*v(7986))
v(3130)=v(3077)*v(316)+v(3088)*v(318)+v(2750)*v(337)+v(2673)*v(348)+v(2717)*v(353)+v(319)*(v(3033)+v(3044)+(v(2739)*v&
&(347)+v(2914)*v(350))/v(323)+v(2966)*v(7986))
v(3128)=v(3076)*v(316)+v(3087)*v(318)+v(2749)*v(337)+v(2672)*v(348)+v(2716)*v(353)+v(319)*(v(3032)+v(3043)+(v(2738)*v&
&(347)+v(2913)*v(350))/v(323)+v(2965)*v(7986))
v(3126)=v(3075)*v(316)+v(3086)*v(318)+v(2748)*v(337)+v(2671)*v(348)+v(2715)*v(353)+v(319)*(v(3031)+v(3042)+(v(2737)*v&
&(347)+v(2912)*v(350))/v(323)+v(2964)*v(7986))
v(3124)=v(3074)*v(316)+v(3085)*v(318)+v(2747)*v(337)+v(2670)*v(348)+v(2714)*v(353)+v(319)*(v(3030)+v(3041)+(v(2736)*v&
&(347)+v(2911)*v(350))/v(323)+v(2963)*v(7986))
v(3191)=(-1d0)+v(3124)
v(3122)=v(3073)*v(316)+v(3084)*v(318)+v(2746)*v(337)+v(2669)*v(348)+v(2713)*v(353)+v(319)*(v(3029)+v(3040)+(v(2735)*v&
&(347)+v(2910)*v(350))/v(323)+v(2962)*v(7986))
v(3120)=v(3072)*v(316)+v(3083)*v(318)+v(2745)*v(337)+v(2668)*v(348)+v(2712)*v(353)+v(319)*(v(3028)+v(3039)+(v(2734)*v&
&(347)+v(2909)*v(350))/v(323)+v(2961)*v(7986))
v(3118)=v(3071)*v(316)+v(3082)*v(318)+v(2744)*v(337)+v(2667)*v(348)+v(2711)*v(353)+v(319)*(v(3027)+v(3038)+(v(2733)*v&
&(347)+v(2908)*v(350))/v(323)+v(2960)*v(7986))
v(3116)=v(3070)*v(316)+v(3081)*v(318)+v(2743)*v(337)+v(2666)*v(348)+v(2710)*v(353)+v(319)*(v(3026)+v(3037)+(v(2732)*v&
&(347)+v(2907)*v(350))/v(323)+v(2959)*v(7986))
v(3114)=v(3069)*v(316)+v(3080)*v(318)+v(2742)*v(337)+v(2665)*v(348)+v(2709)*v(353)+v(319)*(v(3025)+v(3036)+(v(2731)*v&
&(347)+v(2906)*v(350))/v(323)+v(2957)*v(7986))
v(354)=v(318)*v(331)+v(315)*v(343)+v(320)*v(348)
v(355)=v(319)*v(337)+v(316)*v(348)+v(318)*v(353)
v(356)=v(320)*v(324)+v(319)*v(343)+v(317)*v(353)
v(357)=v(359)+(2d0/3d0)*v(360)+v(362)
v(361)=(-2d0/3d0)*v(358)+v(359)+v(364)
v(365)=v(362)+(-2d0/3d0)*v(363)+v(364)
v(366)=v(354)-x(4)-x(9)
v(7988)=2d0*v(366)
v(367)=v(355)-x(11)-x(6)
v(7989)=2d0*v(367)
v(368)=v(356)-x(10)-x(5)
v(7990)=2d0*v(368)
v(3235)=v(223)*v(357)+v(227)*v(361)+v(228)*v(365)+v(366)*v(7786)+v(367)*v(7787)+v(368)*v(7788)
v(3206)=1d0/v(7987)**2
v(3216)=-(v(3204)*v(3206))
v(3215)=-(v(3203)*v(3206))
v(3214)=-(v(3202)*v(3206))
v(3213)=-(v(3201)*v(3206))
v(3212)=-(v(3200)*v(3206))
v(3211)=-(v(3199)*v(3206))
v(3210)=-(v(3198)*v(3206))
v(3209)=-(v(3197)*v(3206))
v(3208)=-(v(3196)*v(3206))
v(3207)=-(v(3195)*v(3206))
v(3205)=-(v(3194)*v(3206))
v(3246)=v(7495)*(v(3216)*v(3235)+v(3193)*(v(1577)*v(357)+v(1604)*v(361)+v(1630)*v(365)+v(3112)*v(7786)+v(3134)*v(7787)&
&+v(3156)*v(7788)+v(223)*v(7947)+v(228)*v(7948)+v(227)*v(7949)+v(1658)*v(7988)+v(1690)*v(7989)+v(1726)*v(7990)))
v(3245)=v(7495)*(v(3215)*v(3235)+v(3193)*(v(1576)*v(357)+v(1603)*v(361)+v(1629)*v(365)+v(3110)*v(7786)+v(3132)*v(7787)&
&+v(3154)*v(7788)+v(223)*v(7950)+v(228)*v(7951)+v(227)*v(7952)+v(1657)*v(7988)+v(1688)*v(7989)+v(1724)*v(7990)))
v(3244)=v(7495)*(v(3214)*v(3235)+v(3193)*(v(1575)*v(357)+v(1602)*v(361)+v(1627)*v(365)+v(3108)*v(7786)+v(3130)*v(7787)&
&+v(3152)*v(7788)+v(223)*v(7953)+v(228)*v(7954)+v(227)*v(7955)+v(1656)*v(7988)+v(1687)*v(7989)+v(1721)*v(7990)))
v(3243)=v(7495)*(v(3213)*v(3235)+v(3193)*(v(1573)*v(357)+v(1600)*v(361)+v(1626)*v(365)+v(3106)*v(7786)+v(3128)*v(7787)&
&+v(3150)*v(7788)+v(223)*v(7956)+v(228)*v(7957)+v(227)*v(7958)+v(1655)*v(7988)+v(1685)*v(7989)+v(1719)*v(7990)))
v(3242)=v(7495)*(v(3212)*v(3235)+v(3193)*(v(1572)*v(357)+v(1599)*v(361)+v(1625)*v(365)+v(3104)*v(7786)+v(3126)*v(7787)&
&+v(3148)*v(7788)+v(223)*v(7959)+v(228)*v(7960)+v(227)*v(7961)+v(1653)*v(7988)+v(1683)*v(7989)+v(1717)*v(7990)))
v(3241)=v(7495)*(v(3211)*v(3235)+v(3193)*(v(1571)*v(357)+v(1598)*v(361)+v(1624)*v(365)+v(3102)*v(7786)+v(3191)*v(7787)&
&+v(3146)*v(7788)+v(223)*v(7962)+v(228)*v(7963)+v(227)*v(7964)+v(1652)*v(7988)+v(1682)*v(7989)+v(1716)*v(7990)))
v(3240)=v(7495)*(v(3210)*v(3235)+v(3193)*(v(1570)*v(357)+v(1597)*v(361)+v(1623)*v(365)+v(3100)*v(7786)+v(3122)*v(7787)&
&+v(3192)*v(7788)+v(223)*v(7965)+v(228)*v(7966)+v(227)*v(7967)+v(1651)*v(7988)+v(1681)*v(7989)+v(1713)*v(7990)))
v(3239)=v(7495)*(v(3209)*v(3235)+v(3193)*(v(1569)*v(357)+v(1596)*v(361)+v(1622)*v(365)+v(3190)*v(7786)+v(3120)*v(7787)&
&+v(3142)*v(7788)+v(223)*v(7968)+v(228)*v(7969)+v(227)*v(7970)+v(1650)*v(7988)+v(1680)*v(7989)+v(1712)*v(7990)))
v(3238)=v(7495)*(v(3208)*v(3235)+v(3193)*(v(227)*v(3170)+v(228)*v(3181)+v(1568)*v(357)+v(1595)*v(361)+v(1621)*v(365)+v&
&(3096)*v(7786)+v(3118)*v(7787)+v(3140)*v(7788)+v(223)*v(7971)+v(1649)*v(7988)+v(1677)*v(7989)+v(1709)*v(7990)))
v(3237)=v(7495)*(v(3207)*v(3235)+v(3193)*(v(223)*v(3158)+v(228)*v(3180)+v(1566)*v(357)+v(1593)*v(361)+v(1619)*v(365)+v&
&(3094)*v(7786)+v(3116)*v(7787)+v(3138)*v(7788)+v(227)*v(7972)+v(1647)*v(7988)+v(1675)*v(7989)+v(1707)*v(7990)))
v(3236)=v(7495)*(v(3205)*v(3235)+v(3193)*(v(1565)*v(357)+v(1591)*v(361)+v(1618)*v(365)+v(3092)*v(7786)+v(3114)*v(7787)&
&+v(3136)*v(7788)+v(223)*v(7973)+v(228)*v(7974)+v(227)*v(7975)+v(1644)*v(7988)+v(1672)*v(7989)+v(1704)*v(7990)))
v(3234)=v(7495)*(v(3216)*v(3217)+v(3193)*(v(1630)*v(7531)+v(1658)*v(7991)+v(1690)*v(7992)+v(1726)*v(7993)+v(1577)*x(7)&
&+v(1604)*x(8)))
v(3233)=v(7495)*(v(3215)*v(3217)+v(3193)*(v(1629)*v(7531)+v(1657)*v(7991)+v(1688)*v(7992)+v(1724)*v(7993)+v(1576)*x(7)&
&+v(1603)*x(8)))
v(3232)=v(7495)*(v(3214)*v(3217)+v(3193)*(v(1627)*v(7531)+v(1656)*v(7991)+v(1687)*v(7992)+v(1721)*v(7993)+v(1575)*x(7)&
&+v(1602)*x(8)))
v(3231)=v(7495)*(v(3213)*v(3217)+v(3193)*(v(1626)*v(7531)+v(1655)*v(7991)+v(1685)*v(7992)+v(1719)*v(7993)+v(1573)*x(7)&
&+v(1600)*x(8)))
v(3230)=v(7495)*(v(3212)*v(3217)+v(3193)*(v(1625)*v(7531)+v(1653)*v(7991)+v(1683)*v(7992)+v(1717)*v(7993)+v(1572)*x(7)&
&+v(1599)*x(8)))
v(3227)=2d0*v(3193)*v(7495)
v(8004)=v(3227)/2d0
v(3229)=v(230)*v(3227)
v(7997)=-(v(3229)*v(7996))
v(7995)=v(3229)*v(7994)
v(3570)=v(229)*v(7995)
v(8024)=v(232)*v(3570)
v(5433)=v(3570)*v(7522)
v(3553)=v(228)*v(7995)
v(3535)=v(227)*v(7995)
v(3518)=v(223)*v(7995)
v(3316)=v(229)*v(7997)
v(8012)=v(232)*v(3316)
v(4391)=v(3316)*v(7522)
v(3300)=v(228)*v(7997)
v(3284)=v(227)*v(7997)
v(3268)=v(223)*v(7997)
v(3228)=v(231)*v(3227)
v(7999)=-(v(3228)*v(7996))
v(7998)=v(3228)*v(7994)
v(3602)=v(230)*v(7998)
v(8020)=v(232)*v(3602)
v(5436)=v(3602)*v(7522)
v(8092)=720d0*v(5436)
v(3569)=v(229)*v(7998)
v(8021)=v(232)*v(3569)
v(5197)=v(3569)*v(7522)
v(3552)=v(228)*v(7998)
v(3534)=v(227)*v(7998)
v(3517)=v(223)*v(7998)
v(3348)=v(230)*v(7999)
v(8008)=v(232)*v(3348)
v(4394)=v(3348)*v(7522)
v(8058)=720d0*v(4394)
v(3315)=v(229)*v(7999)
v(4155)=v(3315)*v(7522)
v(3299)=v(228)*v(7999)
v(3283)=v(227)*v(7999)
v(3267)=v(223)*v(7999)
v(3226)=v(229)*v(3227)
v(8001)=-(v(3226)*v(7996))
v(8000)=v(3226)*v(7994)
v(3551)=v(228)*v(8000)
v(3533)=v(227)*v(8000)
v(3516)=v(223)*v(8000)
v(3298)=v(228)*v(8001)
v(3282)=v(227)*v(8001)
v(3266)=v(223)*v(8001)
v(3225)=(v(227)-v(228))*v(8004)
v(8003)=-(v(3225)*v(7996))
v(8002)=v(3225)*v(7994)
v(3635)=v(231)*v(8002)
v(3601)=v(230)*v(8002)
v(3566)=v(229)*v(8002)
v(3515)=v(223)*v(8002)
v(3380)=v(231)*v(8003)
v(3347)=v(230)*v(8003)
v(3313)=v(229)*v(8003)
v(3265)=v(223)*v(8003)
v(3224)=(v(223)-v(228))*v(8004)
v(8006)=-(v(3224)*v(7996))
v(8005)=v(3224)*v(7994)
v(3634)=v(231)*v(8005)
v(3600)=v(230)*v(8005)
v(3565)=v(229)*v(8005)
v(3530)=v(227)*v(8005)
v(3379)=v(231)*v(8006)
v(3346)=v(230)*v(8006)
v(3312)=v(229)*v(8006)
v(3280)=v(227)*v(8006)
v(3223)=v(7495)*(v(3211)*v(3217)+v(3193)*(v(1624)*v(7531)+v(1652)*v(7991)+v(1682)*v(7992)+v(1716)*v(7993)+v(1571)*x(7)&
&+v(1598)*x(8)))
v(3222)=v(7495)*(v(3210)*v(3217)+v(3193)*(v(1623)*v(7531)+v(1651)*v(7991)+v(1681)*v(7992)+v(1713)*v(7993)+v(1570)*x(7)&
&+v(1597)*x(8)))
v(3221)=v(7495)*(v(3209)*v(3217)+v(3193)*(v(1622)*v(7531)+v(1650)*v(7991)+v(1680)*v(7992)+v(1712)*v(7993)+v(1569)*x(7)&
&+v(1596)*x(8)))
v(3220)=v(7495)*(v(3208)*v(3217)+v(3193)*(v(1621)*v(7531)+v(1649)*v(7991)+v(1677)*v(7992)+v(1709)*v(7993)+v(1568)*x(7)&
&+v(1595)*x(8)))
v(3219)=v(7495)*(v(3207)*v(3217)+v(3193)*(v(1619)*v(7531)+v(1647)*v(7991)+v(1675)*v(7992)+v(1707)*v(7993)+v(1566)*x(7)&
&+v(1593)*x(8)))
v(3218)=v(7495)*(v(3205)*v(3217)+v(3193)*(v(1618)*v(7531)+v(1644)*v(7991)+v(1672)*v(7992)+v(1704)*v(7993)+v(1565)*x(7)&
&+v(1591)*x(8)))
v(387)=(v(3217)*v(3227))/2d0
v(3642)=-v(1726)+v(7994)*(v(231)*v(3234)+v(1726)*v(387)+v(3257)*x(10))
v(3641)=-v(1724)+v(7994)*(v(231)*v(3233)+v(1724)*v(387)+v(3256)*x(10))
v(3640)=-v(1721)+v(7994)*(v(231)*v(3232)+v(1721)*v(387)+v(3255)*x(10))
v(3639)=-v(1719)+v(7994)*(v(231)*v(3231)+v(1719)*v(387)+v(3254)*x(10))
v(3638)=-v(1717)+v(7994)*(v(231)*v(3230)+v(1717)*v(387)+v(3253)*x(10))
v(3633)=-v(1716)+v(7994)*(v(231)*v(3223)+v(1716)*v(387)+v(3252)*x(10))
v(3632)=-v(1713)+v(7994)*(v(231)*v(3222)+v(1713)*v(387)+v(3251)*x(10))
v(3631)=-v(1712)+v(7994)*(v(231)*v(3221)+v(1712)*v(387)+v(3250)*x(10))
v(3630)=-v(1709)+v(7994)*(v(231)*v(3220)+v(1709)*v(387)+v(3249)*x(10))
v(3629)=-v(1707)+v(7994)*(v(231)*v(3219)+v(1707)*v(387)+v(3248)*x(10))
v(3628)=-v(1704)+v(7994)*(v(231)*v(3218)+v(1704)*v(387)+v(3247)*x(10))
v(3609)=-v(1690)+v(7994)*(v(230)*v(3234)+v(1690)*v(387)+v(3257)*x(11))
v(3608)=-v(1688)+v(7994)*(v(230)*v(3233)+v(1688)*v(387)+v(3256)*x(11))
v(3607)=-v(1687)+v(7994)*(v(230)*v(3232)+v(1687)*v(387)+v(3255)*x(11))
v(3606)=-v(1685)+v(7994)*(v(230)*v(3231)+v(1685)*v(387)+v(3254)*x(11))
v(3605)=-v(1683)+v(7994)*(v(230)*v(3230)+v(1683)*v(387)+v(3253)*x(11))
v(3599)=-v(1682)+v(7994)*(v(230)*v(3223)+v(1682)*v(387)+v(3252)*x(11))
v(3598)=-v(1681)+v(7994)*(v(230)*v(3222)+v(1681)*v(387)+v(3251)*x(11))
v(3597)=-v(1680)+v(7994)*(v(230)*v(3221)+v(1680)*v(387)+v(3250)*x(11))
v(3596)=-v(1677)+v(7994)*(v(230)*v(3220)+v(1677)*v(387)+v(3249)*x(11))
v(3595)=-v(1675)+v(7994)*(v(230)*v(3219)+v(1675)*v(387)+v(3248)*x(11))
v(3594)=-v(1672)+v(7994)*(v(230)*v(3218)+v(1672)*v(387)+v(3247)*x(11))
v(3575)=-v(1658)+v(7994)*(v(229)*v(3234)+v(1658)*v(387)+v(3257)*x(9))
v(3574)=-v(1657)+v(7994)*(v(229)*v(3233)+v(1657)*v(387)+v(3256)*x(9))
v(3573)=-v(1656)+v(7994)*(v(229)*v(3232)+v(1656)*v(387)+v(3255)*x(9))
v(3572)=-v(1655)+v(7994)*(v(229)*v(3231)+v(1655)*v(387)+v(3254)*x(9))
v(3571)=-v(1653)+v(7994)*(v(229)*v(3230)+v(1653)*v(387)+v(3253)*x(9))
v(3564)=-v(1652)+v(7994)*(v(229)*v(3223)+v(1652)*v(387)+v(3252)*x(9))
v(3563)=-v(1651)+v(7994)*(v(229)*v(3222)+v(1651)*v(387)+v(3251)*x(9))
v(3562)=-v(1650)+v(7994)*(v(229)*v(3221)+v(1650)*v(387)+v(3250)*x(9))
v(3561)=-v(1649)+v(7994)*(v(229)*v(3220)+v(1649)*v(387)+v(3249)*x(9))
v(3560)=-v(1647)+v(7994)*(v(229)*v(3219)+v(1647)*v(387)+v(3248)*x(9))
v(3559)=-v(1644)+v(7994)*(v(229)*v(3218)+v(1644)*v(387)+v(3247)*x(9))
v(3558)=-v(1630)+(v(228)*v(3234)+v(1630)*v(387)+v(3257)*v(7531))*v(7994)
v(3557)=-v(1629)+(v(228)*v(3233)+v(1629)*v(387)+v(3256)*v(7531))*v(7994)
v(3556)=-v(1627)+(v(228)*v(3232)+v(1627)*v(387)+v(3255)*v(7531))*v(7994)
v(3555)=-v(1626)+(v(228)*v(3231)+v(1626)*v(387)+v(3254)*v(7531))*v(7994)
v(3554)=-v(1625)+(v(228)*v(3230)+v(1625)*v(387)+v(3253)*v(7531))*v(7994)
v(3546)=-v(1624)+(v(228)*v(3223)+v(1624)*v(387)+v(3252)*v(7531))*v(7994)
v(3545)=-v(1623)+(v(228)*v(3222)+v(1623)*v(387)+v(3251)*v(7531))*v(7994)
v(3544)=-v(1622)+(v(228)*v(3221)+v(1622)*v(387)+v(3250)*v(7531))*v(7994)
v(3543)=-v(1621)+(v(228)*v(3220)+v(1621)*v(387)+v(3249)*v(7531))*v(7994)
v(3542)=-v(1619)+(v(228)*v(3219)+v(1619)*v(387)+v(3248)*v(7531))*v(7994)
v(3541)=-v(1618)+(v(228)*v(3218)+v(1618)*v(387)+v(3247)*v(7531))*v(7994)
v(8098)=v(3541)*v(7522)
v(3540)=-v(1604)+v(7994)*(v(227)*v(3234)+v(1604)*v(387)+v(3257)*x(8))
v(3539)=-v(1603)+v(7994)*(v(227)*v(3233)+v(1603)*v(387)+v(3256)*x(8))
v(3538)=-v(1602)+v(7994)*(v(227)*v(3232)+v(1602)*v(387)+v(3255)*x(8))
v(3537)=-v(1600)+v(7994)*(v(227)*v(3231)+v(1600)*v(387)+v(3254)*x(8))
v(3536)=-v(1599)+v(7994)*(v(227)*v(3230)+v(1599)*v(387)+v(3253)*x(8))
v(3529)=-v(1598)+v(7994)*(v(227)*v(3223)+v(1598)*v(387)+v(3252)*x(8))
v(3528)=-v(1597)+v(7994)*(v(227)*v(3222)+v(1597)*v(387)+v(3251)*x(8))
v(3527)=-v(1596)+v(7994)*(v(227)*v(3221)+v(1596)*v(387)+v(3250)*x(8))
v(3526)=-v(1595)+v(7994)*(v(227)*v(3220)+v(1595)*v(387)+v(3249)*x(8))
v(3525)=-v(1593)+v(7994)*(v(227)*v(3219)+v(1593)*v(387)+v(3248)*x(8))
v(3524)=-v(1591)+v(7994)*(v(227)*v(3218)+v(1591)*v(387)+v(3247)*x(8))
v(8091)=v(3524)*v(7522)
v(3523)=-v(1577)+v(7994)*(v(223)*v(3234)+v(1577)*v(387)+v(3257)*x(7))
v(3522)=-v(1576)+v(7994)*(v(223)*v(3233)+v(1576)*v(387)+v(3256)*x(7))
v(3521)=-v(1575)+v(7994)*(v(223)*v(3232)+v(1575)*v(387)+v(3255)*x(7))
v(3520)=-v(1573)+v(7994)*(v(223)*v(3231)+v(1573)*v(387)+v(3254)*x(7))
v(3519)=-v(1572)+v(7994)*(v(223)*v(3230)+v(1572)*v(387)+v(3253)*x(7))
v(3512)=-v(1571)+v(7994)*(v(223)*v(3223)+v(1571)*v(387)+v(3252)*x(7))
v(3511)=-v(1570)+v(7994)*(v(223)*v(3222)+v(1570)*v(387)+v(3251)*x(7))
v(3510)=-v(1569)+v(7994)*(v(223)*v(3221)+v(1569)*v(387)+v(3250)*x(7))
v(3509)=-v(1568)+v(7994)*(v(223)*v(3220)+v(1568)*v(387)+v(3249)*x(7))
v(3508)=-v(1566)+v(7994)*(v(223)*v(3219)+v(1566)*v(387)+v(3248)*x(7))
v(3507)=-v(1565)+v(7994)*(v(223)*v(3218)+v(1565)*v(387)+v(3247)*x(7))
v(8079)=v(3507)*v(7522)
v(378)=(v(3227)*v(3235))/2d0
v(377)=v(7790)*v(7987)
v(3636)=-(v(231)*v(3228))-v(377)
v(3637)=-(v(3636)*v(7994))
v(3603)=-(v(230)*v(3229))-v(377)
v(3604)=-(v(3603)*v(7994))
v(3567)=-(v(229)*v(3226))-v(377)
v(3568)=-(v(3567)*v(7994))
v(3549)=-(v(228)*v(3225))+v(377)
v(3550)=-(v(3549)*v(7994))
v(3547)=-(v(228)*v(3224))+v(377)
v(3548)=-(v(3547)*v(7994))
v(3531)=-(v(227)*v(3225))-v(377)
v(3532)=-(v(3531)*v(7994))
v(3513)=-(v(223)*v(3224))-v(377)
v(3514)=-(v(3513)*v(7994))
v(3386)=-v(1726)+(v(231)*v(3246)+v(3257)*v(368)+v(3156)*v(377)+v(1726)*v(378))*v(7996)
v(3385)=-v(1724)+(v(231)*v(3245)+v(3256)*v(368)+v(3154)*v(377)+v(1724)*v(378))*v(7996)
v(3384)=-v(1721)+(v(231)*v(3244)+v(3255)*v(368)+v(3152)*v(377)+v(1721)*v(378))*v(7996)
v(3383)=-v(1719)+(v(231)*v(3243)+v(3254)*v(368)+v(3150)*v(377)+v(1719)*v(378))*v(7996)
v(3382)=-v(1717)+(v(231)*v(3242)+v(3253)*v(368)+v(3148)*v(377)+v(1717)*v(378))*v(7996)
v(3381)=v(3636)*v(7996)
v(3378)=-v(1716)+(v(231)*v(3241)+v(3252)*v(368)+v(3146)*v(377)+v(1716)*v(378))*v(7996)
v(3377)=-v(1713)+(v(231)*v(3240)+v(3251)*v(368)+v(3192)*v(377)+v(1713)*v(378))*v(7996)
v(3376)=-v(1712)+(v(231)*v(3239)+v(3250)*v(368)+v(3142)*v(377)+v(1712)*v(378))*v(7996)
v(3375)=-v(1709)+(v(231)*v(3238)+v(3249)*v(368)+v(3140)*v(377)+v(1709)*v(378))*v(7996)
v(3374)=-v(1707)+(v(231)*v(3237)+v(3248)*v(368)+v(3138)*v(377)+v(1707)*v(378))*v(7996)
v(3373)=-v(1704)+(v(231)*v(3236)+v(3247)*v(368)+v(3136)*v(377)+v(1704)*v(378))*v(7996)
v(3354)=-v(1690)+(v(230)*v(3246)+v(3257)*v(367)+v(3134)*v(377)+v(1690)*v(378))*v(7996)
v(3353)=-v(1688)+(v(230)*v(3245)+v(3256)*v(367)+v(3132)*v(377)+v(1688)*v(378))*v(7996)
v(3352)=-v(1687)+(v(230)*v(3244)+v(3255)*v(367)+v(3130)*v(377)+v(1687)*v(378))*v(7996)
v(3351)=-v(1685)+(v(230)*v(3243)+v(3254)*v(367)+v(3128)*v(377)+v(1685)*v(378))*v(7996)
v(3350)=-v(1683)+(v(230)*v(3242)+v(3253)*v(367)+v(3126)*v(377)+v(1683)*v(378))*v(7996)
v(3349)=v(3603)*v(7996)
v(3345)=-v(1682)+(v(230)*v(3241)+v(3252)*v(367)+v(3191)*v(377)+v(1682)*v(378))*v(7996)
v(3344)=-v(1681)+(v(230)*v(3240)+v(3251)*v(367)+v(3122)*v(377)+v(1681)*v(378))*v(7996)
v(3343)=-v(1680)+(v(230)*v(3239)+v(3250)*v(367)+v(3120)*v(377)+v(1680)*v(378))*v(7996)
v(3342)=-v(1677)+(v(230)*v(3238)+v(3249)*v(367)+v(3118)*v(377)+v(1677)*v(378))*v(7996)
v(3341)=-v(1675)+(v(230)*v(3237)+v(3248)*v(367)+v(3116)*v(377)+v(1675)*v(378))*v(7996)
v(3340)=-v(1672)+(v(230)*v(3236)+v(3247)*v(367)+v(3114)*v(377)+v(1672)*v(378))*v(7996)
v(3321)=-v(1658)+(v(229)*v(3246)+v(3257)*v(366)+v(3112)*v(377)+v(1658)*v(378))*v(7996)
v(3320)=-v(1657)+(v(229)*v(3245)+v(3256)*v(366)+v(3110)*v(377)+v(1657)*v(378))*v(7996)
v(3319)=-v(1656)+(v(229)*v(3244)+v(3255)*v(366)+v(3108)*v(377)+v(1656)*v(378))*v(7996)
v(3318)=-v(1655)+(v(229)*v(3243)+v(3254)*v(366)+v(3106)*v(377)+v(1655)*v(378))*v(7996)
v(3317)=-v(1653)+(v(229)*v(3242)+v(3253)*v(366)+v(3104)*v(377)+v(1653)*v(378))*v(7996)
v(3314)=v(3567)*v(7996)
v(3311)=-v(1652)+(v(229)*v(3241)+v(3252)*v(366)+v(3102)*v(377)+v(1652)*v(378))*v(7996)
v(3310)=-v(1651)+(v(229)*v(3240)+v(3251)*v(366)+v(3100)*v(377)+v(1651)*v(378))*v(7996)
v(3309)=-v(1650)+(v(229)*v(3239)+v(3250)*v(366)+v(3190)*v(377)+v(1650)*v(378))*v(7996)
v(3308)=-v(1649)+(v(229)*v(3238)+v(3249)*v(366)+v(3096)*v(377)+v(1649)*v(378))*v(7996)
v(3307)=-v(1647)+(v(229)*v(3237)+v(3248)*v(366)+v(3094)*v(377)+v(1647)*v(378))*v(7996)
v(3306)=-v(1644)+(v(229)*v(3236)+v(3247)*v(366)+v(3092)*v(377)+v(1644)*v(378))*v(7996)
v(3305)=-v(1630)+(v(228)*v(3246)+v(3257)*v(365)+v(1630)*v(378)+v(377)*v(7948))*v(7996)
v(3304)=-v(1629)+(v(228)*v(3245)+v(3256)*v(365)+v(1629)*v(378)+v(377)*v(7951))*v(7996)
v(3303)=-v(1627)+(v(228)*v(3244)+v(3255)*v(365)+v(1627)*v(378)+v(377)*v(7954))*v(7996)
v(3302)=-v(1626)+(v(228)*v(3243)+v(3254)*v(365)+v(1626)*v(378)+v(377)*v(7957))*v(7996)
v(3301)=-v(1625)+(v(228)*v(3242)+v(3253)*v(365)+v(1625)*v(378)+v(377)*v(7960))*v(7996)
v(3297)=v(3549)*v(7996)
v(3296)=v(3547)*v(7996)
v(3295)=-v(1624)+(v(228)*v(3241)+v(3252)*v(365)+v(1624)*v(378)+v(377)*v(7963))*v(7996)
v(3294)=-v(1623)+(v(228)*v(3240)+v(3251)*v(365)+v(1623)*v(378)+v(377)*v(7966))*v(7996)
v(3293)=-v(1622)+(v(228)*v(3239)+v(3250)*v(365)+v(1622)*v(378)+v(377)*v(7969))*v(7996)
v(3292)=-v(1621)+(v(228)*v(3238)+v(3249)*v(365)+v(3181)*v(377)+v(1621)*v(378))*v(7996)
v(3291)=-v(1619)+(v(228)*v(3237)+v(3248)*v(365)+v(3180)*v(377)+v(1619)*v(378))*v(7996)
v(3290)=-v(1618)+(v(228)*v(3236)+v(3247)*v(365)+v(1618)*v(378)+v(377)*v(7974))*v(7996)
v(8064)=v(3290)*v(7522)
v(3289)=-v(1604)+(v(227)*v(3246)+v(3257)*v(361)+v(1604)*v(378)+v(377)*v(7949))*v(7996)
v(3288)=-v(1603)+(v(227)*v(3245)+v(3256)*v(361)+v(1603)*v(378)+v(377)*v(7952))*v(7996)
v(3287)=-v(1602)+(v(227)*v(3244)+v(3255)*v(361)+v(1602)*v(378)+v(377)*v(7955))*v(7996)
v(3286)=-v(1600)+(v(227)*v(3243)+v(3254)*v(361)+v(1600)*v(378)+v(377)*v(7958))*v(7996)
v(3285)=-v(1599)+(v(227)*v(3242)+v(3253)*v(361)+v(1599)*v(378)+v(377)*v(7961))*v(7996)
v(3281)=v(3531)*v(7996)
v(3279)=-v(1598)+(v(227)*v(3241)+v(3252)*v(361)+v(1598)*v(378)+v(377)*v(7964))*v(7996)
v(3278)=-v(1597)+(v(227)*v(3240)+v(3251)*v(361)+v(1597)*v(378)+v(377)*v(7967))*v(7996)
v(3277)=-v(1596)+(v(227)*v(3239)+v(3250)*v(361)+v(1596)*v(378)+v(377)*v(7970))*v(7996)
v(3276)=-v(1595)+(v(227)*v(3238)+v(3249)*v(361)+v(3170)*v(377)+v(1595)*v(378))*v(7996)
v(3275)=-v(1593)+(v(227)*v(3237)+v(3248)*v(361)+v(1593)*v(378)+v(377)*v(7972))*v(7996)
v(3274)=-v(1591)+(v(227)*v(3236)+v(3247)*v(361)+v(1591)*v(378)+v(377)*v(7975))*v(7996)
v(8057)=v(3274)*v(7522)
v(3273)=-v(1577)+(v(223)*v(3246)+v(3257)*v(357)+v(1577)*v(378)+v(377)*v(7947))*v(7996)
v(3272)=-v(1576)+(v(223)*v(3245)+v(3256)*v(357)+v(1576)*v(378)+v(377)*v(7950))*v(7996)
v(3271)=-v(1575)+(v(223)*v(3244)+v(3255)*v(357)+v(1575)*v(378)+v(377)*v(7953))*v(7996)
v(3270)=-v(1573)+(v(223)*v(3243)+v(3254)*v(357)+v(1573)*v(378)+v(377)*v(7956))*v(7996)
v(3269)=-v(1572)+(v(223)*v(3242)+v(3253)*v(357)+v(1572)*v(378)+v(377)*v(7959))*v(7996)
v(3264)=v(3513)*v(7996)
v(3263)=-v(1571)+(v(223)*v(3241)+v(3252)*v(357)+v(1571)*v(378)+v(377)*v(7962))*v(7996)
v(3262)=-v(1570)+(v(223)*v(3240)+v(3251)*v(357)+v(1570)*v(378)+v(377)*v(7965))*v(7996)
v(3261)=-v(1569)+(v(223)*v(3239)+v(3250)*v(357)+v(1569)*v(378)+v(377)*v(7968))*v(7996)
v(3260)=-v(1568)+(v(223)*v(3238)+v(3249)*v(357)+v(1568)*v(378)+v(377)*v(7971))*v(7996)
v(3259)=-v(1566)+(v(223)*v(3237)+v(3248)*v(357)+v(3158)*v(377)+v(1566)*v(378))*v(7996)
v(3258)=-v(1565)+(v(223)*v(3236)+v(3247)*v(357)+v(1565)*v(378)+v(377)*v(7973))*v(7996)
v(8045)=v(3258)*v(7522)
v(376)=-v(223)+(v(357)*v(377)+v(223)*v(378))*v(7996)
v(8037)=v(376)*v(7518)+v(8045)
v(8036)=v(376)*v(7522)
v(3765)=v(376)*v(8007)
v(3763)=(v(376)*v(376))
v(3479)=(v(3315)*v(3765))/2d0
v(379)=-v(227)+(v(361)*v(377)+v(227)*v(378))*v(7996)
v(8052)=v(379)*v(7518)+v(8057)
v(8051)=v(379)*v(7522)
v(8011)=v(376)+v(379)
v(4183)=v(379)*v(8007)
v(4181)=(v(379)*v(379))
v(3448)=v(379)*v(8012)
v(380)=-v(228)+(v(365)*v(377)+v(228)*v(378))*v(7996)
v(8062)=v(380)*v(7518)+v(8064)
v(8061)=v(380)*v(7522)
v(8013)=v(379)+v(380)
v(8010)=v(376)+v(380)
v(4453)=v(380)*v(8007)
v(4451)=(v(380)*v(380))
v(3484)=v(380)*v(8008)
v(381)=-v(229)+(v(366)*v(377)+v(229)*v(378))*v(7996)
v(8035)=v(381)*v(7518)+v(3306)*v(7522)
v(8017)=v(381)*v(7522)
v(3482)=v(381)*v(8008)
v(3324)=v(381)*v(8007)
v(3339)=v(3321)*v(3324)
v(3338)=v(3320)*v(3324)
v(3337)=v(3319)*v(3324)
v(3336)=v(3318)*v(3324)
v(3335)=v(3317)*v(3324)
v(3334)=v(3316)*v(3324)
v(3333)=v(3315)*v(3324)
v(3332)=v(3314)*v(3324)
v(3331)=v(3313)*v(3324)
v(3330)=v(3312)*v(3324)
v(3329)=v(3311)*v(3324)
v(3328)=v(3310)*v(3324)
v(3327)=v(3309)*v(3324)
v(3326)=v(3308)*v(3324)
v(3325)=v(3307)*v(3324)
v(3322)=(v(381)*v(381))
v(3323)=v(1738)*v(3322)+v(3306)*v(3324)
v(410)=v(232)*v(3322)
v(382)=-v(230)+(v(367)*v(377)+v(230)*v(378))*v(7996)
v(8050)=v(382)*v(7518)+v(3340)*v(7522)
v(8015)=v(382)*v(7522)
v(8009)=v(232)*v(382)
v(3481)=v(3315)*v(8009)
v(3357)=2d0*v(8009)
v(3372)=v(3354)*v(3357)
v(4198)=v(3339)+v(3372)+v(3289)*v(4183)
v(3371)=v(3353)*v(3357)
v(4197)=v(3338)+v(3371)+v(3288)*v(4183)
v(3370)=v(3352)*v(3357)
v(4196)=v(3337)+v(3370)+v(3287)*v(4183)
v(3369)=v(3351)*v(3357)
v(4195)=v(3336)+v(3369)+v(3286)*v(4183)
v(3368)=v(3350)*v(3357)
v(4194)=v(3335)+v(3368)+v(3285)*v(4183)
v(3367)=v(3349)*v(3357)
v(4193)=v(3334)+v(3367)+v(3284)*v(4183)
v(3366)=v(3348)*v(3357)
v(4192)=v(3333)+v(3366)+v(3283)*v(4183)
v(3365)=v(3316)*v(3357)
v(4191)=v(3332)+v(3365)+v(3282)*v(4183)
v(3364)=v(3347)*v(3357)
v(4190)=v(3331)+v(3364)+v(3281)*v(4183)
v(3363)=v(3346)*v(3357)
v(4189)=v(3330)+v(3363)+v(3280)*v(4183)
v(3362)=v(3345)*v(3357)
v(4188)=v(3329)+v(3362)+v(3279)*v(4183)
v(3361)=v(3344)*v(3357)
v(4187)=v(3328)+v(3361)+v(3278)*v(4183)
v(3360)=v(3343)*v(3357)
v(4186)=v(3327)+v(3360)+v(3277)*v(4183)
v(3359)=v(3342)*v(3357)
v(4185)=v(3326)+v(3359)+v(3276)*v(4183)
v(3358)=v(3341)*v(3357)
v(4184)=v(3325)+v(3358)+v(3275)*v(4183)
v(3355)=(v(382)*v(382))
v(3356)=v(1738)*v(3355)+v(3340)*v(3357)
v(4182)=v(3323)+v(3356)+v(1738)*v(4181)+v(3274)*v(4183)
v(427)=v(232)*v(3355)
v(383)=-v(231)+(v(368)*v(377)+v(231)*v(378))*v(7996)
v(8033)=v(383)*v(7518)+v(3373)*v(7522)
v(8019)=v(383)*v(7522)
v(8018)=v(381)*v(382)+v(383)*v(8010)
v(8016)=v(382)*v(383)+v(381)*v(8011)
v(8014)=v(381)*v(383)+v(382)*v(8013)
v(3490)=v(232)*(v(3354)*v(381)+v(3321)*v(382)+(v(3273)+v(3305))*v(383)+v(3386)*v(8010))
v(3489)=v(232)*(v(3353)*v(381)+v(3320)*v(382)+(v(3272)+v(3304))*v(383)+v(3385)*v(8010))
v(3488)=v(232)*(v(3352)*v(381)+v(3319)*v(382)+(v(3271)+v(3303))*v(383)+v(3384)*v(8010))
v(3487)=v(232)*(v(3351)*v(381)+v(3318)*v(382)+(v(3270)+v(3302))*v(383)+v(3383)*v(8010))
v(3486)=v(232)*(v(3350)*v(381)+v(3317)*v(382)+(v(3269)+v(3301))*v(383)+v(3382)*v(8010))
v(3485)=v(3484)+v(232)*(v(3348)*v(376)+v(3349)*v(381)+v(3316)*v(382)+(v(3268)+v(3300))*v(383))
v(3483)=v(3481)+v(3482)+v(232)*((v(3267)+v(3299))*v(383)+v(3381)*v(8010))
v(3480)=v(3479)+v(232)*(v(3315)*v(380)+v(3316)*v(381)+v(3314)*v(382)+(v(3266)+v(3298))*v(383))
v(3478)=v(232)*(v(3347)*v(381)+v(3313)*v(382)+(v(3265)+v(3297))*v(383)+v(3380)*v(8010))
v(3477)=v(232)*(v(3346)*v(381)+v(3312)*v(382)+(v(3264)+v(3296))*v(383)+v(3379)*v(8010))
v(3476)=v(232)*(v(3345)*v(381)+v(3311)*v(382)+(v(3263)+v(3295))*v(383)+v(3378)*v(8010))
v(3475)=v(232)*(v(3344)*v(381)+v(3310)*v(382)+(v(3262)+v(3294))*v(383)+v(3377)*v(8010))
v(3474)=v(232)*(v(3343)*v(381)+v(3309)*v(382)+(v(3261)+v(3293))*v(383)+v(3376)*v(8010))
v(3473)=v(232)*(v(3342)*v(381)+v(3308)*v(382)+(v(3260)+v(3292))*v(383)+v(3375)*v(8010))
v(3472)=v(232)*(v(3341)*v(381)+v(3307)*v(382)+(v(3259)+v(3291))*v(383)+v(3374)*v(8010))
v(3471)=v(232)*(v(3340)*v(381)+v(3306)*v(382)+(v(3258)+v(3290))*v(383)+v(3373)*v(8010))+v(1738)*v(8018)
v(3454)=v(232)*((v(3273)+v(3289))*v(381)+v(3386)*v(382)+v(3354)*v(383)+v(3321)*v(8011))
v(3453)=v(232)*((v(3272)+v(3288))*v(381)+v(3385)*v(382)+v(3353)*v(383)+v(3320)*v(8011))
v(3452)=v(232)*((v(3271)+v(3287))*v(381)+v(3384)*v(382)+v(3352)*v(383)+v(3319)*v(8011))
v(3451)=v(232)*((v(3270)+v(3286))*v(381)+v(3383)*v(382)+v(3351)*v(383)+v(3318)*v(8011))
v(3450)=v(232)*((v(3269)+v(3285))*v(381)+v(3382)*v(382)+v(3350)*v(383)+v(3317)*v(8011))
v(3449)=v(3448)+v(232)*(v(3316)*v(376)+(v(3268)+v(3284))*v(381)+v(3348)*v(382)+v(3349)*v(383))
v(3447)=v(3479)+v(232)*(v(3315)*v(379)+(v(3267)+v(3283))*v(381)+v(3381)*v(382)+v(3348)*v(383))
v(3445)=v(383)*v(8012)
v(3446)=v(3445)+v(3481)+v(232)*((v(3266)+v(3282))*v(381)+v(3314)*v(8011))
v(3444)=v(232)*((v(3265)+v(3281))*v(381)+v(3380)*v(382)+v(3347)*v(383)+v(3313)*v(8011))
v(3443)=v(232)*((v(3264)+v(3280))*v(381)+v(3379)*v(382)+v(3346)*v(383)+v(3312)*v(8011))
v(3442)=v(232)*((v(3263)+v(3279))*v(381)+v(3378)*v(382)+v(3345)*v(383)+v(3311)*v(8011))
v(3441)=v(232)*((v(3262)+v(3278))*v(381)+v(3377)*v(382)+v(3344)*v(383)+v(3310)*v(8011))
v(3440)=v(232)*((v(3261)+v(3277))*v(381)+v(3376)*v(382)+v(3343)*v(383)+v(3309)*v(8011))
v(3439)=v(232)*((v(3260)+v(3276))*v(381)+v(3375)*v(382)+v(3342)*v(383)+v(3308)*v(8011))
v(3438)=v(232)*((v(3259)+v(3275))*v(381)+v(3374)*v(382)+v(3341)*v(383)+v(3307)*v(8011))
v(3437)=v(232)*((v(3258)+v(3274))*v(381)+v(3373)*v(382)+v(3340)*v(383)+v(3306)*v(8011))+v(1738)*v(8016)
v(3420)=v(232)*(v(3386)*v(381)+(v(3289)+v(3305))*v(382)+v(3321)*v(383)+v(3354)*v(8013))
v(3419)=v(232)*(v(3385)*v(381)+(v(3288)+v(3304))*v(382)+v(3320)*v(383)+v(3353)*v(8013))
v(3418)=v(232)*(v(3384)*v(381)+(v(3287)+v(3303))*v(382)+v(3319)*v(383)+v(3352)*v(8013))
v(3417)=v(232)*(v(3383)*v(381)+(v(3286)+v(3302))*v(382)+v(3318)*v(383)+v(3351)*v(8013))
v(3416)=v(232)*(v(3382)*v(381)+(v(3285)+v(3301))*v(382)+v(3317)*v(383)+v(3350)*v(8013))
v(3415)=v(3445)+v(3482)+v(232)*((v(3284)+v(3300))*v(382)+v(3349)*v(8013))
v(3414)=v(3484)+v(232)*(v(3348)*v(379)+v(3381)*v(381)+(v(3283)+v(3299))*v(382)+v(3315)*v(383))
v(3413)=v(3448)+v(232)*(v(3316)*v(380)+v(3315)*v(381)+(v(3282)+v(3298))*v(382)+v(3314)*v(383))
v(3412)=v(232)*(v(3380)*v(381)+(v(3281)+v(3297))*v(382)+v(3313)*v(383)+v(3347)*v(8013))
v(3411)=v(232)*(v(3379)*v(381)+(v(3280)+v(3296))*v(382)+v(3312)*v(383)+v(3346)*v(8013))
v(3410)=v(232)*(v(3378)*v(381)+(v(3279)+v(3295))*v(382)+v(3311)*v(383)+v(3345)*v(8013))
v(3409)=v(232)*(v(3377)*v(381)+(v(3278)+v(3294))*v(382)+v(3310)*v(383)+v(3344)*v(8013))
v(3408)=v(232)*(v(3376)*v(381)+(v(3277)+v(3293))*v(382)+v(3309)*v(383)+v(3343)*v(8013))
v(3407)=v(232)*(v(3375)*v(381)+(v(3276)+v(3292))*v(382)+v(3308)*v(383)+v(3342)*v(8013))
v(3406)=v(232)*(v(3374)*v(381)+(v(3275)+v(3291))*v(382)+v(3307)*v(383)+v(3341)*v(8013))
v(3405)=v(232)*(v(3373)*v(381)+(v(3274)+v(3290))*v(382)+v(3306)*v(383)+v(3340)*v(8013))+v(1738)*v(8014)
v(3389)=v(383)*v(8007)
v(3404)=v(3386)*v(3389)
v(4468)=v(3372)+v(3404)+v(3305)*v(4453)
v(3780)=v(3339)+v(3404)+v(3273)*v(3765)
v(3403)=v(3385)*v(3389)
v(4467)=v(3371)+v(3403)+v(3304)*v(4453)
v(3779)=v(3338)+v(3403)+v(3272)*v(3765)
v(3402)=v(3384)*v(3389)
v(4466)=v(3370)+v(3402)+v(3303)*v(4453)
v(3778)=v(3337)+v(3402)+v(3271)*v(3765)
v(3401)=v(3383)*v(3389)
v(4465)=v(3369)+v(3401)+v(3302)*v(4453)
v(3777)=v(3336)+v(3401)+v(3270)*v(3765)
v(3400)=v(3382)*v(3389)
v(4464)=v(3368)+v(3400)+v(3301)*v(4453)
v(3776)=v(3335)+v(3400)+v(3269)*v(3765)
v(3399)=v(3348)*v(3389)
v(4463)=v(3367)+v(3399)+v(3300)*v(4453)
v(3775)=v(3334)+v(3399)+v(3268)*v(3765)
v(3398)=v(3381)*v(3389)
v(4462)=v(3366)+v(3398)+v(3299)*v(4453)
v(3774)=v(3333)+v(3398)+v(3267)*v(3765)
v(3397)=v(3315)*v(3389)
v(4461)=v(3365)+v(3397)+v(3298)*v(4453)
v(3773)=v(3332)+v(3397)+v(3266)*v(3765)
v(3396)=v(3380)*v(3389)
v(4460)=v(3364)+v(3396)+v(3297)*v(4453)
v(3772)=v(3331)+v(3396)+v(3265)*v(3765)
v(3395)=v(3379)*v(3389)
v(4459)=v(3363)+v(3395)+v(3296)*v(4453)
v(3771)=v(3330)+v(3395)+v(3264)*v(3765)
v(3394)=v(3378)*v(3389)
v(4458)=v(3362)+v(3394)+v(3295)*v(4453)
v(3770)=v(3329)+v(3394)+v(3263)*v(3765)
v(3393)=v(3377)*v(3389)
v(4457)=v(3361)+v(3393)+v(3294)*v(4453)
v(3769)=v(3328)+v(3393)+v(3262)*v(3765)
v(3392)=v(3376)*v(3389)
v(4456)=v(3360)+v(3392)+v(3293)*v(4453)
v(3768)=v(3327)+v(3392)+v(3261)*v(3765)
v(3391)=v(3375)*v(3389)
v(4455)=v(3359)+v(3391)+v(3292)*v(4453)
v(3767)=v(3326)+v(3391)+v(3260)*v(3765)
v(3390)=v(3374)*v(3389)
v(4454)=v(3358)+v(3390)+v(3291)*v(4453)
v(3766)=v(3325)+v(3390)+v(3259)*v(3765)
v(3387)=(v(383)*v(383))
v(3388)=v(1738)*v(3387)+v(3373)*v(3389)
v(4452)=v(3356)+v(3388)+v(1738)*v(4451)+v(3290)*v(4453)
v(3764)=v(3323)+v(3388)+v(1738)*v(3763)+v(3258)*v(3765)
v(428)=v(232)*v(3387)
v(415)=v(232)*v(8014)
v(3436)=(v(3420)*v(382)+v(3354)*v(415))*v(7522)
v(3435)=(v(3419)*v(382)+v(3353)*v(415))*v(7522)
v(3434)=(v(3418)*v(382)+v(3352)*v(415))*v(7522)
v(3433)=(v(3417)*v(382)+v(3351)*v(415))*v(7522)
v(3432)=(v(3416)*v(382)+v(3350)*v(415))*v(7522)
v(3431)=(v(3415)*v(382)+v(3349)*v(415))*v(7522)
v(3430)=(v(3414)*v(382)+v(3348)*v(415))*v(7522)
v(3429)=(v(3413)*v(382)+v(3316)*v(415))*v(7522)
v(3428)=(v(3412)*v(382)+v(3347)*v(415))*v(7522)
v(3427)=(v(3411)*v(382)+v(3346)*v(415))*v(7522)
v(3426)=(v(3410)*v(382)+v(3345)*v(415))*v(7522)
v(3425)=(v(3409)*v(382)+v(3344)*v(415))*v(7522)
v(3424)=(v(3408)*v(382)+v(3343)*v(415))*v(7522)
v(3423)=(v(3407)*v(382)+v(3342)*v(415))*v(7522)
v(3422)=(v(3406)*v(382)+v(3341)*v(415))*v(7522)
v(3421)=v(3405)*v(8015)+v(415)*v(8050)
v(431)=v(415)*v(8015)
v(396)=v(232)*v(8016)
v(4210)=v(396)*v(4394)
v(4207)=v(396)*v(4155)
v(3789)=v(396)*v(4391)
v(3470)=(v(3454)*v(381)+v(3321)*v(396))*v(7522)
v(3469)=(v(3453)*v(381)+v(3320)*v(396))*v(7522)
v(3468)=(v(3452)*v(381)+v(3319)*v(396))*v(7522)
v(3467)=(v(3451)*v(381)+v(3318)*v(396))*v(7522)
v(3466)=(v(3450)*v(381)+v(3317)*v(396))*v(7522)
v(3465)=v(3789)+v(3449)*v(8017)
v(3464)=v(4207)+v(3447)*v(8017)
v(3463)=(v(3446)*v(381)+v(3314)*v(396))*v(7522)
v(3462)=(v(3444)*v(381)+v(3313)*v(396))*v(7522)
v(3461)=(v(3443)*v(381)+v(3312)*v(396))*v(7522)
v(3460)=(v(3442)*v(381)+v(3311)*v(396))*v(7522)
v(3459)=(v(3441)*v(381)+v(3310)*v(396))*v(7522)
v(3458)=(v(3440)*v(381)+v(3309)*v(396))*v(7522)
v(3457)=(v(3439)*v(381)+v(3308)*v(396))*v(7522)
v(3456)=(v(3438)*v(381)+v(3307)*v(396))*v(7522)
v(3455)=v(3437)*v(8017)+v(396)*v(8035)
v(412)=v(396)*v(8017)
v(395)=v(232)*v(8018)
v(3824)=v(395)*v(4394)
v(3506)=(v(3490)*v(383)+v(3386)*v(395))*v(7522)
v(3505)=(v(3489)*v(383)+v(3385)*v(395))*v(7522)
v(3504)=(v(3488)*v(383)+v(3384)*v(395))*v(7522)
v(3503)=(v(3487)*v(383)+v(3383)*v(395))*v(7522)
v(3502)=(v(3486)*v(383)+v(3382)*v(395))*v(7522)
v(3501)=v(3824)+v(3485)*v(8019)
v(3500)=(v(3483)*v(383)+v(3381)*v(395))*v(7522)
v(3499)=(v(3480)*v(383)+v(3315)*v(395))*v(7522)
v(3498)=(v(3478)*v(383)+v(3380)*v(395))*v(7522)
v(3497)=(v(3477)*v(383)+v(3379)*v(395))*v(7522)
v(3496)=(v(3476)*v(383)+v(3378)*v(395))*v(7522)
v(3495)=(v(3475)*v(383)+v(3377)*v(395))*v(7522)
v(3494)=(v(3474)*v(383)+v(3376)*v(395))*v(7522)
v(3493)=(v(3473)*v(383)+v(3375)*v(395))*v(7522)
v(3492)=(v(3472)*v(383)+v(3374)*v(395))*v(7522)
v(3491)=v(3471)*v(8019)+v(395)*v(8033)
v(430)=v(395)*v(8019)
v(386)=-v(223)+v(7994)*(v(223)*v(387)+v(377)*x(7))
v(8071)=v(386)*v(7518)+v(8079)
v(8070)=v(386)*v(7522)
v(4807)=v(386)*v(8007)
v(4805)=(v(386)*v(386))
v(3735)=v(386)*v(8021)
v(388)=-v(227)+v(7994)*(v(227)*v(387)+v(377)*x(8))
v(8086)=v(388)*v(7518)+v(8091)
v(8085)=v(388)*v(7522)
v(8023)=v(386)+v(388)
v(5225)=v(388)*v(8007)
v(5223)=(v(388)*v(388))
v(3704)=v(388)*v(8024)
v(389)=-v(228)+(v(228)*v(387)+v(377)*v(7531))*v(7994)
v(8096)=v(389)*v(7518)+v(8098)
v(8095)=v(389)*v(7522)
v(8025)=v(388)+v(389)
v(8022)=v(386)+v(389)
v(5495)=v(389)*v(8007)
v(5493)=(v(389)*v(389))
v(3740)=v(389)*v(8020)
v(390)=-v(229)+v(7994)*(v(229)*v(387)+v(377)*x(9))
v(8069)=v(390)*v(7518)+v(3559)*v(7522)
v(8029)=v(390)*v(7522)
v(3738)=v(390)*v(8020)
v(3578)=v(390)*v(8007)
v(3593)=v(3575)*v(3578)
v(3592)=v(3574)*v(3578)
v(3591)=v(3573)*v(3578)
v(3590)=v(3572)*v(3578)
v(3589)=v(3571)*v(3578)
v(3588)=v(3570)*v(3578)
v(3587)=v(3569)*v(3578)
v(3586)=v(3568)*v(3578)
v(3585)=v(3566)*v(3578)
v(3584)=v(3565)*v(3578)
v(3583)=v(3564)*v(3578)
v(3582)=v(3563)*v(3578)
v(3581)=v(3562)*v(3578)
v(3580)=v(3561)*v(3578)
v(3579)=v(3560)*v(3578)
v(3576)=(v(390)*v(390))
v(3577)=v(1738)*v(3576)+v(3559)*v(3578)
v(473)=v(232)*v(3576)
v(391)=-v(230)+v(7994)*(v(230)*v(387)+v(377)*x(11))
v(8084)=v(391)*v(7518)+v(3594)*v(7522)
v(8027)=v(391)*v(7522)
v(3737)=v(391)*v(8021)
v(3612)=v(391)*v(8007)
v(3627)=v(3609)*v(3612)
v(5240)=v(3593)+v(3627)+v(3540)*v(5225)
v(3626)=v(3608)*v(3612)
v(5239)=v(3592)+v(3626)+v(3539)*v(5225)
v(3625)=v(3607)*v(3612)
v(5238)=v(3591)+v(3625)+v(3538)*v(5225)
v(3624)=v(3606)*v(3612)
v(5237)=v(3590)+v(3624)+v(3537)*v(5225)
v(3623)=v(3605)*v(3612)
v(5236)=v(3589)+v(3623)+v(3536)*v(5225)
v(3622)=v(3604)*v(3612)
v(5235)=v(3588)+v(3622)+v(3535)*v(5225)
v(3621)=v(3602)*v(3612)
v(5234)=v(3587)+v(3621)+v(3534)*v(5225)
v(3620)=v(3570)*v(3612)
v(5233)=v(3586)+v(3620)+v(3533)*v(5225)
v(3619)=v(3601)*v(3612)
v(5232)=v(3585)+v(3619)+v(3532)*v(5225)
v(3618)=v(3600)*v(3612)
v(5231)=v(3584)+v(3618)+v(3530)*v(5225)
v(3617)=v(3599)*v(3612)
v(5230)=v(3583)+v(3617)+v(3529)*v(5225)
v(3616)=v(3598)*v(3612)
v(5229)=v(3582)+v(3616)+v(3528)*v(5225)
v(3615)=v(3597)*v(3612)
v(5228)=v(3581)+v(3615)+v(3527)*v(5225)
v(3614)=v(3596)*v(3612)
v(5227)=v(3580)+v(3614)+v(3526)*v(5225)
v(3613)=v(3595)*v(3612)
v(5226)=v(3579)+v(3613)+v(3525)*v(5225)
v(3610)=(v(391)*v(391))
v(3611)=v(1738)*v(3610)+v(3594)*v(3612)
v(5224)=v(3577)+v(3611)+v(1738)*v(5223)+v(3524)*v(5225)
v(490)=v(232)*v(3610)
v(392)=-v(231)+v(7994)*(v(231)*v(387)+v(377)*x(10))
v(8067)=v(392)*v(7518)+v(3628)*v(7522)
v(8031)=v(392)*v(7522)
v(8030)=v(390)*v(391)+v(392)*v(8022)
v(8028)=v(391)*v(392)+v(390)*v(8023)
v(8026)=v(390)*v(392)+v(391)*v(8025)
v(3746)=v(232)*(v(3609)*v(390)+v(3575)*v(391)+(v(3523)+v(3558))*v(392)+v(3642)*v(8022))
v(3745)=v(232)*(v(3608)*v(390)+v(3574)*v(391)+(v(3522)+v(3557))*v(392)+v(3641)*v(8022))
v(3744)=v(232)*(v(3607)*v(390)+v(3573)*v(391)+(v(3521)+v(3556))*v(392)+v(3640)*v(8022))
v(3743)=v(232)*(v(3606)*v(390)+v(3572)*v(391)+(v(3520)+v(3555))*v(392)+v(3639)*v(8022))
v(3742)=v(232)*(v(3605)*v(390)+v(3571)*v(391)+(v(3519)+v(3554))*v(392)+v(3638)*v(8022))
v(3741)=v(3740)+v(232)*(v(3602)*v(386)+v(3604)*v(390)+v(3570)*v(391)+(v(3518)+v(3553))*v(392))
v(3739)=v(3737)+v(3738)+v(232)*((v(3517)+v(3552))*v(392)+v(3637)*v(8022))
v(3736)=v(3735)+v(232)*(v(3569)*v(389)+v(3570)*v(390)+v(3568)*v(391)+(v(3516)+v(3551))*v(392))
v(3734)=v(232)*(v(3601)*v(390)+v(3566)*v(391)+(v(3515)+v(3550))*v(392)+v(3635)*v(8022))
v(3733)=v(232)*(v(3600)*v(390)+v(3565)*v(391)+(v(3514)+v(3548))*v(392)+v(3634)*v(8022))
v(3732)=v(232)*(v(3599)*v(390)+v(3564)*v(391)+(v(3512)+v(3546))*v(392)+v(3633)*v(8022))
v(3731)=v(232)*(v(3598)*v(390)+v(3563)*v(391)+(v(3511)+v(3545))*v(392)+v(3632)*v(8022))
v(3730)=v(232)*(v(3597)*v(390)+v(3562)*v(391)+(v(3510)+v(3544))*v(392)+v(3631)*v(8022))
v(3729)=v(232)*(v(3596)*v(390)+v(3561)*v(391)+(v(3509)+v(3543))*v(392)+v(3630)*v(8022))
v(3728)=v(232)*(v(3595)*v(390)+v(3560)*v(391)+(v(3508)+v(3542))*v(392)+v(3629)*v(8022))
v(3727)=v(232)*(v(3594)*v(390)+v(3559)*v(391)+(v(3507)+v(3541))*v(392)+v(3628)*v(8022))+v(1738)*v(8030)
v(3710)=v(232)*((v(3523)+v(3540))*v(390)+v(3642)*v(391)+v(3609)*v(392)+v(3575)*v(8023))
v(3709)=v(232)*((v(3522)+v(3539))*v(390)+v(3641)*v(391)+v(3608)*v(392)+v(3574)*v(8023))
v(3708)=v(232)*((v(3521)+v(3538))*v(390)+v(3640)*v(391)+v(3607)*v(392)+v(3573)*v(8023))
v(3707)=v(232)*((v(3520)+v(3537))*v(390)+v(3639)*v(391)+v(3606)*v(392)+v(3572)*v(8023))
v(3706)=v(232)*((v(3519)+v(3536))*v(390)+v(3638)*v(391)+v(3605)*v(392)+v(3571)*v(8023))
v(3705)=v(3704)+v(232)*(v(3570)*v(386)+(v(3518)+v(3535))*v(390)+v(3602)*v(391)+v(3604)*v(392))
v(3703)=v(3735)+v(232)*(v(3569)*v(388)+(v(3517)+v(3534))*v(390)+v(3637)*v(391)+v(3602)*v(392))
v(3701)=v(392)*v(8024)
v(3702)=v(3701)+v(3737)+v(232)*((v(3516)+v(3533))*v(390)+v(3568)*v(8023))
v(3700)=v(232)*((v(3515)+v(3532))*v(390)+v(3635)*v(391)+v(3601)*v(392)+v(3566)*v(8023))
v(3699)=v(232)*((v(3514)+v(3530))*v(390)+v(3634)*v(391)+v(3600)*v(392)+v(3565)*v(8023))
v(3698)=v(232)*((v(3512)+v(3529))*v(390)+v(3633)*v(391)+v(3599)*v(392)+v(3564)*v(8023))
v(3697)=v(232)*((v(3511)+v(3528))*v(390)+v(3632)*v(391)+v(3598)*v(392)+v(3563)*v(8023))
v(3696)=v(232)*((v(3510)+v(3527))*v(390)+v(3631)*v(391)+v(3597)*v(392)+v(3562)*v(8023))
v(3695)=v(232)*((v(3509)+v(3526))*v(390)+v(3630)*v(391)+v(3596)*v(392)+v(3561)*v(8023))
v(3694)=v(232)*((v(3508)+v(3525))*v(390)+v(3629)*v(391)+v(3595)*v(392)+v(3560)*v(8023))
v(3693)=v(232)*((v(3507)+v(3524))*v(390)+v(3628)*v(391)+v(3594)*v(392)+v(3559)*v(8023))+v(1738)*v(8028)
v(3676)=v(232)*(v(3642)*v(390)+(v(3540)+v(3558))*v(391)+v(3575)*v(392)+v(3609)*v(8025))
v(3675)=v(232)*(v(3641)*v(390)+(v(3539)+v(3557))*v(391)+v(3574)*v(392)+v(3608)*v(8025))
v(3674)=v(232)*(v(3640)*v(390)+(v(3538)+v(3556))*v(391)+v(3573)*v(392)+v(3607)*v(8025))
v(3673)=v(232)*(v(3639)*v(390)+(v(3537)+v(3555))*v(391)+v(3572)*v(392)+v(3606)*v(8025))
v(3672)=v(232)*(v(3638)*v(390)+(v(3536)+v(3554))*v(391)+v(3571)*v(392)+v(3605)*v(8025))
v(3671)=v(3701)+v(3738)+v(232)*((v(3535)+v(3553))*v(391)+v(3604)*v(8025))
v(3670)=v(3740)+v(232)*(v(3602)*v(388)+v(3637)*v(390)+(v(3534)+v(3552))*v(391)+v(3569)*v(392))
v(3669)=v(3704)+v(232)*(v(3570)*v(389)+v(3569)*v(390)+(v(3533)+v(3551))*v(391)+v(3568)*v(392))
v(3668)=v(232)*(v(3635)*v(390)+(v(3532)+v(3550))*v(391)+v(3566)*v(392)+v(3601)*v(8025))
v(3667)=v(232)*(v(3634)*v(390)+(v(3530)+v(3548))*v(391)+v(3565)*v(392)+v(3600)*v(8025))
v(3666)=v(232)*(v(3633)*v(390)+(v(3529)+v(3546))*v(391)+v(3564)*v(392)+v(3599)*v(8025))
v(3665)=v(232)*(v(3632)*v(390)+(v(3528)+v(3545))*v(391)+v(3563)*v(392)+v(3598)*v(8025))
v(3664)=v(232)*(v(3631)*v(390)+(v(3527)+v(3544))*v(391)+v(3562)*v(392)+v(3597)*v(8025))
v(3663)=v(232)*(v(3630)*v(390)+(v(3526)+v(3543))*v(391)+v(3561)*v(392)+v(3596)*v(8025))
v(3662)=v(232)*(v(3629)*v(390)+(v(3525)+v(3542))*v(391)+v(3560)*v(392)+v(3595)*v(8025))
v(3661)=v(232)*(v(3628)*v(390)+(v(3524)+v(3541))*v(391)+v(3559)*v(392)+v(3594)*v(8025))+v(1738)*v(8026)
v(3645)=v(392)*v(8007)
v(3660)=v(3642)*v(3645)
v(5510)=v(3627)+v(3660)+v(3558)*v(5495)
v(4822)=v(3593)+v(3660)+v(3523)*v(4807)
v(3659)=v(3641)*v(3645)
v(5509)=v(3626)+v(3659)+v(3557)*v(5495)
v(4821)=v(3592)+v(3659)+v(3522)*v(4807)
v(3658)=v(3640)*v(3645)
v(5508)=v(3625)+v(3658)+v(3556)*v(5495)
v(4820)=v(3591)+v(3658)+v(3521)*v(4807)
v(3657)=v(3639)*v(3645)
v(5507)=v(3624)+v(3657)+v(3555)*v(5495)
v(4819)=v(3590)+v(3657)+v(3520)*v(4807)
v(3656)=v(3638)*v(3645)
v(5506)=v(3623)+v(3656)+v(3554)*v(5495)
v(4818)=v(3589)+v(3656)+v(3519)*v(4807)
v(3655)=v(3602)*v(3645)
v(5505)=v(3622)+v(3655)+v(3553)*v(5495)
v(4817)=v(3588)+v(3655)+v(3518)*v(4807)
v(3654)=v(3637)*v(3645)
v(5504)=v(3621)+v(3654)+v(3552)*v(5495)
v(4816)=v(3587)+v(3654)+v(3517)*v(4807)
v(3653)=v(3569)*v(3645)
v(5503)=v(3620)+v(3653)+v(3551)*v(5495)
v(4815)=v(3586)+v(3653)+v(3516)*v(4807)
v(3652)=v(3635)*v(3645)
v(5502)=v(3619)+v(3652)+v(3550)*v(5495)
v(4814)=v(3585)+v(3652)+v(3515)*v(4807)
v(3651)=v(3634)*v(3645)
v(5501)=v(3618)+v(3651)+v(3548)*v(5495)
v(4813)=v(3584)+v(3651)+v(3514)*v(4807)
v(3650)=v(3633)*v(3645)
v(5500)=v(3617)+v(3650)+v(3546)*v(5495)
v(4812)=v(3583)+v(3650)+v(3512)*v(4807)
v(3649)=v(3632)*v(3645)
v(5499)=v(3616)+v(3649)+v(3545)*v(5495)
v(4811)=v(3582)+v(3649)+v(3511)*v(4807)
v(3648)=v(3631)*v(3645)
v(5498)=v(3615)+v(3648)+v(3544)*v(5495)
v(4810)=v(3581)+v(3648)+v(3510)*v(4807)
v(3647)=v(3630)*v(3645)
v(5497)=v(3614)+v(3647)+v(3543)*v(5495)
v(4809)=v(3580)+v(3647)+v(3509)*v(4807)
v(3646)=v(3629)*v(3645)
v(5496)=v(3613)+v(3646)+v(3542)*v(5495)
v(4808)=v(3579)+v(3646)+v(3508)*v(4807)
v(3643)=(v(392)*v(392))
v(3644)=v(1738)*v(3643)+v(3628)*v(3645)
v(5494)=v(3611)+v(3644)+v(1738)*v(5493)+v(3541)*v(5495)
v(4806)=v(3577)+v(3644)+v(1738)*v(4805)+v(3507)*v(4807)
v(491)=v(232)*v(3643)
v(478)=v(232)*v(8026)
v(3692)=(v(3676)*v(391)+v(3609)*v(478))*v(7522)
v(3691)=(v(3675)*v(391)+v(3608)*v(478))*v(7522)
v(3690)=(v(3674)*v(391)+v(3607)*v(478))*v(7522)
v(3689)=(v(3673)*v(391)+v(3606)*v(478))*v(7522)
v(3688)=(v(3672)*v(391)+v(3605)*v(478))*v(7522)
v(3687)=(v(3671)*v(391)+v(3604)*v(478))*v(7522)
v(3686)=(v(3670)*v(391)+v(3602)*v(478))*v(7522)
v(3685)=(v(3669)*v(391)+v(3570)*v(478))*v(7522)
v(3684)=(v(3668)*v(391)+v(3601)*v(478))*v(7522)
v(3683)=(v(3667)*v(391)+v(3600)*v(478))*v(7522)
v(3682)=(v(3666)*v(391)+v(3599)*v(478))*v(7522)
v(3681)=(v(3665)*v(391)+v(3598)*v(478))*v(7522)
v(3680)=(v(3664)*v(391)+v(3597)*v(478))*v(7522)
v(3679)=(v(3663)*v(391)+v(3596)*v(478))*v(7522)
v(3678)=(v(3662)*v(391)+v(3595)*v(478))*v(7522)
v(3677)=v(3661)*v(8027)+v(478)*v(8084)
v(494)=v(478)*v(8027)
v(459)=v(232)*v(8028)
v(5252)=v(459)*v(5436)
v(5249)=v(459)*v(5197)
v(4831)=v(459)*v(5433)
v(3726)=(v(3710)*v(390)+v(3575)*v(459))*v(7522)
v(3725)=(v(3709)*v(390)+v(3574)*v(459))*v(7522)
v(3724)=(v(3708)*v(390)+v(3573)*v(459))*v(7522)
v(3723)=(v(3707)*v(390)+v(3572)*v(459))*v(7522)
v(3722)=(v(3706)*v(390)+v(3571)*v(459))*v(7522)
v(3721)=v(4831)+v(3705)*v(8029)
v(3720)=v(5249)+v(3703)*v(8029)
v(3719)=(v(3702)*v(390)+v(3568)*v(459))*v(7522)
v(3718)=(v(3700)*v(390)+v(3566)*v(459))*v(7522)
v(3717)=(v(3699)*v(390)+v(3565)*v(459))*v(7522)
v(3716)=(v(3698)*v(390)+v(3564)*v(459))*v(7522)
v(3715)=(v(3697)*v(390)+v(3563)*v(459))*v(7522)
v(3714)=(v(3696)*v(390)+v(3562)*v(459))*v(7522)
v(3713)=(v(3695)*v(390)+v(3561)*v(459))*v(7522)
v(3712)=(v(3694)*v(390)+v(3560)*v(459))*v(7522)
v(3711)=v(3693)*v(8029)+v(459)*v(8069)
v(475)=v(459)*v(8029)
v(458)=v(232)*v(8030)
v(4866)=v(458)*v(5436)
v(3762)=(v(3746)*v(392)+v(3642)*v(458))*v(7522)
v(3761)=(v(3745)*v(392)+v(3641)*v(458))*v(7522)
v(3760)=(v(3744)*v(392)+v(3640)*v(458))*v(7522)
v(3759)=(v(3743)*v(392)+v(3639)*v(458))*v(7522)
v(3758)=(v(3742)*v(392)+v(3638)*v(458))*v(7522)
v(3757)=v(4866)+v(3741)*v(8031)
v(3756)=(v(3739)*v(392)+v(3637)*v(458))*v(7522)
v(3755)=(v(3736)*v(392)+v(3569)*v(458))*v(7522)
v(3754)=(v(3734)*v(392)+v(3635)*v(458))*v(7522)
v(3753)=(v(3733)*v(392)+v(3634)*v(458))*v(7522)
v(3752)=(v(3732)*v(392)+v(3633)*v(458))*v(7522)
v(3751)=(v(3731)*v(392)+v(3632)*v(458))*v(7522)
v(3750)=(v(3730)*v(392)+v(3631)*v(458))*v(7522)
v(3749)=(v(3729)*v(392)+v(3630)*v(458))*v(7522)
v(3748)=(v(3728)*v(392)+v(3629)*v(458))*v(7522)
v(3747)=v(3727)*v(8031)+v(458)*v(8067)
v(493)=v(458)*v(8031)
v(393)=v(232)*v(3763)+v(410)+v(428)
v(8034)=v(381)*v(393)+v(382)*v(395)+v(379)*v(396)
v(8032)=v(383)*v(393)+v(380)*v(395)+v(382)*v(396)
v(3863)=v(3470)+v(3506)+(v(376)*v(3780)+v(3273)*v(393))*v(7522)
v(3862)=v(3469)+v(3505)+(v(376)*v(3779)+v(3272)*v(393))*v(7522)
v(3861)=v(3468)+v(3504)+(v(376)*v(3778)+v(3271)*v(393))*v(7522)
v(3860)=v(3467)+v(3503)+(v(376)*v(3777)+v(3270)*v(393))*v(7522)
v(3859)=v(3466)+v(3502)+(v(376)*v(3776)+v(3269)*v(393))*v(7522)
v(3858)=v(3465)+v(3501)+(v(376)*v(3775)+v(3268)*v(393))*v(7522)
v(3857)=v(3464)+v(3500)+(v(376)*v(3774)+v(3267)*v(393))*v(7522)
v(3856)=v(3463)+v(3499)+(v(376)*v(3773)+v(3266)*v(393))*v(7522)
v(3855)=v(3462)+v(3498)+(v(376)*v(3772)+v(3265)*v(393))*v(7522)
v(3854)=v(3461)+v(3497)+(v(376)*v(3771)+v(3264)*v(393))*v(7522)
v(3853)=v(3460)+v(3496)+(v(376)*v(3770)+v(3263)*v(393))*v(7522)
v(3852)=v(3459)+v(3495)+(v(376)*v(3769)+v(3262)*v(393))*v(7522)
v(3851)=v(3458)+v(3494)+(v(376)*v(3768)+v(3261)*v(393))*v(7522)
v(3850)=v(3457)+v(3493)+(v(376)*v(3767)+v(3260)*v(393))*v(7522)
v(3849)=v(3456)+v(3492)+(v(376)*v(3766)+v(3259)*v(393))*v(7522)
v(3848)=v(3455)+v(3491)+v(3764)*v(8036)+v(393)*v(8037)
v(3831)=(v(3454)*v(379)+v(3780)*v(381)+v(3490)*v(382)+v(3321)*v(393)+v(3354)*v(395)+v(3289)*v(396))*v(7522)
v(3830)=(v(3453)*v(379)+v(3779)*v(381)+v(3489)*v(382)+v(3320)*v(393)+v(3353)*v(395)+v(3288)*v(396))*v(7522)
v(3829)=(v(3452)*v(379)+v(3778)*v(381)+v(3488)*v(382)+v(3319)*v(393)+v(3352)*v(395)+v(3287)*v(396))*v(7522)
v(3828)=(v(3451)*v(379)+v(3777)*v(381)+v(3487)*v(382)+v(3318)*v(393)+v(3351)*v(395)+v(3286)*v(396))*v(7522)
v(3827)=(v(3450)*v(379)+v(3776)*v(381)+v(3486)*v(382)+v(3317)*v(393)+v(3350)*v(395)+v(3285)*v(396))*v(7522)
v(3826)=(v(3449)*v(379)+v(3775)*v(381)+v(3485)*v(382)+v(3316)*v(393)+v(3349)*v(395)+v(3284)*v(396))*v(7522)
v(3823)=v(393)*v(4155)
v(3825)=v(3823)+v(3824)+(v(3447)*v(379)+v(3774)*v(381)+v(3483)*v(382)+v(3283)*v(396))*v(7522)
v(3822)=(v(3446)*v(379)+v(3773)*v(381)+v(3480)*v(382)+v(3314)*v(393)+v(3316)*v(395)+v(3282)*v(396))*v(7522)
v(3821)=(v(3444)*v(379)+v(3772)*v(381)+v(3478)*v(382)+v(3313)*v(393)+v(3347)*v(395)+v(3281)*v(396))*v(7522)
v(3820)=(v(3443)*v(379)+v(3771)*v(381)+v(3477)*v(382)+v(3312)*v(393)+v(3346)*v(395)+v(3280)*v(396))*v(7522)
v(3819)=(v(3442)*v(379)+v(3770)*v(381)+v(3476)*v(382)+v(3311)*v(393)+v(3345)*v(395)+v(3279)*v(396))*v(7522)
v(3818)=(v(3441)*v(379)+v(3769)*v(381)+v(3475)*v(382)+v(3310)*v(393)+v(3344)*v(395)+v(3278)*v(396))*v(7522)
v(3817)=(v(3440)*v(379)+v(3768)*v(381)+v(3474)*v(382)+v(3309)*v(393)+v(3343)*v(395)+v(3277)*v(396))*v(7522)
v(3816)=(v(3439)*v(379)+v(3767)*v(381)+v(3473)*v(382)+v(3308)*v(393)+v(3342)*v(395)+v(3276)*v(396))*v(7522)
v(3815)=(v(3438)*v(379)+v(3766)*v(381)+v(3472)*v(382)+v(3307)*v(393)+v(3341)*v(395)+v(3275)*v(396))*v(7522)
v(3814)=(v(3437)*v(379)+v(3764)*v(381)+v(3471)*v(382)+v(3306)*v(393)+v(3340)*v(395)+v(3274)*v(396))*v(7522)+v(7518)*v&
&(8034)
v(3797)=(v(3490)*v(380)+v(3454)*v(382)+v(3780)*v(383)+v(3386)*v(393)+v(3305)*v(395)+v(3354)*v(396))*v(7522)
v(3796)=(v(3489)*v(380)+v(3453)*v(382)+v(3779)*v(383)+v(3385)*v(393)+v(3304)*v(395)+v(3353)*v(396))*v(7522)
v(3795)=(v(3488)*v(380)+v(3452)*v(382)+v(3778)*v(383)+v(3384)*v(393)+v(3303)*v(395)+v(3352)*v(396))*v(7522)
v(3794)=(v(3487)*v(380)+v(3451)*v(382)+v(3777)*v(383)+v(3383)*v(393)+v(3302)*v(395)+v(3351)*v(396))*v(7522)
v(3793)=(v(3486)*v(380)+v(3450)*v(382)+v(3776)*v(383)+v(3382)*v(393)+v(3301)*v(395)+v(3350)*v(396))*v(7522)
v(3792)=(v(3485)*v(380)+v(3449)*v(382)+v(3775)*v(383)+v(3348)*v(393)+v(3300)*v(395)+v(3349)*v(396))*v(7522)
v(3791)=v(4210)+(v(3483)*v(380)+v(3447)*v(382)+v(3774)*v(383)+v(3381)*v(393)+v(3299)*v(395))*v(7522)
v(3790)=v(3789)+v(3823)+(v(3480)*v(380)+v(3446)*v(382)+v(3773)*v(383)+v(3298)*v(395))*v(7522)
v(3788)=(v(3478)*v(380)+v(3444)*v(382)+v(3772)*v(383)+v(3380)*v(393)+v(3297)*v(395)+v(3347)*v(396))*v(7522)
v(3787)=(v(3477)*v(380)+v(3443)*v(382)+v(3771)*v(383)+v(3379)*v(393)+v(3296)*v(395)+v(3346)*v(396))*v(7522)
v(3786)=(v(3476)*v(380)+v(3442)*v(382)+v(3770)*v(383)+v(3378)*v(393)+v(3295)*v(395)+v(3345)*v(396))*v(7522)
v(3785)=(v(3475)*v(380)+v(3441)*v(382)+v(3769)*v(383)+v(3377)*v(393)+v(3294)*v(395)+v(3344)*v(396))*v(7522)
v(3784)=(v(3474)*v(380)+v(3440)*v(382)+v(3768)*v(383)+v(3376)*v(393)+v(3293)*v(395)+v(3343)*v(396))*v(7522)
v(3783)=(v(3473)*v(380)+v(3439)*v(382)+v(3767)*v(383)+v(3375)*v(393)+v(3292)*v(395)+v(3342)*v(396))*v(7522)
v(3782)=(v(3472)*v(380)+v(3438)*v(382)+v(3766)*v(383)+v(3374)*v(393)+v(3291)*v(395)+v(3341)*v(396))*v(7522)
v(3781)=(v(3471)*v(380)+v(3437)*v(382)+v(3764)*v(383)+v(3373)*v(393)+v(3290)*v(395)+v(3340)*v(396))*v(7522)+v(7518)*v&
&(8032)
v(399)=v(7522)*v(8032)
v(3873)=v(399)*v(4394)
v(3813)=(v(3797)*v(383)+v(3386)*v(399))*v(7522)
v(3812)=(v(3796)*v(383)+v(3385)*v(399))*v(7522)
v(3811)=(v(3795)*v(383)+v(3384)*v(399))*v(7522)
v(3810)=(v(3794)*v(383)+v(3383)*v(399))*v(7522)
v(3809)=(v(3793)*v(383)+v(3382)*v(399))*v(7522)
v(3808)=v(3873)+v(3792)*v(8019)
v(3807)=(v(3791)*v(383)+v(3381)*v(399))*v(7522)
v(3806)=(v(3790)*v(383)+v(3315)*v(399))*v(7522)
v(3805)=(v(3788)*v(383)+v(3380)*v(399))*v(7522)
v(3804)=(v(3787)*v(383)+v(3379)*v(399))*v(7522)
v(3803)=(v(3786)*v(383)+v(3378)*v(399))*v(7522)
v(3802)=(v(3785)*v(383)+v(3377)*v(399))*v(7522)
v(3801)=(v(3784)*v(383)+v(3376)*v(399))*v(7522)
v(3800)=(v(3783)*v(383)+v(3375)*v(399))*v(7522)
v(3799)=(v(3782)*v(383)+v(3374)*v(399))*v(7522)
v(3798)=v(3781)*v(8019)+v(399)*v(8033)
v(434)=v(399)*v(8019)
v(398)=v(7522)*v(8034)
v(4260)=v(398)*v(4394)
v(4257)=v(398)*v(4155)
v(3906)=v(398)*v(4391)
v(3847)=(v(381)*v(3831)+v(3321)*v(398))*v(7522)
v(3846)=(v(381)*v(3830)+v(3320)*v(398))*v(7522)
v(3845)=(v(381)*v(3829)+v(3319)*v(398))*v(7522)
v(3844)=(v(381)*v(3828)+v(3318)*v(398))*v(7522)
v(3843)=(v(381)*v(3827)+v(3317)*v(398))*v(7522)
v(3842)=v(3906)+v(3826)*v(8017)
v(3841)=v(4257)+v(3825)*v(8017)
v(3840)=(v(381)*v(3822)+v(3314)*v(398))*v(7522)
v(3839)=(v(381)*v(3821)+v(3313)*v(398))*v(7522)
v(3838)=(v(381)*v(3820)+v(3312)*v(398))*v(7522)
v(3837)=(v(381)*v(3819)+v(3311)*v(398))*v(7522)
v(3836)=(v(381)*v(3818)+v(3310)*v(398))*v(7522)
v(3835)=(v(381)*v(3817)+v(3309)*v(398))*v(7522)
v(3834)=(v(381)*v(3816)+v(3308)*v(398))*v(7522)
v(3833)=(v(381)*v(3815)+v(3307)*v(398))*v(7522)
v(3832)=v(3814)*v(8017)+v(398)*v(8035)
v(414)=v(398)*v(8017)
v(394)=v(412)+v(430)+v(393)*v(8036)
v(8039)=v(383)*v(394)+v(382)*v(398)+v(380)*v(399)
v(8038)=v(381)*v(394)+v(379)*v(398)+v(382)*v(399)
v(3946)=v(3813)+v(3847)+(v(376)*v(3863)+v(3273)*v(394))*v(7522)
v(3945)=v(3812)+v(3846)+(v(376)*v(3862)+v(3272)*v(394))*v(7522)
v(3944)=v(3811)+v(3845)+(v(376)*v(3861)+v(3271)*v(394))*v(7522)
v(3943)=v(3810)+v(3844)+(v(376)*v(3860)+v(3270)*v(394))*v(7522)
v(3942)=v(3809)+v(3843)+(v(376)*v(3859)+v(3269)*v(394))*v(7522)
v(3941)=v(3808)+v(3842)+(v(376)*v(3858)+v(3268)*v(394))*v(7522)
v(3940)=v(3807)+v(3841)+(v(376)*v(3857)+v(3267)*v(394))*v(7522)
v(3939)=v(3806)+v(3840)+(v(376)*v(3856)+v(3266)*v(394))*v(7522)
v(3938)=v(3805)+v(3839)+(v(376)*v(3855)+v(3265)*v(394))*v(7522)
v(3937)=v(3804)+v(3838)+(v(376)*v(3854)+v(3264)*v(394))*v(7522)
v(3936)=v(3803)+v(3837)+(v(376)*v(3853)+v(3263)*v(394))*v(7522)
v(3935)=v(3802)+v(3836)+(v(376)*v(3852)+v(3262)*v(394))*v(7522)
v(3934)=v(3801)+v(3835)+(v(376)*v(3851)+v(3261)*v(394))*v(7522)
v(3933)=v(3800)+v(3834)+(v(376)*v(3850)+v(3260)*v(394))*v(7522)
v(3932)=v(3799)+v(3833)+(v(376)*v(3849)+v(3259)*v(394))*v(7522)
v(3931)=v(3798)+v(3832)+v(3848)*v(8036)+v(394)*v(8037)
v(3914)=(v(3797)*v(380)+v(382)*v(3831)+v(383)*v(3863)+v(3386)*v(394)+v(3354)*v(398)+v(3305)*v(399))*v(7522)
v(3913)=(v(3796)*v(380)+v(382)*v(3830)+v(383)*v(3862)+v(3385)*v(394)+v(3353)*v(398)+v(3304)*v(399))*v(7522)
v(3912)=(v(3795)*v(380)+v(382)*v(3829)+v(383)*v(3861)+v(3384)*v(394)+v(3352)*v(398)+v(3303)*v(399))*v(7522)
v(3911)=(v(3794)*v(380)+v(382)*v(3828)+v(383)*v(3860)+v(3383)*v(394)+v(3351)*v(398)+v(3302)*v(399))*v(7522)
v(3910)=(v(3793)*v(380)+v(382)*v(3827)+v(383)*v(3859)+v(3382)*v(394)+v(3350)*v(398)+v(3301)*v(399))*v(7522)
v(3909)=(v(3792)*v(380)+v(382)*v(3826)+v(383)*v(3858)+v(3348)*v(394)+v(3349)*v(398)+v(3300)*v(399))*v(7522)
v(3908)=v(4260)+(v(3791)*v(380)+v(382)*v(3825)+v(383)*v(3857)+v(3381)*v(394)+v(3299)*v(399))*v(7522)
v(3905)=v(394)*v(4155)
v(3907)=v(3905)+v(3906)+(v(3790)*v(380)+v(382)*v(3822)+v(383)*v(3856)+v(3298)*v(399))*v(7522)
v(3904)=(v(3788)*v(380)+v(382)*v(3821)+v(383)*v(3855)+v(3380)*v(394)+v(3347)*v(398)+v(3297)*v(399))*v(7522)
v(3903)=(v(3787)*v(380)+v(382)*v(3820)+v(383)*v(3854)+v(3379)*v(394)+v(3346)*v(398)+v(3296)*v(399))*v(7522)
v(3902)=(v(3786)*v(380)+v(3819)*v(382)+v(383)*v(3853)+v(3378)*v(394)+v(3345)*v(398)+v(3295)*v(399))*v(7522)
v(3901)=(v(3785)*v(380)+v(3818)*v(382)+v(383)*v(3852)+v(3377)*v(394)+v(3344)*v(398)+v(3294)*v(399))*v(7522)
v(3900)=(v(3784)*v(380)+v(3817)*v(382)+v(383)*v(3851)+v(3376)*v(394)+v(3343)*v(398)+v(3293)*v(399))*v(7522)
v(3899)=(v(3783)*v(380)+v(3816)*v(382)+v(383)*v(3850)+v(3375)*v(394)+v(3342)*v(398)+v(3292)*v(399))*v(7522)
v(3898)=(v(3782)*v(380)+v(3815)*v(382)+v(383)*v(3849)+v(3374)*v(394)+v(3341)*v(398)+v(3291)*v(399))*v(7522)
v(3897)=(v(3781)*v(380)+v(3814)*v(382)+v(383)*v(3848)+v(3373)*v(394)+v(3340)*v(398)+v(3290)*v(399))*v(7522)+v(7518)*v&
&(8039)
v(3880)=(v(3797)*v(382)+v(379)*v(3831)+v(381)*v(3863)+v(3321)*v(394)+v(3289)*v(398)+v(3354)*v(399))*v(7522)
v(3879)=(v(3796)*v(382)+v(379)*v(3830)+v(381)*v(3862)+v(3320)*v(394)+v(3288)*v(398)+v(3353)*v(399))*v(7522)
v(3878)=(v(3795)*v(382)+v(379)*v(3829)+v(381)*v(3861)+v(3319)*v(394)+v(3287)*v(398)+v(3352)*v(399))*v(7522)
v(3877)=(v(3794)*v(382)+v(379)*v(3828)+v(381)*v(3860)+v(3318)*v(394)+v(3286)*v(398)+v(3351)*v(399))*v(7522)
v(3876)=(v(3793)*v(382)+v(379)*v(3827)+v(381)*v(3859)+v(3317)*v(394)+v(3285)*v(398)+v(3350)*v(399))*v(7522)
v(3875)=(v(3792)*v(382)+v(379)*v(3826)+v(381)*v(3858)+v(3316)*v(394)+v(3284)*v(398)+v(3349)*v(399))*v(7522)
v(3874)=v(3873)+v(3905)+(v(3791)*v(382)+v(379)*v(3825)+v(381)*v(3857)+v(3283)*v(398))*v(7522)
v(3872)=(v(3790)*v(382)+v(379)*v(3822)+v(381)*v(3856)+v(3314)*v(394)+v(3282)*v(398)+v(3316)*v(399))*v(7522)
v(3871)=(v(3788)*v(382)+v(379)*v(3821)+v(381)*v(3855)+v(3313)*v(394)+v(3281)*v(398)+v(3347)*v(399))*v(7522)
v(3870)=(v(3787)*v(382)+v(379)*v(3820)+v(381)*v(3854)+v(3312)*v(394)+v(3280)*v(398)+v(3346)*v(399))*v(7522)
v(3869)=(v(379)*v(3819)+v(3786)*v(382)+v(381)*v(3853)+v(3311)*v(394)+v(3279)*v(398)+v(3345)*v(399))*v(7522)
v(3868)=(v(379)*v(3818)+v(3785)*v(382)+v(381)*v(3852)+v(3310)*v(394)+v(3278)*v(398)+v(3344)*v(399))*v(7522)
v(3867)=(v(379)*v(3817)+v(3784)*v(382)+v(381)*v(3851)+v(3309)*v(394)+v(3277)*v(398)+v(3343)*v(399))*v(7522)
v(3866)=(v(379)*v(3816)+v(3783)*v(382)+v(381)*v(3850)+v(3308)*v(394)+v(3276)*v(398)+v(3342)*v(399))*v(7522)
v(3865)=(v(379)*v(3815)+v(3782)*v(382)+v(381)*v(3849)+v(3307)*v(394)+v(3275)*v(398)+v(3341)*v(399))*v(7522)
v(3864)=(v(379)*v(3814)+v(3781)*v(382)+v(381)*v(3848)+v(3306)*v(394)+v(3274)*v(398)+v(3340)*v(399))*v(7522)+v(7518)*v&
&(8038)
v(402)=v(7522)*v(8038)
v(4310)=v(402)*v(4394)
v(4307)=v(402)*v(4155)
v(3955)=v(402)*v(4391)
v(3896)=(v(381)*v(3880)+v(3321)*v(402))*v(7522)
v(3895)=(v(381)*v(3879)+v(3320)*v(402))*v(7522)
v(3894)=(v(381)*v(3878)+v(3319)*v(402))*v(7522)
v(3893)=(v(381)*v(3877)+v(3318)*v(402))*v(7522)
v(3892)=(v(381)*v(3876)+v(3317)*v(402))*v(7522)
v(3891)=v(3955)+v(3875)*v(8017)
v(3890)=v(4307)+v(3874)*v(8017)
v(3889)=(v(381)*v(3872)+v(3314)*v(402))*v(7522)
v(3888)=(v(381)*v(3871)+v(3313)*v(402))*v(7522)
v(3887)=(v(381)*v(3870)+v(3312)*v(402))*v(7522)
v(3886)=(v(381)*v(3869)+v(3311)*v(402))*v(7522)
v(3885)=(v(381)*v(3868)+v(3310)*v(402))*v(7522)
v(3884)=(v(381)*v(3867)+v(3309)*v(402))*v(7522)
v(3883)=(v(381)*v(3866)+v(3308)*v(402))*v(7522)
v(3882)=(v(381)*v(3865)+v(3307)*v(402))*v(7522)
v(3881)=v(3864)*v(8017)+v(402)*v(8035)
v(418)=v(402)*v(8017)
v(401)=v(7522)*v(8039)
v(3990)=v(401)*v(4394)
v(3930)=(v(383)*v(3914)+v(3386)*v(401))*v(7522)
v(3929)=(v(383)*v(3913)+v(3385)*v(401))*v(7522)
v(3928)=(v(383)*v(3912)+v(3384)*v(401))*v(7522)
v(3927)=(v(383)*v(3911)+v(3383)*v(401))*v(7522)
v(3926)=(v(383)*v(3910)+v(3382)*v(401))*v(7522)
v(3925)=v(3990)+v(3909)*v(8019)
v(3924)=(v(383)*v(3908)+v(3381)*v(401))*v(7522)
v(3923)=(v(383)*v(3907)+v(3315)*v(401))*v(7522)
v(3922)=(v(383)*v(3904)+v(3380)*v(401))*v(7522)
v(3921)=(v(383)*v(3903)+v(3379)*v(401))*v(7522)
v(3920)=(v(383)*v(3902)+v(3378)*v(401))*v(7522)
v(3919)=(v(383)*v(3901)+v(3377)*v(401))*v(7522)
v(3918)=(v(383)*v(3900)+v(3376)*v(401))*v(7522)
v(3917)=(v(383)*v(3899)+v(3375)*v(401))*v(7522)
v(3916)=(v(383)*v(3898)+v(3374)*v(401))*v(7522)
v(3915)=v(3897)*v(8019)+v(401)*v(8033)
v(436)=v(401)*v(8019)
v(397)=v(414)+v(434)+v(394)*v(8036)
v(8041)=v(381)*v(397)+v(382)*v(401)+v(379)*v(402)
v(8040)=v(383)*v(397)+v(380)*v(401)+v(382)*v(402)
v(4029)=v(3896)+v(3930)+(v(376)*v(3946)+v(3273)*v(397))*v(7522)
v(4028)=v(3895)+v(3929)+(v(376)*v(3945)+v(3272)*v(397))*v(7522)
v(4027)=v(3894)+v(3928)+(v(376)*v(3944)+v(3271)*v(397))*v(7522)
v(4026)=v(3893)+v(3927)+(v(376)*v(3943)+v(3270)*v(397))*v(7522)
v(4025)=v(3892)+v(3926)+(v(376)*v(3942)+v(3269)*v(397))*v(7522)
v(4024)=v(3891)+v(3925)+(v(376)*v(3941)+v(3268)*v(397))*v(7522)
v(4023)=v(3890)+v(3924)+(v(376)*v(3940)+v(3267)*v(397))*v(7522)
v(4022)=v(3889)+v(3923)+(v(376)*v(3939)+v(3266)*v(397))*v(7522)
v(4021)=v(3888)+v(3922)+(v(376)*v(3938)+v(3265)*v(397))*v(7522)
v(4020)=v(3887)+v(3921)+(v(376)*v(3937)+v(3264)*v(397))*v(7522)
v(4019)=v(3886)+v(3920)+(v(376)*v(3936)+v(3263)*v(397))*v(7522)
v(4018)=v(3885)+v(3919)+(v(376)*v(3935)+v(3262)*v(397))*v(7522)
v(4017)=v(3884)+v(3918)+(v(376)*v(3934)+v(3261)*v(397))*v(7522)
v(4016)=v(3883)+v(3917)+(v(376)*v(3933)+v(3260)*v(397))*v(7522)
v(4015)=v(3882)+v(3916)+(v(376)*v(3932)+v(3259)*v(397))*v(7522)
v(4014)=v(3881)+v(3915)+v(3931)*v(8036)+v(397)*v(8037)
v(3997)=(v(379)*v(3880)+v(382)*v(3914)+v(381)*v(3946)+v(3321)*v(397)+v(3354)*v(401)+v(3289)*v(402))*v(7522)
v(3996)=(v(379)*v(3879)+v(382)*v(3913)+v(381)*v(3945)+v(3320)*v(397)+v(3353)*v(401)+v(3288)*v(402))*v(7522)
v(3995)=(v(379)*v(3878)+v(382)*v(3912)+v(381)*v(3944)+v(3319)*v(397)+v(3352)*v(401)+v(3287)*v(402))*v(7522)
v(3994)=(v(379)*v(3877)+v(382)*v(3911)+v(381)*v(3943)+v(3318)*v(397)+v(3351)*v(401)+v(3286)*v(402))*v(7522)
v(3993)=(v(379)*v(3876)+v(382)*v(3910)+v(381)*v(3942)+v(3317)*v(397)+v(3350)*v(401)+v(3285)*v(402))*v(7522)
v(3992)=(v(379)*v(3875)+v(382)*v(3909)+v(381)*v(3941)+v(3316)*v(397)+v(3349)*v(401)+v(3284)*v(402))*v(7522)
v(3989)=v(397)*v(4155)
v(3991)=v(3989)+v(3990)+(v(379)*v(3874)+v(382)*v(3908)+v(381)*v(3940)+v(3283)*v(402))*v(7522)
v(3988)=(v(379)*v(3872)+v(382)*v(3907)+v(381)*v(3939)+v(3314)*v(397)+v(3316)*v(401)+v(3282)*v(402))*v(7522)
v(3987)=(v(379)*v(3871)+v(382)*v(3904)+v(381)*v(3938)+v(3313)*v(397)+v(3347)*v(401)+v(3281)*v(402))*v(7522)
v(3986)=(v(379)*v(3870)+v(382)*v(3903)+v(381)*v(3937)+v(3312)*v(397)+v(3346)*v(401)+v(3280)*v(402))*v(7522)
v(3985)=(v(379)*v(3869)+v(382)*v(3902)+v(381)*v(3936)+v(3311)*v(397)+v(3345)*v(401)+v(3279)*v(402))*v(7522)
v(3984)=(v(379)*v(3868)+v(382)*v(3901)+v(381)*v(3935)+v(3310)*v(397)+v(3344)*v(401)+v(3278)*v(402))*v(7522)
v(3983)=(v(379)*v(3867)+v(382)*v(3900)+v(381)*v(3934)+v(3309)*v(397)+v(3343)*v(401)+v(3277)*v(402))*v(7522)
v(3982)=(v(379)*v(3866)+v(382)*v(3899)+v(381)*v(3933)+v(3308)*v(397)+v(3342)*v(401)+v(3276)*v(402))*v(7522)
v(3981)=(v(379)*v(3865)+v(382)*v(3898)+v(381)*v(3932)+v(3307)*v(397)+v(3341)*v(401)+v(3275)*v(402))*v(7522)
v(3980)=(v(379)*v(3864)+v(382)*v(3897)+v(381)*v(3931)+v(3306)*v(397)+v(3340)*v(401)+v(3274)*v(402))*v(7522)+v(7518)*v&
&(8041)
v(3963)=(v(382)*v(3880)+v(380)*v(3914)+v(383)*v(3946)+v(3386)*v(397)+v(3305)*v(401)+v(3354)*v(402))*v(7522)
v(3962)=(v(382)*v(3879)+v(380)*v(3913)+v(383)*v(3945)+v(3385)*v(397)+v(3304)*v(401)+v(3353)*v(402))*v(7522)
v(3961)=(v(382)*v(3878)+v(380)*v(3912)+v(383)*v(3944)+v(3384)*v(397)+v(3303)*v(401)+v(3352)*v(402))*v(7522)
v(3960)=(v(382)*v(3877)+v(380)*v(3911)+v(383)*v(3943)+v(3383)*v(397)+v(3302)*v(401)+v(3351)*v(402))*v(7522)
v(3959)=(v(382)*v(3876)+v(380)*v(3910)+v(383)*v(3942)+v(3382)*v(397)+v(3301)*v(401)+v(3350)*v(402))*v(7522)
v(3958)=(v(382)*v(3875)+v(380)*v(3909)+v(383)*v(3941)+v(3348)*v(397)+v(3300)*v(401)+v(3349)*v(402))*v(7522)
v(3957)=v(4310)+(v(382)*v(3874)+v(380)*v(3908)+v(383)*v(3940)+v(3381)*v(397)+v(3299)*v(401))*v(7522)
v(3956)=v(3955)+v(3989)+(v(382)*v(3872)+v(380)*v(3907)+v(383)*v(3939)+v(3298)*v(401))*v(7522)
v(3954)=(v(382)*v(3871)+v(380)*v(3904)+v(383)*v(3938)+v(3380)*v(397)+v(3297)*v(401)+v(3347)*v(402))*v(7522)
v(3953)=(v(382)*v(3870)+v(380)*v(3903)+v(383)*v(3937)+v(3379)*v(397)+v(3296)*v(401)+v(3346)*v(402))*v(7522)
v(3952)=(v(382)*v(3869)+v(380)*v(3902)+v(383)*v(3936)+v(3378)*v(397)+v(3295)*v(401)+v(3345)*v(402))*v(7522)
v(3951)=(v(382)*v(3868)+v(380)*v(3901)+v(383)*v(3935)+v(3377)*v(397)+v(3294)*v(401)+v(3344)*v(402))*v(7522)
v(3950)=(v(382)*v(3867)+v(380)*v(3900)+v(383)*v(3934)+v(3376)*v(397)+v(3293)*v(401)+v(3343)*v(402))*v(7522)
v(3949)=(v(382)*v(3866)+v(380)*v(3899)+v(383)*v(3933)+v(3375)*v(397)+v(3292)*v(401)+v(3342)*v(402))*v(7522)
v(3948)=(v(382)*v(3865)+v(380)*v(3898)+v(383)*v(3932)+v(3374)*v(397)+v(3291)*v(401)+v(3341)*v(402))*v(7522)
v(3947)=(v(382)*v(3864)+v(380)*v(3897)+v(383)*v(3931)+v(3373)*v(397)+v(3290)*v(401)+v(3340)*v(402))*v(7522)+v(7518)*v&
&(8040)
v(405)=v(7522)*v(8040)
v(4089)=v(405)*v(4394)
v(3979)=(v(383)*v(3963)+v(3386)*v(405))*v(7522)
v(3978)=(v(383)*v(3962)+v(3385)*v(405))*v(7522)
v(3977)=(v(383)*v(3961)+v(3384)*v(405))*v(7522)
v(3976)=(v(383)*v(3960)+v(3383)*v(405))*v(7522)
v(3975)=(v(383)*v(3959)+v(3382)*v(405))*v(7522)
v(3974)=v(4089)+v(3958)*v(8019)
v(3973)=(v(383)*v(3957)+v(3381)*v(405))*v(7522)
v(3972)=(v(383)*v(3956)+v(3315)*v(405))*v(7522)
v(3971)=(v(383)*v(3954)+v(3380)*v(405))*v(7522)
v(3970)=(v(383)*v(3953)+v(3379)*v(405))*v(7522)
v(3969)=(v(383)*v(3952)+v(3378)*v(405))*v(7522)
v(3968)=(v(383)*v(3951)+v(3377)*v(405))*v(7522)
v(3967)=(v(383)*v(3950)+v(3376)*v(405))*v(7522)
v(3966)=(v(383)*v(3949)+v(3375)*v(405))*v(7522)
v(3965)=(v(383)*v(3948)+v(3374)*v(405))*v(7522)
v(3964)=v(3947)*v(8019)+v(405)*v(8033)
v(440)=v(405)*v(8019)
v(404)=v(7522)*v(8041)
v(4376)=v(404)*v(4394)
v(4373)=v(404)*v(4155)
v(4054)=v(404)*v(4391)
v(4013)=(v(381)*v(3997)+v(3321)*v(404))*v(7522)
v(4012)=(v(381)*v(3996)+v(3320)*v(404))*v(7522)
v(4011)=(v(381)*v(3995)+v(3319)*v(404))*v(7522)
v(4010)=(v(381)*v(3994)+v(3318)*v(404))*v(7522)
v(4009)=(v(381)*v(3993)+v(3317)*v(404))*v(7522)
v(4008)=v(4054)+v(3992)*v(8017)
v(4007)=v(4373)+v(3991)*v(8017)
v(4006)=(v(381)*v(3988)+v(3314)*v(404))*v(7522)
v(4005)=(v(381)*v(3987)+v(3313)*v(404))*v(7522)
v(4004)=(v(381)*v(3986)+v(3312)*v(404))*v(7522)
v(4003)=(v(381)*v(3985)+v(3311)*v(404))*v(7522)
v(4002)=(v(381)*v(3984)+v(3310)*v(404))*v(7522)
v(4001)=(v(381)*v(3983)+v(3309)*v(404))*v(7522)
v(4000)=(v(381)*v(3982)+v(3308)*v(404))*v(7522)
v(3999)=(v(381)*v(3981)+v(3307)*v(404))*v(7522)
v(3998)=v(3980)*v(8017)+v(404)*v(8035)
v(420)=v(404)*v(8017)
v(400)=v(418)+v(436)+v(397)*v(8036)
v(8043)=v(381)*v(400)+v(379)*v(404)+v(382)*v(405)
v(8042)=v(383)*v(400)+v(382)*v(404)+v(380)*v(405)
v(4096)=(v(382)*v(3963)+v(379)*v(3997)+v(3321)*v(400)+v(381)*v(4029)+v(3289)*v(404)+v(3354)*v(405))*v(7522)
v(4095)=(v(382)*v(3962)+v(379)*v(3996)+v(3320)*v(400)+v(381)*v(4028)+v(3288)*v(404)+v(3353)*v(405))*v(7522)
v(4094)=(v(382)*v(3961)+v(379)*v(3995)+v(3319)*v(400)+v(381)*v(4027)+v(3287)*v(404)+v(3352)*v(405))*v(7522)
v(4093)=(v(382)*v(3960)+v(379)*v(3994)+v(3318)*v(400)+v(381)*v(4026)+v(3286)*v(404)+v(3351)*v(405))*v(7522)
v(4092)=(v(382)*v(3959)+v(379)*v(3993)+v(3317)*v(400)+v(381)*v(4025)+v(3285)*v(404)+v(3350)*v(405))*v(7522)
v(4091)=(v(382)*v(3958)+v(379)*v(3992)+v(3316)*v(400)+v(381)*v(4024)+v(3284)*v(404)+v(3349)*v(405))*v(7522)
v(4088)=v(400)*v(4155)
v(4090)=v(4088)+v(4089)+(v(382)*v(3957)+v(379)*v(3991)+v(381)*v(4023)+v(3283)*v(404))*v(7522)
v(4087)=(v(382)*v(3956)+v(379)*v(3988)+v(3314)*v(400)+v(381)*v(4022)+v(3282)*v(404)+v(3316)*v(405))*v(7522)
v(4086)=(v(382)*v(3954)+v(379)*v(3987)+v(3313)*v(400)+v(381)*v(4021)+v(3281)*v(404)+v(3347)*v(405))*v(7522)
v(4085)=(v(382)*v(3953)+v(379)*v(3986)+v(3312)*v(400)+v(381)*v(4020)+v(3280)*v(404)+v(3346)*v(405))*v(7522)
v(4084)=(v(382)*v(3952)+v(379)*v(3985)+v(3311)*v(400)+v(381)*v(4019)+v(3279)*v(404)+v(3345)*v(405))*v(7522)
v(4083)=(v(382)*v(3951)+v(379)*v(3984)+v(3310)*v(400)+v(381)*v(4018)+v(3278)*v(404)+v(3344)*v(405))*v(7522)
v(4082)=(v(382)*v(3950)+v(379)*v(3983)+v(3309)*v(400)+v(381)*v(4017)+v(3277)*v(404)+v(3343)*v(405))*v(7522)
v(4081)=(v(382)*v(3949)+v(379)*v(3982)+v(3308)*v(400)+v(381)*v(4016)+v(3276)*v(404)+v(3342)*v(405))*v(7522)
v(4080)=(v(382)*v(3948)+v(379)*v(3981)+v(3307)*v(400)+v(381)*v(4015)+v(3275)*v(404)+v(3341)*v(405))*v(7522)
v(4079)=(v(382)*v(3947)+v(379)*v(3980)+v(3306)*v(400)+v(381)*v(4014)+v(3274)*v(404)+v(3340)*v(405))*v(7522)+v(7518)*v&
&(8043)
v(4062)=(v(380)*v(3963)+v(382)*v(3997)+v(3386)*v(400)+v(383)*v(4029)+v(3354)*v(404)+v(3305)*v(405))*v(7522)
v(4061)=(v(380)*v(3962)+v(382)*v(3996)+v(3385)*v(400)+v(383)*v(4028)+v(3353)*v(404)+v(3304)*v(405))*v(7522)
v(4060)=(v(380)*v(3961)+v(382)*v(3995)+v(3384)*v(400)+v(383)*v(4027)+v(3352)*v(404)+v(3303)*v(405))*v(7522)
v(4059)=(v(380)*v(3960)+v(382)*v(3994)+v(3383)*v(400)+v(383)*v(4026)+v(3351)*v(404)+v(3302)*v(405))*v(7522)
v(4058)=(v(380)*v(3959)+v(382)*v(3993)+v(3382)*v(400)+v(383)*v(4025)+v(3350)*v(404)+v(3301)*v(405))*v(7522)
v(4057)=(v(380)*v(3958)+v(382)*v(3992)+v(3348)*v(400)+v(383)*v(4024)+v(3349)*v(404)+v(3300)*v(405))*v(7522)
v(4056)=v(4376)+(v(380)*v(3957)+v(382)*v(3991)+v(3381)*v(400)+v(383)*v(4023)+v(3299)*v(405))*v(7522)
v(4055)=v(4054)+v(4088)+(v(380)*v(3956)+v(382)*v(3988)+v(383)*v(4022)+v(3298)*v(405))*v(7522)
v(4053)=(v(380)*v(3954)+v(382)*v(3987)+v(3380)*v(400)+v(383)*v(4021)+v(3347)*v(404)+v(3297)*v(405))*v(7522)
v(4052)=(v(380)*v(3953)+v(382)*v(3986)+v(3379)*v(400)+v(383)*v(4020)+v(3346)*v(404)+v(3296)*v(405))*v(7522)
v(4051)=(v(380)*v(3952)+v(382)*v(3985)+v(3378)*v(400)+v(383)*v(4019)+v(3345)*v(404)+v(3295)*v(405))*v(7522)
v(4050)=(v(380)*v(3951)+v(382)*v(3984)+v(3377)*v(400)+v(383)*v(4018)+v(3344)*v(404)+v(3294)*v(405))*v(7522)
v(4049)=(v(380)*v(3950)+v(382)*v(3983)+v(3376)*v(400)+v(383)*v(4017)+v(3343)*v(404)+v(3293)*v(405))*v(7522)
v(4048)=(v(380)*v(3949)+v(382)*v(3982)+v(3375)*v(400)+v(383)*v(4016)+v(3342)*v(404)+v(3292)*v(405))*v(7522)
v(4047)=(v(380)*v(3948)+v(382)*v(3981)+v(3374)*v(400)+v(383)*v(4015)+v(3341)*v(404)+v(3291)*v(405))*v(7522)
v(4046)=(v(380)*v(3947)+v(382)*v(3980)+v(3373)*v(400)+v(383)*v(4014)+v(3340)*v(404)+v(3290)*v(405))*v(7522)+v(7518)*v&
&(8042)
v(4045)=v(3979)+v(4013)+(v(3273)*v(400)+v(376)*v(4029))*v(7522)
v(4044)=v(3978)+v(4012)+(v(3272)*v(400)+v(376)*v(4028))*v(7522)
v(4043)=v(3977)+v(4011)+(v(3271)*v(400)+v(376)*v(4027))*v(7522)
v(4042)=v(3976)+v(4010)+(v(3270)*v(400)+v(376)*v(4026))*v(7522)
v(4041)=v(3975)+v(4009)+(v(3269)*v(400)+v(376)*v(4025))*v(7522)
v(4040)=v(3974)+v(4008)+(v(3268)*v(400)+v(376)*v(4024))*v(7522)
v(4039)=v(3973)+v(4007)+(v(3267)*v(400)+v(376)*v(4023))*v(7522)
v(4038)=v(3972)+v(4006)+(v(3266)*v(400)+v(376)*v(4022))*v(7522)
v(4037)=v(3971)+v(4005)+(v(3265)*v(400)+v(376)*v(4021))*v(7522)
v(4036)=v(3970)+v(4004)+(v(3264)*v(400)+v(376)*v(4020))*v(7522)
v(4035)=v(3969)+v(4003)+(v(3263)*v(400)+v(376)*v(4019))*v(7522)
v(4034)=v(3968)+v(4002)+(v(3262)*v(400)+v(376)*v(4018))*v(7522)
v(4033)=v(3967)+v(4001)+(v(3261)*v(400)+v(376)*v(4017))*v(7522)
v(4032)=v(3966)+v(4000)+(v(3260)*v(400)+v(376)*v(4016))*v(7522)
v(4031)=v(3965)+v(3999)+(v(3259)*v(400)+v(376)*v(4015))*v(7522)
v(4030)=v(3964)+v(3998)+v(4014)*v(8036)+v(400)*v(8037)
v(403)=v(420)+v(440)+v(400)*v(8036)
v(8044)=5040d0+v(403)
v(4156)=v(403)*v(4155)
v(8046)=5040d0*v(4155)+v(4156)
v(406)=v(7522)*v(8042)
v(4157)=v(406)*v(4394)
v(4078)=(v(3386)*v(406)+v(383)*v(4062))*v(7522)
v(4077)=(v(3385)*v(406)+v(383)*v(4061))*v(7522)
v(4076)=(v(3384)*v(406)+v(383)*v(4060))*v(7522)
v(4075)=(v(383)*v(4059)+v(3383)*v(406))*v(7522)
v(4074)=(v(383)*v(4058)+v(3382)*v(406))*v(7522)
v(4073)=v(4157)+v(4057)*v(8019)
v(4072)=(v(383)*v(4056)+v(3381)*v(406))*v(7522)
v(4071)=(v(383)*v(4055)+v(3315)*v(406))*v(7522)
v(4070)=(v(383)*v(4053)+v(3380)*v(406))*v(7522)
v(4069)=(v(383)*v(4052)+v(3379)*v(406))*v(7522)
v(4068)=(v(383)*v(4051)+v(3378)*v(406))*v(7522)
v(4067)=(v(383)*v(4050)+v(3377)*v(406))*v(7522)
v(4066)=(v(383)*v(4049)+v(3376)*v(406))*v(7522)
v(4065)=(v(383)*v(4048)+v(3375)*v(406))*v(7522)
v(4064)=(v(383)*v(4047)+v(3374)*v(406))*v(7522)
v(4063)=v(4046)*v(8019)+v(406)*v(8033)
v(442)=v(406)*v(8019)
v(407)=v(7522)*v(8043)
v(8048)=v(382)*v(406)+v(379)*v(407)
v(8047)=v(380)*v(406)+v(382)*v(407)
v(4396)=v(407)*v(4394)
v(4392)=v(407)*v(4155)
v(4164)=(7d0*(360d0*v(3454)+120d0*v(3831)+30d0*v(3880)+6d0*v(3997)+v(4096))+v(7522)*(v(381)*v(4045)+v(3354)*v(406)+v&
&(382)*v(4062)+v(3289)*v(407)+v(379)*v(4096)+v(3321)*v(8044)))/5040d0
v(4163)=(7d0*(360d0*v(3453)+120d0*v(3830)+30d0*v(3879)+6d0*v(3996)+v(4095))+v(7522)*(v(381)*v(4044)+v(3353)*v(406)+v&
&(382)*v(4061)+v(3288)*v(407)+v(379)*v(4095)+v(3320)*v(8044)))/5040d0
v(4162)=(7d0*(360d0*v(3452)+120d0*v(3829)+30d0*v(3878)+6d0*v(3995)+v(4094))+v(7522)*(v(381)*v(4043)+v(3352)*v(406)+v&
&(382)*v(4060)+v(3287)*v(407)+v(379)*v(4094)+v(3319)*v(8044)))/5040d0
v(4161)=(7d0*(360d0*v(3451)+120d0*v(3828)+30d0*v(3877)+6d0*v(3994)+v(4093))+v(7522)*(v(381)*v(4042)+v(382)*v(4059)+v&
&(3351)*v(406)+v(3286)*v(407)+v(379)*v(4093)+v(3318)*v(8044)))/5040d0
v(4160)=(7d0*(360d0*v(3450)+120d0*v(3827)+30d0*v(3876)+6d0*v(3993)+v(4092))+v(7522)*(v(381)*v(4041)+v(382)*v(4058)+v&
&(3350)*v(406)+v(3285)*v(407)+v(379)*v(4092)+v(3317)*v(8044)))/5040d0
v(4159)=(7d0*(360d0*v(3449)+120d0*v(3826)+30d0*v(3875)+6d0*v(3992)+v(4091)+720d0*v(4391))+(v(3316)*v(403)+v(381)*v(4040&
&)+v(382)*v(4057)+v(3349)*v(406)+v(3284)*v(407)+v(379)*v(4091))*v(7522))/5040d0
v(4158)=(2520d0*v(3447)+840d0*v(3825)+210d0*v(3874)+42d0*v(3991)+7d0*v(4090)+v(4157)+(v(381)*v(4039)+v(382)*v(4056)+v&
&(3283)*v(407)+v(379)*v(4090))*v(7522)+v(8046))/5040d0
v(4154)=(7d0*(360d0*v(3446)+120d0*v(3822)+30d0*v(3872)+6d0*v(3988)+v(4087))+v(7522)*(v(381)*v(4038)+v(382)*v(4055)+v&
&(3316)*v(406)+v(3282)*v(407)+v(379)*v(4087)+v(3314)*v(8044)))/5040d0
v(4153)=(7d0*(360d0*v(3444)+120d0*v(3821)+30d0*v(3871)+6d0*v(3987)+v(4086))+v(7522)*(v(381)*v(4037)+v(382)*v(4053)+v&
&(3347)*v(406)+v(3281)*v(407)+v(379)*v(4086)+v(3313)*v(8044)))/5040d0
v(4152)=(7d0*(360d0*v(3443)+120d0*v(3820)+30d0*v(3870)+6d0*v(3986)+v(4085))+v(7522)*(v(381)*v(4036)+v(382)*v(4052)+v&
&(3346)*v(406)+v(3280)*v(407)+v(379)*v(4085)+v(3312)*v(8044)))/5040d0
v(4151)=(7d0*(360d0*v(3442)+120d0*v(3819)+30d0*v(3869)+6d0*v(3985)+v(4084))+v(7522)*(v(381)*v(4035)+v(382)*v(4051)+v&
&(3345)*v(406)+v(3279)*v(407)+v(379)*v(4084)+v(3311)*v(8044)))/5040d0
v(4150)=(7d0*(360d0*v(3441)+120d0*v(3818)+30d0*v(3868)+6d0*v(3984)+v(4083))+v(7522)*(v(381)*v(4034)+v(382)*v(4050)+v&
&(3344)*v(406)+v(3278)*v(407)+v(379)*v(4083)+v(3310)*v(8044)))/5040d0
v(4149)=(7d0*(360d0*v(3440)+120d0*v(3817)+30d0*v(3867)+6d0*v(3983)+v(4082))+v(7522)*(v(381)*v(4033)+v(382)*v(4049)+v&
&(3343)*v(406)+v(3277)*v(407)+v(379)*v(4082)+v(3309)*v(8044)))/5040d0
v(4148)=(7d0*(360d0*v(3439)+120d0*v(3816)+30d0*v(3866)+6d0*v(3982)+v(4081))+v(7522)*(v(381)*v(4032)+v(382)*v(4048)+v&
&(3342)*v(406)+v(3276)*v(407)+v(379)*v(4081)+v(3308)*v(8044)))/5040d0
v(4147)=(7d0*(360d0*v(3438)+120d0*v(3815)+30d0*v(3865)+6d0*v(3981)+v(4080))+v(7522)*(v(381)*v(4031)+v(382)*v(4047)+v&
&(3341)*v(406)+v(3275)*v(407)+v(379)*v(4080)+v(3307)*v(8044)))/5040d0
v(4146)=v(3437)/2d0+v(3814)/6d0+v(3864)/24d0+v(3980)/120d0+v(4079)/720d0+v(8035)+((v(3306)*v(403)+v(381)*v(4030)+v(382&
&)*v(4046)+v(3340)*v(406)+v(3274)*v(407)+v(379)*v(4079))*v(7522)+v(7518)*(v(381)*v(403)+v(8048)))/5040d0
v(4129)=(v(3321)*v(407)+v(381)*v(4096))*v(7522)
v(4145)=(2520d0*v(3780)+840d0*v(3863)+210d0*v(3946)+42d0*v(4029)+7d0*v(4045)+v(4078)+v(4129)+v(7522)*(v(376)*v(4045)+v&
&(3273)*v(8044)))/5040d0
v(4128)=(v(3320)*v(407)+v(381)*v(4095))*v(7522)
v(4144)=(2520d0*v(3779)+840d0*v(3862)+210d0*v(3945)+42d0*v(4028)+7d0*v(4044)+v(4077)+v(4128)+v(7522)*(v(376)*v(4044)+v&
&(3272)*v(8044)))/5040d0
v(4127)=(v(3319)*v(407)+v(381)*v(4094))*v(7522)
v(4143)=(2520d0*v(3778)+840d0*v(3861)+210d0*v(3944)+42d0*v(4027)+7d0*v(4043)+v(4076)+v(4127)+v(7522)*(v(376)*v(4043)+v&
&(3271)*v(8044)))/5040d0
v(4126)=(v(3318)*v(407)+v(381)*v(4093))*v(7522)
v(4142)=(2520d0*v(3777)+840d0*v(3860)+210d0*v(3943)+42d0*v(4026)+7d0*v(4042)+v(4075)+v(4126)+v(7522)*(v(376)*v(4042)+v&
&(3270)*v(8044)))/5040d0
v(4125)=(v(3317)*v(407)+v(381)*v(4092))*v(7522)
v(4141)=(2520d0*v(3776)+840d0*v(3859)+210d0*v(3942)+42d0*v(4025)+7d0*v(4041)+v(4074)+v(4125)+v(7522)*(v(376)*v(4041)+v&
&(3269)*v(8044)))/5040d0
v(4123)=v(407)*v(4391)
v(4124)=v(4123)+v(4091)*v(8017)
v(4140)=(2520d0*v(3775)+840d0*v(3858)+210d0*v(3941)+42d0*v(4024)+7d0*v(4040)+v(4073)+v(4124)+v(7522)*(v(376)*v(4040)+v&
&(3268)*v(8044)))/5040d0
v(4122)=v(4392)+v(4090)*v(8017)
v(4139)=(2520d0*v(3774)+840d0*v(3857)+210d0*v(3940)+42d0*v(4023)+7d0*v(4039)+v(4072)+v(4122)+v(7522)*(v(376)*v(4039)+v&
&(3267)*v(8044)))/5040d0
v(4121)=(v(3314)*v(407)+v(381)*v(4087))*v(7522)
v(4138)=(2520d0*v(3773)+840d0*v(3856)+210d0*v(3939)+42d0*v(4022)+7d0*v(4038)+v(4071)+v(4121)+v(7522)*(v(376)*v(4038)+v&
&(3266)*v(8044)))/5040d0
v(4120)=(v(3313)*v(407)+v(381)*v(4086))*v(7522)
v(4137)=(2520d0*v(3772)+840d0*v(3855)+210d0*v(3938)+42d0*v(4021)+7d0*v(4037)+v(4070)+v(4120)+v(7522)*(v(376)*v(4037)+v&
&(3265)*v(8044)))/5040d0
v(4119)=(v(3312)*v(407)+v(381)*v(4085))*v(7522)
v(4136)=(2520d0*v(3771)+840d0*v(3854)+210d0*v(3937)+42d0*v(4020)+7d0*v(4036)+v(4069)+v(4119)+v(7522)*(v(376)*v(4036)+v&
&(3264)*v(8044)))/5040d0
v(4118)=(v(3311)*v(407)+v(381)*v(4084))*v(7522)
v(4135)=(2520d0*v(3770)+840d0*v(3853)+210d0*v(3936)+42d0*v(4019)+7d0*v(4035)+v(4068)+v(4118)+v(7522)*(v(376)*v(4035)+v&
&(3263)*v(8044)))/5040d0
v(4117)=(v(3310)*v(407)+v(381)*v(4083))*v(7522)
v(4134)=(2520d0*v(3769)+840d0*v(3852)+210d0*v(3935)+42d0*v(4018)+7d0*v(4034)+v(4067)+v(4117)+v(7522)*(v(376)*v(4034)+v&
&(3262)*v(8044)))/5040d0
v(4116)=(v(3309)*v(407)+v(381)*v(4082))*v(7522)
v(4133)=(2520d0*v(3768)+840d0*v(3851)+210d0*v(3934)+42d0*v(4017)+7d0*v(4033)+v(4066)+v(4116)+v(7522)*(v(376)*v(4033)+v&
&(3261)*v(8044)))/5040d0
v(4115)=(v(3308)*v(407)+v(381)*v(4081))*v(7522)
v(4132)=(2520d0*v(3767)+840d0*v(3850)+210d0*v(3933)+42d0*v(4016)+7d0*v(4032)+v(4065)+v(4115)+v(7522)*(v(376)*v(4032)+v&
&(3260)*v(8044)))/5040d0
v(4114)=(v(3307)*v(407)+v(381)*v(4080))*v(7522)
v(4131)=(2520d0*v(3766)+840d0*v(3849)+210d0*v(3932)+42d0*v(4015)+7d0*v(4031)+v(4064)+v(4114)+v(7522)*(v(376)*v(4031)+v&
&(3259)*v(8044)))/5040d0
v(4113)=v(4079)*v(8017)+v(407)*v(8035)
v(4130)=(2520d0*v(3764)+840d0*v(3848)+210d0*v(3931)+42d0*v(4014)+7d0*v(4030)+v(4063)+v(4113)+v(376)*(v(4030)*v(7522)+v&
&(7518)*v(8044))+v(8044)*v(8045))/5040d0
v(4112)=(7d0*(360d0*v(3490)+120d0*v(3797)+30d0*v(3914)+6d0*v(3963)+v(4062))+(5040d0*v(3386)+v(3386)*v(403)+v(383)*v&
&(4045)+v(3305)*v(406)+v(380)*v(4062)+v(3354)*v(407)+v(382)*v(4096))*v(7522))/5040d0
v(4628)=statev(17)*v(4145)+statev(15)*v(4164)+v(4112)*v(7508)
v(4580)=statev(19)*v(4112)+statev(14)*v(4145)+v(4164)*v(7507)
v(4180)=statev(16)*v(4112)+statev(18)*v(4164)+v(4145)*v(7506)
v(4111)=(7d0*(360d0*v(3489)+120d0*v(3796)+30d0*v(3913)+6d0*v(3962)+v(4061))+(5040d0*v(3385)+v(3385)*v(403)+v(383)*v&
&(4044)+v(3304)*v(406)+v(380)*v(4061)+v(3353)*v(407)+v(382)*v(4095))*v(7522))/5040d0
v(4627)=statev(17)*v(4144)+statev(15)*v(4163)+v(4111)*v(7508)
v(4579)=statev(19)*v(4111)+statev(14)*v(4144)+v(4163)*v(7507)
v(4179)=statev(16)*v(4111)+statev(18)*v(4163)+v(4144)*v(7506)
v(4110)=(7d0*(360d0*v(3488)+120d0*v(3795)+30d0*v(3912)+6d0*v(3961)+v(4060))+(5040d0*v(3384)+v(3384)*v(403)+v(383)*v&
&(4043)+v(3303)*v(406)+v(380)*v(4060)+v(3352)*v(407)+v(382)*v(4094))*v(7522))/5040d0
v(4626)=statev(17)*v(4143)+statev(15)*v(4162)+v(4110)*v(7508)
v(4578)=statev(19)*v(4110)+statev(14)*v(4143)+v(4162)*v(7507)
v(4178)=statev(16)*v(4110)+statev(18)*v(4162)+v(4143)*v(7506)
v(4109)=(7d0*(360d0*v(3487)+120d0*v(3794)+30d0*v(3911)+6d0*v(3960)+v(4059))+(5040d0*v(3383)+v(3383)*v(403)+v(383)*v&
&(4042)+v(380)*v(4059)+v(3302)*v(406)+v(3351)*v(407)+v(382)*v(4093))*v(7522))/5040d0
v(4625)=statev(17)*v(4142)+statev(15)*v(4161)+v(4109)*v(7508)
v(4577)=statev(19)*v(4109)+statev(14)*v(4142)+v(4161)*v(7507)
v(4177)=statev(16)*v(4109)+statev(18)*v(4161)+v(4142)*v(7506)
v(4108)=(7d0*(360d0*v(3486)+120d0*v(3793)+30d0*v(3910)+6d0*v(3959)+v(4058))+(5040d0*v(3382)+v(3382)*v(403)+v(383)*v&
&(4041)+v(380)*v(4058)+v(3301)*v(406)+v(3350)*v(407)+v(382)*v(4092))*v(7522))/5040d0
v(4624)=statev(17)*v(4141)+statev(15)*v(4160)+v(4108)*v(7508)
v(4576)=statev(19)*v(4108)+statev(14)*v(4141)+v(4160)*v(7507)
v(4176)=statev(16)*v(4108)+statev(18)*v(4160)+v(4141)*v(7506)
v(4107)=((v(3348)*v(403)+v(383)*v(4040)+v(380)*v(4057)+v(3300)*v(406)+v(3349)*v(407)+v(382)*v(4091))*v(7522)+7d0*&
&(360d0*v(3485)+120d0*v(3792)+30d0*v(3909)+6d0*v(3958)+v(4057)+v(8058)))/5040d0
v(4623)=statev(17)*v(4140)+statev(15)*v(4159)+v(4107)*v(7508)
v(4575)=statev(19)*v(4107)+statev(14)*v(4140)+v(4159)*v(7507)
v(4175)=statev(16)*v(4107)+statev(18)*v(4159)+v(4140)*v(7506)
v(4106)=(2520d0*v(3483)+840d0*v(3791)+210d0*v(3908)+42d0*v(3957)+7d0*v(4056)+v(4396)+v(7522)*(v(383)*v(4039)+v(380)*v&
&(4056)+v(3299)*v(406)+v(382)*v(4090)+v(3381)*v(8044)))/5040d0
v(4622)=statev(17)*v(4139)+statev(15)*v(4158)+v(4106)*v(7508)
v(4574)=statev(19)*v(4106)+statev(14)*v(4139)+v(4158)*v(7507)
v(4174)=statev(16)*v(4106)+statev(18)*v(4158)+v(4139)*v(7506)
v(4105)=(2520d0*v(3480)+840d0*v(3790)+210d0*v(3907)+42d0*v(3956)+7d0*v(4055)+v(4123)+(v(383)*v(4038)+v(380)*v(4055)+v&
&(3298)*v(406)+v(382)*v(4087))*v(7522)+v(8046))/5040d0
v(4621)=statev(17)*v(4138)+statev(15)*v(4154)+v(4105)*v(7508)
v(4573)=statev(19)*v(4105)+statev(14)*v(4138)+v(4154)*v(7507)
v(4173)=statev(16)*v(4105)+statev(18)*v(4154)+v(4138)*v(7506)
v(4104)=(7d0*(360d0*v(3478)+120d0*v(3788)+30d0*v(3904)+6d0*v(3954)+v(4053))+(5040d0*v(3380)+v(3380)*v(403)+v(383)*v&
&(4037)+v(380)*v(4053)+v(3297)*v(406)+v(3347)*v(407)+v(382)*v(4086))*v(7522))/5040d0
v(4620)=statev(17)*v(4137)+statev(15)*v(4153)+v(4104)*v(7508)
v(4572)=statev(19)*v(4104)+statev(14)*v(4137)+v(4153)*v(7507)
v(4172)=statev(16)*v(4104)+statev(18)*v(4153)+v(4137)*v(7506)
v(4103)=(7d0*(360d0*v(3477)+120d0*v(3787)+30d0*v(3903)+6d0*v(3953)+v(4052))+(5040d0*v(3379)+v(3379)*v(403)+v(383)*v&
&(4036)+v(380)*v(4052)+v(3296)*v(406)+v(3346)*v(407)+v(382)*v(4085))*v(7522))/5040d0
v(4619)=statev(17)*v(4136)+statev(15)*v(4152)+v(4103)*v(7508)
v(4571)=statev(19)*v(4103)+statev(14)*v(4136)+v(4152)*v(7507)
v(4171)=statev(16)*v(4103)+statev(18)*v(4152)+v(4136)*v(7506)
v(4102)=(7d0*(360d0*v(3476)+120d0*v(3786)+30d0*v(3902)+6d0*v(3952)+v(4051))+(5040d0*v(3378)+v(3378)*v(403)+v(383)*v&
&(4035)+v(380)*v(4051)+v(3295)*v(406)+v(3345)*v(407)+v(382)*v(4084))*v(7522))/5040d0
v(4618)=statev(17)*v(4135)+statev(15)*v(4151)+v(4102)*v(7508)
v(4570)=statev(19)*v(4102)+statev(14)*v(4135)+v(4151)*v(7507)
v(4170)=statev(16)*v(4102)+statev(18)*v(4151)+v(4135)*v(7506)
v(4101)=(7d0*(360d0*v(3475)+120d0*v(3785)+30d0*v(3901)+6d0*v(3951)+v(4050))+(5040d0*v(3377)+v(3377)*v(403)+v(383)*v&
&(4034)+v(380)*v(4050)+v(3294)*v(406)+v(3344)*v(407)+v(382)*v(4083))*v(7522))/5040d0
v(4617)=statev(17)*v(4134)+statev(15)*v(4150)+v(4101)*v(7508)
v(4569)=statev(19)*v(4101)+statev(14)*v(4134)+v(4150)*v(7507)
v(4169)=statev(16)*v(4101)+statev(18)*v(4150)+v(4134)*v(7506)
v(4100)=(7d0*(360d0*v(3474)+120d0*v(3784)+30d0*v(3900)+6d0*v(3950)+v(4049))+(5040d0*v(3376)+v(3376)*v(403)+v(383)*v&
&(4033)+v(380)*v(4049)+v(3293)*v(406)+v(3343)*v(407)+v(382)*v(4082))*v(7522))/5040d0
v(4616)=statev(17)*v(4133)+statev(15)*v(4149)+v(4100)*v(7508)
v(4568)=statev(19)*v(4100)+statev(14)*v(4133)+v(4149)*v(7507)
v(4168)=statev(16)*v(4100)+statev(18)*v(4149)+v(4133)*v(7506)
v(4099)=(7d0*(360d0*v(3473)+120d0*v(3783)+30d0*v(3899)+6d0*v(3949)+v(4048))+(5040d0*v(3375)+v(3375)*v(403)+v(383)*v&
&(4032)+v(380)*v(4048)+v(3292)*v(406)+v(3342)*v(407)+v(382)*v(4081))*v(7522))/5040d0
v(4615)=statev(17)*v(4132)+statev(15)*v(4148)+v(4099)*v(7508)
v(4567)=statev(19)*v(4099)+statev(14)*v(4132)+v(4148)*v(7507)
v(4167)=statev(16)*v(4099)+statev(18)*v(4148)+v(4132)*v(7506)
v(4098)=(7d0*(360d0*v(3472)+120d0*v(3782)+30d0*v(3898)+6d0*v(3948)+v(4047))+(5040d0*v(3374)+v(3374)*v(403)+v(383)*v&
&(4031)+v(380)*v(4047)+v(3291)*v(406)+v(3341)*v(407)+v(382)*v(4080))*v(7522))/5040d0
v(4614)=statev(17)*v(4131)+statev(15)*v(4147)+v(4098)*v(7508)
v(4566)=statev(19)*v(4098)+statev(14)*v(4131)+v(4147)*v(7507)
v(4166)=statev(16)*v(4098)+statev(18)*v(4147)+v(4131)*v(7506)
v(4097)=v(3471)/2d0+v(3781)/6d0+v(3897)/24d0+v(3947)/120d0+v(4046)/720d0+v(8033)+((v(3373)*v(403)+v(383)*v(4030)+v(380&
&)*v(4046)+v(3290)*v(406)+v(3340)*v(407)+v(382)*v(4079))*v(7522)+v(7518)*(v(383)*v(403)+v(8047)))/5040d0
v(4613)=statev(17)*v(4130)+statev(15)*v(4146)+v(4097)*v(7508)
v(4565)=statev(19)*v(4097)+statev(14)*v(4130)+v(4146)*v(7507)
v(4165)=statev(16)*v(4097)+statev(18)*v(4146)+v(4130)*v(7506)
v(445)=(7d0*(360d0*v(395)+120d0*v(399)+30d0*v(401)+6d0*v(405)+v(406))+v(7522)*(v(383)*v(8044)+v(8047)))/5040d0
v(425)=v(407)*v(8017)
v(8060)=5040d0+v(425)
v(447)=(2520d0*v(393)+840d0*v(394)+210d0*v(397)+42d0*v(400)+7d0*v(403)+v(442)+v(8036)*v(8044)+v(8060))/5040d0
v(409)=(7d0*(360d0*v(396)+120d0*v(398)+30d0*v(402)+6d0*v(404)+v(407))+v(7522)*(v(381)*v(8044)+v(8048)))/5040d0
v(408)=statev(18)*v(409)+statev(16)*v(445)+v(447)*v(7506)
v(411)=v(410)+v(232)*v(4181)+v(427)
v(8049)=v(383)*v(396)+v(382)*v(411)+v(380)*v(415)
v(4248)=v(3436)+v(3470)+(v(3289)*v(411)+v(379)*v(4198))*v(7522)
v(4247)=v(3435)+v(3469)+(v(3288)*v(411)+v(379)*v(4197))*v(7522)
v(4246)=v(3434)+v(3468)+(v(3287)*v(411)+v(379)*v(4196))*v(7522)
v(4245)=v(3433)+v(3467)+(v(3286)*v(411)+v(379)*v(4195))*v(7522)
v(4244)=v(3432)+v(3466)+(v(3285)*v(411)+v(379)*v(4194))*v(7522)
v(4243)=v(3431)+v(3465)+(v(3284)*v(411)+v(379)*v(4193))*v(7522)
v(4242)=v(3430)+v(3464)+(v(3283)*v(411)+v(379)*v(4192))*v(7522)
v(4241)=v(3429)+v(3463)+(v(3282)*v(411)+v(379)*v(4191))*v(7522)
v(4240)=v(3428)+v(3462)+(v(3281)*v(411)+v(379)*v(4190))*v(7522)
v(4239)=v(3427)+v(3461)+(v(3280)*v(411)+v(379)*v(4189))*v(7522)
v(4238)=v(3426)+v(3460)+(v(3279)*v(411)+v(379)*v(4188))*v(7522)
v(4237)=v(3425)+v(3459)+(v(3278)*v(411)+v(379)*v(4187))*v(7522)
v(4236)=v(3424)+v(3458)+(v(3277)*v(411)+v(379)*v(4186))*v(7522)
v(4235)=v(3423)+v(3457)+(v(3276)*v(411)+v(379)*v(4185))*v(7522)
v(4234)=v(3422)+v(3456)+(v(3275)*v(411)+v(379)*v(4184))*v(7522)
v(4233)=v(3421)+v(3455)+v(4182)*v(8051)+v(411)*v(8052)
v(4216)=(v(3420)*v(380)+v(3454)*v(383)+v(3386)*v(396)+v(3354)*v(411)+v(3305)*v(415)+v(382)*v(4198))*v(7522)
v(4215)=(v(3419)*v(380)+v(3453)*v(383)+v(3385)*v(396)+v(3353)*v(411)+v(3304)*v(415)+v(382)*v(4197))*v(7522)
v(4214)=(v(3418)*v(380)+v(3452)*v(383)+v(3384)*v(396)+v(3352)*v(411)+v(3303)*v(415)+v(382)*v(4196))*v(7522)
v(4213)=(v(3417)*v(380)+v(3451)*v(383)+v(3383)*v(396)+v(3351)*v(411)+v(3302)*v(415)+v(382)*v(4195))*v(7522)
v(4212)=(v(3416)*v(380)+v(3450)*v(383)+v(3382)*v(396)+v(3350)*v(411)+v(3301)*v(415)+v(382)*v(4194))*v(7522)
v(4211)=v(4210)+(v(3415)*v(380)+v(3449)*v(383)+v(3349)*v(411)+v(3300)*v(415)+v(382)*v(4193))*v(7522)
v(4209)=(v(3414)*v(380)+v(3447)*v(383)+v(3381)*v(396)+v(3348)*v(411)+v(3299)*v(415)+v(382)*v(4192))*v(7522)
v(4208)=v(4207)+(v(3413)*v(380)+v(3446)*v(383)+v(3316)*v(411)+v(3298)*v(415)+v(382)*v(4191))*v(7522)
v(4206)=(v(3412)*v(380)+v(3444)*v(383)+v(3380)*v(396)+v(3347)*v(411)+v(3297)*v(415)+v(382)*v(4190))*v(7522)
v(4205)=(v(3411)*v(380)+v(3443)*v(383)+v(3379)*v(396)+v(3346)*v(411)+v(3296)*v(415)+v(382)*v(4189))*v(7522)
v(4204)=(v(3410)*v(380)+v(3442)*v(383)+v(3378)*v(396)+v(3345)*v(411)+v(3295)*v(415)+v(382)*v(4188))*v(7522)
v(4203)=(v(3409)*v(380)+v(3441)*v(383)+v(3377)*v(396)+v(3344)*v(411)+v(3294)*v(415)+v(382)*v(4187))*v(7522)
v(4202)=(v(3408)*v(380)+v(3440)*v(383)+v(3376)*v(396)+v(3343)*v(411)+v(3293)*v(415)+v(382)*v(4186))*v(7522)
v(4201)=(v(3407)*v(380)+v(3439)*v(383)+v(3375)*v(396)+v(3342)*v(411)+v(3292)*v(415)+v(382)*v(4185))*v(7522)
v(4200)=(v(3406)*v(380)+v(3438)*v(383)+v(3374)*v(396)+v(3341)*v(411)+v(3291)*v(415)+v(382)*v(4184))*v(7522)
v(4199)=(v(3405)*v(380)+v(3437)*v(383)+v(3373)*v(396)+v(3340)*v(411)+v(3290)*v(415)+v(382)*v(4182))*v(7522)+v(7518)*v&
&(8049)
v(417)=v(7522)*v(8049)
v(4232)=(v(3354)*v(417)+v(382)*v(4216))*v(7522)
v(4231)=(v(3353)*v(417)+v(382)*v(4215))*v(7522)
v(4230)=(v(3352)*v(417)+v(382)*v(4214))*v(7522)
v(4229)=(v(3351)*v(417)+v(382)*v(4213))*v(7522)
v(4228)=(v(3350)*v(417)+v(382)*v(4212))*v(7522)
v(4227)=(v(3349)*v(417)+v(382)*v(4211))*v(7522)
v(4226)=(v(3348)*v(417)+v(382)*v(4209))*v(7522)
v(4225)=(v(3316)*v(417)+v(382)*v(4208))*v(7522)
v(4224)=(v(3347)*v(417)+v(382)*v(4206))*v(7522)
v(4223)=(v(3346)*v(417)+v(382)*v(4205))*v(7522)
v(4222)=(v(3345)*v(417)+v(382)*v(4204))*v(7522)
v(4221)=(v(3344)*v(417)+v(382)*v(4203))*v(7522)
v(4220)=(v(3343)*v(417)+v(382)*v(4202))*v(7522)
v(4219)=(v(3342)*v(417)+v(382)*v(4201))*v(7522)
v(4218)=(v(3341)*v(417)+v(382)*v(4200))*v(7522)
v(4217)=v(4199)*v(8015)+v(417)*v(8050)
v(433)=v(417)*v(8015)
v(413)=v(412)+v(431)+v(411)*v(8051)
v(8053)=v(383)*v(398)+v(382)*v(413)+v(380)*v(417)
v(4298)=v(3847)+v(4232)+(v(3289)*v(413)+v(379)*v(4248))*v(7522)
v(4297)=v(3846)+v(4231)+(v(3288)*v(413)+v(379)*v(4247))*v(7522)
v(4296)=v(3845)+v(4230)+(v(3287)*v(413)+v(379)*v(4246))*v(7522)
v(4295)=v(3844)+v(4229)+(v(3286)*v(413)+v(379)*v(4245))*v(7522)
v(4294)=v(3843)+v(4228)+(v(3285)*v(413)+v(379)*v(4244))*v(7522)
v(4293)=v(3842)+v(4227)+(v(3284)*v(413)+v(379)*v(4243))*v(7522)
v(4292)=v(3841)+v(4226)+(v(3283)*v(413)+v(379)*v(4242))*v(7522)
v(4291)=v(3840)+v(4225)+(v(3282)*v(413)+v(379)*v(4241))*v(7522)
v(4290)=v(3839)+v(4224)+(v(3281)*v(413)+v(379)*v(4240))*v(7522)
v(4289)=v(3838)+v(4223)+(v(3280)*v(413)+v(379)*v(4239))*v(7522)
v(4288)=v(3837)+v(4222)+(v(3279)*v(413)+v(379)*v(4238))*v(7522)
v(4287)=v(3836)+v(4221)+(v(3278)*v(413)+v(379)*v(4237))*v(7522)
v(4286)=v(3835)+v(4220)+(v(3277)*v(413)+v(379)*v(4236))*v(7522)
v(4285)=v(3834)+v(4219)+(v(3276)*v(413)+v(379)*v(4235))*v(7522)
v(4284)=v(3833)+v(4218)+(v(3275)*v(413)+v(379)*v(4234))*v(7522)
v(4283)=v(3832)+v(4217)+v(4233)*v(8051)+v(413)*v(8052)
v(4266)=(v(383)*v(3831)+v(3386)*v(398)+v(3354)*v(413)+v(3305)*v(417)+v(380)*v(4216)+v(382)*v(4248))*v(7522)
v(4265)=(v(383)*v(3830)+v(3385)*v(398)+v(3353)*v(413)+v(3304)*v(417)+v(380)*v(4215)+v(382)*v(4247))*v(7522)
v(4264)=(v(3829)*v(383)+v(3384)*v(398)+v(3352)*v(413)+v(3303)*v(417)+v(380)*v(4214)+v(382)*v(4246))*v(7522)
v(4263)=(v(3828)*v(383)+v(3383)*v(398)+v(3351)*v(413)+v(3302)*v(417)+v(380)*v(4213)+v(382)*v(4245))*v(7522)
v(4262)=(v(3827)*v(383)+v(3382)*v(398)+v(3350)*v(413)+v(3301)*v(417)+v(380)*v(4212)+v(382)*v(4244))*v(7522)
v(4261)=v(4260)+(v(3826)*v(383)+v(3349)*v(413)+v(3300)*v(417)+v(380)*v(4211)+v(382)*v(4243))*v(7522)
v(4259)=(v(3825)*v(383)+v(3381)*v(398)+v(3348)*v(413)+v(3299)*v(417)+v(380)*v(4209)+v(382)*v(4242))*v(7522)
v(4258)=v(4257)+(v(3822)*v(383)+v(3316)*v(413)+v(3298)*v(417)+v(380)*v(4208)+v(382)*v(4241))*v(7522)
v(4256)=(v(3821)*v(383)+v(3380)*v(398)+v(3347)*v(413)+v(3297)*v(417)+v(380)*v(4206)+v(382)*v(4240))*v(7522)
v(4255)=(v(3820)*v(383)+v(3379)*v(398)+v(3346)*v(413)+v(3296)*v(417)+v(380)*v(4205)+v(382)*v(4239))*v(7522)
v(4254)=(v(3819)*v(383)+v(3378)*v(398)+v(3345)*v(413)+v(3295)*v(417)+v(380)*v(4204)+v(382)*v(4238))*v(7522)
v(4253)=(v(3818)*v(383)+v(3377)*v(398)+v(3344)*v(413)+v(3294)*v(417)+v(380)*v(4203)+v(382)*v(4237))*v(7522)
v(4252)=(v(3817)*v(383)+v(3376)*v(398)+v(3343)*v(413)+v(3293)*v(417)+v(380)*v(4202)+v(382)*v(4236))*v(7522)
v(4251)=(v(3816)*v(383)+v(3375)*v(398)+v(3342)*v(413)+v(3292)*v(417)+v(380)*v(4201)+v(382)*v(4235))*v(7522)
v(4250)=(v(3815)*v(383)+v(3374)*v(398)+v(3341)*v(413)+v(3291)*v(417)+v(380)*v(4200)+v(382)*v(4234))*v(7522)
v(4249)=(v(3814)*v(383)+v(3373)*v(398)+v(3340)*v(413)+v(3290)*v(417)+v(380)*v(4199)+v(382)*v(4233))*v(7522)+v(7518)*v&
&(8053)
v(421)=v(7522)*v(8053)
v(4282)=(v(3354)*v(421)+v(382)*v(4266))*v(7522)
v(4281)=(v(3353)*v(421)+v(382)*v(4265))*v(7522)
v(4280)=(v(3352)*v(421)+v(382)*v(4264))*v(7522)
v(4279)=(v(3351)*v(421)+v(382)*v(4263))*v(7522)
v(4278)=(v(3350)*v(421)+v(382)*v(4262))*v(7522)
v(4277)=(v(3349)*v(421)+v(382)*v(4261))*v(7522)
v(4276)=(v(3348)*v(421)+v(382)*v(4259))*v(7522)
v(4275)=(v(3316)*v(421)+v(382)*v(4258))*v(7522)
v(4274)=(v(3347)*v(421)+v(382)*v(4256))*v(7522)
v(4273)=(v(3346)*v(421)+v(382)*v(4255))*v(7522)
v(4272)=(v(3345)*v(421)+v(382)*v(4254))*v(7522)
v(4271)=(v(3344)*v(421)+v(382)*v(4253))*v(7522)
v(4270)=(v(3343)*v(421)+v(382)*v(4252))*v(7522)
v(4269)=(v(3342)*v(421)+v(382)*v(4251))*v(7522)
v(4268)=(v(3341)*v(421)+v(382)*v(4250))*v(7522)
v(4267)=v(4249)*v(8015)+v(421)*v(8050)
v(437)=v(421)*v(8015)
v(416)=v(414)+v(433)+v(413)*v(8051)
v(8054)=v(383)*v(402)+v(382)*v(416)+v(380)*v(421)
v(4348)=v(3896)+v(4282)+(v(3289)*v(416)+v(379)*v(4298))*v(7522)
v(4347)=v(3895)+v(4281)+(v(3288)*v(416)+v(379)*v(4297))*v(7522)
v(4346)=v(3894)+v(4280)+(v(3287)*v(416)+v(379)*v(4296))*v(7522)
v(4345)=v(3893)+v(4279)+(v(3286)*v(416)+v(379)*v(4295))*v(7522)
v(4344)=v(3892)+v(4278)+(v(3285)*v(416)+v(379)*v(4294))*v(7522)
v(4343)=v(3891)+v(4277)+(v(3284)*v(416)+v(379)*v(4293))*v(7522)
v(4342)=v(3890)+v(4276)+(v(3283)*v(416)+v(379)*v(4292))*v(7522)
v(4341)=v(3889)+v(4275)+(v(3282)*v(416)+v(379)*v(4291))*v(7522)
v(4340)=v(3888)+v(4274)+(v(3281)*v(416)+v(379)*v(4290))*v(7522)
v(4339)=v(3887)+v(4273)+(v(3280)*v(416)+v(379)*v(4289))*v(7522)
v(4338)=v(3886)+v(4272)+(v(3279)*v(416)+v(379)*v(4288))*v(7522)
v(4337)=v(3885)+v(4271)+(v(3278)*v(416)+v(379)*v(4287))*v(7522)
v(4336)=v(3884)+v(4270)+(v(3277)*v(416)+v(379)*v(4286))*v(7522)
v(4335)=v(3883)+v(4269)+(v(3276)*v(416)+v(379)*v(4285))*v(7522)
v(4334)=v(3882)+v(4268)+(v(3275)*v(416)+v(379)*v(4284))*v(7522)
v(4333)=v(3881)+v(4267)+v(4283)*v(8051)+v(416)*v(8052)
v(4316)=(v(383)*v(3880)+v(3386)*v(402)+v(3354)*v(416)+v(3305)*v(421)+v(380)*v(4266)+v(382)*v(4298))*v(7522)
v(4315)=(v(383)*v(3879)+v(3385)*v(402)+v(3353)*v(416)+v(3304)*v(421)+v(380)*v(4265)+v(382)*v(4297))*v(7522)
v(4314)=(v(383)*v(3878)+v(3384)*v(402)+v(3352)*v(416)+v(3303)*v(421)+v(380)*v(4264)+v(382)*v(4296))*v(7522)
v(4313)=(v(383)*v(3877)+v(3383)*v(402)+v(3351)*v(416)+v(3302)*v(421)+v(380)*v(4263)+v(382)*v(4295))*v(7522)
v(4312)=(v(383)*v(3876)+v(3382)*v(402)+v(3350)*v(416)+v(3301)*v(421)+v(380)*v(4262)+v(382)*v(4294))*v(7522)
v(4311)=v(4310)+(v(383)*v(3875)+v(3349)*v(416)+v(3300)*v(421)+v(380)*v(4261)+v(382)*v(4293))*v(7522)
v(4309)=(v(383)*v(3874)+v(3381)*v(402)+v(3348)*v(416)+v(3299)*v(421)+v(380)*v(4259)+v(382)*v(4292))*v(7522)
v(4308)=v(4307)+(v(383)*v(3872)+v(3316)*v(416)+v(3298)*v(421)+v(380)*v(4258)+v(382)*v(4291))*v(7522)
v(4306)=(v(383)*v(3871)+v(3380)*v(402)+v(3347)*v(416)+v(3297)*v(421)+v(380)*v(4256)+v(382)*v(4290))*v(7522)
v(4305)=(v(383)*v(3870)+v(3379)*v(402)+v(3346)*v(416)+v(3296)*v(421)+v(380)*v(4255)+v(382)*v(4289))*v(7522)
v(4304)=(v(383)*v(3869)+v(3378)*v(402)+v(3345)*v(416)+v(3295)*v(421)+v(380)*v(4254)+v(382)*v(4288))*v(7522)
v(4303)=(v(383)*v(3868)+v(3377)*v(402)+v(3344)*v(416)+v(3294)*v(421)+v(380)*v(4253)+v(382)*v(4287))*v(7522)
v(4302)=(v(383)*v(3867)+v(3376)*v(402)+v(3343)*v(416)+v(3293)*v(421)+v(380)*v(4252)+v(382)*v(4286))*v(7522)
v(4301)=(v(383)*v(3866)+v(3375)*v(402)+v(3342)*v(416)+v(3292)*v(421)+v(380)*v(4251)+v(382)*v(4285))*v(7522)
v(4300)=(v(383)*v(3865)+v(3374)*v(402)+v(3341)*v(416)+v(3291)*v(421)+v(380)*v(4250)+v(382)*v(4284))*v(7522)
v(4299)=(v(383)*v(3864)+v(3373)*v(402)+v(3340)*v(416)+v(3290)*v(421)+v(380)*v(4249)+v(382)*v(4283))*v(7522)+v(7518)*v&
&(8054)
v(423)=v(7522)*v(8054)
v(4332)=(v(3354)*v(423)+v(382)*v(4316))*v(7522)
v(4331)=(v(3353)*v(423)+v(382)*v(4315))*v(7522)
v(4330)=(v(3352)*v(423)+v(382)*v(4314))*v(7522)
v(4329)=(v(3351)*v(423)+v(382)*v(4313))*v(7522)
v(4328)=(v(3350)*v(423)+v(382)*v(4312))*v(7522)
v(4327)=(v(3349)*v(423)+v(382)*v(4311))*v(7522)
v(4326)=(v(3348)*v(423)+v(382)*v(4309))*v(7522)
v(4325)=(v(3316)*v(423)+v(382)*v(4308))*v(7522)
v(4324)=(v(3347)*v(423)+v(382)*v(4306))*v(7522)
v(4323)=(v(3346)*v(423)+v(382)*v(4305))*v(7522)
v(4322)=(v(3345)*v(423)+v(382)*v(4304))*v(7522)
v(4321)=(v(3344)*v(423)+v(382)*v(4303))*v(7522)
v(4320)=(v(3343)*v(423)+v(382)*v(4302))*v(7522)
v(4319)=(v(3342)*v(423)+v(382)*v(4301))*v(7522)
v(4318)=(v(3341)*v(423)+v(382)*v(4300))*v(7522)
v(4317)=v(4299)*v(8015)+v(423)*v(8050)
v(439)=v(423)*v(8015)
v(419)=v(418)+v(437)+v(416)*v(8051)
v(8055)=v(383)*v(404)+v(382)*v(419)+v(380)*v(423)
v(4382)=(v(383)*v(3997)+v(3386)*v(404)+v(3354)*v(419)+v(3305)*v(423)+v(380)*v(4316)+v(382)*v(4348))*v(7522)
v(4381)=(v(383)*v(3996)+v(3385)*v(404)+v(3353)*v(419)+v(3304)*v(423)+v(380)*v(4315)+v(382)*v(4347))*v(7522)
v(4380)=(v(383)*v(3995)+v(3384)*v(404)+v(3352)*v(419)+v(3303)*v(423)+v(380)*v(4314)+v(382)*v(4346))*v(7522)
v(4379)=(v(383)*v(3994)+v(3383)*v(404)+v(3351)*v(419)+v(3302)*v(423)+v(380)*v(4313)+v(382)*v(4345))*v(7522)
v(4378)=(v(383)*v(3993)+v(3382)*v(404)+v(3350)*v(419)+v(3301)*v(423)+v(380)*v(4312)+v(382)*v(4344))*v(7522)
v(4377)=v(4376)+(v(383)*v(3992)+v(3349)*v(419)+v(3300)*v(423)+v(380)*v(4311)+v(382)*v(4343))*v(7522)
v(4375)=(v(383)*v(3991)+v(3381)*v(404)+v(3348)*v(419)+v(3299)*v(423)+v(380)*v(4309)+v(382)*v(4342))*v(7522)
v(4374)=v(4373)+(v(383)*v(3988)+v(3316)*v(419)+v(3298)*v(423)+v(380)*v(4308)+v(382)*v(4341))*v(7522)
v(4372)=(v(383)*v(3987)+v(3380)*v(404)+v(3347)*v(419)+v(3297)*v(423)+v(380)*v(4306)+v(382)*v(4340))*v(7522)
v(4371)=(v(383)*v(3986)+v(3379)*v(404)+v(3346)*v(419)+v(3296)*v(423)+v(380)*v(4305)+v(382)*v(4339))*v(7522)
v(4370)=(v(383)*v(3985)+v(3378)*v(404)+v(3345)*v(419)+v(3295)*v(423)+v(380)*v(4304)+v(382)*v(4338))*v(7522)
v(4369)=(v(383)*v(3984)+v(3377)*v(404)+v(3344)*v(419)+v(3294)*v(423)+v(380)*v(4303)+v(382)*v(4337))*v(7522)
v(4368)=(v(383)*v(3983)+v(3376)*v(404)+v(3343)*v(419)+v(3293)*v(423)+v(380)*v(4302)+v(382)*v(4336))*v(7522)
v(4367)=(v(383)*v(3982)+v(3375)*v(404)+v(3342)*v(419)+v(3292)*v(423)+v(380)*v(4301)+v(382)*v(4335))*v(7522)
v(4366)=(v(383)*v(3981)+v(3374)*v(404)+v(3341)*v(419)+v(3291)*v(423)+v(380)*v(4300)+v(382)*v(4334))*v(7522)
v(4365)=(v(383)*v(3980)+v(3373)*v(404)+v(3340)*v(419)+v(3290)*v(423)+v(380)*v(4299)+v(382)*v(4333))*v(7522)+v(7518)*v&
&(8055)
v(4364)=v(4013)+v(4332)+(v(3289)*v(419)+v(379)*v(4348))*v(7522)
v(4363)=v(4012)+v(4331)+(v(3288)*v(419)+v(379)*v(4347))*v(7522)
v(4362)=v(4011)+v(4330)+(v(3287)*v(419)+v(379)*v(4346))*v(7522)
v(4361)=v(4010)+v(4329)+(v(3286)*v(419)+v(379)*v(4345))*v(7522)
v(4360)=v(4009)+v(4328)+(v(3285)*v(419)+v(379)*v(4344))*v(7522)
v(4359)=v(4008)+v(4327)+(v(3284)*v(419)+v(379)*v(4343))*v(7522)
v(4358)=v(4007)+v(4326)+(v(3283)*v(419)+v(379)*v(4342))*v(7522)
v(4357)=v(4006)+v(4325)+(v(3282)*v(419)+v(379)*v(4341))*v(7522)
v(4356)=v(4005)+v(4324)+(v(3281)*v(419)+v(379)*v(4340))*v(7522)
v(4355)=v(4004)+v(4323)+(v(3280)*v(419)+v(379)*v(4339))*v(7522)
v(4354)=v(4003)+v(4322)+(v(3279)*v(419)+v(379)*v(4338))*v(7522)
v(4353)=v(4002)+v(4321)+(v(3278)*v(419)+v(379)*v(4337))*v(7522)
v(4352)=v(4001)+v(4320)+(v(3277)*v(419)+v(379)*v(4336))*v(7522)
v(4351)=v(4000)+v(4319)+(v(3276)*v(419)+v(379)*v(4335))*v(7522)
v(4350)=v(3999)+v(4318)+(v(3275)*v(419)+v(379)*v(4334))*v(7522)
v(4349)=v(3998)+v(4317)+v(4333)*v(8051)+v(419)*v(8052)
v(422)=v(420)+v(439)+v(419)*v(8051)
v(8056)=5040d0+v(422)
v(424)=v(7522)*v(8055)
v(8059)=v(383)*v(407)+v(380)*v(424)
v(4418)=(v(3354)*v(424)+v(382)*v(4382))*v(7522)
v(4434)=(v(4129)+2520d0*v(4198)+840d0*v(4248)+210d0*v(4298)+42d0*v(4348)+7d0*v(4364)+v(4418)+v(7522)*(v(379)*v(4364)+v&
&(3289)*v(8056)))/5040d0
v(4417)=(v(3353)*v(424)+v(382)*v(4381))*v(7522)
v(4433)=(v(4128)+2520d0*v(4197)+840d0*v(4247)+210d0*v(4297)+42d0*v(4347)+7d0*v(4363)+v(4417)+v(7522)*(v(379)*v(4363)+v&
&(3288)*v(8056)))/5040d0
v(4416)=(v(3352)*v(424)+v(382)*v(4380))*v(7522)
v(4432)=(v(4127)+2520d0*v(4196)+840d0*v(4246)+210d0*v(4296)+42d0*v(4346)+7d0*v(4362)+v(4416)+v(7522)*(v(379)*v(4362)+v&
&(3287)*v(8056)))/5040d0
v(4415)=(v(3351)*v(424)+v(382)*v(4379))*v(7522)
v(4431)=(v(4126)+2520d0*v(4195)+840d0*v(4245)+210d0*v(4295)+42d0*v(4345)+7d0*v(4361)+v(4415)+v(7522)*(v(379)*v(4361)+v&
&(3286)*v(8056)))/5040d0
v(4414)=(v(3350)*v(424)+v(382)*v(4378))*v(7522)
v(4430)=(v(4125)+2520d0*v(4194)+840d0*v(4244)+210d0*v(4294)+42d0*v(4344)+7d0*v(4360)+v(4414)+v(7522)*(v(379)*v(4360)+v&
&(3285)*v(8056)))/5040d0
v(4413)=(v(3349)*v(424)+v(382)*v(4377))*v(7522)
v(4429)=(v(4124)+2520d0*v(4193)+840d0*v(4243)+210d0*v(4293)+42d0*v(4343)+7d0*v(4359)+v(4413)+v(7522)*(v(379)*v(4359)+v&
&(3284)*v(8056)))/5040d0
v(4412)=(v(3348)*v(424)+v(382)*v(4375))*v(7522)
v(4428)=(v(4122)+2520d0*v(4192)+840d0*v(4242)+210d0*v(4292)+42d0*v(4342)+7d0*v(4358)+v(4412)+v(7522)*(v(379)*v(4358)+v&
&(3283)*v(8056)))/5040d0
v(4411)=(v(3316)*v(424)+v(382)*v(4374))*v(7522)
v(4427)=(v(4121)+2520d0*v(4191)+840d0*v(4241)+210d0*v(4291)+42d0*v(4341)+7d0*v(4357)+v(4411)+v(7522)*(v(379)*v(4357)+v&
&(3282)*v(8056)))/5040d0
v(4410)=(v(3347)*v(424)+v(382)*v(4372))*v(7522)
v(4426)=(v(4120)+2520d0*v(4190)+840d0*v(4240)+210d0*v(4290)+42d0*v(4340)+7d0*v(4356)+v(4410)+v(7522)*(v(379)*v(4356)+v&
&(3281)*v(8056)))/5040d0
v(4409)=(v(3346)*v(424)+v(382)*v(4371))*v(7522)
v(4425)=(v(4119)+2520d0*v(4189)+840d0*v(4239)+210d0*v(4289)+42d0*v(4339)+7d0*v(4355)+v(4409)+v(7522)*(v(379)*v(4355)+v&
&(3280)*v(8056)))/5040d0
v(4408)=(v(3345)*v(424)+v(382)*v(4370))*v(7522)
v(4424)=(v(4118)+2520d0*v(4188)+840d0*v(4238)+210d0*v(4288)+42d0*v(4338)+7d0*v(4354)+v(4408)+v(7522)*(v(379)*v(4354)+v&
&(3279)*v(8056)))/5040d0
v(4407)=(v(3344)*v(424)+v(382)*v(4369))*v(7522)
v(4423)=(v(4117)+2520d0*v(4187)+840d0*v(4237)+210d0*v(4287)+42d0*v(4337)+7d0*v(4353)+v(4407)+v(7522)*(v(379)*v(4353)+v&
&(3278)*v(8056)))/5040d0
v(4406)=(v(3343)*v(424)+v(382)*v(4368))*v(7522)
v(4422)=(v(4116)+2520d0*v(4186)+840d0*v(4236)+210d0*v(4286)+42d0*v(4336)+7d0*v(4352)+v(4406)+v(7522)*(v(379)*v(4352)+v&
&(3277)*v(8056)))/5040d0
v(4405)=(v(3342)*v(424)+v(382)*v(4367))*v(7522)
v(4421)=(v(4115)+2520d0*v(4185)+840d0*v(4235)+210d0*v(4285)+42d0*v(4335)+7d0*v(4351)+v(4405)+v(7522)*(v(379)*v(4351)+v&
&(3276)*v(8056)))/5040d0
v(4404)=(v(3341)*v(424)+v(382)*v(4366))*v(7522)
v(4420)=(v(4114)+2520d0*v(4184)+840d0*v(4234)+210d0*v(4284)+42d0*v(4334)+7d0*v(4350)+v(4404)+v(7522)*(v(379)*v(4350)+v&
&(3275)*v(8056)))/5040d0
v(4403)=v(4365)*v(8015)+v(424)*v(8050)
v(4419)=(v(4113)+2520d0*v(4182)+840d0*v(4233)+210d0*v(4283)+42d0*v(4333)+7d0*v(4349)+v(4403)+v(379)*(v(4349)*v(7522)+v&
&(7518)*v(8056))+v(8056)*v(8057))/5040d0
v(4402)=(7d0*(360d0*v(3420)+120d0*v(4216)+30d0*v(4266)+6d0*v(4316)+v(4382))+v(7522)*(v(3386)*v(407)+v(383)*v(4096)+v&
&(3305)*v(424)+v(382)*v(4364)+v(380)*v(4382)+v(3354)*v(8056)))/5040d0
v(4676)=statev(16)*v(4402)+statev(18)*v(4434)+v(4164)*v(7506)
v(4596)=statev(17)*v(4164)+statev(15)*v(4434)+v(4402)*v(7508)
v(4450)=statev(14)*v(4164)+statev(19)*v(4402)+v(4434)*v(7507)
v(4401)=(7d0*(360d0*v(3419)+120d0*v(4215)+30d0*v(4265)+6d0*v(4315)+v(4381))+v(7522)*(v(3385)*v(407)+v(383)*v(4095)+v&
&(3304)*v(424)+v(382)*v(4363)+v(380)*v(4381)+v(3353)*v(8056)))/5040d0
v(4675)=statev(16)*v(4401)+statev(18)*v(4433)+v(4163)*v(7506)
v(4595)=statev(17)*v(4163)+statev(15)*v(4433)+v(4401)*v(7508)
v(4449)=statev(14)*v(4163)+statev(19)*v(4401)+v(4433)*v(7507)
v(4400)=(7d0*(360d0*v(3418)+120d0*v(4214)+30d0*v(4264)+6d0*v(4314)+v(4380))+v(7522)*(v(3384)*v(407)+v(383)*v(4094)+v&
&(3303)*v(424)+v(382)*v(4362)+v(380)*v(4380)+v(3352)*v(8056)))/5040d0
v(4674)=statev(16)*v(4400)+statev(18)*v(4432)+v(4162)*v(7506)
v(4594)=statev(17)*v(4162)+statev(15)*v(4432)+v(4400)*v(7508)
v(4448)=statev(14)*v(4162)+statev(19)*v(4400)+v(4432)*v(7507)
v(4399)=(7d0*(360d0*v(3417)+120d0*v(4213)+30d0*v(4263)+6d0*v(4313)+v(4379))+v(7522)*(v(3383)*v(407)+v(383)*v(4093)+v&
&(3302)*v(424)+v(382)*v(4361)+v(380)*v(4379)+v(3351)*v(8056)))/5040d0
v(4673)=statev(16)*v(4399)+statev(18)*v(4431)+v(4161)*v(7506)
v(4593)=statev(17)*v(4161)+statev(15)*v(4431)+v(4399)*v(7508)
v(4447)=statev(14)*v(4161)+statev(19)*v(4399)+v(4431)*v(7507)
v(4398)=(7d0*(360d0*v(3416)+120d0*v(4212)+30d0*v(4262)+6d0*v(4312)+v(4378))+v(7522)*(v(3382)*v(407)+v(383)*v(4092)+v&
&(3301)*v(424)+v(382)*v(4360)+v(380)*v(4378)+v(3350)*v(8056)))/5040d0
v(4672)=statev(16)*v(4398)+statev(18)*v(4430)+v(4160)*v(7506)
v(4592)=statev(17)*v(4160)+statev(15)*v(4430)+v(4398)*v(7508)
v(4446)=statev(14)*v(4160)+statev(19)*v(4398)+v(4430)*v(7507)
v(4397)=(2520d0*v(3415)+840d0*v(4211)+210d0*v(4261)+42d0*v(4311)+7d0*v(4377)+v(4396)+v(7522)*(v(383)*v(4091)+v(3300)*v&
&(424)+v(382)*v(4359)+v(380)*v(4377)+v(3349)*v(8056)))/5040d0
v(4671)=statev(16)*v(4397)+statev(18)*v(4429)+v(4159)*v(7506)
v(4591)=statev(17)*v(4159)+statev(15)*v(4429)+v(4397)*v(7508)
v(4445)=statev(14)*v(4159)+statev(19)*v(4397)+v(4429)*v(7507)
v(4395)=((v(3381)*v(407)+v(383)*v(4090)+v(3348)*v(422)+v(3299)*v(424)+v(382)*v(4358)+v(380)*v(4375))*v(7522)+7d0*&
&(360d0*v(3414)+120d0*v(4209)+30d0*v(4259)+6d0*v(4309)+v(4375)+v(8058)))/5040d0
v(4670)=statev(16)*v(4395)+statev(18)*v(4428)+v(4158)*v(7506)
v(4590)=statev(17)*v(4158)+statev(15)*v(4428)+v(4395)*v(7508)
v(4444)=statev(14)*v(4158)+statev(19)*v(4395)+v(4428)*v(7507)
v(4393)=(2520d0*v(3413)+840d0*v(4208)+210d0*v(4258)+42d0*v(4308)+7d0*v(4374)+5040d0*v(4391)+v(4392)+(v(383)*v(4087)+v&
&(3316)*v(422)+v(3298)*v(424)+v(382)*v(4357)+v(380)*v(4374))*v(7522))/5040d0
v(4669)=statev(16)*v(4393)+statev(18)*v(4427)+v(4154)*v(7506)
v(4589)=statev(17)*v(4154)+statev(15)*v(4427)+v(4393)*v(7508)
v(4443)=statev(14)*v(4154)+statev(19)*v(4393)+v(4427)*v(7507)
v(4390)=(7d0*(360d0*v(3412)+120d0*v(4206)+30d0*v(4256)+6d0*v(4306)+v(4372))+v(7522)*(v(3380)*v(407)+v(383)*v(4086)+v&
&(3297)*v(424)+v(382)*v(4356)+v(380)*v(4372)+v(3347)*v(8056)))/5040d0
v(4668)=statev(16)*v(4390)+statev(18)*v(4426)+v(4153)*v(7506)
v(4588)=statev(17)*v(4153)+statev(15)*v(4426)+v(4390)*v(7508)
v(4442)=statev(14)*v(4153)+statev(19)*v(4390)+v(4426)*v(7507)
v(4389)=(7d0*(360d0*v(3411)+120d0*v(4205)+30d0*v(4255)+6d0*v(4305)+v(4371))+v(7522)*(v(3379)*v(407)+v(383)*v(4085)+v&
&(3296)*v(424)+v(382)*v(4355)+v(380)*v(4371)+v(3346)*v(8056)))/5040d0
v(4667)=statev(16)*v(4389)+statev(18)*v(4425)+v(4152)*v(7506)
v(4587)=statev(17)*v(4152)+statev(15)*v(4425)+v(4389)*v(7508)
v(4441)=statev(14)*v(4152)+statev(19)*v(4389)+v(4425)*v(7507)
v(4388)=(7d0*(360d0*v(3410)+120d0*v(4204)+30d0*v(4254)+6d0*v(4304)+v(4370))+v(7522)*(v(3378)*v(407)+v(383)*v(4084)+v&
&(3295)*v(424)+v(382)*v(4354)+v(380)*v(4370)+v(3345)*v(8056)))/5040d0
v(4666)=statev(16)*v(4388)+statev(18)*v(4424)+v(4151)*v(7506)
v(4586)=statev(17)*v(4151)+statev(15)*v(4424)+v(4388)*v(7508)
v(4440)=statev(14)*v(4151)+statev(19)*v(4388)+v(4424)*v(7507)
v(4387)=(7d0*(360d0*v(3409)+120d0*v(4203)+30d0*v(4253)+6d0*v(4303)+v(4369))+v(7522)*(v(3377)*v(407)+v(383)*v(4083)+v&
&(3294)*v(424)+v(382)*v(4353)+v(380)*v(4369)+v(3344)*v(8056)))/5040d0
v(4665)=statev(16)*v(4387)+statev(18)*v(4423)+v(4150)*v(7506)
v(4585)=statev(17)*v(4150)+statev(15)*v(4423)+v(4387)*v(7508)
v(4439)=statev(14)*v(4150)+statev(19)*v(4387)+v(4423)*v(7507)
v(4386)=(7d0*(360d0*v(3408)+120d0*v(4202)+30d0*v(4252)+6d0*v(4302)+v(4368))+v(7522)*(v(3376)*v(407)+v(383)*v(4082)+v&
&(3293)*v(424)+v(382)*v(4352)+v(380)*v(4368)+v(3343)*v(8056)))/5040d0
v(4664)=statev(16)*v(4386)+statev(18)*v(4422)+v(4149)*v(7506)
v(4584)=statev(17)*v(4149)+statev(15)*v(4422)+v(4386)*v(7508)
v(4438)=statev(14)*v(4149)+statev(19)*v(4386)+v(4422)*v(7507)
v(4385)=(7d0*(360d0*v(3407)+120d0*v(4201)+30d0*v(4251)+6d0*v(4301)+v(4367))+v(7522)*(v(3375)*v(407)+v(383)*v(4081)+v&
&(3292)*v(424)+v(382)*v(4351)+v(380)*v(4367)+v(3342)*v(8056)))/5040d0
v(4663)=statev(16)*v(4385)+statev(18)*v(4421)+v(4148)*v(7506)
v(4583)=statev(17)*v(4148)+statev(15)*v(4421)+v(4385)*v(7508)
v(4437)=statev(14)*v(4148)+statev(19)*v(4385)+v(4421)*v(7507)
v(4384)=(7d0*(360d0*v(3406)+120d0*v(4200)+30d0*v(4250)+6d0*v(4300)+v(4366))+v(7522)*(v(3374)*v(407)+v(383)*v(4080)+v&
&(3291)*v(424)+v(382)*v(4350)+v(380)*v(4366)+v(3341)*v(8056)))/5040d0
v(4662)=statev(16)*v(4384)+statev(18)*v(4420)+v(4147)*v(7506)
v(4582)=statev(17)*v(4147)+statev(15)*v(4420)+v(4384)*v(7508)
v(4436)=statev(14)*v(4147)+statev(19)*v(4384)+v(4420)*v(7507)
v(4383)=v(3405)/2d0+v(4199)/6d0+v(4249)/24d0+v(4299)/120d0+v(4365)/720d0+v(8050)+((v(3373)*v(407)+v(383)*v(4079)+v(3340&
&)*v(422)+v(3290)*v(424)+v(382)*v(4349)+v(380)*v(4365))*v(7522)+v(7518)*(v(382)*v(422)+v(8059)))/5040d0
v(4661)=statev(16)*v(4383)+statev(18)*v(4419)+v(4146)*v(7506)
v(4581)=statev(17)*v(4146)+statev(15)*v(4419)+v(4383)*v(7508)
v(4435)=statev(14)*v(4146)+statev(19)*v(4383)+v(4419)*v(7507)
v(444)=(7d0*(360d0*v(415)+120d0*v(417)+30d0*v(421)+6d0*v(423)+v(424))+v(7522)*(v(382)*v(8056)+v(8059)))/5040d0
v(443)=v(424)*v(8015)
v(449)=(2520d0*v(411)+840d0*v(413)+210d0*v(416)+42d0*v(419)+7d0*v(422)+v(443)+v(8051)*v(8056)+v(8060))/5040d0
v(426)=statev(14)*v(409)+statev(19)*v(444)+v(449)*v(7507)
v(429)=v(427)+v(428)+v(232)*v(4451)
v(4484)=v(3436)+v(3506)+(v(3305)*v(429)+v(380)*v(4468))*v(7522)
v(4483)=v(3435)+v(3505)+(v(3304)*v(429)+v(380)*v(4467))*v(7522)
v(4482)=v(3434)+v(3504)+(v(3303)*v(429)+v(380)*v(4466))*v(7522)
v(4481)=v(3433)+v(3503)+(v(3302)*v(429)+v(380)*v(4465))*v(7522)
v(4480)=v(3432)+v(3502)+(v(3301)*v(429)+v(380)*v(4464))*v(7522)
v(4479)=v(3431)+v(3501)+(v(3300)*v(429)+v(380)*v(4463))*v(7522)
v(4478)=v(3430)+v(3500)+(v(3299)*v(429)+v(380)*v(4462))*v(7522)
v(4477)=v(3429)+v(3499)+(v(3298)*v(429)+v(380)*v(4461))*v(7522)
v(4476)=v(3428)+v(3498)+(v(3297)*v(429)+v(380)*v(4460))*v(7522)
v(4475)=v(3427)+v(3497)+(v(3296)*v(429)+v(380)*v(4459))*v(7522)
v(4474)=v(3426)+v(3496)+(v(3295)*v(429)+v(380)*v(4458))*v(7522)
v(4473)=v(3425)+v(3495)+(v(3294)*v(429)+v(380)*v(4457))*v(7522)
v(4472)=v(3424)+v(3494)+(v(3293)*v(429)+v(380)*v(4456))*v(7522)
v(4471)=v(3423)+v(3493)+(v(3292)*v(429)+v(380)*v(4455))*v(7522)
v(4470)=v(3422)+v(3492)+(v(3291)*v(429)+v(380)*v(4454))*v(7522)
v(4469)=v(3421)+v(3491)+v(4452)*v(8061)+v(429)*v(8062)
v(432)=v(430)+v(431)+v(429)*v(8061)
v(4500)=v(3813)+v(4232)+(v(3305)*v(432)+v(380)*v(4484))*v(7522)
v(4499)=v(3812)+v(4231)+(v(3304)*v(432)+v(380)*v(4483))*v(7522)
v(4498)=v(3811)+v(4230)+(v(3303)*v(432)+v(380)*v(4482))*v(7522)
v(4497)=v(3810)+v(4229)+(v(3302)*v(432)+v(380)*v(4481))*v(7522)
v(4496)=v(3809)+v(4228)+(v(3301)*v(432)+v(380)*v(4480))*v(7522)
v(4495)=v(3808)+v(4227)+(v(3300)*v(432)+v(380)*v(4479))*v(7522)
v(4494)=v(3807)+v(4226)+(v(3299)*v(432)+v(380)*v(4478))*v(7522)
v(4493)=v(3806)+v(4225)+(v(3298)*v(432)+v(380)*v(4477))*v(7522)
v(4492)=v(3805)+v(4224)+(v(3297)*v(432)+v(380)*v(4476))*v(7522)
v(4491)=v(3804)+v(4223)+(v(3296)*v(432)+v(380)*v(4475))*v(7522)
v(4490)=v(3803)+v(4222)+(v(3295)*v(432)+v(380)*v(4474))*v(7522)
v(4489)=v(3802)+v(4221)+(v(3294)*v(432)+v(380)*v(4473))*v(7522)
v(4488)=v(3801)+v(4220)+(v(3293)*v(432)+v(380)*v(4472))*v(7522)
v(4487)=v(3800)+v(4219)+(v(3292)*v(432)+v(380)*v(4471))*v(7522)
v(4486)=v(3799)+v(4218)+(v(3291)*v(432)+v(380)*v(4470))*v(7522)
v(4485)=v(3798)+v(4217)+v(4469)*v(8061)+v(432)*v(8062)
v(435)=v(433)+v(434)+v(432)*v(8061)
v(4516)=v(3930)+v(4282)+(v(3305)*v(435)+v(380)*v(4500))*v(7522)
v(4515)=v(3929)+v(4281)+(v(3304)*v(435)+v(380)*v(4499))*v(7522)
v(4514)=v(3928)+v(4280)+(v(3303)*v(435)+v(380)*v(4498))*v(7522)
v(4513)=v(3927)+v(4279)+(v(3302)*v(435)+v(380)*v(4497))*v(7522)
v(4512)=v(3926)+v(4278)+(v(3301)*v(435)+v(380)*v(4496))*v(7522)
v(4511)=v(3925)+v(4277)+(v(3300)*v(435)+v(380)*v(4495))*v(7522)
v(4510)=v(3924)+v(4276)+(v(3299)*v(435)+v(380)*v(4494))*v(7522)
v(4509)=v(3923)+v(4275)+(v(3298)*v(435)+v(380)*v(4493))*v(7522)
v(4508)=v(3922)+v(4274)+(v(3297)*v(435)+v(380)*v(4492))*v(7522)
v(4507)=v(3921)+v(4273)+(v(3296)*v(435)+v(380)*v(4491))*v(7522)
v(4506)=v(3920)+v(4272)+(v(3295)*v(435)+v(380)*v(4490))*v(7522)
v(4505)=v(3919)+v(4271)+(v(3294)*v(435)+v(380)*v(4489))*v(7522)
v(4504)=v(3918)+v(4270)+(v(3293)*v(435)+v(380)*v(4488))*v(7522)
v(4503)=v(3917)+v(4269)+(v(3292)*v(435)+v(380)*v(4487))*v(7522)
v(4502)=v(3916)+v(4268)+(v(3291)*v(435)+v(380)*v(4486))*v(7522)
v(4501)=v(3915)+v(4267)+v(4485)*v(8061)+v(435)*v(8062)
v(438)=v(436)+v(437)+v(435)*v(8061)
v(4532)=v(3979)+v(4332)+(v(3305)*v(438)+v(380)*v(4516))*v(7522)
v(4531)=v(3978)+v(4331)+(v(3304)*v(438)+v(380)*v(4515))*v(7522)
v(4530)=v(3977)+v(4330)+(v(3303)*v(438)+v(380)*v(4514))*v(7522)
v(4529)=v(3976)+v(4329)+(v(3302)*v(438)+v(380)*v(4513))*v(7522)
v(4528)=v(3975)+v(4328)+(v(3301)*v(438)+v(380)*v(4512))*v(7522)
v(4527)=v(3974)+v(4327)+(v(3300)*v(438)+v(380)*v(4511))*v(7522)
v(4526)=v(3973)+v(4326)+(v(3299)*v(438)+v(380)*v(4510))*v(7522)
v(4525)=v(3972)+v(4325)+(v(3298)*v(438)+v(380)*v(4509))*v(7522)
v(4524)=v(3971)+v(4324)+(v(3297)*v(438)+v(380)*v(4508))*v(7522)
v(4523)=v(3970)+v(4323)+(v(3296)*v(438)+v(380)*v(4507))*v(7522)
v(4522)=v(3969)+v(4322)+(v(3295)*v(438)+v(380)*v(4506))*v(7522)
v(4521)=v(3968)+v(4321)+(v(3294)*v(438)+v(380)*v(4505))*v(7522)
v(4520)=v(3967)+v(4320)+(v(3293)*v(438)+v(380)*v(4504))*v(7522)
v(4519)=v(3966)+v(4319)+(v(3292)*v(438)+v(380)*v(4503))*v(7522)
v(4518)=v(3965)+v(4318)+(v(3291)*v(438)+v(380)*v(4502))*v(7522)
v(4517)=v(3964)+v(4317)+v(4501)*v(8061)+v(438)*v(8062)
v(441)=v(439)+v(440)+v(438)*v(8061)
v(8063)=5040d0+v(441)
v(4548)=(v(4078)+v(4418)+2520d0*v(4468)+840d0*v(4484)+210d0*v(4500)+42d0*v(4516)+7d0*v(4532)+v(7522)*(v(380)*v(4532)+v&
&(3305)*v(8063)))/5040d0
v(4740)=statev(14)*v(4112)+statev(19)*v(4548)+v(4402)*v(7507)
v(4612)=statev(18)*v(4402)+statev(16)*v(4548)+v(4112)*v(7506)
v(4564)=statev(17)*v(4112)+statev(15)*v(4402)+v(4548)*v(7508)
v(4547)=(v(4077)+v(4417)+2520d0*v(4467)+840d0*v(4483)+210d0*v(4499)+42d0*v(4515)+7d0*v(4531)+v(7522)*(v(380)*v(4531)+v&
&(3304)*v(8063)))/5040d0
v(4739)=statev(14)*v(4111)+statev(19)*v(4547)+v(4401)*v(7507)
v(4611)=statev(18)*v(4401)+statev(16)*v(4547)+v(4111)*v(7506)
v(4563)=statev(17)*v(4111)+statev(15)*v(4401)+v(4547)*v(7508)
v(4546)=(v(4076)+v(4416)+2520d0*v(4466)+840d0*v(4482)+210d0*v(4498)+42d0*v(4514)+7d0*v(4530)+v(7522)*(v(380)*v(4530)+v&
&(3303)*v(8063)))/5040d0
v(4738)=statev(14)*v(4110)+statev(19)*v(4546)+v(4400)*v(7507)
v(4610)=statev(18)*v(4400)+statev(16)*v(4546)+v(4110)*v(7506)
v(4562)=statev(17)*v(4110)+statev(15)*v(4400)+v(4546)*v(7508)
v(4545)=(v(4075)+v(4415)+2520d0*v(4465)+840d0*v(4481)+210d0*v(4497)+42d0*v(4513)+7d0*v(4529)+v(7522)*(v(380)*v(4529)+v&
&(3302)*v(8063)))/5040d0
v(4737)=statev(14)*v(4109)+statev(19)*v(4545)+v(4399)*v(7507)
v(4609)=statev(18)*v(4399)+statev(16)*v(4545)+v(4109)*v(7506)
v(4561)=statev(17)*v(4109)+statev(15)*v(4399)+v(4545)*v(7508)
v(4544)=(v(4074)+v(4414)+2520d0*v(4464)+840d0*v(4480)+210d0*v(4496)+42d0*v(4512)+7d0*v(4528)+v(7522)*(v(380)*v(4528)+v&
&(3301)*v(8063)))/5040d0
v(4736)=statev(14)*v(4108)+statev(19)*v(4544)+v(4398)*v(7507)
v(4608)=statev(18)*v(4398)+statev(16)*v(4544)+v(4108)*v(7506)
v(4560)=statev(17)*v(4108)+statev(15)*v(4398)+v(4544)*v(7508)
v(4543)=(v(4073)+v(4413)+2520d0*v(4463)+840d0*v(4479)+210d0*v(4495)+42d0*v(4511)+7d0*v(4527)+v(7522)*(v(380)*v(4527)+v&
&(3300)*v(8063)))/5040d0
v(4735)=statev(14)*v(4107)+statev(19)*v(4543)+v(4397)*v(7507)
v(4607)=statev(18)*v(4397)+statev(16)*v(4543)+v(4107)*v(7506)
v(4559)=statev(17)*v(4107)+statev(15)*v(4397)+v(4543)*v(7508)
v(4542)=(v(4072)+v(4412)+2520d0*v(4462)+840d0*v(4478)+210d0*v(4494)+42d0*v(4510)+7d0*v(4526)+v(7522)*(v(380)*v(4526)+v&
&(3299)*v(8063)))/5040d0
v(4734)=statev(14)*v(4106)+statev(19)*v(4542)+v(4395)*v(7507)
v(4606)=statev(18)*v(4395)+statev(16)*v(4542)+v(4106)*v(7506)
v(4558)=statev(17)*v(4106)+statev(15)*v(4395)+v(4542)*v(7508)
v(4541)=(v(4071)+v(4411)+2520d0*v(4461)+840d0*v(4477)+210d0*v(4493)+42d0*v(4509)+7d0*v(4525)+v(7522)*(v(380)*v(4525)+v&
&(3298)*v(8063)))/5040d0
v(4733)=statev(14)*v(4105)+statev(19)*v(4541)+v(4393)*v(7507)
v(4605)=statev(18)*v(4393)+statev(16)*v(4541)+v(4105)*v(7506)
v(4557)=statev(17)*v(4105)+statev(15)*v(4393)+v(4541)*v(7508)
v(4540)=(v(4070)+v(4410)+2520d0*v(4460)+840d0*v(4476)+210d0*v(4492)+42d0*v(4508)+7d0*v(4524)+v(7522)*(v(380)*v(4524)+v&
&(3297)*v(8063)))/5040d0
v(4732)=statev(14)*v(4104)+statev(19)*v(4540)+v(4390)*v(7507)
v(4604)=statev(18)*v(4390)+statev(16)*v(4540)+v(4104)*v(7506)
v(4556)=statev(17)*v(4104)+statev(15)*v(4390)+v(4540)*v(7508)
v(4539)=(v(4069)+v(4409)+2520d0*v(4459)+840d0*v(4475)+210d0*v(4491)+42d0*v(4507)+7d0*v(4523)+v(7522)*(v(380)*v(4523)+v&
&(3296)*v(8063)))/5040d0
v(4731)=statev(14)*v(4103)+statev(19)*v(4539)+v(4389)*v(7507)
v(4603)=statev(18)*v(4389)+statev(16)*v(4539)+v(4103)*v(7506)
v(4555)=statev(17)*v(4103)+statev(15)*v(4389)+v(4539)*v(7508)
v(4538)=(v(4068)+v(4408)+2520d0*v(4458)+840d0*v(4474)+210d0*v(4490)+42d0*v(4506)+7d0*v(4522)+v(7522)*(v(380)*v(4522)+v&
&(3295)*v(8063)))/5040d0
v(4730)=statev(14)*v(4102)+statev(19)*v(4538)+v(4388)*v(7507)
v(4602)=statev(18)*v(4388)+statev(16)*v(4538)+v(4102)*v(7506)
v(4554)=statev(17)*v(4102)+statev(15)*v(4388)+v(4538)*v(7508)
v(4537)=(v(4067)+v(4407)+2520d0*v(4457)+840d0*v(4473)+210d0*v(4489)+42d0*v(4505)+7d0*v(4521)+v(7522)*(v(380)*v(4521)+v&
&(3294)*v(8063)))/5040d0
v(4729)=statev(14)*v(4101)+statev(19)*v(4537)+v(4387)*v(7507)
v(4601)=statev(18)*v(4387)+statev(16)*v(4537)+v(4101)*v(7506)
v(4553)=statev(17)*v(4101)+statev(15)*v(4387)+v(4537)*v(7508)
v(4536)=(v(4066)+v(4406)+2520d0*v(4456)+840d0*v(4472)+210d0*v(4488)+42d0*v(4504)+7d0*v(4520)+v(7522)*(v(380)*v(4520)+v&
&(3293)*v(8063)))/5040d0
v(4728)=statev(14)*v(4100)+statev(19)*v(4536)+v(4386)*v(7507)
v(4600)=statev(18)*v(4386)+statev(16)*v(4536)+v(4100)*v(7506)
v(4552)=statev(17)*v(4100)+statev(15)*v(4386)+v(4536)*v(7508)
v(4535)=(v(4065)+v(4405)+2520d0*v(4455)+840d0*v(4471)+210d0*v(4487)+42d0*v(4503)+7d0*v(4519)+v(7522)*(v(380)*v(4519)+v&
&(3292)*v(8063)))/5040d0
v(4727)=statev(14)*v(4099)+statev(19)*v(4535)+v(4385)*v(7507)
v(4599)=statev(18)*v(4385)+statev(16)*v(4535)+v(4099)*v(7506)
v(4551)=statev(17)*v(4099)+statev(15)*v(4385)+v(4535)*v(7508)
v(4534)=(v(4064)+v(4404)+2520d0*v(4454)+840d0*v(4470)+210d0*v(4486)+42d0*v(4502)+7d0*v(4518)+v(7522)*(v(380)*v(4518)+v&
&(3291)*v(8063)))/5040d0
v(4726)=statev(14)*v(4098)+statev(19)*v(4534)+v(4384)*v(7507)
v(4598)=statev(18)*v(4384)+statev(16)*v(4534)+v(4098)*v(7506)
v(4550)=statev(17)*v(4098)+statev(15)*v(4384)+v(4534)*v(7508)
v(4533)=(v(4063)+v(4403)+2520d0*v(4452)+840d0*v(4469)+210d0*v(4485)+42d0*v(4501)+7d0*v(4517)+v(380)*(v(4517)*v(7522)+v&
&(7518)*v(8063))+v(8063)*v(8064))/5040d0
v(4725)=statev(14)*v(4097)+statev(19)*v(4533)+v(4383)*v(7507)
v(4597)=statev(18)*v(4383)+statev(16)*v(4533)+v(4097)*v(7506)
v(4549)=statev(17)*v(4097)+statev(15)*v(4383)+v(4533)*v(7508)
v(451)=(5040d0+2520d0*v(429)+840d0*v(432)+210d0*v(435)+42d0*v(438)+7d0*v(441)+v(442)+v(443)+v(8061)*v(8063))/5040d0
v(446)=statev(15)*v(444)+statev(17)*v(445)+v(451)*v(7508)
v(448)=statev(19)*v(445)+statev(14)*v(447)+v(409)*v(7507)
v(450)=statev(17)*v(409)+statev(15)*v(449)+v(444)*v(7508)
v(452)=statev(18)*v(444)+statev(16)*v(451)+v(445)*v(7506)
v(453)=statev(15)*v(409)+statev(17)*v(447)+v(445)*v(7508)
v(4660)=v(4180)*v(446)+v(408)*v(4564)-v(453)*v(4612)-v(452)*v(4628)
v(4659)=v(4179)*v(446)+v(408)*v(4563)-v(453)*v(4611)-v(452)*v(4627)
v(4658)=v(4178)*v(446)+v(408)*v(4562)-v(453)*v(4610)-v(452)*v(4626)
v(4657)=v(4177)*v(446)+v(408)*v(4561)-v(453)*v(4609)-v(452)*v(4625)
v(4656)=v(4176)*v(446)+v(408)*v(4560)-v(453)*v(4608)-v(452)*v(4624)
v(4655)=v(4175)*v(446)+v(408)*v(4559)-v(453)*v(4607)-v(452)*v(4623)
v(4654)=v(4174)*v(446)+v(408)*v(4558)-v(453)*v(4606)-v(452)*v(4622)
v(4653)=v(4173)*v(446)+v(408)*v(4557)-v(453)*v(4605)-v(452)*v(4621)
v(4652)=v(4172)*v(446)+v(408)*v(4556)-v(453)*v(4604)-v(452)*v(4620)
v(4651)=v(4171)*v(446)+v(408)*v(4555)-v(453)*v(4603)-v(452)*v(4619)
v(4650)=v(4170)*v(446)+v(408)*v(4554)-v(453)*v(4602)-v(452)*v(4618)
v(4649)=v(4169)*v(446)+v(408)*v(4553)-v(453)*v(4601)-v(452)*v(4617)
v(4648)=v(4168)*v(446)+v(408)*v(4552)-v(453)*v(4600)-v(452)*v(4616)
v(4647)=v(4167)*v(446)+v(408)*v(4551)-v(453)*v(4599)-v(452)*v(4615)
v(4646)=v(4166)*v(446)+v(408)*v(4550)-v(453)*v(4598)-v(452)*v(4614)
v(4645)=v(4165)*v(446)+v(408)*v(4549)-v(453)*v(4597)-v(452)*v(4613)
v(4644)=-(v(4450)*v(453))+v(450)*v(4580)+v(448)*v(4596)-v(426)*v(4628)
v(4643)=-(v(4449)*v(453))+v(450)*v(4579)+v(448)*v(4595)-v(426)*v(4627)
v(4642)=-(v(4448)*v(453))+v(450)*v(4578)+v(448)*v(4594)-v(426)*v(4626)
v(4641)=-(v(4447)*v(453))+v(450)*v(4577)+v(448)*v(4593)-v(426)*v(4625)
v(4640)=-(v(4446)*v(453))+v(450)*v(4576)+v(448)*v(4592)-v(426)*v(4624)
v(4639)=-(v(4445)*v(453))+v(450)*v(4575)+v(448)*v(4591)-v(426)*v(4623)
v(4638)=-(v(4444)*v(453))+v(450)*v(4574)+v(448)*v(4590)-v(426)*v(4622)
v(4637)=-(v(4443)*v(453))+v(450)*v(4573)+v(448)*v(4589)-v(426)*v(4621)
v(4636)=-(v(4442)*v(453))+v(450)*v(4572)+v(448)*v(4588)-v(426)*v(4620)
v(4635)=-(v(4441)*v(453))+v(450)*v(4571)+v(448)*v(4587)-v(426)*v(4619)
v(4634)=-(v(4440)*v(453))+v(450)*v(4570)+v(448)*v(4586)-v(426)*v(4618)
v(4633)=-(v(4439)*v(453))+v(450)*v(4569)+v(448)*v(4585)-v(426)*v(4617)
v(4632)=-(v(4438)*v(453))+v(450)*v(4568)+v(448)*v(4584)-v(426)*v(4616)
v(4631)=-(v(4437)*v(453))+v(450)*v(4567)+v(448)*v(4583)-v(426)*v(4615)
v(4630)=-(v(4436)*v(453))+v(450)*v(4566)+v(448)*v(4582)-v(426)*v(4614)
v(4629)=-(v(4435)*v(453))+v(450)*v(4565)+v(448)*v(4581)-v(426)*v(4613)
v(539)=v(448)*v(450)-v(426)*v(453)
v(5867)=(v(539)*v(539))
v(530)=v(408)*v(446)-v(452)*v(453)
v(5942)=(v(530)*v(530))
v(454)=statev(16)*v(444)+statev(18)*v(449)+v(409)*v(7506)
v(4724)=-(v(454)*v(4564))+v(452)*v(4596)+v(450)*v(4612)-v(446)*v(4676)
v(4723)=-(v(454)*v(4563))+v(452)*v(4595)+v(450)*v(4611)-v(446)*v(4675)
v(4722)=-(v(454)*v(4562))+v(452)*v(4594)+v(450)*v(4610)-v(446)*v(4674)
v(4721)=-(v(454)*v(4561))+v(452)*v(4593)+v(450)*v(4609)-v(446)*v(4673)
v(4720)=-(v(454)*v(4560))+v(452)*v(4592)+v(450)*v(4608)-v(446)*v(4672)
v(4719)=-(v(454)*v(4559))+v(452)*v(4591)+v(450)*v(4607)-v(446)*v(4671)
v(4718)=-(v(454)*v(4558))+v(452)*v(4590)+v(450)*v(4606)-v(446)*v(4670)
v(4717)=-(v(454)*v(4557))+v(452)*v(4589)+v(450)*v(4605)-v(446)*v(4669)
v(4716)=-(v(454)*v(4556))+v(452)*v(4588)+v(450)*v(4604)-v(446)*v(4668)
v(4715)=-(v(454)*v(4555))+v(452)*v(4587)+v(450)*v(4603)-v(446)*v(4667)
v(4714)=-(v(454)*v(4554))+v(452)*v(4586)+v(450)*v(4602)-v(446)*v(4666)
v(4713)=-(v(454)*v(4553))+v(452)*v(4585)+v(450)*v(4601)-v(446)*v(4665)
v(4712)=-(v(454)*v(4552))+v(452)*v(4584)+v(450)*v(4600)-v(446)*v(4664)
v(4711)=-(v(454)*v(4551))+v(452)*v(4583)+v(450)*v(4599)-v(446)*v(4663)
v(4710)=-(v(454)*v(4550))+v(452)*v(4582)+v(450)*v(4598)-v(446)*v(4662)
v(4709)=-(v(454)*v(4549))+v(452)*v(4581)+v(450)*v(4597)-v(446)*v(4661)
v(4708)=-(v(4180)*v(450))-v(408)*v(4596)+v(454)*v(4628)+v(453)*v(4676)
v(4707)=-(v(4179)*v(450))-v(408)*v(4595)+v(454)*v(4627)+v(453)*v(4675)
v(4706)=-(v(4178)*v(450))-v(408)*v(4594)+v(454)*v(4626)+v(453)*v(4674)
v(4705)=-(v(4177)*v(450))-v(408)*v(4593)+v(454)*v(4625)+v(453)*v(4673)
v(4704)=-(v(4176)*v(450))-v(408)*v(4592)+v(454)*v(4624)+v(453)*v(4672)
v(4703)=-(v(4175)*v(450))-v(408)*v(4591)+v(454)*v(4623)+v(453)*v(4671)
v(4702)=-(v(4174)*v(450))-v(408)*v(4590)+v(454)*v(4622)+v(453)*v(4670)
v(4701)=-(v(4173)*v(450))-v(408)*v(4589)+v(454)*v(4621)+v(453)*v(4669)
v(4700)=-(v(4172)*v(450))-v(408)*v(4588)+v(454)*v(4620)+v(453)*v(4668)
v(4699)=-(v(4171)*v(450))-v(408)*v(4587)+v(454)*v(4619)+v(453)*v(4667)
v(4698)=-(v(4170)*v(450))-v(408)*v(4586)+v(454)*v(4618)+v(453)*v(4666)
v(4697)=-(v(4169)*v(450))-v(408)*v(4585)+v(454)*v(4617)+v(453)*v(4665)
v(4696)=-(v(4168)*v(450))-v(408)*v(4584)+v(454)*v(4616)+v(453)*v(4664)
v(4695)=-(v(4167)*v(450))-v(408)*v(4583)+v(454)*v(4615)+v(453)*v(4663)
v(4694)=-(v(4166)*v(450))-v(408)*v(4582)+v(454)*v(4614)+v(453)*v(4662)
v(4693)=-(v(4165)*v(450))-v(408)*v(4581)+v(454)*v(4613)+v(453)*v(4661)
v(4692)=v(4180)*v(426)+v(408)*v(4450)-v(454)*v(4580)-v(448)*v(4676)
v(4691)=v(4179)*v(426)+v(408)*v(4449)-v(454)*v(4579)-v(448)*v(4675)
v(4690)=v(4178)*v(426)+v(408)*v(4448)-v(454)*v(4578)-v(448)*v(4674)
v(4689)=v(4177)*v(426)+v(408)*v(4447)-v(454)*v(4577)-v(448)*v(4673)
v(4688)=v(4176)*v(426)+v(408)*v(4446)-v(454)*v(4576)-v(448)*v(4672)
v(4687)=v(4175)*v(426)+v(408)*v(4445)-v(454)*v(4575)-v(448)*v(4671)
v(4686)=v(4174)*v(426)+v(408)*v(4444)-v(454)*v(4574)-v(448)*v(4670)
v(4685)=v(4173)*v(426)+v(408)*v(4443)-v(454)*v(4573)-v(448)*v(4669)
v(4684)=v(4172)*v(426)+v(408)*v(4442)-v(454)*v(4572)-v(448)*v(4668)
v(4683)=v(4171)*v(426)+v(408)*v(4441)-v(454)*v(4571)-v(448)*v(4667)
v(4682)=v(4170)*v(426)+v(408)*v(4440)-v(454)*v(4570)-v(448)*v(4666)
v(4681)=v(4169)*v(426)+v(408)*v(4439)-v(454)*v(4569)-v(448)*v(4665)
v(4680)=v(4168)*v(426)+v(408)*v(4438)-v(454)*v(4568)-v(448)*v(4664)
v(4679)=v(4167)*v(426)+v(408)*v(4437)-v(454)*v(4567)-v(448)*v(4663)
v(4678)=v(4166)*v(426)+v(408)*v(4436)-v(454)*v(4566)-v(448)*v(4662)
v(4677)=v(4165)*v(426)+v(408)*v(4435)-v(454)*v(4565)-v(448)*v(4661)
v(538)=v(408)*v(426)-v(448)*v(454)
v(5866)=(v(538)*v(538))
v(537)=-(v(408)*v(450))+v(453)*v(454)
v(5865)=(v(537)*v(537))
v(8104)=v(5865)+v(5866)+v(5867)
v(531)=v(450)*v(452)-v(446)*v(454)
v(5904)=(v(531)*v(531))
v(455)=statev(14)*v(445)+statev(19)*v(451)+v(444)*v(7507)
v(5847)=v(455)*v(537)+v(446)*v(538)+v(452)*v(539)
v(5849)=1d0/v(5847)**3
v(8065)=(-2d0)*v(5849)
v(5864)=(v(452)*v(4644)+v(446)*v(4692)+v(455)*v(4708)+v(4740)*v(537)+v(4564)*v(538)+v(4612)*v(539))*v(8065)
v(5863)=(v(452)*v(4643)+v(446)*v(4691)+v(455)*v(4707)+v(4739)*v(537)+v(4563)*v(538)+v(4611)*v(539))*v(8065)
v(5862)=(v(452)*v(4642)+v(446)*v(4690)+v(455)*v(4706)+v(4738)*v(537)+v(4562)*v(538)+v(4610)*v(539))*v(8065)
v(5861)=(v(452)*v(4641)+v(446)*v(4689)+v(455)*v(4705)+v(4737)*v(537)+v(4561)*v(538)+v(4609)*v(539))*v(8065)
v(5860)=(v(452)*v(4640)+v(446)*v(4688)+v(455)*v(4704)+v(4736)*v(537)+v(4560)*v(538)+v(4608)*v(539))*v(8065)
v(5859)=(v(452)*v(4639)+v(446)*v(4687)+v(455)*v(4703)+v(4735)*v(537)+v(4559)*v(538)+v(4607)*v(539))*v(8065)
v(5858)=(v(452)*v(4638)+v(446)*v(4686)+v(455)*v(4702)+v(4734)*v(537)+v(4558)*v(538)+v(4606)*v(539))*v(8065)
v(5857)=(v(452)*v(4637)+v(446)*v(4685)+v(455)*v(4701)+v(4733)*v(537)+v(4557)*v(538)+v(4605)*v(539))*v(8065)
v(5856)=(v(452)*v(4636)+v(446)*v(4684)+v(455)*v(4700)+v(4732)*v(537)+v(4556)*v(538)+v(4604)*v(539))*v(8065)
v(5855)=(v(452)*v(4635)+v(446)*v(4683)+v(455)*v(4699)+v(4731)*v(537)+v(4555)*v(538)+v(4603)*v(539))*v(8065)
v(5854)=(v(452)*v(4634)+v(446)*v(4682)+v(455)*v(4698)+v(4730)*v(537)+v(4554)*v(538)+v(4602)*v(539))*v(8065)
v(5853)=(v(452)*v(4633)+v(446)*v(4681)+v(455)*v(4697)+v(4729)*v(537)+v(4553)*v(538)+v(4601)*v(539))*v(8065)
v(5852)=(v(452)*v(4632)+v(446)*v(4680)+v(455)*v(4696)+v(4728)*v(537)+v(4552)*v(538)+v(4600)*v(539))*v(8065)
v(5851)=(v(452)*v(4631)+v(446)*v(4679)+v(455)*v(4695)+v(4727)*v(537)+v(4551)*v(538)+v(4599)*v(539))*v(8065)
v(5850)=(v(452)*v(4630)+v(446)*v(4678)+v(455)*v(4694)+v(4726)*v(537)+v(4550)*v(538)+v(4598)*v(539))*v(8065)
v(5848)=(v(452)*v(4629)+v(446)*v(4677)+v(455)*v(4693)+v(4725)*v(537)+v(4549)*v(538)+v(4597)*v(539))*v(8065)
v(4804)=v(4450)*v(446)+v(426)*v(4564)-v(455)*v(4596)-v(450)*v(4740)
v(4803)=v(4449)*v(446)+v(426)*v(4563)-v(455)*v(4595)-v(450)*v(4739)
v(4802)=v(4448)*v(446)+v(426)*v(4562)-v(455)*v(4594)-v(450)*v(4738)
v(4801)=v(4447)*v(446)+v(426)*v(4561)-v(455)*v(4593)-v(450)*v(4737)
v(4800)=v(4446)*v(446)+v(426)*v(4560)-v(455)*v(4592)-v(450)*v(4736)
v(4799)=v(4445)*v(446)+v(426)*v(4559)-v(455)*v(4591)-v(450)*v(4735)
v(4798)=v(4444)*v(446)+v(426)*v(4558)-v(455)*v(4590)-v(450)*v(4734)
v(4797)=v(4443)*v(446)+v(426)*v(4557)-v(455)*v(4589)-v(450)*v(4733)
v(4796)=v(4442)*v(446)+v(426)*v(4556)-v(455)*v(4588)-v(450)*v(4732)
v(4795)=v(4441)*v(446)+v(426)*v(4555)-v(455)*v(4587)-v(450)*v(4731)
v(4794)=v(4440)*v(446)+v(426)*v(4554)-v(455)*v(4586)-v(450)*v(4730)
v(4793)=v(4439)*v(446)+v(426)*v(4553)-v(455)*v(4585)-v(450)*v(4729)
v(4792)=v(4438)*v(446)+v(426)*v(4552)-v(455)*v(4584)-v(450)*v(4728)
v(4791)=v(4437)*v(446)+v(426)*v(4551)-v(455)*v(4583)-v(450)*v(4727)
v(4790)=v(4436)*v(446)+v(426)*v(4550)-v(455)*v(4582)-v(450)*v(4726)
v(4789)=v(4435)*v(446)+v(426)*v(4549)-v(455)*v(4581)-v(450)*v(4725)
v(4788)=-(v(448)*v(4564))-v(446)*v(4580)+v(455)*v(4628)+v(453)*v(4740)
v(4787)=-(v(448)*v(4563))-v(446)*v(4579)+v(455)*v(4627)+v(453)*v(4739)
v(4786)=-(v(448)*v(4562))-v(446)*v(4578)+v(455)*v(4626)+v(453)*v(4738)
v(4785)=-(v(448)*v(4561))-v(446)*v(4577)+v(455)*v(4625)+v(453)*v(4737)
v(4784)=-(v(448)*v(4560))-v(446)*v(4576)+v(455)*v(4624)+v(453)*v(4736)
v(4783)=-(v(448)*v(4559))-v(446)*v(4575)+v(455)*v(4623)+v(453)*v(4735)
v(4782)=-(v(448)*v(4558))-v(446)*v(4574)+v(455)*v(4622)+v(453)*v(4734)
v(4781)=-(v(448)*v(4557))-v(446)*v(4573)+v(455)*v(4621)+v(453)*v(4733)
v(4780)=-(v(448)*v(4556))-v(446)*v(4572)+v(455)*v(4620)+v(453)*v(4732)
v(4779)=-(v(448)*v(4555))-v(446)*v(4571)+v(455)*v(4619)+v(453)*v(4731)
v(4778)=-(v(448)*v(4554))-v(446)*v(4570)+v(455)*v(4618)+v(453)*v(4730)
v(4777)=-(v(448)*v(4553))-v(446)*v(4569)+v(455)*v(4617)+v(453)*v(4729)
v(4776)=-(v(448)*v(4552))-v(446)*v(4568)+v(455)*v(4616)+v(453)*v(4728)
v(4775)=-(v(448)*v(4551))-v(446)*v(4567)+v(455)*v(4615)+v(453)*v(4727)
v(4774)=-(v(448)*v(4550))-v(446)*v(4566)+v(455)*v(4614)+v(453)*v(4726)
v(4773)=-(v(448)*v(4549))-v(446)*v(4565)+v(455)*v(4613)+v(453)*v(4725)
v(4772)=-(v(4180)*v(455))+v(452)*v(4580)+v(448)*v(4612)-v(408)*v(4740)
v(4771)=-(v(4179)*v(455))+v(452)*v(4579)+v(448)*v(4611)-v(408)*v(4739)
v(4770)=-(v(4178)*v(455))+v(452)*v(4578)+v(448)*v(4610)-v(408)*v(4738)
v(4769)=-(v(4177)*v(455))+v(452)*v(4577)+v(448)*v(4609)-v(408)*v(4737)
v(4768)=-(v(4176)*v(455))+v(452)*v(4576)+v(448)*v(4608)-v(408)*v(4736)
v(4767)=-(v(4175)*v(455))+v(452)*v(4575)+v(448)*v(4607)-v(408)*v(4735)
v(4766)=-(v(4174)*v(455))+v(452)*v(4574)+v(448)*v(4606)-v(408)*v(4734)
v(4765)=-(v(4173)*v(455))+v(452)*v(4573)+v(448)*v(4605)-v(408)*v(4733)
v(4764)=-(v(4172)*v(455))+v(452)*v(4572)+v(448)*v(4604)-v(408)*v(4732)
v(4763)=-(v(4171)*v(455))+v(452)*v(4571)+v(448)*v(4603)-v(408)*v(4731)
v(4762)=-(v(4170)*v(455))+v(452)*v(4570)+v(448)*v(4602)-v(408)*v(4730)
v(4761)=-(v(4169)*v(455))+v(452)*v(4569)+v(448)*v(4601)-v(408)*v(4729)
v(4760)=-(v(4168)*v(455))+v(452)*v(4568)+v(448)*v(4600)-v(408)*v(4728)
v(4759)=-(v(4167)*v(455))+v(452)*v(4567)+v(448)*v(4599)-v(408)*v(4727)
v(4758)=-(v(4166)*v(455))+v(452)*v(4566)+v(448)*v(4598)-v(408)*v(4726)
v(4757)=-(v(4165)*v(455))+v(452)*v(4565)+v(448)*v(4597)-v(408)*v(4725)
v(4756)=-(v(4450)*v(452))-v(426)*v(4612)+v(455)*v(4676)+v(454)*v(4740)
v(4755)=-(v(4449)*v(452))-v(426)*v(4611)+v(455)*v(4675)+v(454)*v(4739)
v(4754)=-(v(4448)*v(452))-v(426)*v(4610)+v(455)*v(4674)+v(454)*v(4738)
v(4753)=-(v(4447)*v(452))-v(426)*v(4609)+v(455)*v(4673)+v(454)*v(4737)
v(4752)=-(v(4446)*v(452))-v(426)*v(4608)+v(455)*v(4672)+v(454)*v(4736)
v(4751)=-(v(4445)*v(452))-v(426)*v(4607)+v(455)*v(4671)+v(454)*v(4735)
v(4750)=-(v(4444)*v(452))-v(426)*v(4606)+v(455)*v(4670)+v(454)*v(4734)
v(4749)=-(v(4443)*v(452))-v(426)*v(4605)+v(455)*v(4669)+v(454)*v(4733)
v(4748)=-(v(4442)*v(452))-v(426)*v(4604)+v(455)*v(4668)+v(454)*v(4732)
v(4747)=-(v(4441)*v(452))-v(426)*v(4603)+v(455)*v(4667)+v(454)*v(4731)
v(4746)=-(v(4440)*v(452))-v(426)*v(4602)+v(455)*v(4666)+v(454)*v(4730)
v(4745)=-(v(4439)*v(452))-v(426)*v(4601)+v(455)*v(4665)+v(454)*v(4729)
v(4744)=-(v(4438)*v(452))-v(426)*v(4600)+v(455)*v(4664)+v(454)*v(4728)
v(4743)=-(v(4437)*v(452))-v(426)*v(4599)+v(455)*v(4663)+v(454)*v(4727)
v(4742)=-(v(4436)*v(452))-v(426)*v(4598)+v(455)*v(4662)+v(454)*v(4726)
v(4741)=-(v(4435)*v(452))-v(426)*v(4597)+v(455)*v(4661)+v(454)*v(4725)
v(535)=-(v(426)*v(452))+v(454)*v(455)
v(5906)=(v(535)*v(535))
v(534)=v(448)*v(452)-v(408)*v(455)
v(5944)=(v(534)*v(534))
v(533)=-(v(446)*v(448))+v(453)*v(455)
v(8113)=v(530)*v(537)+v(534)*v(538)+v(533)*v(539)
v(5943)=(v(533)*v(533))
v(8101)=v(5942)+v(5943)+v(5944)
v(532)=v(426)*v(446)-v(450)*v(455)
v(8115)=v(530)*v(531)+v(532)*v(533)+v(534)*v(535)
v(8111)=v(531)*v(537)+v(535)*v(538)+v(532)*v(539)
v(5905)=(v(532)*v(532))
v(8102)=v(5904)+v(5905)+v(5906)
v(456)=v(473)+v(232)*v(4805)+v(491)
v(8068)=v(390)*v(456)+v(391)*v(458)+v(388)*v(459)
v(8066)=v(392)*v(456)+v(389)*v(458)+v(391)*v(459)
v(4905)=v(3726)+v(3762)+(v(3523)*v(456)+v(386)*v(4822))*v(7522)
v(4904)=v(3725)+v(3761)+(v(3522)*v(456)+v(386)*v(4821))*v(7522)
v(4903)=v(3724)+v(3760)+(v(3521)*v(456)+v(386)*v(4820))*v(7522)
v(4902)=v(3723)+v(3759)+(v(3520)*v(456)+v(386)*v(4819))*v(7522)
v(4901)=v(3722)+v(3758)+(v(3519)*v(456)+v(386)*v(4818))*v(7522)
v(4900)=v(3721)+v(3757)+(v(3518)*v(456)+v(386)*v(4817))*v(7522)
v(4899)=v(3720)+v(3756)+(v(3517)*v(456)+v(386)*v(4816))*v(7522)
v(4898)=v(3719)+v(3755)+(v(3516)*v(456)+v(386)*v(4815))*v(7522)
v(4897)=v(3718)+v(3754)+(v(3515)*v(456)+v(386)*v(4814))*v(7522)
v(4896)=v(3717)+v(3753)+(v(3514)*v(456)+v(386)*v(4813))*v(7522)
v(4895)=v(3716)+v(3752)+(v(3512)*v(456)+v(386)*v(4812))*v(7522)
v(4894)=v(3715)+v(3751)+(v(3511)*v(456)+v(386)*v(4811))*v(7522)
v(4893)=v(3714)+v(3750)+(v(3510)*v(456)+v(386)*v(4810))*v(7522)
v(4892)=v(3713)+v(3749)+(v(3509)*v(456)+v(386)*v(4809))*v(7522)
v(4891)=v(3712)+v(3748)+(v(3508)*v(456)+v(386)*v(4808))*v(7522)
v(4890)=v(3711)+v(3747)+v(4806)*v(8070)+v(456)*v(8071)
v(4873)=(v(3710)*v(388)+v(3746)*v(391)+v(3575)*v(456)+v(3609)*v(458)+v(3540)*v(459)+v(390)*v(4822))*v(7522)
v(4872)=(v(3709)*v(388)+v(3745)*v(391)+v(3574)*v(456)+v(3608)*v(458)+v(3539)*v(459)+v(390)*v(4821))*v(7522)
v(4871)=(v(3708)*v(388)+v(3744)*v(391)+v(3573)*v(456)+v(3607)*v(458)+v(3538)*v(459)+v(390)*v(4820))*v(7522)
v(4870)=(v(3707)*v(388)+v(3743)*v(391)+v(3572)*v(456)+v(3606)*v(458)+v(3537)*v(459)+v(390)*v(4819))*v(7522)
v(4869)=(v(3706)*v(388)+v(3742)*v(391)+v(3571)*v(456)+v(3605)*v(458)+v(3536)*v(459)+v(390)*v(4818))*v(7522)
v(4868)=(v(3705)*v(388)+v(3741)*v(391)+v(3570)*v(456)+v(3604)*v(458)+v(3535)*v(459)+v(390)*v(4817))*v(7522)
v(4865)=v(456)*v(5197)
v(4867)=v(4865)+v(4866)+(v(3703)*v(388)+v(3739)*v(391)+v(3534)*v(459)+v(390)*v(4816))*v(7522)
v(4864)=(v(3702)*v(388)+v(3736)*v(391)+v(3568)*v(456)+v(3570)*v(458)+v(3533)*v(459)+v(390)*v(4815))*v(7522)
v(4863)=(v(3700)*v(388)+v(3734)*v(391)+v(3566)*v(456)+v(3601)*v(458)+v(3532)*v(459)+v(390)*v(4814))*v(7522)
v(4862)=(v(3699)*v(388)+v(3733)*v(391)+v(3565)*v(456)+v(3600)*v(458)+v(3530)*v(459)+v(390)*v(4813))*v(7522)
v(4861)=(v(3698)*v(388)+v(3732)*v(391)+v(3564)*v(456)+v(3599)*v(458)+v(3529)*v(459)+v(390)*v(4812))*v(7522)
v(4860)=(v(3697)*v(388)+v(3731)*v(391)+v(3563)*v(456)+v(3598)*v(458)+v(3528)*v(459)+v(390)*v(4811))*v(7522)
v(4859)=(v(3696)*v(388)+v(3730)*v(391)+v(3562)*v(456)+v(3597)*v(458)+v(3527)*v(459)+v(390)*v(4810))*v(7522)
v(4858)=(v(3695)*v(388)+v(3729)*v(391)+v(3561)*v(456)+v(3596)*v(458)+v(3526)*v(459)+v(390)*v(4809))*v(7522)
v(4857)=(v(3694)*v(388)+v(3728)*v(391)+v(3560)*v(456)+v(3595)*v(458)+v(3525)*v(459)+v(390)*v(4808))*v(7522)
v(4856)=(v(3693)*v(388)+v(3727)*v(391)+v(3559)*v(456)+v(3594)*v(458)+v(3524)*v(459)+v(390)*v(4806))*v(7522)+v(7518)*v&
&(8068)
v(4839)=(v(3746)*v(389)+v(3710)*v(391)+v(3642)*v(456)+v(3558)*v(458)+v(3609)*v(459)+v(392)*v(4822))*v(7522)
v(4838)=(v(3745)*v(389)+v(3709)*v(391)+v(3641)*v(456)+v(3557)*v(458)+v(3608)*v(459)+v(392)*v(4821))*v(7522)
v(4837)=(v(3744)*v(389)+v(3708)*v(391)+v(3640)*v(456)+v(3556)*v(458)+v(3607)*v(459)+v(392)*v(4820))*v(7522)
v(4836)=(v(3743)*v(389)+v(3707)*v(391)+v(3639)*v(456)+v(3555)*v(458)+v(3606)*v(459)+v(392)*v(4819))*v(7522)
v(4835)=(v(3742)*v(389)+v(3706)*v(391)+v(3638)*v(456)+v(3554)*v(458)+v(3605)*v(459)+v(392)*v(4818))*v(7522)
v(4834)=(v(3741)*v(389)+v(3705)*v(391)+v(3602)*v(456)+v(3553)*v(458)+v(3604)*v(459)+v(392)*v(4817))*v(7522)
v(4833)=v(5252)+(v(3739)*v(389)+v(3703)*v(391)+v(3637)*v(456)+v(3552)*v(458)+v(392)*v(4816))*v(7522)
v(4832)=v(4831)+v(4865)+(v(3736)*v(389)+v(3702)*v(391)+v(3551)*v(458)+v(392)*v(4815))*v(7522)
v(4830)=(v(3734)*v(389)+v(3700)*v(391)+v(3635)*v(456)+v(3550)*v(458)+v(3601)*v(459)+v(392)*v(4814))*v(7522)
v(4829)=(v(3733)*v(389)+v(3699)*v(391)+v(3634)*v(456)+v(3548)*v(458)+v(3600)*v(459)+v(392)*v(4813))*v(7522)
v(4828)=(v(3732)*v(389)+v(3698)*v(391)+v(3633)*v(456)+v(3546)*v(458)+v(3599)*v(459)+v(392)*v(4812))*v(7522)
v(4827)=(v(3731)*v(389)+v(3697)*v(391)+v(3632)*v(456)+v(3545)*v(458)+v(3598)*v(459)+v(392)*v(4811))*v(7522)
v(4826)=(v(3730)*v(389)+v(3696)*v(391)+v(3631)*v(456)+v(3544)*v(458)+v(3597)*v(459)+v(392)*v(4810))*v(7522)
v(4825)=(v(3729)*v(389)+v(3695)*v(391)+v(3630)*v(456)+v(3543)*v(458)+v(3596)*v(459)+v(392)*v(4809))*v(7522)
v(4824)=(v(3728)*v(389)+v(3694)*v(391)+v(3629)*v(456)+v(3542)*v(458)+v(3595)*v(459)+v(392)*v(4808))*v(7522)
v(4823)=(v(3727)*v(389)+v(3693)*v(391)+v(3628)*v(456)+v(3541)*v(458)+v(3594)*v(459)+v(392)*v(4806))*v(7522)+v(7518)*v&
&(8066)
v(462)=v(7522)*v(8066)
v(4915)=v(462)*v(5436)
v(4855)=(v(3642)*v(462)+v(392)*v(4839))*v(7522)
v(4854)=(v(3641)*v(462)+v(392)*v(4838))*v(7522)
v(4853)=(v(3640)*v(462)+v(392)*v(4837))*v(7522)
v(4852)=(v(3639)*v(462)+v(392)*v(4836))*v(7522)
v(4851)=(v(3638)*v(462)+v(392)*v(4835))*v(7522)
v(4850)=v(4915)+v(4834)*v(8031)
v(4849)=(v(3637)*v(462)+v(392)*v(4833))*v(7522)
v(4848)=(v(3569)*v(462)+v(392)*v(4832))*v(7522)
v(4847)=(v(3635)*v(462)+v(392)*v(4830))*v(7522)
v(4846)=(v(3634)*v(462)+v(392)*v(4829))*v(7522)
v(4845)=(v(3633)*v(462)+v(392)*v(4828))*v(7522)
v(4844)=(v(3632)*v(462)+v(392)*v(4827))*v(7522)
v(4843)=(v(3631)*v(462)+v(392)*v(4826))*v(7522)
v(4842)=(v(3630)*v(462)+v(392)*v(4825))*v(7522)
v(4841)=(v(3629)*v(462)+v(392)*v(4824))*v(7522)
v(4840)=v(4823)*v(8031)+v(462)*v(8067)
v(497)=v(462)*v(8031)
v(461)=v(7522)*v(8068)
v(5302)=v(461)*v(5436)
v(5299)=v(461)*v(5197)
v(4948)=v(461)*v(5433)
v(4889)=(v(3575)*v(461)+v(390)*v(4873))*v(7522)
v(4888)=(v(3574)*v(461)+v(390)*v(4872))*v(7522)
v(4887)=(v(3573)*v(461)+v(390)*v(4871))*v(7522)
v(4886)=(v(3572)*v(461)+v(390)*v(4870))*v(7522)
v(4885)=(v(3571)*v(461)+v(390)*v(4869))*v(7522)
v(4884)=v(4948)+v(4868)*v(8029)
v(4883)=v(5299)+v(4867)*v(8029)
v(4882)=(v(3568)*v(461)+v(390)*v(4864))*v(7522)
v(4881)=(v(3566)*v(461)+v(390)*v(4863))*v(7522)
v(4880)=(v(3565)*v(461)+v(390)*v(4862))*v(7522)
v(4879)=(v(3564)*v(461)+v(390)*v(4861))*v(7522)
v(4878)=(v(3563)*v(461)+v(390)*v(4860))*v(7522)
v(4877)=(v(3562)*v(461)+v(390)*v(4859))*v(7522)
v(4876)=(v(3561)*v(461)+v(390)*v(4858))*v(7522)
v(4875)=(v(3560)*v(461)+v(390)*v(4857))*v(7522)
v(4874)=v(4856)*v(8029)+v(461)*v(8069)
v(477)=v(461)*v(8029)
v(457)=v(475)+v(493)+v(456)*v(8070)
v(8073)=v(392)*v(457)+v(391)*v(461)+v(389)*v(462)
v(8072)=v(390)*v(457)+v(388)*v(461)+v(391)*v(462)
v(4988)=v(4855)+v(4889)+(v(3523)*v(457)+v(386)*v(4905))*v(7522)
v(4987)=v(4854)+v(4888)+(v(3522)*v(457)+v(386)*v(4904))*v(7522)
v(4986)=v(4853)+v(4887)+(v(3521)*v(457)+v(386)*v(4903))*v(7522)
v(4985)=v(4852)+v(4886)+(v(3520)*v(457)+v(386)*v(4902))*v(7522)
v(4984)=v(4851)+v(4885)+(v(3519)*v(457)+v(386)*v(4901))*v(7522)
v(4983)=v(4850)+v(4884)+(v(3518)*v(457)+v(386)*v(4900))*v(7522)
v(4982)=v(4849)+v(4883)+(v(3517)*v(457)+v(386)*v(4899))*v(7522)
v(4981)=v(4848)+v(4882)+(v(3516)*v(457)+v(386)*v(4898))*v(7522)
v(4980)=v(4847)+v(4881)+(v(3515)*v(457)+v(386)*v(4897))*v(7522)
v(4979)=v(4846)+v(4880)+(v(3514)*v(457)+v(386)*v(4896))*v(7522)
v(4978)=v(4845)+v(4879)+(v(3512)*v(457)+v(386)*v(4895))*v(7522)
v(4977)=v(4844)+v(4878)+(v(3511)*v(457)+v(386)*v(4894))*v(7522)
v(4976)=v(4843)+v(4877)+(v(3510)*v(457)+v(386)*v(4893))*v(7522)
v(4975)=v(4842)+v(4876)+(v(3509)*v(457)+v(386)*v(4892))*v(7522)
v(4974)=v(4841)+v(4875)+(v(3508)*v(457)+v(386)*v(4891))*v(7522)
v(4973)=v(4840)+v(4874)+v(4890)*v(8070)+v(457)*v(8071)
v(4956)=(v(3642)*v(457)+v(3609)*v(461)+v(3558)*v(462)+v(389)*v(4839)+v(391)*v(4873)+v(392)*v(4905))*v(7522)
v(4955)=(v(3641)*v(457)+v(3608)*v(461)+v(3557)*v(462)+v(389)*v(4838)+v(391)*v(4872)+v(392)*v(4904))*v(7522)
v(4954)=(v(3640)*v(457)+v(3607)*v(461)+v(3556)*v(462)+v(389)*v(4837)+v(391)*v(4871)+v(392)*v(4903))*v(7522)
v(4953)=(v(3639)*v(457)+v(3606)*v(461)+v(3555)*v(462)+v(389)*v(4836)+v(391)*v(4870)+v(392)*v(4902))*v(7522)
v(4952)=(v(3638)*v(457)+v(3605)*v(461)+v(3554)*v(462)+v(389)*v(4835)+v(391)*v(4869)+v(392)*v(4901))*v(7522)
v(4951)=(v(3602)*v(457)+v(3604)*v(461)+v(3553)*v(462)+v(389)*v(4834)+v(391)*v(4868)+v(392)*v(4900))*v(7522)
v(4950)=v(5302)+(v(3637)*v(457)+v(3552)*v(462)+v(389)*v(4833)+v(391)*v(4867)+v(392)*v(4899))*v(7522)
v(4947)=v(457)*v(5197)
v(4949)=v(4947)+v(4948)+(v(3551)*v(462)+v(389)*v(4832)+v(391)*v(4864)+v(392)*v(4898))*v(7522)
v(4946)=(v(3635)*v(457)+v(3601)*v(461)+v(3550)*v(462)+v(389)*v(4830)+v(391)*v(4863)+v(392)*v(4897))*v(7522)
v(4945)=(v(3634)*v(457)+v(3600)*v(461)+v(3548)*v(462)+v(389)*v(4829)+v(391)*v(4862)+v(392)*v(4896))*v(7522)
v(4944)=(v(3633)*v(457)+v(3599)*v(461)+v(3546)*v(462)+v(389)*v(4828)+v(391)*v(4861)+v(392)*v(4895))*v(7522)
v(4943)=(v(3632)*v(457)+v(3598)*v(461)+v(3545)*v(462)+v(389)*v(4827)+v(391)*v(4860)+v(392)*v(4894))*v(7522)
v(4942)=(v(3631)*v(457)+v(3597)*v(461)+v(3544)*v(462)+v(389)*v(4826)+v(391)*v(4859)+v(392)*v(4893))*v(7522)
v(4941)=(v(3630)*v(457)+v(3596)*v(461)+v(3543)*v(462)+v(389)*v(4825)+v(391)*v(4858)+v(392)*v(4892))*v(7522)
v(4940)=(v(3629)*v(457)+v(3595)*v(461)+v(3542)*v(462)+v(389)*v(4824)+v(391)*v(4857)+v(392)*v(4891))*v(7522)
v(4939)=(v(3628)*v(457)+v(3594)*v(461)+v(3541)*v(462)+v(389)*v(4823)+v(391)*v(4856)+v(392)*v(4890))*v(7522)+v(7518)*v&
&(8073)
v(4922)=(v(3575)*v(457)+v(3540)*v(461)+v(3609)*v(462)+v(391)*v(4839)+v(388)*v(4873)+v(390)*v(4905))*v(7522)
v(4921)=(v(3574)*v(457)+v(3539)*v(461)+v(3608)*v(462)+v(391)*v(4838)+v(388)*v(4872)+v(390)*v(4904))*v(7522)
v(4920)=(v(3573)*v(457)+v(3538)*v(461)+v(3607)*v(462)+v(391)*v(4837)+v(388)*v(4871)+v(390)*v(4903))*v(7522)
v(4919)=(v(3572)*v(457)+v(3537)*v(461)+v(3606)*v(462)+v(391)*v(4836)+v(388)*v(4870)+v(390)*v(4902))*v(7522)
v(4918)=(v(3571)*v(457)+v(3536)*v(461)+v(3605)*v(462)+v(391)*v(4835)+v(388)*v(4869)+v(390)*v(4901))*v(7522)
v(4917)=(v(3570)*v(457)+v(3535)*v(461)+v(3604)*v(462)+v(391)*v(4834)+v(388)*v(4868)+v(390)*v(4900))*v(7522)
v(4916)=v(4915)+v(4947)+(v(3534)*v(461)+v(391)*v(4833)+v(388)*v(4867)+v(390)*v(4899))*v(7522)
v(4914)=(v(3568)*v(457)+v(3533)*v(461)+v(3570)*v(462)+v(391)*v(4832)+v(388)*v(4864)+v(390)*v(4898))*v(7522)
v(4913)=(v(3566)*v(457)+v(3532)*v(461)+v(3601)*v(462)+v(391)*v(4830)+v(388)*v(4863)+v(390)*v(4897))*v(7522)
v(4912)=(v(3565)*v(457)+v(3530)*v(461)+v(3600)*v(462)+v(391)*v(4829)+v(388)*v(4862)+v(390)*v(4896))*v(7522)
v(4911)=(v(3564)*v(457)+v(3529)*v(461)+v(3599)*v(462)+v(391)*v(4828)+v(388)*v(4861)+v(390)*v(4895))*v(7522)
v(4910)=(v(3563)*v(457)+v(3528)*v(461)+v(3598)*v(462)+v(391)*v(4827)+v(388)*v(4860)+v(390)*v(4894))*v(7522)
v(4909)=(v(3562)*v(457)+v(3527)*v(461)+v(3597)*v(462)+v(391)*v(4826)+v(388)*v(4859)+v(390)*v(4893))*v(7522)
v(4908)=(v(3561)*v(457)+v(3526)*v(461)+v(3596)*v(462)+v(391)*v(4825)+v(388)*v(4858)+v(390)*v(4892))*v(7522)
v(4907)=(v(3560)*v(457)+v(3525)*v(461)+v(3595)*v(462)+v(391)*v(4824)+v(388)*v(4857)+v(390)*v(4891))*v(7522)
v(4906)=(v(3559)*v(457)+v(3524)*v(461)+v(3594)*v(462)+v(391)*v(4823)+v(388)*v(4856)+v(390)*v(4890))*v(7522)+v(7518)*v&
&(8072)
v(465)=v(7522)*v(8072)
v(5352)=v(465)*v(5436)
v(5349)=v(465)*v(5197)
v(4997)=v(465)*v(5433)
v(4938)=(v(3575)*v(465)+v(390)*v(4922))*v(7522)
v(4937)=(v(3574)*v(465)+v(390)*v(4921))*v(7522)
v(4936)=(v(3573)*v(465)+v(390)*v(4920))*v(7522)
v(4935)=(v(3572)*v(465)+v(390)*v(4919))*v(7522)
v(4934)=(v(3571)*v(465)+v(390)*v(4918))*v(7522)
v(4933)=v(4997)+v(4917)*v(8029)
v(4932)=v(5349)+v(4916)*v(8029)
v(4931)=(v(3568)*v(465)+v(390)*v(4914))*v(7522)
v(4930)=(v(3566)*v(465)+v(390)*v(4913))*v(7522)
v(4929)=(v(3565)*v(465)+v(390)*v(4912))*v(7522)
v(4928)=(v(3564)*v(465)+v(390)*v(4911))*v(7522)
v(4927)=(v(3563)*v(465)+v(390)*v(4910))*v(7522)
v(4926)=(v(3562)*v(465)+v(390)*v(4909))*v(7522)
v(4925)=(v(3561)*v(465)+v(390)*v(4908))*v(7522)
v(4924)=(v(3560)*v(465)+v(390)*v(4907))*v(7522)
v(4923)=v(4906)*v(8029)+v(465)*v(8069)
v(481)=v(465)*v(8029)
v(464)=v(7522)*v(8073)
v(5032)=v(464)*v(5436)
v(4972)=(v(3642)*v(464)+v(392)*v(4956))*v(7522)
v(4971)=(v(3641)*v(464)+v(392)*v(4955))*v(7522)
v(4970)=(v(3640)*v(464)+v(392)*v(4954))*v(7522)
v(4969)=(v(3639)*v(464)+v(392)*v(4953))*v(7522)
v(4968)=(v(3638)*v(464)+v(392)*v(4952))*v(7522)
v(4967)=v(5032)+v(4951)*v(8031)
v(4966)=(v(3637)*v(464)+v(392)*v(4950))*v(7522)
v(4965)=(v(3569)*v(464)+v(392)*v(4949))*v(7522)
v(4964)=(v(3635)*v(464)+v(392)*v(4946))*v(7522)
v(4963)=(v(3634)*v(464)+v(392)*v(4945))*v(7522)
v(4962)=(v(3633)*v(464)+v(392)*v(4944))*v(7522)
v(4961)=(v(3632)*v(464)+v(392)*v(4943))*v(7522)
v(4960)=(v(3631)*v(464)+v(392)*v(4942))*v(7522)
v(4959)=(v(3630)*v(464)+v(392)*v(4941))*v(7522)
v(4958)=(v(3629)*v(464)+v(392)*v(4940))*v(7522)
v(4957)=v(4939)*v(8031)+v(464)*v(8067)
v(499)=v(464)*v(8031)
v(460)=v(477)+v(497)+v(457)*v(8070)
v(8075)=v(390)*v(460)+v(391)*v(464)+v(388)*v(465)
v(8074)=v(392)*v(460)+v(389)*v(464)+v(391)*v(465)
v(5071)=v(4938)+v(4972)+(v(3523)*v(460)+v(386)*v(4988))*v(7522)
v(5070)=v(4937)+v(4971)+(v(3522)*v(460)+v(386)*v(4987))*v(7522)
v(5069)=v(4936)+v(4970)+(v(3521)*v(460)+v(386)*v(4986))*v(7522)
v(5068)=v(4935)+v(4969)+(v(3520)*v(460)+v(386)*v(4985))*v(7522)
v(5067)=v(4934)+v(4968)+(v(3519)*v(460)+v(386)*v(4984))*v(7522)
v(5066)=v(4933)+v(4967)+(v(3518)*v(460)+v(386)*v(4983))*v(7522)
v(5065)=v(4932)+v(4966)+(v(3517)*v(460)+v(386)*v(4982))*v(7522)
v(5064)=v(4931)+v(4965)+(v(3516)*v(460)+v(386)*v(4981))*v(7522)
v(5063)=v(4930)+v(4964)+(v(3515)*v(460)+v(386)*v(4980))*v(7522)
v(5062)=v(4929)+v(4963)+(v(3514)*v(460)+v(386)*v(4979))*v(7522)
v(5061)=v(4928)+v(4962)+(v(3512)*v(460)+v(386)*v(4978))*v(7522)
v(5060)=v(4927)+v(4961)+(v(3511)*v(460)+v(386)*v(4977))*v(7522)
v(5059)=v(4926)+v(4960)+(v(3510)*v(460)+v(386)*v(4976))*v(7522)
v(5058)=v(4925)+v(4959)+(v(3509)*v(460)+v(386)*v(4975))*v(7522)
v(5057)=v(4924)+v(4958)+(v(3508)*v(460)+v(386)*v(4974))*v(7522)
v(5056)=v(4923)+v(4957)+v(4973)*v(8070)+v(460)*v(8071)
v(5039)=(v(3575)*v(460)+v(3609)*v(464)+v(3540)*v(465)+v(388)*v(4922)+v(391)*v(4956)+v(390)*v(4988))*v(7522)
v(5038)=(v(3574)*v(460)+v(3608)*v(464)+v(3539)*v(465)+v(388)*v(4921)+v(391)*v(4955)+v(390)*v(4987))*v(7522)
v(5037)=(v(3573)*v(460)+v(3607)*v(464)+v(3538)*v(465)+v(388)*v(4920)+v(391)*v(4954)+v(390)*v(4986))*v(7522)
v(5036)=(v(3572)*v(460)+v(3606)*v(464)+v(3537)*v(465)+v(388)*v(4919)+v(391)*v(4953)+v(390)*v(4985))*v(7522)
v(5035)=(v(3571)*v(460)+v(3605)*v(464)+v(3536)*v(465)+v(388)*v(4918)+v(391)*v(4952)+v(390)*v(4984))*v(7522)
v(5034)=(v(3570)*v(460)+v(3604)*v(464)+v(3535)*v(465)+v(388)*v(4917)+v(391)*v(4951)+v(390)*v(4983))*v(7522)
v(5031)=v(460)*v(5197)
v(5033)=v(5031)+v(5032)+(v(3534)*v(465)+v(388)*v(4916)+v(391)*v(4950)+v(390)*v(4982))*v(7522)
v(5030)=(v(3568)*v(460)+v(3570)*v(464)+v(3533)*v(465)+v(388)*v(4914)+v(391)*v(4949)+v(390)*v(4981))*v(7522)
v(5029)=(v(3566)*v(460)+v(3601)*v(464)+v(3532)*v(465)+v(388)*v(4913)+v(391)*v(4946)+v(390)*v(4980))*v(7522)
v(5028)=(v(3565)*v(460)+v(3600)*v(464)+v(3530)*v(465)+v(388)*v(4912)+v(391)*v(4945)+v(390)*v(4979))*v(7522)
v(5027)=(v(3564)*v(460)+v(3599)*v(464)+v(3529)*v(465)+v(388)*v(4911)+v(391)*v(4944)+v(390)*v(4978))*v(7522)
v(5026)=(v(3563)*v(460)+v(3598)*v(464)+v(3528)*v(465)+v(388)*v(4910)+v(391)*v(4943)+v(390)*v(4977))*v(7522)
v(5025)=(v(3562)*v(460)+v(3597)*v(464)+v(3527)*v(465)+v(388)*v(4909)+v(391)*v(4942)+v(390)*v(4976))*v(7522)
v(5024)=(v(3561)*v(460)+v(3596)*v(464)+v(3526)*v(465)+v(388)*v(4908)+v(391)*v(4941)+v(390)*v(4975))*v(7522)
v(5023)=(v(3560)*v(460)+v(3595)*v(464)+v(3525)*v(465)+v(388)*v(4907)+v(391)*v(4940)+v(390)*v(4974))*v(7522)
v(5022)=(v(3559)*v(460)+v(3594)*v(464)+v(3524)*v(465)+v(388)*v(4906)+v(391)*v(4939)+v(390)*v(4973))*v(7522)+v(7518)*v&
&(8075)
v(5005)=(v(3642)*v(460)+v(3558)*v(464)+v(3609)*v(465)+v(391)*v(4922)+v(389)*v(4956)+v(392)*v(4988))*v(7522)
v(5004)=(v(3641)*v(460)+v(3557)*v(464)+v(3608)*v(465)+v(391)*v(4921)+v(389)*v(4955)+v(392)*v(4987))*v(7522)
v(5003)=(v(3640)*v(460)+v(3556)*v(464)+v(3607)*v(465)+v(391)*v(4920)+v(389)*v(4954)+v(392)*v(4986))*v(7522)
v(5002)=(v(3639)*v(460)+v(3555)*v(464)+v(3606)*v(465)+v(391)*v(4919)+v(389)*v(4953)+v(392)*v(4985))*v(7522)
v(5001)=(v(3638)*v(460)+v(3554)*v(464)+v(3605)*v(465)+v(391)*v(4918)+v(389)*v(4952)+v(392)*v(4984))*v(7522)
v(5000)=(v(3602)*v(460)+v(3553)*v(464)+v(3604)*v(465)+v(391)*v(4917)+v(389)*v(4951)+v(392)*v(4983))*v(7522)
v(4999)=v(5352)+(v(3637)*v(460)+v(3552)*v(464)+v(391)*v(4916)+v(389)*v(4950)+v(392)*v(4982))*v(7522)
v(4998)=v(4997)+v(5031)+(v(3551)*v(464)+v(391)*v(4914)+v(389)*v(4949)+v(392)*v(4981))*v(7522)
v(4996)=(v(3635)*v(460)+v(3550)*v(464)+v(3601)*v(465)+v(391)*v(4913)+v(389)*v(4946)+v(392)*v(4980))*v(7522)
v(4995)=(v(3634)*v(460)+v(3548)*v(464)+v(3600)*v(465)+v(391)*v(4912)+v(389)*v(4945)+v(392)*v(4979))*v(7522)
v(4994)=(v(3633)*v(460)+v(3546)*v(464)+v(3599)*v(465)+v(391)*v(4911)+v(389)*v(4944)+v(392)*v(4978))*v(7522)
v(4993)=(v(3632)*v(460)+v(3545)*v(464)+v(3598)*v(465)+v(391)*v(4910)+v(389)*v(4943)+v(392)*v(4977))*v(7522)
v(4992)=(v(3631)*v(460)+v(3544)*v(464)+v(3597)*v(465)+v(391)*v(4909)+v(389)*v(4942)+v(392)*v(4976))*v(7522)
v(4991)=(v(3630)*v(460)+v(3543)*v(464)+v(3596)*v(465)+v(391)*v(4908)+v(389)*v(4941)+v(392)*v(4975))*v(7522)
v(4990)=(v(3629)*v(460)+v(3542)*v(464)+v(3595)*v(465)+v(391)*v(4907)+v(389)*v(4940)+v(392)*v(4974))*v(7522)
v(4989)=(v(3628)*v(460)+v(3541)*v(464)+v(3594)*v(465)+v(391)*v(4906)+v(389)*v(4939)+v(392)*v(4973))*v(7522)+v(7518)*v&
&(8074)
v(468)=v(7522)*v(8074)
v(5131)=v(468)*v(5436)
v(5021)=(v(3642)*v(468)+v(392)*v(5005))*v(7522)
v(5020)=(v(3641)*v(468)+v(392)*v(5004))*v(7522)
v(5019)=(v(3640)*v(468)+v(392)*v(5003))*v(7522)
v(5018)=(v(3639)*v(468)+v(392)*v(5002))*v(7522)
v(5017)=(v(3638)*v(468)+v(392)*v(5001))*v(7522)
v(5016)=v(5131)+v(5000)*v(8031)
v(5015)=(v(3637)*v(468)+v(392)*v(4999))*v(7522)
v(5014)=(v(3569)*v(468)+v(392)*v(4998))*v(7522)
v(5013)=(v(3635)*v(468)+v(392)*v(4996))*v(7522)
v(5012)=(v(3634)*v(468)+v(392)*v(4995))*v(7522)
v(5011)=(v(3633)*v(468)+v(392)*v(4994))*v(7522)
v(5010)=(v(3632)*v(468)+v(392)*v(4993))*v(7522)
v(5009)=(v(3631)*v(468)+v(392)*v(4992))*v(7522)
v(5008)=(v(3630)*v(468)+v(392)*v(4991))*v(7522)
v(5007)=(v(3629)*v(468)+v(392)*v(4990))*v(7522)
v(5006)=v(4989)*v(8031)+v(468)*v(8067)
v(503)=v(468)*v(8031)
v(467)=v(7522)*v(8075)
v(5418)=v(467)*v(5436)
v(5415)=v(467)*v(5197)
v(5096)=v(467)*v(5433)
v(5055)=(v(3575)*v(467)+v(390)*v(5039))*v(7522)
v(5054)=(v(3574)*v(467)+v(390)*v(5038))*v(7522)
v(5053)=(v(3573)*v(467)+v(390)*v(5037))*v(7522)
v(5052)=(v(3572)*v(467)+v(390)*v(5036))*v(7522)
v(5051)=(v(3571)*v(467)+v(390)*v(5035))*v(7522)
v(5050)=v(5096)+v(5034)*v(8029)
v(5049)=v(5415)+v(5033)*v(8029)
v(5048)=(v(3568)*v(467)+v(390)*v(5030))*v(7522)
v(5047)=(v(3566)*v(467)+v(390)*v(5029))*v(7522)
v(5046)=(v(3565)*v(467)+v(390)*v(5028))*v(7522)
v(5045)=(v(3564)*v(467)+v(390)*v(5027))*v(7522)
v(5044)=(v(3563)*v(467)+v(390)*v(5026))*v(7522)
v(5043)=(v(3562)*v(467)+v(390)*v(5025))*v(7522)
v(5042)=(v(3561)*v(467)+v(390)*v(5024))*v(7522)
v(5041)=(v(3560)*v(467)+v(390)*v(5023))*v(7522)
v(5040)=v(5022)*v(8029)+v(467)*v(8069)
v(483)=v(467)*v(8029)
v(463)=v(481)+v(499)+v(460)*v(8070)
v(8077)=v(390)*v(463)+v(388)*v(467)+v(391)*v(468)
v(8076)=v(392)*v(463)+v(391)*v(467)+v(389)*v(468)
v(5138)=(v(3575)*v(463)+v(3540)*v(467)+v(3609)*v(468)+v(391)*v(5005)+v(388)*v(5039)+v(390)*v(5071))*v(7522)
v(5137)=(v(3574)*v(463)+v(3539)*v(467)+v(3608)*v(468)+v(391)*v(5004)+v(388)*v(5038)+v(390)*v(5070))*v(7522)
v(5136)=(v(3573)*v(463)+v(3538)*v(467)+v(3607)*v(468)+v(391)*v(5003)+v(388)*v(5037)+v(390)*v(5069))*v(7522)
v(5135)=(v(3572)*v(463)+v(3537)*v(467)+v(3606)*v(468)+v(391)*v(5002)+v(388)*v(5036)+v(390)*v(5068))*v(7522)
v(5134)=(v(3571)*v(463)+v(3536)*v(467)+v(3605)*v(468)+v(391)*v(5001)+v(388)*v(5035)+v(390)*v(5067))*v(7522)
v(5133)=(v(3570)*v(463)+v(3535)*v(467)+v(3604)*v(468)+v(391)*v(5000)+v(388)*v(5034)+v(390)*v(5066))*v(7522)
v(5130)=v(463)*v(5197)
v(5132)=v(5130)+v(5131)+(v(3534)*v(467)+v(391)*v(4999)+v(388)*v(5033)+v(390)*v(5065))*v(7522)
v(5129)=(v(3568)*v(463)+v(3533)*v(467)+v(3570)*v(468)+v(391)*v(4998)+v(388)*v(5030)+v(390)*v(5064))*v(7522)
v(5128)=(v(3566)*v(463)+v(3532)*v(467)+v(3601)*v(468)+v(391)*v(4996)+v(388)*v(5029)+v(390)*v(5063))*v(7522)
v(5127)=(v(3565)*v(463)+v(3530)*v(467)+v(3600)*v(468)+v(391)*v(4995)+v(388)*v(5028)+v(390)*v(5062))*v(7522)
v(5126)=(v(3564)*v(463)+v(3529)*v(467)+v(3599)*v(468)+v(391)*v(4994)+v(388)*v(5027)+v(390)*v(5061))*v(7522)
v(5125)=(v(3563)*v(463)+v(3528)*v(467)+v(3598)*v(468)+v(391)*v(4993)+v(388)*v(5026)+v(390)*v(5060))*v(7522)
v(5124)=(v(3562)*v(463)+v(3527)*v(467)+v(3597)*v(468)+v(391)*v(4992)+v(388)*v(5025)+v(390)*v(5059))*v(7522)
v(5123)=(v(3561)*v(463)+v(3526)*v(467)+v(3596)*v(468)+v(391)*v(4991)+v(388)*v(5024)+v(390)*v(5058))*v(7522)
v(5122)=(v(3560)*v(463)+v(3525)*v(467)+v(3595)*v(468)+v(391)*v(4990)+v(388)*v(5023)+v(390)*v(5057))*v(7522)
v(5121)=(v(3559)*v(463)+v(3524)*v(467)+v(3594)*v(468)+v(391)*v(4989)+v(388)*v(5022)+v(390)*v(5056))*v(7522)+v(7518)*v&
&(8077)
v(5104)=(v(3642)*v(463)+v(3609)*v(467)+v(3558)*v(468)+v(389)*v(5005)+v(391)*v(5039)+v(392)*v(5071))*v(7522)
v(5103)=(v(3641)*v(463)+v(3608)*v(467)+v(3557)*v(468)+v(389)*v(5004)+v(391)*v(5038)+v(392)*v(5070))*v(7522)
v(5102)=(v(3640)*v(463)+v(3607)*v(467)+v(3556)*v(468)+v(389)*v(5003)+v(391)*v(5037)+v(392)*v(5069))*v(7522)
v(5101)=(v(3639)*v(463)+v(3606)*v(467)+v(3555)*v(468)+v(389)*v(5002)+v(391)*v(5036)+v(392)*v(5068))*v(7522)
v(5100)=(v(3638)*v(463)+v(3605)*v(467)+v(3554)*v(468)+v(389)*v(5001)+v(391)*v(5035)+v(392)*v(5067))*v(7522)
v(5099)=(v(3602)*v(463)+v(3604)*v(467)+v(3553)*v(468)+v(389)*v(5000)+v(391)*v(5034)+v(392)*v(5066))*v(7522)
v(5098)=v(5418)+(v(3637)*v(463)+v(3552)*v(468)+v(389)*v(4999)+v(391)*v(5033)+v(392)*v(5065))*v(7522)
v(5097)=v(5096)+v(5130)+(v(3551)*v(468)+v(389)*v(4998)+v(391)*v(5030)+v(392)*v(5064))*v(7522)
v(5095)=(v(3635)*v(463)+v(3601)*v(467)+v(3550)*v(468)+v(389)*v(4996)+v(391)*v(5029)+v(392)*v(5063))*v(7522)
v(5094)=(v(3634)*v(463)+v(3600)*v(467)+v(3548)*v(468)+v(389)*v(4995)+v(391)*v(5028)+v(392)*v(5062))*v(7522)
v(5093)=(v(3633)*v(463)+v(3599)*v(467)+v(3546)*v(468)+v(389)*v(4994)+v(391)*v(5027)+v(392)*v(5061))*v(7522)
v(5092)=(v(3632)*v(463)+v(3598)*v(467)+v(3545)*v(468)+v(389)*v(4993)+v(391)*v(5026)+v(392)*v(5060))*v(7522)
v(5091)=(v(3631)*v(463)+v(3597)*v(467)+v(3544)*v(468)+v(389)*v(4992)+v(391)*v(5025)+v(392)*v(5059))*v(7522)
v(5090)=(v(3630)*v(463)+v(3596)*v(467)+v(3543)*v(468)+v(389)*v(4991)+v(391)*v(5024)+v(392)*v(5058))*v(7522)
v(5089)=(v(3629)*v(463)+v(3595)*v(467)+v(3542)*v(468)+v(389)*v(4990)+v(391)*v(5023)+v(392)*v(5057))*v(7522)
v(5088)=(v(3628)*v(463)+v(3594)*v(467)+v(3541)*v(468)+v(389)*v(4989)+v(391)*v(5022)+v(392)*v(5056))*v(7522)+v(7518)*v&
&(8076)
v(5087)=v(5021)+v(5055)+(v(3523)*v(463)+v(386)*v(5071))*v(7522)
v(5086)=v(5020)+v(5054)+(v(3522)*v(463)+v(386)*v(5070))*v(7522)
v(5085)=v(5019)+v(5053)+(v(3521)*v(463)+v(386)*v(5069))*v(7522)
v(5084)=v(5018)+v(5052)+(v(3520)*v(463)+v(386)*v(5068))*v(7522)
v(5083)=v(5017)+v(5051)+(v(3519)*v(463)+v(386)*v(5067))*v(7522)
v(5082)=v(5016)+v(5050)+(v(3518)*v(463)+v(386)*v(5066))*v(7522)
v(5081)=v(5015)+v(5049)+(v(3517)*v(463)+v(386)*v(5065))*v(7522)
v(5080)=v(5014)+v(5048)+(v(3516)*v(463)+v(386)*v(5064))*v(7522)
v(5079)=v(5013)+v(5047)+(v(3515)*v(463)+v(386)*v(5063))*v(7522)
v(5078)=v(5012)+v(5046)+(v(3514)*v(463)+v(386)*v(5062))*v(7522)
v(5077)=v(5011)+v(5045)+(v(3512)*v(463)+v(386)*v(5061))*v(7522)
v(5076)=v(5010)+v(5044)+(v(3511)*v(463)+v(386)*v(5060))*v(7522)
v(5075)=v(5009)+v(5043)+(v(3510)*v(463)+v(386)*v(5059))*v(7522)
v(5074)=v(5008)+v(5042)+(v(3509)*v(463)+v(386)*v(5058))*v(7522)
v(5073)=v(5007)+v(5041)+(v(3508)*v(463)+v(386)*v(5057))*v(7522)
v(5072)=v(5006)+v(5040)+v(5056)*v(8070)+v(463)*v(8071)
v(466)=v(483)+v(503)+v(463)*v(8070)
v(8078)=5040d0+v(466)
v(5198)=v(466)*v(5197)
v(8080)=5040d0*v(5197)+v(5198)
v(469)=v(7522)*v(8076)
v(5199)=v(469)*v(5436)
v(5120)=(v(3642)*v(469)+v(392)*v(5104))*v(7522)
v(5119)=(v(3641)*v(469)+v(392)*v(5103))*v(7522)
v(5118)=(v(3640)*v(469)+v(392)*v(5102))*v(7522)
v(5117)=(v(3639)*v(469)+v(392)*v(5101))*v(7522)
v(5116)=(v(3638)*v(469)+v(392)*v(5100))*v(7522)
v(5115)=v(5199)+v(5099)*v(8031)
v(5114)=(v(3637)*v(469)+v(392)*v(5098))*v(7522)
v(5113)=(v(3569)*v(469)+v(392)*v(5097))*v(7522)
v(5112)=(v(3635)*v(469)+v(392)*v(5095))*v(7522)
v(5111)=(v(3634)*v(469)+v(392)*v(5094))*v(7522)
v(5110)=(v(3633)*v(469)+v(392)*v(5093))*v(7522)
v(5109)=(v(3632)*v(469)+v(392)*v(5092))*v(7522)
v(5108)=(v(3631)*v(469)+v(392)*v(5091))*v(7522)
v(5107)=(v(3630)*v(469)+v(392)*v(5090))*v(7522)
v(5106)=(v(3629)*v(469)+v(392)*v(5089))*v(7522)
v(5105)=v(5088)*v(8031)+v(469)*v(8067)
v(505)=v(469)*v(8031)
v(470)=v(7522)*v(8077)
v(8082)=v(391)*v(469)+v(388)*v(470)
v(8081)=v(389)*v(469)+v(391)*v(470)
v(5438)=v(470)*v(5436)
v(5434)=v(470)*v(5197)
v(5206)=(7d0*(360d0*v(3710)+120d0*v(4873)+30d0*v(4922)+6d0*v(5039)+v(5138))+v(7522)*(v(3609)*v(469)+v(3540)*v(470)+v&
&(390)*v(5087)+v(391)*v(5104)+v(388)*v(5138)+v(3575)*v(8078)))/5040d0
v(5205)=(7d0*(360d0*v(3709)+120d0*v(4872)+30d0*v(4921)+6d0*v(5038)+v(5137))+v(7522)*(v(3608)*v(469)+v(3539)*v(470)+v&
&(390)*v(5086)+v(391)*v(5103)+v(388)*v(5137)+v(3574)*v(8078)))/5040d0
v(5204)=(7d0*(360d0*v(3708)+120d0*v(4871)+30d0*v(4920)+6d0*v(5037)+v(5136))+v(7522)*(v(3607)*v(469)+v(3538)*v(470)+v&
&(390)*v(5085)+v(391)*v(5102)+v(388)*v(5136)+v(3573)*v(8078)))/5040d0
v(5203)=(7d0*(360d0*v(3707)+120d0*v(4870)+30d0*v(4919)+6d0*v(5036)+v(5135))+v(7522)*(v(3606)*v(469)+v(3537)*v(470)+v&
&(390)*v(5084)+v(391)*v(5101)+v(388)*v(5135)+v(3572)*v(8078)))/5040d0
v(5202)=(7d0*(360d0*v(3706)+120d0*v(4869)+30d0*v(4918)+6d0*v(5035)+v(5134))+v(7522)*(v(3605)*v(469)+v(3536)*v(470)+v&
&(390)*v(5083)+v(391)*v(5100)+v(388)*v(5134)+v(3571)*v(8078)))/5040d0
v(5201)=(7d0*(360d0*v(3705)+120d0*v(4868)+30d0*v(4917)+6d0*v(5034)+v(5133)+720d0*v(5433))+(v(3570)*v(466)+v(3604)*v(469&
&)+v(3535)*v(470)+v(390)*v(5082)+v(391)*v(5099)+v(388)*v(5133))*v(7522))/5040d0
v(5200)=(2520d0*v(3703)+840d0*v(4867)+210d0*v(4916)+42d0*v(5033)+7d0*v(5132)+v(5199)+(v(3534)*v(470)+v(390)*v(5081)+v&
&(391)*v(5098)+v(388)*v(5132))*v(7522)+v(8080))/5040d0
v(5196)=(7d0*(360d0*v(3702)+120d0*v(4864)+30d0*v(4914)+6d0*v(5030)+v(5129))+v(7522)*(v(3570)*v(469)+v(3533)*v(470)+v&
&(390)*v(5080)+v(391)*v(5097)+v(388)*v(5129)+v(3568)*v(8078)))/5040d0
v(5195)=(7d0*(360d0*v(3700)+120d0*v(4863)+30d0*v(4913)+6d0*v(5029)+v(5128))+v(7522)*(v(3601)*v(469)+v(3532)*v(470)+v&
&(390)*v(5079)+v(391)*v(5095)+v(388)*v(5128)+v(3566)*v(8078)))/5040d0
v(5194)=(7d0*(360d0*v(3699)+120d0*v(4862)+30d0*v(4912)+6d0*v(5028)+v(5127))+v(7522)*(v(3600)*v(469)+v(3530)*v(470)+v&
&(390)*v(5078)+v(391)*v(5094)+v(388)*v(5127)+v(3565)*v(8078)))/5040d0
v(5193)=(7d0*(360d0*v(3698)+120d0*v(4861)+30d0*v(4911)+6d0*v(5027)+v(5126))+v(7522)*(v(3599)*v(469)+v(3529)*v(470)+v&
&(390)*v(5077)+v(391)*v(5093)+v(388)*v(5126)+v(3564)*v(8078)))/5040d0
v(5192)=(7d0*(360d0*v(3697)+120d0*v(4860)+30d0*v(4910)+6d0*v(5026)+v(5125))+v(7522)*(v(3598)*v(469)+v(3528)*v(470)+v&
&(390)*v(5076)+v(391)*v(5092)+v(388)*v(5125)+v(3563)*v(8078)))/5040d0
v(5191)=(7d0*(360d0*v(3696)+120d0*v(4859)+30d0*v(4909)+6d0*v(5025)+v(5124))+v(7522)*(v(3597)*v(469)+v(3527)*v(470)+v&
&(390)*v(5075)+v(391)*v(5091)+v(388)*v(5124)+v(3562)*v(8078)))/5040d0
v(5190)=(7d0*(360d0*v(3695)+120d0*v(4858)+30d0*v(4908)+6d0*v(5024)+v(5123))+v(7522)*(v(3596)*v(469)+v(3526)*v(470)+v&
&(390)*v(5074)+v(391)*v(5090)+v(388)*v(5123)+v(3561)*v(8078)))/5040d0
v(5189)=(7d0*(360d0*v(3694)+120d0*v(4857)+30d0*v(4907)+6d0*v(5023)+v(5122))+v(7522)*(v(3595)*v(469)+v(3525)*v(470)+v&
&(390)*v(5073)+v(391)*v(5089)+v(388)*v(5122)+v(3560)*v(8078)))/5040d0
v(5188)=v(3693)/2d0+v(4856)/6d0+v(4906)/24d0+v(5022)/120d0+v(5121)/720d0+v(8069)+((v(3559)*v(466)+v(3594)*v(469)+v(3524&
&)*v(470)+v(390)*v(5072)+v(391)*v(5088)+v(388)*v(5121))*v(7522)+v(7518)*(v(390)*v(466)+v(8082)))/5040d0
v(5171)=(v(3575)*v(470)+v(390)*v(5138))*v(7522)
v(5187)=(2520d0*v(4822)+840d0*v(4905)+210d0*v(4988)+42d0*v(5071)+7d0*v(5087)+v(5120)+v(5171)+v(7522)*(v(386)*v(5087)+v&
&(3523)*v(8078)))/5040d0
v(5170)=(v(3574)*v(470)+v(390)*v(5137))*v(7522)
v(5186)=(2520d0*v(4821)+840d0*v(4904)+210d0*v(4987)+42d0*v(5070)+7d0*v(5086)+v(5119)+v(5170)+v(7522)*(v(386)*v(5086)+v&
&(3522)*v(8078)))/5040d0
v(5169)=(v(3573)*v(470)+v(390)*v(5136))*v(7522)
v(5185)=(2520d0*v(4820)+840d0*v(4903)+210d0*v(4986)+42d0*v(5069)+7d0*v(5085)+v(5118)+v(5169)+v(7522)*(v(386)*v(5085)+v&
&(3521)*v(8078)))/5040d0
v(5168)=(v(3572)*v(470)+v(390)*v(5135))*v(7522)
v(5184)=(2520d0*v(4819)+840d0*v(4902)+210d0*v(4985)+42d0*v(5068)+7d0*v(5084)+v(5117)+v(5168)+v(7522)*(v(386)*v(5084)+v&
&(3520)*v(8078)))/5040d0
v(5167)=(v(3571)*v(470)+v(390)*v(5134))*v(7522)
v(5183)=(2520d0*v(4818)+840d0*v(4901)+210d0*v(4984)+42d0*v(5067)+7d0*v(5083)+v(5116)+v(5167)+v(7522)*(v(386)*v(5083)+v&
&(3519)*v(8078)))/5040d0
v(5165)=v(470)*v(5433)
v(5166)=v(5165)+v(5133)*v(8029)
v(5182)=(2520d0*v(4817)+840d0*v(4900)+210d0*v(4983)+42d0*v(5066)+7d0*v(5082)+v(5115)+v(5166)+v(7522)*(v(386)*v(5082)+v&
&(3518)*v(8078)))/5040d0
v(5164)=v(5434)+v(5132)*v(8029)
v(5181)=(2520d0*v(4816)+840d0*v(4899)+210d0*v(4982)+42d0*v(5065)+7d0*v(5081)+v(5114)+v(5164)+v(7522)*(v(386)*v(5081)+v&
&(3517)*v(8078)))/5040d0
v(5163)=(v(3568)*v(470)+v(390)*v(5129))*v(7522)
v(5180)=(2520d0*v(4815)+840d0*v(4898)+210d0*v(4981)+42d0*v(5064)+7d0*v(5080)+v(5113)+v(5163)+v(7522)*(v(386)*v(5080)+v&
&(3516)*v(8078)))/5040d0
v(5162)=(v(3566)*v(470)+v(390)*v(5128))*v(7522)
v(5179)=(2520d0*v(4814)+840d0*v(4897)+210d0*v(4980)+42d0*v(5063)+7d0*v(5079)+v(5112)+v(5162)+v(7522)*(v(386)*v(5079)+v&
&(3515)*v(8078)))/5040d0
v(5161)=(v(3565)*v(470)+v(390)*v(5127))*v(7522)
v(5178)=(2520d0*v(4813)+840d0*v(4896)+210d0*v(4979)+42d0*v(5062)+7d0*v(5078)+v(5111)+v(5161)+v(7522)*(v(386)*v(5078)+v&
&(3514)*v(8078)))/5040d0
v(5160)=(v(3564)*v(470)+v(390)*v(5126))*v(7522)
v(5177)=(2520d0*v(4812)+840d0*v(4895)+210d0*v(4978)+42d0*v(5061)+7d0*v(5077)+v(5110)+v(5160)+v(7522)*(v(386)*v(5077)+v&
&(3512)*v(8078)))/5040d0
v(5159)=(v(3563)*v(470)+v(390)*v(5125))*v(7522)
v(5176)=(2520d0*v(4811)+840d0*v(4894)+210d0*v(4977)+42d0*v(5060)+7d0*v(5076)+v(5109)+v(5159)+v(7522)*(v(386)*v(5076)+v&
&(3511)*v(8078)))/5040d0
v(5158)=(v(3562)*v(470)+v(390)*v(5124))*v(7522)
v(5175)=(2520d0*v(4810)+840d0*v(4893)+210d0*v(4976)+42d0*v(5059)+7d0*v(5075)+v(5108)+v(5158)+v(7522)*(v(386)*v(5075)+v&
&(3510)*v(8078)))/5040d0
v(5157)=(v(3561)*v(470)+v(390)*v(5123))*v(7522)
v(5174)=(2520d0*v(4809)+840d0*v(4892)+210d0*v(4975)+42d0*v(5058)+7d0*v(5074)+v(5107)+v(5157)+v(7522)*(v(386)*v(5074)+v&
&(3509)*v(8078)))/5040d0
v(5156)=(v(3560)*v(470)+v(390)*v(5122))*v(7522)
v(5173)=(2520d0*v(4808)+840d0*v(4891)+210d0*v(4974)+42d0*v(5057)+7d0*v(5073)+v(5106)+v(5156)+v(7522)*(v(386)*v(5073)+v&
&(3508)*v(8078)))/5040d0
v(5155)=v(5121)*v(8029)+v(470)*v(8069)
v(5172)=(2520d0*v(4806)+840d0*v(4890)+210d0*v(4973)+42d0*v(5056)+7d0*v(5072)+v(5105)+v(5155)+v(386)*(v(5072)*v(7522)+v&
&(7518)*v(8078))+v(8078)*v(8079))/5040d0
v(5154)=(7d0*(360d0*v(3746)+120d0*v(4839)+30d0*v(4956)+6d0*v(5005)+v(5104))+(5040d0*v(3642)+v(3642)*v(466)+v(3558)*v&
&(469)+v(3609)*v(470)+v(392)*v(5087)+v(389)*v(5104)+v(391)*v(5138))*v(7522))/5040d0
v(5670)=statev(26)*v(5187)+statev(24)*v(5206)+v(5154)*v(7511)
v(5622)=statev(28)*v(5154)+statev(23)*v(5187)+v(5206)*v(7510)
v(5222)=statev(25)*v(5154)+statev(27)*v(5206)+v(5187)*v(7509)
v(5153)=(7d0*(360d0*v(3745)+120d0*v(4838)+30d0*v(4955)+6d0*v(5004)+v(5103))+(5040d0*v(3641)+v(3641)*v(466)+v(3557)*v&
&(469)+v(3608)*v(470)+v(392)*v(5086)+v(389)*v(5103)+v(391)*v(5137))*v(7522))/5040d0
v(5669)=statev(26)*v(5186)+statev(24)*v(5205)+v(5153)*v(7511)
v(5621)=statev(28)*v(5153)+statev(23)*v(5186)+v(5205)*v(7510)
v(5221)=statev(25)*v(5153)+statev(27)*v(5205)+v(5186)*v(7509)
v(5152)=(7d0*(360d0*v(3744)+120d0*v(4837)+30d0*v(4954)+6d0*v(5003)+v(5102))+(5040d0*v(3640)+v(3640)*v(466)+v(3556)*v&
&(469)+v(3607)*v(470)+v(392)*v(5085)+v(389)*v(5102)+v(391)*v(5136))*v(7522))/5040d0
v(5668)=statev(26)*v(5185)+statev(24)*v(5204)+v(5152)*v(7511)
v(5620)=statev(28)*v(5152)+statev(23)*v(5185)+v(5204)*v(7510)
v(5220)=statev(25)*v(5152)+statev(27)*v(5204)+v(5185)*v(7509)
v(5151)=(7d0*(360d0*v(3743)+120d0*v(4836)+30d0*v(4953)+6d0*v(5002)+v(5101))+(5040d0*v(3639)+v(3639)*v(466)+v(3555)*v&
&(469)+v(3606)*v(470)+v(392)*v(5084)+v(389)*v(5101)+v(391)*v(5135))*v(7522))/5040d0
v(5667)=statev(26)*v(5184)+statev(24)*v(5203)+v(5151)*v(7511)
v(5619)=statev(28)*v(5151)+statev(23)*v(5184)+v(5203)*v(7510)
v(5219)=statev(25)*v(5151)+statev(27)*v(5203)+v(5184)*v(7509)
v(5150)=(7d0*(360d0*v(3742)+120d0*v(4835)+30d0*v(4952)+6d0*v(5001)+v(5100))+(5040d0*v(3638)+v(3638)*v(466)+v(3554)*v&
&(469)+v(3605)*v(470)+v(392)*v(5083)+v(389)*v(5100)+v(391)*v(5134))*v(7522))/5040d0
v(5666)=statev(26)*v(5183)+statev(24)*v(5202)+v(5150)*v(7511)
v(5618)=statev(28)*v(5150)+statev(23)*v(5183)+v(5202)*v(7510)
v(5218)=statev(25)*v(5150)+statev(27)*v(5202)+v(5183)*v(7509)
v(5149)=((v(3602)*v(466)+v(3553)*v(469)+v(3604)*v(470)+v(392)*v(5082)+v(389)*v(5099)+v(391)*v(5133))*v(7522)+7d0*&
&(360d0*v(3741)+120d0*v(4834)+30d0*v(4951)+6d0*v(5000)+v(5099)+v(8092)))/5040d0
v(5665)=statev(26)*v(5182)+statev(24)*v(5201)+v(5149)*v(7511)
v(5617)=statev(28)*v(5149)+statev(23)*v(5182)+v(5201)*v(7510)
v(5217)=statev(25)*v(5149)+statev(27)*v(5201)+v(5182)*v(7509)
v(5148)=(2520d0*v(3739)+840d0*v(4833)+210d0*v(4950)+42d0*v(4999)+7d0*v(5098)+v(5438)+v(7522)*(v(3552)*v(469)+v(392)*v&
&(5081)+v(389)*v(5098)+v(391)*v(5132)+v(3637)*v(8078)))/5040d0
v(5664)=statev(26)*v(5181)+statev(24)*v(5200)+v(5148)*v(7511)
v(5616)=statev(28)*v(5148)+statev(23)*v(5181)+v(5200)*v(7510)
v(5216)=statev(25)*v(5148)+statev(27)*v(5200)+v(5181)*v(7509)
v(5147)=(2520d0*v(3736)+840d0*v(4832)+210d0*v(4949)+42d0*v(4998)+7d0*v(5097)+v(5165)+(v(3551)*v(469)+v(392)*v(5080)+v&
&(389)*v(5097)+v(391)*v(5129))*v(7522)+v(8080))/5040d0
v(5663)=statev(26)*v(5180)+statev(24)*v(5196)+v(5147)*v(7511)
v(5615)=statev(28)*v(5147)+statev(23)*v(5180)+v(5196)*v(7510)
v(5215)=statev(25)*v(5147)+statev(27)*v(5196)+v(5180)*v(7509)
v(5146)=(7d0*(360d0*v(3734)+120d0*v(4830)+30d0*v(4946)+6d0*v(4996)+v(5095))+(5040d0*v(3635)+v(3635)*v(466)+v(3550)*v&
&(469)+v(3601)*v(470)+v(392)*v(5079)+v(389)*v(5095)+v(391)*v(5128))*v(7522))/5040d0
v(5662)=statev(26)*v(5179)+statev(24)*v(5195)+v(5146)*v(7511)
v(5614)=statev(28)*v(5146)+statev(23)*v(5179)+v(5195)*v(7510)
v(5214)=statev(25)*v(5146)+statev(27)*v(5195)+v(5179)*v(7509)
v(5145)=(7d0*(360d0*v(3733)+120d0*v(4829)+30d0*v(4945)+6d0*v(4995)+v(5094))+(5040d0*v(3634)+v(3634)*v(466)+v(3548)*v&
&(469)+v(3600)*v(470)+v(392)*v(5078)+v(389)*v(5094)+v(391)*v(5127))*v(7522))/5040d0
v(5661)=statev(26)*v(5178)+statev(24)*v(5194)+v(5145)*v(7511)
v(5613)=statev(28)*v(5145)+statev(23)*v(5178)+v(5194)*v(7510)
v(5213)=statev(25)*v(5145)+statev(27)*v(5194)+v(5178)*v(7509)
v(5144)=(7d0*(360d0*v(3732)+120d0*v(4828)+30d0*v(4944)+6d0*v(4994)+v(5093))+(5040d0*v(3633)+v(3633)*v(466)+v(3546)*v&
&(469)+v(3599)*v(470)+v(392)*v(5077)+v(389)*v(5093)+v(391)*v(5126))*v(7522))/5040d0
v(5660)=statev(26)*v(5177)+statev(24)*v(5193)+v(5144)*v(7511)
v(5612)=statev(28)*v(5144)+statev(23)*v(5177)+v(5193)*v(7510)
v(5212)=statev(25)*v(5144)+statev(27)*v(5193)+v(5177)*v(7509)
v(5143)=(7d0*(360d0*v(3731)+120d0*v(4827)+30d0*v(4943)+6d0*v(4993)+v(5092))+(5040d0*v(3632)+v(3632)*v(466)+v(3545)*v&
&(469)+v(3598)*v(470)+v(392)*v(5076)+v(389)*v(5092)+v(391)*v(5125))*v(7522))/5040d0
v(5659)=statev(26)*v(5176)+statev(24)*v(5192)+v(5143)*v(7511)
v(5611)=statev(28)*v(5143)+statev(23)*v(5176)+v(5192)*v(7510)
v(5211)=statev(25)*v(5143)+statev(27)*v(5192)+v(5176)*v(7509)
v(5142)=(7d0*(360d0*v(3730)+120d0*v(4826)+30d0*v(4942)+6d0*v(4992)+v(5091))+(5040d0*v(3631)+v(3631)*v(466)+v(3544)*v&
&(469)+v(3597)*v(470)+v(392)*v(5075)+v(389)*v(5091)+v(391)*v(5124))*v(7522))/5040d0
v(5658)=statev(26)*v(5175)+statev(24)*v(5191)+v(5142)*v(7511)
v(5610)=statev(28)*v(5142)+statev(23)*v(5175)+v(5191)*v(7510)
v(5210)=statev(25)*v(5142)+statev(27)*v(5191)+v(5175)*v(7509)
v(5141)=(7d0*(360d0*v(3729)+120d0*v(4825)+30d0*v(4941)+6d0*v(4991)+v(5090))+(5040d0*v(3630)+v(3630)*v(466)+v(3543)*v&
&(469)+v(3596)*v(470)+v(392)*v(5074)+v(389)*v(5090)+v(391)*v(5123))*v(7522))/5040d0
v(5657)=statev(26)*v(5174)+statev(24)*v(5190)+v(5141)*v(7511)
v(5609)=statev(28)*v(5141)+statev(23)*v(5174)+v(5190)*v(7510)
v(5209)=statev(25)*v(5141)+statev(27)*v(5190)+v(5174)*v(7509)
v(5140)=(7d0*(360d0*v(3728)+120d0*v(4824)+30d0*v(4940)+6d0*v(4990)+v(5089))+(5040d0*v(3629)+v(3629)*v(466)+v(3542)*v&
&(469)+v(3595)*v(470)+v(392)*v(5073)+v(389)*v(5089)+v(391)*v(5122))*v(7522))/5040d0
v(5656)=statev(26)*v(5173)+statev(24)*v(5189)+v(5140)*v(7511)
v(5608)=statev(28)*v(5140)+statev(23)*v(5173)+v(5189)*v(7510)
v(5208)=statev(25)*v(5140)+statev(27)*v(5189)+v(5173)*v(7509)
v(5139)=v(3727)/2d0+v(4823)/6d0+v(4939)/24d0+v(4989)/120d0+v(5088)/720d0+v(8067)+((v(3628)*v(466)+v(3541)*v(469)+v(3594&
&)*v(470)+v(392)*v(5072)+v(389)*v(5088)+v(391)*v(5121))*v(7522)+v(7518)*(v(392)*v(466)+v(8081)))/5040d0
v(5655)=statev(26)*v(5172)+statev(24)*v(5188)+v(5139)*v(7511)
v(5607)=statev(28)*v(5139)+statev(23)*v(5172)+v(5188)*v(7510)
v(5207)=statev(25)*v(5139)+statev(27)*v(5188)+v(5172)*v(7509)
v(508)=(7d0*(360d0*v(458)+120d0*v(462)+30d0*v(464)+6d0*v(468)+v(469))+v(7522)*(v(392)*v(8078)+v(8081)))/5040d0
v(488)=v(470)*v(8029)
v(8094)=5040d0+v(488)
v(510)=(2520d0*v(456)+840d0*v(457)+210d0*v(460)+42d0*v(463)+7d0*v(466)+v(505)+v(8070)*v(8078)+v(8094))/5040d0
v(472)=(7d0*(360d0*v(459)+120d0*v(461)+30d0*v(465)+6d0*v(467)+v(470))+v(7522)*(v(390)*v(8078)+v(8082)))/5040d0
v(471)=statev(27)*v(472)+statev(25)*v(508)+v(510)*v(7509)
v(474)=v(473)+v(490)+v(232)*v(5223)
v(8083)=v(392)*v(459)+v(391)*v(474)+v(389)*v(478)
v(5290)=v(3692)+v(3726)+(v(3540)*v(474)+v(388)*v(5240))*v(7522)
v(5289)=v(3691)+v(3725)+(v(3539)*v(474)+v(388)*v(5239))*v(7522)
v(5288)=v(3690)+v(3724)+(v(3538)*v(474)+v(388)*v(5238))*v(7522)
v(5287)=v(3689)+v(3723)+(v(3537)*v(474)+v(388)*v(5237))*v(7522)
v(5286)=v(3688)+v(3722)+(v(3536)*v(474)+v(388)*v(5236))*v(7522)
v(5285)=v(3687)+v(3721)+(v(3535)*v(474)+v(388)*v(5235))*v(7522)
v(5284)=v(3686)+v(3720)+(v(3534)*v(474)+v(388)*v(5234))*v(7522)
v(5283)=v(3685)+v(3719)+(v(3533)*v(474)+v(388)*v(5233))*v(7522)
v(5282)=v(3684)+v(3718)+(v(3532)*v(474)+v(388)*v(5232))*v(7522)
v(5281)=v(3683)+v(3717)+(v(3530)*v(474)+v(388)*v(5231))*v(7522)
v(5280)=v(3682)+v(3716)+(v(3529)*v(474)+v(388)*v(5230))*v(7522)
v(5279)=v(3681)+v(3715)+(v(3528)*v(474)+v(388)*v(5229))*v(7522)
v(5278)=v(3680)+v(3714)+(v(3527)*v(474)+v(388)*v(5228))*v(7522)
v(5277)=v(3679)+v(3713)+(v(3526)*v(474)+v(388)*v(5227))*v(7522)
v(5276)=v(3678)+v(3712)+(v(3525)*v(474)+v(388)*v(5226))*v(7522)
v(5275)=v(3677)+v(3711)+v(5224)*v(8085)+v(474)*v(8086)
v(5258)=(v(3676)*v(389)+v(3710)*v(392)+v(3642)*v(459)+v(3609)*v(474)+v(3558)*v(478)+v(391)*v(5240))*v(7522)
v(5257)=(v(3675)*v(389)+v(3709)*v(392)+v(3641)*v(459)+v(3608)*v(474)+v(3557)*v(478)+v(391)*v(5239))*v(7522)
v(5256)=(v(3674)*v(389)+v(3708)*v(392)+v(3640)*v(459)+v(3607)*v(474)+v(3556)*v(478)+v(391)*v(5238))*v(7522)
v(5255)=(v(3673)*v(389)+v(3707)*v(392)+v(3639)*v(459)+v(3606)*v(474)+v(3555)*v(478)+v(391)*v(5237))*v(7522)
v(5254)=(v(3672)*v(389)+v(3706)*v(392)+v(3638)*v(459)+v(3605)*v(474)+v(3554)*v(478)+v(391)*v(5236))*v(7522)
v(5253)=v(5252)+(v(3671)*v(389)+v(3705)*v(392)+v(3604)*v(474)+v(3553)*v(478)+v(391)*v(5235))*v(7522)
v(5251)=(v(3670)*v(389)+v(3703)*v(392)+v(3637)*v(459)+v(3602)*v(474)+v(3552)*v(478)+v(391)*v(5234))*v(7522)
v(5250)=v(5249)+(v(3669)*v(389)+v(3702)*v(392)+v(3570)*v(474)+v(3551)*v(478)+v(391)*v(5233))*v(7522)
v(5248)=(v(3668)*v(389)+v(3700)*v(392)+v(3635)*v(459)+v(3601)*v(474)+v(3550)*v(478)+v(391)*v(5232))*v(7522)
v(5247)=(v(3667)*v(389)+v(3699)*v(392)+v(3634)*v(459)+v(3600)*v(474)+v(3548)*v(478)+v(391)*v(5231))*v(7522)
v(5246)=(v(3666)*v(389)+v(3698)*v(392)+v(3633)*v(459)+v(3599)*v(474)+v(3546)*v(478)+v(391)*v(5230))*v(7522)
v(5245)=(v(3665)*v(389)+v(3697)*v(392)+v(3632)*v(459)+v(3598)*v(474)+v(3545)*v(478)+v(391)*v(5229))*v(7522)
v(5244)=(v(3664)*v(389)+v(3696)*v(392)+v(3631)*v(459)+v(3597)*v(474)+v(3544)*v(478)+v(391)*v(5228))*v(7522)
v(5243)=(v(3663)*v(389)+v(3695)*v(392)+v(3630)*v(459)+v(3596)*v(474)+v(3543)*v(478)+v(391)*v(5227))*v(7522)
v(5242)=(v(3662)*v(389)+v(3694)*v(392)+v(3629)*v(459)+v(3595)*v(474)+v(3542)*v(478)+v(391)*v(5226))*v(7522)
v(5241)=(v(3661)*v(389)+v(3693)*v(392)+v(3628)*v(459)+v(3594)*v(474)+v(3541)*v(478)+v(391)*v(5224))*v(7522)+v(7518)*v&
&(8083)
v(480)=v(7522)*v(8083)
v(5274)=(v(3609)*v(480)+v(391)*v(5258))*v(7522)
v(5273)=(v(3608)*v(480)+v(391)*v(5257))*v(7522)
v(5272)=(v(3607)*v(480)+v(391)*v(5256))*v(7522)
v(5271)=(v(3606)*v(480)+v(391)*v(5255))*v(7522)
v(5270)=(v(3605)*v(480)+v(391)*v(5254))*v(7522)
v(5269)=(v(3604)*v(480)+v(391)*v(5253))*v(7522)
v(5268)=(v(3602)*v(480)+v(391)*v(5251))*v(7522)
v(5267)=(v(3570)*v(480)+v(391)*v(5250))*v(7522)
v(5266)=(v(3601)*v(480)+v(391)*v(5248))*v(7522)
v(5265)=(v(3600)*v(480)+v(391)*v(5247))*v(7522)
v(5264)=(v(3599)*v(480)+v(391)*v(5246))*v(7522)
v(5263)=(v(3598)*v(480)+v(391)*v(5245))*v(7522)
v(5262)=(v(3597)*v(480)+v(391)*v(5244))*v(7522)
v(5261)=(v(3596)*v(480)+v(391)*v(5243))*v(7522)
v(5260)=(v(3595)*v(480)+v(391)*v(5242))*v(7522)
v(5259)=v(5241)*v(8027)+v(480)*v(8084)
v(496)=v(480)*v(8027)
v(476)=v(475)+v(494)+v(474)*v(8085)
v(8087)=v(392)*v(461)+v(391)*v(476)+v(389)*v(480)
v(5340)=v(4889)+v(5274)+(v(3540)*v(476)+v(388)*v(5290))*v(7522)
v(5339)=v(4888)+v(5273)+(v(3539)*v(476)+v(388)*v(5289))*v(7522)
v(5338)=v(4887)+v(5272)+(v(3538)*v(476)+v(388)*v(5288))*v(7522)
v(5337)=v(4886)+v(5271)+(v(3537)*v(476)+v(388)*v(5287))*v(7522)
v(5336)=v(4885)+v(5270)+(v(3536)*v(476)+v(388)*v(5286))*v(7522)
v(5335)=v(4884)+v(5269)+(v(3535)*v(476)+v(388)*v(5285))*v(7522)
v(5334)=v(4883)+v(5268)+(v(3534)*v(476)+v(388)*v(5284))*v(7522)
v(5333)=v(4882)+v(5267)+(v(3533)*v(476)+v(388)*v(5283))*v(7522)
v(5332)=v(4881)+v(5266)+(v(3532)*v(476)+v(388)*v(5282))*v(7522)
v(5331)=v(4880)+v(5265)+(v(3530)*v(476)+v(388)*v(5281))*v(7522)
v(5330)=v(4879)+v(5264)+(v(3529)*v(476)+v(388)*v(5280))*v(7522)
v(5329)=v(4878)+v(5263)+(v(3528)*v(476)+v(388)*v(5279))*v(7522)
v(5328)=v(4877)+v(5262)+(v(3527)*v(476)+v(388)*v(5278))*v(7522)
v(5327)=v(4876)+v(5261)+(v(3526)*v(476)+v(388)*v(5277))*v(7522)
v(5326)=v(4875)+v(5260)+(v(3525)*v(476)+v(388)*v(5276))*v(7522)
v(5325)=v(4874)+v(5259)+v(5275)*v(8085)+v(476)*v(8086)
v(5308)=(v(3642)*v(461)+v(3609)*v(476)+v(3558)*v(480)+v(392)*v(4873)+v(389)*v(5258)+v(391)*v(5290))*v(7522)
v(5307)=(v(3641)*v(461)+v(3608)*v(476)+v(3557)*v(480)+v(392)*v(4872)+v(389)*v(5257)+v(391)*v(5289))*v(7522)
v(5306)=(v(3640)*v(461)+v(3607)*v(476)+v(3556)*v(480)+v(392)*v(4871)+v(389)*v(5256)+v(391)*v(5288))*v(7522)
v(5305)=(v(3639)*v(461)+v(3606)*v(476)+v(3555)*v(480)+v(392)*v(4870)+v(389)*v(5255)+v(391)*v(5287))*v(7522)
v(5304)=(v(3638)*v(461)+v(3605)*v(476)+v(3554)*v(480)+v(392)*v(4869)+v(389)*v(5254)+v(391)*v(5286))*v(7522)
v(5303)=v(5302)+(v(3604)*v(476)+v(3553)*v(480)+v(392)*v(4868)+v(389)*v(5253)+v(391)*v(5285))*v(7522)
v(5301)=(v(3637)*v(461)+v(3602)*v(476)+v(3552)*v(480)+v(392)*v(4867)+v(389)*v(5251)+v(391)*v(5284))*v(7522)
v(5300)=v(5299)+(v(3570)*v(476)+v(3551)*v(480)+v(392)*v(4864)+v(389)*v(5250)+v(391)*v(5283))*v(7522)
v(5298)=(v(3635)*v(461)+v(3601)*v(476)+v(3550)*v(480)+v(392)*v(4863)+v(389)*v(5248)+v(391)*v(5282))*v(7522)
v(5297)=(v(3634)*v(461)+v(3600)*v(476)+v(3548)*v(480)+v(392)*v(4862)+v(389)*v(5247)+v(391)*v(5281))*v(7522)
v(5296)=(v(3633)*v(461)+v(3599)*v(476)+v(3546)*v(480)+v(392)*v(4861)+v(389)*v(5246)+v(391)*v(5280))*v(7522)
v(5295)=(v(3632)*v(461)+v(3598)*v(476)+v(3545)*v(480)+v(392)*v(4860)+v(389)*v(5245)+v(391)*v(5279))*v(7522)
v(5294)=(v(3631)*v(461)+v(3597)*v(476)+v(3544)*v(480)+v(392)*v(4859)+v(389)*v(5244)+v(391)*v(5278))*v(7522)
v(5293)=(v(3630)*v(461)+v(3596)*v(476)+v(3543)*v(480)+v(392)*v(4858)+v(389)*v(5243)+v(391)*v(5277))*v(7522)
v(5292)=(v(3629)*v(461)+v(3595)*v(476)+v(3542)*v(480)+v(392)*v(4857)+v(389)*v(5242)+v(391)*v(5276))*v(7522)
v(5291)=(v(3628)*v(461)+v(3594)*v(476)+v(3541)*v(480)+v(392)*v(4856)+v(389)*v(5241)+v(391)*v(5275))*v(7522)+v(7518)*v&
&(8087)
v(484)=v(7522)*v(8087)
v(5324)=(v(3609)*v(484)+v(391)*v(5308))*v(7522)
v(5323)=(v(3608)*v(484)+v(391)*v(5307))*v(7522)
v(5322)=(v(3607)*v(484)+v(391)*v(5306))*v(7522)
v(5321)=(v(3606)*v(484)+v(391)*v(5305))*v(7522)
v(5320)=(v(3605)*v(484)+v(391)*v(5304))*v(7522)
v(5319)=(v(3604)*v(484)+v(391)*v(5303))*v(7522)
v(5318)=(v(3602)*v(484)+v(391)*v(5301))*v(7522)
v(5317)=(v(3570)*v(484)+v(391)*v(5300))*v(7522)
v(5316)=(v(3601)*v(484)+v(391)*v(5298))*v(7522)
v(5315)=(v(3600)*v(484)+v(391)*v(5297))*v(7522)
v(5314)=(v(3599)*v(484)+v(391)*v(5296))*v(7522)
v(5313)=(v(3598)*v(484)+v(391)*v(5295))*v(7522)
v(5312)=(v(3597)*v(484)+v(391)*v(5294))*v(7522)
v(5311)=(v(3596)*v(484)+v(391)*v(5293))*v(7522)
v(5310)=(v(3595)*v(484)+v(391)*v(5292))*v(7522)
v(5309)=v(5291)*v(8027)+v(484)*v(8084)
v(500)=v(484)*v(8027)
v(479)=v(477)+v(496)+v(476)*v(8085)
v(8088)=v(392)*v(465)+v(391)*v(479)+v(389)*v(484)
v(5390)=v(4938)+v(5324)+(v(3540)*v(479)+v(388)*v(5340))*v(7522)
v(5389)=v(4937)+v(5323)+(v(3539)*v(479)+v(388)*v(5339))*v(7522)
v(5388)=v(4936)+v(5322)+(v(3538)*v(479)+v(388)*v(5338))*v(7522)
v(5387)=v(4935)+v(5321)+(v(3537)*v(479)+v(388)*v(5337))*v(7522)
v(5386)=v(4934)+v(5320)+(v(3536)*v(479)+v(388)*v(5336))*v(7522)
v(5385)=v(4933)+v(5319)+(v(3535)*v(479)+v(388)*v(5335))*v(7522)
v(5384)=v(4932)+v(5318)+(v(3534)*v(479)+v(388)*v(5334))*v(7522)
v(5383)=v(4931)+v(5317)+(v(3533)*v(479)+v(388)*v(5333))*v(7522)
v(5382)=v(4930)+v(5316)+(v(3532)*v(479)+v(388)*v(5332))*v(7522)
v(5381)=v(4929)+v(5315)+(v(3530)*v(479)+v(388)*v(5331))*v(7522)
v(5380)=v(4928)+v(5314)+(v(3529)*v(479)+v(388)*v(5330))*v(7522)
v(5379)=v(4927)+v(5313)+(v(3528)*v(479)+v(388)*v(5329))*v(7522)
v(5378)=v(4926)+v(5312)+(v(3527)*v(479)+v(388)*v(5328))*v(7522)
v(5377)=v(4925)+v(5311)+(v(3526)*v(479)+v(388)*v(5327))*v(7522)
v(5376)=v(4924)+v(5310)+(v(3525)*v(479)+v(388)*v(5326))*v(7522)
v(5375)=v(4923)+v(5309)+v(5325)*v(8085)+v(479)*v(8086)
v(5358)=(v(3642)*v(465)+v(3609)*v(479)+v(3558)*v(484)+v(392)*v(4922)+v(389)*v(5308)+v(391)*v(5340))*v(7522)
v(5357)=(v(3641)*v(465)+v(3608)*v(479)+v(3557)*v(484)+v(392)*v(4921)+v(389)*v(5307)+v(391)*v(5339))*v(7522)
v(5356)=(v(3640)*v(465)+v(3607)*v(479)+v(3556)*v(484)+v(392)*v(4920)+v(389)*v(5306)+v(391)*v(5338))*v(7522)
v(5355)=(v(3639)*v(465)+v(3606)*v(479)+v(3555)*v(484)+v(392)*v(4919)+v(389)*v(5305)+v(391)*v(5337))*v(7522)
v(5354)=(v(3638)*v(465)+v(3605)*v(479)+v(3554)*v(484)+v(392)*v(4918)+v(389)*v(5304)+v(391)*v(5336))*v(7522)
v(5353)=v(5352)+(v(3604)*v(479)+v(3553)*v(484)+v(392)*v(4917)+v(389)*v(5303)+v(391)*v(5335))*v(7522)
v(5351)=(v(3637)*v(465)+v(3602)*v(479)+v(3552)*v(484)+v(392)*v(4916)+v(389)*v(5301)+v(391)*v(5334))*v(7522)
v(5350)=v(5349)+(v(3570)*v(479)+v(3551)*v(484)+v(392)*v(4914)+v(389)*v(5300)+v(391)*v(5333))*v(7522)
v(5348)=(v(3635)*v(465)+v(3601)*v(479)+v(3550)*v(484)+v(392)*v(4913)+v(389)*v(5298)+v(391)*v(5332))*v(7522)
v(5347)=(v(3634)*v(465)+v(3600)*v(479)+v(3548)*v(484)+v(392)*v(4912)+v(389)*v(5297)+v(391)*v(5331))*v(7522)
v(5346)=(v(3633)*v(465)+v(3599)*v(479)+v(3546)*v(484)+v(392)*v(4911)+v(389)*v(5296)+v(391)*v(5330))*v(7522)
v(5345)=(v(3632)*v(465)+v(3598)*v(479)+v(3545)*v(484)+v(392)*v(4910)+v(389)*v(5295)+v(391)*v(5329))*v(7522)
v(5344)=(v(3631)*v(465)+v(3597)*v(479)+v(3544)*v(484)+v(392)*v(4909)+v(389)*v(5294)+v(391)*v(5328))*v(7522)
v(5343)=(v(3630)*v(465)+v(3596)*v(479)+v(3543)*v(484)+v(392)*v(4908)+v(389)*v(5293)+v(391)*v(5327))*v(7522)
v(5342)=(v(3629)*v(465)+v(3595)*v(479)+v(3542)*v(484)+v(392)*v(4907)+v(389)*v(5292)+v(391)*v(5326))*v(7522)
v(5341)=(v(3628)*v(465)+v(3594)*v(479)+v(3541)*v(484)+v(392)*v(4906)+v(389)*v(5291)+v(391)*v(5325))*v(7522)+v(7518)*v&
&(8088)
v(486)=v(7522)*v(8088)
v(5374)=(v(3609)*v(486)+v(391)*v(5358))*v(7522)
v(5373)=(v(3608)*v(486)+v(391)*v(5357))*v(7522)
v(5372)=(v(3607)*v(486)+v(391)*v(5356))*v(7522)
v(5371)=(v(3606)*v(486)+v(391)*v(5355))*v(7522)
v(5370)=(v(3605)*v(486)+v(391)*v(5354))*v(7522)
v(5369)=(v(3604)*v(486)+v(391)*v(5353))*v(7522)
v(5368)=(v(3602)*v(486)+v(391)*v(5351))*v(7522)
v(5367)=(v(3570)*v(486)+v(391)*v(5350))*v(7522)
v(5366)=(v(3601)*v(486)+v(391)*v(5348))*v(7522)
v(5365)=(v(3600)*v(486)+v(391)*v(5347))*v(7522)
v(5364)=(v(3599)*v(486)+v(391)*v(5346))*v(7522)
v(5363)=(v(3598)*v(486)+v(391)*v(5345))*v(7522)
v(5362)=(v(3597)*v(486)+v(391)*v(5344))*v(7522)
v(5361)=(v(3596)*v(486)+v(391)*v(5343))*v(7522)
v(5360)=(v(3595)*v(486)+v(391)*v(5342))*v(7522)
v(5359)=v(5341)*v(8027)+v(486)*v(8084)
v(502)=v(486)*v(8027)
v(482)=v(481)+v(500)+v(479)*v(8085)
v(8089)=v(392)*v(467)+v(391)*v(482)+v(389)*v(486)
v(5424)=(v(3642)*v(467)+v(3609)*v(482)+v(3558)*v(486)+v(392)*v(5039)+v(389)*v(5358)+v(391)*v(5390))*v(7522)
v(5423)=(v(3641)*v(467)+v(3608)*v(482)+v(3557)*v(486)+v(392)*v(5038)+v(389)*v(5357)+v(391)*v(5389))*v(7522)
v(5422)=(v(3640)*v(467)+v(3607)*v(482)+v(3556)*v(486)+v(392)*v(5037)+v(389)*v(5356)+v(391)*v(5388))*v(7522)
v(5421)=(v(3639)*v(467)+v(3606)*v(482)+v(3555)*v(486)+v(392)*v(5036)+v(389)*v(5355)+v(391)*v(5387))*v(7522)
v(5420)=(v(3638)*v(467)+v(3605)*v(482)+v(3554)*v(486)+v(392)*v(5035)+v(389)*v(5354)+v(391)*v(5386))*v(7522)
v(5419)=v(5418)+(v(3604)*v(482)+v(3553)*v(486)+v(392)*v(5034)+v(389)*v(5353)+v(391)*v(5385))*v(7522)
v(5417)=(v(3637)*v(467)+v(3602)*v(482)+v(3552)*v(486)+v(392)*v(5033)+v(389)*v(5351)+v(391)*v(5384))*v(7522)
v(5416)=v(5415)+(v(3570)*v(482)+v(3551)*v(486)+v(392)*v(5030)+v(389)*v(5350)+v(391)*v(5383))*v(7522)
v(5414)=(v(3635)*v(467)+v(3601)*v(482)+v(3550)*v(486)+v(392)*v(5029)+v(389)*v(5348)+v(391)*v(5382))*v(7522)
v(5413)=(v(3634)*v(467)+v(3600)*v(482)+v(3548)*v(486)+v(392)*v(5028)+v(389)*v(5347)+v(391)*v(5381))*v(7522)
v(5412)=(v(3633)*v(467)+v(3599)*v(482)+v(3546)*v(486)+v(392)*v(5027)+v(389)*v(5346)+v(391)*v(5380))*v(7522)
v(5411)=(v(3632)*v(467)+v(3598)*v(482)+v(3545)*v(486)+v(392)*v(5026)+v(389)*v(5345)+v(391)*v(5379))*v(7522)
v(5410)=(v(3631)*v(467)+v(3597)*v(482)+v(3544)*v(486)+v(392)*v(5025)+v(389)*v(5344)+v(391)*v(5378))*v(7522)
v(5409)=(v(3630)*v(467)+v(3596)*v(482)+v(3543)*v(486)+v(392)*v(5024)+v(389)*v(5343)+v(391)*v(5377))*v(7522)
v(5408)=(v(3629)*v(467)+v(3595)*v(482)+v(3542)*v(486)+v(392)*v(5023)+v(389)*v(5342)+v(391)*v(5376))*v(7522)
v(5407)=(v(3628)*v(467)+v(3594)*v(482)+v(3541)*v(486)+v(392)*v(5022)+v(389)*v(5341)+v(391)*v(5375))*v(7522)+v(7518)*v&
&(8089)
v(5406)=v(5055)+v(5374)+(v(3540)*v(482)+v(388)*v(5390))*v(7522)
v(5405)=v(5054)+v(5373)+(v(3539)*v(482)+v(388)*v(5389))*v(7522)
v(5404)=v(5053)+v(5372)+(v(3538)*v(482)+v(388)*v(5388))*v(7522)
v(5403)=v(5052)+v(5371)+(v(3537)*v(482)+v(388)*v(5387))*v(7522)
v(5402)=v(5051)+v(5370)+(v(3536)*v(482)+v(388)*v(5386))*v(7522)
v(5401)=v(5050)+v(5369)+(v(3535)*v(482)+v(388)*v(5385))*v(7522)
v(5400)=v(5049)+v(5368)+(v(3534)*v(482)+v(388)*v(5384))*v(7522)
v(5399)=v(5048)+v(5367)+(v(3533)*v(482)+v(388)*v(5383))*v(7522)
v(5398)=v(5047)+v(5366)+(v(3532)*v(482)+v(388)*v(5382))*v(7522)
v(5397)=v(5046)+v(5365)+(v(3530)*v(482)+v(388)*v(5381))*v(7522)
v(5396)=v(5045)+v(5364)+(v(3529)*v(482)+v(388)*v(5380))*v(7522)
v(5395)=v(5044)+v(5363)+(v(3528)*v(482)+v(388)*v(5379))*v(7522)
v(5394)=v(5043)+v(5362)+(v(3527)*v(482)+v(388)*v(5378))*v(7522)
v(5393)=v(5042)+v(5361)+(v(3526)*v(482)+v(388)*v(5377))*v(7522)
v(5392)=v(5041)+v(5360)+(v(3525)*v(482)+v(388)*v(5376))*v(7522)
v(5391)=v(5040)+v(5359)+v(5375)*v(8085)+v(482)*v(8086)
v(485)=v(483)+v(502)+v(482)*v(8085)
v(8090)=5040d0+v(485)
v(487)=v(7522)*v(8089)
v(8093)=v(392)*v(470)+v(389)*v(487)
v(5460)=(v(3609)*v(487)+v(391)*v(5424))*v(7522)
v(5476)=(v(5171)+2520d0*v(5240)+840d0*v(5290)+210d0*v(5340)+42d0*v(5390)+7d0*v(5406)+v(5460)+v(7522)*(v(388)*v(5406)+v&
&(3540)*v(8090)))/5040d0
v(5459)=(v(3608)*v(487)+v(391)*v(5423))*v(7522)
v(5475)=(v(5170)+2520d0*v(5239)+840d0*v(5289)+210d0*v(5339)+42d0*v(5389)+7d0*v(5405)+v(5459)+v(7522)*(v(388)*v(5405)+v&
&(3539)*v(8090)))/5040d0
v(5458)=(v(3607)*v(487)+v(391)*v(5422))*v(7522)
v(5474)=(v(5169)+2520d0*v(5238)+840d0*v(5288)+210d0*v(5338)+42d0*v(5388)+7d0*v(5404)+v(5458)+v(7522)*(v(388)*v(5404)+v&
&(3538)*v(8090)))/5040d0
v(5457)=(v(3606)*v(487)+v(391)*v(5421))*v(7522)
v(5473)=(v(5168)+2520d0*v(5237)+840d0*v(5287)+210d0*v(5337)+42d0*v(5387)+7d0*v(5403)+v(5457)+v(7522)*(v(388)*v(5403)+v&
&(3537)*v(8090)))/5040d0
v(5456)=(v(3605)*v(487)+v(391)*v(5420))*v(7522)
v(5472)=(v(5167)+2520d0*v(5236)+840d0*v(5286)+210d0*v(5336)+42d0*v(5386)+7d0*v(5402)+v(5456)+v(7522)*(v(388)*v(5402)+v&
&(3536)*v(8090)))/5040d0
v(5455)=(v(3604)*v(487)+v(391)*v(5419))*v(7522)
v(5471)=(v(5166)+2520d0*v(5235)+840d0*v(5285)+210d0*v(5335)+42d0*v(5385)+7d0*v(5401)+v(5455)+v(7522)*(v(388)*v(5401)+v&
&(3535)*v(8090)))/5040d0
v(5454)=(v(3602)*v(487)+v(391)*v(5417))*v(7522)
v(5470)=(v(5164)+2520d0*v(5234)+840d0*v(5284)+210d0*v(5334)+42d0*v(5384)+7d0*v(5400)+v(5454)+v(7522)*(v(388)*v(5400)+v&
&(3534)*v(8090)))/5040d0
v(5453)=(v(3570)*v(487)+v(391)*v(5416))*v(7522)
v(5469)=(v(5163)+2520d0*v(5233)+840d0*v(5283)+210d0*v(5333)+42d0*v(5383)+7d0*v(5399)+v(5453)+v(7522)*(v(388)*v(5399)+v&
&(3533)*v(8090)))/5040d0
v(5452)=(v(3601)*v(487)+v(391)*v(5414))*v(7522)
v(5468)=(v(5162)+2520d0*v(5232)+840d0*v(5282)+210d0*v(5332)+42d0*v(5382)+7d0*v(5398)+v(5452)+v(7522)*(v(388)*v(5398)+v&
&(3532)*v(8090)))/5040d0
v(5451)=(v(3600)*v(487)+v(391)*v(5413))*v(7522)
v(5467)=(v(5161)+2520d0*v(5231)+840d0*v(5281)+210d0*v(5331)+42d0*v(5381)+7d0*v(5397)+v(5451)+v(7522)*(v(388)*v(5397)+v&
&(3530)*v(8090)))/5040d0
v(5450)=(v(3599)*v(487)+v(391)*v(5412))*v(7522)
v(5466)=(v(5160)+2520d0*v(5230)+840d0*v(5280)+210d0*v(5330)+42d0*v(5380)+7d0*v(5396)+v(5450)+v(7522)*(v(388)*v(5396)+v&
&(3529)*v(8090)))/5040d0
v(5449)=(v(3598)*v(487)+v(391)*v(5411))*v(7522)
v(5465)=(v(5159)+2520d0*v(5229)+840d0*v(5279)+210d0*v(5329)+42d0*v(5379)+7d0*v(5395)+v(5449)+v(7522)*(v(388)*v(5395)+v&
&(3528)*v(8090)))/5040d0
v(5448)=(v(3597)*v(487)+v(391)*v(5410))*v(7522)
v(5464)=(v(5158)+2520d0*v(5228)+840d0*v(5278)+210d0*v(5328)+42d0*v(5378)+7d0*v(5394)+v(5448)+v(7522)*(v(388)*v(5394)+v&
&(3527)*v(8090)))/5040d0
v(5447)=(v(3596)*v(487)+v(391)*v(5409))*v(7522)
v(5463)=(v(5157)+2520d0*v(5227)+840d0*v(5277)+210d0*v(5327)+42d0*v(5377)+7d0*v(5393)+v(5447)+v(7522)*(v(388)*v(5393)+v&
&(3526)*v(8090)))/5040d0
v(5446)=(v(3595)*v(487)+v(391)*v(5408))*v(7522)
v(5462)=(v(5156)+2520d0*v(5226)+840d0*v(5276)+210d0*v(5326)+42d0*v(5376)+7d0*v(5392)+v(5446)+v(7522)*(v(388)*v(5392)+v&
&(3525)*v(8090)))/5040d0
v(5445)=v(5407)*v(8027)+v(487)*v(8084)
v(5461)=(v(5155)+2520d0*v(5224)+840d0*v(5275)+210d0*v(5325)+42d0*v(5375)+7d0*v(5391)+v(5445)+v(388)*(v(5391)*v(7522)+v&
&(7518)*v(8090))+v(8090)*v(8091))/5040d0
v(5444)=(7d0*(360d0*v(3676)+120d0*v(5258)+30d0*v(5308)+6d0*v(5358)+v(5424))+v(7522)*(v(3642)*v(470)+v(3558)*v(487)+v&
&(392)*v(5138)+v(391)*v(5406)+v(389)*v(5424)+v(3609)*v(8090)))/5040d0
v(5718)=statev(25)*v(5444)+statev(27)*v(5476)+v(5206)*v(7509)
v(5638)=statev(26)*v(5206)+statev(24)*v(5476)+v(5444)*v(7511)
v(5492)=statev(23)*v(5206)+statev(28)*v(5444)+v(5476)*v(7510)
v(5443)=(7d0*(360d0*v(3675)+120d0*v(5257)+30d0*v(5307)+6d0*v(5357)+v(5423))+v(7522)*(v(3641)*v(470)+v(3557)*v(487)+v&
&(392)*v(5137)+v(391)*v(5405)+v(389)*v(5423)+v(3608)*v(8090)))/5040d0
v(5717)=statev(25)*v(5443)+statev(27)*v(5475)+v(5205)*v(7509)
v(5637)=statev(26)*v(5205)+statev(24)*v(5475)+v(5443)*v(7511)
v(5491)=statev(23)*v(5205)+statev(28)*v(5443)+v(5475)*v(7510)
v(5442)=(7d0*(360d0*v(3674)+120d0*v(5256)+30d0*v(5306)+6d0*v(5356)+v(5422))+v(7522)*(v(3640)*v(470)+v(3556)*v(487)+v&
&(392)*v(5136)+v(391)*v(5404)+v(389)*v(5422)+v(3607)*v(8090)))/5040d0
v(5716)=statev(25)*v(5442)+statev(27)*v(5474)+v(5204)*v(7509)
v(5636)=statev(26)*v(5204)+statev(24)*v(5474)+v(5442)*v(7511)
v(5490)=statev(23)*v(5204)+statev(28)*v(5442)+v(5474)*v(7510)
v(5441)=(7d0*(360d0*v(3673)+120d0*v(5255)+30d0*v(5305)+6d0*v(5355)+v(5421))+v(7522)*(v(3639)*v(470)+v(3555)*v(487)+v&
&(392)*v(5135)+v(391)*v(5403)+v(389)*v(5421)+v(3606)*v(8090)))/5040d0
v(5715)=statev(25)*v(5441)+statev(27)*v(5473)+v(5203)*v(7509)
v(5635)=statev(26)*v(5203)+statev(24)*v(5473)+v(5441)*v(7511)
v(5489)=statev(23)*v(5203)+statev(28)*v(5441)+v(5473)*v(7510)
v(5440)=(7d0*(360d0*v(3672)+120d0*v(5254)+30d0*v(5304)+6d0*v(5354)+v(5420))+v(7522)*(v(3638)*v(470)+v(3554)*v(487)+v&
&(392)*v(5134)+v(391)*v(5402)+v(389)*v(5420)+v(3605)*v(8090)))/5040d0
v(5714)=statev(25)*v(5440)+statev(27)*v(5472)+v(5202)*v(7509)
v(5634)=statev(26)*v(5202)+statev(24)*v(5472)+v(5440)*v(7511)
v(5488)=statev(23)*v(5202)+statev(28)*v(5440)+v(5472)*v(7510)
v(5439)=(2520d0*v(3671)+840d0*v(5253)+210d0*v(5303)+42d0*v(5353)+7d0*v(5419)+v(5438)+v(7522)*(v(3553)*v(487)+v(392)*v&
&(5133)+v(391)*v(5401)+v(389)*v(5419)+v(3604)*v(8090)))/5040d0
v(5713)=statev(25)*v(5439)+statev(27)*v(5471)+v(5201)*v(7509)
v(5633)=statev(26)*v(5201)+statev(24)*v(5471)+v(5439)*v(7511)
v(5487)=statev(23)*v(5201)+statev(28)*v(5439)+v(5471)*v(7510)
v(5437)=((v(3637)*v(470)+v(3602)*v(485)+v(3552)*v(487)+v(392)*v(5132)+v(391)*v(5400)+v(389)*v(5417))*v(7522)+7d0*&
&(360d0*v(3670)+120d0*v(5251)+30d0*v(5301)+6d0*v(5351)+v(5417)+v(8092)))/5040d0
v(5712)=statev(25)*v(5437)+statev(27)*v(5470)+v(5200)*v(7509)
v(5632)=statev(26)*v(5200)+statev(24)*v(5470)+v(5437)*v(7511)
v(5486)=statev(23)*v(5200)+statev(28)*v(5437)+v(5470)*v(7510)
v(5435)=(2520d0*v(3669)+840d0*v(5250)+210d0*v(5300)+42d0*v(5350)+7d0*v(5416)+5040d0*v(5433)+v(5434)+(v(3570)*v(485)+v&
&(3551)*v(487)+v(392)*v(5129)+v(391)*v(5399)+v(389)*v(5416))*v(7522))/5040d0
v(5711)=statev(25)*v(5435)+statev(27)*v(5469)+v(5196)*v(7509)
v(5631)=statev(26)*v(5196)+statev(24)*v(5469)+v(5435)*v(7511)
v(5485)=statev(23)*v(5196)+statev(28)*v(5435)+v(5469)*v(7510)
v(5432)=(7d0*(360d0*v(3668)+120d0*v(5248)+30d0*v(5298)+6d0*v(5348)+v(5414))+v(7522)*(v(3635)*v(470)+v(3550)*v(487)+v&
&(392)*v(5128)+v(391)*v(5398)+v(389)*v(5414)+v(3601)*v(8090)))/5040d0
v(5710)=statev(25)*v(5432)+statev(27)*v(5468)+v(5195)*v(7509)
v(5630)=statev(26)*v(5195)+statev(24)*v(5468)+v(5432)*v(7511)
v(5484)=statev(23)*v(5195)+statev(28)*v(5432)+v(5468)*v(7510)
v(5431)=(7d0*(360d0*v(3667)+120d0*v(5247)+30d0*v(5297)+6d0*v(5347)+v(5413))+v(7522)*(v(3634)*v(470)+v(3548)*v(487)+v&
&(392)*v(5127)+v(391)*v(5397)+v(389)*v(5413)+v(3600)*v(8090)))/5040d0
v(5709)=statev(25)*v(5431)+statev(27)*v(5467)+v(5194)*v(7509)
v(5629)=statev(26)*v(5194)+statev(24)*v(5467)+v(5431)*v(7511)
v(5483)=statev(23)*v(5194)+statev(28)*v(5431)+v(5467)*v(7510)
v(5430)=(7d0*(360d0*v(3666)+120d0*v(5246)+30d0*v(5296)+6d0*v(5346)+v(5412))+v(7522)*(v(3633)*v(470)+v(3546)*v(487)+v&
&(392)*v(5126)+v(391)*v(5396)+v(389)*v(5412)+v(3599)*v(8090)))/5040d0
v(5708)=statev(25)*v(5430)+statev(27)*v(5466)+v(5193)*v(7509)
v(5628)=statev(26)*v(5193)+statev(24)*v(5466)+v(5430)*v(7511)
v(5482)=statev(23)*v(5193)+statev(28)*v(5430)+v(5466)*v(7510)
v(5429)=(7d0*(360d0*v(3665)+120d0*v(5245)+30d0*v(5295)+6d0*v(5345)+v(5411))+v(7522)*(v(3632)*v(470)+v(3545)*v(487)+v&
&(392)*v(5125)+v(391)*v(5395)+v(389)*v(5411)+v(3598)*v(8090)))/5040d0
v(5707)=statev(25)*v(5429)+statev(27)*v(5465)+v(5192)*v(7509)
v(5627)=statev(26)*v(5192)+statev(24)*v(5465)+v(5429)*v(7511)
v(5481)=statev(23)*v(5192)+statev(28)*v(5429)+v(5465)*v(7510)
v(5428)=(7d0*(360d0*v(3664)+120d0*v(5244)+30d0*v(5294)+6d0*v(5344)+v(5410))+v(7522)*(v(3631)*v(470)+v(3544)*v(487)+v&
&(392)*v(5124)+v(391)*v(5394)+v(389)*v(5410)+v(3597)*v(8090)))/5040d0
v(5706)=statev(25)*v(5428)+statev(27)*v(5464)+v(5191)*v(7509)
v(5626)=statev(26)*v(5191)+statev(24)*v(5464)+v(5428)*v(7511)
v(5480)=statev(23)*v(5191)+statev(28)*v(5428)+v(5464)*v(7510)
v(5427)=(7d0*(360d0*v(3663)+120d0*v(5243)+30d0*v(5293)+6d0*v(5343)+v(5409))+v(7522)*(v(3630)*v(470)+v(3543)*v(487)+v&
&(392)*v(5123)+v(391)*v(5393)+v(389)*v(5409)+v(3596)*v(8090)))/5040d0
v(5705)=statev(25)*v(5427)+statev(27)*v(5463)+v(5190)*v(7509)
v(5625)=statev(26)*v(5190)+statev(24)*v(5463)+v(5427)*v(7511)
v(5479)=statev(23)*v(5190)+statev(28)*v(5427)+v(5463)*v(7510)
v(5426)=(7d0*(360d0*v(3662)+120d0*v(5242)+30d0*v(5292)+6d0*v(5342)+v(5408))+v(7522)*(v(3629)*v(470)+v(3542)*v(487)+v&
&(392)*v(5122)+v(391)*v(5392)+v(389)*v(5408)+v(3595)*v(8090)))/5040d0
v(5704)=statev(25)*v(5426)+statev(27)*v(5462)+v(5189)*v(7509)
v(5624)=statev(26)*v(5189)+statev(24)*v(5462)+v(5426)*v(7511)
v(5478)=statev(23)*v(5189)+statev(28)*v(5426)+v(5462)*v(7510)
v(5425)=v(3661)/2d0+v(5241)/6d0+v(5291)/24d0+v(5341)/120d0+v(5407)/720d0+v(8084)+((v(3628)*v(470)+v(3594)*v(485)+v(3541&
&)*v(487)+v(392)*v(5121)+v(391)*v(5391)+v(389)*v(5407))*v(7522)+v(7518)*(v(391)*v(485)+v(8093)))/5040d0
v(5703)=statev(25)*v(5425)+statev(27)*v(5461)+v(5188)*v(7509)
v(5623)=statev(26)*v(5188)+statev(24)*v(5461)+v(5425)*v(7511)
v(5477)=statev(23)*v(5188)+statev(28)*v(5425)+v(5461)*v(7510)
v(507)=(7d0*(360d0*v(478)+120d0*v(480)+30d0*v(484)+6d0*v(486)+v(487))+v(7522)*(v(391)*v(8090)+v(8093)))/5040d0
v(506)=v(487)*v(8027)
v(512)=(2520d0*v(474)+840d0*v(476)+210d0*v(479)+42d0*v(482)+7d0*v(485)+v(506)+v(8085)*v(8090)+v(8094))/5040d0
v(489)=statev(23)*v(472)+statev(28)*v(507)+v(512)*v(7510)
v(492)=v(490)+v(491)+v(232)*v(5493)
v(5526)=v(3692)+v(3762)+(v(3558)*v(492)+v(389)*v(5510))*v(7522)
v(5525)=v(3691)+v(3761)+(v(3557)*v(492)+v(389)*v(5509))*v(7522)
v(5524)=v(3690)+v(3760)+(v(3556)*v(492)+v(389)*v(5508))*v(7522)
v(5523)=v(3689)+v(3759)+(v(3555)*v(492)+v(389)*v(5507))*v(7522)
v(5522)=v(3688)+v(3758)+(v(3554)*v(492)+v(389)*v(5506))*v(7522)
v(5521)=v(3687)+v(3757)+(v(3553)*v(492)+v(389)*v(5505))*v(7522)
v(5520)=v(3686)+v(3756)+(v(3552)*v(492)+v(389)*v(5504))*v(7522)
v(5519)=v(3685)+v(3755)+(v(3551)*v(492)+v(389)*v(5503))*v(7522)
v(5518)=v(3684)+v(3754)+(v(3550)*v(492)+v(389)*v(5502))*v(7522)
v(5517)=v(3683)+v(3753)+(v(3548)*v(492)+v(389)*v(5501))*v(7522)
v(5516)=v(3682)+v(3752)+(v(3546)*v(492)+v(389)*v(5500))*v(7522)
v(5515)=v(3681)+v(3751)+(v(3545)*v(492)+v(389)*v(5499))*v(7522)
v(5514)=v(3680)+v(3750)+(v(3544)*v(492)+v(389)*v(5498))*v(7522)
v(5513)=v(3679)+v(3749)+(v(3543)*v(492)+v(389)*v(5497))*v(7522)
v(5512)=v(3678)+v(3748)+(v(3542)*v(492)+v(389)*v(5496))*v(7522)
v(5511)=v(3677)+v(3747)+v(5494)*v(8095)+v(492)*v(8096)
v(495)=v(493)+v(494)+v(492)*v(8095)
v(5542)=v(4855)+v(5274)+(v(3558)*v(495)+v(389)*v(5526))*v(7522)
v(5541)=v(4854)+v(5273)+(v(3557)*v(495)+v(389)*v(5525))*v(7522)
v(5540)=v(4853)+v(5272)+(v(3556)*v(495)+v(389)*v(5524))*v(7522)
v(5539)=v(4852)+v(5271)+(v(3555)*v(495)+v(389)*v(5523))*v(7522)
v(5538)=v(4851)+v(5270)+(v(3554)*v(495)+v(389)*v(5522))*v(7522)
v(5537)=v(4850)+v(5269)+(v(3553)*v(495)+v(389)*v(5521))*v(7522)
v(5536)=v(4849)+v(5268)+(v(3552)*v(495)+v(389)*v(5520))*v(7522)
v(5535)=v(4848)+v(5267)+(v(3551)*v(495)+v(389)*v(5519))*v(7522)
v(5534)=v(4847)+v(5266)+(v(3550)*v(495)+v(389)*v(5518))*v(7522)
v(5533)=v(4846)+v(5265)+(v(3548)*v(495)+v(389)*v(5517))*v(7522)
v(5532)=v(4845)+v(5264)+(v(3546)*v(495)+v(389)*v(5516))*v(7522)
v(5531)=v(4844)+v(5263)+(v(3545)*v(495)+v(389)*v(5515))*v(7522)
v(5530)=v(4843)+v(5262)+(v(3544)*v(495)+v(389)*v(5514))*v(7522)
v(5529)=v(4842)+v(5261)+(v(3543)*v(495)+v(389)*v(5513))*v(7522)
v(5528)=v(4841)+v(5260)+(v(3542)*v(495)+v(389)*v(5512))*v(7522)
v(5527)=v(4840)+v(5259)+v(5511)*v(8095)+v(495)*v(8096)
v(498)=v(496)+v(497)+v(495)*v(8095)
v(5558)=v(4972)+v(5324)+(v(3558)*v(498)+v(389)*v(5542))*v(7522)
v(5557)=v(4971)+v(5323)+(v(3557)*v(498)+v(389)*v(5541))*v(7522)
v(5556)=v(4970)+v(5322)+(v(3556)*v(498)+v(389)*v(5540))*v(7522)
v(5555)=v(4969)+v(5321)+(v(3555)*v(498)+v(389)*v(5539))*v(7522)
v(5554)=v(4968)+v(5320)+(v(3554)*v(498)+v(389)*v(5538))*v(7522)
v(5553)=v(4967)+v(5319)+(v(3553)*v(498)+v(389)*v(5537))*v(7522)
v(5552)=v(4966)+v(5318)+(v(3552)*v(498)+v(389)*v(5536))*v(7522)
v(5551)=v(4965)+v(5317)+(v(3551)*v(498)+v(389)*v(5535))*v(7522)
v(5550)=v(4964)+v(5316)+(v(3550)*v(498)+v(389)*v(5534))*v(7522)
v(5549)=v(4963)+v(5315)+(v(3548)*v(498)+v(389)*v(5533))*v(7522)
v(5548)=v(4962)+v(5314)+(v(3546)*v(498)+v(389)*v(5532))*v(7522)
v(5547)=v(4961)+v(5313)+(v(3545)*v(498)+v(389)*v(5531))*v(7522)
v(5546)=v(4960)+v(5312)+(v(3544)*v(498)+v(389)*v(5530))*v(7522)
v(5545)=v(4959)+v(5311)+(v(3543)*v(498)+v(389)*v(5529))*v(7522)
v(5544)=v(4958)+v(5310)+(v(3542)*v(498)+v(389)*v(5528))*v(7522)
v(5543)=v(4957)+v(5309)+v(5527)*v(8095)+v(498)*v(8096)
v(501)=v(499)+v(500)+v(498)*v(8095)
v(5574)=v(5021)+v(5374)+(v(3558)*v(501)+v(389)*v(5558))*v(7522)
v(5573)=v(5020)+v(5373)+(v(3557)*v(501)+v(389)*v(5557))*v(7522)
v(5572)=v(5019)+v(5372)+(v(3556)*v(501)+v(389)*v(5556))*v(7522)
v(5571)=v(5018)+v(5371)+(v(3555)*v(501)+v(389)*v(5555))*v(7522)
v(5570)=v(5017)+v(5370)+(v(3554)*v(501)+v(389)*v(5554))*v(7522)
v(5569)=v(5016)+v(5369)+(v(3553)*v(501)+v(389)*v(5553))*v(7522)
v(5568)=v(5015)+v(5368)+(v(3552)*v(501)+v(389)*v(5552))*v(7522)
v(5567)=v(5014)+v(5367)+(v(3551)*v(501)+v(389)*v(5551))*v(7522)
v(5566)=v(5013)+v(5366)+(v(3550)*v(501)+v(389)*v(5550))*v(7522)
v(5565)=v(5012)+v(5365)+(v(3548)*v(501)+v(389)*v(5549))*v(7522)
v(5564)=v(5011)+v(5364)+(v(3546)*v(501)+v(389)*v(5548))*v(7522)
v(5563)=v(5010)+v(5363)+(v(3545)*v(501)+v(389)*v(5547))*v(7522)
v(5562)=v(5009)+v(5362)+(v(3544)*v(501)+v(389)*v(5546))*v(7522)
v(5561)=v(5008)+v(5361)+(v(3543)*v(501)+v(389)*v(5545))*v(7522)
v(5560)=v(5007)+v(5360)+(v(3542)*v(501)+v(389)*v(5544))*v(7522)
v(5559)=v(5006)+v(5359)+v(5543)*v(8095)+v(501)*v(8096)
v(504)=v(502)+v(503)+v(501)*v(8095)
v(8097)=5040d0+v(504)
v(5590)=(v(5120)+v(5460)+2520d0*v(5510)+840d0*v(5526)+210d0*v(5542)+42d0*v(5558)+7d0*v(5574)+v(7522)*(v(389)*v(5574)+v&
&(3558)*v(8097)))/5040d0
v(5782)=statev(23)*v(5154)+statev(28)*v(5590)+v(5444)*v(7510)
v(5654)=statev(27)*v(5444)+statev(25)*v(5590)+v(5154)*v(7509)
v(5606)=statev(26)*v(5154)+statev(24)*v(5444)+v(5590)*v(7511)
v(5589)=(v(5119)+v(5459)+2520d0*v(5509)+840d0*v(5525)+210d0*v(5541)+42d0*v(5557)+7d0*v(5573)+v(7522)*(v(389)*v(5573)+v&
&(3557)*v(8097)))/5040d0
v(5781)=statev(23)*v(5153)+statev(28)*v(5589)+v(5443)*v(7510)
v(5653)=statev(27)*v(5443)+statev(25)*v(5589)+v(5153)*v(7509)
v(5605)=statev(26)*v(5153)+statev(24)*v(5443)+v(5589)*v(7511)
v(5588)=(v(5118)+v(5458)+2520d0*v(5508)+840d0*v(5524)+210d0*v(5540)+42d0*v(5556)+7d0*v(5572)+v(7522)*(v(389)*v(5572)+v&
&(3556)*v(8097)))/5040d0
v(5780)=statev(23)*v(5152)+statev(28)*v(5588)+v(5442)*v(7510)
v(5652)=statev(27)*v(5442)+statev(25)*v(5588)+v(5152)*v(7509)
v(5604)=statev(26)*v(5152)+statev(24)*v(5442)+v(5588)*v(7511)
v(5587)=(v(5117)+v(5457)+2520d0*v(5507)+840d0*v(5523)+210d0*v(5539)+42d0*v(5555)+7d0*v(5571)+v(7522)*(v(389)*v(5571)+v&
&(3555)*v(8097)))/5040d0
v(5779)=statev(23)*v(5151)+statev(28)*v(5587)+v(5441)*v(7510)
v(5651)=statev(27)*v(5441)+statev(25)*v(5587)+v(5151)*v(7509)
v(5603)=statev(26)*v(5151)+statev(24)*v(5441)+v(5587)*v(7511)
v(5586)=(v(5116)+v(5456)+2520d0*v(5506)+840d0*v(5522)+210d0*v(5538)+42d0*v(5554)+7d0*v(5570)+v(7522)*(v(389)*v(5570)+v&
&(3554)*v(8097)))/5040d0
v(5778)=statev(23)*v(5150)+statev(28)*v(5586)+v(5440)*v(7510)
v(5650)=statev(27)*v(5440)+statev(25)*v(5586)+v(5150)*v(7509)
v(5602)=statev(26)*v(5150)+statev(24)*v(5440)+v(5586)*v(7511)
v(5585)=(v(5115)+v(5455)+2520d0*v(5505)+840d0*v(5521)+210d0*v(5537)+42d0*v(5553)+7d0*v(5569)+v(7522)*(v(389)*v(5569)+v&
&(3553)*v(8097)))/5040d0
v(5777)=statev(23)*v(5149)+statev(28)*v(5585)+v(5439)*v(7510)
v(5649)=statev(27)*v(5439)+statev(25)*v(5585)+v(5149)*v(7509)
v(5601)=statev(26)*v(5149)+statev(24)*v(5439)+v(5585)*v(7511)
v(5584)=(v(5114)+v(5454)+2520d0*v(5504)+840d0*v(5520)+210d0*v(5536)+42d0*v(5552)+7d0*v(5568)+v(7522)*(v(389)*v(5568)+v&
&(3552)*v(8097)))/5040d0
v(5776)=statev(23)*v(5148)+statev(28)*v(5584)+v(5437)*v(7510)
v(5648)=statev(27)*v(5437)+statev(25)*v(5584)+v(5148)*v(7509)
v(5600)=statev(26)*v(5148)+statev(24)*v(5437)+v(5584)*v(7511)
v(5583)=(v(5113)+v(5453)+2520d0*v(5503)+840d0*v(5519)+210d0*v(5535)+42d0*v(5551)+7d0*v(5567)+v(7522)*(v(389)*v(5567)+v&
&(3551)*v(8097)))/5040d0
v(5775)=statev(23)*v(5147)+statev(28)*v(5583)+v(5435)*v(7510)
v(5647)=statev(27)*v(5435)+statev(25)*v(5583)+v(5147)*v(7509)
v(5599)=statev(26)*v(5147)+statev(24)*v(5435)+v(5583)*v(7511)
v(5582)=(v(5112)+v(5452)+2520d0*v(5502)+840d0*v(5518)+210d0*v(5534)+42d0*v(5550)+7d0*v(5566)+v(7522)*(v(389)*v(5566)+v&
&(3550)*v(8097)))/5040d0
v(5774)=statev(23)*v(5146)+statev(28)*v(5582)+v(5432)*v(7510)
v(5646)=statev(27)*v(5432)+statev(25)*v(5582)+v(5146)*v(7509)
v(5598)=statev(26)*v(5146)+statev(24)*v(5432)+v(5582)*v(7511)
v(5581)=(v(5111)+v(5451)+2520d0*v(5501)+840d0*v(5517)+210d0*v(5533)+42d0*v(5549)+7d0*v(5565)+v(7522)*(v(389)*v(5565)+v&
&(3548)*v(8097)))/5040d0
v(5773)=statev(23)*v(5145)+statev(28)*v(5581)+v(5431)*v(7510)
v(5645)=statev(27)*v(5431)+statev(25)*v(5581)+v(5145)*v(7509)
v(5597)=statev(26)*v(5145)+statev(24)*v(5431)+v(5581)*v(7511)
v(5580)=(v(5110)+v(5450)+2520d0*v(5500)+840d0*v(5516)+210d0*v(5532)+42d0*v(5548)+7d0*v(5564)+v(7522)*(v(389)*v(5564)+v&
&(3546)*v(8097)))/5040d0
v(5772)=statev(23)*v(5144)+statev(28)*v(5580)+v(5430)*v(7510)
v(5644)=statev(27)*v(5430)+statev(25)*v(5580)+v(5144)*v(7509)
v(5596)=statev(26)*v(5144)+statev(24)*v(5430)+v(5580)*v(7511)
v(5579)=(v(5109)+v(5449)+2520d0*v(5499)+840d0*v(5515)+210d0*v(5531)+42d0*v(5547)+7d0*v(5563)+v(7522)*(v(389)*v(5563)+v&
&(3545)*v(8097)))/5040d0
v(5771)=statev(23)*v(5143)+statev(28)*v(5579)+v(5429)*v(7510)
v(5643)=statev(27)*v(5429)+statev(25)*v(5579)+v(5143)*v(7509)
v(5595)=statev(26)*v(5143)+statev(24)*v(5429)+v(5579)*v(7511)
v(5578)=(v(5108)+v(5448)+2520d0*v(5498)+840d0*v(5514)+210d0*v(5530)+42d0*v(5546)+7d0*v(5562)+v(7522)*(v(389)*v(5562)+v&
&(3544)*v(8097)))/5040d0
v(5770)=statev(23)*v(5142)+statev(28)*v(5578)+v(5428)*v(7510)
v(5642)=statev(27)*v(5428)+statev(25)*v(5578)+v(5142)*v(7509)
v(5594)=statev(26)*v(5142)+statev(24)*v(5428)+v(5578)*v(7511)
v(5577)=(v(5107)+v(5447)+2520d0*v(5497)+840d0*v(5513)+210d0*v(5529)+42d0*v(5545)+7d0*v(5561)+v(7522)*(v(389)*v(5561)+v&
&(3543)*v(8097)))/5040d0
v(5769)=statev(23)*v(5141)+statev(28)*v(5577)+v(5427)*v(7510)
v(5641)=statev(27)*v(5427)+statev(25)*v(5577)+v(5141)*v(7509)
v(5593)=statev(26)*v(5141)+statev(24)*v(5427)+v(5577)*v(7511)
v(5576)=(v(5106)+v(5446)+2520d0*v(5496)+840d0*v(5512)+210d0*v(5528)+42d0*v(5544)+7d0*v(5560)+v(7522)*(v(389)*v(5560)+v&
&(3542)*v(8097)))/5040d0
v(5768)=statev(23)*v(5140)+statev(28)*v(5576)+v(5426)*v(7510)
v(5640)=statev(27)*v(5426)+statev(25)*v(5576)+v(5140)*v(7509)
v(5592)=statev(26)*v(5140)+statev(24)*v(5426)+v(5576)*v(7511)
v(5575)=(v(5105)+v(5445)+2520d0*v(5494)+840d0*v(5511)+210d0*v(5527)+42d0*v(5543)+7d0*v(5559)+v(389)*(v(5559)*v(7522)+v&
&(7518)*v(8097))+v(8097)*v(8098))/5040d0
v(5767)=statev(23)*v(5139)+statev(28)*v(5575)+v(5425)*v(7510)
v(5639)=statev(27)*v(5425)+statev(25)*v(5575)+v(5139)*v(7509)
v(5591)=statev(26)*v(5139)+statev(24)*v(5425)+v(5575)*v(7511)
v(514)=(5040d0+2520d0*v(492)+840d0*v(495)+210d0*v(498)+42d0*v(501)+7d0*v(504)+v(505)+v(506)+v(8095)*v(8097))/5040d0
v(509)=statev(24)*v(507)+statev(26)*v(508)+v(514)*v(7511)
v(511)=statev(28)*v(508)+statev(23)*v(510)+v(472)*v(7510)
v(513)=statev(26)*v(472)+statev(24)*v(512)+v(507)*v(7511)
v(515)=statev(27)*v(507)+statev(25)*v(514)+v(508)*v(7509)
v(516)=statev(24)*v(472)+statev(26)*v(510)+v(508)*v(7511)
v(5702)=v(509)*v(5222)+v(471)*v(5606)-v(516)*v(5654)-v(515)*v(5670)
v(5701)=v(509)*v(5221)+v(471)*v(5605)-v(516)*v(5653)-v(515)*v(5669)
v(5700)=v(509)*v(5220)+v(471)*v(5604)-v(516)*v(5652)-v(515)*v(5668)
v(5699)=v(509)*v(5219)+v(471)*v(5603)-v(516)*v(5651)-v(515)*v(5667)
v(5698)=v(509)*v(5218)+v(471)*v(5602)-v(516)*v(5650)-v(515)*v(5666)
v(5697)=v(509)*v(5217)+v(471)*v(5601)-v(516)*v(5649)-v(515)*v(5665)
v(5696)=v(509)*v(5216)+v(471)*v(5600)-v(516)*v(5648)-v(515)*v(5664)
v(5695)=v(509)*v(5215)+v(471)*v(5599)-v(516)*v(5647)-v(515)*v(5663)
v(5694)=v(509)*v(5214)+v(471)*v(5598)-v(516)*v(5646)-v(515)*v(5662)
v(5693)=v(509)*v(5213)+v(471)*v(5597)-v(516)*v(5645)-v(515)*v(5661)
v(5692)=v(509)*v(5212)+v(471)*v(5596)-v(516)*v(5644)-v(515)*v(5660)
v(5691)=v(509)*v(5211)+v(471)*v(5595)-v(516)*v(5643)-v(515)*v(5659)
v(5690)=v(509)*v(5210)+v(471)*v(5594)-v(516)*v(5642)-v(515)*v(5658)
v(5689)=v(509)*v(5209)+v(471)*v(5593)-v(516)*v(5641)-v(515)*v(5657)
v(5688)=v(509)*v(5208)+v(471)*v(5592)-v(516)*v(5640)-v(515)*v(5656)
v(5687)=v(509)*v(5207)+v(471)*v(5591)-v(516)*v(5639)-v(515)*v(5655)
v(5686)=-(v(516)*v(5492))+v(513)*v(5622)+v(511)*v(5638)-v(489)*v(5670)
v(5685)=-(v(516)*v(5491))+v(513)*v(5621)+v(511)*v(5637)-v(489)*v(5669)
v(5684)=-(v(516)*v(5490))+v(513)*v(5620)+v(511)*v(5636)-v(489)*v(5668)
v(5683)=-(v(516)*v(5489))+v(513)*v(5619)+v(511)*v(5635)-v(489)*v(5667)
v(5682)=-(v(516)*v(5488))+v(513)*v(5618)+v(511)*v(5634)-v(489)*v(5666)
v(5681)=-(v(516)*v(5487))+v(513)*v(5617)+v(511)*v(5633)-v(489)*v(5665)
v(5680)=-(v(516)*v(5486))+v(513)*v(5616)+v(511)*v(5632)-v(489)*v(5664)
v(5679)=-(v(516)*v(5485))+v(513)*v(5615)+v(511)*v(5631)-v(489)*v(5663)
v(5678)=-(v(516)*v(5484))+v(513)*v(5614)+v(511)*v(5630)-v(489)*v(5662)
v(5677)=-(v(516)*v(5483))+v(513)*v(5613)+v(511)*v(5629)-v(489)*v(5661)
v(5676)=-(v(516)*v(5482))+v(513)*v(5612)+v(511)*v(5628)-v(489)*v(5660)
v(5675)=-(v(516)*v(5481))+v(513)*v(5611)+v(511)*v(5627)-v(489)*v(5659)
v(5674)=-(v(516)*v(5480))+v(513)*v(5610)+v(511)*v(5626)-v(489)*v(5658)
v(5673)=-(v(516)*v(5479))+v(513)*v(5609)+v(511)*v(5625)-v(489)*v(5657)
v(5672)=-(v(516)*v(5478))+v(513)*v(5608)+v(511)*v(5624)-v(489)*v(5656)
v(5671)=-(v(516)*v(5477))+v(513)*v(5607)+v(511)*v(5623)-v(489)*v(5655)
v(562)=v(511)*v(513)-v(489)*v(516)
v(6016)=(v(562)*v(562))
v(553)=v(471)*v(509)-v(515)*v(516)
v(6091)=(v(553)*v(553))
v(517)=statev(25)*v(507)+statev(27)*v(512)+v(472)*v(7509)
v(5766)=-(v(517)*v(5606))+v(515)*v(5638)+v(513)*v(5654)-v(509)*v(5718)
v(5765)=-(v(517)*v(5605))+v(515)*v(5637)+v(513)*v(5653)-v(509)*v(5717)
v(5764)=-(v(517)*v(5604))+v(515)*v(5636)+v(513)*v(5652)-v(509)*v(5716)
v(5763)=-(v(517)*v(5603))+v(515)*v(5635)+v(513)*v(5651)-v(509)*v(5715)
v(5762)=-(v(517)*v(5602))+v(515)*v(5634)+v(513)*v(5650)-v(509)*v(5714)
v(5761)=-(v(517)*v(5601))+v(515)*v(5633)+v(513)*v(5649)-v(509)*v(5713)
v(5760)=-(v(517)*v(5600))+v(515)*v(5632)+v(513)*v(5648)-v(509)*v(5712)
v(5759)=-(v(517)*v(5599))+v(515)*v(5631)+v(513)*v(5647)-v(509)*v(5711)
v(5758)=-(v(517)*v(5598))+v(515)*v(5630)+v(513)*v(5646)-v(509)*v(5710)
v(5757)=-(v(517)*v(5597))+v(515)*v(5629)+v(513)*v(5645)-v(509)*v(5709)
v(5756)=-(v(517)*v(5596))+v(515)*v(5628)+v(513)*v(5644)-v(509)*v(5708)
v(5755)=-(v(517)*v(5595))+v(515)*v(5627)+v(513)*v(5643)-v(509)*v(5707)
v(5754)=-(v(517)*v(5594))+v(515)*v(5626)+v(513)*v(5642)-v(509)*v(5706)
v(5753)=-(v(517)*v(5593))+v(515)*v(5625)+v(513)*v(5641)-v(509)*v(5705)
v(5752)=-(v(517)*v(5592))+v(515)*v(5624)+v(513)*v(5640)-v(509)*v(5704)
v(5751)=-(v(517)*v(5591))+v(515)*v(5623)+v(513)*v(5639)-v(509)*v(5703)
v(5750)=-(v(513)*v(5222))-v(471)*v(5638)+v(517)*v(5670)+v(516)*v(5718)
v(5749)=-(v(513)*v(5221))-v(471)*v(5637)+v(517)*v(5669)+v(516)*v(5717)
v(5748)=-(v(513)*v(5220))-v(471)*v(5636)+v(517)*v(5668)+v(516)*v(5716)
v(5747)=-(v(513)*v(5219))-v(471)*v(5635)+v(517)*v(5667)+v(516)*v(5715)
v(5746)=-(v(513)*v(5218))-v(471)*v(5634)+v(517)*v(5666)+v(516)*v(5714)
v(5745)=-(v(513)*v(5217))-v(471)*v(5633)+v(517)*v(5665)+v(516)*v(5713)
v(5744)=-(v(513)*v(5216))-v(471)*v(5632)+v(517)*v(5664)+v(516)*v(5712)
v(5743)=-(v(513)*v(5215))-v(471)*v(5631)+v(517)*v(5663)+v(516)*v(5711)
v(5742)=-(v(513)*v(5214))-v(471)*v(5630)+v(517)*v(5662)+v(516)*v(5710)
v(5741)=-(v(513)*v(5213))-v(471)*v(5629)+v(517)*v(5661)+v(516)*v(5709)
v(5740)=-(v(513)*v(5212))-v(471)*v(5628)+v(517)*v(5660)+v(516)*v(5708)
v(5739)=-(v(513)*v(5211))-v(471)*v(5627)+v(517)*v(5659)+v(516)*v(5707)
v(5738)=-(v(513)*v(5210))-v(471)*v(5626)+v(517)*v(5658)+v(516)*v(5706)
v(5737)=-(v(513)*v(5209))-v(471)*v(5625)+v(517)*v(5657)+v(516)*v(5705)
v(5736)=-(v(513)*v(5208))-v(471)*v(5624)+v(517)*v(5656)+v(516)*v(5704)
v(5735)=-(v(513)*v(5207))-v(471)*v(5623)+v(517)*v(5655)+v(516)*v(5703)
v(5734)=v(489)*v(5222)+v(471)*v(5492)-v(517)*v(5622)-v(511)*v(5718)
v(5733)=v(489)*v(5221)+v(471)*v(5491)-v(517)*v(5621)-v(511)*v(5717)
v(5732)=v(489)*v(5220)+v(471)*v(5490)-v(517)*v(5620)-v(511)*v(5716)
v(5731)=v(489)*v(5219)+v(471)*v(5489)-v(517)*v(5619)-v(511)*v(5715)
v(5730)=v(489)*v(5218)+v(471)*v(5488)-v(517)*v(5618)-v(511)*v(5714)
v(5729)=v(489)*v(5217)+v(471)*v(5487)-v(517)*v(5617)-v(511)*v(5713)
v(5728)=v(489)*v(5216)+v(471)*v(5486)-v(517)*v(5616)-v(511)*v(5712)
v(5727)=v(489)*v(5215)+v(471)*v(5485)-v(517)*v(5615)-v(511)*v(5711)
v(5726)=v(489)*v(5214)+v(471)*v(5484)-v(517)*v(5614)-v(511)*v(5710)
v(5725)=v(489)*v(5213)+v(471)*v(5483)-v(517)*v(5613)-v(511)*v(5709)
v(5724)=v(489)*v(5212)+v(471)*v(5482)-v(517)*v(5612)-v(511)*v(5708)
v(5723)=v(489)*v(5211)+v(471)*v(5481)-v(517)*v(5611)-v(511)*v(5707)
v(5722)=v(489)*v(5210)+v(471)*v(5480)-v(517)*v(5610)-v(511)*v(5706)
v(5721)=v(489)*v(5209)+v(471)*v(5479)-v(517)*v(5609)-v(511)*v(5705)
v(5720)=v(489)*v(5208)+v(471)*v(5478)-v(517)*v(5608)-v(511)*v(5704)
v(5719)=v(489)*v(5207)+v(471)*v(5477)-v(517)*v(5607)-v(511)*v(5703)
v(561)=v(471)*v(489)-v(511)*v(517)
v(6015)=(v(561)*v(561))
v(560)=-(v(471)*v(513))+v(516)*v(517)
v(6014)=(v(560)*v(560))
v(8109)=v(6014)+v(6015)+v(6016)
v(554)=v(513)*v(515)-v(509)*v(517)
v(6053)=(v(554)*v(554))
v(518)=statev(23)*v(508)+statev(28)*v(514)+v(507)*v(7510)
v(5996)=v(518)*v(560)+v(509)*v(561)+v(515)*v(562)
v(5998)=1d0/v(5996)**3
v(8099)=(-2d0)*v(5998)
v(6013)=(v(5606)*v(561)+v(562)*v(5654)+v(515)*v(5686)+v(509)*v(5734)+v(518)*v(5750)+v(560)*v(5782))*v(8099)
v(6012)=(v(5605)*v(561)+v(562)*v(5653)+v(515)*v(5685)+v(509)*v(5733)+v(518)*v(5749)+v(560)*v(5781))*v(8099)
v(6011)=(v(5604)*v(561)+v(562)*v(5652)+v(515)*v(5684)+v(509)*v(5732)+v(518)*v(5748)+v(560)*v(5780))*v(8099)
v(6010)=(v(5603)*v(561)+v(562)*v(5651)+v(515)*v(5683)+v(509)*v(5731)+v(518)*v(5747)+v(560)*v(5779))*v(8099)
v(6009)=(v(5602)*v(561)+v(562)*v(5650)+v(515)*v(5682)+v(509)*v(5730)+v(518)*v(5746)+v(560)*v(5778))*v(8099)
v(6008)=(v(5601)*v(561)+v(562)*v(5649)+v(515)*v(5681)+v(509)*v(5729)+v(518)*v(5745)+v(560)*v(5777))*v(8099)
v(6007)=(v(5600)*v(561)+v(562)*v(5648)+v(515)*v(5680)+v(509)*v(5728)+v(518)*v(5744)+v(560)*v(5776))*v(8099)
v(6006)=(v(5599)*v(561)+v(562)*v(5647)+v(515)*v(5679)+v(509)*v(5727)+v(518)*v(5743)+v(560)*v(5775))*v(8099)
v(6005)=(v(5598)*v(561)+v(562)*v(5646)+v(515)*v(5678)+v(509)*v(5726)+v(518)*v(5742)+v(560)*v(5774))*v(8099)
v(6004)=(v(5597)*v(561)+v(562)*v(5645)+v(515)*v(5677)+v(509)*v(5725)+v(518)*v(5741)+v(560)*v(5773))*v(8099)
v(6003)=(v(5596)*v(561)+v(562)*v(5644)+v(515)*v(5676)+v(509)*v(5724)+v(518)*v(5740)+v(560)*v(5772))*v(8099)
v(6002)=(v(5595)*v(561)+v(562)*v(5643)+v(515)*v(5675)+v(509)*v(5723)+v(518)*v(5739)+v(560)*v(5771))*v(8099)
v(6001)=(v(5594)*v(561)+v(562)*v(5642)+v(515)*v(5674)+v(509)*v(5722)+v(518)*v(5738)+v(560)*v(5770))*v(8099)
v(6000)=(v(5593)*v(561)+v(562)*v(5641)+v(515)*v(5673)+v(509)*v(5721)+v(518)*v(5737)+v(560)*v(5769))*v(8099)
v(5999)=(v(5592)*v(561)+v(562)*v(5640)+v(515)*v(5672)+v(509)*v(5720)+v(518)*v(5736)+v(560)*v(5768))*v(8099)
v(5997)=(v(5591)*v(561)+v(562)*v(5639)+v(515)*v(5671)+v(509)*v(5719)+v(518)*v(5735)+v(560)*v(5767))*v(8099)
v(5846)=v(509)*v(5492)+v(489)*v(5606)-v(518)*v(5638)-v(513)*v(5782)
v(5845)=v(509)*v(5491)+v(489)*v(5605)-v(518)*v(5637)-v(513)*v(5781)
v(5844)=v(509)*v(5490)+v(489)*v(5604)-v(518)*v(5636)-v(513)*v(5780)
v(5843)=v(509)*v(5489)+v(489)*v(5603)-v(518)*v(5635)-v(513)*v(5779)
v(5842)=v(509)*v(5488)+v(489)*v(5602)-v(518)*v(5634)-v(513)*v(5778)
v(5841)=v(509)*v(5487)+v(489)*v(5601)-v(518)*v(5633)-v(513)*v(5777)
v(5840)=v(509)*v(5486)+v(489)*v(5600)-v(518)*v(5632)-v(513)*v(5776)
v(5839)=v(509)*v(5485)+v(489)*v(5599)-v(518)*v(5631)-v(513)*v(5775)
v(5838)=v(509)*v(5484)+v(489)*v(5598)-v(518)*v(5630)-v(513)*v(5774)
v(5837)=v(509)*v(5483)+v(489)*v(5597)-v(518)*v(5629)-v(513)*v(5773)
v(5836)=v(509)*v(5482)+v(489)*v(5596)-v(518)*v(5628)-v(513)*v(5772)
v(5835)=v(509)*v(5481)+v(489)*v(5595)-v(518)*v(5627)-v(513)*v(5771)
v(5834)=v(509)*v(5480)+v(489)*v(5594)-v(518)*v(5626)-v(513)*v(5770)
v(5833)=v(509)*v(5479)+v(489)*v(5593)-v(518)*v(5625)-v(513)*v(5769)
v(5832)=v(509)*v(5478)+v(489)*v(5592)-v(518)*v(5624)-v(513)*v(5768)
v(5831)=v(509)*v(5477)+v(489)*v(5591)-v(518)*v(5623)-v(513)*v(5767)
v(5830)=-(v(511)*v(5606))-v(509)*v(5622)+v(518)*v(5670)+v(516)*v(5782)
v(5829)=-(v(511)*v(5605))-v(509)*v(5621)+v(518)*v(5669)+v(516)*v(5781)
v(5828)=-(v(511)*v(5604))-v(509)*v(5620)+v(518)*v(5668)+v(516)*v(5780)
v(5827)=-(v(511)*v(5603))-v(509)*v(5619)+v(518)*v(5667)+v(516)*v(5779)
v(5826)=-(v(511)*v(5602))-v(509)*v(5618)+v(518)*v(5666)+v(516)*v(5778)
v(5825)=-(v(511)*v(5601))-v(509)*v(5617)+v(518)*v(5665)+v(516)*v(5777)
v(5824)=-(v(511)*v(5600))-v(509)*v(5616)+v(518)*v(5664)+v(516)*v(5776)
v(5823)=-(v(511)*v(5599))-v(509)*v(5615)+v(518)*v(5663)+v(516)*v(5775)
v(5822)=-(v(511)*v(5598))-v(509)*v(5614)+v(518)*v(5662)+v(516)*v(5774)
v(5821)=-(v(511)*v(5597))-v(509)*v(5613)+v(518)*v(5661)+v(516)*v(5773)
v(5820)=-(v(511)*v(5596))-v(509)*v(5612)+v(518)*v(5660)+v(516)*v(5772)
v(5819)=-(v(511)*v(5595))-v(509)*v(5611)+v(518)*v(5659)+v(516)*v(5771)
v(5818)=-(v(511)*v(5594))-v(509)*v(5610)+v(518)*v(5658)+v(516)*v(5770)
v(5817)=-(v(511)*v(5593))-v(509)*v(5609)+v(518)*v(5657)+v(516)*v(5769)
v(5816)=-(v(511)*v(5592))-v(509)*v(5608)+v(518)*v(5656)+v(516)*v(5768)
v(5815)=-(v(511)*v(5591))-v(509)*v(5607)+v(518)*v(5655)+v(516)*v(5767)
v(5814)=-(v(518)*v(5222))+v(515)*v(5622)+v(511)*v(5654)-v(471)*v(5782)
v(5813)=-(v(518)*v(5221))+v(515)*v(5621)+v(511)*v(5653)-v(471)*v(5781)
v(5812)=-(v(518)*v(5220))+v(515)*v(5620)+v(511)*v(5652)-v(471)*v(5780)
v(5811)=-(v(518)*v(5219))+v(515)*v(5619)+v(511)*v(5651)-v(471)*v(5779)
v(5810)=-(v(518)*v(5218))+v(515)*v(5618)+v(511)*v(5650)-v(471)*v(5778)
v(5809)=-(v(518)*v(5217))+v(515)*v(5617)+v(511)*v(5649)-v(471)*v(5777)
v(5808)=-(v(518)*v(5216))+v(515)*v(5616)+v(511)*v(5648)-v(471)*v(5776)
v(5807)=-(v(518)*v(5215))+v(515)*v(5615)+v(511)*v(5647)-v(471)*v(5775)
v(5806)=-(v(518)*v(5214))+v(515)*v(5614)+v(511)*v(5646)-v(471)*v(5774)
v(5805)=-(v(518)*v(5213))+v(515)*v(5613)+v(511)*v(5645)-v(471)*v(5773)
v(5804)=-(v(518)*v(5212))+v(515)*v(5612)+v(511)*v(5644)-v(471)*v(5772)
v(5803)=-(v(518)*v(5211))+v(515)*v(5611)+v(511)*v(5643)-v(471)*v(5771)
v(5802)=-(v(518)*v(5210))+v(515)*v(5610)+v(511)*v(5642)-v(471)*v(5770)
v(5801)=-(v(518)*v(5209))+v(515)*v(5609)+v(511)*v(5641)-v(471)*v(5769)
v(5800)=-(v(518)*v(5208))+v(515)*v(5608)+v(511)*v(5640)-v(471)*v(5768)
v(5799)=-(v(518)*v(5207))+v(515)*v(5607)+v(511)*v(5639)-v(471)*v(5767)
v(5798)=-(v(515)*v(5492))-v(489)*v(5654)+v(518)*v(5718)+v(517)*v(5782)
v(5797)=-(v(515)*v(5491))-v(489)*v(5653)+v(518)*v(5717)+v(517)*v(5781)
v(5796)=-(v(515)*v(5490))-v(489)*v(5652)+v(518)*v(5716)+v(517)*v(5780)
v(5795)=-(v(515)*v(5489))-v(489)*v(5651)+v(518)*v(5715)+v(517)*v(5779)
v(5794)=-(v(515)*v(5488))-v(489)*v(5650)+v(518)*v(5714)+v(517)*v(5778)
v(5793)=-(v(515)*v(5487))-v(489)*v(5649)+v(518)*v(5713)+v(517)*v(5777)
v(5792)=-(v(515)*v(5486))-v(489)*v(5648)+v(518)*v(5712)+v(517)*v(5776)
v(5791)=-(v(515)*v(5485))-v(489)*v(5647)+v(518)*v(5711)+v(517)*v(5775)
v(5790)=-(v(515)*v(5484))-v(489)*v(5646)+v(518)*v(5710)+v(517)*v(5774)
v(5789)=-(v(515)*v(5483))-v(489)*v(5645)+v(518)*v(5709)+v(517)*v(5773)
v(5788)=-(v(515)*v(5482))-v(489)*v(5644)+v(518)*v(5708)+v(517)*v(5772)
v(5787)=-(v(515)*v(5481))-v(489)*v(5643)+v(518)*v(5707)+v(517)*v(5771)
v(5786)=-(v(515)*v(5480))-v(489)*v(5642)+v(518)*v(5706)+v(517)*v(5770)
v(5785)=-(v(515)*v(5479))-v(489)*v(5641)+v(518)*v(5705)+v(517)*v(5769)
v(5784)=-(v(515)*v(5478))-v(489)*v(5640)+v(518)*v(5704)+v(517)*v(5768)
v(5783)=-(v(515)*v(5477))-v(489)*v(5639)+v(518)*v(5703)+v(517)*v(5767)
v(558)=-(v(489)*v(515))+v(517)*v(518)
v(6055)=(v(558)*v(558))
v(557)=v(511)*v(515)-v(471)*v(518)
v(6093)=(v(557)*v(557))
v(556)=-(v(509)*v(511))+v(516)*v(518)
v(8112)=v(553)*v(560)+v(557)*v(561)+v(556)*v(562)
v(6092)=(v(556)*v(556))
v(8106)=v(6091)+v(6092)+v(6093)
v(555)=v(489)*v(509)-v(513)*v(518)
v(8114)=v(553)*v(554)+v(555)*v(556)+v(557)*v(558)
v(8110)=v(554)*v(560)+v(558)*v(561)+v(555)*v(562)
v(6054)=(v(555)*v(555))
v(8107)=v(6053)+v(6054)+v(6055)
v(519)=1d0/v(5847)**2
v(8100)=(-2d0)*v(519)
v(7254)=v(519)*v(8111)
v(7221)=v(519)*v(8113)
v(7188)=v(519)*v(8115)
v(5948)=v(533)*v(8100)
v(5947)=v(534)*v(8100)
v(5946)=v(530)*v(8100)
v(5963)=v(4660)*v(5946)+v(4772)*v(5947)+v(4788)*v(5948)-v(5864)*v(8101)
v(5979)=v(5963)/3d0
v(5962)=v(4659)*v(5946)+v(4771)*v(5947)+v(4787)*v(5948)-v(5863)*v(8101)
v(5978)=v(5962)/3d0
v(5961)=v(4658)*v(5946)+v(4770)*v(5947)+v(4786)*v(5948)-v(5862)*v(8101)
v(5977)=v(5961)/3d0
v(5960)=v(4657)*v(5946)+v(4769)*v(5947)+v(4785)*v(5948)-v(5861)*v(8101)
v(5976)=v(5960)/3d0
v(5959)=v(4656)*v(5946)+v(4768)*v(5947)+v(4784)*v(5948)-v(5860)*v(8101)
v(5975)=v(5959)/3d0
v(5958)=v(4655)*v(5946)+v(4767)*v(5947)+v(4783)*v(5948)-v(5859)*v(8101)
v(5974)=v(5958)/3d0
v(5957)=v(4654)*v(5946)+v(4766)*v(5947)+v(4782)*v(5948)-v(5858)*v(8101)
v(5973)=v(5957)/3d0
v(5956)=v(4653)*v(5946)+v(4765)*v(5947)+v(4781)*v(5948)-v(5857)*v(8101)
v(5972)=v(5956)/3d0
v(5955)=v(4652)*v(5946)+v(4764)*v(5947)+v(4780)*v(5948)-v(5856)*v(8101)
v(5971)=v(5955)/3d0
v(5954)=v(4651)*v(5946)+v(4763)*v(5947)+v(4779)*v(5948)-v(5855)*v(8101)
v(5970)=v(5954)/3d0
v(5953)=v(4650)*v(5946)+v(4762)*v(5947)+v(4778)*v(5948)-v(5854)*v(8101)
v(5969)=v(5953)/3d0
v(5952)=v(4649)*v(5946)+v(4761)*v(5947)+v(4777)*v(5948)-v(5853)*v(8101)
v(5968)=v(5952)/3d0
v(5951)=v(4648)*v(5946)+v(4760)*v(5947)+v(4776)*v(5948)-v(5852)*v(8101)
v(5967)=v(5951)/3d0
v(5950)=v(4647)*v(5946)+v(4759)*v(5947)+v(4775)*v(5948)-v(5851)*v(8101)
v(5966)=v(5950)/3d0
v(5949)=v(4646)*v(5946)+v(4758)*v(5947)+v(4774)*v(5948)-v(5850)*v(8101)
v(5965)=v(5949)/3d0
v(5945)=v(4645)*v(5946)+v(4757)*v(5947)+v(4773)*v(5948)-v(5848)*v(8101)
v(5964)=v(5945)/3d0
v(5910)=-(v(532)*v(8100))
v(5909)=-(v(535)*v(8100))
v(5908)=-(v(531)*v(8100))
v(5925)=v(4724)*v(5908)+v(4756)*v(5909)+v(4804)*v(5910)+v(5864)*v(8102)
v(5941)=-v(5925)/3d0
v(5924)=v(4723)*v(5908)+v(4755)*v(5909)+v(4803)*v(5910)+v(5863)*v(8102)
v(5940)=-v(5924)/3d0
v(5923)=v(4722)*v(5908)+v(4754)*v(5909)+v(4802)*v(5910)+v(5862)*v(8102)
v(5939)=-v(5923)/3d0
v(5922)=v(4721)*v(5908)+v(4753)*v(5909)+v(4801)*v(5910)+v(5861)*v(8102)
v(5938)=-v(5922)/3d0
v(5921)=v(4720)*v(5908)+v(4752)*v(5909)+v(4800)*v(5910)+v(5860)*v(8102)
v(5937)=-v(5921)/3d0
v(5920)=v(4719)*v(5908)+v(4751)*v(5909)+v(4799)*v(5910)+v(5859)*v(8102)
v(5936)=-v(5920)/3d0
v(5919)=v(4718)*v(5908)+v(4750)*v(5909)+v(4798)*v(5910)+v(5858)*v(8102)
v(5935)=-v(5919)/3d0
v(5918)=v(4717)*v(5908)+v(4749)*v(5909)+v(4797)*v(5910)+v(5857)*v(8102)
v(5934)=-v(5918)/3d0
v(5917)=v(4716)*v(5908)+v(4748)*v(5909)+v(4796)*v(5910)+v(5856)*v(8102)
v(5933)=-v(5917)/3d0
v(5916)=v(4715)*v(5908)+v(4747)*v(5909)+v(4795)*v(5910)+v(5855)*v(8102)
v(5932)=-v(5916)/3d0
v(5915)=v(4714)*v(5908)+v(4746)*v(5909)+v(4794)*v(5910)+v(5854)*v(8102)
v(5931)=-v(5915)/3d0
v(5914)=v(4713)*v(5908)+v(4745)*v(5909)+v(4793)*v(5910)+v(5853)*v(8102)
v(5930)=-v(5914)/3d0
v(5913)=v(4712)*v(5908)+v(4744)*v(5909)+v(4792)*v(5910)+v(5852)*v(8102)
v(5929)=-v(5913)/3d0
v(5912)=v(4711)*v(5908)+v(4743)*v(5909)+v(4791)*v(5910)+v(5851)*v(8102)
v(5928)=-v(5912)/3d0
v(5911)=v(4710)*v(5908)+v(4742)*v(5909)+v(4790)*v(5910)+v(5850)*v(8102)
v(5927)=-v(5911)/3d0
v(5907)=v(4709)*v(5908)+v(4741)*v(5909)+v(4789)*v(5910)+v(5848)*v(8102)
v(5926)=-v(5907)/3d0
v(5888)=1d0/v(519)**0.13333333333333333d1
v(8103)=-v(5888)/3d0
v(5903)=v(5864)*v(8103)
v(5902)=v(5863)*v(8103)
v(5901)=v(5862)*v(8103)
v(5900)=v(5861)*v(8103)
v(5899)=v(5860)*v(8103)
v(5898)=v(5859)*v(8103)
v(5897)=v(5858)*v(8103)
v(5896)=v(5857)*v(8103)
v(5895)=v(5856)*v(8103)
v(5894)=v(5855)*v(8103)
v(5893)=v(5854)*v(8103)
v(5892)=v(5853)*v(8103)
v(5891)=v(5852)*v(8103)
v(5890)=v(5851)*v(8103)
v(5889)=v(5850)*v(8103)
v(5887)=v(5848)*v(8103)
v(5871)=v(537)*v(8100)
v(5870)=v(538)*v(8100)
v(5869)=v(539)*v(8100)
v(5886)=v(4644)*v(5869)+v(4692)*v(5870)+v(4708)*v(5871)-v(5864)*v(8104)
v(5995)=v(5886)/3d0
v(5885)=v(4643)*v(5869)+v(4691)*v(5870)+v(4707)*v(5871)-v(5863)*v(8104)
v(5994)=v(5885)/3d0
v(5884)=v(4642)*v(5869)+v(4690)*v(5870)+v(4706)*v(5871)-v(5862)*v(8104)
v(5993)=v(5884)/3d0
v(5883)=v(4641)*v(5869)+v(4689)*v(5870)+v(4705)*v(5871)-v(5861)*v(8104)
v(5992)=v(5883)/3d0
v(5882)=v(4640)*v(5869)+v(4688)*v(5870)+v(4704)*v(5871)-v(5860)*v(8104)
v(5991)=v(5882)/3d0
v(5881)=v(4639)*v(5869)+v(4687)*v(5870)+v(4703)*v(5871)-v(5859)*v(8104)
v(5990)=v(5881)/3d0
v(5880)=v(4638)*v(5869)+v(4686)*v(5870)+v(4702)*v(5871)-v(5858)*v(8104)
v(5989)=v(5880)/3d0
v(5879)=v(4637)*v(5869)+v(4685)*v(5870)+v(4701)*v(5871)-v(5857)*v(8104)
v(5988)=v(5879)/3d0
v(5878)=v(4636)*v(5869)+v(4684)*v(5870)+v(4700)*v(5871)-v(5856)*v(8104)
v(5987)=v(5878)/3d0
v(5877)=v(4635)*v(5869)+v(4683)*v(5870)+v(4699)*v(5871)-v(5855)*v(8104)
v(5986)=v(5877)/3d0
v(5876)=v(4634)*v(5869)+v(4682)*v(5870)+v(4698)*v(5871)-v(5854)*v(8104)
v(5985)=v(5876)/3d0
v(5875)=v(4633)*v(5869)+v(4681)*v(5870)+v(4697)*v(5871)-v(5853)*v(8104)
v(5984)=v(5875)/3d0
v(5874)=v(4632)*v(5869)+v(4680)*v(5870)+v(4696)*v(5871)-v(5852)*v(8104)
v(5983)=v(5874)/3d0
v(5873)=v(4631)*v(5869)+v(4679)*v(5870)+v(4695)*v(5871)-v(5851)*v(8104)
v(5982)=v(5873)/3d0
v(5872)=v(4630)*v(5869)+v(4678)*v(5870)+v(4694)*v(5871)-v(5850)*v(8104)
v(5981)=v(5872)/3d0
v(5868)=v(4629)*v(5869)+v(4677)*v(5870)+v(4693)*v(5871)-v(5848)*v(8104)
v(5980)=v(5868)/3d0
v(526)=-(v(519)*v(8104))
v(524)=1d0/v(519)**0.3333333333333333d0
v(8179)=-(mpar(9)*v(524))
v(523)=v(519)*v(8102)
v(528)=-v(523)/3d0
v(522)=-(v(519)*v(8101))
v(527)=v(522)/3d0
v(7140)=(-2d0/3d0)*v(526)+v(527)+v(528)
v(521)=v(526)/3d0
v(7104)=v(521)+(-2d0/3d0)*v(522)+v(528)
v(7070)=v(521)+(2d0/3d0)*v(523)+v(527)
v(542)=1d0/v(5996)**2
v(8105)=(-2d0)*v(542)
v(6213)=v(542)*v(8110)
v(6196)=v(542)*v(8112)
v(6179)=v(542)*v(8114)
v(6097)=v(556)*v(8105)
v(6096)=v(557)*v(8105)
v(6095)=v(553)*v(8105)
v(6112)=v(5702)*v(6095)+v(5814)*v(6096)+v(5830)*v(6097)-v(6013)*v(8106)
v(6128)=v(6112)/3d0
v(6111)=v(5701)*v(6095)+v(5813)*v(6096)+v(5829)*v(6097)-v(6012)*v(8106)
v(6127)=v(6111)/3d0
v(6110)=v(5700)*v(6095)+v(5812)*v(6096)+v(5828)*v(6097)-v(6011)*v(8106)
v(6126)=v(6110)/3d0
v(6109)=v(5699)*v(6095)+v(5811)*v(6096)+v(5827)*v(6097)-v(6010)*v(8106)
v(6125)=v(6109)/3d0
v(6108)=v(5698)*v(6095)+v(5810)*v(6096)+v(5826)*v(6097)-v(6009)*v(8106)
v(6124)=v(6108)/3d0
v(6107)=v(5697)*v(6095)+v(5809)*v(6096)+v(5825)*v(6097)-v(6008)*v(8106)
v(6123)=v(6107)/3d0
v(6106)=v(5696)*v(6095)+v(5808)*v(6096)+v(5824)*v(6097)-v(6007)*v(8106)
v(6122)=v(6106)/3d0
v(6105)=v(5695)*v(6095)+v(5807)*v(6096)+v(5823)*v(6097)-v(6006)*v(8106)
v(6121)=v(6105)/3d0
v(6104)=v(5694)*v(6095)+v(5806)*v(6096)+v(5822)*v(6097)-v(6005)*v(8106)
v(6120)=v(6104)/3d0
v(6103)=v(5693)*v(6095)+v(5805)*v(6096)+v(5821)*v(6097)-v(6004)*v(8106)
v(6119)=v(6103)/3d0
v(6102)=v(5692)*v(6095)+v(5804)*v(6096)+v(5820)*v(6097)-v(6003)*v(8106)
v(6118)=v(6102)/3d0
v(6101)=v(5691)*v(6095)+v(5803)*v(6096)+v(5819)*v(6097)-v(6002)*v(8106)
v(6117)=v(6101)/3d0
v(6100)=v(5690)*v(6095)+v(5802)*v(6096)+v(5818)*v(6097)-v(6001)*v(8106)
v(6116)=v(6100)/3d0
v(6099)=v(5689)*v(6095)+v(5801)*v(6096)+v(5817)*v(6097)-v(6000)*v(8106)
v(6115)=v(6099)/3d0
v(6098)=v(5688)*v(6095)+v(5800)*v(6096)+v(5816)*v(6097)-v(5999)*v(8106)
v(6114)=v(6098)/3d0
v(6094)=v(5687)*v(6095)+v(5799)*v(6096)+v(5815)*v(6097)-v(5997)*v(8106)
v(6113)=v(6094)/3d0
v(6059)=-(v(555)*v(8105))
v(6058)=-(v(558)*v(8105))
v(6057)=-(v(554)*v(8105))
v(6074)=v(5766)*v(6057)+v(5798)*v(6058)+v(5846)*v(6059)+v(6013)*v(8107)
v(6090)=-v(6074)/3d0
v(6073)=v(5765)*v(6057)+v(5797)*v(6058)+v(5845)*v(6059)+v(6012)*v(8107)
v(6089)=-v(6073)/3d0
v(6072)=v(5764)*v(6057)+v(5796)*v(6058)+v(5844)*v(6059)+v(6011)*v(8107)
v(6088)=-v(6072)/3d0
v(6071)=v(5763)*v(6057)+v(5795)*v(6058)+v(5843)*v(6059)+v(6010)*v(8107)
v(6087)=-v(6071)/3d0
v(6070)=v(5762)*v(6057)+v(5794)*v(6058)+v(5842)*v(6059)+v(6009)*v(8107)
v(6086)=-v(6070)/3d0
v(6069)=v(5761)*v(6057)+v(5793)*v(6058)+v(5841)*v(6059)+v(6008)*v(8107)
v(6085)=-v(6069)/3d0
v(6068)=v(5760)*v(6057)+v(5792)*v(6058)+v(5840)*v(6059)+v(6007)*v(8107)
v(6084)=-v(6068)/3d0
v(6067)=v(5759)*v(6057)+v(5791)*v(6058)+v(5839)*v(6059)+v(6006)*v(8107)
v(6083)=-v(6067)/3d0
v(6066)=v(5758)*v(6057)+v(5790)*v(6058)+v(5838)*v(6059)+v(6005)*v(8107)
v(6082)=-v(6066)/3d0
v(6065)=v(5757)*v(6057)+v(5789)*v(6058)+v(5837)*v(6059)+v(6004)*v(8107)
v(6081)=-v(6065)/3d0
v(6064)=v(5756)*v(6057)+v(5788)*v(6058)+v(5836)*v(6059)+v(6003)*v(8107)
v(6080)=-v(6064)/3d0
v(6063)=v(5755)*v(6057)+v(5787)*v(6058)+v(5835)*v(6059)+v(6002)*v(8107)
v(6079)=-v(6063)/3d0
v(6062)=v(5754)*v(6057)+v(5786)*v(6058)+v(5834)*v(6059)+v(6001)*v(8107)
v(6078)=-v(6062)/3d0
v(6061)=v(5753)*v(6057)+v(5785)*v(6058)+v(5833)*v(6059)+v(6000)*v(8107)
v(6077)=-v(6061)/3d0
v(6060)=v(5752)*v(6057)+v(5784)*v(6058)+v(5832)*v(6059)+v(5999)*v(8107)
v(6076)=-v(6060)/3d0
v(6056)=v(5751)*v(6057)+v(5783)*v(6058)+v(5831)*v(6059)+v(5997)*v(8107)
v(6075)=-v(6056)/3d0
v(6037)=1d0/v(542)**0.13333333333333333d1
v(8108)=-v(6037)/3d0
v(6052)=v(6013)*v(8108)
v(6051)=v(6012)*v(8108)
v(6050)=v(6011)*v(8108)
v(6049)=v(6010)*v(8108)
v(6048)=v(6009)*v(8108)
v(6047)=v(6008)*v(8108)
v(6046)=v(6007)*v(8108)
v(6045)=v(6006)*v(8108)
v(6044)=v(6005)*v(8108)
v(6043)=v(6004)*v(8108)
v(6042)=v(6003)*v(8108)
v(6041)=v(6002)*v(8108)
v(6040)=v(6001)*v(8108)
v(6039)=v(6000)*v(8108)
v(6038)=v(5999)*v(8108)
v(6036)=v(5997)*v(8108)
v(6020)=v(560)*v(8105)
v(6019)=v(561)*v(8105)
v(6018)=v(562)*v(8105)
v(6035)=v(5686)*v(6018)+v(5734)*v(6019)+v(5750)*v(6020)-v(6013)*v(8109)
v(6144)=v(6035)/3d0
v(6034)=v(5685)*v(6018)+v(5733)*v(6019)+v(5749)*v(6020)-v(6012)*v(8109)
v(6143)=v(6034)/3d0
v(6033)=v(5684)*v(6018)+v(5732)*v(6019)+v(5748)*v(6020)-v(6011)*v(8109)
v(6142)=v(6033)/3d0
v(6032)=v(5683)*v(6018)+v(5731)*v(6019)+v(5747)*v(6020)-v(6010)*v(8109)
v(6141)=v(6032)/3d0
v(6031)=v(5682)*v(6018)+v(5730)*v(6019)+v(5746)*v(6020)-v(6009)*v(8109)
v(6140)=v(6031)/3d0
v(6030)=v(5681)*v(6018)+v(5729)*v(6019)+v(5745)*v(6020)-v(6008)*v(8109)
v(6139)=v(6030)/3d0
v(6029)=v(5680)*v(6018)+v(5728)*v(6019)+v(5744)*v(6020)-v(6007)*v(8109)
v(6138)=v(6029)/3d0
v(6028)=v(5679)*v(6018)+v(5727)*v(6019)+v(5743)*v(6020)-v(6006)*v(8109)
v(6137)=v(6028)/3d0
v(6027)=v(5678)*v(6018)+v(5726)*v(6019)+v(5742)*v(6020)-v(6005)*v(8109)
v(6136)=v(6027)/3d0
v(6026)=v(5677)*v(6018)+v(5725)*v(6019)+v(5741)*v(6020)-v(6004)*v(8109)
v(6135)=v(6026)/3d0
v(6025)=v(5676)*v(6018)+v(5724)*v(6019)+v(5740)*v(6020)-v(6003)*v(8109)
v(6134)=v(6025)/3d0
v(6024)=v(5675)*v(6018)+v(5723)*v(6019)+v(5739)*v(6020)-v(6002)*v(8109)
v(6133)=v(6024)/3d0
v(6023)=v(5674)*v(6018)+v(5722)*v(6019)+v(5738)*v(6020)-v(6001)*v(8109)
v(6132)=v(6023)/3d0
v(6022)=v(5673)*v(6018)+v(5721)*v(6019)+v(5737)*v(6020)-v(6000)*v(8109)
v(6131)=v(6022)/3d0
v(6021)=v(5672)*v(6018)+v(5720)*v(6019)+v(5736)*v(6020)-v(5999)*v(8109)
v(6130)=v(6021)/3d0
v(6017)=v(5671)*v(6018)+v(5719)*v(6019)+v(5735)*v(6020)-v(5997)*v(8109)
v(6129)=v(6017)/3d0
v(549)=-(v(542)*v(8109))
v(547)=1d0/v(542)**0.3333333333333333d0
v(8178)=-(mpar(11)*v(547))
v(6229)=mpar(11)*(v(6052)*v(6213)+v(547)*(v(542)*(v(555)*v(5686)+v(558)*v(5734)+v(554)*v(5750)+v(560)*v(5766)+v(561)*v&
&(5798)+v(562)*v(5846))+v(6013)*v(8110)))
v(7286)=v(3156)-v(6229)+mpar(9)*(-(v(5903)*v(7254))-v(524)*(v(519)*(v(4708)*v(531)+v(4644)*v(532)+v(4692)*v(535)+v(4724&
&)*v(537)+v(4756)*v(538)+v(4804)*v(539))+v(5864)*v(8111)))
v(8190)=2d0*v(7286)
v(6228)=mpar(11)*(v(6051)*v(6213)+v(547)*(v(542)*(v(555)*v(5685)+v(558)*v(5733)+v(554)*v(5749)+v(560)*v(5765)+v(561)*v&
&(5797)+v(562)*v(5845))+v(6012)*v(8110)))
v(7284)=v(3154)-v(6228)+mpar(9)*(-(v(5902)*v(7254))-v(524)*(v(519)*(v(4707)*v(531)+v(4643)*v(532)+v(4691)*v(535)+v(4723&
&)*v(537)+v(4755)*v(538)+v(4803)*v(539))+v(5863)*v(8111)))
v(8197)=2d0*v(7284)
v(6227)=mpar(11)*(v(6050)*v(6213)+v(547)*(v(542)*(v(555)*v(5684)+v(558)*v(5732)+v(554)*v(5748)+v(560)*v(5764)+v(561)*v&
&(5796)+v(562)*v(5844))+v(6011)*v(8110)))
v(7282)=v(3152)-v(6227)+mpar(9)*(-(v(5901)*v(7254))-v(524)*(v(519)*(v(4706)*v(531)+v(4642)*v(532)+v(4690)*v(535)+v(4722&
&)*v(537)+v(4754)*v(538)+v(4802)*v(539))+v(5862)*v(8111)))
v(8200)=2d0*v(7282)
v(6226)=mpar(11)*(v(6049)*v(6213)+v(547)*(v(542)*(v(555)*v(5683)+v(558)*v(5731)+v(554)*v(5747)+v(560)*v(5763)+v(561)*v&
&(5795)+v(562)*v(5843))+v(6010)*v(8110)))
v(7280)=v(3150)-v(6226)+mpar(9)*(-(v(5900)*v(7254))-v(524)*(v(519)*(v(4705)*v(531)+v(4641)*v(532)+v(4689)*v(535)+v(4721&
&)*v(537)+v(4753)*v(538)+v(4801)*v(539))+v(5861)*v(8111)))
v(8203)=2d0*v(7280)
v(6225)=mpar(11)*(v(6048)*v(6213)+v(547)*(v(542)*(v(555)*v(5682)+v(558)*v(5730)+v(554)*v(5746)+v(560)*v(5762)+v(561)*v&
&(5794)+v(562)*v(5842))+v(6009)*v(8110)))
v(7278)=v(3148)-v(6225)+mpar(9)*(-(v(5899)*v(7254))-v(524)*(v(519)*(v(4704)*v(531)+v(4640)*v(532)+v(4688)*v(535)+v(4720&
&)*v(537)+v(4752)*v(538)+v(4800)*v(539))+v(5860)*v(8111)))
v(8206)=2d0*v(7278)
v(6224)=mpar(11)*(v(6047)*v(6213)+v(547)*(v(542)*(v(555)*v(5681)+v(558)*v(5729)+v(554)*v(5745)+v(560)*v(5761)+v(561)*v&
&(5793)+v(562)*v(5841))+v(6008)*v(8110)))
v(7276)=-v(6224)+mpar(9)*(-(v(5898)*v(7254))-v(524)*(v(519)*(v(4703)*v(531)+v(4639)*v(532)+v(4687)*v(535)+v(4719)*v(537&
&)+v(4751)*v(538)+v(4799)*v(539))+v(5859)*v(8111)))
v(8209)=2d0*v(7276)
v(6223)=mpar(11)*(v(6046)*v(6213)+v(547)*(v(542)*(v(555)*v(5680)+v(558)*v(5728)+v(554)*v(5744)+v(560)*v(5760)+v(561)*v&
&(5792)+v(562)*v(5840))+v(6007)*v(8110)))
v(7274)=-v(6223)+mpar(9)*(-(v(5897)*v(7254))-v(524)*(v(519)*(v(4702)*v(531)+v(4638)*v(532)+v(4686)*v(535)+v(4718)*v(537&
&)+v(4750)*v(538)+v(4798)*v(539))+v(5858)*v(8111)))
v(8212)=2d0*v(7274)
v(6222)=mpar(11)*(v(6045)*v(6213)+v(547)*(v(542)*(v(555)*v(5679)+v(558)*v(5727)+v(554)*v(5743)+v(560)*v(5759)+v(561)*v&
&(5791)+v(562)*v(5839))+v(6006)*v(8110)))
v(7272)=-v(6222)+mpar(9)*(-(v(5896)*v(7254))-v(524)*(v(519)*(v(4701)*v(531)+v(4637)*v(532)+v(4685)*v(535)+v(4717)*v(537&
&)+v(4749)*v(538)+v(4797)*v(539))+v(5857)*v(8111)))
v(8215)=2d0*v(7272)
v(6221)=mpar(11)*(v(6044)*v(6213)+v(547)*(v(542)*(v(555)*v(5678)+v(558)*v(5726)+v(554)*v(5742)+v(560)*v(5758)+v(561)*v&
&(5790)+v(562)*v(5838))+v(6005)*v(8110)))
v(7270)=-v(6221)+mpar(9)*(-(v(5895)*v(7254))-v(524)*(v(519)*(v(4700)*v(531)+v(4636)*v(532)+v(4684)*v(535)+v(4716)*v(537&
&)+v(4748)*v(538)+v(4796)*v(539))+v(5856)*v(8111)))
v(8218)=2d0*v(7270)
v(6220)=mpar(11)*(v(6043)*v(6213)+v(547)*(v(542)*(v(555)*v(5677)+v(558)*v(5725)+v(554)*v(5741)+v(560)*v(5757)+v(561)*v&
&(5789)+v(562)*v(5837))+v(6004)*v(8110)))
v(7268)=-v(6220)+mpar(9)*(-(v(5894)*v(7254))-v(524)*(v(519)*(v(4699)*v(531)+v(4635)*v(532)+v(4683)*v(535)+v(4715)*v(537&
&)+v(4747)*v(538)+v(4795)*v(539))+v(5855)*v(8111)))
v(8221)=2d0*v(7268)
v(6219)=mpar(11)*(v(6042)*v(6213)+v(547)*(v(542)*(v(555)*v(5676)+v(558)*v(5724)+v(554)*v(5740)+v(560)*v(5756)+v(561)*v&
&(5788)+v(562)*v(5836))+v(6003)*v(8110)))
v(7266)=v(3146)-v(6219)+mpar(9)*(-(v(5893)*v(7254))-v(524)*(v(519)*(v(4698)*v(531)+v(4634)*v(532)+v(4682)*v(535)+v(4714&
&)*v(537)+v(4746)*v(538)+v(4794)*v(539))+v(5854)*v(8111)))
v(8224)=2d0*v(7266)
v(6218)=mpar(11)*(v(6041)*v(6213)+v(547)*(v(542)*(v(555)*v(5675)+v(558)*v(5723)+v(554)*v(5739)+v(560)*v(5755)+v(561)*v&
&(5787)+v(562)*v(5835))+v(6002)*v(8110)))
v(7264)=v(3144)-v(6218)+mpar(9)*(-(v(5892)*v(7254))-v(524)*(v(519)*(v(4697)*v(531)+v(4633)*v(532)+v(4681)*v(535)+v(4713&
&)*v(537)+v(4745)*v(538)+v(4793)*v(539))+v(5853)*v(8111)))
v(8227)=2d0*v(7264)
v(6217)=mpar(11)*(v(6040)*v(6213)+v(547)*(v(542)*(v(555)*v(5674)+v(558)*v(5722)+v(554)*v(5738)+v(560)*v(5754)+v(561)*v&
&(5786)+v(562)*v(5834))+v(6001)*v(8110)))
v(7262)=v(3142)-v(6217)+mpar(9)*(-(v(5891)*v(7254))-v(524)*(v(519)*(v(4696)*v(531)+v(4632)*v(532)+v(4680)*v(535)+v(4712&
&)*v(537)+v(4744)*v(538)+v(4792)*v(539))+v(5852)*v(8111)))
v(8230)=2d0*v(7262)
v(6216)=mpar(11)*(v(6039)*v(6213)+v(547)*(v(542)*(v(555)*v(5673)+v(558)*v(5721)+v(554)*v(5737)+v(560)*v(5753)+v(561)*v&
&(5785)+v(562)*v(5833))+v(6000)*v(8110)))
v(7260)=v(3140)-v(6216)+mpar(9)*(-(v(5890)*v(7254))-v(524)*(v(519)*(v(4695)*v(531)+v(4631)*v(532)+v(4679)*v(535)+v(4711&
&)*v(537)+v(4743)*v(538)+v(4791)*v(539))+v(5851)*v(8111)))
v(8233)=2d0*v(7260)
v(6215)=mpar(11)*(v(6038)*v(6213)+v(547)*(v(542)*(v(555)*v(5672)+v(558)*v(5720)+v(554)*v(5736)+v(560)*v(5752)+v(561)*v&
&(5784)+v(562)*v(5832))+v(5999)*v(8110)))
v(7258)=v(3138)-v(6215)+mpar(9)*(-(v(5889)*v(7254))-v(524)*(v(519)*(v(4694)*v(531)+v(4630)*v(532)+v(4678)*v(535)+v(4710&
&)*v(537)+v(4742)*v(538)+v(4790)*v(539))+v(5850)*v(8111)))
v(8236)=2d0*v(7258)
v(6214)=mpar(11)*(v(6036)*v(6213)+v(547)*(v(542)*(v(555)*v(5671)+v(558)*v(5719)+v(554)*v(5735)+v(560)*v(5751)+v(561)*v&
&(5783)+v(562)*v(5831))+v(5997)*v(8110)))
v(7256)=v(3136)-v(6214)+mpar(9)*(-(v(5887)*v(7254))-v(524)*(v(519)*(v(4693)*v(531)+v(4629)*v(532)+v(4677)*v(535)+v(4709&
&)*v(537)+v(4741)*v(538)+v(4789)*v(539))+v(5848)*v(8111)))
v(8194)=2d0*v(7256)
v(6212)=mpar(11)*(v(6052)*v(6196)+v(547)*(v(542)*(v(556)*v(5686)+v(560)*v(5702)+v(557)*v(5734)+v(553)*v(5750)+v(561)*v&
&(5814)+v(562)*v(5830))+v(6013)*v(8112)))
v(7253)=v(3134)-v(6212)+mpar(9)*(-(v(5903)*v(7221))-v(524)*(v(519)*(v(4708)*v(530)+v(4644)*v(533)+v(4692)*v(534)+v(4660&
&)*v(537)+v(4772)*v(538)+v(4788)*v(539))+v(5864)*v(8113)))
v(8189)=2d0*v(7253)
v(6211)=mpar(11)*(v(6051)*v(6196)+v(547)*(v(542)*(v(556)*v(5685)+v(560)*v(5701)+v(557)*v(5733)+v(553)*v(5749)+v(561)*v&
&(5813)+v(562)*v(5829))+v(6012)*v(8112)))
v(7251)=v(3132)-v(6211)+mpar(9)*(-(v(5902)*v(7221))-v(524)*(v(519)*(v(4707)*v(530)+v(4643)*v(533)+v(4691)*v(534)+v(4659&
&)*v(537)+v(4771)*v(538)+v(4787)*v(539))+v(5863)*v(8113)))
v(8196)=2d0*v(7251)
v(6210)=mpar(11)*(v(6050)*v(6196)+v(547)*(v(542)*(v(556)*v(5684)+v(560)*v(5700)+v(557)*v(5732)+v(553)*v(5748)+v(561)*v&
&(5812)+v(562)*v(5828))+v(6011)*v(8112)))
v(7249)=v(3130)-v(6210)+mpar(9)*(-(v(5901)*v(7221))-v(524)*(v(519)*(v(4706)*v(530)+v(4642)*v(533)+v(4690)*v(534)+v(4658&
&)*v(537)+v(4770)*v(538)+v(4786)*v(539))+v(5862)*v(8113)))
v(8199)=2d0*v(7249)
v(6209)=mpar(11)*(v(6049)*v(6196)+v(547)*(v(542)*(v(556)*v(5683)+v(560)*v(5699)+v(557)*v(5731)+v(553)*v(5747)+v(561)*v&
&(5811)+v(562)*v(5827))+v(6010)*v(8112)))
v(7247)=v(3128)-v(6209)+mpar(9)*(-(v(5900)*v(7221))-v(524)*(v(519)*(v(4705)*v(530)+v(4641)*v(533)+v(4689)*v(534)+v(4657&
&)*v(537)+v(4769)*v(538)+v(4785)*v(539))+v(5861)*v(8113)))
v(8202)=2d0*v(7247)
v(6208)=mpar(11)*(v(6048)*v(6196)+v(547)*(v(542)*(v(556)*v(5682)+v(560)*v(5698)+v(557)*v(5730)+v(553)*v(5746)+v(561)*v&
&(5810)+v(562)*v(5826))+v(6009)*v(8112)))
v(7245)=v(3126)-v(6208)+mpar(9)*(-(v(5899)*v(7221))-v(524)*(v(519)*(v(4704)*v(530)+v(4640)*v(533)+v(4688)*v(534)+v(4656&
&)*v(537)+v(4768)*v(538)+v(4784)*v(539))+v(5860)*v(8113)))
v(8205)=2d0*v(7245)
v(6207)=mpar(11)*(v(6047)*v(6196)+v(547)*(v(542)*(v(556)*v(5681)+v(560)*v(5697)+v(557)*v(5729)+v(553)*v(5745)+v(561)*v&
&(5809)+v(562)*v(5825))+v(6008)*v(8112)))
v(7243)=-v(6207)+mpar(9)*(-(v(5898)*v(7221))-v(524)*(v(519)*(v(4703)*v(530)+v(4639)*v(533)+v(4687)*v(534)+v(4655)*v(537&
&)+v(4767)*v(538)+v(4783)*v(539))+v(5859)*v(8113)))
v(8208)=2d0*v(7243)
v(6206)=mpar(11)*(v(6046)*v(6196)+v(547)*(v(542)*(v(556)*v(5680)+v(560)*v(5696)+v(557)*v(5728)+v(553)*v(5744)+v(561)*v&
&(5808)+v(562)*v(5824))+v(6007)*v(8112)))
v(7241)=-v(6206)+mpar(9)*(-(v(5897)*v(7221))-v(524)*(v(519)*(v(4702)*v(530)+v(4638)*v(533)+v(4686)*v(534)+v(4654)*v(537&
&)+v(4766)*v(538)+v(4782)*v(539))+v(5858)*v(8113)))
v(8211)=2d0*v(7241)
v(6205)=mpar(11)*(v(6045)*v(6196)+v(547)*(v(542)*(v(556)*v(5679)+v(560)*v(5695)+v(557)*v(5727)+v(553)*v(5743)+v(561)*v&
&(5807)+v(562)*v(5823))+v(6006)*v(8112)))
v(7239)=-v(6205)+mpar(9)*(-(v(5896)*v(7221))-v(524)*(v(519)*(v(4701)*v(530)+v(4637)*v(533)+v(4685)*v(534)+v(4653)*v(537&
&)+v(4765)*v(538)+v(4781)*v(539))+v(5857)*v(8113)))
v(8214)=2d0*v(7239)
v(6204)=mpar(11)*(v(6044)*v(6196)+v(547)*(v(542)*(v(556)*v(5678)+v(560)*v(5694)+v(557)*v(5726)+v(553)*v(5742)+v(561)*v&
&(5806)+v(562)*v(5822))+v(6005)*v(8112)))
v(7237)=-v(6204)+mpar(9)*(-(v(5895)*v(7221))-v(524)*(v(519)*(v(4700)*v(530)+v(4636)*v(533)+v(4684)*v(534)+v(4652)*v(537&
&)+v(4764)*v(538)+v(4780)*v(539))+v(5856)*v(8113)))
v(8217)=2d0*v(7237)
v(6203)=mpar(11)*(v(6043)*v(6196)+v(547)*(v(542)*(v(556)*v(5677)+v(560)*v(5693)+v(557)*v(5725)+v(553)*v(5741)+v(561)*v&
&(5805)+v(562)*v(5821))+v(6004)*v(8112)))
v(7235)=-v(6203)+mpar(9)*(-(v(5894)*v(7221))-v(524)*(v(519)*(v(4699)*v(530)+v(4635)*v(533)+v(4683)*v(534)+v(4651)*v(537&
&)+v(4763)*v(538)+v(4779)*v(539))+v(5855)*v(8113)))
v(8220)=2d0*v(7235)
v(6202)=mpar(11)*(v(6042)*v(6196)+v(547)*(v(542)*(v(556)*v(5676)+v(560)*v(5692)+v(557)*v(5724)+v(553)*v(5740)+v(561)*v&
&(5804)+v(562)*v(5820))+v(6003)*v(8112)))
v(7233)=v(3124)-v(6202)+mpar(9)*(-(v(5893)*v(7221))-v(524)*(v(519)*(v(4698)*v(530)+v(4634)*v(533)+v(4682)*v(534)+v(4650&
&)*v(537)+v(4762)*v(538)+v(4778)*v(539))+v(5854)*v(8113)))
v(8223)=2d0*v(7233)
v(6201)=mpar(11)*(v(6041)*v(6196)+v(547)*(v(542)*(v(556)*v(5675)+v(560)*v(5691)+v(557)*v(5723)+v(553)*v(5739)+v(561)*v&
&(5803)+v(562)*v(5819))+v(6002)*v(8112)))
v(7231)=v(3122)-v(6201)+mpar(9)*(-(v(5892)*v(7221))-v(524)*(v(519)*(v(4697)*v(530)+v(4633)*v(533)+v(4681)*v(534)+v(4649&
&)*v(537)+v(4761)*v(538)+v(4777)*v(539))+v(5853)*v(8113)))
v(8226)=2d0*v(7231)
v(6200)=mpar(11)*(v(6040)*v(6196)+v(547)*(v(542)*(v(556)*v(5674)+v(560)*v(5690)+v(557)*v(5722)+v(553)*v(5738)+v(561)*v&
&(5802)+v(562)*v(5818))+v(6001)*v(8112)))
v(7229)=v(3120)-v(6200)+mpar(9)*(-(v(5891)*v(7221))-v(524)*(v(519)*(v(4696)*v(530)+v(4632)*v(533)+v(4680)*v(534)+v(4648&
&)*v(537)+v(4760)*v(538)+v(4776)*v(539))+v(5852)*v(8113)))
v(8229)=2d0*v(7229)
v(6199)=mpar(11)*(v(6039)*v(6196)+v(547)*(v(542)*(v(556)*v(5673)+v(560)*v(5689)+v(557)*v(5721)+v(553)*v(5737)+v(561)*v&
&(5801)+v(562)*v(5817))+v(6000)*v(8112)))
v(7227)=v(3118)-v(6199)+mpar(9)*(-(v(5890)*v(7221))-v(524)*(v(519)*(v(4695)*v(530)+v(4631)*v(533)+v(4679)*v(534)+v(4647&
&)*v(537)+v(4759)*v(538)+v(4775)*v(539))+v(5851)*v(8113)))
v(8232)=2d0*v(7227)
v(6198)=mpar(11)*(v(6038)*v(6196)+v(547)*(v(542)*(v(556)*v(5672)+v(560)*v(5688)+v(557)*v(5720)+v(553)*v(5736)+v(561)*v&
&(5800)+v(562)*v(5816))+v(5999)*v(8112)))
v(7225)=v(3116)-v(6198)+mpar(9)*(-(v(5889)*v(7221))-v(524)*(v(519)*(v(4694)*v(530)+v(4630)*v(533)+v(4678)*v(534)+v(4646&
&)*v(537)+v(4758)*v(538)+v(4774)*v(539))+v(5850)*v(8113)))
v(8235)=2d0*v(7225)
v(6197)=mpar(11)*(v(6036)*v(6196)+v(547)*(v(542)*(v(556)*v(5671)+v(560)*v(5687)+v(557)*v(5719)+v(553)*v(5735)+v(561)*v&
&(5799)+v(562)*v(5815))+v(5997)*v(8112)))
v(7223)=v(3114)-v(6197)+mpar(9)*(-(v(5887)*v(7221))-v(524)*(v(519)*(v(4693)*v(530)+v(4629)*v(533)+v(4677)*v(534)+v(4645&
&)*v(537)+v(4757)*v(538)+v(4773)*v(539))+v(5848)*v(8113)))
v(8193)=2d0*v(7223)
v(6195)=mpar(11)*(v(6052)*v(6179)+v(547)*(v(542)*(v(554)*v(5702)+v(553)*v(5766)+v(557)*v(5798)+v(558)*v(5814)+v(555)*v&
&(5830)+v(556)*v(5846))+v(6013)*v(8114)))
v(7220)=v(3112)-v(6195)+mpar(9)*(-(v(5903)*v(7188))-v(524)*(v(519)*(v(4724)*v(530)+v(4660)*v(531)+v(4788)*v(532)+v(4804&
&)*v(533)+v(4756)*v(534)+v(4772)*v(535))+v(5864)*v(8115)))
v(8188)=2d0*v(7220)
v(6194)=mpar(11)*(v(6051)*v(6179)+v(547)*(v(542)*(v(554)*v(5701)+v(553)*v(5765)+v(557)*v(5797)+v(558)*v(5813)+v(555)*v&
&(5829)+v(556)*v(5845))+v(6012)*v(8114)))
v(7218)=v(3110)-v(6194)+mpar(9)*(-(v(5902)*v(7188))-v(524)*(v(519)*(v(4723)*v(530)+v(4659)*v(531)+v(4787)*v(532)+v(4803&
&)*v(533)+v(4755)*v(534)+v(4771)*v(535))+v(5863)*v(8115)))
v(8195)=2d0*v(7218)
v(6193)=mpar(11)*(v(6050)*v(6179)+v(547)*(v(542)*(v(554)*v(5700)+v(553)*v(5764)+v(557)*v(5796)+v(558)*v(5812)+v(555)*v&
&(5828)+v(556)*v(5844))+v(6011)*v(8114)))
v(7216)=v(3108)-v(6193)+mpar(9)*(-(v(5901)*v(7188))-v(524)*(v(519)*(v(4722)*v(530)+v(4658)*v(531)+v(4786)*v(532)+v(4802&
&)*v(533)+v(4754)*v(534)+v(4770)*v(535))+v(5862)*v(8115)))
v(8198)=2d0*v(7216)
v(6192)=mpar(11)*(v(6049)*v(6179)+v(547)*(v(542)*(v(554)*v(5699)+v(553)*v(5763)+v(557)*v(5795)+v(558)*v(5811)+v(555)*v&
&(5827)+v(556)*v(5843))+v(6010)*v(8114)))
v(7214)=v(3106)-v(6192)+mpar(9)*(-(v(5900)*v(7188))-v(524)*(v(519)*(v(4721)*v(530)+v(4657)*v(531)+v(4785)*v(532)+v(4801&
&)*v(533)+v(4753)*v(534)+v(4769)*v(535))+v(5861)*v(8115)))
v(8201)=2d0*v(7214)
v(6191)=mpar(11)*(v(6048)*v(6179)+v(547)*(v(542)*(v(554)*v(5698)+v(553)*v(5762)+v(557)*v(5794)+v(558)*v(5810)+v(555)*v&
&(5826)+v(556)*v(5842))+v(6009)*v(8114)))
v(7212)=v(3104)-v(6191)+mpar(9)*(-(v(5899)*v(7188))-v(524)*(v(519)*(v(4720)*v(530)+v(4656)*v(531)+v(4784)*v(532)+v(4800&
&)*v(533)+v(4752)*v(534)+v(4768)*v(535))+v(5860)*v(8115)))
v(8204)=2d0*v(7212)
v(6190)=mpar(11)*(v(6047)*v(6179)+v(547)*(v(542)*(v(554)*v(5697)+v(553)*v(5761)+v(557)*v(5793)+v(558)*v(5809)+v(555)*v&
&(5825)+v(556)*v(5841))+v(6008)*v(8114)))
v(7210)=-v(6190)+mpar(9)*(-(v(5898)*v(7188))-v(524)*(v(519)*(v(4719)*v(530)+v(4655)*v(531)+v(4783)*v(532)+v(4799)*v(533&
&)+v(4751)*v(534)+v(4767)*v(535))+v(5859)*v(8115)))
v(8207)=2d0*v(7210)
v(6189)=mpar(11)*(v(6046)*v(6179)+v(547)*(v(542)*(v(554)*v(5696)+v(553)*v(5760)+v(557)*v(5792)+v(558)*v(5808)+v(555)*v&
&(5824)+v(556)*v(5840))+v(6007)*v(8114)))
v(7208)=-v(6189)+mpar(9)*(-(v(5897)*v(7188))-v(524)*(v(519)*(v(4718)*v(530)+v(4654)*v(531)+v(4782)*v(532)+v(4798)*v(533&
&)+v(4750)*v(534)+v(4766)*v(535))+v(5858)*v(8115)))
v(8210)=2d0*v(7208)
v(6188)=mpar(11)*(v(6045)*v(6179)+v(547)*(v(542)*(v(554)*v(5695)+v(553)*v(5759)+v(557)*v(5791)+v(558)*v(5807)+v(555)*v&
&(5823)+v(556)*v(5839))+v(6006)*v(8114)))
v(7206)=-v(6188)+mpar(9)*(-(v(5896)*v(7188))-v(524)*(v(519)*(v(4717)*v(530)+v(4653)*v(531)+v(4781)*v(532)+v(4797)*v(533&
&)+v(4749)*v(534)+v(4765)*v(535))+v(5857)*v(8115)))
v(8213)=2d0*v(7206)
v(6187)=mpar(11)*(v(6044)*v(6179)+v(547)*(v(542)*(v(554)*v(5694)+v(553)*v(5758)+v(557)*v(5790)+v(558)*v(5806)+v(555)*v&
&(5822)+v(556)*v(5838))+v(6005)*v(8114)))
v(7204)=-v(6187)+mpar(9)*(-(v(5895)*v(7188))-v(524)*(v(519)*(v(4716)*v(530)+v(4652)*v(531)+v(4780)*v(532)+v(4796)*v(533&
&)+v(4748)*v(534)+v(4764)*v(535))+v(5856)*v(8115)))
v(8216)=2d0*v(7204)
v(6186)=mpar(11)*(v(6043)*v(6179)+v(547)*(v(542)*(v(554)*v(5693)+v(553)*v(5757)+v(557)*v(5789)+v(558)*v(5805)+v(555)*v&
&(5821)+v(556)*v(5837))+v(6004)*v(8114)))
v(7202)=-v(6186)+mpar(9)*(-(v(5894)*v(7188))-v(524)*(v(519)*(v(4715)*v(530)+v(4651)*v(531)+v(4779)*v(532)+v(4795)*v(533&
&)+v(4747)*v(534)+v(4763)*v(535))+v(5855)*v(8115)))
v(8219)=2d0*v(7202)
v(6185)=mpar(11)*(v(6042)*v(6179)+v(547)*(v(542)*(v(554)*v(5692)+v(553)*v(5756)+v(557)*v(5788)+v(558)*v(5804)+v(555)*v&
&(5820)+v(556)*v(5836))+v(6003)*v(8114)))
v(7200)=v(3102)-v(6185)+mpar(9)*(-(v(5893)*v(7188))-v(524)*(v(519)*(v(4714)*v(530)+v(4650)*v(531)+v(4778)*v(532)+v(4794&
&)*v(533)+v(4746)*v(534)+v(4762)*v(535))+v(5854)*v(8115)))
v(8222)=2d0*v(7200)
v(6184)=mpar(11)*(v(6041)*v(6179)+v(547)*(v(542)*(v(554)*v(5691)+v(553)*v(5755)+v(557)*v(5787)+v(558)*v(5803)+v(555)*v&
&(5819)+v(556)*v(5835))+v(6002)*v(8114)))
v(7198)=v(3100)-v(6184)+mpar(9)*(-(v(5892)*v(7188))-v(524)*(v(519)*(v(4713)*v(530)+v(4649)*v(531)+v(4777)*v(532)+v(4793&
&)*v(533)+v(4745)*v(534)+v(4761)*v(535))+v(5853)*v(8115)))
v(8225)=2d0*v(7198)
v(6183)=mpar(11)*(v(6040)*v(6179)+v(547)*(v(542)*(v(554)*v(5690)+v(553)*v(5754)+v(557)*v(5786)+v(558)*v(5802)+v(555)*v&
&(5818)+v(556)*v(5834))+v(6001)*v(8114)))
v(7196)=v(3098)-v(6183)+mpar(9)*(-(v(5891)*v(7188))-v(524)*(v(519)*(v(4712)*v(530)+v(4648)*v(531)+v(4776)*v(532)+v(4792&
&)*v(533)+v(4744)*v(534)+v(4760)*v(535))+v(5852)*v(8115)))
v(8228)=2d0*v(7196)
v(6182)=mpar(11)*(v(6039)*v(6179)+v(547)*(v(542)*(v(554)*v(5689)+v(553)*v(5753)+v(557)*v(5785)+v(558)*v(5801)+v(555)*v&
&(5817)+v(556)*v(5833))+v(6000)*v(8114)))
v(7194)=v(3096)-v(6182)+mpar(9)*(-(v(5890)*v(7188))-v(524)*(v(519)*(v(4711)*v(530)+v(4647)*v(531)+v(4775)*v(532)+v(4791&
&)*v(533)+v(4743)*v(534)+v(4759)*v(535))+v(5851)*v(8115)))
v(8231)=2d0*v(7194)
v(6181)=mpar(11)*(v(6038)*v(6179)+v(547)*(v(542)*(v(554)*v(5688)+v(553)*v(5752)+v(557)*v(5784)+v(558)*v(5800)+v(555)*v&
&(5816)+v(556)*v(5832))+v(5999)*v(8114)))
v(7192)=v(3094)-v(6181)+mpar(9)*(-(v(5889)*v(7188))-v(524)*(v(519)*(v(4710)*v(530)+v(4646)*v(531)+v(4774)*v(532)+v(4790&
&)*v(533)+v(4742)*v(534)+v(4758)*v(535))+v(5850)*v(8115)))
v(8234)=2d0*v(7192)
v(6180)=mpar(11)*(v(6036)*v(6179)+v(547)*(v(542)*(v(554)*v(5687)+v(553)*v(5751)+v(557)*v(5783)+v(558)*v(5799)+v(555)*v&
&(5815)+v(556)*v(5831))+v(5997)*v(8114)))
v(7190)=v(3092)-v(6180)+mpar(9)*(-(v(5887)*v(7188))-v(524)*(v(519)*(v(4709)*v(530)+v(4645)*v(531)+v(4773)*v(532)+v(4789&
&)*v(533)+v(4741)*v(534)+v(4757)*v(535))+v(5848)*v(8115)))
v(8192)=2d0*v(7190)
v(546)=v(542)*v(8107)
v(551)=-v(546)/3d0
v(545)=-(v(542)*v(8106))
v(550)=v(545)/3d0
v(7138)=(-2d0/3d0)*v(549)+v(550)+v(551)
v(7187)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6035)+v(6090)+v(6128)))-v(6052)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5886)&
&+v(5941)+v(5979)))-v(5903)*v(7140))+v(7948)
v(7184)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6034)+v(6089)+v(6127)))-v(6051)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5885)&
&+v(5940)+v(5978)))-v(5902)*v(7140))+v(7951)
v(7181)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6033)+v(6088)+v(6126)))-v(6050)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5884)&
&+v(5939)+v(5977)))-v(5901)*v(7140))+v(7954)
v(7178)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6032)+v(6087)+v(6125)))-v(6049)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5883)&
&+v(5938)+v(5976)))-v(5900)*v(7140))+v(7957)
v(7175)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6031)+v(6086)+v(6124)))-v(6048)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5882)&
&+v(5937)+v(5975)))-v(5899)*v(7140))+v(7960)
v(7172)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6030)+v(6085)+v(6123)))-v(6047)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5881)&
&+v(5936)+v(5974)))-v(5898)*v(7140))
v(7169)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6029)+v(6084)+v(6122)))-v(6046)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5880)&
&+v(5935)+v(5973)))-v(5897)*v(7140))
v(7166)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6028)+v(6083)+v(6121)))-v(6045)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5879)&
&+v(5934)+v(5972)))-v(5896)*v(7140))
v(7163)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6027)+v(6082)+v(6120)))-v(6044)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5878)&
&+v(5933)+v(5971)))-v(5895)*v(7140))
v(7160)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6026)+v(6081)+v(6119)))-v(6043)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5877)&
&+v(5932)+v(5970)))-v(5894)*v(7140))
v(7157)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6025)+v(6080)+v(6118)))-v(6042)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5876)&
&+v(5931)+v(5969)))-v(5893)*v(7140))+v(7963)
v(7154)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6024)+v(6079)+v(6117)))-v(6041)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5875)&
&+v(5930)+v(5968)))-v(5892)*v(7140))+v(7966)
v(7151)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6023)+v(6078)+v(6116)))-v(6040)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5874)&
&+v(5929)+v(5967)))-v(5891)*v(7140))+v(7969)
v(7148)=v(2894)+(2d0/3d0)*v(2908)+v(2946)+mpar(11)*(-(v(547)*((-2d0/3d0)*v(6022)+v(6077)+v(6115)))-v(6039)*v(7138))&
&+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5873)+v(5928)+v(5966)))-v(5890)*v(7140))
v(7145)=v(2893)+(2d0/3d0)*v(2907)+v(2945)+mpar(11)*(-(v(547)*((-2d0/3d0)*v(6021)+v(6076)+v(6114)))-v(6038)*v(7138))&
&+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5872)+v(5927)+v(5965)))-v(5889)*v(7140))
v(7142)=mpar(11)*(-(v(547)*((-2d0/3d0)*v(6017)+v(6075)+v(6113)))-v(6036)*v(7138))+mpar(9)*(-(v(524)*((-2d0/3d0)*v(5868)&
&+v(5926)+v(5964)))-v(5887)*v(7140))+v(7974)
v(544)=v(549)/3d0
v(6162)=v(544)+(-2d0/3d0)*v(545)+v(551)
v(6178)=mpar(11)*(v(547)*(v(6090)+(-2d0/3d0)*v(6112)+v(6144))+v(6052)*v(6162))
v(7137)=-v(6178)+mpar(9)*(-(v(524)*(v(5941)+(-2d0/3d0)*v(5963)+v(5995)))-v(5903)*v(7104))+v(7949)
v(6177)=mpar(11)*(v(547)*(v(6089)+(-2d0/3d0)*v(6111)+v(6143))+v(6051)*v(6162))
v(7135)=-v(6177)+mpar(9)*(-(v(524)*(v(5940)+(-2d0/3d0)*v(5962)+v(5994)))-v(5902)*v(7104))+v(7952)
v(6176)=mpar(11)*(v(547)*(v(6088)+(-2d0/3d0)*v(6110)+v(6142))+v(6050)*v(6162))
v(7133)=-v(6176)+mpar(9)*(-(v(524)*(v(5939)+(-2d0/3d0)*v(5961)+v(5993)))-v(5901)*v(7104))+v(7955)
v(6175)=mpar(11)*(v(547)*(v(6087)+(-2d0/3d0)*v(6109)+v(6141))+v(6049)*v(6162))
v(7131)=-v(6175)+mpar(9)*(-(v(524)*(v(5938)+(-2d0/3d0)*v(5960)+v(5992)))-v(5900)*v(7104))+v(7958)
v(6174)=mpar(11)*(v(547)*(v(6086)+(-2d0/3d0)*v(6108)+v(6140))+v(6048)*v(6162))
v(7129)=-v(6174)+mpar(9)*(-(v(524)*(v(5937)+(-2d0/3d0)*v(5959)+v(5991)))-v(5899)*v(7104))+v(7961)
v(6173)=mpar(11)*(v(547)*(v(6085)+(-2d0/3d0)*v(6107)+v(6139))+v(6047)*v(6162))
v(7127)=-v(6173)+mpar(9)*(-(v(524)*(v(5936)+(-2d0/3d0)*v(5958)+v(5990)))-v(5898)*v(7104))
v(6172)=mpar(11)*(v(547)*(v(6084)+(-2d0/3d0)*v(6106)+v(6138))+v(6046)*v(6162))
v(7125)=-v(6172)+mpar(9)*(-(v(524)*(v(5935)+(-2d0/3d0)*v(5957)+v(5989)))-v(5897)*v(7104))
v(6171)=mpar(11)*(v(547)*(v(6083)+(-2d0/3d0)*v(6105)+v(6137))+v(6045)*v(6162))
v(7123)=-v(6171)+mpar(9)*(-(v(524)*(v(5934)+(-2d0/3d0)*v(5956)+v(5988)))-v(5896)*v(7104))
v(6170)=mpar(11)*(v(547)*(v(6082)+(-2d0/3d0)*v(6104)+v(6136))+v(6044)*v(6162))
v(7121)=-v(6170)+mpar(9)*(-(v(524)*(v(5933)+(-2d0/3d0)*v(5955)+v(5987)))-v(5895)*v(7104))
v(6169)=mpar(11)*(v(547)*(v(6081)+(-2d0/3d0)*v(6103)+v(6135))+v(6043)*v(6162))
v(7119)=-v(6169)+mpar(9)*(-(v(524)*(v(5932)+(-2d0/3d0)*v(5954)+v(5986)))-v(5894)*v(7104))
v(6168)=mpar(11)*(v(547)*(v(6080)+(-2d0/3d0)*v(6102)+v(6134))+v(6042)*v(6162))
v(7117)=-v(6168)+mpar(9)*(-(v(524)*(v(5931)+(-2d0/3d0)*v(5953)+v(5985)))-v(5893)*v(7104))+v(7964)
v(6167)=mpar(11)*(v(547)*(v(6079)+(-2d0/3d0)*v(6101)+v(6133))+v(6041)*v(6162))
v(7115)=-v(6167)+mpar(9)*(-(v(524)*(v(5930)+(-2d0/3d0)*v(5952)+v(5984)))-v(5892)*v(7104))+v(7967)
v(6166)=mpar(11)*(v(547)*(v(6078)+(-2d0/3d0)*v(6100)+v(6132))+v(6040)*v(6162))
v(7113)=-v(6166)+mpar(9)*(-(v(524)*(v(5929)+(-2d0/3d0)*v(5951)+v(5983)))-v(5891)*v(7104))+v(7970)
v(6165)=mpar(11)*(v(547)*(v(6077)+(-2d0/3d0)*v(6099)+v(6131))+v(6039)*v(6162))
v(7111)=v(2894)+v(2919)+(2d0/3d0)*v(2935)-v(6165)+mpar(9)*(-(v(524)*(v(5928)+(-2d0/3d0)*v(5950)+v(5982)))-v(5890)*v&
&(7104))
v(6164)=mpar(11)*(v(547)*(v(6076)+(-2d0/3d0)*v(6098)+v(6130))+v(6038)*v(6162))
v(7109)=v(2893)+v(2918)-v(6164)+mpar(9)*(-(v(524)*(v(5927)+(-2d0/3d0)*v(5949)+v(5981)))-v(5889)*v(7104))+v(7108)
v(6163)=mpar(11)*(v(547)*(v(6075)+(-2d0/3d0)*v(6094)+v(6129))+v(6036)*v(6162))
v(7106)=-v(6163)+mpar(9)*(-(v(524)*(v(5926)+(-2d0/3d0)*v(5945)+v(5980)))-v(5887)*v(7104))+v(7975)
v(6145)=v(544)+(2d0/3d0)*v(546)+v(550)
v(6161)=mpar(11)*(v(547)*((2d0/3d0)*v(6074)+v(6128)+v(6144))+v(6052)*v(6145))
v(7103)=-v(6161)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5925)+v(5979)+v(5995)))-v(5903)*v(7070))+v(7947)
v(6160)=mpar(11)*(v(547)*((2d0/3d0)*v(6073)+v(6127)+v(6143))+v(6051)*v(6145))
v(7101)=-v(6160)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5924)+v(5978)+v(5994)))-v(5902)*v(7070))+v(7950)
v(6159)=mpar(11)*(v(547)*((2d0/3d0)*v(6072)+v(6126)+v(6142))+v(6050)*v(6145))
v(7099)=-v(6159)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5923)+v(5977)+v(5993)))-v(5901)*v(7070))+v(7953)
v(6158)=mpar(11)*(v(547)*((2d0/3d0)*v(6071)+v(6125)+v(6141))+v(6049)*v(6145))
v(7097)=-v(6158)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5922)+v(5976)+v(5992)))-v(5900)*v(7070))+v(7956)
v(6157)=mpar(11)*(v(547)*((2d0/3d0)*v(6070)+v(6124)+v(6140))+v(6048)*v(6145))
v(7095)=-v(6157)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5921)+v(5975)+v(5991)))-v(5899)*v(7070))+v(7959)
v(6156)=mpar(11)*(v(547)*((2d0/3d0)*v(6069)+v(6123)+v(6139))+v(6047)*v(6145))
v(7093)=-v(6156)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5920)+v(5974)+v(5990)))-v(5898)*v(7070))
v(6155)=mpar(11)*(v(547)*((2d0/3d0)*v(6068)+v(6122)+v(6138))+v(6046)*v(6145))
v(7091)=-v(6155)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5919)+v(5973)+v(5989)))-v(5897)*v(7070))
v(6154)=mpar(11)*(v(547)*((2d0/3d0)*v(6067)+v(6121)+v(6137))+v(6045)*v(6145))
v(7089)=-v(6154)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5918)+v(5972)+v(5988)))-v(5896)*v(7070))
v(6153)=mpar(11)*(v(547)*((2d0/3d0)*v(6066)+v(6120)+v(6136))+v(6044)*v(6145))
v(7087)=-v(6153)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5917)+v(5971)+v(5987)))-v(5895)*v(7070))
v(6152)=mpar(11)*(v(547)*((2d0/3d0)*v(6065)+v(6119)+v(6135))+v(6043)*v(6145))
v(7085)=-v(6152)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5916)+v(5970)+v(5986)))-v(5894)*v(7070))
v(6151)=mpar(11)*(v(547)*((2d0/3d0)*v(6064)+v(6118)+v(6134))+v(6042)*v(6145))
v(7083)=-v(6151)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5915)+v(5969)+v(5985)))-v(5893)*v(7070))+v(7962)
v(6150)=mpar(11)*(v(547)*((2d0/3d0)*v(6063)+v(6117)+v(6133))+v(6041)*v(6145))
v(7081)=-v(6150)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5914)+v(5968)+v(5984)))-v(5892)*v(7070))+v(7965)
v(6149)=mpar(11)*(v(547)*((2d0/3d0)*v(6062)+v(6116)+v(6132))+v(6040)*v(6145))
v(7079)=-v(6149)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5913)+v(5967)+v(5983)))-v(5891)*v(7070))+v(7968)
v(6148)=mpar(11)*(v(547)*((2d0/3d0)*v(6061)+v(6115)+v(6131))+v(6039)*v(6145))
v(7077)=v(2919)+v(2946)-v(6148)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5912)+v(5966)+v(5982)))-v(5890)*v(7070))+v(7076)
v(6147)=mpar(11)*(v(547)*((2d0/3d0)*v(6060)+v(6114)+v(6130))+v(6038)*v(6145))
v(7074)=(2d0/3d0)*v(2882)+v(2918)+v(2945)-v(6147)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5911)+v(5965)+v(5981)))-v(5889)*v(7070&
&))
v(6146)=mpar(11)*(v(547)*((2d0/3d0)*v(6056)+v(6113)+v(6129))+v(6036)*v(6145))
v(7072)=-v(6146)+mpar(9)*(-(v(524)*((2d0/3d0)*v(5907)+v(5964)+v(5980)))-v(5887)*v(7070))+v(7973)
v(565)=-v(117)+v(7496)*x(12)
v(8134)=v(565)*v(7522)
v(6318)=-(v(565)*v(8007))
v(6323)=-(v(6318)*v(7496))
v(6315)=(v(565)*v(565))
v(6299)=v(565)*v(8122)
v(566)=-v(119)+v(7496)*x(13)
v(8131)=v(566)*v(7522)
v(8116)=v(232)*v(566)
v(6630)=-(v(566)*v(8007))
v(6627)=(v(566)*v(566))
v(6306)=v(7496)*v(8116)
v(6635)=2d0*v(6306)
v(6284)=-(v(768)*v(8116))
v(567)=-v(120)+v(7496)*v(7532)
v(8128)=v(567)*v(7522)
v(8117)=v(232)*v(567)
v(6818)=-(v(567)*v(8007))
v(6815)=(v(567)*v(567))
v(6304)=-(v(782)*v(8117))
v(6286)=v(7496)*v(8117)
v(6832)=-(v(567)*v(6286)*v(8118))
v(6267)=v(6286)+v(6306)
v(568)=-v(121)+v(7496)*x(14)
v(8120)=v(232)*v(568)
v(8119)=v(568)*v(7522)
v(6385)=v(6323)*v(8119)
v(6337)=-(v(6286)*v(8119))
v(6302)=-(v(782)*v(8120))
v(6266)=v(7496)*v(8120)
v(8121)=v(6266)*v(7522)
v(6609)=v(6266)/2d0
v(8155)=5040d0*v(6609)
v(6359)=v(566)*v(8121)
v(6358)=v(6359)+v(6385)
v(6371)=v(6358)*v(8119)
v(6293)=v(568)*v(8121)
v(6234)=(-2d0)*v(8120)
v(6239)=-(v(6234)*v(7496))
v(6238)=v(6234)*v(768)
v(6237)=v(6234)*v(767)
v(6236)=v(6234)*v(766)
v(6235)=v(6234)*v(765)
v(6233)=v(6234)*v(764)
v(6231)=(v(568)*v(568))
v(6232)=v(1738)*v(6231)
v(588)=v(232)*v(6231)
v(569)=-v(122)+v(7496)*x(16)
v(8124)=-(v(232)*v(569))
v(8123)=v(569)*v(7522)
v(6669)=v(6635)*v(8123)
v(6301)=v(569)*v(8122)
v(6276)=v(6266)*v(8123)
v(6264)=v(7496)*v(8124)
v(6775)=-v(6264)/2d0
v(6274)=v(6264)*v(8123)
v(6665)=v(6274)+v(6293)
v(6243)=2d0*v(8124)
v(6248)=-(v(6243)*v(7496))
v(6247)=v(6243)*v(783)
v(6634)=v(6238)+v(6247)+v(6630)*v(714)
v(6246)=v(6243)*v(782)
v(6633)=v(6237)+v(6246)+v(6630)*v(713)
v(6245)=v(6243)*v(768)
v(6632)=v(6236)+v(6245)+v(6630)*v(712)
v(6244)=v(6243)*v(781)
v(6631)=v(6235)+v(6244)+v(6630)*v(711)
v(6242)=v(6243)*v(780)
v(6629)=v(6233)+v(6242)+v(6630)*v(710)
v(6240)=(v(569)*v(569))
v(6241)=v(1738)*v(6240)
v(6628)=v(6232)+v(6241)+v(1738)*v(6627)
v(605)=v(232)*v(6240)
v(570)=-v(123)+v(7496)*x(15)
v(8133)=v(568)*v(569)-v(566)*v(570)
v(8130)=-(v(567)*v(568))+v(569)*v(570)
v(8127)=-(v(565)*v(569))+v(568)*v(570)
v(8126)=v(232)*v(570)
v(8125)=v(570)*v(7522)
v(6387)=v(6323)*v(8125)
v(6363)=-(v(6306)*v(8125))
v(6334)=v(6239)*v(8125)
v(6598)=v(6334)/6d0
v(6425)=v(6334)*v(8123)
v(6374)=v(6334)*v(8119)
v(6347)=v(6334)*v(8125)
v(6305)=v(6304)-v(232)*(-(v(570)*v(714))+v(569)*v(768)+v(565)*v(782)+v(568)*v(783))
v(6303)=v(6301)+v(6302)-v(232)*(-(v(570)*v(713))-v(566)*v(797))
v(6300)=v(6299)-v(232)*(-(v(570)*v(712))+v(569)*v(766)+v(567)*v(767)+v(568)*v(768))
v(6298)=-(v(232)*(-(v(570)*v(711))+v(569)*v(765)+v(568)*v(781)+v(565)*v(796)+v(567)*v(796)))
v(6297)=-(v(232)*(-(v(570)*v(710))+v(569)*v(764)+v(568)*v(780)+v(565)*v(795)+v(567)*v(795)))
v(6296)=v(1738)*v(8133)
v(6285)=v(6284)-v(232)*(-(v(568)*v(737))+v(565)*v(768)+v(569)*v(782)+v(570)*v(783))
v(6283)=v(6299)-v(232)*(-(v(568)*v(736))+v(566)*v(767)+v(570)*v(782)+v(569)*v(797))
v(6281)=-(v(768)*v(8126))
v(6282)=v(6281)+v(6301)-v(232)*(-(v(568)*v(735))-v(567)*v(766))
v(6280)=-(v(232)*(-(v(568)*v(734))+v(565)*v(765)+v(566)*v(765)+v(570)*v(781)+v(569)*v(796)))
v(6279)=-(v(232)*(-(v(568)*v(733))+v(565)*v(764)+v(566)*v(764)+v(570)*v(780)+v(569)*v(795)))
v(6278)=v(1738)*v(8130)
v(6265)=v(7496)*v(8126)
v(6614)=-v(6265)/2d0
v(8150)=(-5040d0)*v(6614)
v(6313)=-(v(6265)*v(8125))
v(6384)=v(6293)+v(6313)
v(6295)=v(6265)*v(8119)
v(6275)=v(6265)*v(8123)
v(6263)=v(6281)+v(6302)-v(232)*(-(v(569)*v(704))-v(565)*v(783))
v(6262)=v(6304)-v(232)*(-(v(569)*v(703))+v(570)*v(767)+v(566)*v(782)+v(568)*v(797))
v(6261)=v(6284)-v(232)*(-(v(569)*v(702))+v(570)*v(766)+v(568)*v(767)+v(567)*v(768))
v(6260)=-(v(232)*(-(v(569)*v(701))+v(570)*v(765)+v(566)*v(781)+v(567)*v(781)+v(568)*v(796)))
v(6259)=-(v(232)*(-(v(569)*v(700))+v(570)*v(764)+v(566)*v(780)+v(567)*v(780)+v(568)*v(795)))
v(6258)=v(1738)*v(8127)
v(6252)=(-2d0)*v(8126)
v(6257)=-(v(6252)*v(7496))
v(6256)=v(6252)*v(782)
v(6822)=v(6247)+v(6256)+v(6818)*v(737)
v(6322)=v(6238)+v(6256)+v(6318)*v(704)
v(6255)=v(6252)*v(797)
v(6821)=v(6246)+v(6255)+v(6818)*v(736)
v(6321)=v(6237)+v(6255)+v(6318)*v(703)
v(6254)=v(6252)*v(767)
v(6820)=v(6245)+v(6254)+v(6818)*v(735)
v(6320)=v(6236)+v(6254)+v(6318)*v(702)
v(6253)=v(6252)*v(796)
v(6819)=v(6244)+v(6253)+v(6818)*v(734)
v(6319)=v(6235)+v(6253)+v(6318)*v(701)
v(6251)=v(6252)*v(795)
v(6817)=v(6242)+v(6251)+v(6818)*v(733)
v(6317)=v(6233)+v(6251)+v(6318)*v(700)
v(6249)=(v(570)*v(570))
v(6250)=v(1738)*v(6249)
v(6816)=v(6241)+v(6250)+v(1738)*v(6815)
v(6316)=v(6232)+v(6250)+v(1738)*v(6315)
v(606)=v(232)*v(6249)
v(593)=v(232)*v(8127)
v(6644)=v(593)*v(6592)
v(6646)=v(6295)-v(6644)+v(6669)
v(6655)=v(6646)*v(8123)
v(6645)=v(6646)-v(6669)+v(6264)*v(8128)
v(6654)=v(6645)*v(8123)
v(6700)=v(6371)+v(6654)+v(6665)*v(8131)
v(6277)=v(6644)+v(6267)*v(8123)
v(8129)=v(6277)+v(6295)
v(6835)=v(6248)*v(8128)+v(8129)
v(6670)=v(6669)+v(8129)
v(6273)=v(7522)*(v(569)*v(6263)-v(593)*v(783))
v(6272)=v(7522)*(v(569)*v(6262)-v(593)*v(782))
v(6271)=v(7522)*(v(569)*v(6261)-v(593)*v(768))
v(6270)=v(7522)*(v(569)*v(6260)-v(593)*v(781))
v(6269)=v(7522)*(v(569)*v(6259)-v(593)*v(780))
v(6268)=v(569)*(v(593)*v(7518)+v(6258)*v(7522))
v(609)=v(593)*v(8123)
v(574)=v(232)*v(8130)
v(6642)=v(574)*v(6771)
v(6639)=v(574)*v(6604)
v(6336)=v(574)*v(6592)
v(6360)=-v(6275)+v(6336)+v(6359)
v(6372)=v(6360)*v(8119)
v(6338)=v(6275)+v(6336)-v(6337)
v(6881)=v(6338)/6d0
v(6657)=v(6338)*v(8123)
v(6349)=v(6338)*v(8125)
v(6327)=v(574)*v(6768)
v(6294)=v(6336)+v(6337)
v(8132)=v(6275)+v(6294)
v(6668)=v(6239)*v(8131)+v(8132)
v(6386)=v(6385)+v(8132)
v(6292)=v(6327)+v(6285)*v(8119)
v(6291)=v(6639)+v(6283)*v(8119)
v(6290)=v(7522)*(v(568)*v(6282)-v(574)*v(766))
v(6289)=v(7522)*(v(568)*v(6280)-v(574)*v(765))
v(6288)=v(7522)*(v(568)*v(6279)-v(574)*v(764))
v(6287)=v(568)*(v(574)*v(7518)+v(6278)*v(7522))
v(590)=v(574)*v(8119)
v(573)=v(232)*v(8133)
v(6355)=v(573)*v(6771)
v(6331)=v(573)*v(6592)
v(8135)=v(6276)-v(6331)
v(6364)=v(6276)+v(6331)-v(6363)
v(6801)=v(6364)/6d0
v(6656)=v(6364)*v(8123)
v(6375)=v(6364)*v(8119)
v(6449)=v(6349)+v(6375)+v(6334)*v(8134)
v(6333)=-(v(6265)*v(8128))+v(8135)
v(6346)=v(6333)*v(8125)
v(6446)=v(6346)+v(6372)+v(6384)*v(8134)
v(6332)=v(6387)+v(8135)
v(6345)=v(6332)*v(8125)
v(6314)=v(6331)+v(6363)
v(8136)=v(6276)+v(6314)
v(6834)=v(6257)*v(8128)+v(8136)
v(6388)=v(6387)+v(8136)
v(6312)=v(6355)+v(6305)*v(8125)
v(6311)=v(7522)*(v(570)*v(6303)-v(573)*v(797))
v(6310)=v(7522)*(v(570)*v(6300)-v(573)*v(767))
v(6309)=v(7522)*(v(570)*v(6298)-v(573)*v(796))
v(6308)=v(7522)*(v(570)*v(6297)-v(573)*v(795))
v(6307)=v(570)*(v(573)*v(7518)+v(6296)*v(7522))
v(608)=v(573)*v(8125)
v(571)=v(588)+v(606)+v(232)*v(6315)
v(8138)=v(568)*v(571)+v(569)*v(573)+v(566)*v(574)
v(8137)=v(570)*v(571)+v(567)*v(573)+v(569)*v(574)
v(6382)=v(571)*v(6592)
v(6383)=v(6293)+v(6382)+v(6323)*v(8134)
v(6396)=(v(569)*v(6332)+v(566)*v(6358)+v(568)*v(6383))*v(7522)
v(6409)=v(6396)*v(8119)
v(6381)=v(6292)+v(6312)+(v(565)*v(6322)-v(571)*v(704))*v(7522)
v(6380)=v(6291)+v(6311)+(v(565)*v(6321)-v(571)*v(703))*v(7522)
v(6379)=v(6290)+v(6310)+(v(565)*v(6320)-v(571)*v(702))*v(7522)
v(6378)=v(6289)+v(6309)+(v(565)*v(6319)-v(571)*v(701))*v(7522)
v(6377)=v(6288)+v(6308)+(v(565)*v(6317)-v(571)*v(700))*v(7522)
v(6376)=v(6287)+v(6307)+v(565)*(v(571)*v(7518)+v(6316)*v(7522))
v(6361)=-v(6274)+v(6382)-v(6306)*v(8128)
v(6362)=v(6361)+v(6239)*v(8119)
v(6357)=v(7522)*(v(566)*v(6285)+v(569)*v(6305)+v(568)*v(6322)-v(574)*v(714)-v(571)*v(768)-v(573)*v(783))
v(6354)=v(571)*v(6604)
v(6356)=v(6354)+v(6355)+(v(566)*v(6283)+v(569)*v(6303)+v(568)*v(6321)-v(574)*v(713))*v(7522)
v(6353)=v(7522)*(v(566)*v(6282)+v(569)*v(6300)+v(568)*v(6320)-v(574)*v(712)-v(571)*v(766)-v(573)*v(768))
v(6352)=v(7522)*(v(566)*v(6280)+v(569)*v(6298)+v(568)*v(6319)-v(574)*v(711)-v(571)*v(765)-v(573)*v(781))
v(6351)=v(7522)*(v(566)*v(6279)+v(569)*v(6297)+v(568)*v(6317)-v(574)*v(710)-v(571)*v(764)-v(573)*v(780))
v(6350)=(v(566)*v(6278)+v(569)*v(6296)+v(568)*v(6316))*v(7522)+v(7518)*v(8138)
v(6335)=v(6361)+v(6257)*v(8125)
v(6400)=(v(566)*v(6334)+v(569)*v(6335)+v(568)*v(6388))*v(7522)
v(6486)=v(6400)*v(8123)
v(6436)=v(6400)*v(8125)
v(6412)=v(6400)*v(8119)
v(6330)=v(7522)*(v(569)*v(6285)+v(567)*v(6305)+v(570)*v(6322)-v(573)*v(737)-v(571)*v(782)-v(574)*v(783))
v(6329)=v(6642)+v(7522)*(v(569)*v(6283)+v(567)*v(6303)+v(570)*v(6321)-v(573)*v(736)-v(571)*v(797))
v(6328)=v(6327)+v(6354)+(v(569)*v(6282)+v(567)*v(6300)+v(570)*v(6320)-v(573)*v(735))*v(7522)
v(6326)=v(7522)*(v(569)*v(6280)+v(567)*v(6298)+v(570)*v(6319)-v(573)*v(734)-v(574)*v(781)-v(571)*v(796))
v(6325)=v(7522)*(v(569)*v(6279)+v(567)*v(6297)+v(570)*v(6317)-v(573)*v(733)-v(574)*v(780)-v(571)*v(795))
v(6324)=(v(569)*v(6278)+v(567)*v(6296)+v(570)*v(6316))*v(7522)+v(7518)*v(8137)
v(577)=v(7522)*v(8137)
v(6401)=v(577)*v(6592)
v(6423)=-v(6401)+(v(567)*v(6333)+v(569)*v(6360)+v(570)*v(6384))*v(7522)
v(6435)=v(6423)*v(8125)
v(6422)=-v(6401)+(v(567)*v(6332)+v(569)*v(6358)+v(570)*v(6383))*v(7522)
v(6434)=v(6422)*v(8125)
v(6402)=v(6374)+v(6401)+v(6657)+v(6364)*v(8131)
v(6704)=-v(6401)+v(6402)
v(6691)=v(6402)*v(8123)
v(6413)=v(6402)*v(8119)
v(6393)=v(577)*v(6771)
v(6348)=v(6401)+v(6335)*v(8125)
v(6846)=v(6348)+v(6657)+v(6834)*v(8128)
v(6448)=v(6348)+v(6374)+v(6388)*v(8134)
v(6344)=v(6393)+v(6330)*v(8125)
v(6343)=v(7522)*(v(570)*v(6329)-v(577)*v(797))
v(6342)=v(7522)*(v(570)*v(6328)-v(577)*v(767))
v(6341)=v(7522)*(v(570)*v(6326)-v(577)*v(796))
v(6340)=v(7522)*(v(570)*v(6325)-v(577)*v(795))
v(6339)=v(570)*(v(577)*v(7518)+v(6324)*v(7522))
v(612)=v(577)*v(8125)
v(576)=v(7522)*v(8138)
v(6677)=v(576)*v(6771)
v(6674)=v(576)*v(6604)
v(6418)=v(576)*v(6768)
v(6397)=v(576)*v(6592)
v(6427)=v(6347)+v(6397)+v(6656)+v(6338)*v(8128)
v(6845)=-v(6397)+v(6427)
v(6857)=v(6436)+v(6691)+v(6845)*v(8128)
v(6692)=v(6427)*v(8123)
v(6739)=v(6412)+v(6692)+v(6704)*v(8131)
v(6438)=v(6427)*v(8125)
v(6510)=v(6413)+v(6438)+v(6449)*v(8134)
v(6398)=v(6397)+(v(569)*v(6333)+v(566)*v(6360)+v(568)*v(6384))*v(7522)
v(6410)=v(6398)*v(8119)
v(6507)=v(6410)+v(6435)+v(6446)*v(8134)
v(6373)=v(6397)+v(6362)*v(8119)
v(6703)=v(6373)+v(6656)+v(6668)*v(8131)
v(6447)=v(6347)+v(6373)+v(6386)*v(8134)
v(6370)=v(6418)+v(6357)*v(8119)
v(6369)=v(6674)+v(6356)*v(8119)
v(6368)=v(7522)*(v(568)*v(6353)-v(576)*v(766))
v(6367)=v(7522)*(v(568)*v(6352)-v(576)*v(765))
v(6366)=v(7522)*(v(568)*v(6351)-v(576)*v(764))
v(6365)=v(568)*(v(576)*v(7518)+v(6350)*v(7522))
v(592)=v(576)*v(8119)
v(572)=v(590)+v(608)+v(571)*v(8134)
v(8141)=v(570)*v(572)+v(569)*v(576)+v(567)*v(577)
v(8140)=v(568)*v(572)+v(566)*v(576)+v(569)*v(577)
v(6444)=v(6344)+v(6370)+(v(565)*v(6381)-v(572)*v(704))*v(7522)
v(6443)=v(6343)+v(6369)+(v(565)*v(6380)-v(572)*v(703))*v(7522)
v(6442)=v(6342)+v(6368)+(v(565)*v(6379)-v(572)*v(702))*v(7522)
v(6441)=v(6341)+v(6367)+(v(565)*v(6378)-v(572)*v(701))*v(7522)
v(6440)=v(6340)+v(6366)+(v(565)*v(6377)-v(572)*v(700))*v(7522)
v(6439)=v(6339)+v(6365)+v(565)*(v(572)*v(7518)+v(6376)*v(7522))
v(6424)=v(572)*v(6592)
v(8139)=v(6424)+v(6425)
v(6445)=v(6345)+v(6371)+v(6424)+v(6383)*v(8134)
v(6483)=(v(566)*v(6396)+v(569)*v(6422)+v(568)*v(6445))*v(7522)
v(6495)=v(6483)*v(8119)
v(6426)=(v(567)*v(6335)+v(570)*v(6388))*v(7522)+v(8139)
v(6421)=v(7522)*(v(567)*v(6330)+v(569)*v(6357)+v(570)*v(6381)-v(577)*v(737)-v(572)*v(782)-v(576)*v(783))
v(6420)=v(6677)+v(7522)*(v(567)*v(6329)+v(569)*v(6356)+v(570)*v(6380)-v(577)*v(736)-v(572)*v(797))
v(6417)=v(572)*v(6604)
v(6419)=v(6417)+v(6418)+(v(567)*v(6328)+v(569)*v(6353)+v(570)*v(6379)-v(577)*v(735))*v(7522)
v(6416)=v(7522)*(v(567)*v(6326)+v(569)*v(6352)+v(570)*v(6378)-v(577)*v(734)-v(576)*v(781)-v(572)*v(796))
v(6415)=v(7522)*(v(567)*v(6325)+v(569)*v(6351)+v(570)*v(6377)-v(577)*v(733)-v(576)*v(780)-v(572)*v(795))
v(6414)=(v(567)*v(6324)+v(569)*v(6350)+v(570)*v(6376))*v(7522)+v(7518)*v(8141)
v(6399)=(v(566)*v(6362)+v(568)*v(6386))*v(7522)+v(8139)
v(6460)=(v(569)*v(6399)+v(567)*v(6400)+v(570)*v(6447))*v(7522)
v(6558)=v(6460)*v(8123)
v(6498)=v(6460)*v(8119)
v(6472)=v(6460)*v(8125)
v(6395)=v(7522)*(v(569)*v(6330)+v(566)*v(6357)+v(568)*v(6381)-v(576)*v(714)-v(572)*v(768)-v(577)*v(783))
v(6394)=v(6393)+v(6417)+(v(569)*v(6329)+v(566)*v(6356)+v(568)*v(6380)-v(576)*v(713))*v(7522)
v(6392)=v(7522)*(v(569)*v(6328)+v(566)*v(6353)+v(568)*v(6379)-v(576)*v(712)-v(572)*v(766)-v(577)*v(768))
v(6391)=v(7522)*(v(569)*v(6326)+v(566)*v(6352)+v(568)*v(6378)-v(576)*v(711)-v(572)*v(765)-v(577)*v(781))
v(6390)=v(7522)*(v(569)*v(6325)+v(566)*v(6351)+v(568)*v(6377)-v(576)*v(710)-v(572)*v(764)-v(577)*v(780))
v(6389)=(v(569)*v(6324)+v(566)*v(6350)+v(568)*v(6376))*v(7522)+v(7518)*v(8140)
v(580)=v(7522)*v(8140)
v(6712)=v(580)*v(6771)
v(6709)=v(580)*v(6604)
v(6462)=v(580)*v(6592)
v(6484)=v(6462)+(v(566)*v(6398)+v(569)*v(6423)+v(568)*v(6446))*v(7522)
v(6496)=v(6484)*v(8119)
v(6463)=v(6462)+v(6691)+(v(567)*v(6427)+v(570)*v(6449))*v(7522)
v(6727)=v(6463)*v(8123)
v(6750)=v(6498)+v(6727)+v(6739)*v(8131)
v(6474)=v(6463)*v(8125)
v(6453)=v(580)*v(6768)
v(6411)=v(6462)+v(6399)*v(8119)
v(6738)=v(6411)+v(6691)+v(6703)*v(8131)
v(6508)=v(6411)+v(6436)+v(6447)*v(8134)
v(6408)=v(6453)+v(6395)*v(8119)
v(6407)=v(6709)+v(6394)*v(8119)
v(6406)=v(7522)*(v(568)*v(6392)-v(580)*v(766))
v(6405)=v(7522)*(v(568)*v(6391)-v(580)*v(765))
v(6404)=v(7522)*(v(568)*v(6390)-v(580)*v(764))
v(6403)=v(568)*(v(580)*v(7518)+v(6389)*v(7522))
v(596)=v(580)*v(8119)
v(579)=v(7522)*v(8141)
v(6480)=v(579)*v(6771)
v(6457)=v(579)*v(6592)
v(6488)=v(6457)+v(6692)+(v(566)*v(6402)+v(568)*v(6449))*v(7522)
v(6726)=v(6488)*v(8123)
v(6869)=v(6472)+v(6726)+v(6857)*v(8128)
v(6499)=v(6488)*v(8119)
v(6521)=v(6474)+v(6499)+v(6510)*v(8134)
v(6459)=-v(6457)+(v(569)*v(6398)+v(567)*v(6423)+v(570)*v(6446))*v(7522)
v(6471)=v(6459)*v(8125)
v(6518)=v(6471)+v(6496)+v(6507)*v(8134)
v(6458)=-v(6457)+(v(569)*v(6396)+v(567)*v(6422)+v(570)*v(6445))*v(7522)
v(6470)=v(6458)*v(8125)
v(6437)=v(6457)+v(6426)*v(8125)
v(6858)=v(6437)+v(6692)+v(6846)*v(8128)
v(6509)=v(6412)+v(6437)+v(6448)*v(8134)
v(6433)=v(6480)+v(6421)*v(8125)
v(6432)=v(7522)*(v(570)*v(6420)-v(579)*v(797))
v(6431)=v(7522)*(v(570)*v(6419)-v(579)*v(767))
v(6430)=v(7522)*(v(570)*v(6416)-v(579)*v(796))
v(6429)=v(7522)*(v(570)*v(6415)-v(579)*v(795))
v(6428)=v(570)*(v(579)*v(7518)+v(6414)*v(7522))
v(614)=v(579)*v(8125)
v(575)=v(592)+v(612)+v(572)*v(8134)
v(8144)=v(568)*v(575)+v(569)*v(579)+v(566)*v(580)
v(8143)=v(570)*v(575)+v(567)*v(579)+v(569)*v(580)
v(6505)=v(6408)+v(6433)+(v(565)*v(6444)-v(575)*v(704))*v(7522)
v(6504)=v(6407)+v(6432)+(v(565)*v(6443)-v(575)*v(703))*v(7522)
v(6503)=v(6406)+v(6431)+(v(565)*v(6442)-v(575)*v(702))*v(7522)
v(6502)=v(6405)+v(6430)+(v(565)*v(6441)-v(575)*v(701))*v(7522)
v(6501)=v(6404)+v(6429)+(v(565)*v(6440)-v(575)*v(700))*v(7522)
v(6500)=v(6403)+v(6428)+v(565)*(v(575)*v(7518)+v(6439)*v(7522))
v(6485)=v(575)*v(6592)
v(8142)=v(6485)+v(6486)
v(6506)=v(6409)+v(6434)+v(6485)+v(6445)*v(8134)
v(6556)=(v(569)*v(6458)+v(566)*v(6483)+v(568)*v(6506))*v(7522)
v(6580)=v(6556)*v(8119)
v(6487)=(v(566)*v(6399)+v(568)*v(6447))*v(7522)+v(8142)
v(6532)=(v(567)*v(6460)+v(569)*v(6487)+v(570)*v(6508))*v(7522)
v(6612)=v(6532)*v(8123)
v(6584)=v(6532)*v(8119)
v(6545)=v(6532)*v(8125)
v(6482)=v(7522)*(v(566)*v(6395)+v(569)*v(6421)+v(568)*v(6444)-v(580)*v(714)-v(575)*v(768)-v(579)*v(783))
v(6479)=v(575)*v(6604)
v(6481)=v(6479)+v(6480)+(v(566)*v(6394)+v(569)*v(6420)+v(568)*v(6443)-v(580)*v(713))*v(7522)
v(6478)=v(7522)*(v(566)*v(6392)+v(569)*v(6419)+v(568)*v(6442)-v(580)*v(712)-v(575)*v(766)-v(579)*v(768))
v(6477)=v(7522)*(v(566)*v(6391)+v(569)*v(6416)+v(568)*v(6441)-v(580)*v(711)-v(575)*v(765)-v(579)*v(781))
v(6476)=v(7522)*(v(566)*v(6390)+v(569)*v(6415)+v(568)*v(6440)-v(580)*v(710)-v(575)*v(764)-v(579)*v(780))
v(6475)=(v(566)*v(6389)+v(569)*v(6414)+v(568)*v(6439))*v(7522)+v(7518)*v(8144)
v(6461)=(v(567)*v(6426)+v(570)*v(6448))*v(7522)+v(8142)
v(6456)=v(7522)*(v(569)*v(6395)+v(567)*v(6421)+v(570)*v(6444)-v(579)*v(737)-v(575)*v(782)-v(580)*v(783))
v(6455)=v(6712)+v(7522)*(v(569)*v(6394)+v(567)*v(6420)+v(570)*v(6443)-v(579)*v(736)-v(575)*v(797))
v(6454)=v(6453)+v(6479)+(v(569)*v(6392)+v(567)*v(6419)+v(570)*v(6442)-v(579)*v(735))*v(7522)
v(6452)=v(7522)*(v(569)*v(6391)+v(567)*v(6416)+v(570)*v(6441)-v(579)*v(734)-v(580)*v(781)-v(575)*v(796))
v(6451)=v(7522)*(v(569)*v(6390)+v(567)*v(6415)+v(570)*v(6440)-v(579)*v(733)-v(580)*v(780)-v(575)*v(795))
v(6450)=(v(569)*v(6389)+v(567)*v(6414)+v(570)*v(6439))*v(7522)+v(7518)*v(8143)
v(583)=v(7522)*v(8143)
v(6553)=v(583)*v(6771)
v(6529)=v(583)*v(6592)
v(6560)=v(6529)+v(6727)+(v(566)*v(6488)+v(568)*v(6510))*v(7522)
v(6788)=v(6560)*v(8123)
v(6882)=(v(6545)+v(6788)+210d0*v(6845)+42d0*v(6857)+7d0*v(6869)+5040d0*v(6881)+v(6869)*v(8128))/5040d0
v(6585)=v(6560)*v(8119)
v(6531)=-v(6529)+(v(567)*v(6459)+v(569)*v(6484)+v(570)*v(6507))*v(7522)
v(6544)=v(6531)*v(8125)
v(6530)=-v(6529)+(v(567)*v(6458)+v(569)*v(6483)+v(570)*v(6506))*v(7522)
v(6543)=v(6530)*v(8125)
v(6473)=v(6529)+v(6461)*v(8125)
v(6870)=v(6473)+v(6727)+v(6858)*v(8128)
v(6520)=v(6473)+v(6498)+v(6509)*v(8134)
v(6469)=v(6553)+v(6456)*v(8125)
v(6468)=v(7522)*(v(570)*v(6455)-v(583)*v(797))
v(6467)=v(7522)*(v(570)*v(6454)-v(583)*v(767))
v(6466)=v(7522)*(v(570)*v(6452)-v(583)*v(796))
v(6465)=v(7522)*(v(570)*v(6451)-v(583)*v(795))
v(6464)=v(570)*(v(583)*v(7518)+v(6450)*v(7522))
v(618)=v(583)*v(8125)
v(582)=v(7522)*v(8144)
v(6758)=v(582)*v(6771)
v(6755)=v(582)*v(6604)
v(6535)=v(582)*v(6592)
v(6557)=v(6535)+(v(569)*v(6459)+v(566)*v(6484)+v(568)*v(6507))*v(7522)
v(6581)=v(6557)*v(8119)
v(6595)=(840d0*v(6384)+210d0*v(6446)+42d0*v(6507)+7d0*v(6518)+v(6544)+v(6581)+v(6518)*v(8134))/5040d0
v(6536)=v(6535)+v(6726)+(v(567)*v(6463)+v(570)*v(6510))*v(7522)
v(6789)=v(6536)*v(8123)
v(8149)=v(6789)+5040d0*v(6801)
v(6802)=(v(6584)+210d0*v(6704)+42d0*v(6739)+7d0*v(6750)+v(6750)*v(8131)+v(8149))/5040d0
v(6547)=v(6536)*v(8125)
v(6599)=(210d0*v(6449)+42d0*v(6510)+7d0*v(6521)+v(6547)+v(6585)+5040d0*v(6598)+v(6521)*v(8134))/5040d0
v(6525)=v(582)*v(6768)
v(6497)=v(6535)+v(6487)*v(8119)
v(6749)=v(6497)+v(6726)+v(6738)*v(8131)
v(6519)=v(6472)+v(6497)+v(6508)*v(8134)
v(6494)=v(6525)+v(6482)*v(8119)
v(6493)=v(6755)+v(6481)*v(8119)
v(6492)=v(7522)*(v(568)*v(6478)-v(582)*v(766))
v(6491)=v(7522)*(v(568)*v(6477)-v(582)*v(765))
v(6490)=v(7522)*(v(568)*v(6476)-v(582)*v(764))
v(6489)=v(568)*(v(582)*v(7518)+v(6475)*v(7522))
v(598)=v(582)*v(8119)
v(578)=v(596)+v(614)+v(575)*v(8134)
v(8152)=v(568)*v(578)+v(566)*v(582)+v(569)*v(583)
v(8148)=v(570)*v(578)+v(569)*v(582)+v(567)*v(583)
v(6555)=v(7522)*(v(569)*v(6456)+v(566)*v(6482)+v(568)*v(6505)-v(582)*v(714)-v(578)*v(768)-v(583)*v(783))
v(6552)=v(578)*v(6604)
v(6554)=v(6552)+v(6553)+(v(569)*v(6455)+v(566)*v(6481)+v(568)*v(6504)-v(582)*v(713))*v(7522)
v(6551)=v(7522)*(v(569)*v(6454)+v(566)*v(6478)+v(568)*v(6503)-v(582)*v(712)-v(578)*v(766)-v(583)*v(768))
v(6550)=v(7522)*(v(569)*v(6452)+v(566)*v(6477)+v(568)*v(6502)-v(582)*v(711)-v(578)*v(765)-v(583)*v(781))
v(6549)=v(7522)*(v(569)*v(6451)+v(566)*v(6476)+v(568)*v(6501)-v(582)*v(710)-v(578)*v(764)-v(583)*v(780))
v(6548)=(v(569)*v(6450)+v(566)*v(6475)+v(568)*v(6500))*v(7522)+v(7518)*v(8152)
v(8160)=v(6548)*v(7522)
v(6533)=v(578)*v(6592)
v(8145)=v(6533)+v(6558)
v(6559)=(v(566)*v(6487)+v(568)*v(6508))*v(7522)+v(8145)
v(6570)=v(6400)/24d0+v(6460)/120d0+v(6532)/720d0+v(6598)+v(6775)+((v(570)*v(6519)+v(567)*v(6532)+v(569)*v(6559))*v(7522&
&))/5040d0
v(7021)=statev(53)*v(6570)
v(6976)=v(6570)*v(7515)
v(6917)=statev(56)*v(6570)
v(6534)=(v(567)*v(6461)+v(570)*v(6509))*v(7522)+v(8145)
v(6528)=v(7522)*(v(567)*v(6456)+v(569)*v(6482)+v(570)*v(6505)-v(583)*v(737)-v(578)*v(782)-v(582)*v(783))
v(6527)=v(6758)+v(7522)*(v(567)*v(6455)+v(569)*v(6481)+v(570)*v(6504)-v(583)*v(736)-v(578)*v(797))
v(6526)=v(6525)+v(6552)+(v(567)*v(6454)+v(569)*v(6478)+v(570)*v(6503)-v(583)*v(735))*v(7522)
v(6524)=v(7522)*(v(567)*v(6452)+v(569)*v(6477)+v(570)*v(6502)-v(583)*v(734)-v(582)*v(781)-v(578)*v(796))
v(6523)=v(7522)*(v(567)*v(6451)+v(569)*v(6476)+v(570)*v(6501)-v(583)*v(733)-v(582)*v(780)-v(578)*v(795))
v(6522)=(v(567)*v(6450)+v(569)*v(6475)+v(570)*v(6500))*v(7522)+v(7518)*v(8148)
v(6517)=v(6470)+v(6495)+v(6533)+v(6506)*v(8134)
v(6610)=(840d0*v(6358)+210d0*v(6396)+42d0*v(6483)+7d0*v(6556)+v(6517)*v(8119)+v(6530)*v(8123)+v(6556)*v(8131)+v(8155))&
&/5040d0
v(6516)=v(6469)+v(6494)+(v(565)*v(6505)-v(578)*v(704))*v(7522)
v(6515)=v(6468)+v(6493)+(v(565)*v(6504)-v(578)*v(703))*v(7522)
v(6514)=v(6467)+v(6492)+(v(565)*v(6503)-v(578)*v(702))*v(7522)
v(6513)=v(6466)+v(6491)+(v(565)*v(6502)-v(578)*v(701))*v(7522)
v(6512)=v(6465)+v(6490)+(v(565)*v(6501)-v(578)*v(700))*v(7522)
v(6511)=v(6464)+v(6489)+v(565)*(v(578)*v(7518)+v(6500)*v(7522))
v(581)=v(598)+v(618)+v(578)*v(8134)
v(8153)=5040d0+v(581)
v(8158)=v(6511)*v(7522)+v(7518)*v(8153)
v(6605)=v(581)*v(6604)
v(8159)=5040d0*v(6604)+v(6605)
v(6593)=v(581)*v(6592)
v(8146)=v(6593)+v(8164)
v(8147)=v(6612)+v(8146)
v(6613)=((-2520d0)*v(6286)+840d0*v(6362)+210d0*v(6399)+42d0*v(6487)+7d0*v(6559)+v(6519)*v(8119)+v(6559)*v(8131)+v(8147)&
&)/5040d0
v(6594)=((-5040d0)*v(6267)+840d0*v(6383)+210d0*v(6445)+42d0*v(6506)+7d0*v(6517)+v(6543)+v(6580)+v(6517)*v(8134)+v(8146)&
&)/5040d0
v(6571)=((-2520d0)*v(6306)+840d0*v(6335)+210d0*v(6426)+42d0*v(6461)+7d0*v(6534)+v(6520)*v(8125)+v(6534)*v(8128)+v(8147)&
&)/5040d0
v(584)=v(7522)*v(8148)
v(8154)=v(584)*v(7518)+v(6522)*v(7522)
v(6606)=v(584)*v(6771)
v(6567)=v(584)*v(6592)
v(6615)=(210d0*v(6402)+42d0*v(6488)+7d0*v(6560)+v(6567)+v(6521)*v(8119)+v(6560)*v(8131)+v(8149)+v(8150))/5040d0
v(7022)=v(6615)*v(7516)
v(7023)=statev(58)*v(6882)+v(7021)+v(7022)
v(6943)=statev(54)*v(6615)
v(6928)=statev(57)*v(6615)
v(6929)=statev(55)*v(6882)+v(6928)+v(6976)
v(6893)=v(6917)+v(6943)+v(6882)*v(7517)
v(6569)=(840d0*v(6333)+210d0*v(6423)+42d0*v(6459)+7d0*v(6531)-v(6567)+v(6557)*v(8123)+v(6518)*v(8125)+v(6531)*v(8128)-v&
&(8150))/5040d0
v(6568)=(840d0*v(6332)+210d0*v(6422)+42d0*v(6458)+7d0*v(6530)-v(6567)+v(6556)*v(8123)+v(6517)*v(8125)+v(6530)*v(8128))&
&/5040d0
v(6938)=statev(56)*v(6594)+statev(54)*v(6610)+v(6568)*v(7517)
v(6902)=statev(58)*v(6568)+statev(53)*v(6594)+v(6610)*v(7516)
v(6622)=statev(55)*v(6568)+statev(57)*v(6610)+v(6594)*v(7515)
v(6546)=v(6567)+v(6534)*v(8125)
v(8151)=5040d0*v(6265)+v(6546)
v(6883)=(v(6789)+840d0*v(6834)+210d0*v(6846)+42d0*v(6858)+7d0*v(6870)+v(6870)*v(8128)+v(8151))/5040d0
v(6597)=(840d0*v(6388)+210d0*v(6448)+42d0*v(6509)+7d0*v(6520)+v(6584)+v(6520)*v(8134)+v(8151))/5040d0
v(6941)=statev(54)*v(6570)+statev(56)*v(6597)+v(6571)*v(7517)
v(6905)=statev(58)*v(6571)+statev(53)*v(6597)+v(6570)*v(7516)
v(6625)=statev(57)*v(6570)+statev(55)*v(6571)+v(6597)*v(7515)
v(6542)=v(6606)+v(6528)*v(8125)
v(6541)=v(7522)*(v(570)*v(6527)-v(584)*v(797))
v(6540)=v(7522)*(v(570)*v(6526)-v(584)*v(767))
v(6539)=v(7522)*(v(570)*v(6524)-v(584)*v(796))
v(6538)=v(7522)*(v(570)*v(6523)-v(584)*v(795))
v(6537)=v(570)*v(8154)
v(620)=v(584)*v(8125)
v(585)=v(7522)*v(8152)
v(8157)=v(585)*v(7518)
v(8172)=v(8157)+v(8160)
v(6773)=v(585)*v(6771)
v(6769)=v(585)*v(6604)
v(6608)=(7d0*(360d0*v(6285)+120d0*v(6357)+30d0*v(6395)+6d0*v(6482)+v(6555)+720d0*v(6768))+v(7522)*(v(568)*v(6516)+v(569&
&)*v(6528)+v(566)*v(6555)-v(585)*v(714)-v(581)*v(768)-v(584)*v(783)))/5040d0
v(6607)=(2520d0*v(6283)+840d0*v(6356)+210d0*v(6394)+42d0*v(6481)+7d0*v(6554)+v(6606)+(v(568)*v(6515)+v(569)*v(6527)+v&
&(566)*v(6554)-v(585)*v(713))*v(7522)+v(8159))/5040d0
v(6603)=(7d0*(360d0*v(6282)+120d0*v(6353)+30d0*v(6392)+6d0*v(6478)+v(6551))+v(7522)*(v(568)*v(6514)+v(569)*v(6526)+v&
&(566)*v(6551)-v(585)*v(712)-v(584)*v(768)-v(766)*v(8153)))/5040d0
v(6602)=(7d0*(360d0*v(6280)+120d0*v(6352)+30d0*v(6391)+6d0*v(6477)+v(6550))+v(7522)*(v(568)*v(6513)+v(569)*v(6524)+v&
&(566)*v(6550)-v(585)*v(711)-v(584)*v(781)-v(765)*v(8153)))/5040d0
v(6601)=(7d0*(360d0*v(6279)+120d0*v(6351)+30d0*v(6390)+6d0*v(6476)+v(6549))+v(7522)*(v(568)*v(6512)+v(569)*v(6523)+v&
&(566)*v(6549)-v(585)*v(710)-v(584)*v(780)-v(764)*v(8153)))/5040d0
v(6600)=(2520d0*v(6278)+840d0*v(6350)+210d0*v(6389)+42d0*v(6475)+7d0*v(6548)+v(6548)*v(8131)+v(569)*v(8154)+v(566)*v&
&(8157)+v(568)*v(8158))/5040d0
v(6582)=v(585)*v(6592)
v(6611)=(840d0*v(6360)+210d0*v(6398)+42d0*v(6484)+7d0*v(6557)+v(6582)+v(6518)*v(8119)+v(6531)*v(8123)+v(6557)*v(8131)+v&
&(8155))/5040d0
v(6939)=statev(56)*v(6595)+statev(54)*v(6611)+v(6569)*v(7517)
v(6903)=statev(58)*v(6569)+statev(53)*v(6595)+v(6611)*v(7516)
v(6623)=statev(55)*v(6569)+statev(57)*v(6611)+v(6595)*v(7515)
v(6583)=v(6582)+v(6559)*v(8119)
v(8156)=5040d0*v(6266)+v(6583)
v(6800)=(840d0*v(6668)+210d0*v(6703)+42d0*v(6738)+7d0*v(6749)+v(6788)+v(6749)*v(8131)+v(8156))/5040d0
v(6975)=statev(55)*v(6615)+statev(57)*v(6800)+v(6613)*v(7515)
v(6916)=statev(56)*v(6613)+statev(54)*v(6800)+v(6615)*v(7517)
v(6812)=statev(53)*v(6613)+statev(58)*v(6615)+v(6800)*v(7516)
v(6596)=(840d0*v(6386)+210d0*v(6447)+42d0*v(6508)+7d0*v(6519)+v(6545)+v(6519)*v(8134)+v(8156))/5040d0
v(6940)=statev(56)*v(6596)+statev(54)*v(6613)+v(6570)*v(7517)
v(6904)=statev(58)*v(6570)+statev(53)*v(6596)+v(6613)*v(7516)
v(6624)=statev(55)*v(6570)+statev(57)*v(6613)+v(6596)*v(7515)
v(6578)=v(585)*v(6768)
v(6579)=v(6578)+v(6555)*v(8119)
v(6591)=(2520d0*v(6322)+840d0*v(6381)+210d0*v(6444)+42d0*v(6505)+7d0*v(6516)+v(6542)+v(6579)+v(7522)*(v(565)*v(6516)-v&
&(704)*v(8153)))/5040d0
v(6577)=v(6769)+v(6554)*v(8119)
v(6590)=(2520d0*v(6321)+840d0*v(6380)+210d0*v(6443)+42d0*v(6504)+7d0*v(6515)+v(6541)+v(6577)+v(7522)*(v(565)*v(6515)-v&
&(703)*v(8153)))/5040d0
v(6576)=v(7522)*(v(568)*v(6551)-v(585)*v(766))
v(6589)=(2520d0*v(6320)+840d0*v(6379)+210d0*v(6442)+42d0*v(6503)+7d0*v(6514)+v(6540)+v(6576)+v(7522)*(v(565)*v(6514)-v&
&(702)*v(8153)))/5040d0
v(6575)=v(7522)*(v(568)*v(6550)-v(585)*v(765))
v(6588)=(2520d0*v(6319)+840d0*v(6378)+210d0*v(6441)+42d0*v(6502)+7d0*v(6513)+v(6539)+v(6575)+v(7522)*(v(565)*v(6513)-v&
&(701)*v(8153)))/5040d0
v(6574)=v(7522)*(v(568)*v(6549)-v(585)*v(764))
v(6587)=(2520d0*v(6317)+840d0*v(6377)+210d0*v(6440)+42d0*v(6501)+7d0*v(6512)+v(6538)+v(6574)+v(7522)*(v(565)*v(6512)-v&
&(700)*v(8153)))/5040d0
v(6573)=v(568)*v(8172)
v(6586)=(2520d0*v(6316)+840d0*v(6376)+210d0*v(6439)+42d0*v(6500)+7d0*v(6511)+v(6537)+v(6573)+v(565)*v(8158))/5040d0
v(6572)=v(6427)/24d0+v(6463)/120d0+v(6536)/720d0+v(6609)+v(6881)+(v(6582)+v(6788)+(v(570)*v(6521)+v(567)*v(6536))*v&
&(7522))/5040d0
v(7024)=statev(53)*v(6571)+statev(58)*v(6883)+v(6572)*v(7516)
v(6977)=statev(55)*v(6572)
v(6978)=statev(57)*v(6802)+v(6976)+v(6977)
v(6942)=v(6572)*v(7517)
v(6944)=statev(56)*v(6599)+v(6942)+v(6943)
v(6930)=statev(57)*v(6572)+statev(55)*v(6883)+v(6571)*v(7515)
v(6918)=statev(54)*v(6802)+v(6917)+v(6942)
v(6906)=statev(58)*v(6572)
v(6907)=statev(53)*v(6599)+v(6906)+v(7022)
v(6894)=statev(56)*v(6571)+statev(54)*v(6572)+v(6883)*v(7517)
v(6813)=v(6906)+v(7021)+v(6802)*v(7516)
v(6626)=v(6928)+v(6977)+v(6599)*v(7515)
v(6566)=(v(7522)*(v(570)*v(6516)+v(567)*v(6528)+v(569)*v(6555)-v(584)*v(737)-v(581)*v(782)-v(585)*v(783))+7d0*(360d0*v&
&(6305)+120d0*v(6330)+30d0*v(6421)+6d0*v(6456)+v(6528)+v(8169)))/5040d0
v(6937)=statev(56)*v(6591)+statev(54)*v(6608)+v(6566)*v(7517)
v(6901)=statev(58)*v(6566)+statev(53)*v(6591)+v(6608)*v(7516)
v(6621)=statev(55)*v(6566)+statev(57)*v(6608)+v(6591)*v(7515)
v(6565)=(2520d0*v(6303)+840d0*v(6329)+210d0*v(6420)+42d0*v(6455)+7d0*v(6527)+v(6773)+v(7522)*(v(570)*v(6515)+v(567)*v&
&(6527)+v(569)*v(6554)-v(584)*v(736)-v(797)*v(8153)))/5040d0
v(6936)=statev(56)*v(6590)+statev(54)*v(6607)+v(6565)*v(7517)
v(6900)=statev(58)*v(6565)+statev(53)*v(6590)+v(6607)*v(7516)
v(6620)=statev(55)*v(6565)+statev(57)*v(6607)+v(6590)*v(7515)
v(6564)=(2520d0*v(6300)+840d0*v(6328)+210d0*v(6419)+42d0*v(6454)+7d0*v(6526)+v(6578)+(v(570)*v(6514)+v(567)*v(6526)+v&
&(569)*v(6551)-v(584)*v(735))*v(7522)+v(8159))/5040d0
v(6935)=statev(56)*v(6589)+statev(54)*v(6603)+v(6564)*v(7517)
v(6899)=statev(58)*v(6564)+statev(53)*v(6589)+v(6603)*v(7516)
v(6619)=statev(55)*v(6564)+statev(57)*v(6603)+v(6589)*v(7515)
v(6563)=(7d0*(360d0*v(6298)+120d0*v(6326)+30d0*v(6416)+6d0*v(6452)+v(6524))+v(7522)*(v(570)*v(6513)+v(567)*v(6524)+v&
&(569)*v(6550)-v(584)*v(734)-v(585)*v(781)-5040d0*v(796)-v(581)*v(796)))/5040d0
v(6934)=statev(56)*v(6588)+statev(54)*v(6602)+v(6563)*v(7517)
v(6898)=statev(58)*v(6563)+statev(53)*v(6588)+v(6602)*v(7516)
v(6618)=statev(55)*v(6563)+statev(57)*v(6602)+v(6588)*v(7515)
v(6562)=(7d0*(360d0*v(6297)+120d0*v(6325)+30d0*v(6415)+6d0*v(6451)+v(6523))+v(7522)*(v(570)*v(6512)+v(567)*v(6523)+v&
&(569)*v(6549)-v(584)*v(733)-v(585)*v(780)-5040d0*v(795)-v(581)*v(795)))/5040d0
v(6933)=statev(56)*v(6587)+statev(54)*v(6601)+v(6562)*v(7517)
v(6897)=statev(58)*v(6562)+statev(53)*v(6587)+v(6601)*v(7516)
v(6617)=statev(55)*v(6562)+statev(57)*v(6601)+v(6587)*v(7515)
v(6561)=(2520d0*v(6296)+840d0*v(6324)+210d0*v(6414)+42d0*v(6450)+7d0*v(6522)+v(567)*v(8154)+v(569)*v(8157)+v(570)*v&
&(8158)+v(569)*v(8160))/5040d0
v(6932)=statev(56)*v(6586)+statev(54)*v(6600)+v(6561)*v(7517)
v(6896)=statev(58)*v(6561)+statev(53)*v(6586)+v(6600)*v(7516)
v(6616)=statev(55)*v(6561)+statev(57)*v(6600)+v(6586)*v(7515)
v(623)=(7d0*(360d0*v(573)+120d0*v(577)+30d0*v(579)+6d0*v(583)+v(584))+v(7522)*(v(567)*v(584)+v(569)*v(585)+v(570)*v&
&(8153)))/5040d0
v(603)=v(585)*v(8119)
v(8174)=5040d0+v(603)
v(625)=(2520d0*v(571)+840d0*v(572)+210d0*v(575)+42d0*v(578)+7d0*v(581)+v(620)+v(8134)*v(8153)+v(8174))/5040d0
v(587)=(7d0*(360d0*v(574)+120d0*v(576)+30d0*v(580)+6d0*v(582)+v(585))+v(7522)*(v(569)*v(584)+v(566)*v(585)+v(568)*v&
&(8153)))/5040d0
v(586)=statev(57)*v(587)+statev(55)*v(623)+v(625)*v(7515)
v(589)=v(588)+v(605)+v(232)*v(6627)
v(8161)=v(570)*v(574)+v(569)*v(589)+v(567)*v(593)
v(6666)=v(589)*v(6592)
v(6667)=v(6293)+v(6666)+v(6635)*v(8131)
v(6664)=v(6273)+v(6292)+(v(566)*v(6634)-v(589)*v(714))*v(7522)
v(6663)=v(6272)+v(6291)+(v(566)*v(6633)-v(589)*v(713))*v(7522)
v(6662)=v(6271)+v(6290)+(v(566)*v(6632)-v(589)*v(712))*v(7522)
v(6661)=v(6270)+v(6289)+(v(566)*v(6631)-v(589)*v(711))*v(7522)
v(6660)=v(6269)+v(6288)+(v(566)*v(6629)-v(589)*v(710))*v(7522)
v(6659)=v(6268)+v(6287)+v(566)*(v(589)*v(7518)+v(6628)*v(7522))
v(6647)=-v(6313)+v(6666)+(v(569)*v(6248)+v(567)*v(6267))*v(7522)
v(6643)=v(6642)+v(7522)*(v(567)*v(6263)+v(570)*v(6285)+v(569)*v(6634)-v(593)*v(737)-v(589)*v(783))
v(6641)=v(7522)*(v(567)*v(6262)+v(570)*v(6283)+v(569)*v(6633)-v(593)*v(736)-v(589)*v(782)-v(574)*v(797))
v(6640)=v(6639)+v(7522)*(v(567)*v(6261)+v(570)*v(6282)+v(569)*v(6632)-v(593)*v(735)-v(589)*v(768))
v(6638)=v(7522)*(v(567)*v(6260)+v(570)*v(6280)+v(569)*v(6631)-v(593)*v(734)-v(589)*v(781)-v(574)*v(796))
v(6637)=v(7522)*(v(567)*v(6259)+v(570)*v(6279)+v(569)*v(6629)-v(593)*v(733)-v(589)*v(780)-v(574)*v(795))
v(6636)=(v(567)*v(6258)+v(570)*v(6278)+v(569)*v(6628))*v(7522)+v(7518)*v(8161)
v(595)=v(7522)*v(8161)
v(6679)=v(595)*v(6592)
v(6681)=-v(6679)+(v(570)*v(6360)+v(567)*v(6646)+v(569)*v(6667))*v(7522)
v(6690)=v(6681)*v(8123)
v(6680)=-v(6679)+(v(570)*v(6358)+v(567)*v(6645)+v(569)*v(6665))*v(7522)
v(6689)=v(6680)*v(8123)
v(6735)=v(6409)+v(6689)+v(6700)*v(8131)
v(6658)=v(6679)+v(6647)*v(8123)
v(6847)=v(6349)+v(6658)+v(6835)*v(8128)
v(6705)=v(6375)+v(6658)+v(6670)*v(8131)
v(6653)=v(7522)*(v(569)*v(6643)-v(595)*v(783))
v(6652)=v(7522)*(v(569)*v(6641)-v(595)*v(782))
v(6651)=v(7522)*(v(569)*v(6640)-v(595)*v(768))
v(6650)=v(7522)*(v(569)*v(6638)-v(595)*v(781))
v(6649)=v(7522)*(v(569)*v(6637)-v(595)*v(780))
v(6648)=v(569)*(v(595)*v(7518)+v(6636)*v(7522))
v(611)=v(595)*v(8123)
v(591)=v(590)+v(609)+v(589)*v(8131)
v(8162)=v(570)*v(576)+v(569)*v(591)+v(567)*v(595)
v(6701)=v(591)*v(6592)
v(6702)=v(6372)+v(6655)+v(6701)+v(6667)*v(8131)
v(6699)=v(6370)+v(6653)+(v(566)*v(6664)-v(591)*v(714))*v(7522)
v(6698)=v(6369)+v(6652)+(v(566)*v(6663)-v(591)*v(713))*v(7522)
v(6697)=v(6368)+v(6651)+(v(566)*v(6662)-v(591)*v(712))*v(7522)
v(6696)=v(6367)+v(6650)+(v(566)*v(6661)-v(591)*v(711))*v(7522)
v(6695)=v(6366)+v(6649)+(v(566)*v(6660)-v(591)*v(710))*v(7522)
v(6694)=v(6365)+v(6648)+v(566)*(v(591)*v(7518)+v(6659)*v(7522))
v(6682)=v(6425)+v(6701)+(v(567)*v(6647)+v(569)*v(6670))*v(7522)
v(6678)=v(6677)+v(7522)*(v(570)*v(6357)+v(567)*v(6643)+v(569)*v(6664)-v(595)*v(737)-v(591)*v(783))
v(6676)=v(7522)*(v(570)*v(6356)+v(567)*v(6641)+v(569)*v(6663)-v(595)*v(736)-v(591)*v(782)-v(576)*v(797))
v(6675)=v(6674)+v(7522)*(v(570)*v(6353)+v(567)*v(6640)+v(569)*v(6662)-v(595)*v(735)-v(591)*v(768))
v(6673)=v(7522)*(v(570)*v(6352)+v(567)*v(6638)+v(569)*v(6661)-v(595)*v(734)-v(591)*v(781)-v(576)*v(796))
v(6672)=v(7522)*(v(570)*v(6351)+v(567)*v(6637)+v(569)*v(6660)-v(595)*v(733)-v(591)*v(780)-v(576)*v(795))
v(6671)=(v(570)*v(6350)+v(567)*v(6636)+v(569)*v(6659))*v(7522)+v(7518)*v(8162)
v(599)=v(7522)*v(8162)
v(6714)=v(599)*v(6592)
v(6716)=-v(6714)+(v(570)*v(6398)+v(567)*v(6681)+v(569)*v(6702))*v(7522)
v(6725)=v(6716)*v(8123)
v(6715)=-v(6714)+(v(570)*v(6396)+v(567)*v(6680)+v(569)*v(6700))*v(7522)
v(6724)=v(6715)*v(8123)
v(6747)=v(6495)+v(6724)+v(6735)*v(8131)
v(6693)=v(6714)+v(6682)*v(8123)
v(6859)=v(6438)+v(6693)+v(6847)*v(8128)
v(6740)=v(6413)+v(6693)+v(6705)*v(8131)
v(6688)=v(7522)*(v(569)*v(6678)-v(599)*v(783))
v(6687)=v(7522)*(v(569)*v(6676)-v(599)*v(782))
v(6686)=v(7522)*(v(569)*v(6675)-v(599)*v(768))
v(6685)=v(7522)*(v(569)*v(6673)-v(599)*v(781))
v(6684)=v(7522)*(v(569)*v(6672)-v(599)*v(780))
v(6683)=v(569)*(v(599)*v(7518)+v(6671)*v(7522))
v(615)=v(599)*v(8123)
v(594)=v(592)+v(611)+v(591)*v(8131)
v(8163)=v(570)*v(580)+v(569)*v(594)+v(567)*v(599)
v(6736)=v(594)*v(6592)
v(6737)=v(6410)+v(6690)+v(6736)+v(6702)*v(8131)
v(6734)=v(6408)+v(6688)+(v(566)*v(6699)-v(594)*v(714))*v(7522)
v(6733)=v(6407)+v(6687)+(v(566)*v(6698)-v(594)*v(713))*v(7522)
v(6732)=v(6406)+v(6686)+(v(566)*v(6697)-v(594)*v(712))*v(7522)
v(6731)=v(6405)+v(6685)+(v(566)*v(6696)-v(594)*v(711))*v(7522)
v(6730)=v(6404)+v(6684)+(v(566)*v(6695)-v(594)*v(710))*v(7522)
v(6729)=v(6403)+v(6683)+v(566)*(v(594)*v(7518)+v(6694)*v(7522))
v(6717)=v(6736)+(v(570)*v(6402)+v(567)*v(6682)+v(569)*v(6705))*v(7522)
v(6713)=v(6712)+v(7522)*(v(570)*v(6395)+v(567)*v(6678)+v(569)*v(6699)-v(599)*v(737)-v(594)*v(783))
v(6711)=v(7522)*(v(570)*v(6394)+v(567)*v(6676)+v(569)*v(6698)-v(599)*v(736)-v(594)*v(782)-v(580)*v(797))
v(6710)=v(6709)+v(7522)*(v(570)*v(6392)+v(567)*v(6675)+v(569)*v(6697)-v(599)*v(735)-v(594)*v(768))
v(6708)=v(7522)*(v(570)*v(6391)+v(567)*v(6673)+v(569)*v(6696)-v(599)*v(734)-v(594)*v(781)-v(580)*v(796))
v(6707)=v(7522)*(v(570)*v(6390)+v(567)*v(6672)+v(569)*v(6695)-v(599)*v(733)-v(594)*v(780)-v(580)*v(795))
v(6706)=(v(570)*v(6389)+v(567)*v(6671)+v(569)*v(6694))*v(7522)+v(7518)*v(8163)
v(601)=v(7522)*v(8163)
v(6760)=v(601)*v(6592)
v(6762)=-v(6760)+(v(570)*v(6484)+v(567)*v(6716)+v(569)*v(6737))*v(7522)
v(6787)=v(6762)*v(8123)
v(6761)=-v(6760)+(v(570)*v(6483)+v(567)*v(6715)+v(569)*v(6735))*v(7522)
v(6786)=v(6761)*v(8123)
v(6797)=(v(6580)+840d0*v(6665)+210d0*v(6700)+42d0*v(6735)+7d0*v(6747)+v(6786)+v(6747)*v(8131))/5040d0
v(6728)=v(6760)+v(6717)*v(8123)
v(6871)=v(6474)+v(6728)+v(6859)*v(8128)
v(6751)=v(6499)+v(6728)+v(6740)*v(8131)
v(6723)=v(7522)*(v(569)*v(6713)-v(601)*v(783))
v(6722)=v(7522)*(v(569)*v(6711)-v(601)*v(782))
v(6721)=v(7522)*(v(569)*v(6710)-v(601)*v(768))
v(6720)=v(7522)*(v(569)*v(6708)-v(601)*v(781))
v(6719)=v(7522)*(v(569)*v(6707)-v(601)*v(780))
v(6718)=v(569)*(v(601)*v(7518)+v(6706)*v(7522))
v(617)=v(601)*v(8123)
v(597)=v(596)+v(615)+v(594)*v(8131)
v(8166)=v(570)*v(582)+v(569)*v(597)+v(567)*v(601)
v(6763)=v(597)*v(6592)
v(6764)=v(6763)+(v(570)*v(6488)+v(567)*v(6717)+v(569)*v(6740))*v(7522)
v(6759)=v(6758)+v(7522)*(v(570)*v(6482)+v(567)*v(6713)+v(569)*v(6734)-v(601)*v(737)-v(597)*v(783))
v(6757)=v(7522)*(v(570)*v(6481)+v(567)*v(6711)+v(569)*v(6733)-v(601)*v(736)-v(597)*v(782)-v(582)*v(797))
v(6756)=v(6755)+v(7522)*(v(570)*v(6478)+v(567)*v(6710)+v(569)*v(6732)-v(601)*v(735)-v(597)*v(768))
v(6754)=v(7522)*(v(570)*v(6477)+v(567)*v(6708)+v(569)*v(6731)-v(601)*v(734)-v(597)*v(781)-v(582)*v(796))
v(6753)=v(7522)*(v(570)*v(6476)+v(567)*v(6707)+v(569)*v(6730)-v(601)*v(733)-v(597)*v(780)-v(582)*v(795))
v(6752)=(v(570)*v(6475)+v(567)*v(6706)+v(569)*v(6729))*v(7522)+v(7518)*v(8166)
v(8171)=v(6752)*v(7522)
v(6748)=v(6496)+v(6725)+v(6763)+v(6737)*v(8131)
v(6746)=v(6494)+v(6723)+(v(566)*v(6734)-v(597)*v(714))*v(7522)
v(6745)=v(6493)+v(6722)+(v(566)*v(6733)-v(597)*v(713))*v(7522)
v(6744)=v(6492)+v(6721)+(v(566)*v(6732)-v(597)*v(712))*v(7522)
v(6743)=v(6491)+v(6720)+(v(566)*v(6731)-v(597)*v(711))*v(7522)
v(6742)=v(6490)+v(6719)+(v(566)*v(6730)-v(597)*v(710))*v(7522)
v(6741)=v(6489)+v(6718)+v(566)*(v(597)*v(7518)+v(6729)*v(7522))
v(600)=v(598)+v(617)+v(597)*v(8131)
v(8167)=5040d0+v(600)
v(8173)=v(6741)*v(7522)+v(7518)*v(8167)
v(6798)=v(600)*v(6592)
v(8165)=v(6798)+v(8164)
v(6799)=v(6306)+(v(6581)+840d0*v(6667)+210d0*v(6702)+42d0*v(6737)+7d0*v(6748)+v(6787)+v(6748)*v(8131)+v(8165))/5040d0
v(6779)=(2520d0*v(6267)+840d0*v(6647)+210d0*v(6682)+42d0*v(6717)+7d0*v(6764)+(v(570)*v(6560)+v(569)*v(6751)+v(567)*v&
&(6764))*v(7522)+v(8165))/5040d0
v(602)=v(7522)*v(8166)
v(8170)=v(602)*v(7518)
v(6785)=v(7522)*(v(569)*v(6759)-v(602)*v(783))
v(6796)=(v(6579)+2520d0*v(6634)+840d0*v(6664)+210d0*v(6699)+42d0*v(6734)+7d0*v(6746)+v(6785)+v(7522)*(v(566)*v(6746)-v&
&(714)*v(8167)))/5040d0
v(6784)=v(7522)*(v(569)*v(6757)-v(602)*v(782))
v(6795)=(v(6577)+2520d0*v(6633)+840d0*v(6663)+210d0*v(6698)+42d0*v(6733)+7d0*v(6745)+v(6784)+v(7522)*(v(566)*v(6745)-v&
&(713)*v(8167)))/5040d0
v(6783)=v(7522)*(v(569)*v(6756)-v(602)*v(768))
v(6794)=(v(6576)+2520d0*v(6632)+840d0*v(6662)+210d0*v(6697)+42d0*v(6732)+7d0*v(6744)+v(6783)+v(7522)*(v(566)*v(6744)-v&
&(712)*v(8167)))/5040d0
v(6782)=v(7522)*(v(569)*v(6754)-v(602)*v(781))
v(6793)=(v(6575)+2520d0*v(6631)+840d0*v(6661)+210d0*v(6696)+42d0*v(6731)+7d0*v(6743)+v(6782)+v(7522)*(v(566)*v(6743)-v&
&(711)*v(8167)))/5040d0
v(6781)=v(7522)*(v(569)*v(6753)-v(602)*v(780))
v(6792)=(v(6574)+2520d0*v(6629)+840d0*v(6660)+210d0*v(6695)+42d0*v(6730)+7d0*v(6742)+v(6781)+v(7522)*(v(566)*v(6742)-v&
&(710)*v(8167)))/5040d0
v(6780)=v(569)*(v(8170)+v(8171))
v(6791)=(v(6573)+2520d0*v(6628)+840d0*v(6659)+210d0*v(6694)+42d0*v(6729)+7d0*v(6741)+v(6780)+v(566)*v(8173))/5040d0
v(6777)=-(v(602)*v(6592))
v(6790)=-v(6777)+v(6764)*v(8123)
v(8168)=(-5040d0)*v(6264)+v(6790)
v(6884)=(v(6547)+840d0*v(6835)+210d0*v(6847)+42d0*v(6859)+7d0*v(6871)+v(6871)*v(8128)+v(8168))/5040d0
v(7025)=statev(53)*v(6572)+statev(58)*v(6884)+v(6779)*v(7516)
v(6931)=statev(57)*v(6779)+statev(55)*v(6884)+v(6572)*v(7515)
v(6895)=statev(56)*v(6572)+statev(54)*v(6779)+v(6884)*v(7517)
v(6803)=(v(6585)+840d0*v(6670)+210d0*v(6705)+42d0*v(6740)+7d0*v(6751)+v(6751)*v(8131)+v(8168))/5040d0
v(6979)=statev(55)*v(6779)+statev(57)*v(6803)+v(6615)*v(7515)
v(6919)=statev(56)*v(6615)+statev(54)*v(6803)+v(6779)*v(7517)
v(6814)=statev(53)*v(6615)+statev(58)*v(6779)+v(6803)*v(7516)
v(6778)=(840d0*v(6646)+210d0*v(6681)+42d0*v(6716)+7d0*v(6762)+v(6777)+(v(570)*v(6557)+v(569)*v(6748)+v(567)*v(6762))*v&
&(7522))/5040d0
v(6974)=statev(55)*v(6778)+statev(57)*v(6799)+v(6611)*v(7515)
v(6915)=statev(56)*v(6611)+statev(54)*v(6799)+v(6778)*v(7517)
v(6811)=statev(53)*v(6611)+statev(58)*v(6778)+v(6799)*v(7516)
v(6776)=(840d0*v(6645)+210d0*v(6680)+42d0*v(6715)+7d0*v(6761)-5040d0*v(6775)+v(6777)+(v(570)*v(6556)+v(569)*v(6747)+v&
&(567)*v(6761))*v(7522))/5040d0
v(6973)=statev(55)*v(6776)+statev(57)*v(6797)+v(6610)*v(7515)
v(6914)=statev(56)*v(6610)+statev(54)*v(6797)+v(6776)*v(7517)
v(6810)=statev(53)*v(6610)+statev(58)*v(6776)+v(6797)*v(7516)
v(6774)=(2520d0*v(6263)+840d0*v(6643)+210d0*v(6678)+42d0*v(6713)+7d0*v(6759)+v(6773)+v(7522)*(v(570)*v(6555)+v(569)*v&
&(6746)+v(567)*v(6759)-v(602)*v(737)-v(783)*v(8167)))/5040d0
v(6972)=statev(55)*v(6774)+statev(57)*v(6796)+v(6608)*v(7515)
v(6913)=statev(56)*v(6608)+statev(54)*v(6796)+v(6774)*v(7517)
v(6809)=statev(53)*v(6608)+statev(58)*v(6774)+v(6796)*v(7516)
v(6772)=(v(7522)*(v(570)*v(6554)+v(569)*v(6745)+v(567)*v(6757)-v(602)*v(736)-v(600)*v(782)-v(585)*v(797))+7d0*(360d0*v&
&(6262)+120d0*v(6641)+30d0*v(6676)+6d0*v(6711)+v(6757)+v(8169)))/5040d0
v(6971)=statev(55)*v(6772)+statev(57)*v(6795)+v(6607)*v(7515)
v(6912)=statev(56)*v(6607)+statev(54)*v(6795)+v(6772)*v(7517)
v(6808)=statev(53)*v(6607)+statev(58)*v(6772)+v(6795)*v(7516)
v(6770)=(2520d0*v(6261)+840d0*v(6640)+210d0*v(6675)+42d0*v(6710)+7d0*v(6756)+5040d0*v(6768)+v(6769)+v(7522)*(v(570)*v&
&(6551)+v(569)*v(6744)+v(567)*v(6756)-v(602)*v(735)-v(600)*v(768)))/5040d0
v(6970)=statev(55)*v(6770)+statev(57)*v(6794)+v(6603)*v(7515)
v(6911)=statev(56)*v(6603)+statev(54)*v(6794)+v(6770)*v(7517)
v(6807)=statev(53)*v(6603)+statev(58)*v(6770)+v(6794)*v(7516)
v(6767)=(7d0*(360d0*v(6260)+120d0*v(6638)+30d0*v(6673)+6d0*v(6708)+v(6754))+v(7522)*(v(570)*v(6550)+v(569)*v(6743)+v&
&(567)*v(6754)-v(602)*v(734)-v(585)*v(796)-v(781)*v(8167)))/5040d0
v(6969)=statev(55)*v(6767)+statev(57)*v(6793)+v(6602)*v(7515)
v(6910)=statev(56)*v(6602)+statev(54)*v(6793)+v(6767)*v(7517)
v(6806)=statev(53)*v(6602)+statev(58)*v(6767)+v(6793)*v(7516)
v(6766)=(7d0*(360d0*v(6259)+120d0*v(6637)+30d0*v(6672)+6d0*v(6707)+v(6753))+v(7522)*(v(570)*v(6549)+v(569)*v(6742)+v&
&(567)*v(6753)-v(602)*v(733)-v(585)*v(795)-v(780)*v(8167)))/5040d0
v(6968)=statev(55)*v(6766)+statev(57)*v(6792)+v(6601)*v(7515)
v(6909)=statev(56)*v(6601)+statev(54)*v(6792)+v(6766)*v(7517)
v(6805)=statev(53)*v(6601)+statev(58)*v(6766)+v(6792)*v(7516)
v(6765)=(2520d0*v(6258)+840d0*v(6636)+210d0*v(6671)+42d0*v(6706)+7d0*v(6752)+v(567)*v(8170)+v(567)*v(8171)+v(570)*v&
&(8172)+v(569)*v(8173))/5040d0
v(6967)=statev(55)*v(6765)+statev(57)*v(6791)+v(6600)*v(7515)
v(6908)=statev(56)*v(6600)+statev(54)*v(6791)+v(6765)*v(7517)
v(6804)=statev(53)*v(6600)+statev(58)*v(6765)+v(6791)*v(7516)
v(622)=(7d0*(360d0*v(593)+120d0*v(595)+30d0*v(599)+6d0*v(601)+v(602))+v(7522)*(v(570)*v(585)+v(567)*v(602)+v(569)*v&
&(8167)))/5040d0
v(621)=v(602)*v(8123)
v(627)=(2520d0*v(589)+840d0*v(591)+210d0*v(594)+42d0*v(597)+7d0*v(600)+v(621)+v(8131)*v(8167)+v(8174))/5040d0
v(604)=statev(53)*v(587)+statev(58)*v(622)+v(627)*v(7516)
v(607)=v(605)+v(606)+v(232)*v(6815)
v(6831)=-(v(607)*v(6592))
v(6833)=v(6313)+v(6831)+v(6832)
v(6830)=v(6274)-v(6313)+v(6833)
v(6829)=v(6273)+v(6312)+(v(567)*v(6822)-v(607)*v(737))*v(7522)
v(6828)=v(6272)+v(6311)+(v(567)*v(6821)-v(607)*v(736))*v(7522)
v(6827)=v(6271)+v(6310)+(v(567)*v(6820)-v(607)*v(735))*v(7522)
v(6826)=v(6270)+v(6309)+(v(567)*v(6819)-v(607)*v(734))*v(7522)
v(6825)=v(6269)+v(6308)+(v(567)*v(6817)-v(607)*v(733))*v(7522)
v(6824)=v(6268)+v(6307)+v(567)*(v(607)*v(7518)+v(6816)*v(7522))
v(610)=v(608)+v(609)+v(607)*v(8128)
v(6843)=-(v(610)*v(6592))
v(6844)=v(6346)+v(6655)+v(6843)+v(6833)*v(8128)
v(6842)=v(6345)+v(6654)+v(6843)+v(6830)*v(8128)
v(6841)=v(6344)+v(6653)+(v(567)*v(6829)-v(610)*v(737))*v(7522)
v(6840)=v(6343)+v(6652)+(v(567)*v(6828)-v(610)*v(736))*v(7522)
v(6839)=v(6342)+v(6651)+(v(567)*v(6827)-v(610)*v(735))*v(7522)
v(6838)=v(6341)+v(6650)+(v(567)*v(6826)-v(610)*v(734))*v(7522)
v(6837)=v(6340)+v(6649)+(v(567)*v(6825)-v(610)*v(733))*v(7522)
v(6836)=v(6339)+v(6648)+v(567)*(v(610)*v(7518)+v(6824)*v(7522))
v(613)=v(611)+v(612)+v(610)*v(8128)
v(6855)=-(v(613)*v(6592))
v(6856)=v(6435)+v(6690)+v(6855)+v(6844)*v(8128)
v(6854)=v(6434)+v(6689)+v(6855)+v(6842)*v(8128)
v(6853)=v(6433)+v(6688)+(v(567)*v(6841)-v(613)*v(737))*v(7522)
v(6852)=v(6432)+v(6687)+(v(567)*v(6840)-v(613)*v(736))*v(7522)
v(6851)=v(6431)+v(6686)+(v(567)*v(6839)-v(613)*v(735))*v(7522)
v(6850)=v(6430)+v(6685)+(v(567)*v(6838)-v(613)*v(734))*v(7522)
v(6849)=v(6429)+v(6684)+(v(567)*v(6837)-v(613)*v(733))*v(7522)
v(6848)=v(6428)+v(6683)+v(567)*(v(613)*v(7518)+v(6836)*v(7522))
v(616)=v(614)+v(615)+v(613)*v(8128)
v(6867)=-(v(616)*v(6592))
v(6868)=v(6471)+v(6725)+v(6867)+v(6856)*v(8128)
v(6866)=v(6470)+v(6724)+v(6867)+v(6854)*v(8128)
v(6865)=v(6469)+v(6723)+(v(567)*v(6853)-v(616)*v(737))*v(7522)
v(6864)=v(6468)+v(6722)+(v(567)*v(6852)-v(616)*v(736))*v(7522)
v(6863)=v(6467)+v(6721)+(v(567)*v(6851)-v(616)*v(735))*v(7522)
v(6862)=v(6466)+v(6720)+(v(567)*v(6850)-v(616)*v(734))*v(7522)
v(6861)=v(6465)+v(6719)+(v(567)*v(6849)-v(616)*v(733))*v(7522)
v(6860)=v(6464)+v(6718)+v(567)*(v(616)*v(7518)+v(6848)*v(7522))
v(619)=v(617)+v(618)+v(616)*v(8128)
v(8176)=5040d0+v(619)
v(6879)=-(v(619)*v(6592))
v(8175)=(-5040d0)*v(6286)+v(6879)-v(8164)
v(6880)=(v(6544)+v(6787)+840d0*v(6833)+210d0*v(6844)+42d0*v(6856)+7d0*v(6868)+v(6868)*v(8128)+v(8175))/5040d0
v(7020)=statev(53)*v(6569)+statev(58)*v(6880)+v(6778)*v(7516)
v(6927)=statev(57)*v(6778)+statev(55)*v(6880)+v(6569)*v(7515)
v(6892)=statev(56)*v(6569)+statev(54)*v(6778)+v(6880)*v(7517)
v(6878)=(v(6543)+v(6786)+840d0*v(6830)+210d0*v(6842)+42d0*v(6854)+7d0*v(6866)+v(6866)*v(8128)+v(8175))/5040d0
v(7019)=statev(53)*v(6568)+statev(58)*v(6878)+v(6776)*v(7516)
v(6926)=statev(57)*v(6776)+statev(55)*v(6878)+v(6568)*v(7515)
v(6891)=statev(56)*v(6568)+statev(54)*v(6776)+v(6878)*v(7517)
v(6877)=(v(6542)+v(6785)+2520d0*v(6822)+840d0*v(6829)+210d0*v(6841)+42d0*v(6853)+7d0*v(6865)+v(7522)*(v(567)*v(6865)-v&
&(737)*v(8176)))/5040d0
v(7018)=statev(53)*v(6566)+statev(58)*v(6877)+v(6774)*v(7516)
v(6925)=statev(57)*v(6774)+statev(55)*v(6877)+v(6566)*v(7515)
v(6890)=statev(56)*v(6566)+statev(54)*v(6774)+v(6877)*v(7517)
v(6876)=(v(6541)+v(6784)+2520d0*v(6821)+840d0*v(6828)+210d0*v(6840)+42d0*v(6852)+7d0*v(6864)+v(7522)*(v(567)*v(6864)-v&
&(736)*v(8176)))/5040d0
v(7017)=statev(53)*v(6565)+statev(58)*v(6876)+v(6772)*v(7516)
v(6924)=statev(57)*v(6772)+statev(55)*v(6876)+v(6565)*v(7515)
v(6889)=statev(56)*v(6565)+statev(54)*v(6772)+v(6876)*v(7517)
v(6875)=(v(6540)+v(6783)+2520d0*v(6820)+840d0*v(6827)+210d0*v(6839)+42d0*v(6851)+7d0*v(6863)+v(7522)*(v(567)*v(6863)-v&
&(735)*v(8176)))/5040d0
v(7016)=statev(53)*v(6564)+statev(58)*v(6875)+v(6770)*v(7516)
v(6923)=statev(57)*v(6770)+statev(55)*v(6875)+v(6564)*v(7515)
v(6888)=statev(56)*v(6564)+statev(54)*v(6770)+v(6875)*v(7517)
v(6874)=(v(6539)+v(6782)+2520d0*v(6819)+840d0*v(6826)+210d0*v(6838)+42d0*v(6850)+7d0*v(6862)+v(7522)*(v(567)*v(6862)-v&
&(734)*v(8176)))/5040d0
v(7015)=statev(53)*v(6563)+statev(58)*v(6874)+v(6767)*v(7516)
v(6922)=statev(57)*v(6767)+statev(55)*v(6874)+v(6563)*v(7515)
v(6887)=statev(56)*v(6563)+statev(54)*v(6767)+v(6874)*v(7517)
v(6873)=(v(6538)+v(6781)+2520d0*v(6817)+840d0*v(6825)+210d0*v(6837)+42d0*v(6849)+7d0*v(6861)+v(7522)*(v(567)*v(6861)-v&
&(733)*v(8176)))/5040d0
v(7014)=statev(53)*v(6562)+statev(58)*v(6873)+v(6766)*v(7516)
v(6921)=statev(57)*v(6766)+statev(55)*v(6873)+v(6562)*v(7515)
v(6886)=statev(56)*v(6562)+statev(54)*v(6766)+v(6873)*v(7517)
v(6872)=(v(6537)+v(6780)+2520d0*v(6816)+840d0*v(6824)+210d0*v(6836)+42d0*v(6848)+7d0*v(6860)+v(567)*(v(6860)*v(7522)+v&
&(7518)*v(8176)))/5040d0
v(7013)=statev(53)*v(6561)+statev(58)*v(6872)+v(6765)*v(7516)
v(6920)=statev(57)*v(6765)+statev(55)*v(6872)+v(6561)*v(7515)
v(6885)=statev(56)*v(6561)+statev(54)*v(6765)+v(6872)*v(7517)
v(629)=(5040d0+2520d0*v(607)+840d0*v(610)+210d0*v(613)+42d0*v(616)+7d0*v(619)+v(620)+v(621)+v(8128)*v(8176))/5040d0
v(624)=statev(54)*v(622)+statev(56)*v(623)+v(629)*v(7517)
v(626)=statev(58)*v(623)+statev(53)*v(625)+v(587)*v(7516)
v(628)=statev(56)*v(587)+statev(54)*v(627)+v(622)*v(7517)
v(630)=statev(57)*v(622)+statev(55)*v(629)+v(623)*v(7515)
v(631)=statev(54)*v(587)+statev(56)*v(625)+v(623)*v(7517)
v(6966)=v(624)*v(6626)+v(586)*v(6895)-v(631)*v(6931)-v(630)*v(6944)
v(6965)=v(624)*v(6625)+v(586)*v(6894)-v(631)*v(6930)-v(630)*v(6941)
v(6964)=v(624)*v(6624)+v(586)*v(6893)-v(631)*v(6929)-v(630)*v(6940)
v(6963)=v(624)*v(6623)+v(586)*v(6892)-v(631)*v(6927)-v(630)*v(6939)
v(6962)=v(624)*v(6622)+v(586)*v(6891)-v(631)*v(6926)-v(630)*v(6938)
v(6961)=v(624)*v(6621)+v(586)*v(6890)-v(631)*v(6925)-v(630)*v(6937)
v(6960)=v(624)*v(6620)+v(586)*v(6889)-v(631)*v(6924)-v(630)*v(6936)
v(6959)=v(624)*v(6619)+v(586)*v(6888)-v(631)*v(6923)-v(630)*v(6935)
v(6958)=v(624)*v(6618)+v(586)*v(6887)-v(631)*v(6922)-v(630)*v(6934)
v(6957)=v(624)*v(6617)+v(586)*v(6886)-v(631)*v(6921)-v(630)*v(6933)
v(6956)=v(624)*v(6616)+v(586)*v(6885)-v(631)*v(6920)-v(630)*v(6932)
v(6955)=-(v(631)*v(6814))+v(628)*v(6907)+v(626)*v(6919)-v(604)*v(6944)
v(6954)=-(v(631)*v(6813))+v(628)*v(6905)+v(626)*v(6918)-v(604)*v(6941)
v(6953)=-(v(631)*v(6812))+v(628)*v(6904)+v(626)*v(6916)-v(604)*v(6940)
v(6952)=-(v(631)*v(6811))+v(628)*v(6903)+v(626)*v(6915)-v(604)*v(6939)
v(6951)=-(v(631)*v(6810))+v(628)*v(6902)+v(626)*v(6914)-v(604)*v(6938)
v(6950)=-(v(631)*v(6809))+v(628)*v(6901)+v(626)*v(6913)-v(604)*v(6937)
v(6949)=-(v(631)*v(6808))+v(628)*v(6900)+v(626)*v(6912)-v(604)*v(6936)
v(6948)=-(v(631)*v(6807))+v(628)*v(6899)+v(626)*v(6911)-v(604)*v(6935)
v(6947)=-(v(631)*v(6806))+v(628)*v(6898)+v(626)*v(6910)-v(604)*v(6934)
v(6946)=-(v(631)*v(6805))+v(628)*v(6897)+v(626)*v(6909)-v(604)*v(6933)
v(6945)=-(v(631)*v(6804))+v(628)*v(6896)+v(626)*v(6908)-v(604)*v(6932)
v(674)=v(626)*v(628)-v(604)*v(631)
v(7374)=(v(674)*v(674))
v(666)=v(586)*v(624)-v(630)*v(631)
v(7344)=(v(666)*v(666))
v(632)=statev(55)*v(622)+statev(57)*v(627)+v(587)*v(7515)
v(7012)=-(v(632)*v(6895))+v(630)*v(6919)+v(628)*v(6931)-v(624)*v(6979)
v(7011)=-(v(632)*v(6894))+v(630)*v(6918)+v(628)*v(6930)-v(624)*v(6978)
v(7010)=-(v(632)*v(6893))+v(630)*v(6916)+v(628)*v(6929)-v(624)*v(6975)
v(7009)=-(v(632)*v(6892))+v(630)*v(6915)+v(628)*v(6927)-v(624)*v(6974)
v(7008)=-(v(632)*v(6891))+v(630)*v(6914)+v(628)*v(6926)-v(624)*v(6973)
v(7007)=-(v(632)*v(6890))+v(630)*v(6913)+v(628)*v(6925)-v(624)*v(6972)
v(7006)=-(v(632)*v(6889))+v(630)*v(6912)+v(628)*v(6924)-v(624)*v(6971)
v(7005)=-(v(632)*v(6888))+v(630)*v(6911)+v(628)*v(6923)-v(624)*v(6970)
v(7004)=-(v(632)*v(6887))+v(630)*v(6910)+v(628)*v(6922)-v(624)*v(6969)
v(7003)=-(v(632)*v(6886))+v(630)*v(6909)+v(628)*v(6921)-v(624)*v(6968)
v(7002)=-(v(632)*v(6885))+v(630)*v(6908)+v(628)*v(6920)-v(624)*v(6967)
v(7001)=-(v(628)*v(6626))-v(586)*v(6919)+v(632)*v(6944)+v(631)*v(6979)
v(7000)=-(v(628)*v(6625))-v(586)*v(6918)+v(632)*v(6941)+v(631)*v(6978)
v(6999)=-(v(628)*v(6624))-v(586)*v(6916)+v(632)*v(6940)+v(631)*v(6975)
v(6998)=-(v(628)*v(6623))-v(586)*v(6915)+v(632)*v(6939)+v(631)*v(6974)
v(6997)=-(v(628)*v(6622))-v(586)*v(6914)+v(632)*v(6938)+v(631)*v(6973)
v(6996)=-(v(628)*v(6621))-v(586)*v(6913)+v(632)*v(6937)+v(631)*v(6972)
v(6995)=-(v(628)*v(6620))-v(586)*v(6912)+v(632)*v(6936)+v(631)*v(6971)
v(6994)=-(v(628)*v(6619))-v(586)*v(6911)+v(632)*v(6935)+v(631)*v(6970)
v(6993)=-(v(628)*v(6618))-v(586)*v(6910)+v(632)*v(6934)+v(631)*v(6969)
v(6992)=-(v(628)*v(6617))-v(586)*v(6909)+v(632)*v(6933)+v(631)*v(6968)
v(6991)=-(v(628)*v(6616))-v(586)*v(6908)+v(632)*v(6932)+v(631)*v(6967)
v(6990)=v(604)*v(6626)+v(586)*v(6814)-v(632)*v(6907)-v(626)*v(6979)
v(6989)=v(604)*v(6625)+v(586)*v(6813)-v(632)*v(6905)-v(626)*v(6978)
v(6988)=v(604)*v(6624)+v(586)*v(6812)-v(632)*v(6904)-v(626)*v(6975)
v(6987)=v(604)*v(6623)+v(586)*v(6811)-v(632)*v(6903)-v(626)*v(6974)
v(6986)=v(604)*v(6622)+v(586)*v(6810)-v(632)*v(6902)-v(626)*v(6973)
v(6985)=v(604)*v(6621)+v(586)*v(6809)-v(632)*v(6901)-v(626)*v(6972)
v(6984)=v(604)*v(6620)+v(586)*v(6808)-v(632)*v(6900)-v(626)*v(6971)
v(6983)=v(604)*v(6619)+v(586)*v(6807)-v(632)*v(6899)-v(626)*v(6970)
v(6982)=v(604)*v(6618)+v(586)*v(6806)-v(632)*v(6898)-v(626)*v(6969)
v(6981)=v(604)*v(6617)+v(586)*v(6805)-v(632)*v(6897)-v(626)*v(6968)
v(6980)=v(604)*v(6616)+v(586)*v(6804)-v(632)*v(6896)-v(626)*v(6967)
v(675)=v(586)*v(604)-v(626)*v(632)
v(7375)=(v(675)*v(675))
v(673)=-(v(586)*v(628))+v(631)*v(632)
v(7373)=(v(673)*v(673))
v(8184)=v(7373)+v(7374)+v(7375)
v(667)=v(628)*v(630)-v(624)*v(632)
v(7327)=(v(667)*v(667))
v(633)=statev(53)*v(623)+statev(58)*v(629)+v(622)*v(7516)
v(7314)=v(633)*v(673)+v(630)*v(674)+v(624)*v(675)
v(7316)=1d0/v(7314)**3
v(8177)=(-2d0)*v(7316)
v(7326)=(v(675)*v(6895)+v(674)*v(6931)+v(630)*v(6955)+v(624)*v(6990)+v(633)*v(7001)+v(673)*v(7025))*v(8177)
v(7325)=(v(675)*v(6894)+v(674)*v(6930)+v(630)*v(6954)+v(624)*v(6989)+v(633)*v(7000)+v(673)*v(7024))*v(8177)
v(7324)=(v(675)*v(6893)+v(674)*v(6929)+v(630)*v(6953)+v(624)*v(6988)+v(633)*v(6999)+v(673)*v(7023))*v(8177)
v(7323)=(v(675)*v(6892)+v(674)*v(6927)+v(630)*v(6952)+v(624)*v(6987)+v(633)*v(6998)+v(673)*v(7020))*v(8177)
v(7322)=(v(675)*v(6891)+v(674)*v(6926)+v(630)*v(6951)+v(624)*v(6986)+v(633)*v(6997)+v(673)*v(7019))*v(8177)
v(7321)=(v(675)*v(6890)+v(674)*v(6925)+v(630)*v(6950)+v(624)*v(6985)+v(633)*v(6996)+v(673)*v(7018))*v(8177)
v(7320)=(v(675)*v(6889)+v(674)*v(6924)+v(630)*v(6949)+v(624)*v(6984)+v(633)*v(6995)+v(673)*v(7017))*v(8177)
v(7319)=(v(675)*v(6888)+v(674)*v(6923)+v(630)*v(6948)+v(624)*v(6983)+v(633)*v(6994)+v(673)*v(7016))*v(8177)
v(7318)=(v(675)*v(6887)+v(674)*v(6922)+v(630)*v(6947)+v(624)*v(6982)+v(633)*v(6993)+v(673)*v(7015))*v(8177)
v(7317)=(v(675)*v(6886)+v(674)*v(6921)+v(630)*v(6946)+v(624)*v(6981)+v(633)*v(6992)+v(673)*v(7014))*v(8177)
v(7315)=(v(675)*v(6885)+v(674)*v(6920)+v(630)*v(6945)+v(624)*v(6980)+v(633)*v(6991)+v(673)*v(7013))*v(8177)
v(7069)=v(624)*v(6814)+v(604)*v(6895)-v(633)*v(6919)-v(628)*v(7025)
v(7068)=v(624)*v(6813)+v(604)*v(6894)-v(633)*v(6918)-v(628)*v(7024)
v(7067)=v(624)*v(6812)+v(604)*v(6893)-v(633)*v(6916)-v(628)*v(7023)
v(7066)=v(624)*v(6811)+v(604)*v(6892)-v(633)*v(6915)-v(628)*v(7020)
v(7065)=v(624)*v(6810)+v(604)*v(6891)-v(633)*v(6914)-v(628)*v(7019)
v(7064)=v(624)*v(6809)+v(604)*v(6890)-v(633)*v(6913)-v(628)*v(7018)
v(7063)=v(624)*v(6808)+v(604)*v(6889)-v(633)*v(6912)-v(628)*v(7017)
v(7062)=v(624)*v(6807)+v(604)*v(6888)-v(633)*v(6911)-v(628)*v(7016)
v(7061)=v(624)*v(6806)+v(604)*v(6887)-v(633)*v(6910)-v(628)*v(7015)
v(7060)=v(624)*v(6805)+v(604)*v(6886)-v(633)*v(6909)-v(628)*v(7014)
v(7059)=v(624)*v(6804)+v(604)*v(6885)-v(633)*v(6908)-v(628)*v(7013)
v(7058)=-(v(626)*v(6895))-v(624)*v(6907)+v(633)*v(6944)+v(631)*v(7025)
v(7057)=-(v(626)*v(6894))-v(624)*v(6905)+v(633)*v(6941)+v(631)*v(7024)
v(7056)=-(v(626)*v(6893))-v(624)*v(6904)+v(633)*v(6940)+v(631)*v(7023)
v(7055)=-(v(626)*v(6892))-v(624)*v(6903)+v(633)*v(6939)+v(631)*v(7020)
v(7054)=-(v(626)*v(6891))-v(624)*v(6902)+v(633)*v(6938)+v(631)*v(7019)
v(7053)=-(v(626)*v(6890))-v(624)*v(6901)+v(633)*v(6937)+v(631)*v(7018)
v(7052)=-(v(626)*v(6889))-v(624)*v(6900)+v(633)*v(6936)+v(631)*v(7017)
v(7051)=-(v(626)*v(6888))-v(624)*v(6899)+v(633)*v(6935)+v(631)*v(7016)
v(7050)=-(v(626)*v(6887))-v(624)*v(6898)+v(633)*v(6934)+v(631)*v(7015)
v(7049)=-(v(626)*v(6886))-v(624)*v(6897)+v(633)*v(6933)+v(631)*v(7014)
v(7048)=-(v(626)*v(6885))-v(624)*v(6896)+v(633)*v(6932)+v(631)*v(7013)
v(7047)=-(v(633)*v(6626))+v(630)*v(6907)+v(626)*v(6931)-v(586)*v(7025)
v(7046)=-(v(633)*v(6625))+v(630)*v(6905)+v(626)*v(6930)-v(586)*v(7024)
v(7045)=-(v(633)*v(6624))+v(630)*v(6904)+v(626)*v(6929)-v(586)*v(7023)
v(7044)=-(v(633)*v(6623))+v(630)*v(6903)+v(626)*v(6927)-v(586)*v(7020)
v(7043)=-(v(633)*v(6622))+v(630)*v(6902)+v(626)*v(6926)-v(586)*v(7019)
v(7042)=-(v(633)*v(6621))+v(630)*v(6901)+v(626)*v(6925)-v(586)*v(7018)
v(7041)=-(v(633)*v(6620))+v(630)*v(6900)+v(626)*v(6924)-v(586)*v(7017)
v(7040)=-(v(633)*v(6619))+v(630)*v(6899)+v(626)*v(6923)-v(586)*v(7016)
v(7039)=-(v(633)*v(6618))+v(630)*v(6898)+v(626)*v(6922)-v(586)*v(7015)
v(7038)=-(v(633)*v(6617))+v(630)*v(6897)+v(626)*v(6921)-v(586)*v(7014)
v(7037)=-(v(633)*v(6616))+v(630)*v(6896)+v(626)*v(6920)-v(586)*v(7013)
v(7036)=-(v(630)*v(6814))-v(604)*v(6931)+v(633)*v(6979)+v(632)*v(7025)
v(7035)=-(v(630)*v(6813))-v(604)*v(6930)+v(633)*v(6978)+v(632)*v(7024)
v(7034)=-(v(630)*v(6812))-v(604)*v(6929)+v(633)*v(6975)+v(632)*v(7023)
v(7033)=-(v(630)*v(6811))-v(604)*v(6927)+v(633)*v(6974)+v(632)*v(7020)
v(7032)=-(v(630)*v(6810))-v(604)*v(6926)+v(633)*v(6973)+v(632)*v(7019)
v(7031)=-(v(630)*v(6809))-v(604)*v(6925)+v(633)*v(6972)+v(632)*v(7018)
v(7030)=-(v(630)*v(6808))-v(604)*v(6924)+v(633)*v(6971)+v(632)*v(7017)
v(7029)=-(v(630)*v(6807))-v(604)*v(6923)+v(633)*v(6970)+v(632)*v(7016)
v(7028)=-(v(630)*v(6806))-v(604)*v(6922)+v(633)*v(6969)+v(632)*v(7015)
v(7027)=-(v(630)*v(6805))-v(604)*v(6921)+v(633)*v(6968)+v(632)*v(7014)
v(7026)=-(v(630)*v(6804))-v(604)*v(6920)+v(633)*v(6967)+v(632)*v(7013)
v(671)=-(v(604)*v(630))+v(632)*v(633)
v(7329)=(v(671)*v(671))
v(670)=v(626)*v(630)-v(586)*v(633)
v(7346)=(v(670)*v(670))
v(669)=-(v(624)*v(626))+v(631)*v(633)
v(8239)=v(666)*v(673)+v(669)*v(674)+v(670)*v(675)
v(7345)=(v(669)*v(669))
v(8186)=v(7344)+v(7345)+v(7346)
v(668)=v(604)*v(624)-v(628)*v(633)
v(8238)=v(667)*v(673)+v(668)*v(674)+v(671)*v(675)
v(8237)=v(666)*v(667)+v(668)*v(669)+v(670)*v(671)
v(7328)=(v(668)*v(668))
v(8187)=v(7327)+v(7328)+v(7329)
v(635)=(2d0/3d0)*v(352)+v(636)+v(638)+v(6145)*v(8178)+v(7070)*v(8179)
v(637)=(2d0/3d0)*v(342)+v(636)+v(639)+v(6162)*v(8178)+v(7104)*v(8179)
v(640)=(2d0/3d0)*v(347)+v(638)+v(639)+v(7138)*v(8178)+v(7140)*v(8179)
v(641)=v(354)+v(6179)*v(8178)+v(7188)*v(8179)
v(8182)=2d0*v(641)
v(642)=v(355)+v(6196)*v(8178)+v(7221)*v(8179)
v(8181)=2d0*v(642)
v(643)=v(356)+v(6213)*v(8178)+v(7254)*v(8179)
v(8180)=2d0*v(643)
v(7293)=v(169)*v(635)+v(183)*v(637)+v(191)*v(640)+v(1536)*v(641)+v(1540)*v(642)+v(214)*v(8180)
v(7292)=v(168)*v(635)+v(181)*v(637)+v(190)*v(640)+v(1539)*v(641)+v(207)*v(8180)+v(205)*v(8181)
v(7291)=v(167)*v(635)+v(178)*v(637)+v(187)*v(640)+v(199)*v(8180)+v(198)*v(8181)+v(196)*v(8182)
v(7290)=v(166)*v(635)+v(174)*v(637)+v(186)*v(640)+v(191)*v(8180)+v(190)*v(8181)+v(187)*v(8182)
v(7289)=v(161)*v(635)+v(172)*v(637)+v(174)*v(640)+v(183)*v(8180)+v(181)*v(8181)+v(178)*v(8182)
v(7288)=v(156)*v(635)+v(161)*v(637)+v(166)*v(640)+v(169)*v(8180)+v(168)*v(8181)+v(167)*v(8182)
v(7298)=1d0/sqrt(v(635)*v(7288)+v(637)*v(7289)+v(640)*v(7290)+v(7293)*v(8180)+v(7292)*v(8181)+v(7291)*v(8182))
v(8191)=v(7298)/2d0
v(656)=1d0/v(7314)**2
v(8183)=2d0*v(656)
v(7432)=v(656)*v(8239)
v(7430)=v(656)*v(8238)
v(7428)=v(656)*v(8237)
v(7380)=v(673)*v(8183)
v(7379)=v(675)*v(8183)
v(7378)=v(674)*v(8183)
v(7400)=(-(v(6955)*v(7378))-v(6990)*v(7379)-v(7001)*v(7380)-v(7326)*v(8184))/3d0
v(7398)=(-(v(6954)*v(7378))-v(6989)*v(7379)-v(7000)*v(7380)-v(7325)*v(8184))/3d0
v(7396)=(-(v(6953)*v(7378))-v(6988)*v(7379)-v(6999)*v(7380)-v(7324)*v(8184))/3d0
v(7394)=(-(v(6952)*v(7378))-v(6987)*v(7379)-v(6998)*v(7380)-v(7323)*v(8184))/3d0
v(7392)=(-(v(6951)*v(7378))-v(6986)*v(7379)-v(6997)*v(7380)-v(7322)*v(8184))/3d0
v(7390)=(-(v(6950)*v(7378))-v(6985)*v(7379)-v(6996)*v(7380)-v(7321)*v(8184))/3d0
v(7388)=(-(v(6949)*v(7378))-v(6984)*v(7379)-v(6995)*v(7380)-v(7320)*v(8184))/3d0
v(7386)=(-(v(6948)*v(7378))-v(6983)*v(7379)-v(6994)*v(7380)-v(7319)*v(8184))/3d0
v(7384)=(-(v(6947)*v(7378))-v(6982)*v(7379)-v(6993)*v(7380)-v(7318)*v(8184))/3d0
v(7382)=(-(v(6946)*v(7378))-v(6981)*v(7379)-v(6992)*v(7380)-v(7317)*v(8184))/3d0
v(7377)=(-(v(6945)*v(7378))-v(6980)*v(7379)-v(6991)*v(7380)-v(7315)*v(8184))/3d0
v(7362)=1d0/v(656)**0.13333333333333333d1
v(8185)=-v(7362)/3d0
v(7372)=v(7326)*v(8185)
v(7371)=v(7325)*v(8185)
v(7370)=v(7324)*v(8185)
v(7369)=v(7323)*v(8185)
v(7368)=v(7322)*v(8185)
v(7367)=v(7321)*v(8185)
v(7366)=v(7320)*v(8185)
v(7365)=v(7319)*v(8185)
v(7364)=v(7318)*v(8185)
v(7363)=v(7317)*v(8185)
v(7361)=v(7315)*v(8185)
v(7350)=-(v(669)*v(8183))
v(7349)=-(v(670)*v(8183))
v(7348)=-(v(666)*v(8183))
v(7360)=v(6966)*v(7348)+v(7047)*v(7349)+v(7058)*v(7350)-v(7326)*v(8186)
v(7359)=v(6965)*v(7348)+v(7046)*v(7349)+v(7057)*v(7350)-v(7325)*v(8186)
v(7358)=v(6964)*v(7348)+v(7045)*v(7349)+v(7056)*v(7350)-v(7324)*v(8186)
v(7357)=v(6963)*v(7348)+v(7044)*v(7349)+v(7055)*v(7350)-v(7323)*v(8186)
v(7356)=v(6962)*v(7348)+v(7043)*v(7349)+v(7054)*v(7350)-v(7322)*v(8186)
v(7355)=v(6961)*v(7348)+v(7042)*v(7349)+v(7053)*v(7350)-v(7321)*v(8186)
v(7354)=v(6960)*v(7348)+v(7041)*v(7349)+v(7052)*v(7350)-v(7320)*v(8186)
v(7353)=v(6959)*v(7348)+v(7040)*v(7349)+v(7051)*v(7350)-v(7319)*v(8186)
v(7352)=v(6958)*v(7348)+v(7039)*v(7349)+v(7050)*v(7350)-v(7318)*v(8186)
v(7351)=v(6957)*v(7348)+v(7038)*v(7349)+v(7049)*v(7350)-v(7317)*v(8186)
v(7347)=v(6956)*v(7348)+v(7037)*v(7349)+v(7048)*v(7350)-v(7315)*v(8186)
v(7333)=-(v(668)*v(8183))
v(7332)=-(v(671)*v(8183))
v(7331)=-(v(667)*v(8183))
v(7343)=v(7012)*v(7331)+v(7036)*v(7332)+v(7069)*v(7333)-v(7326)*v(8187)
v(7342)=v(7011)*v(7331)+v(7035)*v(7332)+v(7068)*v(7333)-v(7325)*v(8187)
v(7341)=v(7010)*v(7331)+v(7034)*v(7332)+v(7067)*v(7333)-v(7324)*v(8187)
v(7340)=v(7009)*v(7331)+v(7033)*v(7332)+v(7066)*v(7333)-v(7323)*v(8187)
v(7339)=v(7008)*v(7331)+v(7032)*v(7332)+v(7065)*v(7333)-v(7322)*v(8187)
v(7338)=v(7007)*v(7331)+v(7031)*v(7332)+v(7064)*v(7333)-v(7321)*v(8187)
v(7337)=v(7006)*v(7331)+v(7030)*v(7332)+v(7063)*v(7333)-v(7320)*v(8187)
v(7336)=v(7005)*v(7331)+v(7029)*v(7332)+v(7062)*v(7333)-v(7319)*v(8187)
v(7335)=v(7004)*v(7331)+v(7028)*v(7332)+v(7061)*v(7333)-v(7318)*v(8187)
v(7334)=v(7003)*v(7331)+v(7027)*v(7332)+v(7060)*v(7333)-v(7317)*v(8187)
v(7330)=v(7002)*v(7331)+v(7026)*v(7332)+v(7059)*v(7333)-v(7315)*v(8187)
v(663)=-(v(656)*v(8187))
v(662)=-(v(656)*v(8186))
v(660)=1d0/v(656)**0.3333333333333333d0
v(661)=-(v(656)*v(8184))/3d0
v(7426)=v(661)+(-2d0/3d0)*v(662)+v(663)/3d0
v(7424)=v(661)+v(662)/3d0+(-2d0/3d0)*v(663)
dRdX(1,1)=v(8191)*(v(7072)*v(7288)+v(7106)*v(7289)+v(7142)*v(7290)+v(7291)*v(8192)+v(8182)*(v(1305)*v(635)+v(1365)*v&
&(637)+v(1413)*v(640)+v(167)*v(7072)+v(178)*v(7106)+v(187)*v(7142)+v(1539)*v(7223)+v(1536)*v(7256)+v(1473)*v(8180)+v&
&(1461)*v(8181)+v(1449)*v(8182)+v(196)*v(8192))+v(7292)*v(8193)+v(8181)*(v(1317)*v(635)+v(1377)*v(637)+v(1425)*v(640)+v&
&(168)*v(7072)+v(181)*v(7106)+v(190)*v(7142)+v(1539)*v(7190)+v(1540)*v(7256)+v(1497)*v(8180)+v(1485)*v(8181)+v(1461)*v&
&(8182)+v(205)*v(8193))+v(7293)*v(8194)+v(635)*(v(1269)*v(635)+v(1281)*v(637)+v(1293)*v(640)+v(156)*v(7072)+v(161)*v&
&(7106)+v(166)*v(7142)+v(1329)*v(8180)+v(1317)*v(8181)+v(1305)*v(8182)+v(167)*v(8192)+v(168)*v(8193)+v(169)*v(8194))+v&
&(637)*(v(1281)*v(635)+v(1341)*v(637)+v(1353)*v(640)+v(161)*v(7072)+v(172)*v(7106)+v(174)*v(7142)+v(1389)*v(8180)+v(1377&
&)*v(8181)+v(1365)*v(8182)+v(178)*v(8192)+v(181)*v(8193)+v(183)*v(8194))+v(640)*(v(1293)*v(635)+v(1353)*v(637)+v(1401)*v&
&(640)+v(166)*v(7072)+v(174)*v(7106)+v(186)*v(7142)+v(1437)*v(8180)+v(1425)*v(8181)+v(1413)*v(8182)+v(187)*v(8192)+v(190&
&)*v(8193)+v(191)*v(8194))+v(8180)*(v(1329)*v(635)+v(1389)*v(637)+v(1437)*v(640)+v(169)*v(7072)+v(183)*v(7106)+v(191)*v&
&(7142)+v(1536)*v(7190)+v(1540)*v(7223)+v(1509)*v(8180)+v(1497)*v(8181)+v(1473)*v(8182)+v(214)*v(8194)))+v(7518)*(-(mpar&
&(4)*mpar(5)*dexp(-(mpar(4)*v(116))))-mpar(6)*mpar(7)*dexp(-(mpar(6)*v(116))))
dRdX(1,2)=v(8191)*(v(7074)*v(7288)+v(7109)*v(7289)+v(7145)*v(7290)+v(635)*(v(1271)*v(635)+v(1283)*v(637)+v(1295)*v(640)&
&+v(156)*v(7074)+v(161)*v(7109)+v(166)*v(7145)+v(1645)*v(7192)+v(1673)*v(7225)+v(1705)*v(7258)+v(1331)*v(8180)+v(1319)*v&
&(8181)+v(1307)*v(8182))+v(637)*(v(1283)*v(635)+v(1343)*v(637)+v(1355)*v(640)+v(161)*v(7074)+v(172)*v(7109)+v(174)*v&
&(7145)+v(1648)*v(7192)+v(1676)*v(7225)+v(1708)*v(7258)+v(1391)*v(8180)+v(1379)*v(8181)+v(1367)*v(8182))+v(7291)*v(8234)&
&+v(8182)*(v(1307)*v(635)+v(1367)*v(637)+v(1415)*v(640)+v(167)*v(7074)+v(178)*v(7109)+v(187)*v(7145)+v(1539)*v(7225)+v&
&(1536)*v(7258)+v(1475)*v(8180)+v(1463)*v(8181)+v(1451)*v(8182)+v(196)*v(8234))+v(7292)*v(8235)+v(8181)*(v(1319)*v(635)&
&+v(1379)*v(637)+v(1427)*v(640)+v(168)*v(7074)+v(181)*v(7109)+v(190)*v(7145)+v(1539)*v(7192)+v(1540)*v(7258)+v(1499)*v&
&(8180)+v(1487)*v(8181)+v(1463)*v(8182)+v(205)*v(8235))+v(7293)*v(8236)+v(640)*(v(1295)*v(635)+v(1355)*v(637)+v(1403)*v&
&(640)+v(166)*v(7074)+v(174)*v(7109)+v(186)*v(7145)+v(1439)*v(8180)+v(1427)*v(8181)+v(1415)*v(8182)+v(187)*v(8234)+v(190&
&)*v(8235)+v(191)*v(8236))+v(8180)*(v(1331)*v(635)+v(1391)*v(637)+v(1439)*v(640)+v(169)*v(7074)+v(183)*v(7109)+v(191)*v&
&(7145)+v(1536)*v(7192)+v(1540)*v(7225)+v(1511)*v(8180)+v(1499)*v(8181)+v(1475)*v(8182)+v(214)*v(8236)))
dRdX(1,3)=v(8191)*(v(7077)*v(7288)+v(7111)*v(7289)+v(7148)*v(7290)+v(635)*(v(1272)*v(635)+v(1284)*v(637)+v(1296)*v(640)&
&+v(156)*v(7077)+v(161)*v(7111)+v(166)*v(7148)+v(1645)*v(7194)+v(1673)*v(7227)+v(1705)*v(7260)+v(1332)*v(8180)+v(1320)*v&
&(8181)+v(1308)*v(8182))+v(637)*(v(1284)*v(635)+v(1344)*v(637)+v(1356)*v(640)+v(161)*v(7077)+v(172)*v(7111)+v(174)*v&
&(7148)+v(1648)*v(7194)+v(1676)*v(7227)+v(1708)*v(7260)+v(1392)*v(8180)+v(1380)*v(8181)+v(1368)*v(8182))+v(7291)*v(8231)&
&+v(8182)*(v(1308)*v(635)+v(1368)*v(637)+v(1416)*v(640)+v(167)*v(7077)+v(178)*v(7111)+v(187)*v(7148)+v(1539)*v(7227)+v&
&(1536)*v(7260)+v(1476)*v(8180)+v(1464)*v(8181)+v(1452)*v(8182)+v(196)*v(8231))+v(7292)*v(8232)+v(8181)*(v(1320)*v(635)&
&+v(1380)*v(637)+v(1428)*v(640)+v(168)*v(7077)+v(181)*v(7111)+v(190)*v(7148)+v(1539)*v(7194)+v(1540)*v(7260)+v(1500)*v&
&(8180)+v(1488)*v(8181)+v(1464)*v(8182)+v(205)*v(8232))+v(7293)*v(8233)+v(640)*(v(1296)*v(635)+v(1356)*v(637)+v(1404)*v&
&(640)+v(166)*v(7077)+v(174)*v(7111)+v(186)*v(7148)+v(1440)*v(8180)+v(1428)*v(8181)+v(1416)*v(8182)+v(187)*v(8231)+v(190&
&)*v(8232)+v(191)*v(8233))+v(8180)*(v(1332)*v(635)+v(1392)*v(637)+v(1440)*v(640)+v(169)*v(7077)+v(183)*v(7111)+v(191)*v&
&(7148)+v(1536)*v(7194)+v(1540)*v(7227)+v(1512)*v(8180)+v(1500)*v(8181)+v(1476)*v(8182)+v(214)*v(8233)))
dRdX(1,4)=v(8191)*(v(7079)*v(7288)+v(7113)*v(7289)+v(7151)*v(7290)+v(635)*(v(1273)*v(635)+v(1285)*v(637)+v(1297)*v(640)&
&+v(156)*v(7079)+v(161)*v(7113)+v(166)*v(7151)+v(1645)*v(7196)+v(1673)*v(7229)+v(1705)*v(7262)+v(1333)*v(8180)+v(1321)*v&
&(8181)+v(1309)*v(8182))+v(637)*(v(1285)*v(635)+v(1345)*v(637)+v(1357)*v(640)+v(161)*v(7079)+v(172)*v(7113)+v(174)*v&
&(7151)+v(1648)*v(7196)+v(1676)*v(7229)+v(1708)*v(7262)+v(1393)*v(8180)+v(1381)*v(8181)+v(1369)*v(8182))+v(7291)*v(8228)&
&+v(8182)*(v(1309)*v(635)+v(1369)*v(637)+v(1417)*v(640)+v(167)*v(7079)+v(178)*v(7113)+v(187)*v(7151)+v(1539)*v(7229)+v&
&(1536)*v(7262)+v(1477)*v(8180)+v(1465)*v(8181)+v(1453)*v(8182)+v(196)*v(8228))+v(7292)*v(8229)+v(8181)*(v(1321)*v(635)&
&+v(1381)*v(637)+v(1429)*v(640)+v(168)*v(7079)+v(181)*v(7113)+v(190)*v(7151)+v(1539)*v(7196)+v(1540)*v(7262)+v(1501)*v&
&(8180)+v(1489)*v(8181)+v(1465)*v(8182)+v(205)*v(8229))+v(7293)*v(8230)+v(640)*(v(1297)*v(635)+v(1357)*v(637)+v(1405)*v&
&(640)+v(166)*v(7079)+v(174)*v(7113)+v(186)*v(7151)+v(1441)*v(8180)+v(1429)*v(8181)+v(1417)*v(8182)+v(187)*v(8228)+v(190&
&)*v(8229)+v(191)*v(8230))+v(8180)*(v(1333)*v(635)+v(1393)*v(637)+v(1441)*v(640)+v(169)*v(7079)+v(183)*v(7113)+v(191)*v&
&(7151)+v(1536)*v(7196)+v(1540)*v(7229)+v(1513)*v(8180)+v(1501)*v(8181)+v(1477)*v(8182)+v(214)*v(8230)))
dRdX(1,5)=v(8191)*(v(7081)*v(7288)+v(7115)*v(7289)+v(7154)*v(7290)+v(635)*(v(1274)*v(635)+v(1286)*v(637)+v(1298)*v(640)&
&+v(156)*v(7081)+v(161)*v(7115)+v(166)*v(7154)+v(1645)*v(7198)+v(1673)*v(7231)+v(1705)*v(7264)+v(1334)*v(8180)+v(1322)*v&
&(8181)+v(1310)*v(8182))+v(637)*(v(1286)*v(635)+v(1346)*v(637)+v(1358)*v(640)+v(161)*v(7081)+v(172)*v(7115)+v(174)*v&
&(7154)+v(1648)*v(7198)+v(1676)*v(7231)+v(1708)*v(7264)+v(1394)*v(8180)+v(1382)*v(8181)+v(1370)*v(8182))+v(7291)*v(8225)&
&+v(8182)*(v(1310)*v(635)+v(1370)*v(637)+v(1418)*v(640)+v(167)*v(7081)+v(178)*v(7115)+v(187)*v(7154)+v(1539)*v(7231)+v&
&(1536)*v(7264)+v(1478)*v(8180)+v(1466)*v(8181)+v(1454)*v(8182)+v(196)*v(8225))+v(7292)*v(8226)+v(8181)*(v(1322)*v(635)&
&+v(1382)*v(637)+v(1430)*v(640)+v(168)*v(7081)+v(181)*v(7115)+v(190)*v(7154)+v(1539)*v(7198)+v(1540)*v(7264)+v(1502)*v&
&(8180)+v(1490)*v(8181)+v(1466)*v(8182)+v(205)*v(8226))+v(7293)*v(8227)+v(640)*(v(1298)*v(635)+v(1358)*v(637)+v(1406)*v&
&(640)+v(166)*v(7081)+v(174)*v(7115)+v(186)*v(7154)+v(1442)*v(8180)+v(1430)*v(8181)+v(1418)*v(8182)+v(187)*v(8225)+v(190&
&)*v(8226)+v(191)*v(8227))+v(8180)*(v(1334)*v(635)+v(1394)*v(637)+v(1442)*v(640)+v(169)*v(7081)+v(183)*v(7115)+v(191)*v&
&(7154)+v(1536)*v(7198)+v(1540)*v(7231)+v(1514)*v(8180)+v(1502)*v(8181)+v(1478)*v(8182)+v(214)*v(8227)))
dRdX(1,6)=v(8191)*(v(7083)*v(7288)+v(7117)*v(7289)+v(7157)*v(7290)+v(635)*(v(1275)*v(635)+v(1287)*v(637)+v(1299)*v(640)&
&+v(156)*v(7083)+v(161)*v(7117)+v(166)*v(7157)+v(1645)*v(7200)+v(1673)*v(7233)+v(1705)*v(7266)+v(1335)*v(8180)+v(1323)*v&
&(8181)+v(1311)*v(8182))+v(637)*(v(1287)*v(635)+v(1347)*v(637)+v(1359)*v(640)+v(161)*v(7083)+v(172)*v(7117)+v(174)*v&
&(7157)+v(1648)*v(7200)+v(1676)*v(7233)+v(1708)*v(7266)+v(1395)*v(8180)+v(1383)*v(8181)+v(1371)*v(8182))+v(7291)*v(8222)&
&+v(8182)*(v(1311)*v(635)+v(1371)*v(637)+v(1419)*v(640)+v(167)*v(7083)+v(178)*v(7117)+v(187)*v(7157)+v(1539)*v(7233)+v&
&(1536)*v(7266)+v(1479)*v(8180)+v(1467)*v(8181)+v(1455)*v(8182)+v(196)*v(8222))+v(7292)*v(8223)+v(8181)*(v(1323)*v(635)&
&+v(1383)*v(637)+v(1431)*v(640)+v(168)*v(7083)+v(181)*v(7117)+v(190)*v(7157)+v(1539)*v(7200)+v(1540)*v(7266)+v(1503)*v&
&(8180)+v(1491)*v(8181)+v(1467)*v(8182)+v(205)*v(8223))+v(7293)*v(8224)+v(640)*(v(1299)*v(635)+v(1359)*v(637)+v(1407)*v&
&(640)+v(166)*v(7083)+v(174)*v(7117)+v(186)*v(7157)+v(1443)*v(8180)+v(1431)*v(8181)+v(1419)*v(8182)+v(187)*v(8222)+v(190&
&)*v(8223)+v(191)*v(8224))+v(8180)*(v(1335)*v(635)+v(1395)*v(637)+v(1443)*v(640)+v(169)*v(7083)+v(183)*v(7117)+v(191)*v&
&(7157)+v(1536)*v(7200)+v(1540)*v(7233)+v(1515)*v(8180)+v(1503)*v(8181)+v(1479)*v(8182)+v(214)*v(8224)))
dRdX(1,7)=v(8191)*(v(635)*(v(156)*v(7085)+v(161)*v(7119)+v(166)*v(7160)+v(1645)*v(7202)+v(1673)*v(7235)+v(1705)*v(7268)&
&)+v(637)*(v(161)*v(7085)+v(172)*v(7119)+v(174)*v(7160)+v(1648)*v(7202)+v(1676)*v(7235)+v(1708)*v(7268))+v(7085)*v(7288)&
&+v(7119)*v(7289)+v(7160)*v(7290)+v(7291)*v(8219)+v(8182)*(v(167)*v(7085)+v(178)*v(7119)+v(187)*v(7160)+v(1539)*v(7235)&
&+v(1536)*v(7268)+v(196)*v(8219))+v(7292)*v(8220)+v(8181)*(v(168)*v(7085)+v(181)*v(7119)+v(190)*v(7160)+v(1539)*v(7202)&
&+v(1540)*v(7268)+v(205)*v(8220))+v(7293)*v(8221)+v(640)*(v(166)*v(7085)+v(174)*v(7119)+v(186)*v(7160)+v(187)*v(8219)+v&
&(190)*v(8220)+v(191)*v(8221))+v(8180)*(v(169)*v(7085)+v(183)*v(7119)+v(191)*v(7160)+v(1536)*v(7202)+v(1540)*v(7235)+v&
&(214)*v(8221)))
dRdX(1,8)=v(8191)*(v(635)*(v(156)*v(7087)+v(161)*v(7121)+v(166)*v(7163)+v(1645)*v(7204)+v(1673)*v(7237)+v(1705)*v(7270)&
&)+v(637)*(v(161)*v(7087)+v(172)*v(7121)+v(174)*v(7163)+v(1648)*v(7204)+v(1676)*v(7237)+v(1708)*v(7270))+v(7087)*v(7288)&
&+v(7121)*v(7289)+v(7163)*v(7290)+v(7291)*v(8216)+v(8182)*(v(167)*v(7087)+v(178)*v(7121)+v(187)*v(7163)+v(1539)*v(7237)&
&+v(1536)*v(7270)+v(196)*v(8216))+v(7292)*v(8217)+v(8181)*(v(168)*v(7087)+v(181)*v(7121)+v(190)*v(7163)+v(1539)*v(7204)&
&+v(1540)*v(7270)+v(205)*v(8217))+v(7293)*v(8218)+v(640)*(v(166)*v(7087)+v(174)*v(7121)+v(186)*v(7163)+v(187)*v(8216)+v&
&(190)*v(8217)+v(191)*v(8218))+v(8180)*(v(169)*v(7087)+v(183)*v(7121)+v(191)*v(7163)+v(1536)*v(7204)+v(1540)*v(7237)+v&
&(214)*v(8218)))
dRdX(1,9)=v(8191)*(v(635)*(v(156)*v(7089)+v(161)*v(7123)+v(166)*v(7166)+v(1645)*v(7206)+v(1673)*v(7239)+v(1705)*v(7272)&
&)+v(637)*(v(161)*v(7089)+v(172)*v(7123)+v(174)*v(7166)+v(1648)*v(7206)+v(1676)*v(7239)+v(1708)*v(7272))+v(7089)*v(7288)&
&+v(7123)*v(7289)+v(7166)*v(7290)+v(7291)*v(8213)+v(8182)*(v(167)*v(7089)+v(178)*v(7123)+v(187)*v(7166)+v(1539)*v(7239)&
&+v(1536)*v(7272)+v(196)*v(8213))+v(7292)*v(8214)+v(8181)*(v(168)*v(7089)+v(181)*v(7123)+v(190)*v(7166)+v(1539)*v(7206)&
&+v(1540)*v(7272)+v(205)*v(8214))+v(7293)*v(8215)+v(640)*(v(166)*v(7089)+v(174)*v(7123)+v(186)*v(7166)+v(187)*v(8213)+v&
&(190)*v(8214)+v(191)*v(8215))+v(8180)*(v(169)*v(7089)+v(183)*v(7123)+v(191)*v(7166)+v(1536)*v(7206)+v(1540)*v(7239)+v&
&(214)*v(8215)))
dRdX(1,10)=v(8191)*(v(635)*(v(156)*v(7091)+v(161)*v(7125)+v(166)*v(7169)+v(1645)*v(7208)+v(1673)*v(7241)+v(1705)*v(7274&
&))+v(637)*(v(161)*v(7091)+v(172)*v(7125)+v(174)*v(7169)+v(1648)*v(7208)+v(1676)*v(7241)+v(1708)*v(7274))+v(7091)*v(7288&
&)+v(7125)*v(7289)+v(7169)*v(7290)+v(7291)*v(8210)+v(8182)*(v(167)*v(7091)+v(178)*v(7125)+v(187)*v(7169)+v(1539)*v(7241)&
&+v(1536)*v(7274)+v(196)*v(8210))+v(7292)*v(8211)+v(8181)*(v(168)*v(7091)+v(181)*v(7125)+v(190)*v(7169)+v(1539)*v(7208)&
&+v(1540)*v(7274)+v(205)*v(8211))+v(7293)*v(8212)+v(640)*(v(166)*v(7091)+v(174)*v(7125)+v(186)*v(7169)+v(187)*v(8210)+v&
&(190)*v(8211)+v(191)*v(8212))+v(8180)*(v(169)*v(7091)+v(183)*v(7125)+v(191)*v(7169)+v(1536)*v(7208)+v(1540)*v(7241)+v&
&(214)*v(8212)))
dRdX(1,11)=v(8191)*(v(635)*(v(156)*v(7093)+v(161)*v(7127)+v(166)*v(7172)+v(1645)*v(7210)+v(1673)*v(7243)+v(1705)*v(7276&
&))+v(637)*(v(161)*v(7093)+v(172)*v(7127)+v(174)*v(7172)+v(1648)*v(7210)+v(1676)*v(7243)+v(1708)*v(7276))+v(7093)*v(7288&
&)+v(7127)*v(7289)+v(7172)*v(7290)+v(7291)*v(8207)+v(8182)*(v(167)*v(7093)+v(178)*v(7127)+v(187)*v(7172)+v(1539)*v(7243)&
&+v(1536)*v(7276)+v(196)*v(8207))+v(7292)*v(8208)+v(8181)*(v(168)*v(7093)+v(181)*v(7127)+v(190)*v(7172)+v(1539)*v(7210)&
&+v(1540)*v(7276)+v(205)*v(8208))+v(7293)*v(8209)+v(640)*(v(166)*v(7093)+v(174)*v(7127)+v(186)*v(7172)+v(187)*v(8207)+v&
&(190)*v(8208)+v(191)*v(8209))+v(8180)*(v(169)*v(7093)+v(183)*v(7127)+v(191)*v(7172)+v(1536)*v(7210)+v(1540)*v(7243)+v&
&(214)*v(8209)))
dRdX(1,12)=v(8191)*(v(7095)*v(7288)+v(7129)*v(7289)+v(7175)*v(7290)+v(635)*(v(1276)*v(635)+v(1288)*v(637)+v(1300)*v(640&
&)+v(156)*v(7095)+v(161)*v(7129)+v(166)*v(7175)+v(1645)*v(7212)+v(1673)*v(7245)+v(1705)*v(7278)+v(1336)*v(8180)+v(1324&
&)*v(8181)+v(1312)*v(8182))+v(637)*(v(1288)*v(635)+v(1348)*v(637)+v(1360)*v(640)+v(161)*v(7095)+v(172)*v(7129)+v(174)*v&
&(7175)+v(1648)*v(7212)+v(1676)*v(7245)+v(1708)*v(7278)+v(1396)*v(8180)+v(1384)*v(8181)+v(1372)*v(8182))+v(7291)*v(8204)&
&+v(8182)*(v(1312)*v(635)+v(1372)*v(637)+v(1420)*v(640)+v(167)*v(7095)+v(178)*v(7129)+v(187)*v(7175)+v(1539)*v(7245)+v&
&(1536)*v(7278)+v(1480)*v(8180)+v(1468)*v(8181)+v(1456)*v(8182)+v(196)*v(8204))+v(7292)*v(8205)+v(8181)*(v(1324)*v(635)&
&+v(1384)*v(637)+v(1432)*v(640)+v(168)*v(7095)+v(181)*v(7129)+v(190)*v(7175)+v(1539)*v(7212)+v(1540)*v(7278)+v(1504)*v&
&(8180)+v(1492)*v(8181)+v(1468)*v(8182)+v(205)*v(8205))+v(7293)*v(8206)+v(640)*(v(1300)*v(635)+v(1360)*v(637)+v(1408)*v&
&(640)+v(166)*v(7095)+v(174)*v(7129)+v(186)*v(7175)+v(1444)*v(8180)+v(1432)*v(8181)+v(1420)*v(8182)+v(187)*v(8204)+v(190&
&)*v(8205)+v(191)*v(8206))+v(8180)*(v(1336)*v(635)+v(1396)*v(637)+v(1444)*v(640)+v(169)*v(7095)+v(183)*v(7129)+v(191)*v&
&(7175)+v(1536)*v(7212)+v(1540)*v(7245)+v(1516)*v(8180)+v(1504)*v(8181)+v(1480)*v(8182)+v(214)*v(8206)))
dRdX(1,13)=v(8191)*(v(7097)*v(7288)+v(7131)*v(7289)+v(7178)*v(7290)+v(635)*(v(1277)*v(635)+v(1289)*v(637)+v(1301)*v(640&
&)+v(156)*v(7097)+v(161)*v(7131)+v(166)*v(7178)+v(1645)*v(7214)+v(1673)*v(7247)+v(1705)*v(7280)+v(1337)*v(8180)+v(1325&
&)*v(8181)+v(1313)*v(8182))+v(637)*(v(1289)*v(635)+v(1349)*v(637)+v(1361)*v(640)+v(161)*v(7097)+v(172)*v(7131)+v(174)*v&
&(7178)+v(1648)*v(7214)+v(1676)*v(7247)+v(1708)*v(7280)+v(1397)*v(8180)+v(1385)*v(8181)+v(1373)*v(8182))+v(7291)*v(8201)&
&+v(8182)*(v(1313)*v(635)+v(1373)*v(637)+v(1421)*v(640)+v(167)*v(7097)+v(178)*v(7131)+v(187)*v(7178)+v(1539)*v(7247)+v&
&(1536)*v(7280)+v(1481)*v(8180)+v(1469)*v(8181)+v(1457)*v(8182)+v(196)*v(8201))+v(7292)*v(8202)+v(8181)*(v(1325)*v(635)&
&+v(1385)*v(637)+v(1433)*v(640)+v(168)*v(7097)+v(181)*v(7131)+v(190)*v(7178)+v(1539)*v(7214)+v(1540)*v(7280)+v(1505)*v&
&(8180)+v(1493)*v(8181)+v(1469)*v(8182)+v(205)*v(8202))+v(7293)*v(8203)+v(640)*(v(1301)*v(635)+v(1361)*v(637)+v(1409)*v&
&(640)+v(166)*v(7097)+v(174)*v(7131)+v(186)*v(7178)+v(1445)*v(8180)+v(1433)*v(8181)+v(1421)*v(8182)+v(187)*v(8201)+v(190&
&)*v(8202)+v(191)*v(8203))+v(8180)*(v(1337)*v(635)+v(1397)*v(637)+v(1445)*v(640)+v(169)*v(7097)+v(183)*v(7131)+v(191)*v&
&(7178)+v(1536)*v(7214)+v(1540)*v(7247)+v(1517)*v(8180)+v(1505)*v(8181)+v(1481)*v(8182)+v(214)*v(8203)))
dRdX(1,14)=v(8191)*(v(7099)*v(7288)+v(7133)*v(7289)+v(7181)*v(7290)+v(635)*(v(1278)*v(635)+v(1290)*v(637)+v(1302)*v(640&
&)+v(156)*v(7099)+v(161)*v(7133)+v(166)*v(7181)+v(1645)*v(7216)+v(1673)*v(7249)+v(1705)*v(7282)+v(1338)*v(8180)+v(1326&
&)*v(8181)+v(1314)*v(8182))+v(637)*(v(1290)*v(635)+v(1350)*v(637)+v(1362)*v(640)+v(161)*v(7099)+v(172)*v(7133)+v(174)*v&
&(7181)+v(1648)*v(7216)+v(1676)*v(7249)+v(1708)*v(7282)+v(1398)*v(8180)+v(1386)*v(8181)+v(1374)*v(8182))+v(7291)*v(8198)&
&+v(8182)*(v(1314)*v(635)+v(1374)*v(637)+v(1422)*v(640)+v(167)*v(7099)+v(178)*v(7133)+v(187)*v(7181)+v(1539)*v(7249)+v&
&(1536)*v(7282)+v(1482)*v(8180)+v(1470)*v(8181)+v(1458)*v(8182)+v(196)*v(8198))+v(7292)*v(8199)+v(8181)*(v(1326)*v(635)&
&+v(1386)*v(637)+v(1434)*v(640)+v(168)*v(7099)+v(181)*v(7133)+v(190)*v(7181)+v(1539)*v(7216)+v(1540)*v(7282)+v(1506)*v&
&(8180)+v(1494)*v(8181)+v(1470)*v(8182)+v(205)*v(8199))+v(7293)*v(8200)+v(640)*(v(1302)*v(635)+v(1362)*v(637)+v(1410)*v&
&(640)+v(166)*v(7099)+v(174)*v(7133)+v(186)*v(7181)+v(1446)*v(8180)+v(1434)*v(8181)+v(1422)*v(8182)+v(187)*v(8198)+v(190&
&)*v(8199)+v(191)*v(8200))+v(8180)*(v(1338)*v(635)+v(1398)*v(637)+v(1446)*v(640)+v(169)*v(7099)+v(183)*v(7133)+v(191)*v&
&(7181)+v(1536)*v(7216)+v(1540)*v(7249)+v(1518)*v(8180)+v(1506)*v(8181)+v(1482)*v(8182)+v(214)*v(8200)))
dRdX(1,15)=v(8191)*(v(7101)*v(7288)+v(7135)*v(7289)+v(7184)*v(7290)+v(635)*(v(1279)*v(635)+v(1291)*v(637)+v(1303)*v(640&
&)+v(156)*v(7101)+v(161)*v(7135)+v(166)*v(7184)+v(1645)*v(7218)+v(1673)*v(7251)+v(1705)*v(7284)+v(1339)*v(8180)+v(1327&
&)*v(8181)+v(1315)*v(8182))+v(637)*(v(1291)*v(635)+v(1351)*v(637)+v(1363)*v(640)+v(161)*v(7101)+v(172)*v(7135)+v(174)*v&
&(7184)+v(1648)*v(7218)+v(1676)*v(7251)+v(1708)*v(7284)+v(1399)*v(8180)+v(1387)*v(8181)+v(1375)*v(8182))+v(7291)*v(8195)&
&+v(8182)*(v(1315)*v(635)+v(1375)*v(637)+v(1423)*v(640)+v(167)*v(7101)+v(178)*v(7135)+v(187)*v(7184)+v(1539)*v(7251)+v&
&(1536)*v(7284)+v(1483)*v(8180)+v(1471)*v(8181)+v(1459)*v(8182)+v(196)*v(8195))+v(7292)*v(8196)+v(8181)*(v(1327)*v(635)&
&+v(1387)*v(637)+v(1435)*v(640)+v(168)*v(7101)+v(181)*v(7135)+v(190)*v(7184)+v(1539)*v(7218)+v(1540)*v(7284)+v(1507)*v&
&(8180)+v(1495)*v(8181)+v(1471)*v(8182)+v(205)*v(8196))+v(7293)*v(8197)+v(640)*(v(1303)*v(635)+v(1363)*v(637)+v(1411)*v&
&(640)+v(166)*v(7101)+v(174)*v(7135)+v(186)*v(7184)+v(1447)*v(8180)+v(1435)*v(8181)+v(1423)*v(8182)+v(187)*v(8195)+v(190&
&)*v(8196)+v(191)*v(8197))+v(8180)*(v(1339)*v(635)+v(1399)*v(637)+v(1447)*v(640)+v(169)*v(7101)+v(183)*v(7135)+v(191)*v&
&(7184)+v(1536)*v(7218)+v(1540)*v(7251)+v(1519)*v(8180)+v(1507)*v(8181)+v(1483)*v(8182)+v(214)*v(8197)))
dRdX(1,16)=(v(7103)*v(7288)+v(7137)*v(7289)+v(7187)*v(7290)+v(7291)*v(8188)+v(8182)*(v(1316)*v(635)+v(1376)*v(637)+v&
&(1424)*v(640)+v(167)*v(7103)+v(178)*v(7137)+v(187)*v(7187)+v(1539)*v(7253)+v(1536)*v(7286)+v(1484)*v(8180)+v(1472)*v&
&(8181)+v(1460)*v(8182)+v(196)*v(8188))+v(7292)*v(8189)+v(8181)*(v(1328)*v(635)+v(1388)*v(637)+v(1436)*v(640)+v(168)*v&
&(7103)+v(181)*v(7137)+v(190)*v(7187)+v(1539)*v(7220)+v(1540)*v(7286)+v(1508)*v(8180)+v(1496)*v(8181)+v(1472)*v(8182)+v&
&(205)*v(8189))+v(7293)*v(8190)+v(635)*(v(1280)*v(635)+v(1292)*v(637)+v(1304)*v(640)+v(156)*v(7103)+v(161)*v(7137)+v(166&
&)*v(7187)+v(1340)*v(8180)+v(1328)*v(8181)+v(1316)*v(8182)+v(167)*v(8188)+v(168)*v(8189)+v(169)*v(8190))+v(637)*(v(1292&
&)*v(635)+v(1352)*v(637)+v(1364)*v(640)+v(161)*v(7103)+v(172)*v(7137)+v(174)*v(7187)+v(1400)*v(8180)+v(1388)*v(8181)+v&
&(1376)*v(8182)+v(178)*v(8188)+v(181)*v(8189)+v(183)*v(8190))+v(640)*(v(1304)*v(635)+v(1364)*v(637)+v(1412)*v(640)+v(166&
&)*v(7103)+v(174)*v(7137)+v(186)*v(7187)+v(1448)*v(8180)+v(1436)*v(8181)+v(1424)*v(8182)+v(187)*v(8188)+v(190)*v(8189)+v&
&(191)*v(8190))+v(8180)*(v(1340)*v(635)+v(1400)*v(637)+v(1448)*v(640)+v(169)*v(7103)+v(183)*v(7137)+v(191)*v(7187)+v&
&(1536)*v(7220)+v(1540)*v(7253)+v(1520)*v(8180)+v(1508)*v(8181)+v(1484)*v(8182)+v(214)*v(8190)))*v(8191)
dRdX(2,1)=-v(7072)
dRdX(2,2)=1d0-v(7074)
dRdX(2,3)=-v(7077)
dRdX(2,4)=-v(7079)
dRdX(2,5)=-v(7081)
dRdX(2,6)=-v(7083)
dRdX(2,7)=-v(7085)
dRdX(2,8)=-v(7087)
dRdX(2,9)=-v(7089)
dRdX(2,10)=-v(7091)
dRdX(2,11)=-v(7093)
dRdX(2,12)=-v(7095)
dRdX(2,13)=-v(7097)
dRdX(2,14)=-v(7099)
dRdX(2,15)=-v(7101)
dRdX(2,16)=-v(7103)
dRdX(3,1)=-v(7106)
dRdX(3,2)=-v(7109)
dRdX(3,3)=1d0-v(7111)
dRdX(3,4)=-v(7113)
dRdX(3,5)=-v(7115)
dRdX(3,6)=-v(7117)
dRdX(3,7)=-v(7119)
dRdX(3,8)=-v(7121)
dRdX(3,9)=-v(7123)
dRdX(3,10)=-v(7125)
dRdX(3,11)=-v(7127)
dRdX(3,12)=-v(7129)
dRdX(3,13)=-v(7131)
dRdX(3,14)=-v(7133)
dRdX(3,15)=-v(7135)
dRdX(3,16)=-v(7137)
dRdX(4,1)=-v(7190)
dRdX(4,2)=-v(7192)
dRdX(4,3)=-v(7194)
dRdX(4,4)=1d0-v(7196)
dRdX(4,5)=-v(7198)
dRdX(4,6)=-v(7200)
dRdX(4,7)=-v(7202)
dRdX(4,8)=-v(7204)
dRdX(4,9)=-v(7206)
dRdX(4,10)=-v(7208)
dRdX(4,11)=-v(7210)
dRdX(4,12)=-v(7212)
dRdX(4,13)=-v(7214)
dRdX(4,14)=-v(7216)
dRdX(4,15)=-v(7218)
dRdX(4,16)=-v(7220)
dRdX(5,1)=-v(7256)
dRdX(5,2)=-v(7258)
dRdX(5,3)=-v(7260)
dRdX(5,4)=-v(7262)
dRdX(5,5)=1d0-v(7264)
dRdX(5,6)=-v(7266)
dRdX(5,7)=-v(7268)
dRdX(5,8)=-v(7270)
dRdX(5,9)=-v(7272)
dRdX(5,10)=-v(7274)
dRdX(5,11)=-v(7276)
dRdX(5,12)=-v(7278)
dRdX(5,13)=-v(7280)
dRdX(5,14)=-v(7282)
dRdX(5,15)=-v(7284)
dRdX(5,16)=-v(7286)
dRdX(6,1)=-v(7223)
dRdX(6,2)=-v(7225)
dRdX(6,3)=-v(7227)
dRdX(6,4)=-v(7229)
dRdX(6,5)=-v(7231)
dRdX(6,6)=1d0-v(7233)
dRdX(6,7)=-v(7235)
dRdX(6,8)=-v(7237)
dRdX(6,9)=-v(7239)
dRdX(6,10)=-v(7241)
dRdX(6,11)=-v(7243)
dRdX(6,12)=-v(7245)
dRdX(6,13)=-v(7247)
dRdX(6,14)=-v(7249)
dRdX(6,15)=-v(7251)
dRdX(6,16)=-v(7253)
dRdX(7,1)=-v(6146)
dRdX(7,2)=-v(6147)
dRdX(7,3)=-v(6148)
dRdX(7,4)=-v(6149)
dRdX(7,5)=-v(6150)
dRdX(7,6)=-v(6151)
dRdX(7,7)=1d0-v(6152)
dRdX(7,8)=-v(6153)
dRdX(7,9)=-v(6154)
dRdX(7,10)=-v(6155)
dRdX(7,11)=-v(6156)
dRdX(7,12)=-v(6157)
dRdX(7,13)=-v(6158)
dRdX(7,14)=-v(6159)
dRdX(7,15)=-v(6160)
dRdX(7,16)=-v(6161)
dRdX(8,1)=-v(6163)
dRdX(8,2)=-v(6164)
dRdX(8,3)=-v(6165)
dRdX(8,4)=-v(6166)
dRdX(8,5)=-v(6167)
dRdX(8,6)=-v(6168)
dRdX(8,7)=-v(6169)
dRdX(8,8)=1d0-v(6170)
dRdX(8,9)=-v(6171)
dRdX(8,10)=-v(6172)
dRdX(8,11)=-v(6173)
dRdX(8,12)=-v(6174)
dRdX(8,13)=-v(6175)
dRdX(8,14)=-v(6176)
dRdX(8,15)=-v(6177)
dRdX(8,16)=-v(6178)
dRdX(9,1)=-v(6180)
dRdX(9,2)=-v(6181)
dRdX(9,3)=-v(6182)
dRdX(9,4)=-v(6183)
dRdX(9,5)=-v(6184)
dRdX(9,6)=-v(6185)
dRdX(9,7)=-v(6186)
dRdX(9,8)=-v(6187)
dRdX(9,9)=1d0-v(6188)
dRdX(9,10)=-v(6189)
dRdX(9,11)=-v(6190)
dRdX(9,12)=-v(6191)
dRdX(9,13)=-v(6192)
dRdX(9,14)=-v(6193)
dRdX(9,15)=-v(6194)
dRdX(9,16)=-v(6195)
dRdX(10,1)=-v(6214)
dRdX(10,2)=-v(6215)
dRdX(10,3)=-v(6216)
dRdX(10,4)=-v(6217)
dRdX(10,5)=-v(6218)
dRdX(10,6)=-v(6219)
dRdX(10,7)=-v(6220)
dRdX(10,8)=-v(6221)
dRdX(10,9)=-v(6222)
dRdX(10,10)=1d0-v(6223)
dRdX(10,11)=-v(6224)
dRdX(10,12)=-v(6225)
dRdX(10,13)=-v(6226)
dRdX(10,14)=-v(6227)
dRdX(10,15)=-v(6228)
dRdX(10,16)=-v(6229)
dRdX(11,1)=-v(6197)
dRdX(11,2)=-v(6198)
dRdX(11,3)=-v(6199)
dRdX(11,4)=-v(6200)
dRdX(11,5)=-v(6201)
dRdX(11,6)=-v(6202)
dRdX(11,7)=-v(6203)
dRdX(11,8)=-v(6204)
dRdX(11,9)=-v(6205)
dRdX(11,10)=-v(6206)
dRdX(11,11)=1d0-v(6207)
dRdX(11,12)=-v(6208)
dRdX(11,13)=-v(6209)
dRdX(11,14)=-v(6210)
dRdX(11,15)=-v(6211)
dRdX(11,16)=-v(6212)
dRdX(12,1)=mpar(15)*(-(v(660)*((-2d0/3d0)*v(7330)+v(7347)/3d0+v(7377)))-v(7361)*v(7424))
dRdX(12,2)=mpar(15)*(-(v(660)*((-2d0/3d0)*v(7334)+v(7351)/3d0+v(7382)))-v(7363)*v(7424))
dRdX(12,3)=mpar(15)*(-(v(660)*((-2d0/3d0)*v(7335)+v(7352)/3d0+v(7384)))-v(7364)*v(7424))
dRdX(12,4)=mpar(15)*(-(v(660)*((-2d0/3d0)*v(7336)+v(7353)/3d0+v(7386)))-v(7365)*v(7424))
dRdX(12,5)=mpar(15)*(-(v(660)*((-2d0/3d0)*v(7337)+v(7354)/3d0+v(7388)))-v(7366)*v(7424))
dRdX(12,6)=mpar(15)*(-(v(660)*((-2d0/3d0)*v(7338)+v(7355)/3d0+v(7390)))-v(7367)*v(7424))
dRdX(12,7)=0d0
dRdX(12,8)=0d0
dRdX(12,9)=0d0
dRdX(12,10)=0d0
dRdX(12,11)=0d0
dRdX(12,12)=1d0+mpar(15)*(-(v(660)*((-2d0/3d0)*v(7339)+v(7356)/3d0+v(7392)))-v(7368)*v(7424))
dRdX(12,13)=mpar(15)*(-(v(660)*((-2d0/3d0)*v(7340)+v(7357)/3d0+v(7394)))-v(7369)*v(7424))
dRdX(12,14)=mpar(15)*(-(v(660)*((-2d0/3d0)*v(7341)+v(7358)/3d0+v(7396)))-v(7370)*v(7424))
dRdX(12,15)=mpar(15)*(-(v(660)*((-2d0/3d0)*v(7342)+v(7359)/3d0+v(7398)))-v(7371)*v(7424))
dRdX(12,16)=mpar(15)*(-(v(660)*((-2d0/3d0)*v(7343)+v(7360)/3d0+v(7400)))-v(7372)*v(7424))
dRdX(13,1)=mpar(15)*(-(v(660)*(v(7330)/3d0+(-2d0/3d0)*v(7347)+v(7377)))-v(7361)*v(7426))
dRdX(13,2)=mpar(15)*(-(v(660)*(v(7334)/3d0+(-2d0/3d0)*v(7351)+v(7382)))-v(7363)*v(7426))
dRdX(13,3)=mpar(15)*(-(v(660)*(v(7335)/3d0+(-2d0/3d0)*v(7352)+v(7384)))-v(7364)*v(7426))
dRdX(13,4)=mpar(15)*(-(v(660)*(v(7336)/3d0+(-2d0/3d0)*v(7353)+v(7386)))-v(7365)*v(7426))
dRdX(13,5)=mpar(15)*(-(v(660)*(v(7337)/3d0+(-2d0/3d0)*v(7354)+v(7388)))-v(7366)*v(7426))
dRdX(13,6)=mpar(15)*(-(v(660)*(v(7338)/3d0+(-2d0/3d0)*v(7355)+v(7390)))-v(7367)*v(7426))
dRdX(13,7)=0d0
dRdX(13,8)=0d0
dRdX(13,9)=0d0
dRdX(13,10)=0d0
dRdX(13,11)=0d0
dRdX(13,12)=mpar(15)*(-(v(660)*(v(7339)/3d0+(-2d0/3d0)*v(7356)+v(7392)))-v(7368)*v(7426))
dRdX(13,13)=1d0+mpar(15)*(-(v(660)*(v(7340)/3d0+(-2d0/3d0)*v(7357)+v(7394)))-v(7369)*v(7426))
dRdX(13,14)=mpar(15)*(-(v(660)*(v(7341)/3d0+(-2d0/3d0)*v(7358)+v(7396)))-v(7370)*v(7426))
dRdX(13,15)=mpar(15)*(-(v(660)*(v(7342)/3d0+(-2d0/3d0)*v(7359)+v(7398)))-v(7371)*v(7426))
dRdX(13,16)=mpar(15)*(-(v(660)*(v(7343)/3d0+(-2d0/3d0)*v(7360)+v(7400)))-v(7372)*v(7426))
dRdX(14,1)=mpar(15)*(-(v(7361)*v(7428))-v(660)*(v(656)*(v(667)*v(6956)+v(666)*v(7002)+v(670)*v(7026)+v(671)*v(7037)+v&
&(668)*v(7048)+v(669)*v(7059))+v(7315)*v(8237)))
dRdX(14,2)=mpar(15)*(-(v(7363)*v(7428))-v(660)*(v(656)*(v(667)*v(6957)+v(666)*v(7003)+v(670)*v(7027)+v(671)*v(7038)+v&
&(668)*v(7049)+v(669)*v(7060))+v(7317)*v(8237)))
dRdX(14,3)=mpar(15)*(-(v(7364)*v(7428))-v(660)*(v(656)*(v(667)*v(6958)+v(666)*v(7004)+v(670)*v(7028)+v(671)*v(7039)+v&
&(668)*v(7050)+v(669)*v(7061))+v(7318)*v(8237)))
dRdX(14,4)=mpar(15)*(-(v(7365)*v(7428))-v(660)*(v(656)*(v(667)*v(6959)+v(666)*v(7005)+v(670)*v(7029)+v(671)*v(7040)+v&
&(668)*v(7051)+v(669)*v(7062))+v(7319)*v(8237)))
dRdX(14,5)=mpar(15)*(-(v(7366)*v(7428))-v(660)*(v(656)*(v(667)*v(6960)+v(666)*v(7006)+v(670)*v(7030)+v(671)*v(7041)+v&
&(668)*v(7052)+v(669)*v(7063))+v(7320)*v(8237)))
dRdX(14,6)=mpar(15)*(-(v(7367)*v(7428))-v(660)*(v(656)*(v(667)*v(6961)+v(666)*v(7007)+v(670)*v(7031)+v(671)*v(7042)+v&
&(668)*v(7053)+v(669)*v(7064))+v(7321)*v(8237)))
dRdX(14,7)=0d0
dRdX(14,8)=0d0
dRdX(14,9)=0d0
dRdX(14,10)=0d0
dRdX(14,11)=0d0
dRdX(14,12)=mpar(15)*(-(v(7368)*v(7428))-v(660)*(v(656)*(v(667)*v(6962)+v(666)*v(7008)+v(670)*v(7032)+v(671)*v(7043)+v&
&(668)*v(7054)+v(669)*v(7065))+v(7322)*v(8237)))
dRdX(14,13)=mpar(15)*(-(v(7369)*v(7428))-v(660)*(v(656)*(v(667)*v(6963)+v(666)*v(7009)+v(670)*v(7033)+v(671)*v(7044)+v&
&(668)*v(7055)+v(669)*v(7066))+v(7323)*v(8237)))
dRdX(14,14)=1d0+mpar(15)*(-(v(7370)*v(7428))-v(660)*(v(656)*(v(667)*v(6964)+v(666)*v(7010)+v(670)*v(7034)+v(671)*v(7045&
&)+v(668)*v(7056)+v(669)*v(7067))+v(7324)*v(8237)))
dRdX(14,15)=mpar(15)*(-(v(7371)*v(7428))-v(660)*(v(656)*(v(667)*v(6965)+v(666)*v(7011)+v(670)*v(7035)+v(671)*v(7046)+v&
&(668)*v(7057)+v(669)*v(7068))+v(7325)*v(8237)))
dRdX(14,16)=mpar(15)*(-(v(7372)*v(7428))-v(660)*(v(656)*(v(667)*v(6966)+v(666)*v(7012)+v(670)*v(7036)+v(671)*v(7047)+v&
&(668)*v(7058)+v(669)*v(7069))+v(7326)*v(8237)))
dRdX(15,1)=mpar(15)*(-(v(7361)*v(7430))-v(660)*(v(656)*(v(668)*v(6945)+v(671)*v(6980)+v(667)*v(6991)+v(673)*v(7002)+v&
&(675)*v(7026)+v(674)*v(7059))+v(7315)*v(8238)))
dRdX(15,2)=mpar(15)*(-(v(7363)*v(7430))-v(660)*(v(656)*(v(668)*v(6946)+v(671)*v(6981)+v(667)*v(6992)+v(673)*v(7003)+v&
&(675)*v(7027)+v(674)*v(7060))+v(7317)*v(8238)))
dRdX(15,3)=mpar(15)*(-(v(7364)*v(7430))-v(660)*(v(656)*(v(668)*v(6947)+v(671)*v(6982)+v(667)*v(6993)+v(673)*v(7004)+v&
&(675)*v(7028)+v(674)*v(7061))+v(7318)*v(8238)))
dRdX(15,4)=mpar(15)*(-(v(7365)*v(7430))-v(660)*(v(656)*(v(668)*v(6948)+v(671)*v(6983)+v(667)*v(6994)+v(673)*v(7005)+v&
&(675)*v(7029)+v(674)*v(7062))+v(7319)*v(8238)))
dRdX(15,5)=mpar(15)*(-(v(7366)*v(7430))-v(660)*(v(656)*(v(668)*v(6949)+v(671)*v(6984)+v(667)*v(6995)+v(673)*v(7006)+v&
&(675)*v(7030)+v(674)*v(7063))+v(7320)*v(8238)))
dRdX(15,6)=mpar(15)*(-(v(7367)*v(7430))-v(660)*(v(656)*(v(668)*v(6950)+v(671)*v(6985)+v(667)*v(6996)+v(673)*v(7007)+v&
&(675)*v(7031)+v(674)*v(7064))+v(7321)*v(8238)))
dRdX(15,7)=0d0
dRdX(15,8)=0d0
dRdX(15,9)=0d0
dRdX(15,10)=0d0
dRdX(15,11)=0d0
dRdX(15,12)=mpar(15)*(-(v(7368)*v(7430))-v(660)*(v(656)*(v(668)*v(6951)+v(671)*v(6986)+v(667)*v(6997)+v(673)*v(7008)+v&
&(675)*v(7032)+v(674)*v(7065))+v(7322)*v(8238)))
dRdX(15,13)=mpar(15)*(-(v(7369)*v(7430))-v(660)*(v(656)*(v(668)*v(6952)+v(671)*v(6987)+v(667)*v(6998)+v(673)*v(7009)+v&
&(675)*v(7033)+v(674)*v(7066))+v(7323)*v(8238)))
dRdX(15,14)=mpar(15)*(-(v(7370)*v(7430))-v(660)*(v(656)*(v(668)*v(6953)+v(671)*v(6988)+v(667)*v(6999)+v(673)*v(7010)+v&
&(675)*v(7034)+v(674)*v(7067))+v(7324)*v(8238)))
dRdX(15,15)=1d0+mpar(15)*(-(v(7371)*v(7430))-v(660)*(v(656)*(v(668)*v(6954)+v(671)*v(6989)+v(667)*v(7000)+v(673)*v(7011&
&)+v(675)*v(7035)+v(674)*v(7068))+v(7325)*v(8238)))
dRdX(15,16)=mpar(15)*(-(v(7372)*v(7430))-v(660)*(v(656)*(v(668)*v(6955)+v(671)*v(6990)+v(667)*v(7001)+v(673)*v(7012)+v&
&(675)*v(7036)+v(674)*v(7069))+v(7326)*v(8238)))
dRdX(16,1)=mpar(15)*(-(v(7361)*v(7432))-v(660)*(v(656)*(v(669)*v(6945)+v(673)*v(6956)+v(670)*v(6980)+v(666)*v(6991)+v&
&(675)*v(7037)+v(674)*v(7048))+v(7315)*v(8239)))
dRdX(16,2)=mpar(15)*(-(v(7363)*v(7432))-v(660)*(v(656)*(v(669)*v(6946)+v(673)*v(6957)+v(670)*v(6981)+v(666)*v(6992)+v&
&(675)*v(7038)+v(674)*v(7049))+v(7317)*v(8239)))
dRdX(16,3)=mpar(15)*(-(v(7364)*v(7432))-v(660)*(v(656)*(v(669)*v(6947)+v(673)*v(6958)+v(670)*v(6982)+v(666)*v(6993)+v&
&(675)*v(7039)+v(674)*v(7050))+v(7318)*v(8239)))
dRdX(16,4)=mpar(15)*(-(v(7365)*v(7432))-v(660)*(v(656)*(v(669)*v(6948)+v(673)*v(6959)+v(670)*v(6983)+v(666)*v(6994)+v&
&(675)*v(7040)+v(674)*v(7051))+v(7319)*v(8239)))
dRdX(16,5)=mpar(15)*(-(v(7366)*v(7432))-v(660)*(v(656)*(v(669)*v(6949)+v(673)*v(6960)+v(670)*v(6984)+v(666)*v(6995)+v&
&(675)*v(7041)+v(674)*v(7052))+v(7320)*v(8239)))
dRdX(16,6)=mpar(15)*(-(v(7367)*v(7432))-v(660)*(v(656)*(v(669)*v(6950)+v(673)*v(6961)+v(670)*v(6985)+v(666)*v(6996)+v&
&(675)*v(7042)+v(674)*v(7053))+v(7321)*v(8239)))
dRdX(16,7)=0d0
dRdX(16,8)=0d0
dRdX(16,9)=0d0
dRdX(16,10)=0d0
dRdX(16,11)=0d0
dRdX(16,12)=mpar(15)*(-(v(7368)*v(7432))-v(660)*(v(656)*(v(669)*v(6951)+v(673)*v(6962)+v(670)*v(6986)+v(666)*v(6997)+v&
&(675)*v(7043)+v(674)*v(7054))+v(7322)*v(8239)))
dRdX(16,13)=mpar(15)*(-(v(7369)*v(7432))-v(660)*(v(656)*(v(669)*v(6952)+v(673)*v(6963)+v(670)*v(6987)+v(666)*v(6998)+v&
&(675)*v(7044)+v(674)*v(7055))+v(7323)*v(8239)))
dRdX(16,14)=mpar(15)*(-(v(7370)*v(7432))-v(660)*(v(656)*(v(669)*v(6953)+v(673)*v(6964)+v(670)*v(6988)+v(666)*v(6999)+v&
&(675)*v(7045)+v(674)*v(7056))+v(7324)*v(8239)))
dRdX(16,15)=mpar(15)*(-(v(7371)*v(7432))-v(660)*(v(656)*(v(669)*v(6954)+v(673)*v(6965)+v(670)*v(6989)+v(666)*v(7000)+v&
&(675)*v(7046)+v(674)*v(7057))+v(7325)*v(8239)))
dRdX(16,16)=1d0+mpar(15)*(-(v(7372)*v(7432))-v(660)*(v(656)*(v(669)*v(6955)+v(673)*v(6966)+v(670)*v(6990)+v(666)*v(7001&
&)+v(675)*v(7047)+v(674)*v(7058))+v(7326)*v(8239)))
END SUBROUTINE
!**************************************************************
!* AceGen 6.702 Windows (4 May 16) *
!* Co. J. Korelc 2013 4 Dec 19 21:46:47 *
!**************************************************************
! User : Full professional version
! Notebook : MainFile
! Evaluation time : 707 s Mode : Optimal
! Number of formulae : 5439 Method: Automatic
! Subroutine : plastic_output size: 157507
! Total size of Mathematica code : 157507 subexpressions
! Total size of Fortran code : 368811 bytes
!******************* S U B R O U T I N E **********************
SUBROUTINE plastic_output(x,mpar,statev,Fnew,Jinv,sigma,ddsdde,statevNew,dwp)
USE SMSUtility
IMPLICIT NONE
DOUBLE PRECISION v(6428),x(16),mpar(16),statev(58),Fnew(9),Jinv(16,16),sigma(6),ddsdde(6,6),statevNew(58),dwp
v(6379)=1d0/mpar(16)
v(6378)=v(6379)*x(12)
v(6041)=1d0/mpar(12)
v(6037)=1d0/mpar(10)
v(5722)=8d0*x(5)*x(6)
v(5712)=8d0*x(4)
v(5724)=v(5712)*x(6)
v(5723)=v(5712)*x(5)
v(5709)=2d0*x(5)
v(5708)=2d0*x(4)
v(5706)=x(5)**2
v(5716)=4d0*v(5706)
v(5704)=x(6)**2
v(5714)=4d0*v(5704)
v(5702)=x(4)**2
v(5711)=4d0*v(5702)
v(5685)=2d0*x(6)
v(5666)=mpar(14)**2
v(5675)=4d0*v(5666)
v(5674)=2d0*v(5666)
v(5605)=2d0*mpar(14)
v(5575)=(-8d0)*statev(48)
v(5569)=(-8d0)*statev(47)
v(5555)=1d0/(Fnew(6)*(Fnew(4)*Fnew(5)-Fnew(2)*Fnew(7))+Fnew(3)*(Fnew(1)*Fnew(2)-Fnew(4)*Fnew(8))+(-(Fnew(1)*Fnew(5))&
&+Fnew(7)*Fnew(8))*Fnew(9))
v(6423)=v(5555)/4d0
v(5554)=2d0*x(15)
v(5553)=2d0*x(16)
v(5552)=2d0*x(14)
v(5551)=-x(12)-x(13)
v(5550)=-x(7)-x(8)
v(5549)=2d0*v(5704)
v(5548)=2d0*v(5706)
v(5547)=2d0*v(5702)
v(5546)=x(3)**2
v(5545)=x(2)**2
v(5544)=2d0*x(2)
v(5543)=2d0*x(3)
v(5542)=-x(2)-x(3)
v(5707)=(v(5542)*v(5542))
v(5541)=dabs(x(1))
v(5540)=4d0*x(6)
v(5736)=v(5540)*x(3)
v(5718)=v(5540)*v(5542)
v(5539)=4d0*x(5)
v(5732)=v(5539)*x(3)
v(5717)=v(5539)*v(5542)
v(5538)=4d0*x(4)
v(5737)=v(5538)*x(3)
v(5719)=v(5538)*v(5542)
v(5537)=dsign(1.d0,x(1))
v(5536)=1d0+statev(52)
v(5535)=1d0+statev(51)
v(5534)=1d0+statev(50)
v(5533)=1d0+statev(3)
v(5532)=1d0+statev(2)
v(5531)=1d0+statev(1)
v(5530)=1d0+statev(22)
v(5529)=1d0+statev(21)
v(5528)=1d0+statev(20)
v(5527)=1d0+statev(13)
v(5526)=1d0+statev(12)
v(5525)=1d0+statev(11)
v(5524)=(-1d0/3d0)+statev(40)
v(5581)=2d0*v(5524)
v(5523)=(-1d0/3d0)+statev(36)
v(5580)=2d0*v(5523)
v(5522)=(-1d0/3d0)+statev(35)
v(5579)=2d0*v(5522)
v(5521)=0.5d0+statev(34)
v(5578)=4d0*v(5521)
v(5520)=0.5d0+statev(33)
v(5577)=4d0*v(5520)
v(5519)=0.5d0+statev(32)
v(5576)=4d0*v(5519)
v(5518)=(2d0/3d0)+statev(31)
v(5517)=(2d0/3d0)+statev(30)
v(5516)=(2d0/3d0)+statev(29)
v(5515)=1d0-mpar(8)
v(2489)=2d0*v(5537)*v(5541)
v(1638)=dexp((-7d0)*mpar(13)*v(5541))
v(1641)=(-1d0)+v(1638)
v(5571)=v(1641)/7d0
v(1497)=(-2d0)*v(5542)
v(5735)=-(v(1497)*x(3))
v(1498)=v(1497)+v(5543)
v(1496)=v(1497)+v(5544)
v(216)=v(5545)+v(5546)+v(5547)+v(5548)+v(5549)+v(5707)
v(1510)=0.1d-19+v(216)
v(1509)=1d0/sqrt(v(1510))
v(1512)=-v(1509)/(2d0*v(1510))
v(1516)=v(1512)*v(5540)
v(1585)=v(1516)*x(4)
v(1708)=v(1585)*v(5569)
v(1554)=v(1516)*v(5542)
v(1531)=v(1516)*x(3)
v(1521)=v(1516)*x(2)
v(1515)=v(1512)*v(5539)
v(1599)=v(1515)*x(6)
v(1584)=v(1515)*x(4)
v(5582)=2d0*v(1584)
v(1697)=v(1584)*v(5575)
v(1553)=v(1515)*v(5542)
v(1530)=v(1515)*x(3)
v(1520)=v(1515)*x(2)
v(1514)=v(1512)*v(5538)
v(1552)=v(1514)*v(5542)
v(1529)=v(1514)*x(3)
v(1519)=v(1514)*x(2)
v(1513)=v(1498)*v(1512)
v(1613)=v(1513)*x(5)
v(1598)=v(1513)*x(6)
v(1582)=v(1513)*x(4)
v(1518)=v(1513)*x(2)
v(1511)=v(1496)*v(1512)
v(1612)=v(1511)*x(5)
v(1597)=v(1511)*x(6)
v(1581)=v(1511)*x(4)
v(1527)=v(1511)*x(3)
v(1502)=1d0/sqrt(v(216))
v(1504)=-v(1502)/(2d0*v(216))
v(1508)=v(1504)*v(5540)
v(1507)=v(1504)*v(5539)
v(1506)=v(1504)*v(5538)
v(1505)=v(1498)*v(1504)
v(1503)=v(1496)*v(1504)
v(1614)=v(1509)+v(1515)*x(5)
v(1600)=v(1509)+v(1516)*x(6)
v(1583)=v(1509)+v(1514)*x(4)
v(1551)=-v(1509)+v(1513)*v(5542)
v(1550)=-v(1509)+v(1511)*v(5542)
v(1528)=v(1509)+v(1513)*x(3)
v(1517)=v(1509)+v(1511)*x(2)
v(1625)=v(1554)*v(5551)+v(1585)*v(5552)+v(1600)*v(5553)+v(1599)*v(5554)+v(1521)*x(12)+v(1531)*x(13)
v(1624)=v(1553)*v(5551)+v(1584)*v(5552)+v(1599)*v(5553)+v(1614)*v(5554)+v(1520)*x(12)+v(1530)*x(13)
v(1623)=v(1552)*v(5551)+v(1583)*v(5552)+v(1585)*v(5553)+v(1584)*v(5554)+v(1519)*x(12)+v(1529)*x(13)
v(1622)=v(1551)*v(5551)+v(1582)*v(5552)+v(1598)*v(5553)+v(1613)*v(5554)+v(1518)*x(12)+v(1528)*x(13)
v(1621)=v(1550)*v(5551)+v(1581)*v(5552)+v(1597)*v(5553)+v(1612)*v(5554)+v(1517)*x(12)+v(1527)*x(13)
v(117)=v(1509)*x(2)
v(5557)=(-2d0)*v(117)
v(5556)=(-4d0)*v(117)
v(1710)=statev(38)*v(5556)
v(1698)=statev(39)*v(5556)
v(1686)=statev(37)*v(5556)
v(1637)=v(1521)*v(5557)
v(1636)=v(1520)*v(5557)
v(1635)=v(1519)*v(5557)
v(1634)=v(1518)*v(5557)
v(1633)=v(1517)*v(5557)
v(217)=-(v(117)*x(12))
v(119)=v(1509)*x(3)
v(5559)=(-2d0)*v(119)
v(5558)=(-4d0)*v(119)
v(1711)=statev(42)*v(5558)
v(1699)=statev(43)*v(5558)
v(1687)=statev(41)*v(5558)
v(1549)=v(1531)*v(5559)
v(1548)=v(1530)*v(5559)
v(1547)=v(1529)*v(5559)
v(1546)=v(1528)*v(5559)
v(1545)=v(1527)*v(5559)
v(1544)=v(1521)*v(5559)
v(1542)=v(1520)*v(5559)
v(1540)=v(1519)*v(5559)
v(1538)=-(v(119)*v(1518))-v(117)*v(1528)
v(1537)=-(v(119)*v(1517))-v(117)*v(1527)
v(218)=-(v(119)*x(13))
v(137)=(-1d0/3d0)-v(117)*v(119)
v(127)=(2d0/3d0)-(v(119)*v(119))
v(120)=v(1509)*v(5542)
v(5561)=(-2d0)*v(120)
v(5560)=(-4d0)*v(120)
v(1678)=statev(46)*v(5560)
v(5592)=v(1678)+v(1699)
v(1676)=statev(45)*v(5560)
v(5593)=v(1676)+v(1711)
v(1673)=statev(44)*v(5560)
v(5590)=v(1673)+v(1687)
v(1627)=v(119)-v(120)
v(1626)=v(117)-v(120)
v(1580)=v(1554)*v(5561)
v(1579)=v(1553)*v(5561)
v(1578)=v(1552)*v(5561)
v(1577)=v(1551)*v(5561)
v(1576)=v(1550)*v(5561)
v(1575)=v(1521)*v(5561)
v(1573)=v(1520)*v(5561)
v(1571)=v(1519)*v(5561)
v(1569)=-(v(120)*v(1518))-v(117)*v(1551)
v(1568)=-(v(120)*v(1517))-v(117)*v(1550)
v(1567)=v(1531)*v(5561)
v(1565)=v(1530)*v(5561)
v(1563)=v(1529)*v(5561)
v(1561)=-(v(120)*v(1528))-v(119)*v(1551)
v(1560)=-(v(120)*v(1527))-v(119)*v(1550)
v(219)=-(v(120)*v(5551))
v(144)=(-1d0/3d0)-v(119)*v(120)
v(139)=(-1d0/3d0)-v(117)*v(120)
v(129)=(2d0/3d0)-(v(120)*v(120))
v(121)=v(1509)*x(4)
v(5563)=(-2d0)*v(121)
v(5562)=(-4d0)*v(121)
v(1653)=statev(44)*v(5562)
v(5574)=2d0*v(1653)
v(1645)=statev(41)*v(5562)
v(5573)=2d0*v(1645)
v(1642)=statev(37)*v(5562)
v(5572)=2d0*v(1642)
v(1596)=v(1585)*v(5563)
v(1595)=v(1584)*v(5563)
v(1594)=v(1583)*v(5563)
v(1593)=v(1582)*v(5563)
v(1592)=v(1581)*v(5563)
v(220)=v(5563)*x(14)
v(131)=0.5d0-(v(121)*v(121))
v(122)=v(1509)*x(6)
v(5566)=(-2d0)*v(122)
v(5565)=(-4d0)*v(122)
v(5564)=(-8d0)*v(122)
v(1700)=statev(49)*v(5564)
v(1659)=statev(47)*v(5564)
v(1654)=statev(45)*v(5565)
v(5587)=2d0*v(1654)
v(1647)=statev(42)*v(5565)
v(5585)=2d0*v(1647)
v(1643)=statev(38)*v(5565)
v(5583)=2d0*v(1643)
v(1611)=v(1600)*v(5566)
v(1610)=v(1599)*v(5566)
v(1609)=v(1585)*v(5566)
v(1608)=v(1598)*v(5566)
v(1607)=v(1597)*v(5566)
v(221)=v(5566)*x(16)
v(133)=0.5d0-(v(122)*v(122))
v(123)=v(1509)*x(5)
v(5570)=(-2d0)*v(123)
v(5568)=(-4d0)*v(123)
v(5567)=(-8d0)*v(123)
v(1664)=statev(49)*v(5567)
v(5597)=2d0*v(1664)
v(1661)=statev(48)*v(5567)
v(5600)=v(1659)+v(1661)
v(5591)=2d0*v(1661)
v(5596)=2d0*v(1659)+v(5591)
v(1655)=statev(46)*v(5568)
v(5595)=v(1653)+v(1654)+v(1655)
v(5588)=2d0*v(1655)
v(1649)=statev(43)*v(5568)
v(5599)=v(1645)+v(1647)+v(1649)
v(5586)=2d0*v(1649)
v(5594)=v(5585)+v(5586)
v(1644)=statev(39)*v(5568)
v(5598)=v(1642)+v(1643)+v(1644)
v(5584)=2d0*v(1644)
v(5589)=v(5583)+v(5584)
v(1632)=v(1599)*v(5570)
v(1712)=v(5571)*(v(1599)*v(1700)+v(122)*v(1708)+v(1637)*v(5516)+v(1549)*v(5517)+v(1580)*v(5518)+v(1596)*v(5576)+v(1611&
&)*v(5577)+v(1632)*v(5578)+v(1544)*v(5579)+v(1575)*v(5580)+v(1567)*v(5581)+v(1521)*(v(1643)+v(5572)+v(5584))+v(1531)*(v&
&(1647)+v(5573)+v(5586))+v(1554)*(v(1654)+v(5574)+v(5588))+v(1585)*v(5591)+v(1600)*(v(1664)+v(1710)+v(121)*v(5569)+v&
&(5593)))
v(5644)=v(117)*v(1712)
v(5633)=v(119)*v(1712)
v(5620)=v(120)*v(1712)
v(5611)=v(121)*v(1712)
v(1631)=v(1614)*v(5570)
v(1701)=v(5571)*(v(1599)*v(1664)+v(123)*v(1697)+v(1636)*v(5516)+v(1548)*v(5517)+v(1579)*v(5518)+v(1595)*v(5576)+v(1610&
&)*v(5577)+v(1631)*v(5578)+v(1542)*v(5579)+v(1573)*v(5580)+v(1565)*v(5581)+v(1659)*v(5582)+v(1520)*(v(1644)+v(5572)+v&
&(5583))+v(1530)*(v(1649)+v(5573)+v(5585))+v(1553)*(v(1655)+v(5574)+v(5587))+v(1614)*(v(1698)+v(1700)+v(121)*v(5575)+v&
&(5592)))
v(5645)=v(117)*v(1701)
v(5634)=v(119)*v(1701)
v(5621)=v(120)*v(1701)
v(5613)=v(121)*v(1701)
v(1630)=-(v(123)*v(5582))
v(1689)=v(5571)*(v(121)*(v(1697)+v(1708))+v(1635)*v(5516)+v(1547)*v(5517)+v(1578)*v(5518)+v(1594)*v(5576)+v(1609)*v&
&(5577)+v(1630)*v(5578)+v(1540)*v(5579)+v(1571)*v(5580)+v(1563)*v(5581)+v(1700)*v(5582)+v(1552)*(v(1653)+v(5587)+v(5588)&
&)+v(1519)*(v(1642)+v(5589))+v(1529)*(v(1645)+v(5594))+v(1583)*(v(1686)+v(5590)+v(5600)))
v(5652)=v(117)*v(1689)
v(5641)=v(119)*v(1689)
v(5630)=v(120)*v(1689)
v(5626)=-(v(122)*v(1689))
v(1629)=v(1613)*v(5570)
v(1679)=v(5571)*(v(1634)*v(5516)+v(1546)*v(5517)+v(1577)*v(5518)+v(1593)*v(5576)+v(1608)*v(5577)+v(1629)*v(5578)+v(1538&
&)*v(5579)+v(1569)*v(5580)+v(1561)*v(5581)+v(1518)*(v(5572)+v(5589))+v(1613)*v(5592)+v(1551)*v(5595)+v(1582)*(v(5590)+v&
&(5596))+v(1598)*(v(5593)+v(5597))+v(1528)*v(5599))
v(1628)=v(1612)*v(5570)
v(1669)=v(5571)*(v(1612)*(v(1678)+v(1698))+v(1633)*v(5516)+v(1545)*v(5517)+v(1576)*v(5518)+v(1592)*v(5576)+v(1607)*v&
&(5577)+v(1628)*v(5578)+v(1537)*v(5579)+v(1568)*v(5580)+v(1560)*v(5581)+v(1527)*(v(5573)+v(5594))+v(1550)*v(5595)+v(1581&
&)*(v(1673)+v(1686)+v(5596))+v(1597)*(v(1676)+v(1710)+v(5597))+v(1517)*v(5598))
v(222)=v(5570)*x(15)
v(226)=-v(217)-v(218)-v(219)-v(220)-v(221)-v(222)
v(2477)=-(v(1599)*v(226))
v(2473)=-(v(1584)*v(226))
v(2464)=-(v(123)*v(226))+x(15)
v(5756)=-(v(1502)*v(2464))
v(2452)=-(v(1585)*v(226))
v(2443)=-(v(122)*v(226))+x(16)
v(5761)=-(v(1502)*v(2443))
v(2426)=-(v(121)*v(226))+x(14)
v(5766)=-(v(1502)*v(2426))
v(2411)=-(v(120)*v(226))+v(5551)
v(5771)=-(v(1502)*v(2411))
v(2395)=-(v(119)*v(226))+x(13)
v(5774)=-(v(1502)*v(2395))
v(2380)=-(v(117)*v(226))+x(12)
v(5786)=-(v(1502)*v(2380))
v(157)=1d0+v(217)+v(218)+v(219)+v(220)+v(221)+v(222)
v(5668)=0.15d1*v(157)
v(135)=0.5d0-(v(123)*v(123))
v(124)=(2d0/3d0)-(v(117)*v(117))
v(1639)=v(122)*v(1664)+v(124)*v(5516)+v(127)*v(5517)+v(129)*v(5518)+v(131)*v(5576)+v(133)*v(5577)+v(135)*v(5578)+v(137&
&)*v(5579)+v(139)*v(5580)+v(144)*v(5581)+v(120)*v(5595)+v(117)*v(5598)+v(119)*v(5599)+v(121)*v(5600)
v(1640)=-(mpar(13)*v(1638)*v(1639)*v(5537))
v(5604)=mpar(14)*v(1640)
v(5603)=-(v(121)*v(1640))
v(5602)=-(v(122)*v(1640))
v(5601)=-(v(123)*v(1640))
v(1997)=v(122)*v(5601)
v(1989)=v(121)*v(5601)
v(1980)=v(121)*v(5602)
v(1968)=v(120)*v(5601)
v(1955)=v(120)*v(5602)
v(1941)=v(120)*v(5603)
v(1928)=v(119)*v(5601)
v(1914)=v(119)*v(5602)
v(1899)=v(119)*v(5603)
v(1882)=v(144)*v(5604)
v(1868)=v(117)*v(5601)
v(1854)=v(117)*v(5602)
v(1839)=v(117)*v(5603)
v(1822)=v(139)*v(5604)
v(1804)=v(137)*v(5604)
v(1786)=v(135)*v(5604)
v(1797)=v(1786)*v(5605)
v(1768)=v(133)*v(5604)
v(1779)=v(1768)*v(5605)
v(1750)=v(131)*v(5604)
v(1761)=v(1750)*v(5605)
v(1738)=v(129)*v(5604)
v(1726)=v(127)*v(5604)
v(1714)=v(124)*v(5604)
v(126)=v(1639)*v(5571)
v(5665)=-(v(121)*v(126))
v(5649)=v(126)*v(1521)
v(5648)=v(126)*v(1517)+v(117)*v(1669)
v(5643)=v(126)*v(1520)
v(5642)=-(v(117)*v(126))
v(5638)=v(126)*v(1531)
v(5636)=v(126)*v(1528)+v(119)*v(1679)
v(5632)=v(126)*v(1530)
v(5631)=-(v(119)*v(126))
v(5629)=v(126)*v(1583)
v(5625)=v(126)*v(1554)
v(5624)=v(126)*v(1550)+v(120)*v(1669)
v(5623)=v(126)*v(1551)+v(120)*v(1679)
v(5619)=v(126)*v(1553)
v(5618)=-(v(120)*v(126))
v(5615)=v(121)*v(1689)+v(5629)
v(5614)=v(126)*v(1585)
v(5610)=-(v(126)*v(1600))
v(5609)=v(126)*v(1584)
v(5608)=-(v(126)*v(1614))
v(5607)=(-2d0)*v(126)
v(5647)=-(v(117)*v(1679))+v(1518)*v(5607)
v(5637)=-(v(119)*v(1669))+v(1527)*v(5607)
v(5617)=-(v(121)*v(1669))+v(1581)*v(5607)
v(5616)=-(v(121)*v(1679))+v(1582)*v(5607)
v(5606)=v(126)*v(1599)
v(2004)=-(v(122)*(v(123)*v(1712)+v(5606)))+v(123)*v(5610)
v(2003)=-(v(123)*(v(122)*v(1701)+v(5606)))+v(122)*v(5608)
v(2001)=v(123)*(-(v(122)*v(1679))+v(1598)*v(5607))
v(1999)=v(123)*(-(v(122)*v(1669))+v(1597)*v(5607))
v(1995)=v(121)*v(5608)-v(123)*(v(5609)+v(5613))
v(1994)=-(v(121)*v(5609))-v(123)*v(5615)
v(1993)=v(123)*v(5616)
v(1991)=v(123)*v(5617)
v(1988)=v(121)*v(5610)-v(122)*(v(5611)+v(5614))
v(1986)=-(v(122)*v(5609))
v(5612)=2d0*v(1986)
v(2002)=v(5612)+v(123)*v(5626)
v(1996)=-(v(123)*v(5611))+v(5612)
v(1987)=v(5612)-v(122)*v(5613)
v(1985)=-(v(121)*v(5614))-v(122)*v(5615)
v(1984)=v(122)*v(5616)
v(1982)=v(122)*v(5617)
v(1972)=v(120)*v(5608)-v(123)*(v(5619)+v(5621))
v(1970)=v(1613)*v(5618)-v(123)*v(5623)
v(1969)=v(1612)*v(5618)-v(123)*v(5624)
v(1961)=v(120)*v(5610)-v(122)*(v(5620)+v(5625))
v(1959)=-(v(122)*v(5619))
v(5622)=2d0*v(1959)
v(1973)=-(v(123)*v(5620))+v(5622)
v(1960)=-(v(122)*v(5621))+v(5622)
v(1957)=v(1598)*v(5618)-v(122)*v(5623)
v(1956)=v(1597)*v(5618)-v(122)*v(5624)
v(1947)=-(v(121)*v(5625))
v(5627)=2d0*v(1947)
v(1958)=v(120)*v(5626)+v(5627)
v(1948)=-(v(120)*v(5611))+v(5627)
v(1945)=-(v(121)*v(5619))
v(5628)=2d0*v(1945)
v(1971)=v(5628)-v(123)*v(5630)
v(1946)=-(v(120)*v(5613))+v(5628)
v(1944)=-(v(120)*v(5629))-v(121)*(v(126)*v(1552)+v(5630))
v(1943)=v(1582)*v(5618)-v(121)*v(5623)
v(1942)=v(1581)*v(5618)-v(121)*v(5624)
v(1933)=v(119)*v(5608)-v(123)*(v(5632)+v(5634))
v(1931)=v(1613)*v(5631)-v(123)*v(5636)
v(1930)=v(123)*v(5637)
v(1921)=v(1600)*v(5631)-v(122)*(v(5633)+v(5638))
v(1919)=-(v(122)*v(5632))
v(5635)=2d0*v(1919)
v(1934)=-(v(123)*v(5633))+v(5635)
v(1920)=-(v(122)*v(5634))+v(5635)
v(1917)=v(1598)*v(5631)-v(122)*v(5636)
v(1916)=v(122)*v(5637)
v(1906)=-(v(121)*v(5638))
v(5639)=2d0*v(1906)
v(1918)=v(119)*v(5626)+v(5639)
v(1907)=-(v(119)*v(5611))+v(5639)
v(1904)=-(v(121)*v(5632))
v(5640)=2d0*v(1904)
v(1932)=v(5640)-v(123)*v(5641)
v(1905)=-(v(119)*v(5613))+v(5640)
v(1903)=-(v(119)*v(5629))-v(121)*(v(126)*v(1529)+v(5641))
v(1902)=v(1582)*v(5631)-v(121)*v(5636)
v(1901)=v(121)*v(5637)
v(1892)=mpar(14)*(v(126)*v(1567)+v(144)*v(1712))
v(1890)=mpar(14)*(v(126)*v(1565)+v(144)*v(1701))
v(1888)=mpar(14)*(v(126)*v(1563)+v(144)*v(1689))
v(1886)=mpar(14)*(v(126)*v(1561)+v(144)*v(1679))
v(1884)=mpar(14)*(v(126)*v(1560)+v(144)*v(1669))
v(1873)=v(117)*v(5608)-v(123)*(v(5643)+v(5645))
v(1871)=v(123)*v(5647)
v(1869)=v(1612)*v(5642)-v(123)*v(5648)
v(1861)=v(1600)*v(5642)-v(122)*(v(5644)+v(5649))
v(1859)=-(v(122)*v(5643))
v(5646)=2d0*v(1859)
v(1874)=-(v(123)*v(5644))+v(5646)
v(1860)=-(v(122)*v(5645))+v(5646)
v(1857)=v(122)*v(5647)
v(1855)=v(1597)*v(5642)-v(122)*v(5648)
v(1846)=-(v(121)*v(5649))
v(5650)=2d0*v(1846)
v(1858)=v(117)*v(5626)+v(5650)
v(1847)=-(v(117)*v(5611))+v(5650)
v(1844)=-(v(121)*v(5643))
v(5651)=2d0*v(1844)
v(1872)=v(5651)-v(123)*v(5652)
v(1845)=-(v(117)*v(5613))+v(5651)
v(1843)=-(v(117)*v(5629))-v(121)*(v(126)*v(1519)+v(5652))
v(1842)=v(121)*v(5647)
v(1840)=v(1581)*v(5642)-v(121)*v(5648)
v(1832)=mpar(14)*(v(126)*v(1575)+v(139)*v(1712))
v(1830)=mpar(14)*(v(126)*v(1573)+v(139)*v(1701))
v(1828)=mpar(14)*(v(126)*v(1571)+v(139)*v(1689))
v(1826)=mpar(14)*(v(126)*v(1569)+v(139)*v(1679))
v(1824)=mpar(14)*(v(126)*v(1568)+v(139)*v(1669))
v(1814)=mpar(14)*(v(126)*v(1544)+v(137)*v(1712))
v(1812)=mpar(14)*(v(126)*v(1542)+v(137)*v(1701))
v(1810)=mpar(14)*(v(126)*v(1540)+v(137)*v(1689))
v(1808)=mpar(14)*(v(126)*v(1538)+v(137)*v(1679))
v(1806)=mpar(14)*(v(126)*v(1537)+v(137)*v(1669))
v(1796)=mpar(14)*(v(126)*v(1632)+v(135)*v(1712))
v(1802)=v(1796)*v(5605)
v(1794)=mpar(14)*(v(126)*v(1631)+v(135)*v(1701))
v(1801)=v(1794)*v(5605)
v(1792)=mpar(14)*(v(126)*v(1630)+v(135)*v(1689))
v(1800)=v(1792)*v(5605)
v(1790)=mpar(14)*(v(126)*v(1629)+v(135)*v(1679))
v(1799)=v(1790)*v(5605)
v(1788)=mpar(14)*(v(126)*v(1628)+v(135)*v(1669))
v(1798)=v(1788)*v(5605)
v(1778)=mpar(14)*(v(126)*v(1611)+v(133)*v(1712))
v(1784)=v(1778)*v(5605)
v(1776)=mpar(14)*(v(126)*v(1610)+v(133)*v(1701))
v(1783)=v(1776)*v(5605)
v(1774)=mpar(14)*(v(126)*v(1609)+v(133)*v(1689))
v(1782)=v(1774)*v(5605)
v(1772)=mpar(14)*(v(126)*v(1608)+v(133)*v(1679))
v(1781)=v(1772)*v(5605)
v(1770)=mpar(14)*(v(126)*v(1607)+v(133)*v(1669))
v(1780)=v(1770)*v(5605)
v(1760)=mpar(14)*(v(126)*v(1596)+v(131)*v(1712))
v(1766)=v(1760)*v(5605)
v(1758)=mpar(14)*(v(126)*v(1595)+v(131)*v(1701))
v(1765)=v(1758)*v(5605)
v(1756)=mpar(14)*(v(126)*v(1594)+v(131)*v(1689))
v(1764)=v(1756)*v(5605)
v(1754)=mpar(14)*(v(126)*v(1593)+v(131)*v(1679))
v(1763)=v(1754)*v(5605)
v(1752)=mpar(14)*(v(126)*v(1592)+v(131)*v(1669))
v(1762)=v(1752)*v(5605)
v(1748)=mpar(14)*(v(126)*v(1580)+v(129)*v(1712))
v(1746)=mpar(14)*(v(126)*v(1579)+v(129)*v(1701))
v(1744)=mpar(14)*(v(126)*v(1578)+v(129)*v(1689))
v(1742)=mpar(14)*(v(126)*v(1577)+v(129)*v(1679))
v(1740)=mpar(14)*(v(126)*v(1576)+v(129)*v(1669))
v(1736)=mpar(14)*(v(126)*v(1549)+v(127)*v(1712))
v(1734)=mpar(14)*(v(126)*v(1548)+v(127)*v(1701))
v(1732)=mpar(14)*(v(126)*v(1547)+v(127)*v(1689))
v(1730)=mpar(14)*(v(126)*v(1546)+v(127)*v(1679))
v(1728)=mpar(14)*(v(126)*v(1545)+v(127)*v(1669))
v(1724)=mpar(14)*(v(126)*v(1637)+v(124)*v(1712))
v(1722)=mpar(14)*(v(126)*v(1636)+v(124)*v(1701))
v(1720)=mpar(14)*(v(126)*v(1635)+v(124)*v(1689))
v(1718)=mpar(14)*(v(126)*v(1634)+v(124)*v(1679))
v(1716)=mpar(14)*(v(126)*v(1633)+v(124)*v(1669))
v(125)=statev(29)+v(124)*v(126)
v(158)=(2d0/3d0)+mpar(14)*v(125)
v(5673)=2d0*v(158)
v(128)=statev(30)+v(126)*v(127)
v(170)=(2d0/3d0)+mpar(14)*v(128)
v(5725)=v(158)+v(170)
v(5671)=2d0*v(170)
v(130)=statev(31)+v(126)*v(129)
v(173)=(2d0/3d0)+mpar(14)*v(130)
v(5701)=v(158)+v(173)
v(5696)=v(170)+v(173)
v(5669)=2d0*v(173)
v(132)=statev(32)+v(126)*v(131)
v(192)=0.5d0+mpar(14)*v(132)
v(5683)=4d0*v(192)
v(175)=v(192)*v(5605)
v(134)=statev(33)+v(126)*v(133)
v(200)=0.5d0+mpar(14)*v(134)
v(5681)=4d0*v(200)
v(179)=v(200)*v(5605)
v(5686)=v(175)+v(179)
v(136)=statev(34)+v(126)*v(135)
v(208)=0.5d0+mpar(14)*v(136)
v(5677)=4d0*v(208)
v(182)=v(208)*v(5605)
v(5689)=v(175)+v(182)
v(5679)=v(179)+v(182)
v(138)=statev(35)+v(126)*v(137)
v(159)=(-1d0/3d0)+mpar(14)*v(138)
v(5653)=2d0*v(159)
v(1820)=v(1814)*v(5653)
v(1819)=v(1812)*v(5653)
v(1818)=v(1810)*v(5653)
v(1817)=v(1808)*v(5653)
v(1816)=v(1806)*v(5653)
v(1815)=v(1804)*v(5653)
v(171)=(v(159)*v(159))
v(140)=statev(36)+v(126)*v(139)
v(160)=(-1d0/3d0)+mpar(14)*v(140)
v(5654)=2d0*v(160)
v(1838)=v(1832)*v(5654)
v(1837)=v(1830)*v(5654)
v(1836)=v(1828)*v(5654)
v(1835)=v(1826)*v(5654)
v(1834)=v(1824)*v(5654)
v(1833)=v(1822)*v(5654)
v(184)=(v(160)*v(160))
v(141)=statev(37)+v(121)*v(5642)
v(5655)=2d0*v(141)
v(1853)=v(1847)*v(5655)
v(1852)=v(1845)*v(5655)
v(1851)=v(1843)*v(5655)
v(1850)=v(1842)*v(5655)
v(1849)=v(1840)*v(5655)
v(1848)=v(1839)*v(5655)
v(193)=(v(141)*v(141))
v(142)=statev(38)+v(122)*v(5642)
v(5656)=2d0*v(142)
v(1867)=v(1861)*v(5656)
v(1866)=v(1860)*v(5656)
v(1865)=v(1858)*v(5656)
v(1864)=v(1857)*v(5656)
v(1863)=v(1855)*v(5656)
v(1862)=v(1854)*v(5656)
v(201)=(v(142)*v(142))
v(143)=statev(39)+v(123)*v(5642)
v(5657)=2d0*v(143)
v(1880)=v(1874)*v(5657)
v(1879)=v(1873)*v(5657)
v(1878)=v(1872)*v(5657)
v(1877)=v(1871)*v(5657)
v(1876)=v(1869)*v(5657)
v(1875)=v(1868)*v(5657)
v(209)=(v(143)*v(143))
v(145)=statev(40)+v(126)*v(144)
v(162)=(-1d0/3d0)+mpar(14)*v(145)
v(5658)=2d0*v(162)
v(1898)=v(1892)*v(5658)
v(1897)=v(1890)*v(5658)
v(1896)=v(1888)*v(5658)
v(1895)=v(1886)*v(5658)
v(1894)=v(1884)*v(5658)
v(1893)=v(1882)*v(5658)
v(185)=(v(162)*v(162))
v(146)=statev(41)+v(121)*v(5631)
v(5659)=2d0*v(146)
v(1913)=v(1907)*v(5659)
v(1912)=v(1905)*v(5659)
v(1911)=v(1903)*v(5659)
v(1910)=v(1902)*v(5659)
v(1909)=v(1901)*v(5659)
v(1908)=v(1899)*v(5659)
v(194)=(v(146)*v(146))
v(147)=statev(42)+v(122)*v(5631)
v(5660)=2d0*v(147)
v(1927)=v(1921)*v(5660)
v(1926)=v(1920)*v(5660)
v(1925)=v(1918)*v(5660)
v(1924)=v(1917)*v(5660)
v(1923)=v(1916)*v(5660)
v(1922)=v(1914)*v(5660)
v(202)=(v(147)*v(147))
v(148)=statev(43)+v(123)*v(5631)
v(5661)=2d0*v(148)
v(1940)=v(1934)*v(5661)
v(1939)=v(1933)*v(5661)
v(1938)=v(1932)*v(5661)
v(1937)=v(1931)*v(5661)
v(1936)=v(1930)*v(5661)
v(1935)=v(1928)*v(5661)
v(210)=(v(148)*v(148))
v(149)=statev(44)+v(121)*v(5618)
v(5662)=2d0*v(149)
v(1954)=v(1948)*v(5662)
v(1953)=v(1946)*v(5662)
v(1952)=v(1944)*v(5662)
v(1951)=v(1943)*v(5662)
v(1950)=v(1942)*v(5662)
v(1949)=v(1941)*v(5662)
v(195)=(v(149)*v(149))
v(150)=statev(45)+v(122)*v(5618)
v(5663)=2d0*v(150)
v(1967)=v(1961)*v(5663)
v(1966)=v(1960)*v(5663)
v(1965)=v(1958)*v(5663)
v(1964)=v(1957)*v(5663)
v(1963)=v(1956)*v(5663)
v(1962)=v(1955)*v(5663)
v(203)=(v(150)*v(150))
v(151)=statev(46)+v(123)*v(5618)
v(5664)=2d0*v(151)
v(1979)=v(1973)*v(5664)
v(1978)=v(1972)*v(5664)
v(1977)=v(1971)*v(5664)
v(1976)=v(1970)*v(5664)
v(1975)=v(1969)*v(5664)
v(1974)=v(1968)*v(5664)
v(211)=(v(151)*v(151))
v(152)=statev(47)+v(122)*v(5665)
v(153)=statev(48)+v(123)*v(5665)
v(154)=statev(49)-v(122)*v(123)*v(126)
v(2219)=(v(173)*v(173))+v(184)+v(185)+2d0*(v(195)+v(203)+v(211))*v(5666)
v(5667)=0.15d1*v(2219)
v(2229)=v(5566)*v(5667)
v(2228)=v(5570)*v(5667)
v(2227)=v(5563)*v(5667)
v(2226)=-(v(1627)*v(5667))
v(2225)=-(v(1626)*v(5667))
v(2224)=-(v(1625)*v(5667))+v(5668)*(v(1838)+v(1898)+2d0*(v(1954)+v(1967)+v(1979))*v(5666)+v(1748)*v(5669))
v(2223)=-(v(1624)*v(5667))+v(5668)*(v(1837)+v(1897)+2d0*(v(1953)+v(1966)+v(1978))*v(5666)+v(1746)*v(5669))
v(2222)=-(v(1623)*v(5667))+v(5668)*(v(1836)+v(1896)+2d0*(v(1952)+v(1965)+v(1977))*v(5666)+v(1744)*v(5669))
v(2221)=-(v(1622)*v(5667))+v(5668)*(v(1835)+v(1895)+2d0*(v(1951)+v(1964)+v(1976))*v(5666)+v(1742)*v(5669))
v(2220)=-(v(1621)*v(5667))+v(5668)*(v(1834)+v(1894)+2d0*(v(1950)+v(1963)+v(1975))*v(5666)+v(1740)*v(5669))
v(2218)=v(5668)*(v(1833)+v(1893)+2d0*(v(1949)+v(1962)+v(1974))*v(5666)+v(1738)*v(5669))
v(2159)=(v(170)*v(170))+v(171)+v(185)+2d0*(v(194)+v(202)+v(210))*v(5666)
v(5670)=0.15d1*v(2159)
v(2169)=v(5566)*v(5670)
v(2168)=v(5570)*v(5670)
v(2167)=v(5563)*v(5670)
v(2166)=-(v(1627)*v(5670))
v(2165)=-(v(1626)*v(5670))
v(2164)=-(v(1625)*v(5670))+v(5668)*(v(1820)+v(1898)+2d0*(v(1913)+v(1927)+v(1940))*v(5666)+v(1736)*v(5671))
v(2163)=-(v(1624)*v(5670))+v(5668)*(v(1819)+v(1897)+2d0*(v(1912)+v(1926)+v(1939))*v(5666)+v(1734)*v(5671))
v(2162)=-(v(1623)*v(5670))+v(5668)*(v(1818)+v(1896)+2d0*(v(1911)+v(1925)+v(1938))*v(5666)+v(1732)*v(5671))
v(2161)=-(v(1622)*v(5670))+v(5668)*(v(1817)+v(1895)+2d0*(v(1910)+v(1924)+v(1937))*v(5666)+v(1730)*v(5671))
v(2160)=-(v(1621)*v(5670))+v(5668)*(v(1816)+v(1894)+2d0*(v(1909)+v(1923)+v(1936))*v(5666)+v(1728)*v(5671))
v(2158)=v(5668)*(v(1815)+v(1893)+2d0*(v(1908)+v(1922)+v(1935))*v(5666)+v(1726)*v(5671))
v(2087)=(v(158)*v(158))+v(171)+v(184)+2d0*(v(193)+v(201)+v(209))*v(5666)
v(5672)=0.15d1*v(2087)
v(2097)=v(5566)*v(5672)
v(2096)=v(5570)*v(5672)
v(2095)=v(5563)*v(5672)
v(2094)=-(v(1627)*v(5672))
v(2093)=-(v(1626)*v(5672))
v(2092)=-(v(1625)*v(5672))+v(5668)*(v(1820)+v(1838)+2d0*(v(1853)+v(1867)+v(1880))*v(5666)+v(1724)*v(5673))
v(2091)=-(v(1624)*v(5672))+v(5668)*(v(1819)+v(1837)+2d0*(v(1852)+v(1866)+v(1879))*v(5666)+v(1722)*v(5673))
v(2090)=-(v(1623)*v(5672))+v(5668)*(v(1818)+v(1836)+2d0*(v(1851)+v(1865)+v(1878))*v(5666)+v(1720)*v(5673))
v(2089)=-(v(1622)*v(5672))+v(5668)*(v(1817)+v(1835)+2d0*(v(1850)+v(1864)+v(1877))*v(5666)+v(1718)*v(5673))
v(2088)=-(v(1621)*v(5672))+v(5668)*(v(1816)+v(1834)+2d0*(v(1849)+v(1863)+v(1876))*v(5666)+v(1716)*v(5673))
v(2086)=v(5668)*(v(1815)+v(1833)+2d0*(v(1848)+v(1862)+v(1875))*v(5666)+v(1714)*v(5673))
v(2085)=v(1847)*v(5674)
v(2084)=v(1845)*v(5674)
v(2083)=v(1843)*v(5674)
v(2082)=v(1842)*v(5674)
v(2081)=v(1840)*v(5674)
v(2080)=v(1839)*v(5674)
v(2079)=v(1861)*v(5674)
v(2078)=v(1860)*v(5674)
v(2077)=v(1858)*v(5674)
v(2076)=v(1857)*v(5674)
v(2075)=v(1855)*v(5674)
v(2074)=v(1854)*v(5674)
v(2073)=v(1874)*v(5674)
v(2072)=v(1873)*v(5674)
v(2071)=v(1872)*v(5674)
v(2070)=v(1871)*v(5674)
v(2069)=v(1869)*v(5674)
v(2068)=v(1868)*v(5674)
v(2067)=v(1921)*v(5674)
v(2066)=v(1920)*v(5674)
v(2065)=v(1918)*v(5674)
v(2064)=v(1917)*v(5674)
v(2063)=v(1916)*v(5674)
v(2062)=v(1914)*v(5674)
v(2061)=v(1934)*v(5674)
v(2060)=v(1933)*v(5674)
v(2059)=v(1932)*v(5674)
v(2058)=v(1931)*v(5674)
v(2057)=v(1930)*v(5674)
v(2056)=v(1928)*v(5674)
v(2055)=v(1907)*v(5674)
v(2054)=v(1905)*v(5674)
v(2053)=v(1903)*v(5674)
v(2052)=v(1902)*v(5674)
v(2051)=v(1901)*v(5674)
v(2050)=v(1899)*v(5674)
v(2049)=v(1988)*v(5674)
v(2048)=v(1987)*v(5674)
v(2047)=v(1985)*v(5674)
v(2046)=v(1984)*v(5674)
v(2045)=v(1982)*v(5674)
v(2044)=v(1980)*v(5674)
v(2043)=v(1973)*v(5674)
v(2042)=v(1972)*v(5674)
v(2041)=v(1971)*v(5674)
v(2040)=v(1970)*v(5674)
v(2039)=v(1969)*v(5674)
v(2038)=v(1968)*v(5674)
v(2037)=v(2004)*v(5674)
v(2036)=v(2003)*v(5674)
v(2035)=v(2002)*v(5674)
v(2034)=v(2001)*v(5674)
v(2033)=v(1999)*v(5674)
v(2032)=v(1997)*v(5674)
v(2026)=v(152)*v(5675)
v(2031)=v(1988)*v(2026)
v(2030)=v(1987)*v(2026)
v(2029)=v(1985)*v(2026)
v(2028)=v(1984)*v(2026)
v(2027)=v(1982)*v(2026)
v(2025)=v(1980)*v(2026)
v(2024)=v(1996)*v(5674)
v(2023)=v(1995)*v(5674)
v(2022)=v(1994)*v(5674)
v(2021)=v(1993)*v(5674)
v(2020)=v(1991)*v(5674)
v(2019)=v(1989)*v(5674)
v(2013)=v(153)*v(5675)
v(2018)=v(1996)*v(2013)
v(2017)=v(1995)*v(2013)
v(2016)=v(1994)*v(2013)
v(2015)=v(1993)*v(2013)
v(2014)=v(1991)*v(2013)
v(2012)=v(1989)*v(2013)
v(2266)=v(5668)*(v(2012)+v(2025)+(v(1848)+v(1908)+v(1949))*v(5666)+v(1750)*v(5683))
v(2006)=v(154)*v(5675)
v(2011)=v(2004)*v(2006)
v(2010)=v(2003)*v(2006)
v(2009)=v(2002)*v(2006)
v(2008)=v(2001)*v(2006)
v(2007)=v(1999)*v(2006)
v(2005)=v(1997)*v(2006)
v(2326)=v(5668)*(v(2005)+v(2012)+(v(1875)+v(1935)+v(1974))*v(5666)+v(1786)*v(5677))
v(2302)=v(5668)*(v(2005)+v(2025)+(v(1862)+v(1922)+v(1962))*v(5666)+v(1768)*v(5681))
v(213)=(v(154)*v(154))*v(5674)
v(212)=(v(153)*v(153))*v(5674)
v(2327)=2d0*(v(208)*v(208))+v(212)+v(213)+(v(209)+v(210)+v(211))*v(5666)
v(5676)=0.15d1*v(2327)
v(2337)=v(5566)*v(5676)
v(2336)=v(5570)*v(5676)
v(2335)=v(5563)*v(5676)
v(2334)=-(v(1627)*v(5676))
v(2333)=-(v(1626)*v(5676))
v(2332)=-(v(1625)*v(5676))+v(5668)*(v(2011)+v(2018)+(v(1880)+v(1940)+v(1979))*v(5666)+v(1796)*v(5677))
v(2331)=-(v(1624)*v(5676))+v(5668)*(v(2010)+v(2017)+(v(1879)+v(1939)+v(1978))*v(5666)+v(1794)*v(5677))
v(2330)=-(v(1623)*v(5676))+v(5668)*(v(2009)+v(2016)+(v(1878)+v(1938)+v(1977))*v(5666)+v(1792)*v(5677))
v(2329)=-(v(1622)*v(5676))+v(5668)*(v(2008)+v(2015)+(v(1877)+v(1937)+v(1976))*v(5666)+v(1790)*v(5677))
v(2328)=-(v(1621)*v(5676))+v(5668)*(v(2007)+v(2014)+(v(1876)+v(1936)+v(1975))*v(5666)+v(1788)*v(5677))
v(206)=v(153)*v(5674)
v(2315)=v(152)*v(206)+(v(142)*v(143)+v(147)*v(148)+v(150)*v(151))*v(5666)+v(154)*v(5679)
v(5678)=0.15d1*v(2315)
v(2325)=v(5566)*v(5678)
v(2485)=v(2325)*v(5539)
v(2324)=v(5570)*v(5678)
v(2365)=v(2324)*v(5685)
v(5715)=v(2365)*v(5709)
v(5705)=v(2365)*v(5685)
v(2323)=v(5563)*v(5678)
v(2322)=-(v(1627)*v(5678))
v(2321)=-(v(1626)*v(5678))
v(2320)=-(v(1625)*v(5678))+v(5668)*(v(154)*(v(1784)+v(1802))+v(152)*v(2024)+v(1988)*v(206)+(v(143)*v(1861)+v(142)*v&
&(1874)+v(148)*v(1921)+v(147)*v(1934)+v(151)*v(1961)+v(150)*v(1973))*v(5666)+v(2004)*v(5679))
v(2319)=-(v(1624)*v(5678))+v(5668)*(v(154)*(v(1783)+v(1801))+v(152)*v(2023)+v(1987)*v(206)+(v(143)*v(1860)+v(142)*v&
&(1873)+v(148)*v(1920)+v(147)*v(1933)+v(151)*v(1960)+v(150)*v(1972))*v(5666)+v(2003)*v(5679))
v(2318)=-(v(1623)*v(5678))+v(5668)*(v(154)*(v(1782)+v(1800))+v(152)*v(2022)+v(1985)*v(206)+(v(143)*v(1858)+v(142)*v&
&(1872)+v(148)*v(1918)+v(147)*v(1932)+v(151)*v(1958)+v(150)*v(1971))*v(5666)+v(2002)*v(5679))
v(2317)=-(v(1622)*v(5678))+v(5668)*(v(154)*(v(1781)+v(1799))+v(152)*v(2021)+v(1984)*v(206)+(v(143)*v(1857)+v(142)*v&
&(1871)+v(148)*v(1917)+v(147)*v(1931)+v(151)*v(1957)+v(150)*v(1970))*v(5666)+v(2001)*v(5679))
v(2316)=-(v(1621)*v(5678))+v(5668)*(v(154)*(v(1780)+v(1798))+v(152)*v(2020)+v(1982)*v(206)+(v(143)*v(1855)+v(142)*v&
&(1869)+v(148)*v(1916)+v(147)*v(1930)+v(151)*v(1956)+v(150)*v(1969))*v(5666)+v(1999)*v(5679))
v(2314)=v(5668)*(v(154)*(v(1779)+v(1797))+v(152)*v(2019)+v(1980)*v(206)+(v(143)*v(1854)+v(142)*v(1868)+v(148)*v(1914)+v&
&(147)*v(1928)+v(151)*v(1955)+v(150)*v(1968))*v(5666)+v(1997)*v(5679))
v(204)=(v(152)*v(152))*v(5674)
v(2303)=2d0*(v(200)*v(200))+v(204)+v(213)+(v(201)+v(202)+v(203))*v(5666)
v(5680)=0.15d1*v(2303)
v(2313)=v(5566)*v(5680)
v(2312)=v(5570)*v(5680)
v(2311)=v(5563)*v(5680)
v(2310)=-(v(1627)*v(5680))
v(2309)=-(v(1626)*v(5680))
v(2308)=-(v(1625)*v(5680))+v(5668)*(v(2011)+v(2031)+(v(1867)+v(1927)+v(1967))*v(5666)+v(1778)*v(5681))
v(2307)=-(v(1624)*v(5680))+v(5668)*(v(2010)+v(2030)+(v(1866)+v(1926)+v(1966))*v(5666)+v(1776)*v(5681))
v(2306)=-(v(1623)*v(5680))+v(5668)*(v(2009)+v(2029)+(v(1865)+v(1925)+v(1965))*v(5666)+v(1774)*v(5681))
v(2305)=-(v(1622)*v(5680))+v(5668)*(v(2008)+v(2028)+(v(1864)+v(1924)+v(1964))*v(5666)+v(1772)*v(5681))
v(2304)=-(v(1621)*v(5680))+v(5668)*(v(2007)+v(2027)+(v(1863)+v(1923)+v(1963))*v(5666)+v(1770)*v(5681))
v(2267)=2d0*(v(192)*v(192))+v(204)+v(212)+(v(193)+v(194)+v(195))*v(5666)
v(5682)=0.15d1*v(2267)
v(2277)=v(5566)*v(5682)
v(2276)=v(5570)*v(5682)
v(2275)=v(5563)*v(5682)
v(2274)=-(v(1627)*v(5682))
v(2273)=-(v(1626)*v(5682))
v(2272)=-(v(1625)*v(5682))+v(5668)*(v(2018)+v(2031)+(v(1853)+v(1913)+v(1954))*v(5666)+v(1760)*v(5683))
v(2271)=-(v(1624)*v(5682))+v(5668)*(v(2017)+v(2030)+(v(1852)+v(1912)+v(1953))*v(5666)+v(1758)*v(5683))
v(2270)=-(v(1623)*v(5682))+v(5668)*(v(2016)+v(2029)+(v(1851)+v(1911)+v(1952))*v(5666)+v(1756)*v(5683))
v(2269)=-(v(1622)*v(5682))+v(5668)*(v(2015)+v(2028)+(v(1850)+v(1910)+v(1951))*v(5666)+v(1754)*v(5683))
v(2268)=-(v(1621)*v(5682))+v(5668)*(v(2014)+v(2027)+(v(1849)+v(1909)+v(1950))*v(5666)+v(1752)*v(5683))
v(197)=v(154)*v(5674)
v(2279)=v(153)*v(197)+(v(141)*v(142)+v(146)*v(147)+v(149)*v(150))*v(5666)+v(152)*v(5686)
v(5684)=0.15d1*v(2279)
v(2289)=v(5566)*v(5684)
v(2288)=v(5570)*v(5684)
v(2287)=v(5563)*v(5684)
v(2462)=v(2287)*v(5540)
v(2364)=v(2287)*v(5685)
v(5720)=v(2364)*v(5708)
v(5703)=v(2364)*v(5685)
v(2286)=-(v(1627)*v(5684))
v(2285)=-(v(1626)*v(5684))
v(2284)=-(v(1625)*v(5684))+v(5668)*(v(152)*(v(1766)+v(1784))+v(197)*v(1996)+v(153)*v(2037)+(v(142)*v(1847)+v(141)*v&
&(1861)+v(147)*v(1907)+v(146)*v(1921)+v(150)*v(1948)+v(149)*v(1961))*v(5666)+v(1988)*v(5686))
v(2283)=-(v(1624)*v(5684))+v(5668)*(v(152)*(v(1765)+v(1783))+v(197)*v(1995)+v(153)*v(2036)+(v(142)*v(1845)+v(141)*v&
&(1860)+v(147)*v(1905)+v(146)*v(1920)+v(150)*v(1946)+v(149)*v(1960))*v(5666)+v(1987)*v(5686))
v(2282)=-(v(1623)*v(5684))+v(5668)*(v(152)*(v(1764)+v(1782))+v(197)*v(1994)+v(153)*v(2035)+(v(142)*v(1843)+v(141)*v&
&(1858)+v(147)*v(1903)+v(146)*v(1918)+v(150)*v(1944)+v(149)*v(1958))*v(5666)+v(1985)*v(5686))
v(2281)=-(v(1622)*v(5684))+v(5668)*(v(152)*(v(1763)+v(1781))+v(197)*v(1993)+v(153)*v(2034)+(v(142)*v(1842)+v(141)*v&
&(1857)+v(147)*v(1902)+v(146)*v(1917)+v(150)*v(1943)+v(149)*v(1957))*v(5666)+v(1984)*v(5686))
v(2280)=-(v(1621)*v(5684))+v(5668)*(v(152)*(v(1762)+v(1780))+v(197)*v(1991)+v(153)*v(2033)+(v(142)*v(1840)+v(141)*v&
&(1855)+v(147)*v(1901)+v(146)*v(1916)+v(150)*v(1942)+v(149)*v(1956))*v(5666)+v(1982)*v(5686))
v(2278)=v(5668)*(v(152)*(v(1761)+v(1779))+v(197)*v(1989)+v(153)*v(2032)+(v(142)*v(1839)+v(141)*v(1854)+v(147)*v(1899)+v&
&(146)*v(1914)+v(150)*v(1941)+v(149)*v(1955))*v(5666)+v(1980)*v(5686))
v(2255)=mpar(14)*(v(143)*v(160)+v(148)*v(162)+v(151)*v(173))+v(151)*v(182)+v(150)*v(197)+v(149)*v(206)
v(5687)=0.15d1*v(2255)
v(2265)=v(5566)*v(5687)
v(2264)=v(5570)*v(5687)
v(2263)=v(5563)*v(5687)
v(2262)=-(v(1627)*v(5687))
v(2261)=-(v(1626)*v(5687))
v(2260)=(v(151)*v(1802)+v(1961)*v(197)+v(182)*v(1973)+mpar(14)*(v(151)*v(1748)+v(143)*v(1832)+v(160)*v(1874)+v(148)*v&
&(1892)+v(162)*v(1934)+v(173)*v(1973))+v(149)*v(2024)+v(150)*v(2037)+v(1948)*v(206))*v(5668)-v(1625)*v(5687)
v(2259)=(v(151)*v(1801)+v(1960)*v(197)+v(182)*v(1972)+mpar(14)*(v(151)*v(1746)+v(143)*v(1830)+v(160)*v(1873)+v(148)*v&
&(1890)+v(162)*v(1933)+v(173)*v(1972))+v(149)*v(2023)+v(150)*v(2036)+v(1946)*v(206))*v(5668)-v(1624)*v(5687)
v(5760)=v(2259)*v(5542)
v(2258)=(v(151)*v(1800)+v(1958)*v(197)+v(182)*v(1971)+mpar(14)*(v(151)*v(1744)+v(143)*v(1828)+v(160)*v(1872)+v(148)*v&
&(1888)+v(162)*v(1932)+v(173)*v(1971))+v(149)*v(2022)+v(150)*v(2035)+v(1944)*v(206))*v(5668)-v(1623)*v(5687)
v(2257)=(v(151)*v(1799)+v(1957)*v(197)+v(182)*v(1970)+mpar(14)*(v(151)*v(1742)+v(143)*v(1826)+v(160)*v(1871)+v(148)*v&
&(1886)+v(162)*v(1931)+v(173)*v(1970))+v(149)*v(2021)+v(150)*v(2034)+v(1943)*v(206))*v(5668)-v(1622)*v(5687)
v(2256)=(v(151)*v(1798)+v(182)*v(1969)+mpar(14)*(v(151)*v(1740)+v(143)*v(1824)+v(160)*v(1869)+v(148)*v(1884)+v(162)*v&
&(1930)+v(173)*v(1969))+v(1956)*v(197)+v(149)*v(2020)+v(150)*v(2033)+v(1942)*v(206))*v(5668)-v(1621)*v(5687)
v(2254)=(v(151)*v(1797)+v(182)*v(1968)+mpar(14)*(v(151)*v(1738)+v(143)*v(1822)+v(160)*v(1868)+v(148)*v(1882)+v(162)*v&
&(1928)+v(173)*v(1968))+v(1955)*v(197)+v(149)*v(2019)+v(150)*v(2032)+v(1941)*v(206))*v(5668)
v(189)=v(5664)*v(5666)
v(188)=v(152)*v(5674)
v(2291)=v(154)*v(188)+(v(141)*v(143)+v(146)*v(148)+v(149)*v(151))*v(5666)+v(153)*v(5689)
v(5688)=0.15d1*v(2291)
v(2301)=v(5566)*v(5688)
v(2300)=v(5570)*v(5688)
v(2299)=v(5563)*v(5688)
v(2484)=v(2299)*v(5539)
v(2362)=v(2299)*v(5709)
v(5721)=v(2362)*v(5708)
v(5713)=v(2362)*v(5709)
v(2298)=-(v(1627)*v(5688))
v(2297)=-(v(1626)*v(5688))
v(2296)=-(v(1625)*v(5688))+v(5668)*(v(153)*(v(1766)+v(1802))+v(188)*v(2004)+v(154)*v(2049)+(v(143)*v(1847)+v(141)*v&
&(1874)+v(148)*v(1907)+v(146)*v(1934)+v(151)*v(1948)+v(149)*v(1973))*v(5666)+v(1996)*v(5689))
v(2295)=-(v(1624)*v(5688))+v(5668)*(v(153)*(v(1765)+v(1801))+v(188)*v(2003)+v(154)*v(2048)+(v(143)*v(1845)+v(141)*v&
&(1873)+v(148)*v(1905)+v(146)*v(1933)+v(151)*v(1946)+v(149)*v(1972))*v(5666)+v(1995)*v(5689))
v(2294)=-(v(1623)*v(5688))+v(5668)*(v(153)*(v(1764)+v(1800))+v(188)*v(2002)+v(154)*v(2047)+(v(143)*v(1843)+v(141)*v&
&(1872)+v(148)*v(1903)+v(146)*v(1932)+v(151)*v(1944)+v(149)*v(1971))*v(5666)+v(1994)*v(5689))
v(2293)=-(v(1622)*v(5688))+v(5668)*(v(153)*(v(1763)+v(1799))+v(188)*v(2001)+v(154)*v(2046)+(v(143)*v(1842)+v(141)*v&
&(1871)+v(148)*v(1902)+v(146)*v(1931)+v(151)*v(1943)+v(149)*v(1970))*v(5666)+v(1993)*v(5689))
v(2292)=-(v(1621)*v(5688))+v(5668)*(v(153)*(v(1762)+v(1798))+v(188)*v(1999)+v(154)*v(2045)+(v(143)*v(1840)+v(141)*v&
&(1869)+v(148)*v(1901)+v(146)*v(1930)+v(151)*v(1942)+v(149)*v(1969))*v(5666)+v(1991)*v(5689))
v(2290)=v(5668)*(v(153)*(v(1761)+v(1797))+v(188)*v(1997)+v(154)*v(2044)+(v(143)*v(1839)+v(141)*v(1868)+v(148)*v(1899)+v&
&(146)*v(1928)+v(151)*v(1941)+v(149)*v(1968))*v(5666)+v(1989)*v(5689))
v(2243)=mpar(14)*(v(142)*v(160)+v(147)*v(162)+v(150)*v(173))+v(150)*v(179)+v(149)*v(188)+v(154)*v(189)
v(5690)=0.15d1*v(2243)
v(2253)=v(5566)*v(5690)
v(2252)=v(5570)*v(5690)
v(2251)=v(5563)*v(5690)
v(2250)=-(v(1627)*v(5690))
v(2249)=-(v(1626)*v(5690))
v(2248)=(v(150)*v(1784)+v(188)*v(1948)+v(179)*v(1961)+mpar(14)*(v(150)*v(1748)+v(142)*v(1832)+v(160)*v(1861)+v(147)*v&
&(1892)+v(162)*v(1921)+v(173)*v(1961))+v(189)*v(2004)+v(154)*v(2043)+v(149)*v(2049))*v(5668)-v(1625)*v(5690)
v(5764)=v(2248)*v(5542)
v(2247)=(v(150)*v(1783)+v(188)*v(1946)+v(179)*v(1960)+mpar(14)*(v(150)*v(1746)+v(142)*v(1830)+v(160)*v(1860)+v(147)*v&
&(1890)+v(162)*v(1920)+v(173)*v(1960))+v(189)*v(2003)+v(154)*v(2042)+v(149)*v(2048))*v(5668)-v(1624)*v(5690)
v(2246)=(v(150)*v(1782)+v(188)*v(1944)+v(179)*v(1958)+mpar(14)*(v(150)*v(1744)+v(142)*v(1828)+v(160)*v(1858)+v(147)*v&
&(1888)+v(162)*v(1918)+v(173)*v(1958))+v(189)*v(2002)+v(154)*v(2041)+v(149)*v(2047))*v(5668)-v(1623)*v(5690)
v(2245)=(v(150)*v(1781)+v(188)*v(1943)+v(179)*v(1957)+mpar(14)*(v(150)*v(1742)+v(142)*v(1826)+v(160)*v(1857)+v(147)*v&
&(1886)+v(162)*v(1917)+v(173)*v(1957))+v(189)*v(2001)+v(154)*v(2040)+v(149)*v(2046))*v(5668)-v(1622)*v(5690)
v(2244)=(v(150)*v(1780)+v(188)*v(1942)+v(179)*v(1956)+mpar(14)*(v(150)*v(1740)+v(142)*v(1824)+v(160)*v(1855)+v(147)*v&
&(1884)+v(162)*v(1916)+v(173)*v(1956))+v(189)*v(1999)+v(154)*v(2039)+v(149)*v(2045))*v(5668)-v(1621)*v(5690)
v(2242)=(v(150)*v(1779)+v(188)*v(1941)+v(179)*v(1955)+mpar(14)*(v(150)*v(1738)+v(142)*v(1822)+v(160)*v(1854)+v(147)*v&
&(1882)+v(162)*v(1914)+v(173)*v(1955))+v(189)*v(1997)+v(154)*v(2038)+v(149)*v(2044))*v(5668)
v(2231)=mpar(14)*(v(141)*v(160)+v(146)*v(162)+v(149)*v(173))+v(149)*v(175)+v(150)*v(188)+v(153)*v(189)
v(5691)=0.15d1*v(2231)
v(2241)=v(5566)*v(5691)
v(2240)=v(5570)*v(5691)
v(2239)=v(5563)*v(5691)
v(2238)=-(v(1627)*v(5691))
v(2237)=-(v(1626)*v(5691))
v(2236)=(v(149)*v(1766)+v(175)*v(1948)+mpar(14)*(v(149)*v(1748)+v(141)*v(1832)+v(160)*v(1847)+v(146)*v(1892)+v(162)*v&
&(1907)+v(173)*v(1948))+v(188)*v(1961)+v(189)*v(1996)+v(153)*v(2043)+v(150)*v(2049))*v(5668)-v(1625)*v(5691)
v(2235)=(v(149)*v(1765)+v(175)*v(1946)+mpar(14)*(v(149)*v(1746)+v(141)*v(1830)+v(160)*v(1845)+v(146)*v(1890)+v(162)*v&
&(1905)+v(173)*v(1946))+v(188)*v(1960)+v(189)*v(1995)+v(153)*v(2042)+v(150)*v(2048))*v(5668)-v(1624)*v(5691)
v(2234)=(v(149)*v(1764)+v(175)*v(1944)+mpar(14)*(v(149)*v(1744)+v(141)*v(1828)+v(160)*v(1843)+v(146)*v(1888)+v(162)*v&
&(1903)+v(173)*v(1944))+v(188)*v(1958)+v(189)*v(1994)+v(153)*v(2041)+v(150)*v(2047))*v(5668)-v(1623)*v(5691)
v(5770)=v(2234)*v(5542)
v(2233)=(v(149)*v(1763)+v(175)*v(1943)+mpar(14)*(v(149)*v(1742)+v(141)*v(1826)+v(160)*v(1842)+v(146)*v(1886)+v(162)*v&
&(1902)+v(173)*v(1943))+v(188)*v(1957)+v(189)*v(1993)+v(153)*v(2040)+v(150)*v(2046))*v(5668)-v(1622)*v(5691)
v(2232)=(v(149)*v(1762)+v(175)*v(1942)+mpar(14)*(v(149)*v(1740)+v(141)*v(1824)+v(160)*v(1840)+v(146)*v(1884)+v(162)*v&
&(1901)+v(173)*v(1942))+v(188)*v(1956)+v(189)*v(1991)+v(153)*v(2039)+v(150)*v(2045))*v(5668)-v(1621)*v(5691)
v(2230)=(v(149)*v(1761)+v(175)*v(1941)+mpar(14)*(v(149)*v(1738)+v(141)*v(1822)+v(160)*v(1839)+v(146)*v(1882)+v(162)*v&
&(1899)+v(173)*v(1941))+v(188)*v(1955)+v(189)*v(1989)+v(153)*v(2038)+v(150)*v(2044))*v(5668)
v(180)=v(5659)*v(5666)
v(177)=v(5661)*v(5666)
v(2195)=mpar(14)*(v(142)*v(159)+v(150)*v(162)+v(147)*v(170))+v(154)*v(177)+v(147)*v(179)+v(152)*v(180)
v(5692)=0.15d1*v(2195)
v(2205)=v(5566)*v(5692)
v(2204)=v(5570)*v(5692)
v(2203)=v(5563)*v(5692)
v(2202)=-(v(1627)*v(5692))
v(2201)=-(v(1626)*v(5692))
v(2200)=(v(147)*v(1784)+v(179)*v(1921)+mpar(14)*(v(147)*v(1736)+v(142)*v(1814)+v(159)*v(1861)+v(150)*v(1892)+v(170)*v&
&(1921)+v(162)*v(1961))+v(180)*v(1988)+v(177)*v(2004)+v(152)*v(2055)+v(154)*v(2061))*v(5668)-v(1625)*v(5692)
v(5763)=v(2200)*x(3)
v(2199)=(v(147)*v(1783)+v(179)*v(1920)+mpar(14)*(v(147)*v(1734)+v(142)*v(1812)+v(159)*v(1860)+v(150)*v(1890)+v(170)*v&
&(1920)+v(162)*v(1960))+v(180)*v(1987)+v(177)*v(2003)+v(152)*v(2054)+v(154)*v(2060))*v(5668)-v(1624)*v(5692)
v(2198)=(v(147)*v(1782)+v(179)*v(1918)+mpar(14)*(v(147)*v(1732)+v(142)*v(1810)+v(159)*v(1858)+v(150)*v(1888)+v(170)*v&
&(1918)+v(162)*v(1958))+v(180)*v(1985)+v(177)*v(2002)+v(152)*v(2053)+v(154)*v(2059))*v(5668)-v(1623)*v(5692)
v(2197)=(v(147)*v(1781)+v(179)*v(1917)+mpar(14)*(v(147)*v(1730)+v(142)*v(1808)+v(159)*v(1857)+v(150)*v(1886)+v(170)*v&
&(1917)+v(162)*v(1957))+v(180)*v(1984)+v(177)*v(2001)+v(152)*v(2052)+v(154)*v(2058))*v(5668)-v(1622)*v(5692)
v(2196)=(v(147)*v(1780)+v(179)*v(1916)+mpar(14)*(v(147)*v(1728)+v(142)*v(1806)+v(159)*v(1855)+v(150)*v(1884)+v(170)*v&
&(1916)+v(162)*v(1956))+v(180)*v(1982)+v(177)*v(1999)+v(152)*v(2051)+v(154)*v(2057))*v(5668)-v(1621)*v(5692)
v(2194)=(v(147)*v(1779)+v(179)*v(1914)+mpar(14)*(v(147)*v(1726)+v(142)*v(1804)+v(159)*v(1854)+v(150)*v(1882)+v(170)*v&
&(1914)+v(162)*v(1955))+v(180)*v(1980)+v(177)*v(1997)+v(152)*v(2050)+v(154)*v(2056))*v(5668)
v(176)=v(5660)*v(5666)
v(2207)=mpar(14)*(v(143)*v(159)+v(151)*v(162)+v(148)*v(170))+v(154)*v(176)+v(153)*v(180)+v(148)*v(182)
v(5693)=0.15d1*v(2207)
v(2217)=v(5566)*v(5693)
v(2216)=v(5570)*v(5693)
v(2215)=v(5563)*v(5693)
v(2214)=-(v(1627)*v(5693))
v(2213)=-(v(1626)*v(5693))
v(2212)=(v(148)*v(1802)+v(182)*v(1934)+mpar(14)*(v(148)*v(1736)+v(143)*v(1814)+v(159)*v(1874)+v(151)*v(1892)+v(170)*v&
&(1934)+v(162)*v(1973))+v(180)*v(1996)+v(176)*v(2004)+v(153)*v(2055)+v(154)*v(2067))*v(5668)-v(1625)*v(5693)
v(2211)=(v(148)*v(1801)+v(182)*v(1933)+mpar(14)*(v(148)*v(1734)+v(143)*v(1812)+v(159)*v(1873)+v(151)*v(1890)+v(170)*v&
&(1933)+v(162)*v(1972))+v(180)*v(1995)+v(176)*v(2003)+v(153)*v(2054)+v(154)*v(2066))*v(5668)-v(1624)*v(5693)
v(5758)=v(2211)*x(3)
v(2210)=(v(148)*v(1800)+v(182)*v(1932)+mpar(14)*(v(148)*v(1732)+v(143)*v(1810)+v(159)*v(1872)+v(151)*v(1888)+v(170)*v&
&(1932)+v(162)*v(1971))+v(180)*v(1994)+v(176)*v(2002)+v(153)*v(2053)+v(154)*v(2065))*v(5668)-v(1623)*v(5693)
v(2209)=(v(148)*v(1799)+v(182)*v(1931)+mpar(14)*(v(148)*v(1730)+v(143)*v(1808)+v(159)*v(1871)+v(151)*v(1886)+v(170)*v&
&(1931)+v(162)*v(1970))+v(180)*v(1993)+v(176)*v(2001)+v(153)*v(2052)+v(154)*v(2064))*v(5668)-v(1622)*v(5693)
v(2208)=(v(148)*v(1798)+v(182)*v(1930)+mpar(14)*(v(148)*v(1728)+v(143)*v(1806)+v(159)*v(1869)+v(151)*v(1884)+v(170)*v&
&(1930)+v(162)*v(1969))+v(180)*v(1991)+v(176)*v(1999)+v(153)*v(2051)+v(154)*v(2063))*v(5668)-v(1621)*v(5693)
v(2206)=(v(148)*v(1797)+v(182)*v(1928)+mpar(14)*(v(148)*v(1726)+v(143)*v(1804)+v(159)*v(1868)+v(151)*v(1882)+v(170)*v&
&(1928)+v(162)*v(1968))+v(180)*v(1989)+v(176)*v(1997)+v(153)*v(2050)+v(154)*v(2062))*v(5668)
v(2183)=mpar(14)*(v(141)*v(159)+v(149)*v(162)+v(146)*v(170))+v(146)*v(175)+v(152)*v(176)+v(153)*v(177)
v(5694)=0.15d1*v(2183)
v(2193)=v(5566)*v(5694)
v(2192)=v(5570)*v(5694)
v(2191)=v(5563)*v(5694)
v(2190)=-(v(1627)*v(5694))
v(2189)=-(v(1626)*v(5694))
v(2188)=(v(146)*v(1766)+v(175)*v(1907)+mpar(14)*(v(146)*v(1736)+v(141)*v(1814)+v(159)*v(1847)+v(149)*v(1892)+v(170)*v&
&(1907)+v(162)*v(1948))+v(176)*v(1988)+v(177)*v(1996)+v(153)*v(2061)+v(152)*v(2067))*v(5668)-v(1625)*v(5694)
v(2187)=(v(146)*v(1765)+v(175)*v(1905)+mpar(14)*(v(146)*v(1734)+v(141)*v(1812)+v(159)*v(1845)+v(149)*v(1890)+v(170)*v&
&(1905)+v(162)*v(1946))+v(176)*v(1987)+v(177)*v(1995)+v(153)*v(2060)+v(152)*v(2066))*v(5668)-v(1624)*v(5694)
v(2186)=(v(146)*v(1764)+v(175)*v(1903)+mpar(14)*(v(146)*v(1732)+v(141)*v(1810)+v(159)*v(1843)+v(149)*v(1888)+v(170)*v&
&(1903)+v(162)*v(1944))+v(176)*v(1985)+v(177)*v(1994)+v(153)*v(2059)+v(152)*v(2065))*v(5668)-v(1623)*v(5694)
v(5769)=v(2186)*x(3)
v(2185)=(v(146)*v(1763)+v(175)*v(1902)+mpar(14)*(v(146)*v(1730)+v(141)*v(1808)+v(159)*v(1842)+v(149)*v(1886)+v(170)*v&
&(1902)+v(162)*v(1943))+v(176)*v(1984)+v(177)*v(1993)+v(153)*v(2058)+v(152)*v(2064))*v(5668)-v(1622)*v(5694)
v(2184)=(v(146)*v(1762)+v(175)*v(1901)+mpar(14)*(v(146)*v(1728)+v(141)*v(1806)+v(159)*v(1840)+v(149)*v(1884)+v(170)*v&
&(1901)+v(162)*v(1942))+v(176)*v(1982)+v(177)*v(1991)+v(153)*v(2057)+v(152)*v(2063))*v(5668)-v(1621)*v(5694)
v(2182)=(v(146)*v(1761)+v(175)*v(1899)+mpar(14)*(v(146)*v(1726)+v(141)*v(1804)+v(159)*v(1839)+v(149)*v(1882)+v(170)*v&
&(1899)+v(162)*v(1941))+v(176)*v(1980)+v(177)*v(1989)+v(153)*v(2056)+v(152)*v(2062))*v(5668)
v(2171)=v(159)*v(160)+v(150)*v(176)+v(151)*v(177)+v(149)*v(180)+v(162)*v(5696)
v(5695)=0.15d1*v(2171)
v(2181)=v(5566)*v(5695)
v(5773)=v(2181)*v(5542)
v(2180)=v(5570)*v(5695)
v(5775)=v(2180)*v(5542)
v(2179)=v(5563)*v(5695)
v(5776)=v(2179)*v(5542)
v(2178)=-(v(1627)*v(5695))
v(5777)=v(2178)*v(5542)
v(2177)=-(v(1626)*v(5695))
v(5778)=v(2177)*v(5542)
v(2176)=-(v(1625)*v(5695))+v(5668)*(v(162)*(v(1736)+v(1748))+v(160)*v(1814)+v(159)*v(1832)+v(180)*v(1948)+v(176)*v(1961&
&)+v(177)*v(1973)+v(149)*v(2055)+v(151)*v(2061)+v(150)*v(2067)+v(1892)*v(5696))
v(2175)=-(v(1624)*v(5695))+v(5668)*(v(162)*(v(1734)+v(1746))+v(160)*v(1812)+v(159)*v(1830)+v(180)*v(1946)+v(176)*v(1960&
&)+v(177)*v(1972)+v(149)*v(2054)+v(151)*v(2060)+v(150)*v(2066)+v(1890)*v(5696))
v(2174)=-(v(1623)*v(5695))+v(5668)*(v(162)*(v(1732)+v(1744))+v(160)*v(1810)+v(159)*v(1828)+v(180)*v(1944)+v(176)*v(1958&
&)+v(177)*v(1971)+v(149)*v(2053)+v(151)*v(2059)+v(150)*v(2065)+v(1888)*v(5696))
v(2173)=-(v(1622)*v(5695))+v(5668)*(v(162)*(v(1730)+v(1742))+v(160)*v(1808)+v(159)*v(1826)+v(180)*v(1943)+v(176)*v(1957&
&)+v(177)*v(1970)+v(149)*v(2052)+v(151)*v(2058)+v(150)*v(2064)+v(1886)*v(5696))
v(5780)=-(v(1497)*v(2173))+v(2185)*v(5538)+v(2209)*v(5539)+v(2197)*v(5540)
v(2172)=-(v(1621)*v(5695))+v(5668)*(v(162)*(v(1728)+v(1740))+v(160)*v(1806)+v(159)*v(1824)+v(180)*v(1942)+v(176)*v(1956&
&)+v(177)*v(1969)+v(149)*v(2051)+v(151)*v(2057)+v(150)*v(2063)+v(1884)*v(5696))
v(5781)=-(v(1497)*v(2172))+v(2184)*v(5538)+v(2208)*v(5539)+v(2196)*v(5540)
v(2170)=v(5668)*(v(162)*(v(1726)+v(1738))+v(160)*v(1804)+v(159)*v(1822)+v(180)*v(1941)+v(176)*v(1955)+v(177)*v(1968)+v&
&(149)*v(2050)+v(151)*v(2056)+v(150)*v(2062)+v(1882)*v(5696))
v(5782)=v(2170)*v(5542)
v(165)=v(5657)*v(5666)
v(164)=v(5656)*v(5666)
v(2123)=mpar(14)*(v(141)*v(158)+v(146)*v(159)+v(149)*v(160))+v(152)*v(164)+v(153)*v(165)+v(141)*v(175)
v(5697)=0.15d1*v(2123)
v(2133)=v(5566)*v(5697)
v(2132)=v(5570)*v(5697)
v(2131)=v(5563)*v(5697)
v(2130)=-(v(1627)*v(5697))
v(2129)=-(v(1626)*v(5697))
v(2128)=(v(141)*v(1766)+v(175)*v(1847)+mpar(14)*(v(141)*v(1724)+v(146)*v(1814)+v(149)*v(1832)+v(158)*v(1847)+v(159)*v&
&(1907)+v(160)*v(1948))+v(164)*v(1988)+v(165)*v(1996)+v(153)*v(2073)+v(152)*v(2079))*v(5668)-v(1625)*v(5697)
v(2127)=(v(141)*v(1765)+v(175)*v(1845)+mpar(14)*(v(141)*v(1722)+v(146)*v(1812)+v(149)*v(1830)+v(158)*v(1845)+v(159)*v&
&(1905)+v(160)*v(1946))+v(164)*v(1987)+v(165)*v(1995)+v(153)*v(2072)+v(152)*v(2078))*v(5668)-v(1624)*v(5697)
v(2126)=(v(141)*v(1764)+v(175)*v(1843)+mpar(14)*(v(141)*v(1720)+v(146)*v(1810)+v(149)*v(1828)+v(158)*v(1843)+v(159)*v&
&(1903)+v(160)*v(1944))+v(164)*v(1985)+v(165)*v(1994)+v(153)*v(2071)+v(152)*v(2077))*v(5668)-v(1623)*v(5697)
v(5768)=v(2126)*x(2)
v(2125)=(v(141)*v(1763)+v(175)*v(1842)+mpar(14)*(v(141)*v(1718)+v(146)*v(1808)+v(149)*v(1826)+v(158)*v(1842)+v(159)*v&
&(1902)+v(160)*v(1943))+v(164)*v(1984)+v(165)*v(1993)+v(153)*v(2070)+v(152)*v(2076))*v(5668)-v(1622)*v(5697)
v(2124)=(v(141)*v(1762)+v(175)*v(1840)+mpar(14)*(v(141)*v(1716)+v(146)*v(1806)+v(149)*v(1824)+v(158)*v(1840)+v(159)*v&
&(1901)+v(160)*v(1942))+v(164)*v(1982)+v(165)*v(1991)+v(153)*v(2069)+v(152)*v(2075))*v(5668)-v(1621)*v(5697)
v(2122)=(v(141)*v(1761)+v(175)*v(1839)+mpar(14)*(v(141)*v(1714)+v(146)*v(1804)+v(149)*v(1822)+v(158)*v(1839)+v(159)*v&
&(1899)+v(160)*v(1941))+v(164)*v(1980)+v(165)*v(1989)+v(153)*v(2068)+v(152)*v(2074))*v(5668)
v(163)=v(5655)*v(5666)
v(2147)=mpar(14)*(v(143)*v(158)+v(148)*v(159)+v(151)*v(160))+v(153)*v(163)+v(154)*v(164)+v(143)*v(182)
v(5698)=0.15d1*v(2147)
v(2157)=v(5566)*v(5698)
v(2156)=v(5570)*v(5698)
v(2155)=v(5563)*v(5698)
v(2154)=-(v(1627)*v(5698))
v(2153)=-(v(1626)*v(5698))
v(2152)=(v(143)*v(1802)+v(182)*v(1874)+mpar(14)*(v(143)*v(1724)+v(148)*v(1814)+v(151)*v(1832)+v(158)*v(1874)+v(159)*v&
&(1934)+v(160)*v(1973))+v(163)*v(1996)+v(164)*v(2004)+v(154)*v(2079)+v(153)*v(2085))*v(5668)-v(1625)*v(5698)
v(2151)=(v(143)*v(1801)+v(182)*v(1873)+mpar(14)*(v(143)*v(1722)+v(148)*v(1812)+v(151)*v(1830)+v(158)*v(1873)+v(159)*v&
&(1933)+v(160)*v(1972))+v(163)*v(1995)+v(164)*v(2003)+v(154)*v(2078)+v(153)*v(2084))*v(5668)-v(1624)*v(5698)
v(5757)=v(2151)*x(2)
v(2150)=(v(143)*v(1800)+v(182)*v(1872)+mpar(14)*(v(143)*v(1720)+v(148)*v(1810)+v(151)*v(1828)+v(158)*v(1872)+v(159)*v&
&(1932)+v(160)*v(1971))+v(163)*v(1994)+v(164)*v(2002)+v(154)*v(2077)+v(153)*v(2083))*v(5668)-v(1623)*v(5698)
v(2149)=(v(143)*v(1799)+v(182)*v(1871)+mpar(14)*(v(143)*v(1718)+v(148)*v(1808)+v(151)*v(1826)+v(158)*v(1871)+v(159)*v&
&(1931)+v(160)*v(1970))+v(163)*v(1993)+v(164)*v(2001)+v(154)*v(2076)+v(153)*v(2082))*v(5668)-v(1622)*v(5698)
v(2148)=(v(143)*v(1798)+v(182)*v(1869)+mpar(14)*(v(143)*v(1716)+v(148)*v(1806)+v(151)*v(1824)+v(158)*v(1869)+v(159)*v&
&(1930)+v(160)*v(1969))+v(163)*v(1991)+v(164)*v(1999)+v(154)*v(2075)+v(153)*v(2081))*v(5668)-v(1621)*v(5698)
v(2146)=(v(143)*v(1797)+v(182)*v(1868)+mpar(14)*(v(143)*v(1714)+v(148)*v(1804)+v(151)*v(1822)+v(158)*v(1868)+v(159)*v&
&(1928)+v(160)*v(1968))+v(163)*v(1989)+v(164)*v(1997)+v(154)*v(2074)+v(153)*v(2080))*v(5668)
v(2135)=mpar(14)*(v(142)*v(158)+v(147)*v(159)+v(150)*v(160))+v(152)*v(163)+v(154)*v(165)+v(142)*v(179)
v(5699)=0.15d1*v(2135)
v(2145)=v(5566)*v(5699)
v(2144)=v(5570)*v(5699)
v(2143)=v(5563)*v(5699)
v(2142)=-(v(1627)*v(5699))
v(2141)=-(v(1626)*v(5699))
v(2140)=(v(142)*v(1784)+v(179)*v(1861)+mpar(14)*(v(142)*v(1724)+v(147)*v(1814)+v(150)*v(1832)+v(158)*v(1861)+v(159)*v&
&(1921)+v(160)*v(1961))+v(163)*v(1988)+v(165)*v(2004)+v(154)*v(2073)+v(152)*v(2085))*v(5668)-v(1625)*v(5699)
v(5762)=v(2140)*x(2)
v(2139)=(v(142)*v(1783)+v(179)*v(1860)+mpar(14)*(v(142)*v(1722)+v(147)*v(1812)+v(150)*v(1830)+v(158)*v(1860)+v(159)*v&
&(1920)+v(160)*v(1960))+v(163)*v(1987)+v(165)*v(2003)+v(154)*v(2072)+v(152)*v(2084))*v(5668)-v(1624)*v(5699)
v(2138)=(v(142)*v(1782)+v(179)*v(1858)+mpar(14)*(v(142)*v(1720)+v(147)*v(1810)+v(150)*v(1828)+v(158)*v(1858)+v(159)*v&
&(1918)+v(160)*v(1958))+v(163)*v(1985)+v(165)*v(2002)+v(154)*v(2071)+v(152)*v(2083))*v(5668)-v(1623)*v(5699)
v(2137)=(v(142)*v(1781)+v(179)*v(1857)+mpar(14)*(v(142)*v(1718)+v(147)*v(1808)+v(150)*v(1826)+v(158)*v(1857)+v(159)*v&
&(1917)+v(160)*v(1957))+v(163)*v(1984)+v(165)*v(2001)+v(154)*v(2070)+v(152)*v(2082))*v(5668)-v(1622)*v(5699)
v(2136)=(v(142)*v(1780)+v(179)*v(1855)+mpar(14)*(v(142)*v(1716)+v(147)*v(1806)+v(150)*v(1824)+v(158)*v(1855)+v(159)*v&
&(1916)+v(160)*v(1956))+v(163)*v(1982)+v(165)*v(1999)+v(154)*v(2069)+v(152)*v(2081))*v(5668)-v(1621)*v(5699)
v(2134)=(v(142)*v(1779)+v(179)*v(1854)+mpar(14)*(v(142)*v(1714)+v(147)*v(1804)+v(150)*v(1822)+v(158)*v(1854)+v(159)*v&
&(1914)+v(160)*v(1955))+v(163)*v(1980)+v(165)*v(1997)+v(154)*v(2068)+v(152)*v(2080))*v(5668)
v(2111)=v(159)*v(162)+v(149)*v(163)+v(150)*v(164)+v(151)*v(165)+v(160)*v(5701)
v(5700)=0.15d1*v(2111)
v(2121)=v(5566)*v(5700)
v(5784)=v(2121)*v(5542)
v(2120)=v(5570)*v(5700)
v(5787)=v(2120)*v(5542)
v(2119)=v(5563)*v(5700)
v(5789)=v(2119)*v(5542)
v(2118)=-(v(1627)*v(5700))
v(5791)=v(2118)*v(5542)
v(2117)=-(v(1626)*v(5700))
v(5793)=v(2117)*v(5542)
v(2116)=-(v(1625)*v(5700))+v(5668)*(v(160)*(v(1724)+v(1748))+v(162)*v(1814)+v(159)*v(1892)+v(163)*v(1948)+v(164)*v(1961&
&)+v(165)*v(1973)+v(151)*v(2073)+v(150)*v(2079)+v(149)*v(2085)+v(1832)*v(5701))
v(2115)=-(v(1624)*v(5700))+v(5668)*(v(160)*(v(1722)+v(1746))+v(162)*v(1812)+v(159)*v(1890)+v(163)*v(1946)+v(164)*v(1960&
&)+v(165)*v(1972)+v(151)*v(2072)+v(150)*v(2078)+v(149)*v(2084)+v(1830)*v(5701))
v(2114)=-(v(1623)*v(5700))+v(5668)*(v(160)*(v(1720)+v(1744))+v(162)*v(1810)+v(159)*v(1888)+v(163)*v(1944)+v(164)*v(1958&
&)+v(165)*v(1971)+v(151)*v(2071)+v(150)*v(2077)+v(149)*v(2083)+v(1828)*v(5701))
v(2113)=-(v(1622)*v(5700))+v(5668)*(v(160)*(v(1718)+v(1742))+v(162)*v(1808)+v(159)*v(1886)+v(163)*v(1943)+v(164)*v(1957&
&)+v(165)*v(1970)+v(151)*v(2070)+v(150)*v(2076)+v(149)*v(2082)+v(1826)*v(5701))
v(2112)=-(v(1621)*v(5700))+v(5668)*(v(160)*(v(1716)+v(1740))+v(162)*v(1806)+v(159)*v(1884)+v(163)*v(1942)+v(164)*v(1956&
&)+v(165)*v(1969)+v(151)*v(2069)+v(150)*v(2075)+v(149)*v(2081)+v(1824)*v(5701))
v(2110)=v(5668)*(v(160)*(v(1714)+v(1738))+v(162)*v(1804)+v(159)*v(1882)+v(163)*v(1941)+v(164)*v(1955)+v(165)*v(1968)+v&
&(151)*v(2068)+v(150)*v(2074)+v(149)*v(2080)+v(1822)*v(5701))
v(5801)=v(2110)*v(5542)
v(2099)=v(160)*v(162)+v(146)*v(163)+v(147)*v(164)+v(148)*v(165)+v(159)*v(5725)
v(5710)=0.15d1*v(2099)
v(2109)=v(5566)*v(5710)
v(5783)=v(2109)*x(3)
v(2366)=v(2097)*v(5545)+v(2169)*v(5546)+2d0*v(5703)+2d0*v(5705)+v(2229)*v(5707)+v(2277)*v(5711)+v(2313)*v(5714)+v(2337&
&)*v(5716)+v(2265)*v(5717)+v(2253)*v(5718)+v(2241)*v(5719)+v(2301)*v(5723)+v(5543)*(v(2205)*v(5685)+v(2193)*v(5708)+v&
&(2217)*v(5709)+v(5773))+v(5544)*(v(2145)*v(5685)+v(2133)*v(5708)+v(2157)*v(5709)+v(5783)+v(5784))
v(2108)=v(5570)*v(5710)
v(5785)=v(2108)*x(3)
v(2363)=v(2096)*v(5545)+v(2168)*v(5546)+v(2228)*v(5707)+v(2276)*v(5711)+2d0*v(5713)+v(2312)*v(5714)+2d0*v(5715)+v(2336&
&)*v(5716)+v(2264)*v(5717)+v(2252)*v(5718)+v(2240)*v(5719)+v(2288)*v(5724)+v(5543)*(v(2204)*v(5685)+v(2192)*v(5708)+v&
&(2216)*v(5709)+v(5775))+v(5544)*(v(2144)*v(5685)+v(2132)*v(5708)+v(2156)*v(5709)+v(5785)+v(5787))
v(2107)=v(5563)*v(5710)
v(5788)=v(2107)*x(3)
v(2361)=v(2095)*v(5545)+v(2167)*v(5546)+v(2227)*v(5707)+v(2275)*v(5711)+v(2311)*v(5714)+v(2335)*v(5716)+v(2263)*v(5717)&
&+v(2251)*v(5718)+v(2239)*v(5719)+2d0*v(5720)+2d0*v(5721)+v(2323)*v(5722)+v(5543)*(v(2203)*v(5685)+v(2191)*v(5708)+v&
&(2215)*v(5709)+v(5776))+v(5544)*(v(2143)*v(5685)+v(2131)*v(5708)+v(2155)*v(5709)+v(5788)+v(5789))
v(2106)=-(v(1627)*v(5710))
v(5790)=v(2106)*x(3)
v(2360)=v(2094)*v(5545)+v(2166)*v(5546)+v(2226)*v(5707)+v(2274)*v(5711)+v(2310)*v(5714)+v(2334)*v(5716)+v(2262)*v(5717)&
&+v(2250)*v(5718)+v(2238)*v(5719)+v(2322)*v(5722)+v(2298)*v(5723)+v(2286)*v(5724)+v(5543)*(v(2202)*v(5685)+v(2190)*v&
&(5708)+v(2214)*v(5709)+v(5777))+v(5544)*(v(2142)*v(5685)+v(2130)*v(5708)+v(2154)*v(5709)+v(5790)+v(5791))
v(2105)=-(v(1626)*v(5710))
v(5792)=v(2105)*x(3)
v(2359)=v(2093)*v(5545)+v(2165)*v(5546)+v(2225)*v(5707)+v(2273)*v(5711)+v(2309)*v(5714)+v(2333)*v(5716)+v(2261)*v(5717)&
&+v(2249)*v(5718)+v(2237)*v(5719)+v(2321)*v(5722)+v(2297)*v(5723)+v(2285)*v(5724)+v(5543)*(v(2201)*v(5685)+v(2189)*v&
&(5708)+v(2213)*v(5709)+v(5778))+v(5544)*(v(2141)*v(5685)+v(2129)*v(5708)+v(2153)*v(5709)+v(5792)+v(5793))
v(2104)=-(v(1625)*v(5710))+v(5668)*(v(159)*(v(1724)+v(1736))+v(162)*v(1832)+v(160)*v(1892)+v(163)*v(1907)+v(164)*v(1921&
&)+v(165)*v(1934)+v(148)*v(2073)+v(147)*v(2079)+v(146)*v(2085)+v(1814)*v(5725))
v(5794)=-(v(1497)*v(2116))+v(2128)*v(5538)+v(2152)*v(5539)+v(2104)*v(5543)
v(2103)=-(v(1624)*v(5710))+v(5668)*(v(159)*(v(1722)+v(1734))+v(162)*v(1830)+v(160)*v(1890)+v(163)*v(1905)+v(164)*v(1920&
&)+v(165)*v(1933)+v(148)*v(2072)+v(147)*v(2078)+v(146)*v(2084)+v(1812)*v(5725))
v(5795)=-(v(1497)*v(2115))+v(2127)*v(5538)+v(2139)*v(5540)+v(2103)*v(5543)
v(2102)=-(v(1623)*v(5710))+v(5668)*(v(159)*(v(1720)+v(1732))+v(162)*v(1828)+v(160)*v(1888)+v(163)*v(1903)+v(164)*v(1918&
&)+v(165)*v(1932)+v(148)*v(2071)+v(147)*v(2077)+v(146)*v(2083)+v(1810)*v(5725))
v(5797)=-(v(1497)*v(2114))+v(2150)*v(5539)+v(2138)*v(5540)+v(2102)*v(5543)
v(2101)=-(v(1622)*v(5710))+v(5668)*(v(159)*(v(1718)+v(1730))+v(162)*v(1826)+v(160)*v(1886)+v(163)*v(1902)+v(164)*v(1917&
&)+v(165)*v(1931)+v(148)*v(2070)+v(147)*v(2076)+v(146)*v(2082)+v(1808)*v(5725))
v(5798)=-(v(1497)*v(2113))+v(2125)*v(5538)+v(2149)*v(5539)+v(2137)*v(5540)+v(2101)*v(5543)
v(2100)=-(v(1621)*v(5710))+v(5668)*(v(159)*(v(1716)+v(1728))+v(162)*v(1824)+v(160)*v(1884)+v(163)*v(1901)+v(164)*v(1916&
&)+v(165)*v(1930)+v(148)*v(2069)+v(147)*v(2075)+v(146)*v(2081)+v(1806)*v(5725))
v(5799)=-(v(1497)*v(2112))+v(2124)*v(5538)+v(2148)*v(5539)+v(2136)*v(5540)+v(2100)*v(5543)
v(2098)=v(5668)*(v(159)*(v(1714)+v(1726))+v(162)*v(1822)+v(160)*v(1882)+v(163)*v(1899)+v(164)*v(1914)+v(165)*v(1928)+v&
&(148)*v(2068)+v(147)*v(2074)+v(146)*v(2080)+v(1804)*v(5725))
v(5800)=v(2098)*x(3)
v(2338)=v(2086)*v(5545)+v(2158)*v(5546)+v(2218)*v(5707)+v(2266)*v(5711)+v(2302)*v(5714)+v(2326)*v(5716)+v(2254)*v(5717)&
&+v(2242)*v(5718)+v(2230)*v(5719)+v(2314)*v(5722)+v(2290)*v(5723)+v(2278)*v(5724)+v(5543)*(v(2194)*v(5685)+v(2182)*v&
&(5708)+v(2206)*v(5709)+v(5782))+v(5544)*(v(2134)*v(5685)+v(2122)*v(5708)+v(2146)*v(5709)+v(5800)+v(5801))
v(156)=v(157)*v(5672)
v(5753)=v(156)*x(2)
v(161)=v(157)*v(5710)
v(5754)=v(161)*x(3)
v(5750)=v(161)*x(2)
v(2398)=2d0*v(161)
v(166)=v(157)*v(5700)
v(5755)=v(166)*v(5542)
v(2384)=(-2d0)*v(166)
v(2340)=v(166)*x(2)
v(167)=v(157)*v(5697)
v(5749)=v(167)*x(2)
v(2429)=2d0*v(167)
v(168)=v(157)*v(5699)
v(5747)=v(168)*x(2)
v(2446)=2d0*v(168)
v(169)=v(157)*v(5698)
v(5744)=v(169)*x(2)
v(2467)=2d0*v(169)
v(5729)=v(5755)+v(2429)*x(4)+v(2467)*x(5)+v(2446)*x(6)
v(2339)=v(5729)+v(5753)+v(5754)
v(172)=v(157)*v(5670)
v(5751)=v(172)*x(3)
v(174)=v(157)*v(5695)
v(5752)=v(174)*v(5542)
v(2400)=(-2d0)*v(174)
v(2341)=v(174)*x(3)
v(178)=v(157)*v(5694)
v(2432)=2d0*v(178)
v(181)=v(157)*v(5692)
v(2449)=2d0*v(181)
v(183)=v(157)*v(5693)
v(2470)=2d0*v(183)
v(5727)=v(5752)+v(2432)*x(4)+v(2470)*x(5)+v(2449)*x(6)
v(2348)=v(5727)+v(5750)+v(5751)
v(186)=v(157)*v(5667)
v(2415)=(-2d0)*v(186)
v(2342)=v(186)*v(5542)
v(187)=v(157)*v(5691)
v(2430)=2d0*v(187)
v(2343)=v(2430)*x(4)
v(190)=v(157)*v(5690)
v(2447)=2d0*v(190)
v(2344)=v(2447)*x(6)
v(191)=v(157)*v(5687)
v(2468)=2d0*v(191)
v(2345)=v(2468)*x(5)
v(5726)=-v(2342)-v(2343)-v(2344)-v(2345)
v(2347)=-v(2340)-v(2341)+v(5726)
v(5728)=v(2347)+v(5726)
v(2349)=v(2348)+v(2089)*v(5545)+v(2161)*v(5546)+v(2221)*v(5707)+v(2269)*v(5711)+v(2305)*v(5714)+v(2329)*v(5716)+v(2257&
&)*v(5717)+v(2245)*v(5718)+v(2233)*v(5719)+v(2317)*v(5722)+v(2293)*v(5723)+v(2281)*v(5724)+v(5727)+v(5728)+(v(161)-v(166&
&)+v(5798))*x(2)+(v(172)-v(174)+v(5780))*x(3)
v(2346)=v(2339)+v(2088)*v(5545)+v(2160)*v(5546)+v(2220)*v(5707)+v(2268)*v(5711)+v(2304)*v(5714)+v(2328)*v(5716)+v(2256&
&)*v(5717)+v(2244)*v(5718)+v(2232)*v(5719)+v(2316)*v(5722)+v(2292)*v(5723)+v(2280)*v(5724)+v(5728)+v(5729)+(v(156)-v(166&
&)+v(5799))*x(2)+(v(161)-v(174)+v(5781))*x(3)
v(196)=v(157)*v(5682)
v(198)=v(157)*v(5684)
v(2451)=4d0*v(198)
v(2356)=2d0*v(198)
v(5733)=v(2356)*x(4)
v(5731)=v(2356)*x(6)
v(199)=v(157)*v(5688)
v(2472)=4d0*v(199)
v(2353)=2d0*v(199)
v(5738)=v(2353)*x(4)
v(5730)=v(2353)*x(5)
v(5748)=v(2430)*v(5542)+2d0*v(5730)+2d0*v(5731)+v(2432)*x(3)
v(2350)=v(187)*v(5542)+v(196)*v(5708)+v(5730)+v(5731)+v(5749)+v(178)*x(3)
v(5740)=2d0*v(2350)
v(2351)=v(2090)*v(5545)+v(2162)*v(5546)+v(2222)*v(5707)+v(2270)*v(5711)+v(2306)*v(5714)+v(2330)*v(5716)+v(2258)*v(5717)&
&+v(2246)*v(5718)+v(2318)*v(5722)+v(2210)*v(5732)+v(2174)*v(5735)+v(2198)*v(5736)+v(5740)+v(5748)+v(5538)*(v(196)+v(2282&
&)*v(5685)+v(2294)*v(5709)+v(5768)+v(5769)+v(5770))+(v(2429)+v(5797))*x(2)
v(205)=v(157)*v(5680)
v(207)=v(157)*v(5678)
v(2476)=4d0*v(207)
v(2357)=2d0*v(207)
v(5739)=v(2357)*x(6)
v(5743)=v(2468)*v(5542)+2d0*v(5738)+2d0*v(5739)+v(2470)*x(3)
v(5734)=v(2357)*x(5)
v(5746)=v(2447)*v(5542)+2d0*v(5733)+2d0*v(5734)+v(2449)*x(3)
v(2355)=v(190)*v(5542)+v(205)*v(5685)+v(5733)+v(5734)+v(5747)+v(181)*x(3)
v(5742)=2d0*v(2355)
v(2358)=v(2092)*v(5545)+v(2164)*v(5546)+v(2224)*v(5707)+v(2272)*v(5711)+v(2308)*v(5714)+v(2332)*v(5716)+v(2260)*v(5717)&
&+v(2236)*v(5719)+v(2296)*v(5723)+v(2212)*v(5732)+v(2176)*v(5735)+v(2188)*v(5737)+v(5742)+v(5746)+v(5540)*(v(205)+v(2284&
&)*v(5708)+v(2320)*v(5709)+v(5762)+v(5763)+v(5764))+(v(2446)+v(5794))*x(2)
v(214)=v(157)*v(5676)
v(2352)=v(191)*v(5542)+v(214)*v(5709)+v(5738)+v(5739)+v(5744)+v(183)*x(3)
v(5741)=2d0*v(2352)
v(2354)=v(2091)*v(5545)+v(2163)*v(5546)+v(2223)*v(5707)+v(2271)*v(5711)+v(2307)*v(5714)+v(2331)*v(5716)+v(2247)*v(5718)&
&+v(2235)*v(5719)+v(2283)*v(5724)+v(2175)*v(5735)+v(2199)*v(5736)+v(2187)*v(5737)+v(5741)+v(5743)+v(5539)*(v(214)+v(2319&
&)*v(5685)+v(2295)*v(5708)+v(5757)+v(5758)+v(5760))+(v(2467)+v(5795))*x(2)
v(215)=-(v(2347)*v(5542))+v(2339)*x(2)+v(2348)*x(3)+v(5740)*x(4)+v(5741)*x(5)+v(5742)*x(6)
v(5796)=-(v(215)*v(2380))
v(5779)=-(v(215)*v(2395))
v(5772)=-(v(215)*v(2411))
v(5767)=-(v(215)*v(2426))
v(5765)=-(v(215)*v(2443))
v(5759)=-(v(215)*v(2464))
v(5745)=v(1502)*v(215)
v(2480)=v(123)*v(5745)
v(2465)=v(214)*v(5539)+v(5743)+2d0*v(5744)-v(2464)*v(5745)
v(2457)=v(122)*v(5745)
v(2487)=-(v(2457)*v(5570))
v(2444)=v(205)*v(5540)-v(2443)*v(5745)+v(5746)+2d0*v(5747)
v(2438)=v(121)*v(5745)
v(2482)=-(v(2438)*v(5570))
v(2459)=-(v(2438)*v(5566))
v(2427)=v(196)*v(5538)-v(2426)*v(5745)+v(5748)+2d0*v(5749)
v(2423)=-(v(120)*v(5745))
v(2412)=2d0*v(2340)+2d0*v(2341)+2d0*v(2342)+v(187)*v(5538)+v(191)*v(5539)+v(190)*v(5540)-v(2411)*v(5745)
v(2407)=v(119)*v(5745)
v(2396)=v(178)*v(5538)+v(183)*v(5539)+v(181)*v(5540)-v(2395)*v(5745)+2d0*v(5750)+2d0*v(5751)+2d0*v(5752)
v(2391)=v(117)*v(5745)
v(2381)=v(167)*v(5538)+v(169)*v(5539)+v(168)*v(5540)-v(2380)*v(5745)+2d0*v(5753)+2d0*v(5754)+2d0*v(5755)
v(2367)=1d0/sqrt(v(215))
v(5802)=v(2367)/2d0
v(2369)=-(v(5802)/v(215))
v(2379)=v(2366)*v(2369)
v(2378)=v(2363)*v(2369)
v(2377)=v(2361)*v(2369)
v(2376)=v(2360)*v(2369)
v(2375)=v(2359)*v(2369)
v(2374)=v(2358)*v(2369)
v(2373)=v(2354)*v(2369)
v(2372)=v(2351)*v(2369)
v(2371)=v(2349)*v(2369)
v(2370)=v(2346)*v(2369)
v(2368)=v(2338)*v(2369)
v(2488)=(v(2379)*v(2465)+v(2367)*(-(v(1497)*v(2265))+v(2487)+v(2301)*v(5538)+v(2337)*v(5539)+v(2325)*v(5540)+v(2217)*v&
&(5543)+v(2157)*v(5544)+v(2366)*v(5756)))/2d0
v(2486)=(v(2378)*v(2465)+v(2367)*(-(v(1497)*v(2264))+v(2484)+v(2485)+v(2336)*v(5539)+v(2216)*v(5543)+v(2156)*v(5544)+((&
&-1d0)-v(123)*v(5570))*v(5745)+v(2363)*v(5756)))/2d0
v(2483)=(v(2377)*v(2465)+v(2367)*(-(v(1497)*v(2263))+v(2482)+v(2299)*v(5538)+v(2335)*v(5539)+v(2323)*v(5540)+v(2215)*v&
&(5543)+v(2155)*v(5544)+v(2361)*v(5756)))/2d0
v(2481)=(v(2376)*v(2465)+v(2367)*(-(v(1497)*v(2262))+v(1627)*v(2480)+v(2298)*v(5538)+v(2334)*v(5539)+v(2322)*v(5540)+v&
&(2214)*v(5543)+v(2154)*v(5544)+v(2360)*v(5756)))/2d0
v(2479)=(v(2375)*v(2465)+v(2367)*(-(v(1497)*v(2261))+v(1626)*v(2480)+v(2297)*v(5538)+v(2333)*v(5539)+v(2321)*v(5540)+v&
&(2213)*v(5543)+v(2153)*v(5544)+v(2359)*v(5756)))/2d0
v(2478)=(v(2374)*v(2465)+v(2367)*(-(v(1497)*v(2260))+v(2476)+v(2296)*v(5538)+v(2332)*v(5539)+v(2320)*v(5540)+v(2212)*v&
&(5543)+v(2152)*v(5544)+(v(123)*v(1625)-v(2477))*v(5745)+v(2358)*v(5756)+v(1508)*v(5759)))/2d0
v(2475)=(v(2373)*v(2465)+v(2367)*(4d0*v(214)+v(2295)*v(5538)+v(2331)*v(5539)+v(2319)*v(5540)+(v(123)*v(1624)+v(1614)*v&
&(226))*v(5745)+v(2354)*v(5756)+2d0*v(5757)+2d0*v(5758)+v(1507)*v(5759)+2d0*v(5760)))/2d0
v(2474)=(v(2372)*v(2465)+v(2367)*(-(v(1497)*v(2258))+v(2472)+v(2294)*v(5538)+v(2330)*v(5539)+v(2318)*v(5540)+v(2210)*v&
&(5543)+v(2150)*v(5544)+(v(123)*v(1623)-v(2473))*v(5745)+v(2351)*v(5756)+v(1506)*v(5759)))/2d0
v(2471)=(v(2371)*v(2465)+v(2367)*(-(v(1497)*v(2257))-v(2468)+v(2470)+v(2293)*v(5538)+v(2329)*v(5539)+v(2317)*v(5540)+v&
&(2209)*v(5543)+v(2149)*v(5544)+(v(123)*v(1622)+v(1613)*v(226))*v(5745)+v(2349)*v(5756)+v(1505)*v(5759)))/2d0
v(2469)=(v(2370)*v(2465)+v(2367)*(-(v(1497)*v(2256))+v(2467)-v(2468)+v(2292)*v(5538)+v(2328)*v(5539)+v(2316)*v(5540)+v&
&(2208)*v(5543)+v(2148)*v(5544)+(v(123)*v(1621)+v(1612)*v(226))*v(5745)+v(2346)*v(5756)+v(1503)*v(5759)))/2d0
v(2466)=(v(2368)*v(2465)+v(2367)*(-(v(1497)*v(2254))+v(2290)*v(5538)+v(2326)*v(5539)+v(2314)*v(5540)+v(2206)*v(5543)+v&
&(2146)*v(5544)+v(2338)*v(5756)))/2d0
v(2463)=(v(2379)*v(2444)+v(2367)*(-(v(1497)*v(2253))+v(2462)+v(2485)+v(2313)*v(5540)+v(2205)*v(5543)+v(2145)*v(5544)+((&
&-1d0)-v(122)*v(5566))*v(5745)+v(2366)*v(5761)))/2d0
v(2461)=(v(2378)*v(2444)+v(2367)*(-(v(1497)*v(2252))+v(2487)+v(2288)*v(5538)+v(2324)*v(5539)+v(2312)*v(5540)+v(2204)*v&
&(5543)+v(2144)*v(5544)+v(2363)*v(5761)))/2d0
v(2460)=(v(2377)*v(2444)+v(2367)*(-(v(1497)*v(2251))+v(2459)+v(2287)*v(5538)+v(2323)*v(5539)+v(2311)*v(5540)+v(2203)*v&
&(5543)+v(2143)*v(5544)+v(2361)*v(5761)))/2d0
v(2458)=(v(2376)*v(2444)+v(2367)*(-(v(1497)*v(2250))+v(1627)*v(2457)+v(2286)*v(5538)+v(2322)*v(5539)+v(2310)*v(5540)+v&
&(2202)*v(5543)+v(2142)*v(5544)+v(2360)*v(5761)))/2d0
v(2456)=(v(2375)*v(2444)+v(2367)*(-(v(1497)*v(2249))+v(1626)*v(2457)+v(2285)*v(5538)+v(2321)*v(5539)+v(2309)*v(5540)+v&
&(2201)*v(5543)+v(2141)*v(5544)+v(2359)*v(5761)))/2d0
v(2455)=(v(2374)*v(2444)+v(2367)*(4d0*v(205)+v(2284)*v(5538)+v(2320)*v(5539)+v(2308)*v(5540)+(v(122)*v(1625)+v(1600)*v&
&(226))*v(5745)+v(2358)*v(5761)+2d0*v(5762)+2d0*v(5763)+2d0*v(5764)+v(1508)*v(5765)))/2d0
v(2454)=(v(2373)*v(2444)+v(2367)*(-(v(1497)*v(2247))+v(2476)+v(2283)*v(5538)+v(2319)*v(5539)+v(2307)*v(5540)+v(2199)*v&
&(5543)+v(2139)*v(5544)+(v(122)*v(1624)-v(2477))*v(5745)+v(2354)*v(5761)+v(1507)*v(5765)))/2d0
v(2453)=(v(2372)*v(2444)+v(2367)*(-(v(1497)*v(2246))+v(2451)+v(2282)*v(5538)+v(2318)*v(5539)+v(2306)*v(5540)+v(2198)*v&
&(5543)+v(2138)*v(5544)+(v(122)*v(1623)-v(2452))*v(5745)+v(2351)*v(5761)+v(1506)*v(5765)))/2d0
v(2450)=(v(2371)*v(2444)+v(2367)*(-(v(1497)*v(2245))-v(2447)+v(2449)+v(2281)*v(5538)+v(2317)*v(5539)+v(2305)*v(5540)+v&
&(2197)*v(5543)+v(2137)*v(5544)+(v(122)*v(1622)+v(1598)*v(226))*v(5745)+v(2349)*v(5761)+v(1505)*v(5765)))/2d0
v(2448)=(v(2370)*v(2444)+v(2367)*(-(v(1497)*v(2244))+v(2446)-v(2447)+v(2280)*v(5538)+v(2316)*v(5539)+v(2304)*v(5540)+v&
&(2196)*v(5543)+v(2136)*v(5544)+(v(122)*v(1621)+v(1597)*v(226))*v(5745)+v(2346)*v(5761)+v(1503)*v(5765)))/2d0
v(2445)=(v(2368)*v(2444)+v(2367)*(-(v(1497)*v(2242))+v(2278)*v(5538)+v(2314)*v(5539)+v(2302)*v(5540)+v(2194)*v(5543)+v&
&(2134)*v(5544)+v(2338)*v(5761)))/2d0
v(2442)=(v(2379)*v(2427)+v(2367)*(-(v(1497)*v(2241))+v(2459)+v(2277)*v(5538)+v(2301)*v(5539)+v(2289)*v(5540)+v(2193)*v&
&(5543)+v(2133)*v(5544)+v(2366)*v(5766)))/2d0
v(2441)=(v(2378)*v(2427)+v(2367)*(-(v(1497)*v(2240))+v(2482)+v(2276)*v(5538)+v(2300)*v(5539)+v(2288)*v(5540)+v(2192)*v&
&(5543)+v(2132)*v(5544)+v(2363)*v(5766)))/2d0
v(2440)=(v(2377)*v(2427)+v(2367)*(-(v(1497)*v(2239))+v(2462)+v(2484)+v(2275)*v(5538)+v(2191)*v(5543)+v(2131)*v(5544)+((&
&-1d0)-v(121)*v(5563))*v(5745)+v(2361)*v(5766)))/2d0
v(2439)=(v(2376)*v(2427)+v(2367)*(-(v(1497)*v(2238))+v(1627)*v(2438)+v(2274)*v(5538)+v(2298)*v(5539)+v(2286)*v(5540)+v&
&(2190)*v(5543)+v(2130)*v(5544)+v(2360)*v(5766)))/2d0
v(2437)=(v(2375)*v(2427)+v(2367)*(-(v(1497)*v(2237))+v(1626)*v(2438)+v(2273)*v(5538)+v(2297)*v(5539)+v(2285)*v(5540)+v&
&(2189)*v(5543)+v(2129)*v(5544)+v(2359)*v(5766)))/2d0
v(2436)=(v(2374)*v(2427)+v(2367)*(-(v(1497)*v(2236))+v(2451)+v(2272)*v(5538)+v(2296)*v(5539)+v(2284)*v(5540)+v(2188)*v&
&(5543)+v(2128)*v(5544)+(v(121)*v(1625)-v(2452))*v(5745)+v(2358)*v(5766)+v(1508)*v(5767)))/2d0
v(2435)=(v(2373)*v(2427)+v(2367)*(-(v(1497)*v(2235))+v(2472)+v(2271)*v(5538)+v(2295)*v(5539)+v(2283)*v(5540)+v(2187)*v&
&(5543)+v(2127)*v(5544)+(v(121)*v(1624)-v(2473))*v(5745)+v(2354)*v(5766)+v(1507)*v(5767)))/2d0
v(2434)=(v(2372)*v(2427)+v(2367)*(4d0*v(196)+v(2270)*v(5538)+v(2294)*v(5539)+v(2282)*v(5540)+(v(121)*v(1623)+v(1583)*v&
&(226))*v(5745)+v(2351)*v(5766)+v(1506)*v(5767)+2d0*v(5768)+2d0*v(5769)+2d0*v(5770)))/2d0
v(2433)=(v(2371)*v(2427)+v(2367)*(-(v(1497)*v(2233))-v(2430)+v(2432)+v(2269)*v(5538)+v(2293)*v(5539)+v(2281)*v(5540)+v&
&(2185)*v(5543)+v(2125)*v(5544)+(v(121)*v(1622)+v(1582)*v(226))*v(5745)+v(2349)*v(5766)+v(1505)*v(5767)))/2d0
v(2431)=(v(2370)*v(2427)+v(2367)*(-(v(1497)*v(2232))+v(2429)-v(2430)+v(2268)*v(5538)+v(2292)*v(5539)+v(2280)*v(5540)+v&
&(2184)*v(5543)+v(2124)*v(5544)+(v(121)*v(1621)+v(1581)*v(226))*v(5745)+v(2346)*v(5766)+v(1503)*v(5767)))/2d0
v(2428)=(v(2368)*v(2427)+v(2367)*(-(v(1497)*v(2230))+v(2266)*v(5538)+v(2290)*v(5539)+v(2278)*v(5540)+v(2182)*v(5543)+v&
&(2122)*v(5544)+v(2338)*v(5766)))/2d0
v(2425)=(v(2379)*v(2412)+v(2367)*(-(v(1497)*v(2229))+v(2241)*v(5538)+v(2265)*v(5539)+v(2253)*v(5540)+v(2181)*v(5543)+v&
&(2121)*v(5544)+v(2423)*v(5566)+v(2366)*v(5771)))/2d0
v(2424)=(v(2378)*v(2412)+v(2367)*(-(v(1497)*v(2228))+v(2240)*v(5538)+v(2264)*v(5539)+v(2252)*v(5540)+v(2180)*v(5543)+v&
&(2120)*v(5544)+v(2423)*v(5570)+v(2363)*v(5771)))/2d0
v(2422)=(v(2377)*v(2412)+v(2367)*(-(v(1497)*v(2227))+v(2239)*v(5538)+v(2263)*v(5539)+v(2251)*v(5540)+v(2179)*v(5543)+v&
&(2119)*v(5544)+v(2423)*v(5563)+v(2361)*v(5771)))/2d0
v(2421)=(v(2376)*v(2412)+v(2367)*(-(v(1497)*v(2226))+v(2238)*v(5538)+v(2262)*v(5539)+v(2250)*v(5540)+v(2178)*v(5543)+v&
&(2118)*v(5544)+(1d0+v(120)*v(1627))*v(5745)+v(2360)*v(5771)))/2d0
v(2420)=(v(2375)*v(2412)+v(2367)*(-(v(1497)*v(2225))+v(2237)*v(5538)+v(2261)*v(5539)+v(2249)*v(5540)+v(2177)*v(5543)+v&
&(2117)*v(5544)+(1d0+v(120)*v(1626))*v(5745)+v(2359)*v(5771)))/2d0
v(2419)=(v(2374)*v(2412)+v(2367)*(4d0*v(190)-v(1497)*v(2224)+v(2236)*v(5538)+v(2260)*v(5539)+v(2248)*v(5540)+v(2176)*v&
&(5543)+v(2116)*v(5544)+(v(120)*v(1625)+v(1554)*v(226))*v(5745)+v(2358)*v(5771)+v(1508)*v(5772)))/2d0
v(2418)=(v(2373)*v(2412)+v(2367)*(4d0*v(191)-v(1497)*v(2223)+v(2235)*v(5538)+v(2259)*v(5539)+v(2247)*v(5540)+v(2175)*v&
&(5543)+v(2115)*v(5544)+(v(120)*v(1624)+v(1553)*v(226))*v(5745)+v(2354)*v(5771)+v(1507)*v(5772)))/2d0
v(2417)=(v(2372)*v(2412)+v(2367)*(4d0*v(187)-v(1497)*v(2222)+v(2234)*v(5538)+v(2258)*v(5539)+v(2246)*v(5540)+v(2174)*v&
&(5543)+v(2114)*v(5544)+(v(120)*v(1623)+v(1552)*v(226))*v(5745)+v(2351)*v(5771)+v(1506)*v(5772)))/2d0
v(2416)=(v(2371)*v(2412)+v(2367)*(-(v(1497)*v(2221))-v(2400)+v(2415)+v(2233)*v(5538)+v(2257)*v(5539)+v(2245)*v(5540)+v&
&(2173)*v(5543)+v(2113)*v(5544)+(v(120)*v(1622)+v(1551)*v(226))*v(5745)+v(2349)*v(5771)+v(1505)*v(5772)))/2d0
v(2414)=(v(2370)*v(2412)+v(2367)*(-(v(1497)*v(2220))-v(2384)+v(2415)+v(2232)*v(5538)+v(2256)*v(5539)+v(2244)*v(5540)+v&
&(2172)*v(5543)+v(2112)*v(5544)+(v(120)*v(1621)+v(1550)*v(226))*v(5745)+v(2346)*v(5771)+v(1503)*v(5772)))/2d0
v(2413)=(v(2368)*v(2412)+v(2367)*(-(v(1497)*v(2218))+v(2230)*v(5538)+v(2254)*v(5539)+v(2242)*v(5540)+v(2170)*v(5543)+v&
&(2110)*v(5544)+v(2338)*v(5771)))/2d0
v(5849)=v(2413)*v(5541)
v(2410)=(v(2379)*v(2396)+v(2367)*(v(2193)*v(5538)+v(2217)*v(5539)+v(2205)*v(5540)+v(2169)*v(5543)+v(2109)*v(5544)-v&
&(2407)*v(5566)+2d0*v(5773)+v(2366)*v(5774)))/2d0
v(2409)=(v(2378)*v(2396)+v(2367)*(v(2192)*v(5538)+v(2216)*v(5539)+v(2204)*v(5540)+v(2168)*v(5543)+v(2108)*v(5544)-v&
&(2407)*v(5570)+v(2363)*v(5774)+2d0*v(5775)))/2d0
v(2408)=(v(2377)*v(2396)+v(2367)*(v(2191)*v(5538)+v(2215)*v(5539)+v(2203)*v(5540)+v(2167)*v(5543)+v(2107)*v(5544)-v&
&(2407)*v(5563)+v(2361)*v(5774)+2d0*v(5776)))/2d0
v(2406)=(v(2376)*v(2396)+v(2367)*(v(2190)*v(5538)+v(2214)*v(5539)+v(2202)*v(5540)+v(2166)*v(5543)+v(2106)*v(5544)+((&
&-1d0)+v(119)*v(1627))*v(5745)+v(2360)*v(5774)+2d0*v(5777)))/2d0
v(2405)=(v(2375)*v(2396)+v(2367)*(v(1626)*v(2407)+v(2189)*v(5538)+v(2213)*v(5539)+v(2201)*v(5540)+v(2165)*v(5543)+v&
&(2105)*v(5544)+v(2359)*v(5774)+2d0*v(5778)))/2d0
v(2404)=(v(2374)*v(2396)+v(2367)*(4d0*v(181)-v(1497)*v(2176)+v(2188)*v(5538)+v(2212)*v(5539)+v(2200)*v(5540)+v(2164)*v&
&(5543)+v(2104)*v(5544)+(v(119)*v(1625)+v(1531)*v(226))*v(5745)+v(2358)*v(5774)+v(1508)*v(5779)))/2d0
v(2403)=(v(2373)*v(2396)+v(2367)*(4d0*v(183)-v(1497)*v(2175)+v(2187)*v(5538)+v(2211)*v(5539)+v(2199)*v(5540)+v(2163)*v&
&(5543)+v(2103)*v(5544)+(v(119)*v(1624)+v(1530)*v(226))*v(5745)+v(2354)*v(5774)+v(1507)*v(5779)))/2d0
v(2402)=(v(2372)*v(2396)+v(2367)*(4d0*v(178)-v(1497)*v(2174)+v(2186)*v(5538)+v(2210)*v(5539)+v(2198)*v(5540)+v(2162)*v&
&(5543)+v(2102)*v(5544)+(v(119)*v(1623)+v(1529)*v(226))*v(5745)+v(2351)*v(5774)+v(1506)*v(5779)))/2d0
v(2401)=(v(2371)*v(2396)+v(2367)*(2d0*v(172)+v(2400)+v(2161)*v(5543)+v(2101)*v(5544)+(v(119)*v(1622)+v(1528)*v(226))*v&
&(5745)+v(2349)*v(5774)+v(1505)*v(5779)+v(5780)))/2d0
v(2399)=(v(2370)*v(2396)+v(2367)*(v(2398)+v(2400)+v(2160)*v(5543)+v(2100)*v(5544)+(v(119)*v(1621)+v(1527)*v(226))*v&
&(5745)+v(2346)*v(5774)+v(1503)*v(5779)+v(5781)))/2d0
v(2397)=(v(2368)*v(2396)+v(2367)*(v(2182)*v(5538)+v(2206)*v(5539)+v(2194)*v(5540)+v(2158)*v(5543)+v(2098)*v(5544)+v&
&(2338)*v(5774)+2d0*v(5782)))/2d0
v(5843)=v(2397)*v(5541)
v(2394)=(v(2379)*v(2381)+v(2367)*(v(2133)*v(5538)+v(2157)*v(5539)+v(2145)*v(5540)+v(2097)*v(5544)-v(2391)*v(5566)+2d0*v&
&(5783)+2d0*v(5784)+v(2366)*v(5786)))/2d0
v(2393)=(v(2378)*v(2381)+v(2367)*(v(2132)*v(5538)+v(2156)*v(5539)+v(2144)*v(5540)+v(2096)*v(5544)-v(2391)*v(5570)+2d0*v&
&(5785)+v(2363)*v(5786)+2d0*v(5787)))/2d0
v(2392)=(v(2377)*v(2381)+v(2367)*(v(2131)*v(5538)+v(2155)*v(5539)+v(2143)*v(5540)+v(2095)*v(5544)-v(2391)*v(5563)+v&
&(2361)*v(5786)+2d0*v(5788)+2d0*v(5789)))/2d0
v(2390)=(v(2376)*v(2381)+v(2367)*(v(1627)*v(2391)+v(2130)*v(5538)+v(2154)*v(5539)+v(2142)*v(5540)+v(2094)*v(5544)+v&
&(2360)*v(5786)+2d0*v(5790)+2d0*v(5791)))/2d0
v(2389)=(v(2375)*v(2381)+v(2367)*(v(2129)*v(5538)+v(2153)*v(5539)+v(2141)*v(5540)+v(2093)*v(5544)+((-1d0)+v(117)*v(1626&
&))*v(5745)+v(2359)*v(5786)+2d0*v(5792)+2d0*v(5793)))/2d0
v(2388)=(v(2374)*v(2381)+v(2367)*(4d0*v(168)+v(2140)*v(5540)+v(2092)*v(5544)+(v(117)*v(1625)+v(1521)*v(226))*v(5745)+v&
&(2358)*v(5786)+v(5794)+v(1508)*v(5796)))/2d0
v(2387)=(v(2373)*v(2381)+v(2367)*(4d0*v(169)+v(2151)*v(5539)+v(2091)*v(5544)+(v(117)*v(1624)+v(1520)*v(226))*v(5745)+v&
&(2354)*v(5786)+v(5795)+v(1507)*v(5796)))/2d0
v(2386)=(v(2372)*v(2381)+v(2367)*(4d0*v(167)+v(2126)*v(5538)+v(2090)*v(5544)+(v(117)*v(1623)+v(1519)*v(226))*v(5745)+v&
&(2351)*v(5786)+v(1506)*v(5796)+v(5797)))/2d0
v(2385)=(v(2371)*v(2381)+v(2367)*(v(2384)+v(2398)+v(2089)*v(5544)+(v(117)*v(1622)+v(1518)*v(226))*v(5745)+v(2349)*v&
&(5786)+v(1505)*v(5796)+v(5798)))/2d0
v(2383)=(v(2370)*v(2381)+v(2367)*(2d0*v(156)+v(2384)+v(2088)*v(5544)+(v(117)*v(1621)+v(1517)*v(226))*v(5745)+v(2346)*v&
&(5786)+v(1503)*v(5796)+v(5799)))/2d0
v(2382)=(v(2368)*v(2381)+v(2367)*(v(2122)*v(5538)+v(2146)*v(5539)+v(2134)*v(5540)+v(2086)*v(5544)+v(2338)*v(5786)+2d0*v&
&(5800)+2d0*v(5801)))/2d0
v(5832)=v(2382)*v(5541)
v(223)=v(2381)*v(5802)
v(5824)=v(223)*v(5537)+v(5832)
v(5823)=v(223)*v(5541)
v(369)=(v(223)*v(223))
v(227)=v(2396)*v(5802)
v(5838)=v(227)*v(5537)+v(5843)
v(5837)=v(227)*v(5541)
v(5804)=v(223)+v(227)
v(370)=(v(227)*v(227))
v(228)=v(2412)*v(5802)
v(5847)=v(228)*v(5537)+v(5849)
v(5846)=v(228)*v(5541)
v(5806)=v(227)+v(228)
v(5803)=v(223)+v(228)
v(371)=(v(228)*v(228))
v(229)=v(2427)*v(5802)
v(6034)=2d0*v(229)
v(5822)=v(229)*v(5537)+v(2428)*v(5541)
v(5816)=v(229)*v(5541)
v(372)=(v(229)*v(229))
v(230)=v(2444)*v(5802)
v(6035)=2d0*v(230)
v(5836)=v(230)*v(5537)+v(2445)*v(5541)
v(5814)=v(230)*v(5541)
v(373)=(v(230)*v(230))
v(231)=v(2465)*v(5802)
v(6036)=2d0*v(231)
v(5820)=v(231)*v(5537)+v(2466)*v(5541)
v(5818)=v(231)*v(5541)
v(5817)=v(229)*v(230)+v(231)*v(5803)
v(5815)=v(230)*v(231)+v(229)*v(5804)
v(5813)=v(229)*v(231)+v(230)*v(5806)
v(374)=(v(231)*v(231))
v(232)=(v(5541)*v(5541))
v(5807)=2d0*v(232)
v(5812)=v(223)*v(5807)
v(5811)=v(228)*v(5807)
v(5810)=v(231)*v(5807)
v(5809)=v(227)*v(5807)
v(5808)=v(230)*v(5807)
v(5805)=v(229)*v(5807)
v(2610)=v(232)*(v(231)*(v(2394)+v(2425))+v(230)*v(2442)+v(229)*v(2463)+v(2488)*v(5803))
v(2609)=v(232)*(v(231)*(v(2393)+v(2424))+v(230)*v(2441)+v(229)*v(2461)+v(2486)*v(5803))
v(2608)=v(232)*(v(231)*(v(2392)+v(2422))+v(230)*v(2440)+v(229)*v(2460)+v(2483)*v(5803))
v(2607)=v(232)*(v(231)*(v(2390)+v(2421))+v(230)*v(2439)+v(229)*v(2458)+v(2481)*v(5803))
v(2606)=v(232)*(v(231)*(v(2389)+v(2420))+v(230)*v(2437)+v(229)*v(2456)+v(2479)*v(5803))
v(2605)=v(232)*(v(231)*(v(2388)+v(2419))+v(230)*v(2436)+v(229)*v(2455)+v(2478)*v(5803))
v(2604)=v(232)*(v(231)*(v(2387)+v(2418))+v(230)*v(2435)+v(229)*v(2454)+v(2475)*v(5803))
v(2603)=v(232)*(v(231)*(v(2386)+v(2417))+v(230)*v(2434)+v(229)*v(2453)+v(2474)*v(5803))
v(2602)=v(232)*(v(231)*(v(2385)+v(2416))+v(230)*v(2433)+v(229)*v(2450)+v(2471)*v(5803))
v(2601)=v(232)*(v(231)*(v(2383)+v(2414))+v(230)*v(2431)+v(229)*v(2448)+v(2469)*v(5803))
v(2600)=v(232)*(v(231)*(v(2382)+v(2413))+v(230)*v(2428)+v(229)*v(2445)+v(2466)*v(5803))+v(2489)*v(5817)
v(2588)=v(232)*(v(229)*(v(2394)+v(2410))+v(231)*v(2463)+v(230)*v(2488)+v(2442)*v(5804))
v(2587)=v(232)*(v(229)*(v(2393)+v(2409))+v(231)*v(2461)+v(230)*v(2486)+v(2441)*v(5804))
v(2586)=v(232)*(v(229)*(v(2392)+v(2408))+v(231)*v(2460)+v(230)*v(2483)+v(2440)*v(5804))
v(2585)=v(232)*(v(229)*(v(2390)+v(2406))+v(231)*v(2458)+v(230)*v(2481)+v(2439)*v(5804))
v(2584)=v(232)*(v(229)*(v(2389)+v(2405))+v(231)*v(2456)+v(230)*v(2479)+v(2437)*v(5804))
v(2583)=v(232)*(v(229)*(v(2388)+v(2404))+v(231)*v(2455)+v(230)*v(2478)+v(2436)*v(5804))
v(2582)=v(232)*(v(229)*(v(2387)+v(2403))+v(231)*v(2454)+v(230)*v(2475)+v(2435)*v(5804))
v(2581)=v(232)*(v(229)*(v(2386)+v(2402))+v(231)*v(2453)+v(230)*v(2474)+v(2434)*v(5804))
v(2580)=v(232)*(v(229)*(v(2385)+v(2401))+v(231)*v(2450)+v(230)*v(2471)+v(2433)*v(5804))
v(2579)=v(232)*(v(229)*(v(2383)+v(2399))+v(231)*v(2448)+v(230)*v(2469)+v(2431)*v(5804))
v(2578)=v(232)*(v(229)*(v(2382)+v(2397))+v(231)*v(2445)+v(230)*v(2466)+v(2428)*v(5804))+v(2489)*v(5815)
v(2577)=v(2442)*v(5805)
v(2575)=v(2441)*v(5805)
v(2573)=v(2440)*v(5805)
v(2571)=v(2439)*v(5805)
v(2569)=v(2437)*v(5805)
v(2567)=v(2436)*v(5805)
v(2565)=v(2435)*v(5805)
v(2563)=v(2434)*v(5805)
v(2561)=v(2433)*v(5805)
v(2559)=v(2431)*v(5805)
v(2557)=v(2489)*v(372)+v(2428)*v(5805)
v(2544)=v(232)*(v(230)*(v(2410)+v(2425))+v(231)*v(2442)+v(229)*v(2488)+v(2463)*v(5806))
v(2543)=v(232)*(v(230)*(v(2409)+v(2424))+v(231)*v(2441)+v(229)*v(2486)+v(2461)*v(5806))
v(2542)=v(232)*(v(230)*(v(2408)+v(2422))+v(231)*v(2440)+v(229)*v(2483)+v(2460)*v(5806))
v(2541)=v(232)*(v(230)*(v(2406)+v(2421))+v(231)*v(2439)+v(229)*v(2481)+v(2458)*v(5806))
v(2540)=v(232)*(v(230)*(v(2405)+v(2420))+v(231)*v(2437)+v(229)*v(2479)+v(2456)*v(5806))
v(2539)=v(232)*(v(230)*(v(2404)+v(2419))+v(231)*v(2436)+v(229)*v(2478)+v(2455)*v(5806))
v(2538)=v(232)*(v(230)*(v(2403)+v(2418))+v(231)*v(2435)+v(229)*v(2475)+v(2454)*v(5806))
v(2537)=v(232)*(v(230)*(v(2402)+v(2417))+v(231)*v(2434)+v(229)*v(2474)+v(2453)*v(5806))
v(2536)=v(232)*(v(230)*(v(2401)+v(2416))+v(231)*v(2433)+v(229)*v(2471)+v(2450)*v(5806))
v(2535)=v(232)*(v(230)*(v(2399)+v(2414))+v(231)*v(2431)+v(229)*v(2469)+v(2448)*v(5806))
v(2534)=v(232)*(v(230)*(v(2397)+v(2413))+v(231)*v(2428)+v(229)*v(2466)+v(2445)*v(5806))+v(2489)*v(5813)
v(2533)=v(2463)*v(5808)
v(2929)=v(2533)+v(2577)+v(2410)*v(5809)
v(2531)=v(2461)*v(5808)
v(2927)=v(2531)+v(2575)+v(2409)*v(5809)
v(2529)=v(2460)*v(5808)
v(2925)=v(2529)+v(2573)+v(2408)*v(5809)
v(2527)=v(2458)*v(5808)
v(2923)=v(2527)+v(2571)+v(2406)*v(5809)
v(2525)=v(2456)*v(5808)
v(2921)=v(2525)+v(2569)+v(2405)*v(5809)
v(2523)=v(2455)*v(5808)
v(2919)=v(2523)+v(2567)+v(2404)*v(5809)
v(2521)=v(2454)*v(5808)
v(2917)=v(2521)+v(2565)+v(2403)*v(5809)
v(2519)=v(2453)*v(5808)
v(2915)=v(2519)+v(2563)+v(2402)*v(5809)
v(2517)=v(2450)*v(5808)
v(2913)=v(2517)+v(2561)+v(2401)*v(5809)
v(2515)=v(2448)*v(5808)
v(2911)=v(2515)+v(2559)+v(2399)*v(5809)
v(2513)=v(2489)*v(373)+v(2445)*v(5808)
v(2909)=v(2513)+v(2557)+v(2489)*v(370)+v(2397)*v(5809)
v(2511)=v(2488)*v(5810)
v(3116)=v(2511)+v(2533)+v(2425)*v(5811)
v(2643)=v(2511)+v(2577)+v(2394)*v(5812)
v(2509)=v(2486)*v(5810)
v(3114)=v(2509)+v(2531)+v(2424)*v(5811)
v(2641)=v(2509)+v(2575)+v(2393)*v(5812)
v(2507)=v(2483)*v(5810)
v(3112)=v(2507)+v(2529)+v(2422)*v(5811)
v(2639)=v(2507)+v(2573)+v(2392)*v(5812)
v(2505)=v(2481)*v(5810)
v(3110)=v(2505)+v(2527)+v(2421)*v(5811)
v(2637)=v(2505)+v(2571)+v(2390)*v(5812)
v(2503)=v(2479)*v(5810)
v(3108)=v(2503)+v(2525)+v(2420)*v(5811)
v(2635)=v(2503)+v(2569)+v(2389)*v(5812)
v(2501)=v(2478)*v(5810)
v(3106)=v(2501)+v(2523)+v(2419)*v(5811)
v(2633)=v(2501)+v(2567)+v(2388)*v(5812)
v(2499)=v(2475)*v(5810)
v(3104)=v(2499)+v(2521)+v(2418)*v(5811)
v(2631)=v(2499)+v(2565)+v(2387)*v(5812)
v(2497)=v(2474)*v(5810)
v(3102)=v(2497)+v(2519)+v(2417)*v(5811)
v(2629)=v(2497)+v(2563)+v(2386)*v(5812)
v(2495)=v(2471)*v(5810)
v(3100)=v(2495)+v(2517)+v(2416)*v(5811)
v(2627)=v(2495)+v(2561)+v(2385)*v(5812)
v(2493)=v(2469)*v(5810)
v(3098)=v(2493)+v(2515)+v(2414)*v(5811)
v(2625)=v(2493)+v(2559)+v(2383)*v(5812)
v(2491)=v(2489)*v(374)+v(2466)*v(5810)
v(3096)=v(2491)+v(2513)+v(2489)*v(371)+v(2413)*v(5811)
v(2623)=v(2491)+v(2557)+v(2489)*v(369)+v(2382)*v(5812)
v(268)=v(232)*v(374)
v(267)=v(232)*v(373)
v(255)=v(232)*v(5813)
v(2555)=(v(230)*v(2544)+v(2463)*v(255))*v(5541)
v(2554)=(v(230)*v(2543)+v(2461)*v(255))*v(5541)
v(2553)=(v(230)*v(2542)+v(2460)*v(255))*v(5541)
v(2552)=(v(230)*v(2541)+v(2458)*v(255))*v(5541)
v(2551)=(v(230)*v(2540)+v(2456)*v(255))*v(5541)
v(2550)=(v(230)*v(2539)+v(2455)*v(255))*v(5541)
v(2549)=(v(230)*v(2538)+v(2454)*v(255))*v(5541)
v(2548)=(v(230)*v(2537)+v(2453)*v(255))*v(5541)
v(2547)=(v(230)*v(2536)+v(2450)*v(255))*v(5541)
v(2546)=(v(230)*v(2535)+v(2448)*v(255))*v(5541)
v(2545)=v(2534)*v(5814)+v(255)*v(5836)
v(271)=v(255)*v(5814)
v(250)=v(232)*v(372)
v(236)=v(232)*v(5815)
v(2599)=(v(236)*v(2442)+v(229)*v(2588))*v(5541)
v(2598)=(v(236)*v(2441)+v(229)*v(2587))*v(5541)
v(2597)=(v(236)*v(2440)+v(229)*v(2586))*v(5541)
v(2596)=(v(236)*v(2439)+v(229)*v(2585))*v(5541)
v(2595)=(v(236)*v(2437)+v(229)*v(2584))*v(5541)
v(2594)=(v(236)*v(2436)+v(229)*v(2583))*v(5541)
v(2593)=(v(236)*v(2435)+v(229)*v(2582))*v(5541)
v(2592)=(v(236)*v(2434)+v(229)*v(2581))*v(5541)
v(2591)=(v(236)*v(2433)+v(229)*v(2580))*v(5541)
v(2590)=(v(236)*v(2431)+v(229)*v(2579))*v(5541)
v(2589)=v(2578)*v(5816)+v(236)*v(5822)
v(252)=v(236)*v(5816)
v(235)=v(232)*v(5817)
v(2621)=(v(235)*v(2488)+v(231)*v(2610))*v(5541)
v(2620)=(v(235)*v(2486)+v(231)*v(2609))*v(5541)
v(2619)=(v(235)*v(2483)+v(231)*v(2608))*v(5541)
v(2618)=(v(235)*v(2481)+v(231)*v(2607))*v(5541)
v(2617)=(v(235)*v(2479)+v(231)*v(2606))*v(5541)
v(2616)=(v(235)*v(2478)+v(231)*v(2605))*v(5541)
v(2615)=(v(235)*v(2475)+v(231)*v(2604))*v(5541)
v(2614)=(v(235)*v(2474)+v(231)*v(2603))*v(5541)
v(2613)=(v(235)*v(2471)+v(231)*v(2602))*v(5541)
v(2612)=(v(235)*v(2469)+v(231)*v(2601))*v(5541)
v(2611)=v(2600)*v(5818)+v(235)*v(5820)
v(270)=v(235)*v(5818)
v(233)=v(250)+v(268)+v(232)*v(369)
v(5821)=v(229)*v(233)+v(230)*v(235)+v(227)*v(236)
v(5819)=v(231)*v(233)+v(228)*v(235)+v(230)*v(236)
v(2698)=v(2599)+v(2621)+(v(233)*v(2394)+v(223)*v(2643))*v(5541)
v(2697)=v(2598)+v(2620)+(v(233)*v(2393)+v(223)*v(2641))*v(5541)
v(2696)=v(2597)+v(2619)+(v(233)*v(2392)+v(223)*v(2639))*v(5541)
v(2695)=v(2596)+v(2618)+(v(233)*v(2390)+v(223)*v(2637))*v(5541)
v(2694)=v(2595)+v(2617)+(v(233)*v(2389)+v(223)*v(2635))*v(5541)
v(2693)=v(2594)+v(2616)+(v(233)*v(2388)+v(223)*v(2633))*v(5541)
v(2692)=v(2593)+v(2615)+(v(233)*v(2387)+v(223)*v(2631))*v(5541)
v(2691)=v(2592)+v(2614)+(v(233)*v(2386)+v(223)*v(2629))*v(5541)
v(2690)=v(2591)+v(2613)+(v(233)*v(2385)+v(223)*v(2627))*v(5541)
v(2689)=v(2590)+v(2612)+(v(233)*v(2383)+v(223)*v(2625))*v(5541)
v(2688)=v(2589)+v(2611)+v(2623)*v(5823)+v(233)*v(5824)
v(2676)=(v(236)*v(2410)+v(233)*v(2442)+v(235)*v(2463)+v(227)*v(2588)+v(230)*v(2610)+v(229)*v(2643))*v(5541)
v(2675)=(v(236)*v(2409)+v(233)*v(2441)+v(235)*v(2461)+v(227)*v(2587)+v(230)*v(2609)+v(229)*v(2641))*v(5541)
v(2674)=(v(236)*v(2408)+v(233)*v(2440)+v(235)*v(2460)+v(227)*v(2586)+v(230)*v(2608)+v(229)*v(2639))*v(5541)
v(2673)=(v(236)*v(2406)+v(233)*v(2439)+v(235)*v(2458)+v(227)*v(2585)+v(230)*v(2607)+v(229)*v(2637))*v(5541)
v(2672)=(v(236)*v(2405)+v(233)*v(2437)+v(235)*v(2456)+v(227)*v(2584)+v(230)*v(2606)+v(229)*v(2635))*v(5541)
v(2671)=(v(236)*v(2404)+v(233)*v(2436)+v(235)*v(2455)+v(227)*v(2583)+v(230)*v(2605)+v(229)*v(2633))*v(5541)
v(2670)=(v(236)*v(2403)+v(233)*v(2435)+v(235)*v(2454)+v(227)*v(2582)+v(230)*v(2604)+v(229)*v(2631))*v(5541)
v(2669)=(v(236)*v(2402)+v(233)*v(2434)+v(235)*v(2453)+v(227)*v(2581)+v(230)*v(2603)+v(229)*v(2629))*v(5541)
v(2668)=(v(236)*v(2401)+v(233)*v(2433)+v(235)*v(2450)+v(227)*v(2580)+v(230)*v(2602)+v(229)*v(2627))*v(5541)
v(2667)=(v(236)*v(2399)+v(233)*v(2431)+v(235)*v(2448)+v(227)*v(2579)+v(230)*v(2601)+v(229)*v(2625))*v(5541)
v(2666)=(v(236)*v(2397)+v(233)*v(2428)+v(235)*v(2445)+v(227)*v(2578)+v(230)*v(2600)+v(229)*v(2623))*v(5541)+v(5537)*v&
&(5821)
v(2654)=(v(235)*v(2425)+v(236)*v(2463)+v(233)*v(2488)+v(230)*v(2588)+v(228)*v(2610)+v(231)*v(2643))*v(5541)
v(2653)=(v(235)*v(2424)+v(236)*v(2461)+v(233)*v(2486)+v(230)*v(2587)+v(228)*v(2609)+v(231)*v(2641))*v(5541)
v(2652)=(v(235)*v(2422)+v(236)*v(2460)+v(233)*v(2483)+v(230)*v(2586)+v(228)*v(2608)+v(231)*v(2639))*v(5541)
v(2651)=(v(235)*v(2421)+v(236)*v(2458)+v(233)*v(2481)+v(230)*v(2585)+v(228)*v(2607)+v(231)*v(2637))*v(5541)
v(2650)=(v(235)*v(2420)+v(236)*v(2456)+v(233)*v(2479)+v(230)*v(2584)+v(228)*v(2606)+v(231)*v(2635))*v(5541)
v(2649)=(v(235)*v(2419)+v(236)*v(2455)+v(233)*v(2478)+v(230)*v(2583)+v(228)*v(2605)+v(231)*v(2633))*v(5541)
v(2648)=(v(235)*v(2418)+v(236)*v(2454)+v(233)*v(2475)+v(230)*v(2582)+v(228)*v(2604)+v(231)*v(2631))*v(5541)
v(2647)=(v(235)*v(2417)+v(236)*v(2453)+v(233)*v(2474)+v(230)*v(2581)+v(228)*v(2603)+v(231)*v(2629))*v(5541)
v(2646)=(v(235)*v(2416)+v(236)*v(2450)+v(233)*v(2471)+v(230)*v(2580)+v(228)*v(2602)+v(231)*v(2627))*v(5541)
v(2645)=(v(235)*v(2414)+v(236)*v(2448)+v(233)*v(2469)+v(230)*v(2579)+v(228)*v(2601)+v(231)*v(2625))*v(5541)
v(2644)=(v(235)*v(2413)+v(236)*v(2445)+v(233)*v(2466)+v(230)*v(2578)+v(228)*v(2600)+v(231)*v(2623))*v(5541)+v(5537)*v&
&(5819)
v(239)=v(5541)*v(5819)
v(2665)=(v(239)*v(2488)+v(231)*v(2654))*v(5541)
v(2664)=(v(239)*v(2486)+v(231)*v(2653))*v(5541)
v(2663)=(v(239)*v(2483)+v(231)*v(2652))*v(5541)
v(2662)=(v(239)*v(2481)+v(231)*v(2651))*v(5541)
v(2661)=(v(239)*v(2479)+v(231)*v(2650))*v(5541)
v(2660)=(v(239)*v(2478)+v(231)*v(2649))*v(5541)
v(2659)=(v(239)*v(2475)+v(231)*v(2648))*v(5541)
v(2658)=(v(239)*v(2474)+v(231)*v(2647))*v(5541)
v(2657)=(v(239)*v(2471)+v(231)*v(2646))*v(5541)
v(2656)=(v(239)*v(2469)+v(231)*v(2645))*v(5541)
v(2655)=v(2644)*v(5818)+v(239)*v(5820)
v(274)=v(239)*v(5818)
v(238)=v(5541)*v(5821)
v(2687)=(v(238)*v(2442)+v(229)*v(2676))*v(5541)
v(2686)=(v(238)*v(2441)+v(229)*v(2675))*v(5541)
v(2685)=(v(238)*v(2440)+v(229)*v(2674))*v(5541)
v(2684)=(v(238)*v(2439)+v(229)*v(2673))*v(5541)
v(2683)=(v(238)*v(2437)+v(229)*v(2672))*v(5541)
v(2682)=(v(238)*v(2436)+v(229)*v(2671))*v(5541)
v(2681)=(v(238)*v(2435)+v(229)*v(2670))*v(5541)
v(2680)=(v(238)*v(2434)+v(229)*v(2669))*v(5541)
v(2679)=(v(238)*v(2433)+v(229)*v(2668))*v(5541)
v(2678)=(v(238)*v(2431)+v(229)*v(2667))*v(5541)
v(2677)=v(2666)*v(5816)+v(238)*v(5822)
v(254)=v(238)*v(5816)
v(234)=v(252)+v(270)+v(233)*v(5823)
v(5826)=v(231)*v(234)+v(230)*v(238)+v(228)*v(239)
v(5825)=v(229)*v(234)+v(227)*v(238)+v(230)*v(239)
v(2753)=v(2665)+v(2687)+(v(234)*v(2394)+v(223)*v(2698))*v(5541)
v(2752)=v(2664)+v(2686)+(v(234)*v(2393)+v(223)*v(2697))*v(5541)
v(2751)=v(2663)+v(2685)+(v(234)*v(2392)+v(223)*v(2696))*v(5541)
v(2750)=v(2662)+v(2684)+(v(234)*v(2390)+v(223)*v(2695))*v(5541)
v(2749)=v(2661)+v(2683)+(v(234)*v(2389)+v(223)*v(2694))*v(5541)
v(2748)=v(2660)+v(2682)+(v(234)*v(2388)+v(223)*v(2693))*v(5541)
v(2747)=v(2659)+v(2681)+(v(234)*v(2387)+v(223)*v(2692))*v(5541)
v(2746)=v(2658)+v(2680)+(v(234)*v(2386)+v(223)*v(2691))*v(5541)
v(2745)=v(2657)+v(2679)+(v(234)*v(2385)+v(223)*v(2690))*v(5541)
v(2744)=v(2656)+v(2678)+(v(234)*v(2383)+v(223)*v(2689))*v(5541)
v(2743)=v(2655)+v(2677)+v(2688)*v(5823)+v(234)*v(5824)
v(2731)=(v(239)*v(2425)+v(238)*v(2463)+v(234)*v(2488)+v(228)*v(2654)+v(230)*v(2676)+v(231)*v(2698))*v(5541)
v(2730)=(v(239)*v(2424)+v(238)*v(2461)+v(234)*v(2486)+v(228)*v(2653)+v(230)*v(2675)+v(231)*v(2697))*v(5541)
v(2729)=(v(239)*v(2422)+v(238)*v(2460)+v(234)*v(2483)+v(228)*v(2652)+v(230)*v(2674)+v(231)*v(2696))*v(5541)
v(2728)=(v(239)*v(2421)+v(238)*v(2458)+v(234)*v(2481)+v(228)*v(2651)+v(230)*v(2673)+v(231)*v(2695))*v(5541)
v(2727)=(v(239)*v(2420)+v(238)*v(2456)+v(234)*v(2479)+v(228)*v(2650)+v(230)*v(2672)+v(231)*v(2694))*v(5541)
v(2726)=(v(239)*v(2419)+v(238)*v(2455)+v(234)*v(2478)+v(228)*v(2649)+v(230)*v(2671)+v(231)*v(2693))*v(5541)
v(2725)=(v(239)*v(2418)+v(238)*v(2454)+v(234)*v(2475)+v(228)*v(2648)+v(230)*v(2670)+v(231)*v(2692))*v(5541)
v(2724)=(v(239)*v(2417)+v(238)*v(2453)+v(234)*v(2474)+v(228)*v(2647)+v(230)*v(2669)+v(231)*v(2691))*v(5541)
v(2723)=(v(239)*v(2416)+v(238)*v(2450)+v(234)*v(2471)+v(228)*v(2646)+v(230)*v(2668)+v(231)*v(2690))*v(5541)
v(2722)=(v(239)*v(2414)+v(238)*v(2448)+v(234)*v(2469)+v(228)*v(2645)+v(230)*v(2667)+v(231)*v(2689))*v(5541)
v(2721)=(v(239)*v(2413)+v(238)*v(2445)+v(234)*v(2466)+v(228)*v(2644)+v(230)*v(2666)+v(231)*v(2688))*v(5541)+v(5537)*v&
&(5826)
v(2709)=(v(238)*v(2410)+v(234)*v(2442)+v(239)*v(2463)+v(230)*v(2654)+v(227)*v(2676)+v(229)*v(2698))*v(5541)
v(2708)=(v(238)*v(2409)+v(234)*v(2441)+v(239)*v(2461)+v(230)*v(2653)+v(227)*v(2675)+v(229)*v(2697))*v(5541)
v(2707)=(v(238)*v(2408)+v(234)*v(2440)+v(239)*v(2460)+v(230)*v(2652)+v(227)*v(2674)+v(229)*v(2696))*v(5541)
v(2706)=(v(238)*v(2406)+v(234)*v(2439)+v(239)*v(2458)+v(230)*v(2651)+v(227)*v(2673)+v(229)*v(2695))*v(5541)
v(2705)=(v(238)*v(2405)+v(234)*v(2437)+v(239)*v(2456)+v(230)*v(2650)+v(227)*v(2672)+v(229)*v(2694))*v(5541)
v(2704)=(v(238)*v(2404)+v(234)*v(2436)+v(239)*v(2455)+v(230)*v(2649)+v(227)*v(2671)+v(229)*v(2693))*v(5541)
v(2703)=(v(238)*v(2403)+v(234)*v(2435)+v(239)*v(2454)+v(230)*v(2648)+v(227)*v(2670)+v(229)*v(2692))*v(5541)
v(2702)=(v(238)*v(2402)+v(234)*v(2434)+v(239)*v(2453)+v(230)*v(2647)+v(227)*v(2669)+v(229)*v(2691))*v(5541)
v(2701)=(v(238)*v(2401)+v(234)*v(2433)+v(239)*v(2450)+v(230)*v(2646)+v(227)*v(2668)+v(229)*v(2690))*v(5541)
v(2700)=(v(238)*v(2399)+v(234)*v(2431)+v(239)*v(2448)+v(230)*v(2645)+v(227)*v(2667)+v(229)*v(2689))*v(5541)
v(2699)=(v(238)*v(2397)+v(234)*v(2428)+v(239)*v(2445)+v(230)*v(2644)+v(227)*v(2666)+v(229)*v(2688))*v(5541)+v(5537)*v&
&(5825)
v(242)=v(5541)*v(5825)
v(2720)=(v(242)*v(2442)+v(229)*v(2709))*v(5541)
v(2719)=(v(242)*v(2441)+v(229)*v(2708))*v(5541)
v(2718)=(v(242)*v(2440)+v(229)*v(2707))*v(5541)
v(2717)=(v(242)*v(2439)+v(229)*v(2706))*v(5541)
v(2716)=(v(242)*v(2437)+v(229)*v(2705))*v(5541)
v(2715)=(v(242)*v(2436)+v(229)*v(2704))*v(5541)
v(2714)=(v(242)*v(2435)+v(229)*v(2703))*v(5541)
v(2713)=(v(242)*v(2434)+v(229)*v(2702))*v(5541)
v(2712)=(v(242)*v(2433)+v(229)*v(2701))*v(5541)
v(2711)=(v(242)*v(2431)+v(229)*v(2700))*v(5541)
v(2710)=v(2699)*v(5816)+v(242)*v(5822)
v(258)=v(242)*v(5816)
v(241)=v(5541)*v(5826)
v(2742)=(v(241)*v(2488)+v(231)*v(2731))*v(5541)
v(2741)=(v(241)*v(2486)+v(231)*v(2730))*v(5541)
v(2740)=(v(241)*v(2483)+v(231)*v(2729))*v(5541)
v(2739)=(v(241)*v(2481)+v(231)*v(2728))*v(5541)
v(2738)=(v(241)*v(2479)+v(231)*v(2727))*v(5541)
v(2737)=(v(241)*v(2478)+v(231)*v(2726))*v(5541)
v(2736)=(v(241)*v(2475)+v(231)*v(2725))*v(5541)
v(2735)=(v(241)*v(2474)+v(231)*v(2724))*v(5541)
v(2734)=(v(241)*v(2471)+v(231)*v(2723))*v(5541)
v(2733)=(v(241)*v(2469)+v(231)*v(2722))*v(5541)
v(2732)=v(2721)*v(5818)+v(241)*v(5820)
v(276)=v(241)*v(5818)
v(237)=v(254)+v(274)+v(234)*v(5823)
v(5828)=v(229)*v(237)+v(230)*v(241)+v(227)*v(242)
v(5827)=v(231)*v(237)+v(228)*v(241)+v(230)*v(242)
v(2808)=v(2720)+v(2742)+(v(237)*v(2394)+v(223)*v(2753))*v(5541)
v(2807)=v(2719)+v(2741)+(v(237)*v(2393)+v(223)*v(2752))*v(5541)
v(2806)=v(2718)+v(2740)+(v(237)*v(2392)+v(223)*v(2751))*v(5541)
v(2805)=v(2717)+v(2739)+(v(237)*v(2390)+v(223)*v(2750))*v(5541)
v(2804)=v(2716)+v(2738)+(v(237)*v(2389)+v(223)*v(2749))*v(5541)
v(2803)=v(2715)+v(2737)+(v(237)*v(2388)+v(223)*v(2748))*v(5541)
v(2802)=v(2714)+v(2736)+(v(237)*v(2387)+v(223)*v(2747))*v(5541)
v(2801)=v(2713)+v(2735)+(v(237)*v(2386)+v(223)*v(2746))*v(5541)
v(2800)=v(2712)+v(2734)+(v(237)*v(2385)+v(223)*v(2745))*v(5541)
v(2799)=v(2711)+v(2733)+(v(237)*v(2383)+v(223)*v(2744))*v(5541)
v(2798)=v(2710)+v(2732)+v(2743)*v(5823)+v(237)*v(5824)
v(2786)=(v(2410)*v(242)+v(237)*v(2442)+v(241)*v(2463)+v(227)*v(2709)+v(230)*v(2731)+v(229)*v(2753))*v(5541)
v(2785)=(v(2409)*v(242)+v(237)*v(2441)+v(241)*v(2461)+v(227)*v(2708)+v(230)*v(2730)+v(229)*v(2752))*v(5541)
v(2784)=(v(2408)*v(242)+v(237)*v(2440)+v(241)*v(2460)+v(227)*v(2707)+v(230)*v(2729)+v(229)*v(2751))*v(5541)
v(2783)=(v(2406)*v(242)+v(237)*v(2439)+v(241)*v(2458)+v(227)*v(2706)+v(230)*v(2728)+v(229)*v(2750))*v(5541)
v(2782)=(v(2405)*v(242)+v(237)*v(2437)+v(241)*v(2456)+v(227)*v(2705)+v(230)*v(2727)+v(229)*v(2749))*v(5541)
v(2781)=(v(2404)*v(242)+v(237)*v(2436)+v(241)*v(2455)+v(227)*v(2704)+v(230)*v(2726)+v(229)*v(2748))*v(5541)
v(2780)=(v(2403)*v(242)+v(237)*v(2435)+v(241)*v(2454)+v(227)*v(2703)+v(230)*v(2725)+v(229)*v(2747))*v(5541)
v(2779)=(v(2402)*v(242)+v(237)*v(2434)+v(241)*v(2453)+v(227)*v(2702)+v(230)*v(2724)+v(229)*v(2746))*v(5541)
v(2778)=(v(2401)*v(242)+v(237)*v(2433)+v(241)*v(2450)+v(227)*v(2701)+v(230)*v(2723)+v(229)*v(2745))*v(5541)
v(2777)=(v(2399)*v(242)+v(237)*v(2431)+v(241)*v(2448)+v(227)*v(2700)+v(230)*v(2722)+v(229)*v(2744))*v(5541)
v(2776)=(v(2397)*v(242)+v(237)*v(2428)+v(241)*v(2445)+v(227)*v(2699)+v(230)*v(2721)+v(229)*v(2743))*v(5541)+v(5537)*v&
&(5828)
v(2764)=(v(241)*v(2425)+v(242)*v(2463)+v(237)*v(2488)+v(230)*v(2709)+v(228)*v(2731)+v(231)*v(2753))*v(5541)
v(2763)=(v(241)*v(2424)+v(242)*v(2461)+v(237)*v(2486)+v(230)*v(2708)+v(228)*v(2730)+v(231)*v(2752))*v(5541)
v(2762)=(v(241)*v(2422)+v(242)*v(2460)+v(237)*v(2483)+v(230)*v(2707)+v(228)*v(2729)+v(231)*v(2751))*v(5541)
v(2761)=(v(241)*v(2421)+v(242)*v(2458)+v(237)*v(2481)+v(230)*v(2706)+v(228)*v(2728)+v(231)*v(2750))*v(5541)
v(2760)=(v(241)*v(2420)+v(242)*v(2456)+v(237)*v(2479)+v(230)*v(2705)+v(228)*v(2727)+v(231)*v(2749))*v(5541)
v(2759)=(v(241)*v(2419)+v(242)*v(2455)+v(237)*v(2478)+v(230)*v(2704)+v(228)*v(2726)+v(231)*v(2748))*v(5541)
v(2758)=(v(241)*v(2418)+v(242)*v(2454)+v(237)*v(2475)+v(230)*v(2703)+v(228)*v(2725)+v(231)*v(2747))*v(5541)
v(2757)=(v(241)*v(2417)+v(242)*v(2453)+v(237)*v(2474)+v(230)*v(2702)+v(228)*v(2724)+v(231)*v(2746))*v(5541)
v(2756)=(v(241)*v(2416)+v(242)*v(2450)+v(237)*v(2471)+v(230)*v(2701)+v(228)*v(2723)+v(231)*v(2745))*v(5541)
v(2755)=(v(241)*v(2414)+v(242)*v(2448)+v(237)*v(2469)+v(230)*v(2700)+v(228)*v(2722)+v(231)*v(2744))*v(5541)
v(2754)=(v(241)*v(2413)+v(242)*v(2445)+v(237)*v(2466)+v(230)*v(2699)+v(228)*v(2721)+v(231)*v(2743))*v(5541)+v(5537)*v&
&(5827)
v(245)=v(5541)*v(5827)
v(2775)=(v(245)*v(2488)+v(231)*v(2764))*v(5541)
v(2774)=(v(245)*v(2486)+v(231)*v(2763))*v(5541)
v(2773)=(v(245)*v(2483)+v(231)*v(2762))*v(5541)
v(2772)=(v(245)*v(2481)+v(231)*v(2761))*v(5541)
v(2771)=(v(245)*v(2479)+v(231)*v(2760))*v(5541)
v(2770)=(v(245)*v(2478)+v(231)*v(2759))*v(5541)
v(2769)=(v(245)*v(2475)+v(231)*v(2758))*v(5541)
v(2768)=(v(245)*v(2474)+v(231)*v(2757))*v(5541)
v(2767)=(v(245)*v(2471)+v(231)*v(2756))*v(5541)
v(2766)=(v(245)*v(2469)+v(231)*v(2755))*v(5541)
v(2765)=v(2754)*v(5818)+v(245)*v(5820)
v(280)=v(245)*v(5818)
v(244)=v(5541)*v(5828)
v(2797)=(v(244)*v(2442)+v(229)*v(2786))*v(5541)
v(2796)=(v(244)*v(2441)+v(229)*v(2785))*v(5541)
v(2795)=(v(244)*v(2440)+v(229)*v(2784))*v(5541)
v(2794)=(v(2439)*v(244)+v(229)*v(2783))*v(5541)
v(2793)=(v(2437)*v(244)+v(229)*v(2782))*v(5541)
v(2792)=(v(2436)*v(244)+v(229)*v(2781))*v(5541)
v(2791)=(v(2435)*v(244)+v(229)*v(2780))*v(5541)
v(2790)=(v(2434)*v(244)+v(229)*v(2779))*v(5541)
v(2789)=(v(2433)*v(244)+v(229)*v(2778))*v(5541)
v(2788)=(v(2431)*v(244)+v(229)*v(2777))*v(5541)
v(2787)=v(2776)*v(5816)+v(244)*v(5822)
v(260)=v(244)*v(5816)
v(240)=v(258)+v(276)+v(237)*v(5823)
v(5830)=v(229)*v(240)+v(227)*v(244)+v(230)*v(245)
v(5829)=v(231)*v(240)+v(230)*v(244)+v(228)*v(245)
v(2852)=(v(2410)*v(244)+v(240)*v(2442)+v(245)*v(2463)+v(230)*v(2764)+v(227)*v(2786)+v(229)*v(2808))*v(5541)
v(2851)=(v(2409)*v(244)+v(240)*v(2441)+v(245)*v(2461)+v(230)*v(2763)+v(227)*v(2785)+v(229)*v(2807))*v(5541)
v(2850)=(v(2408)*v(244)+v(240)*v(2440)+v(245)*v(2460)+v(230)*v(2762)+v(227)*v(2784)+v(229)*v(2806))*v(5541)
v(2849)=(v(240)*v(2439)+v(2406)*v(244)+v(245)*v(2458)+v(230)*v(2761)+v(227)*v(2783)+v(229)*v(2805))*v(5541)
v(2848)=(v(240)*v(2437)+v(2405)*v(244)+v(245)*v(2456)+v(230)*v(2760)+v(227)*v(2782)+v(229)*v(2804))*v(5541)
v(2847)=(v(240)*v(2436)+v(2404)*v(244)+v(245)*v(2455)+v(230)*v(2759)+v(227)*v(2781)+v(229)*v(2803))*v(5541)
v(2846)=(v(240)*v(2435)+v(2403)*v(244)+v(245)*v(2454)+v(230)*v(2758)+v(227)*v(2780)+v(229)*v(2802))*v(5541)
v(2845)=(v(240)*v(2434)+v(2402)*v(244)+v(245)*v(2453)+v(230)*v(2757)+v(227)*v(2779)+v(229)*v(2801))*v(5541)
v(2844)=(v(240)*v(2433)+v(2401)*v(244)+v(245)*v(2450)+v(230)*v(2756)+v(227)*v(2778)+v(229)*v(2800))*v(5541)
v(2843)=(v(240)*v(2431)+v(2399)*v(244)+v(2448)*v(245)+v(230)*v(2755)+v(227)*v(2777)+v(229)*v(2799))*v(5541)
v(2842)=(v(240)*v(2428)+v(2397)*v(244)+v(2445)*v(245)+v(230)*v(2754)+v(227)*v(2776)+v(229)*v(2798))*v(5541)+v(5537)*v&
&(5830)
v(2830)=(v(2425)*v(245)+v(244)*v(2463)+v(240)*v(2488)+v(228)*v(2764)+v(230)*v(2786)+v(231)*v(2808))*v(5541)
v(2829)=(v(2424)*v(245)+v(244)*v(2461)+v(240)*v(2486)+v(228)*v(2763)+v(230)*v(2785)+v(231)*v(2807))*v(5541)
v(2828)=(v(2422)*v(245)+v(244)*v(2460)+v(240)*v(2483)+v(228)*v(2762)+v(230)*v(2784)+v(231)*v(2806))*v(5541)
v(2827)=(v(2421)*v(245)+v(244)*v(2458)+v(240)*v(2481)+v(228)*v(2761)+v(230)*v(2783)+v(231)*v(2805))*v(5541)
v(2826)=(v(2420)*v(245)+v(244)*v(2456)+v(240)*v(2479)+v(228)*v(2760)+v(230)*v(2782)+v(231)*v(2804))*v(5541)
v(2825)=(v(2419)*v(245)+v(244)*v(2455)+v(240)*v(2478)+v(228)*v(2759)+v(230)*v(2781)+v(231)*v(2803))*v(5541)
v(2824)=(v(2418)*v(245)+v(244)*v(2454)+v(240)*v(2475)+v(228)*v(2758)+v(230)*v(2780)+v(231)*v(2802))*v(5541)
v(2823)=(v(2417)*v(245)+v(244)*v(2453)+v(240)*v(2474)+v(228)*v(2757)+v(230)*v(2779)+v(231)*v(2801))*v(5541)
v(2822)=(v(2416)*v(245)+v(244)*v(2450)+v(240)*v(2471)+v(228)*v(2756)+v(230)*v(2778)+v(231)*v(2800))*v(5541)
v(2821)=(v(244)*v(2448)+v(2414)*v(245)+v(240)*v(2469)+v(228)*v(2755)+v(230)*v(2777)+v(231)*v(2799))*v(5541)
v(2820)=(v(244)*v(2445)+v(2413)*v(245)+v(240)*v(2466)+v(228)*v(2754)+v(230)*v(2776)+v(231)*v(2798))*v(5541)+v(5537)*v&
&(5829)
v(2819)=v(2775)+v(2797)+(v(2394)*v(240)+v(223)*v(2808))*v(5541)
v(2818)=v(2774)+v(2796)+(v(2393)*v(240)+v(223)*v(2807))*v(5541)
v(2817)=v(2773)+v(2795)+(v(2392)*v(240)+v(223)*v(2806))*v(5541)
v(2816)=v(2772)+v(2794)+(v(2390)*v(240)+v(223)*v(2805))*v(5541)
v(2815)=v(2771)+v(2793)+(v(2389)*v(240)+v(223)*v(2804))*v(5541)
v(2814)=v(2770)+v(2792)+(v(2388)*v(240)+v(223)*v(2803))*v(5541)
v(2813)=v(2769)+v(2791)+(v(2387)*v(240)+v(223)*v(2802))*v(5541)
v(2812)=v(2768)+v(2790)+(v(2386)*v(240)+v(223)*v(2801))*v(5541)
v(2811)=v(2767)+v(2789)+(v(2385)*v(240)+v(223)*v(2800))*v(5541)
v(2810)=v(2766)+v(2788)+(v(2383)*v(240)+v(223)*v(2799))*v(5541)
v(2809)=v(2765)+v(2787)+v(2798)*v(5823)+v(240)*v(5824)
v(243)=v(260)+v(280)+v(240)*v(5823)
v(5831)=5040d0+v(243)
v(246)=v(5541)*v(5829)
v(2841)=(v(246)*v(2488)+v(231)*v(2830))*v(5541)
v(2840)=(v(246)*v(2486)+v(231)*v(2829))*v(5541)
v(2839)=(v(246)*v(2483)+v(231)*v(2828))*v(5541)
v(2838)=(v(246)*v(2481)+v(231)*v(2827))*v(5541)
v(2837)=(v(246)*v(2479)+v(231)*v(2826))*v(5541)
v(2836)=(v(246)*v(2478)+v(231)*v(2825))*v(5541)
v(2835)=(v(246)*v(2475)+v(231)*v(2824))*v(5541)
v(2834)=(v(246)*v(2474)+v(231)*v(2823))*v(5541)
v(2833)=(v(246)*v(2471)+v(231)*v(2822))*v(5541)
v(2832)=(v(246)*v(2469)+v(231)*v(2821))*v(5541)
v(2831)=v(2820)*v(5818)+v(246)*v(5820)
v(282)=v(246)*v(5818)
v(247)=v(5541)*v(5830)
v(5834)=v(230)*v(246)+v(227)*v(247)
v(5833)=v(228)*v(246)+v(230)*v(247)
v(2896)=(7d0*(360d0*v(2588)+120d0*v(2676)+30d0*v(2709)+6d0*v(2786)+v(2852))+v(5541)*(v(246)*v(2463)+v(2410)*v(247)+v&
&(229)*v(2819)+v(230)*v(2830)+v(227)*v(2852)+v(2442)*v(5831)))/5040d0
v(2895)=(7d0*(360d0*v(2587)+120d0*v(2675)+30d0*v(2708)+6d0*v(2785)+v(2851))+v(5541)*(v(246)*v(2461)+v(2409)*v(247)+v&
&(229)*v(2818)+v(230)*v(2829)+v(227)*v(2851)+v(2441)*v(5831)))/5040d0
v(2894)=(7d0*(360d0*v(2586)+120d0*v(2674)+30d0*v(2707)+6d0*v(2784)+v(2850))+v(5541)*(v(246)*v(2460)+v(2408)*v(247)+v&
&(229)*v(2817)+v(230)*v(2828)+v(227)*v(2850)+v(2440)*v(5831)))/5040d0
v(2893)=(7d0*(360d0*v(2585)+120d0*v(2673)+30d0*v(2706)+6d0*v(2783)+v(2849))+v(5541)*(v(2458)*v(246)+v(2406)*v(247)+v&
&(229)*v(2816)+v(230)*v(2827)+v(227)*v(2849)+v(2439)*v(5831)))/5040d0
v(2892)=(7d0*(360d0*v(2584)+120d0*v(2672)+30d0*v(2705)+6d0*v(2782)+v(2848))+v(5541)*(v(2456)*v(246)+v(2405)*v(247)+v&
&(229)*v(2815)+v(230)*v(2826)+v(227)*v(2848)+v(2437)*v(5831)))/5040d0
v(2891)=(7d0*(360d0*v(2583)+120d0*v(2671)+30d0*v(2704)+6d0*v(2781)+v(2847))+v(5541)*(v(2455)*v(246)+v(2404)*v(247)+v&
&(229)*v(2814)+v(230)*v(2825)+v(227)*v(2847)+v(2436)*v(5831)))/5040d0
v(2890)=(7d0*(360d0*v(2582)+120d0*v(2670)+30d0*v(2703)+6d0*v(2780)+v(2846))+v(5541)*(v(2454)*v(246)+v(2403)*v(247)+v&
&(229)*v(2813)+v(230)*v(2824)+v(227)*v(2846)+v(2435)*v(5831)))/5040d0
v(2889)=(7d0*(360d0*v(2581)+120d0*v(2669)+30d0*v(2702)+6d0*v(2779)+v(2845))+v(5541)*(v(2453)*v(246)+v(2402)*v(247)+v&
&(229)*v(2812)+v(230)*v(2823)+v(227)*v(2845)+v(2434)*v(5831)))/5040d0
v(2888)=(7d0*(360d0*v(2580)+120d0*v(2668)+30d0*v(2701)+6d0*v(2778)+v(2844))+v(5541)*(v(2450)*v(246)+v(2401)*v(247)+v&
&(229)*v(2811)+v(230)*v(2822)+v(227)*v(2844)+v(2433)*v(5831)))/5040d0
v(2887)=(7d0*(360d0*v(2579)+120d0*v(2667)+30d0*v(2700)+6d0*v(2777)+v(2843))+v(5541)*(v(2448)*v(246)+v(2399)*v(247)+v&
&(229)*v(2810)+v(230)*v(2821)+v(227)*v(2843)+v(2431)*v(5831)))/5040d0
v(2886)=v(2578)/2d0+v(2666)/6d0+v(2699)/24d0+v(2776)/120d0+v(2842)/720d0+v(5822)+((v(2428)*v(243)+v(2445)*v(246)+v(2397&
&)*v(247)+v(229)*v(2809)+v(230)*v(2820)+v(227)*v(2842))*v(5541)+v(5537)*(v(229)*v(243)+v(5834)))/5040d0
v(2874)=(v(2442)*v(247)+v(229)*v(2852))*v(5541)
v(2885)=(2520d0*v(2643)+840d0*v(2698)+210d0*v(2753)+42d0*v(2808)+7d0*v(2819)+v(2841)+v(2874)+v(5541)*(v(223)*v(2819)+v&
&(2394)*v(5831)))/5040d0
v(2873)=(v(2441)*v(247)+v(229)*v(2851))*v(5541)
v(2884)=(2520d0*v(2641)+840d0*v(2697)+210d0*v(2752)+42d0*v(2807)+7d0*v(2818)+v(2840)+v(2873)+v(5541)*(v(223)*v(2818)+v&
&(2393)*v(5831)))/5040d0
v(2872)=(v(2440)*v(247)+v(229)*v(2850))*v(5541)
v(2883)=(2520d0*v(2639)+840d0*v(2696)+210d0*v(2751)+42d0*v(2806)+7d0*v(2817)+v(2839)+v(2872)+v(5541)*(v(223)*v(2817)+v&
&(2392)*v(5831)))/5040d0
v(2871)=(v(2439)*v(247)+v(229)*v(2849))*v(5541)
v(2882)=(2520d0*v(2637)+840d0*v(2695)+210d0*v(2750)+42d0*v(2805)+7d0*v(2816)+v(2838)+v(2871)+v(5541)*(v(223)*v(2816)+v&
&(2390)*v(5831)))/5040d0
v(2870)=(v(2437)*v(247)+v(229)*v(2848))*v(5541)
v(2881)=(2520d0*v(2635)+840d0*v(2694)+210d0*v(2749)+42d0*v(2804)+7d0*v(2815)+v(2837)+v(2870)+v(5541)*(v(223)*v(2815)+v&
&(2389)*v(5831)))/5040d0
v(2869)=(v(2436)*v(247)+v(229)*v(2847))*v(5541)
v(2880)=(2520d0*v(2633)+840d0*v(2693)+210d0*v(2748)+42d0*v(2803)+7d0*v(2814)+v(2836)+v(2869)+v(5541)*(v(223)*v(2814)+v&
&(2388)*v(5831)))/5040d0
v(2868)=(v(2435)*v(247)+v(229)*v(2846))*v(5541)
v(2879)=(2520d0*v(2631)+840d0*v(2692)+210d0*v(2747)+42d0*v(2802)+7d0*v(2813)+v(2835)+v(2868)+v(5541)*(v(223)*v(2813)+v&
&(2387)*v(5831)))/5040d0
v(2867)=(v(2434)*v(247)+v(229)*v(2845))*v(5541)
v(2878)=(2520d0*v(2629)+840d0*v(2691)+210d0*v(2746)+42d0*v(2801)+7d0*v(2812)+v(2834)+v(2867)+v(5541)*(v(223)*v(2812)+v&
&(2386)*v(5831)))/5040d0
v(2866)=(v(2433)*v(247)+v(229)*v(2844))*v(5541)
v(2877)=(2520d0*v(2627)+840d0*v(2690)+210d0*v(2745)+42d0*v(2800)+7d0*v(2811)+v(2833)+v(2866)+v(5541)*(v(223)*v(2811)+v&
&(2385)*v(5831)))/5040d0
v(2865)=(v(2431)*v(247)+v(229)*v(2843))*v(5541)
v(2876)=(2520d0*v(2625)+840d0*v(2689)+210d0*v(2744)+42d0*v(2799)+7d0*v(2810)+v(2832)+v(2865)+v(5541)*(v(223)*v(2810)+v&
&(2383)*v(5831)))/5040d0
v(2864)=v(2842)*v(5816)+v(247)*v(5822)
v(2875)=(2520d0*v(2623)+840d0*v(2688)+210d0*v(2743)+42d0*v(2798)+7d0*v(2809)+v(2831)+v(2864)+v(223)*(v(2809)*v(5541)+v&
&(5537)*v(5831))+v(5831)*v(5832))/5040d0
v(2863)=(7d0*(360d0*v(2610)+120d0*v(2654)+30d0*v(2731)+6d0*v(2764)+v(2830))+(v(2425)*v(246)+v(2463)*v(247)+5040d0*v&
&(2488)+v(243)*v(2488)+v(231)*v(2819)+v(228)*v(2830)+v(230)*v(2852))*v(5541))/5040d0
v(3226)=statev(7)*v(2885)+statev(5)*v(2896)+v(2863)*v(5533)
v(3193)=statev(9)*v(2863)+statev(4)*v(2885)+v(2896)*v(5532)
v(2907)=statev(6)*v(2863)+statev(8)*v(2896)+v(2885)*v(5531)
v(2862)=(7d0*(360d0*v(2609)+120d0*v(2653)+30d0*v(2730)+6d0*v(2763)+v(2829))+(v(2424)*v(246)+v(2461)*v(247)+5040d0*v&
&(2486)+v(243)*v(2486)+v(231)*v(2818)+v(228)*v(2829)+v(230)*v(2851))*v(5541))/5040d0
v(3225)=statev(7)*v(2884)+statev(5)*v(2895)+v(2862)*v(5533)
v(3192)=statev(9)*v(2862)+statev(4)*v(2884)+v(2895)*v(5532)
v(2906)=statev(6)*v(2862)+statev(8)*v(2895)+v(2884)*v(5531)
v(2861)=(7d0*(360d0*v(2608)+120d0*v(2652)+30d0*v(2729)+6d0*v(2762)+v(2828))+(v(2422)*v(246)+v(2460)*v(247)+5040d0*v&
&(2483)+v(243)*v(2483)+v(231)*v(2817)+v(228)*v(2828)+v(230)*v(2850))*v(5541))/5040d0
v(3224)=statev(7)*v(2883)+statev(5)*v(2894)+v(2861)*v(5533)
v(3191)=statev(9)*v(2861)+statev(4)*v(2883)+v(2894)*v(5532)
v(2905)=statev(6)*v(2861)+statev(8)*v(2894)+v(2883)*v(5531)
v(2860)=(7d0*(360d0*v(2607)+120d0*v(2651)+30d0*v(2728)+6d0*v(2761)+v(2827))+(v(2421)*v(246)+v(2458)*v(247)+5040d0*v&
&(2481)+v(243)*v(2481)+v(231)*v(2816)+v(228)*v(2827)+v(230)*v(2849))*v(5541))/5040d0
v(3223)=statev(7)*v(2882)+statev(5)*v(2893)+v(2860)*v(5533)
v(3190)=statev(9)*v(2860)+statev(4)*v(2882)+v(2893)*v(5532)
v(2904)=statev(6)*v(2860)+statev(8)*v(2893)+v(2882)*v(5531)
v(2859)=(7d0*(360d0*v(2606)+120d0*v(2650)+30d0*v(2727)+6d0*v(2760)+v(2826))+(v(2420)*v(246)+v(2456)*v(247)+5040d0*v&
&(2479)+v(243)*v(2479)+v(231)*v(2815)+v(228)*v(2826)+v(230)*v(2848))*v(5541))/5040d0
v(3222)=statev(7)*v(2881)+statev(5)*v(2892)+v(2859)*v(5533)
v(3189)=statev(9)*v(2859)+statev(4)*v(2881)+v(2892)*v(5532)
v(2903)=statev(6)*v(2859)+statev(8)*v(2892)+v(2881)*v(5531)
v(2858)=(7d0*(360d0*v(2605)+120d0*v(2649)+30d0*v(2726)+6d0*v(2759)+v(2825))+(v(2419)*v(246)+v(2455)*v(247)+5040d0*v&
&(2478)+v(243)*v(2478)+v(231)*v(2814)+v(228)*v(2825)+v(230)*v(2847))*v(5541))/5040d0
v(3221)=statev(7)*v(2880)+statev(5)*v(2891)+v(2858)*v(5533)
v(3188)=statev(9)*v(2858)+statev(4)*v(2880)+v(2891)*v(5532)
v(2902)=statev(6)*v(2858)+statev(8)*v(2891)+v(2880)*v(5531)
v(2857)=(7d0*(360d0*v(2604)+120d0*v(2648)+30d0*v(2725)+6d0*v(2758)+v(2824))+(v(2418)*v(246)+v(2454)*v(247)+5040d0*v&
&(2475)+v(243)*v(2475)+v(231)*v(2813)+v(228)*v(2824)+v(230)*v(2846))*v(5541))/5040d0
v(3220)=statev(7)*v(2879)+statev(5)*v(2890)+v(2857)*v(5533)
v(3187)=statev(9)*v(2857)+statev(4)*v(2879)+v(2890)*v(5532)
v(2901)=statev(6)*v(2857)+statev(8)*v(2890)+v(2879)*v(5531)
v(2856)=(7d0*(360d0*v(2603)+120d0*v(2647)+30d0*v(2724)+6d0*v(2757)+v(2823))+(v(2417)*v(246)+v(2453)*v(247)+5040d0*v&
&(2474)+v(243)*v(2474)+v(231)*v(2812)+v(228)*v(2823)+v(230)*v(2845))*v(5541))/5040d0
v(3219)=statev(7)*v(2878)+statev(5)*v(2889)+v(2856)*v(5533)
v(3186)=statev(9)*v(2856)+statev(4)*v(2878)+v(2889)*v(5532)
v(2900)=statev(6)*v(2856)+statev(8)*v(2889)+v(2878)*v(5531)
v(2855)=(7d0*(360d0*v(2602)+120d0*v(2646)+30d0*v(2723)+6d0*v(2756)+v(2822))+(v(2416)*v(246)+v(2450)*v(247)+5040d0*v&
&(2471)+v(243)*v(2471)+v(231)*v(2811)+v(228)*v(2822)+v(230)*v(2844))*v(5541))/5040d0
v(3218)=statev(7)*v(2877)+statev(5)*v(2888)+v(2855)*v(5533)
v(3185)=statev(9)*v(2855)+statev(4)*v(2877)+v(2888)*v(5532)
v(2899)=statev(6)*v(2855)+statev(8)*v(2888)+v(2877)*v(5531)
v(2854)=(7d0*(360d0*v(2601)+120d0*v(2645)+30d0*v(2722)+6d0*v(2755)+v(2821))+(v(2414)*v(246)+5040d0*v(2469)+v(243)*v&
&(2469)+v(2448)*v(247)+v(231)*v(2810)+v(228)*v(2821)+v(230)*v(2843))*v(5541))/5040d0
v(3217)=statev(7)*v(2876)+statev(5)*v(2887)+v(2854)*v(5533)
v(3184)=statev(9)*v(2854)+statev(4)*v(2876)+v(2887)*v(5532)
v(2898)=statev(6)*v(2854)+statev(8)*v(2887)+v(2876)*v(5531)
v(2853)=v(2600)/2d0+v(2644)/6d0+v(2721)/24d0+v(2754)/120d0+v(2820)/720d0+v(5820)+((v(2413)*v(246)+v(243)*v(2466)+v(2445&
&)*v(247)+v(231)*v(2809)+v(228)*v(2820)+v(230)*v(2842))*v(5541)+v(5537)*(v(231)*v(243)+v(5833)))/5040d0
v(3216)=statev(7)*v(2875)+statev(5)*v(2886)+v(2853)*v(5533)
v(3183)=statev(9)*v(2853)+statev(4)*v(2875)+v(2886)*v(5532)
v(2897)=statev(6)*v(2853)+statev(8)*v(2886)+v(2875)*v(5531)
v(285)=(7d0*(360d0*v(235)+120d0*v(239)+30d0*v(241)+6d0*v(245)+v(246))+v(5541)*(v(231)*v(5831)+v(5833)))/5040d0
v(265)=v(247)*v(5816)
v(5845)=5040d0+v(265)
v(287)=(2520d0*v(233)+840d0*v(234)+210d0*v(237)+42d0*v(240)+7d0*v(243)+v(282)+v(5823)*v(5831)+v(5845))/5040d0
v(249)=(7d0*(360d0*v(236)+120d0*v(238)+30d0*v(242)+6d0*v(244)+v(247))+v(5541)*(v(229)*v(5831)+v(5834)))/5040d0
v(248)=statev(8)*v(249)+statev(6)*v(285)+v(287)*v(5531)
v(251)=v(250)+v(267)+v(232)*v(370)
v(5835)=v(231)*v(236)+v(230)*v(251)+v(228)*v(255)
v(2962)=v(2555)+v(2599)+(v(2410)*v(251)+v(227)*v(2929))*v(5541)
v(2961)=v(2554)+v(2598)+(v(2409)*v(251)+v(227)*v(2927))*v(5541)
v(2960)=v(2553)+v(2597)+(v(2408)*v(251)+v(227)*v(2925))*v(5541)
v(2959)=v(2552)+v(2596)+(v(2406)*v(251)+v(227)*v(2923))*v(5541)
v(2958)=v(2551)+v(2595)+(v(2405)*v(251)+v(227)*v(2921))*v(5541)
v(2957)=v(2550)+v(2594)+(v(2404)*v(251)+v(227)*v(2919))*v(5541)
v(2956)=v(2549)+v(2593)+(v(2403)*v(251)+v(227)*v(2917))*v(5541)
v(2955)=v(2548)+v(2592)+(v(2402)*v(251)+v(227)*v(2915))*v(5541)
v(2954)=v(2547)+v(2591)+(v(2401)*v(251)+v(227)*v(2913))*v(5541)
v(2953)=v(2546)+v(2590)+(v(2399)*v(251)+v(227)*v(2911))*v(5541)
v(2952)=v(2545)+v(2589)+v(2909)*v(5837)+v(251)*v(5838)
v(2940)=(v(236)*v(2488)+v(2463)*v(251)+v(228)*v(2544)+v(2425)*v(255)+v(231)*v(2588)+v(230)*v(2929))*v(5541)
v(2939)=(v(236)*v(2486)+v(2461)*v(251)+v(228)*v(2543)+v(2424)*v(255)+v(231)*v(2587)+v(230)*v(2927))*v(5541)
v(2938)=(v(236)*v(2483)+v(2460)*v(251)+v(228)*v(2542)+v(2422)*v(255)+v(231)*v(2586)+v(230)*v(2925))*v(5541)
v(2937)=(v(236)*v(2481)+v(2458)*v(251)+v(228)*v(2541)+v(2421)*v(255)+v(231)*v(2585)+v(230)*v(2923))*v(5541)
v(2936)=(v(236)*v(2479)+v(2456)*v(251)+v(228)*v(2540)+v(2420)*v(255)+v(231)*v(2584)+v(230)*v(2921))*v(5541)
v(2935)=(v(236)*v(2478)+v(2455)*v(251)+v(228)*v(2539)+v(2419)*v(255)+v(231)*v(2583)+v(230)*v(2919))*v(5541)
v(2934)=(v(236)*v(2475)+v(2454)*v(251)+v(228)*v(2538)+v(2418)*v(255)+v(231)*v(2582)+v(230)*v(2917))*v(5541)
v(2933)=(v(236)*v(2474)+v(2453)*v(251)+v(228)*v(2537)+v(2417)*v(255)+v(231)*v(2581)+v(230)*v(2915))*v(5541)
v(2932)=(v(236)*v(2471)+v(2450)*v(251)+v(228)*v(2536)+v(2416)*v(255)+v(231)*v(2580)+v(230)*v(2913))*v(5541)
v(2931)=(v(236)*v(2469)+v(2448)*v(251)+v(228)*v(2535)+v(2414)*v(255)+v(231)*v(2579)+v(230)*v(2911))*v(5541)
v(2930)=(v(236)*v(2466)+v(2445)*v(251)+v(228)*v(2534)+v(2413)*v(255)+v(231)*v(2578)+v(230)*v(2909))*v(5541)+v(5537)*v&
&(5835)
v(257)=v(5541)*v(5835)
v(2951)=(v(2463)*v(257)+v(230)*v(2940))*v(5541)
v(2950)=(v(2461)*v(257)+v(230)*v(2939))*v(5541)
v(2949)=(v(2460)*v(257)+v(230)*v(2938))*v(5541)
v(2948)=(v(2458)*v(257)+v(230)*v(2937))*v(5541)
v(2947)=(v(2456)*v(257)+v(230)*v(2936))*v(5541)
v(2946)=(v(2455)*v(257)+v(230)*v(2935))*v(5541)
v(2945)=(v(2454)*v(257)+v(230)*v(2934))*v(5541)
v(2944)=(v(2453)*v(257)+v(230)*v(2933))*v(5541)
v(2943)=(v(2450)*v(257)+v(230)*v(2932))*v(5541)
v(2942)=(v(2448)*v(257)+v(230)*v(2931))*v(5541)
v(2941)=v(2930)*v(5814)+v(257)*v(5836)
v(273)=v(257)*v(5814)
v(253)=v(252)+v(271)+v(251)*v(5837)
v(5839)=v(231)*v(238)+v(230)*v(253)+v(228)*v(257)
v(2995)=v(2687)+v(2951)+(v(2410)*v(253)+v(227)*v(2962))*v(5541)
v(2994)=v(2686)+v(2950)+(v(2409)*v(253)+v(227)*v(2961))*v(5541)
v(2993)=v(2685)+v(2949)+(v(2408)*v(253)+v(227)*v(2960))*v(5541)
v(2992)=v(2684)+v(2948)+(v(2406)*v(253)+v(227)*v(2959))*v(5541)
v(2991)=v(2683)+v(2947)+(v(2405)*v(253)+v(227)*v(2958))*v(5541)
v(2990)=v(2682)+v(2946)+(v(2404)*v(253)+v(227)*v(2957))*v(5541)
v(2989)=v(2681)+v(2945)+(v(2403)*v(253)+v(227)*v(2956))*v(5541)
v(2988)=v(2680)+v(2944)+(v(2402)*v(253)+v(227)*v(2955))*v(5541)
v(2987)=v(2679)+v(2943)+(v(2401)*v(253)+v(227)*v(2954))*v(5541)
v(2986)=v(2678)+v(2942)+(v(2399)*v(253)+v(227)*v(2953))*v(5541)
v(2985)=v(2677)+v(2941)+v(2952)*v(5837)+v(253)*v(5838)
v(2973)=(v(238)*v(2488)+v(2463)*v(253)+v(2425)*v(257)+v(231)*v(2676)+v(228)*v(2940)+v(230)*v(2962))*v(5541)
v(2972)=(v(238)*v(2486)+v(2461)*v(253)+v(2424)*v(257)+v(231)*v(2675)+v(228)*v(2939)+v(230)*v(2961))*v(5541)
v(2971)=(v(238)*v(2483)+v(2460)*v(253)+v(2422)*v(257)+v(231)*v(2674)+v(228)*v(2938)+v(230)*v(2960))*v(5541)
v(2970)=(v(238)*v(2481)+v(2458)*v(253)+v(2421)*v(257)+v(231)*v(2673)+v(228)*v(2937)+v(230)*v(2959))*v(5541)
v(2969)=(v(238)*v(2479)+v(2456)*v(253)+v(2420)*v(257)+v(231)*v(2672)+v(228)*v(2936)+v(230)*v(2958))*v(5541)
v(2968)=(v(238)*v(2478)+v(2455)*v(253)+v(2419)*v(257)+v(231)*v(2671)+v(228)*v(2935)+v(230)*v(2957))*v(5541)
v(2967)=(v(238)*v(2475)+v(2454)*v(253)+v(2418)*v(257)+v(231)*v(2670)+v(228)*v(2934)+v(230)*v(2956))*v(5541)
v(2966)=(v(238)*v(2474)+v(2453)*v(253)+v(2417)*v(257)+v(231)*v(2669)+v(228)*v(2933)+v(230)*v(2955))*v(5541)
v(2965)=(v(238)*v(2471)+v(2450)*v(253)+v(2416)*v(257)+v(231)*v(2668)+v(228)*v(2932)+v(230)*v(2954))*v(5541)
v(2964)=(v(238)*v(2469)+v(2448)*v(253)+v(2414)*v(257)+v(231)*v(2667)+v(228)*v(2931)+v(230)*v(2953))*v(5541)
v(2963)=(v(238)*v(2466)+v(2445)*v(253)+v(2413)*v(257)+v(231)*v(2666)+v(228)*v(2930)+v(230)*v(2952))*v(5541)+v(5537)*v&
&(5839)
v(261)=v(5541)*v(5839)
v(2984)=(v(2463)*v(261)+v(230)*v(2973))*v(5541)
v(2983)=(v(2461)*v(261)+v(230)*v(2972))*v(5541)
v(2982)=(v(2460)*v(261)+v(230)*v(2971))*v(5541)
v(2981)=(v(2458)*v(261)+v(230)*v(2970))*v(5541)
v(2980)=(v(2456)*v(261)+v(230)*v(2969))*v(5541)
v(2979)=(v(2455)*v(261)+v(230)*v(2968))*v(5541)
v(2978)=(v(2454)*v(261)+v(230)*v(2967))*v(5541)
v(2977)=(v(2453)*v(261)+v(230)*v(2966))*v(5541)
v(2976)=(v(2450)*v(261)+v(230)*v(2965))*v(5541)
v(2975)=(v(2448)*v(261)+v(230)*v(2964))*v(5541)
v(2974)=v(2963)*v(5814)+v(261)*v(5836)
v(277)=v(261)*v(5814)
v(256)=v(254)+v(273)+v(253)*v(5837)
v(5840)=v(231)*v(242)+v(230)*v(256)+v(228)*v(261)
v(3028)=v(2720)+v(2984)+(v(2410)*v(256)+v(227)*v(2995))*v(5541)
v(3027)=v(2719)+v(2983)+(v(2409)*v(256)+v(227)*v(2994))*v(5541)
v(3026)=v(2718)+v(2982)+(v(2408)*v(256)+v(227)*v(2993))*v(5541)
v(3025)=v(2717)+v(2981)+(v(2406)*v(256)+v(227)*v(2992))*v(5541)
v(3024)=v(2716)+v(2980)+(v(2405)*v(256)+v(227)*v(2991))*v(5541)
v(3023)=v(2715)+v(2979)+(v(2404)*v(256)+v(227)*v(2990))*v(5541)
v(3022)=v(2714)+v(2978)+(v(2403)*v(256)+v(227)*v(2989))*v(5541)
v(3021)=v(2713)+v(2977)+(v(2402)*v(256)+v(227)*v(2988))*v(5541)
v(3020)=v(2712)+v(2976)+(v(2401)*v(256)+v(227)*v(2987))*v(5541)
v(3019)=v(2711)+v(2975)+(v(2399)*v(256)+v(227)*v(2986))*v(5541)
v(3018)=v(2710)+v(2974)+v(2985)*v(5837)+v(256)*v(5838)
v(3006)=(v(242)*v(2488)+v(2463)*v(256)+v(2425)*v(261)+v(231)*v(2709)+v(228)*v(2973)+v(230)*v(2995))*v(5541)
v(3005)=(v(242)*v(2486)+v(2461)*v(256)+v(2424)*v(261)+v(231)*v(2708)+v(228)*v(2972)+v(230)*v(2994))*v(5541)
v(3004)=(v(242)*v(2483)+v(2460)*v(256)+v(2422)*v(261)+v(231)*v(2707)+v(228)*v(2971)+v(230)*v(2993))*v(5541)
v(3003)=(v(242)*v(2481)+v(2458)*v(256)+v(2421)*v(261)+v(231)*v(2706)+v(228)*v(2970)+v(230)*v(2992))*v(5541)
v(3002)=(v(242)*v(2479)+v(2456)*v(256)+v(2420)*v(261)+v(231)*v(2705)+v(228)*v(2969)+v(230)*v(2991))*v(5541)
v(3001)=(v(242)*v(2478)+v(2455)*v(256)+v(2419)*v(261)+v(231)*v(2704)+v(228)*v(2968)+v(230)*v(2990))*v(5541)
v(3000)=(v(242)*v(2475)+v(2454)*v(256)+v(2418)*v(261)+v(231)*v(2703)+v(228)*v(2967)+v(230)*v(2989))*v(5541)
v(2999)=(v(242)*v(2474)+v(2453)*v(256)+v(2417)*v(261)+v(231)*v(2702)+v(228)*v(2966)+v(230)*v(2988))*v(5541)
v(2998)=(v(242)*v(2471)+v(2450)*v(256)+v(2416)*v(261)+v(231)*v(2701)+v(228)*v(2965)+v(230)*v(2987))*v(5541)
v(2997)=(v(242)*v(2469)+v(2448)*v(256)+v(2414)*v(261)+v(231)*v(2700)+v(228)*v(2964)+v(230)*v(2986))*v(5541)
v(2996)=(v(242)*v(2466)+v(2445)*v(256)+v(2413)*v(261)+v(231)*v(2699)+v(228)*v(2963)+v(230)*v(2985))*v(5541)+v(5537)*v&
&(5840)
v(263)=v(5541)*v(5840)
v(3017)=(v(2463)*v(263)+v(230)*v(3006))*v(5541)
v(3016)=(v(2461)*v(263)+v(230)*v(3005))*v(5541)
v(3015)=(v(2460)*v(263)+v(230)*v(3004))*v(5541)
v(3014)=(v(2458)*v(263)+v(230)*v(3003))*v(5541)
v(3013)=(v(2456)*v(263)+v(230)*v(3002))*v(5541)
v(3012)=(v(2455)*v(263)+v(230)*v(3001))*v(5541)
v(3011)=(v(2454)*v(263)+v(230)*v(3000))*v(5541)
v(3010)=(v(2453)*v(263)+v(230)*v(2999))*v(5541)
v(3009)=(v(2450)*v(263)+v(230)*v(2998))*v(5541)
v(3008)=(v(2448)*v(263)+v(230)*v(2997))*v(5541)
v(3007)=v(2996)*v(5814)+v(263)*v(5836)
v(279)=v(263)*v(5814)
v(259)=v(258)+v(277)+v(256)*v(5837)
v(5841)=v(231)*v(244)+v(230)*v(259)+v(228)*v(263)
v(3050)=(v(244)*v(2488)+v(2463)*v(259)+v(2425)*v(263)+v(231)*v(2786)+v(228)*v(3006)+v(230)*v(3028))*v(5541)
v(3049)=(v(244)*v(2486)+v(2461)*v(259)+v(2424)*v(263)+v(231)*v(2785)+v(228)*v(3005)+v(230)*v(3027))*v(5541)
v(3048)=(v(244)*v(2483)+v(2460)*v(259)+v(2422)*v(263)+v(231)*v(2784)+v(228)*v(3004)+v(230)*v(3026))*v(5541)
v(3047)=(v(244)*v(2481)+v(2458)*v(259)+v(2421)*v(263)+v(231)*v(2783)+v(228)*v(3003)+v(230)*v(3025))*v(5541)
v(3046)=(v(244)*v(2479)+v(2456)*v(259)+v(2420)*v(263)+v(231)*v(2782)+v(228)*v(3002)+v(230)*v(3024))*v(5541)
v(3045)=(v(244)*v(2478)+v(2455)*v(259)+v(2419)*v(263)+v(231)*v(2781)+v(228)*v(3001)+v(230)*v(3023))*v(5541)
v(3044)=(v(244)*v(2475)+v(2454)*v(259)+v(2418)*v(263)+v(231)*v(2780)+v(228)*v(3000)+v(230)*v(3022))*v(5541)
v(3043)=(v(244)*v(2474)+v(2453)*v(259)+v(2417)*v(263)+v(231)*v(2779)+v(228)*v(2999)+v(230)*v(3021))*v(5541)
v(3042)=(v(244)*v(2471)+v(2450)*v(259)+v(2416)*v(263)+v(231)*v(2778)+v(228)*v(2998)+v(230)*v(3020))*v(5541)
v(3041)=(v(244)*v(2469)+v(2448)*v(259)+v(2414)*v(263)+v(231)*v(2777)+v(228)*v(2997)+v(230)*v(3019))*v(5541)
v(3040)=(v(244)*v(2466)+v(2445)*v(259)+v(2413)*v(263)+v(231)*v(2776)+v(228)*v(2996)+v(230)*v(3018))*v(5541)+v(5537)*v&
&(5841)
v(3039)=v(2797)+v(3017)+(v(2410)*v(259)+v(227)*v(3028))*v(5541)
v(3038)=v(2796)+v(3016)+(v(2409)*v(259)+v(227)*v(3027))*v(5541)
v(3037)=v(2795)+v(3015)+(v(2408)*v(259)+v(227)*v(3026))*v(5541)
v(3036)=v(2794)+v(3014)+(v(2406)*v(259)+v(227)*v(3025))*v(5541)
v(3035)=v(2793)+v(3013)+(v(2405)*v(259)+v(227)*v(3024))*v(5541)
v(3034)=v(2792)+v(3012)+(v(2404)*v(259)+v(227)*v(3023))*v(5541)
v(3033)=v(2791)+v(3011)+(v(2403)*v(259)+v(227)*v(3022))*v(5541)
v(3032)=v(2790)+v(3010)+(v(2402)*v(259)+v(227)*v(3021))*v(5541)
v(3031)=v(2789)+v(3009)+(v(2401)*v(259)+v(227)*v(3020))*v(5541)
v(3030)=v(2788)+v(3008)+(v(2399)*v(259)+v(227)*v(3019))*v(5541)
v(3029)=v(2787)+v(3007)+v(3018)*v(5837)+v(259)*v(5838)
v(262)=v(260)+v(279)+v(259)*v(5837)
v(5842)=5040d0+v(262)
v(264)=v(5541)*v(5841)
v(5844)=v(231)*v(247)+v(228)*v(264)
v(3072)=(v(2463)*v(264)+v(230)*v(3050))*v(5541)
v(3083)=(v(2874)+2520d0*v(2929)+840d0*v(2962)+210d0*v(2995)+42d0*v(3028)+7d0*v(3039)+v(3072)+v(5541)*(v(227)*v(3039)+v&
&(2410)*v(5842)))/5040d0
v(3071)=(v(2461)*v(264)+v(230)*v(3049))*v(5541)
v(3082)=(v(2873)+2520d0*v(2927)+840d0*v(2961)+210d0*v(2994)+42d0*v(3027)+7d0*v(3038)+v(3071)+v(5541)*(v(227)*v(3038)+v&
&(2409)*v(5842)))/5040d0
v(3070)=(v(2460)*v(264)+v(230)*v(3048))*v(5541)
v(3081)=(v(2872)+2520d0*v(2925)+840d0*v(2960)+210d0*v(2993)+42d0*v(3026)+7d0*v(3037)+v(3070)+v(5541)*(v(227)*v(3037)+v&
&(2408)*v(5842)))/5040d0
v(3069)=(v(2458)*v(264)+v(230)*v(3047))*v(5541)
v(3080)=(v(2871)+2520d0*v(2923)+840d0*v(2959)+210d0*v(2992)+42d0*v(3025)+7d0*v(3036)+v(3069)+v(5541)*(v(227)*v(3036)+v&
&(2406)*v(5842)))/5040d0
v(3068)=(v(2456)*v(264)+v(230)*v(3046))*v(5541)
v(3079)=(v(2870)+2520d0*v(2921)+840d0*v(2958)+210d0*v(2991)+42d0*v(3024)+7d0*v(3035)+v(3068)+v(5541)*(v(227)*v(3035)+v&
&(2405)*v(5842)))/5040d0
v(3067)=(v(2455)*v(264)+v(230)*v(3045))*v(5541)
v(3078)=(v(2869)+2520d0*v(2919)+840d0*v(2957)+210d0*v(2990)+42d0*v(3023)+7d0*v(3034)+v(3067)+v(5541)*(v(227)*v(3034)+v&
&(2404)*v(5842)))/5040d0
v(3066)=(v(2454)*v(264)+v(230)*v(3044))*v(5541)
v(3077)=(v(2868)+2520d0*v(2917)+840d0*v(2956)+210d0*v(2989)+42d0*v(3022)+7d0*v(3033)+v(3066)+v(5541)*(v(227)*v(3033)+v&
&(2403)*v(5842)))/5040d0
v(3065)=(v(2453)*v(264)+v(230)*v(3043))*v(5541)
v(3076)=(v(2867)+2520d0*v(2915)+840d0*v(2955)+210d0*v(2988)+42d0*v(3021)+7d0*v(3032)+v(3065)+v(5541)*(v(227)*v(3032)+v&
&(2402)*v(5842)))/5040d0
v(3064)=(v(2450)*v(264)+v(230)*v(3042))*v(5541)
v(3075)=(v(2866)+2520d0*v(2913)+840d0*v(2954)+210d0*v(2987)+42d0*v(3020)+7d0*v(3031)+v(3064)+v(5541)*(v(227)*v(3031)+v&
&(2401)*v(5842)))/5040d0
v(3063)=(v(2448)*v(264)+v(230)*v(3041))*v(5541)
v(3074)=(v(2865)+2520d0*v(2911)+840d0*v(2953)+210d0*v(2986)+42d0*v(3019)+7d0*v(3030)+v(3063)+v(5541)*(v(227)*v(3030)+v&
&(2399)*v(5842)))/5040d0
v(3062)=v(3040)*v(5814)+v(264)*v(5836)
v(3073)=(v(2864)+2520d0*v(2909)+840d0*v(2952)+210d0*v(2985)+42d0*v(3018)+7d0*v(3029)+v(3062)+v(227)*(v(3029)*v(5541)+v&
&(5537)*v(5842))+v(5842)*v(5843))/5040d0
v(3061)=(7d0*(360d0*v(2544)+120d0*v(2940)+30d0*v(2973)+6d0*v(3006)+v(3050))+v(5541)*(v(247)*v(2488)+v(2425)*v(264)+v&
&(231)*v(2852)+v(230)*v(3039)+v(228)*v(3050)+v(2463)*v(5842)))/5040d0
v(3259)=statev(6)*v(3061)+statev(8)*v(3083)+v(2896)*v(5531)
v(3204)=statev(7)*v(2896)+statev(5)*v(3083)+v(3061)*v(5533)
v(3094)=statev(4)*v(2896)+statev(9)*v(3061)+v(3083)*v(5532)
v(3060)=(7d0*(360d0*v(2543)+120d0*v(2939)+30d0*v(2972)+6d0*v(3005)+v(3049))+v(5541)*(v(247)*v(2486)+v(2424)*v(264)+v&
&(231)*v(2851)+v(230)*v(3038)+v(228)*v(3049)+v(2461)*v(5842)))/5040d0
v(3258)=statev(6)*v(3060)+statev(8)*v(3082)+v(2895)*v(5531)
v(3203)=statev(7)*v(2895)+statev(5)*v(3082)+v(3060)*v(5533)
v(3093)=statev(4)*v(2895)+statev(9)*v(3060)+v(3082)*v(5532)
v(3059)=(7d0*(360d0*v(2542)+120d0*v(2938)+30d0*v(2971)+6d0*v(3004)+v(3048))+v(5541)*(v(247)*v(2483)+v(2422)*v(264)+v&
&(231)*v(2850)+v(230)*v(3037)+v(228)*v(3048)+v(2460)*v(5842)))/5040d0
v(3257)=statev(6)*v(3059)+statev(8)*v(3081)+v(2894)*v(5531)
v(3202)=statev(7)*v(2894)+statev(5)*v(3081)+v(3059)*v(5533)
v(3092)=statev(4)*v(2894)+statev(9)*v(3059)+v(3081)*v(5532)
v(3058)=(7d0*(360d0*v(2541)+120d0*v(2937)+30d0*v(2970)+6d0*v(3003)+v(3047))+v(5541)*(v(247)*v(2481)+v(2421)*v(264)+v&
&(231)*v(2849)+v(230)*v(3036)+v(228)*v(3047)+v(2458)*v(5842)))/5040d0
v(3256)=statev(6)*v(3058)+statev(8)*v(3080)+v(2893)*v(5531)
v(3201)=statev(7)*v(2893)+statev(5)*v(3080)+v(3058)*v(5533)
v(3091)=statev(4)*v(2893)+statev(9)*v(3058)+v(3080)*v(5532)
v(3057)=(7d0*(360d0*v(2540)+120d0*v(2936)+30d0*v(2969)+6d0*v(3002)+v(3046))+v(5541)*(v(247)*v(2479)+v(2420)*v(264)+v&
&(231)*v(2848)+v(230)*v(3035)+v(228)*v(3046)+v(2456)*v(5842)))/5040d0
v(3255)=statev(6)*v(3057)+statev(8)*v(3079)+v(2892)*v(5531)
v(3200)=statev(7)*v(2892)+statev(5)*v(3079)+v(3057)*v(5533)
v(3090)=statev(4)*v(2892)+statev(9)*v(3057)+v(3079)*v(5532)
v(3056)=(7d0*(360d0*v(2539)+120d0*v(2935)+30d0*v(2968)+6d0*v(3001)+v(3045))+v(5541)*(v(247)*v(2478)+v(2419)*v(264)+v&
&(231)*v(2847)+v(230)*v(3034)+v(228)*v(3045)+v(2455)*v(5842)))/5040d0
v(3254)=statev(6)*v(3056)+statev(8)*v(3078)+v(2891)*v(5531)
v(3199)=statev(7)*v(2891)+statev(5)*v(3078)+v(3056)*v(5533)
v(3089)=statev(4)*v(2891)+statev(9)*v(3056)+v(3078)*v(5532)
v(3055)=(7d0*(360d0*v(2538)+120d0*v(2934)+30d0*v(2967)+6d0*v(3000)+v(3044))+v(5541)*(v(247)*v(2475)+v(2418)*v(264)+v&
&(231)*v(2846)+v(230)*v(3033)+v(228)*v(3044)+v(2454)*v(5842)))/5040d0
v(3253)=statev(6)*v(3055)+statev(8)*v(3077)+v(2890)*v(5531)
v(3198)=statev(7)*v(2890)+statev(5)*v(3077)+v(3055)*v(5533)
v(3088)=statev(4)*v(2890)+statev(9)*v(3055)+v(3077)*v(5532)
v(3054)=(7d0*(360d0*v(2537)+120d0*v(2933)+30d0*v(2966)+6d0*v(2999)+v(3043))+v(5541)*(v(247)*v(2474)+v(2417)*v(264)+v&
&(231)*v(2845)+v(230)*v(3032)+v(228)*v(3043)+v(2453)*v(5842)))/5040d0
v(3252)=statev(6)*v(3054)+statev(8)*v(3076)+v(2889)*v(5531)
v(3197)=statev(7)*v(2889)+statev(5)*v(3076)+v(3054)*v(5533)
v(3087)=statev(4)*v(2889)+statev(9)*v(3054)+v(3076)*v(5532)
v(3053)=(7d0*(360d0*v(2536)+120d0*v(2932)+30d0*v(2965)+6d0*v(2998)+v(3042))+v(5541)*(v(247)*v(2471)+v(2416)*v(264)+v&
&(231)*v(2844)+v(230)*v(3031)+v(228)*v(3042)+v(2450)*v(5842)))/5040d0
v(3251)=statev(6)*v(3053)+statev(8)*v(3075)+v(2888)*v(5531)
v(3196)=statev(7)*v(2888)+statev(5)*v(3075)+v(3053)*v(5533)
v(3086)=statev(4)*v(2888)+statev(9)*v(3053)+v(3075)*v(5532)
v(3052)=(7d0*(360d0*v(2535)+120d0*v(2931)+30d0*v(2964)+6d0*v(2997)+v(3041))+v(5541)*(v(2469)*v(247)+v(2414)*v(264)+v&
&(231)*v(2843)+v(230)*v(3030)+v(228)*v(3041)+v(2448)*v(5842)))/5040d0
v(3250)=statev(6)*v(3052)+statev(8)*v(3074)+v(2887)*v(5531)
v(3195)=statev(7)*v(2887)+statev(5)*v(3074)+v(3052)*v(5533)
v(3085)=statev(4)*v(2887)+statev(9)*v(3052)+v(3074)*v(5532)
v(3051)=v(2534)/2d0+v(2930)/6d0+v(2963)/24d0+v(2996)/120d0+v(3040)/720d0+v(5836)+((v(2466)*v(247)+v(2445)*v(262)+v(2413&
&)*v(264)+v(231)*v(2842)+v(230)*v(3029)+v(228)*v(3040))*v(5541)+v(5537)*(v(230)*v(262)+v(5844)))/5040d0
v(3249)=statev(6)*v(3051)+statev(8)*v(3073)+v(2886)*v(5531)
v(3194)=statev(7)*v(2886)+statev(5)*v(3073)+v(3051)*v(5533)
v(3084)=statev(4)*v(2886)+statev(9)*v(3051)+v(3073)*v(5532)
v(284)=(7d0*(360d0*v(255)+120d0*v(257)+30d0*v(261)+6d0*v(263)+v(264))+v(5541)*(v(230)*v(5842)+v(5844)))/5040d0
v(283)=v(264)*v(5814)
v(289)=(2520d0*v(251)+840d0*v(253)+210d0*v(256)+42d0*v(259)+7d0*v(262)+v(283)+v(5837)*v(5842)+v(5845))/5040d0
v(266)=statev(4)*v(249)+statev(9)*v(284)+v(289)*v(5532)
v(269)=v(267)+v(268)+v(232)*v(371)
v(3127)=v(2555)+v(2621)+(v(2425)*v(269)+v(228)*v(3116))*v(5541)
v(3126)=v(2554)+v(2620)+(v(2424)*v(269)+v(228)*v(3114))*v(5541)
v(3125)=v(2553)+v(2619)+(v(2422)*v(269)+v(228)*v(3112))*v(5541)
v(3124)=v(2552)+v(2618)+(v(2421)*v(269)+v(228)*v(3110))*v(5541)
v(3123)=v(2551)+v(2617)+(v(2420)*v(269)+v(228)*v(3108))*v(5541)
v(3122)=v(2550)+v(2616)+(v(2419)*v(269)+v(228)*v(3106))*v(5541)
v(3121)=v(2549)+v(2615)+(v(2418)*v(269)+v(228)*v(3104))*v(5541)
v(3120)=v(2548)+v(2614)+(v(2417)*v(269)+v(228)*v(3102))*v(5541)
v(3119)=v(2547)+v(2613)+(v(2416)*v(269)+v(228)*v(3100))*v(5541)
v(3118)=v(2546)+v(2612)+(v(2414)*v(269)+v(228)*v(3098))*v(5541)
v(3117)=v(2545)+v(2611)+v(3096)*v(5846)+v(269)*v(5847)
v(272)=v(270)+v(271)+v(269)*v(5846)
v(3138)=v(2665)+v(2951)+(v(2425)*v(272)+v(228)*v(3127))*v(5541)
v(3137)=v(2664)+v(2950)+(v(2424)*v(272)+v(228)*v(3126))*v(5541)
v(3136)=v(2663)+v(2949)+(v(2422)*v(272)+v(228)*v(3125))*v(5541)
v(3135)=v(2662)+v(2948)+(v(2421)*v(272)+v(228)*v(3124))*v(5541)
v(3134)=v(2661)+v(2947)+(v(2420)*v(272)+v(228)*v(3123))*v(5541)
v(3133)=v(2660)+v(2946)+(v(2419)*v(272)+v(228)*v(3122))*v(5541)
v(3132)=v(2659)+v(2945)+(v(2418)*v(272)+v(228)*v(3121))*v(5541)
v(3131)=v(2658)+v(2944)+(v(2417)*v(272)+v(228)*v(3120))*v(5541)
v(3130)=v(2657)+v(2943)+(v(2416)*v(272)+v(228)*v(3119))*v(5541)
v(3129)=v(2656)+v(2942)+(v(2414)*v(272)+v(228)*v(3118))*v(5541)
v(3128)=v(2655)+v(2941)+v(3117)*v(5846)+v(272)*v(5847)
v(275)=v(273)+v(274)+v(272)*v(5846)
v(3149)=v(2742)+v(2984)+(v(2425)*v(275)+v(228)*v(3138))*v(5541)
v(3148)=v(2741)+v(2983)+(v(2424)*v(275)+v(228)*v(3137))*v(5541)
v(3147)=v(2740)+v(2982)+(v(2422)*v(275)+v(228)*v(3136))*v(5541)
v(3146)=v(2739)+v(2981)+(v(2421)*v(275)+v(228)*v(3135))*v(5541)
v(3145)=v(2738)+v(2980)+(v(2420)*v(275)+v(228)*v(3134))*v(5541)
v(3144)=v(2737)+v(2979)+(v(2419)*v(275)+v(228)*v(3133))*v(5541)
v(3143)=v(2736)+v(2978)+(v(2418)*v(275)+v(228)*v(3132))*v(5541)
v(3142)=v(2735)+v(2977)+(v(2417)*v(275)+v(228)*v(3131))*v(5541)
v(3141)=v(2734)+v(2976)+(v(2416)*v(275)+v(228)*v(3130))*v(5541)
v(3140)=v(2733)+v(2975)+(v(2414)*v(275)+v(228)*v(3129))*v(5541)
v(3139)=v(2732)+v(2974)+v(3128)*v(5846)+v(275)*v(5847)
v(278)=v(276)+v(277)+v(275)*v(5846)
v(3160)=v(2775)+v(3017)+(v(2425)*v(278)+v(228)*v(3149))*v(5541)
v(3159)=v(2774)+v(3016)+(v(2424)*v(278)+v(228)*v(3148))*v(5541)
v(3158)=v(2773)+v(3015)+(v(2422)*v(278)+v(228)*v(3147))*v(5541)
v(3157)=v(2772)+v(3014)+(v(2421)*v(278)+v(228)*v(3146))*v(5541)
v(3156)=v(2771)+v(3013)+(v(2420)*v(278)+v(228)*v(3145))*v(5541)
v(3155)=v(2770)+v(3012)+(v(2419)*v(278)+v(228)*v(3144))*v(5541)
v(3154)=v(2769)+v(3011)+(v(2418)*v(278)+v(228)*v(3143))*v(5541)
v(3153)=v(2768)+v(3010)+(v(2417)*v(278)+v(228)*v(3142))*v(5541)
v(3152)=v(2767)+v(3009)+(v(2416)*v(278)+v(228)*v(3141))*v(5541)
v(3151)=v(2766)+v(3008)+(v(2414)*v(278)+v(228)*v(3140))*v(5541)
v(3150)=v(2765)+v(3007)+v(3139)*v(5846)+v(278)*v(5847)
v(281)=v(279)+v(280)+v(278)*v(5846)
v(5848)=5040d0+v(281)
v(3171)=(v(2841)+v(3072)+2520d0*v(3116)+840d0*v(3127)+210d0*v(3138)+42d0*v(3149)+7d0*v(3160)+v(5541)*(v(228)*v(3160)+v&
&(2425)*v(5848)))/5040d0
v(3303)=statev(4)*v(2863)+statev(9)*v(3171)+v(3061)*v(5532)
v(3215)=statev(8)*v(3061)+statev(6)*v(3171)+v(2863)*v(5531)
v(3182)=statev(7)*v(2863)+statev(5)*v(3061)+v(3171)*v(5533)
v(3170)=(v(2840)+v(3071)+2520d0*v(3114)+840d0*v(3126)+210d0*v(3137)+42d0*v(3148)+7d0*v(3159)+v(5541)*(v(228)*v(3159)+v&
&(2424)*v(5848)))/5040d0
v(3302)=statev(4)*v(2862)+statev(9)*v(3170)+v(3060)*v(5532)
v(3214)=statev(8)*v(3060)+statev(6)*v(3170)+v(2862)*v(5531)
v(3181)=statev(7)*v(2862)+statev(5)*v(3060)+v(3170)*v(5533)
v(3169)=(v(2839)+v(3070)+2520d0*v(3112)+840d0*v(3125)+210d0*v(3136)+42d0*v(3147)+7d0*v(3158)+v(5541)*(v(228)*v(3158)+v&
&(2422)*v(5848)))/5040d0
v(3301)=statev(4)*v(2861)+statev(9)*v(3169)+v(3059)*v(5532)
v(3213)=statev(8)*v(3059)+statev(6)*v(3169)+v(2861)*v(5531)
v(3180)=statev(7)*v(2861)+statev(5)*v(3059)+v(3169)*v(5533)
v(3168)=(v(2838)+v(3069)+2520d0*v(3110)+840d0*v(3124)+210d0*v(3135)+42d0*v(3146)+7d0*v(3157)+v(5541)*(v(228)*v(3157)+v&
&(2421)*v(5848)))/5040d0
v(3300)=statev(4)*v(2860)+statev(9)*v(3168)+v(3058)*v(5532)
v(3212)=statev(8)*v(3058)+statev(6)*v(3168)+v(2860)*v(5531)
v(3179)=statev(7)*v(2860)+statev(5)*v(3058)+v(3168)*v(5533)
v(3167)=(v(2837)+v(3068)+2520d0*v(3108)+840d0*v(3123)+210d0*v(3134)+42d0*v(3145)+7d0*v(3156)+v(5541)*(v(228)*v(3156)+v&
&(2420)*v(5848)))/5040d0
v(3299)=statev(4)*v(2859)+statev(9)*v(3167)+v(3057)*v(5532)
v(3211)=statev(8)*v(3057)+statev(6)*v(3167)+v(2859)*v(5531)
v(3178)=statev(7)*v(2859)+statev(5)*v(3057)+v(3167)*v(5533)
v(3166)=(v(2836)+v(3067)+2520d0*v(3106)+840d0*v(3122)+210d0*v(3133)+42d0*v(3144)+7d0*v(3155)+v(5541)*(v(228)*v(3155)+v&
&(2419)*v(5848)))/5040d0
v(3298)=statev(4)*v(2858)+statev(9)*v(3166)+v(3056)*v(5532)
v(3210)=statev(8)*v(3056)+statev(6)*v(3166)+v(2858)*v(5531)
v(3177)=statev(7)*v(2858)+statev(5)*v(3056)+v(3166)*v(5533)
v(3165)=(v(2835)+v(3066)+2520d0*v(3104)+840d0*v(3121)+210d0*v(3132)+42d0*v(3143)+7d0*v(3154)+v(5541)*(v(228)*v(3154)+v&
&(2418)*v(5848)))/5040d0
v(3297)=statev(4)*v(2857)+statev(9)*v(3165)+v(3055)*v(5532)
v(3209)=statev(8)*v(3055)+statev(6)*v(3165)+v(2857)*v(5531)
v(3176)=statev(7)*v(2857)+statev(5)*v(3055)+v(3165)*v(5533)
v(3164)=(v(2834)+v(3065)+2520d0*v(3102)+840d0*v(3120)+210d0*v(3131)+42d0*v(3142)+7d0*v(3153)+v(5541)*(v(228)*v(3153)+v&
&(2417)*v(5848)))/5040d0
v(3296)=statev(4)*v(2856)+statev(9)*v(3164)+v(3054)*v(5532)
v(3208)=statev(8)*v(3054)+statev(6)*v(3164)+v(2856)*v(5531)
v(3175)=statev(7)*v(2856)+statev(5)*v(3054)+v(3164)*v(5533)
v(3163)=(v(2833)+v(3064)+2520d0*v(3100)+840d0*v(3119)+210d0*v(3130)+42d0*v(3141)+7d0*v(3152)+v(5541)*(v(228)*v(3152)+v&
&(2416)*v(5848)))/5040d0
v(3295)=statev(4)*v(2855)+statev(9)*v(3163)+v(3053)*v(5532)
v(3207)=statev(8)*v(3053)+statev(6)*v(3163)+v(2855)*v(5531)
v(3174)=statev(7)*v(2855)+statev(5)*v(3053)+v(3163)*v(5533)
v(3162)=(v(2832)+v(3063)+2520d0*v(3098)+840d0*v(3118)+210d0*v(3129)+42d0*v(3140)+7d0*v(3151)+v(5541)*(v(228)*v(3151)+v&
&(2414)*v(5848)))/5040d0
v(3294)=statev(4)*v(2854)+statev(9)*v(3162)+v(3052)*v(5532)
v(3206)=statev(8)*v(3052)+statev(6)*v(3162)+v(2854)*v(5531)
v(3173)=statev(7)*v(2854)+statev(5)*v(3052)+v(3162)*v(5533)
v(3161)=(v(2831)+v(3062)+2520d0*v(3096)+840d0*v(3117)+210d0*v(3128)+42d0*v(3139)+7d0*v(3150)+v(228)*(v(3150)*v(5541)+v&
&(5537)*v(5848))+v(5848)*v(5849))/5040d0
v(3293)=statev(4)*v(2853)+statev(9)*v(3161)+v(3051)*v(5532)
v(3205)=statev(8)*v(3051)+statev(6)*v(3161)+v(2853)*v(5531)
v(3172)=statev(7)*v(2853)+statev(5)*v(3051)+v(3161)*v(5533)
v(291)=(5040d0+2520d0*v(269)+840d0*v(272)+210d0*v(275)+42d0*v(278)+7d0*v(281)+v(282)+v(283)+v(5846)*v(5848))/5040d0
v(286)=statev(5)*v(284)+statev(7)*v(285)+v(291)*v(5533)
v(288)=statev(9)*v(285)+statev(4)*v(287)+v(249)*v(5532)
v(290)=statev(7)*v(249)+statev(5)*v(289)+v(284)*v(5533)
v(292)=statev(8)*v(284)+statev(6)*v(291)+v(285)*v(5531)
v(293)=statev(5)*v(249)+statev(7)*v(287)+v(285)*v(5533)
v(3248)=v(286)*v(2907)+v(248)*v(3182)-v(293)*v(3215)-v(292)*v(3226)
v(3247)=v(286)*v(2906)+v(248)*v(3181)-v(293)*v(3214)-v(292)*v(3225)
v(3246)=v(286)*v(2905)+v(248)*v(3180)-v(293)*v(3213)-v(292)*v(3224)
v(3245)=v(286)*v(2904)+v(248)*v(3179)-v(293)*v(3212)-v(292)*v(3223)
v(3244)=v(286)*v(2903)+v(248)*v(3178)-v(293)*v(3211)-v(292)*v(3222)
v(3243)=v(286)*v(2902)+v(248)*v(3177)-v(293)*v(3210)-v(292)*v(3221)
v(3242)=v(286)*v(2901)+v(248)*v(3176)-v(293)*v(3209)-v(292)*v(3220)
v(3241)=v(286)*v(2900)+v(248)*v(3175)-v(293)*v(3208)-v(292)*v(3219)
v(3240)=v(286)*v(2899)+v(248)*v(3174)-v(293)*v(3207)-v(292)*v(3218)
v(3239)=v(286)*v(2898)+v(248)*v(3173)-v(293)*v(3206)-v(292)*v(3217)
v(3238)=v(286)*v(2897)+v(248)*v(3172)-v(293)*v(3205)-v(292)*v(3216)
v(3237)=-(v(293)*v(3094))+v(290)*v(3193)+v(288)*v(3204)-v(266)*v(3226)
v(3236)=-(v(293)*v(3093))+v(290)*v(3192)+v(288)*v(3203)-v(266)*v(3225)
v(3235)=-(v(293)*v(3092))+v(290)*v(3191)+v(288)*v(3202)-v(266)*v(3224)
v(3234)=-(v(293)*v(3091))+v(290)*v(3190)+v(288)*v(3201)-v(266)*v(3223)
v(3233)=-(v(293)*v(3090))+v(290)*v(3189)+v(288)*v(3200)-v(266)*v(3222)
v(3232)=-(v(293)*v(3089))+v(290)*v(3188)+v(288)*v(3199)-v(266)*v(3221)
v(3231)=-(v(293)*v(3088))+v(290)*v(3187)+v(288)*v(3198)-v(266)*v(3220)
v(3230)=-(v(293)*v(3087))+v(290)*v(3186)+v(288)*v(3197)-v(266)*v(3219)
v(3229)=-(v(293)*v(3086))+v(290)*v(3185)+v(288)*v(3196)-v(266)*v(3218)
v(3228)=-(v(293)*v(3085))+v(290)*v(3184)+v(288)*v(3195)-v(266)*v(3217)
v(3227)=-(v(293)*v(3084))+v(290)*v(3183)+v(288)*v(3194)-v(266)*v(3216)
v(304)=v(288)*v(290)-v(266)*v(293)
v(300)=v(248)*v(286)-v(292)*v(293)
v(294)=statev(6)*v(284)+statev(8)*v(289)+v(249)*v(5531)
v(3292)=v(266)*v(2907)+v(248)*v(3094)-v(294)*v(3193)-v(288)*v(3259)
v(3291)=v(266)*v(2906)+v(248)*v(3093)-v(294)*v(3192)-v(288)*v(3258)
v(3290)=v(266)*v(2905)+v(248)*v(3092)-v(294)*v(3191)-v(288)*v(3257)
v(3289)=v(266)*v(2904)+v(248)*v(3091)-v(294)*v(3190)-v(288)*v(3256)
v(3288)=v(266)*v(2903)+v(248)*v(3090)-v(294)*v(3189)-v(288)*v(3255)
v(3287)=v(266)*v(2902)+v(248)*v(3089)-v(294)*v(3188)-v(288)*v(3254)
v(3286)=v(266)*v(2901)+v(248)*v(3088)-v(294)*v(3187)-v(288)*v(3253)
v(3285)=v(266)*v(2900)+v(248)*v(3087)-v(294)*v(3186)-v(288)*v(3252)
v(3284)=v(266)*v(2899)+v(248)*v(3086)-v(294)*v(3185)-v(288)*v(3251)
v(3283)=v(266)*v(2898)+v(248)*v(3085)-v(294)*v(3184)-v(288)*v(3250)
v(3282)=v(266)*v(2897)+v(248)*v(3084)-v(294)*v(3183)-v(288)*v(3249)
v(3281)=-(v(290)*v(2907))-v(248)*v(3204)+v(294)*v(3226)+v(293)*v(3259)
v(3280)=-(v(290)*v(2906))-v(248)*v(3203)+v(294)*v(3225)+v(293)*v(3258)
v(3279)=-(v(290)*v(2905))-v(248)*v(3202)+v(294)*v(3224)+v(293)*v(3257)
v(3278)=-(v(290)*v(2904))-v(248)*v(3201)+v(294)*v(3223)+v(293)*v(3256)
v(3277)=-(v(290)*v(2903))-v(248)*v(3200)+v(294)*v(3222)+v(293)*v(3255)
v(3276)=-(v(290)*v(2902))-v(248)*v(3199)+v(294)*v(3221)+v(293)*v(3254)
v(3275)=-(v(290)*v(2901))-v(248)*v(3198)+v(294)*v(3220)+v(293)*v(3253)
v(3274)=-(v(290)*v(2900))-v(248)*v(3197)+v(294)*v(3219)+v(293)*v(3252)
v(3273)=-(v(2899)*v(290))-v(248)*v(3196)+v(294)*v(3218)+v(293)*v(3251)
v(3272)=-(v(2898)*v(290))-v(248)*v(3195)+v(294)*v(3217)+v(293)*v(3250)
v(3271)=-(v(2897)*v(290))-v(248)*v(3194)+v(294)*v(3216)+v(293)*v(3249)
v(3270)=-(v(294)*v(3182))+v(292)*v(3204)+v(290)*v(3215)-v(286)*v(3259)
v(3269)=-(v(294)*v(3181))+v(292)*v(3203)+v(290)*v(3214)-v(286)*v(3258)
v(3268)=-(v(294)*v(3180))+v(292)*v(3202)+v(290)*v(3213)-v(286)*v(3257)
v(3267)=-(v(294)*v(3179))+v(292)*v(3201)+v(290)*v(3212)-v(286)*v(3256)
v(3266)=-(v(294)*v(3178))+v(292)*v(3200)+v(290)*v(3211)-v(286)*v(3255)
v(3265)=-(v(294)*v(3177))+v(292)*v(3199)+v(290)*v(3210)-v(286)*v(3254)
v(3264)=-(v(294)*v(3176))+v(292)*v(3198)+v(290)*v(3209)-v(286)*v(3253)
v(3263)=-(v(294)*v(3175))+v(292)*v(3197)+v(290)*v(3208)-v(286)*v(3252)
v(3262)=-(v(294)*v(3174))+v(292)*v(3196)+v(290)*v(3207)-v(286)*v(3251)
v(3261)=-(v(294)*v(3173))+v(292)*v(3195)+v(290)*v(3206)-v(286)*v(3250)
v(3260)=-(v(294)*v(3172))+v(292)*v(3194)+v(290)*v(3205)-v(286)*v(3249)
v(308)=v(290)*v(292)-v(286)*v(294)
v(306)=-(v(248)*v(290))+v(293)*v(294)
v(305)=v(248)*v(266)-v(288)*v(294)
v(295)=statev(4)*v(285)+statev(9)*v(291)+v(284)*v(5532)
v(3348)=v(292)*v(304)+v(286)*v(305)+v(295)*v(306)
v(3350)=1d0/v(3348)**2
v(3360)=-((v(305)*v(3182)+v(304)*v(3215)+v(292)*v(3237)+v(295)*v(3281)+v(286)*v(3292)+v(306)*v(3303))*v(3350))
v(5850)=v(3348)*v(3360)
v(5927)=v(3248)+v(300)*v(5850)
v(5896)=v(3281)+v(306)*v(5850)
v(5895)=v(3292)+v(305)*v(5850)
v(5894)=v(3237)+v(304)*v(5850)
v(5861)=v(3270)+v(308)*v(5850)
v(3359)=-((v(305)*v(3181)+v(304)*v(3214)+v(292)*v(3236)+v(295)*v(3280)+v(286)*v(3291)+v(306)*v(3302))*v(3350))
v(5851)=v(3348)*v(3359)
v(5930)=v(3247)+v(300)*v(5851)
v(5899)=v(3280)+v(306)*v(5851)
v(5898)=v(3291)+v(305)*v(5851)
v(5897)=v(3236)+v(304)*v(5851)
v(5864)=v(3269)+v(308)*v(5851)
v(3358)=-((v(305)*v(3180)+v(304)*v(3213)+v(292)*v(3235)+v(295)*v(3279)+v(286)*v(3290)+v(306)*v(3301))*v(3350))
v(5852)=v(3348)*v(3358)
v(5933)=v(3246)+v(300)*v(5852)
v(5902)=v(3279)+v(306)*v(5852)
v(5901)=v(3290)+v(305)*v(5852)
v(5900)=v(3235)+v(304)*v(5852)
v(5867)=v(3268)+v(308)*v(5852)
v(3357)=-((v(305)*v(3179)+v(304)*v(3212)+v(292)*v(3234)+v(295)*v(3278)+v(286)*v(3289)+v(306)*v(3300))*v(3350))
v(5853)=v(3348)*v(3357)
v(5936)=v(3245)+v(300)*v(5853)
v(5905)=v(3278)+v(306)*v(5853)
v(5904)=v(3289)+v(305)*v(5853)
v(5903)=v(3234)+v(304)*v(5853)
v(5870)=v(3267)+v(308)*v(5853)
v(3356)=-((v(305)*v(3178)+v(304)*v(3211)+v(292)*v(3233)+v(295)*v(3277)+v(286)*v(3288)+v(306)*v(3299))*v(3350))
v(5854)=v(3348)*v(3356)
v(5939)=v(3244)+v(300)*v(5854)
v(5908)=v(3277)+v(306)*v(5854)
v(5907)=v(3288)+v(305)*v(5854)
v(5906)=v(3233)+v(304)*v(5854)
v(5873)=v(3266)+v(308)*v(5854)
v(3355)=-((v(305)*v(3177)+v(304)*v(3210)+v(292)*v(3232)+v(295)*v(3276)+v(286)*v(3287)+v(306)*v(3298))*v(3350))
v(5855)=v(3348)*v(3355)
v(5942)=v(3243)+v(300)*v(5855)
v(5911)=v(3276)+v(306)*v(5855)
v(5910)=v(3287)+v(305)*v(5855)
v(5909)=v(3232)+v(304)*v(5855)
v(5876)=v(3265)+v(308)*v(5855)
v(3354)=-((v(305)*v(3176)+v(304)*v(3209)+v(292)*v(3231)+v(295)*v(3275)+v(286)*v(3286)+v(306)*v(3297))*v(3350))
v(5856)=v(3348)*v(3354)
v(5945)=v(3242)+v(300)*v(5856)
v(5914)=v(3275)+v(306)*v(5856)
v(5913)=v(3286)+v(305)*v(5856)
v(5912)=v(3231)+v(304)*v(5856)
v(5879)=v(3264)+v(308)*v(5856)
v(3353)=-((v(305)*v(3175)+v(304)*v(3208)+v(292)*v(3230)+v(295)*v(3274)+v(286)*v(3285)+v(306)*v(3296))*v(3350))
v(5857)=v(3348)*v(3353)
v(5948)=v(3241)+v(300)*v(5857)
v(5917)=v(3274)+v(306)*v(5857)
v(5916)=v(3285)+v(305)*v(5857)
v(5915)=v(3230)+v(304)*v(5857)
v(5882)=v(3263)+v(308)*v(5857)
v(3352)=-((v(305)*v(3174)+v(304)*v(3207)+v(292)*v(3229)+v(295)*v(3273)+v(286)*v(3284)+v(306)*v(3295))*v(3350))
v(5858)=v(3348)*v(3352)
v(5951)=v(3240)+v(300)*v(5858)
v(5920)=v(3273)+v(306)*v(5858)
v(5919)=v(3284)+v(305)*v(5858)
v(5918)=v(3229)+v(304)*v(5858)
v(5885)=v(3262)+v(308)*v(5858)
v(3351)=-((v(305)*v(3173)+v(304)*v(3206)+v(292)*v(3228)+v(295)*v(3272)+v(286)*v(3283)+v(306)*v(3294))*v(3350))
v(5859)=v(3348)*v(3351)
v(5954)=v(3239)+v(300)*v(5859)
v(5923)=v(3272)+v(306)*v(5859)
v(5922)=v(3283)+v(305)*v(5859)
v(5921)=v(3228)+v(304)*v(5859)
v(5888)=v(3261)+v(308)*v(5859)
v(3349)=-((v(305)*v(3172)+v(304)*v(3205)+v(292)*v(3227)+v(295)*v(3271)+v(286)*v(3282)+v(306)*v(3293))*v(3350))
v(5860)=v(3348)*v(3349)
v(5957)=v(3238)+v(300)*v(5860)
v(5926)=v(3271)+v(306)*v(5860)
v(5925)=v(3282)+v(305)*v(5860)
v(5924)=v(3227)+v(304)*v(5860)
v(5891)=v(3260)+v(308)*v(5860)
v(3347)=-(v(2907)*v(295))+v(292)*v(3193)+v(288)*v(3215)-v(248)*v(3303)
v(3346)=-(v(2906)*v(295))+v(292)*v(3192)+v(288)*v(3214)-v(248)*v(3302)
v(3345)=-(v(2905)*v(295))+v(292)*v(3191)+v(288)*v(3213)-v(248)*v(3301)
v(3344)=-(v(2904)*v(295))+v(292)*v(3190)+v(288)*v(3212)-v(248)*v(3300)
v(3343)=-(v(2903)*v(295))+v(292)*v(3189)+v(288)*v(3211)-v(248)*v(3299)
v(3342)=-(v(2902)*v(295))+v(292)*v(3188)+v(288)*v(3210)-v(248)*v(3298)
v(3341)=-(v(2901)*v(295))+v(292)*v(3187)+v(288)*v(3209)-v(248)*v(3297)
v(3340)=-(v(2900)*v(295))+v(292)*v(3186)+v(288)*v(3208)-v(248)*v(3296)
v(3339)=-(v(2899)*v(295))+v(292)*v(3185)+v(288)*v(3207)-v(248)*v(3295)
v(3338)=-(v(2898)*v(295))+v(292)*v(3184)+v(288)*v(3206)-v(248)*v(3294)
v(3337)=-(v(2897)*v(295))+v(292)*v(3183)+v(288)*v(3205)-v(248)*v(3293)
v(3336)=-(v(288)*v(3182))-v(286)*v(3193)+v(295)*v(3226)+v(293)*v(3303)
v(3335)=-(v(288)*v(3181))-v(286)*v(3192)+v(295)*v(3225)+v(293)*v(3302)
v(3334)=-(v(288)*v(3180))-v(286)*v(3191)+v(295)*v(3224)+v(293)*v(3301)
v(3333)=-(v(288)*v(3179))-v(286)*v(3190)+v(295)*v(3223)+v(293)*v(3300)
v(3332)=-(v(288)*v(3178))-v(286)*v(3189)+v(295)*v(3222)+v(293)*v(3299)
v(3331)=-(v(288)*v(3177))-v(286)*v(3188)+v(295)*v(3221)+v(293)*v(3298)
v(3330)=-(v(288)*v(3176))-v(286)*v(3187)+v(295)*v(3220)+v(293)*v(3297)
v(3329)=-(v(288)*v(3175))-v(286)*v(3186)+v(295)*v(3219)+v(293)*v(3296)
v(3328)=-(v(288)*v(3174))-v(286)*v(3185)+v(295)*v(3218)+v(293)*v(3295)
v(3327)=-(v(288)*v(3173))-v(286)*v(3184)+v(295)*v(3217)+v(293)*v(3294)
v(3326)=-(v(288)*v(3172))-v(286)*v(3183)+v(295)*v(3216)+v(293)*v(3293)
v(3325)=v(286)*v(3094)+v(266)*v(3182)-v(295)*v(3204)-v(290)*v(3303)
v(3324)=v(286)*v(3093)+v(266)*v(3181)-v(295)*v(3203)-v(290)*v(3302)
v(3323)=v(286)*v(3092)+v(266)*v(3180)-v(295)*v(3202)-v(290)*v(3301)
v(3322)=v(286)*v(3091)+v(266)*v(3179)-v(295)*v(3201)-v(290)*v(3300)
v(3321)=v(286)*v(3090)+v(266)*v(3178)-v(295)*v(3200)-v(290)*v(3299)
v(3320)=v(286)*v(3089)+v(266)*v(3177)-v(295)*v(3199)-v(290)*v(3298)
v(3319)=v(286)*v(3088)+v(266)*v(3176)-v(295)*v(3198)-v(290)*v(3297)
v(3318)=v(286)*v(3087)+v(266)*v(3175)-v(295)*v(3197)-v(290)*v(3296)
v(3317)=v(286)*v(3086)+v(266)*v(3174)-v(295)*v(3196)-v(290)*v(3295)
v(3316)=v(286)*v(3085)+v(266)*v(3173)-v(295)*v(3195)-v(290)*v(3294)
v(3315)=v(286)*v(3084)+v(266)*v(3172)-v(295)*v(3194)-v(290)*v(3293)
v(3314)=-(v(292)*v(3094))-v(266)*v(3215)+v(295)*v(3259)+v(294)*v(3303)
v(3313)=-(v(292)*v(3093))-v(266)*v(3214)+v(295)*v(3258)+v(294)*v(3302)
v(3312)=-(v(292)*v(3092))-v(266)*v(3213)+v(295)*v(3257)+v(294)*v(3301)
v(3311)=-(v(292)*v(3091))-v(266)*v(3212)+v(295)*v(3256)+v(294)*v(3300)
v(3310)=-(v(292)*v(3090))-v(266)*v(3211)+v(295)*v(3255)+v(294)*v(3299)
v(3309)=-(v(292)*v(3089))-v(266)*v(3210)+v(295)*v(3254)+v(294)*v(3298)
v(3308)=-(v(292)*v(3088))-v(266)*v(3209)+v(295)*v(3253)+v(294)*v(3297)
v(3307)=-(v(292)*v(3087))-v(266)*v(3208)+v(295)*v(3252)+v(294)*v(3296)
v(3306)=-(v(292)*v(3086))-v(266)*v(3207)+v(295)*v(3251)+v(294)*v(3295)
v(3305)=-(v(292)*v(3085))-v(266)*v(3206)+v(295)*v(3250)+v(294)*v(3294)
v(3304)=-(v(292)*v(3084))-v(266)*v(3205)+v(295)*v(3249)+v(294)*v(3293)
v(310)=-(v(266)*v(292))+v(294)*v(295)
v(5893)=v(3304)+v(310)*v(5860)
v(5890)=v(3305)+v(310)*v(5859)
v(5887)=v(3306)+v(310)*v(5858)
v(5884)=v(3307)+v(310)*v(5857)
v(5881)=v(3308)+v(310)*v(5856)
v(5878)=v(3309)+v(310)*v(5855)
v(5875)=v(3310)+v(310)*v(5854)
v(5872)=v(3311)+v(310)*v(5853)
v(5869)=v(3312)+v(310)*v(5852)
v(5866)=v(3313)+v(310)*v(5851)
v(5863)=v(3314)+v(310)*v(5850)
v(309)=v(266)*v(286)-v(290)*v(295)
v(5892)=v(3315)+v(309)*v(5860)
v(5889)=v(3316)+v(309)*v(5859)
v(5886)=v(3317)+v(309)*v(5858)
v(5883)=v(3318)+v(309)*v(5857)
v(5880)=v(3319)+v(309)*v(5856)
v(5877)=v(3320)+v(309)*v(5855)
v(5874)=v(3321)+v(309)*v(5854)
v(5871)=v(3322)+v(309)*v(5853)
v(5868)=v(3323)+v(309)*v(5852)
v(5865)=v(3324)+v(309)*v(5851)
v(5862)=v(3325)+v(309)*v(5850)
v(302)=-(v(286)*v(288))+v(293)*v(295)
v(5959)=v(3326)+v(302)*v(5860)
v(5956)=v(3327)+v(302)*v(5859)
v(5953)=v(3328)+v(302)*v(5858)
v(5950)=v(3329)+v(302)*v(5857)
v(5947)=v(3330)+v(302)*v(5856)
v(5944)=v(3331)+v(302)*v(5855)
v(5941)=v(3332)+v(302)*v(5854)
v(5938)=v(3333)+v(302)*v(5853)
v(5935)=v(3334)+v(302)*v(5852)
v(5932)=v(3335)+v(302)*v(5851)
v(5929)=v(3336)+v(302)*v(5850)
v(301)=v(288)*v(292)-v(248)*v(295)
v(5958)=v(3337)+v(301)*v(5860)
v(5955)=v(3338)+v(301)*v(5859)
v(5952)=v(3339)+v(301)*v(5858)
v(5949)=v(3340)+v(301)*v(5857)
v(5946)=v(3341)+v(301)*v(5856)
v(5943)=v(3342)+v(301)*v(5855)
v(5940)=v(3343)+v(301)*v(5854)
v(5937)=v(3344)+v(301)*v(5853)
v(5934)=v(3345)+v(301)*v(5852)
v(5931)=v(3346)+v(301)*v(5851)
v(5928)=v(3347)+v(301)*v(5850)
v(3459)=(Fnew(9)*v(5927)+Fnew(3)*v(5928)+Fnew(6)*v(5929))/v(3348)
v(3458)=(Fnew(9)*v(5930)+Fnew(3)*v(5931)+Fnew(6)*v(5932))/v(3348)
v(3457)=(Fnew(9)*v(5933)+Fnew(3)*v(5934)+Fnew(6)*v(5935))/v(3348)
v(3456)=(Fnew(9)*v(5936)+Fnew(3)*v(5937)+Fnew(6)*v(5938))/v(3348)
v(3455)=(Fnew(9)*v(5939)+Fnew(3)*v(5940)+Fnew(6)*v(5941))/v(3348)
v(3454)=(Fnew(9)*v(5942)+Fnew(3)*v(5943)+Fnew(6)*v(5944))/v(3348)
v(3453)=(Fnew(9)*v(5945)+Fnew(3)*v(5946)+Fnew(6)*v(5947))/v(3348)
v(3452)=(Fnew(9)*v(5948)+Fnew(3)*v(5949)+Fnew(6)*v(5950))/v(3348)
v(3451)=(Fnew(9)*v(5951)+Fnew(3)*v(5952)+Fnew(6)*v(5953))/v(3348)
v(3450)=(Fnew(9)*v(5954)+Fnew(3)*v(5955)+Fnew(6)*v(5956))/v(3348)
v(3449)=(Fnew(9)*v(5957)+Fnew(3)*v(5958)+Fnew(6)*v(5959))/v(3348)
v(3448)=(Fnew(2)*v(5861)+Fnew(8)*v(5862)+Fnew(5)*v(5863))/v(3348)
v(3447)=(Fnew(2)*v(5864)+Fnew(8)*v(5865)+Fnew(5)*v(5866))/v(3348)
v(3446)=(Fnew(2)*v(5867)+Fnew(8)*v(5868)+Fnew(5)*v(5869))/v(3348)
v(3445)=(Fnew(2)*v(5870)+Fnew(8)*v(5871)+Fnew(5)*v(5872))/v(3348)
v(3444)=(Fnew(2)*v(5873)+Fnew(8)*v(5874)+Fnew(5)*v(5875))/v(3348)
v(3443)=(Fnew(2)*v(5876)+Fnew(8)*v(5877)+Fnew(5)*v(5878))/v(3348)
v(3442)=(Fnew(2)*v(5879)+Fnew(8)*v(5880)+Fnew(5)*v(5881))/v(3348)
v(3441)=(Fnew(2)*v(5882)+Fnew(8)*v(5883)+Fnew(5)*v(5884))/v(3348)
v(3440)=(Fnew(2)*v(5885)+Fnew(8)*v(5886)+Fnew(5)*v(5887))/v(3348)
v(3439)=(Fnew(2)*v(5888)+Fnew(8)*v(5889)+Fnew(5)*v(5890))/v(3348)
v(3438)=(Fnew(2)*v(5891)+Fnew(8)*v(5892)+Fnew(5)*v(5893))/v(3348)
v(3437)=(Fnew(1)*v(5894)+Fnew(7)*v(5895)+Fnew(4)*v(5896))/v(3348)
v(3436)=(Fnew(1)*v(5897)+Fnew(7)*v(5898)+Fnew(4)*v(5899))/v(3348)
v(3435)=(Fnew(1)*v(5900)+Fnew(7)*v(5901)+Fnew(4)*v(5902))/v(3348)
v(3434)=(Fnew(1)*v(5903)+Fnew(7)*v(5904)+Fnew(4)*v(5905))/v(3348)
v(3433)=(Fnew(1)*v(5906)+Fnew(7)*v(5907)+Fnew(4)*v(5908))/v(3348)
v(3432)=(Fnew(1)*v(5909)+Fnew(7)*v(5910)+Fnew(4)*v(5911))/v(3348)
v(3431)=(Fnew(1)*v(5912)+Fnew(7)*v(5913)+Fnew(4)*v(5914))/v(3348)
v(3430)=(Fnew(1)*v(5915)+Fnew(7)*v(5916)+Fnew(4)*v(5917))/v(3348)
v(3429)=(Fnew(1)*v(5918)+Fnew(7)*v(5919)+Fnew(4)*v(5920))/v(3348)
v(3428)=(Fnew(1)*v(5921)+Fnew(7)*v(5922)+Fnew(4)*v(5923))/v(3348)
v(3427)=(Fnew(1)*v(5924)+Fnew(7)*v(5925)+Fnew(4)*v(5926))/v(3348)
v(3426)=(Fnew(9)*v(5861)+Fnew(6)*v(5862)+Fnew(3)*v(5863))/v(3348)
v(3425)=(Fnew(9)*v(5864)+Fnew(6)*v(5865)+Fnew(3)*v(5866))/v(3348)
v(3424)=(Fnew(9)*v(5867)+Fnew(6)*v(5868)+Fnew(3)*v(5869))/v(3348)
v(3423)=(Fnew(9)*v(5870)+Fnew(6)*v(5871)+Fnew(3)*v(5872))/v(3348)
v(3422)=(Fnew(9)*v(5873)+Fnew(6)*v(5874)+Fnew(3)*v(5875))/v(3348)
v(3421)=(Fnew(9)*v(5876)+Fnew(6)*v(5877)+Fnew(3)*v(5878))/v(3348)
v(3420)=(Fnew(9)*v(5879)+Fnew(6)*v(5880)+Fnew(3)*v(5881))/v(3348)
v(3419)=(Fnew(9)*v(5882)+Fnew(6)*v(5883)+Fnew(3)*v(5884))/v(3348)
v(3418)=(Fnew(9)*v(5885)+Fnew(6)*v(5886)+Fnew(3)*v(5887))/v(3348)
v(3417)=(Fnew(9)*v(5888)+Fnew(6)*v(5889)+Fnew(3)*v(5890))/v(3348)
v(3416)=(Fnew(9)*v(5891)+Fnew(6)*v(5892)+Fnew(3)*v(5893))/v(3348)
v(3415)=(Fnew(8)*v(5894)+Fnew(5)*v(5895)+Fnew(2)*v(5896))/v(3348)
v(3414)=(Fnew(8)*v(5897)+Fnew(5)*v(5898)+Fnew(2)*v(5899))/v(3348)
v(3413)=(Fnew(8)*v(5900)+Fnew(5)*v(5901)+Fnew(2)*v(5902))/v(3348)
v(3412)=(Fnew(8)*v(5903)+Fnew(5)*v(5904)+Fnew(2)*v(5905))/v(3348)
v(3411)=(Fnew(8)*v(5906)+Fnew(5)*v(5907)+Fnew(2)*v(5908))/v(3348)
v(3410)=(Fnew(8)*v(5909)+Fnew(5)*v(5910)+Fnew(2)*v(5911))/v(3348)
v(3409)=(Fnew(8)*v(5912)+Fnew(5)*v(5913)+Fnew(2)*v(5914))/v(3348)
v(3408)=(Fnew(8)*v(5915)+Fnew(5)*v(5916)+Fnew(2)*v(5917))/v(3348)
v(3407)=(Fnew(8)*v(5918)+Fnew(5)*v(5919)+Fnew(2)*v(5920))/v(3348)
v(3406)=(Fnew(8)*v(5921)+Fnew(5)*v(5922)+Fnew(2)*v(5923))/v(3348)
v(3405)=(Fnew(8)*v(5924)+Fnew(5)*v(5925)+Fnew(2)*v(5926))/v(3348)
v(3404)=(Fnew(4)*v(5927)+Fnew(7)*v(5928)+Fnew(1)*v(5929))/v(3348)
v(3403)=(Fnew(4)*v(5930)+Fnew(7)*v(5931)+Fnew(1)*v(5932))/v(3348)
v(3402)=(Fnew(4)*v(5933)+Fnew(7)*v(5934)+Fnew(1)*v(5935))/v(3348)
v(3401)=(Fnew(4)*v(5936)+Fnew(7)*v(5937)+Fnew(1)*v(5938))/v(3348)
v(3400)=(Fnew(4)*v(5939)+Fnew(7)*v(5940)+Fnew(1)*v(5941))/v(3348)
v(3399)=(Fnew(4)*v(5942)+Fnew(7)*v(5943)+Fnew(1)*v(5944))/v(3348)
v(3398)=(Fnew(4)*v(5945)+Fnew(7)*v(5946)+Fnew(1)*v(5947))/v(3348)
v(3397)=(Fnew(4)*v(5948)+Fnew(7)*v(5949)+Fnew(1)*v(5950))/v(3348)
v(3396)=(Fnew(4)*v(5951)+Fnew(7)*v(5952)+Fnew(1)*v(5953))/v(3348)
v(3395)=(Fnew(4)*v(5954)+Fnew(7)*v(5955)+Fnew(1)*v(5956))/v(3348)
v(3394)=(Fnew(4)*v(5957)+Fnew(7)*v(5958)+Fnew(1)*v(5959))/v(3348)
v(3393)=(Fnew(6)*v(5894)+Fnew(3)*v(5895)+Fnew(9)*v(5896))/v(3348)
v(3392)=(Fnew(6)*v(5897)+Fnew(3)*v(5898)+Fnew(9)*v(5899))/v(3348)
v(3391)=(Fnew(6)*v(5900)+Fnew(3)*v(5901)+Fnew(9)*v(5902))/v(3348)
v(3390)=(Fnew(6)*v(5903)+Fnew(3)*v(5904)+Fnew(9)*v(5905))/v(3348)
v(3389)=(Fnew(6)*v(5906)+Fnew(3)*v(5907)+Fnew(9)*v(5908))/v(3348)
v(3388)=(Fnew(6)*v(5909)+Fnew(3)*v(5910)+Fnew(9)*v(5911))/v(3348)
v(3387)=(Fnew(6)*v(5912)+Fnew(3)*v(5913)+Fnew(9)*v(5914))/v(3348)
v(3386)=(Fnew(6)*v(5915)+Fnew(3)*v(5916)+Fnew(9)*v(5917))/v(3348)
v(3385)=(Fnew(6)*v(5918)+Fnew(3)*v(5919)+Fnew(9)*v(5920))/v(3348)
v(3384)=(Fnew(6)*v(5921)+Fnew(3)*v(5922)+Fnew(9)*v(5923))/v(3348)
v(3383)=(Fnew(6)*v(5924)+Fnew(3)*v(5925)+Fnew(9)*v(5926))/v(3348)
v(3382)=(Fnew(2)*v(5927)+Fnew(5)*v(5928)+Fnew(8)*v(5929))/v(3348)
v(3381)=(Fnew(2)*v(5930)+Fnew(5)*v(5931)+Fnew(8)*v(5932))/v(3348)
v(3380)=(Fnew(2)*v(5933)+Fnew(5)*v(5934)+Fnew(8)*v(5935))/v(3348)
v(3379)=(Fnew(2)*v(5936)+Fnew(5)*v(5937)+Fnew(8)*v(5938))/v(3348)
v(3378)=(Fnew(2)*v(5939)+Fnew(5)*v(5940)+Fnew(8)*v(5941))/v(3348)
v(3377)=(Fnew(2)*v(5942)+Fnew(5)*v(5943)+Fnew(8)*v(5944))/v(3348)
v(3376)=(Fnew(2)*v(5945)+Fnew(5)*v(5946)+Fnew(8)*v(5947))/v(3348)
v(3375)=(Fnew(2)*v(5948)+Fnew(5)*v(5949)+Fnew(8)*v(5950))/v(3348)
v(3374)=(Fnew(2)*v(5951)+Fnew(5)*v(5952)+Fnew(8)*v(5953))/v(3348)
v(3373)=(Fnew(2)*v(5954)+Fnew(5)*v(5955)+Fnew(8)*v(5956))/v(3348)
v(3372)=(Fnew(2)*v(5957)+Fnew(5)*v(5958)+Fnew(8)*v(5959))/v(3348)
v(3371)=(Fnew(4)*v(5861)+Fnew(1)*v(5862)+Fnew(7)*v(5863))/v(3348)
v(3370)=(Fnew(4)*v(5864)+Fnew(1)*v(5865)+Fnew(7)*v(5866))/v(3348)
v(3369)=(Fnew(4)*v(5867)+Fnew(1)*v(5868)+Fnew(7)*v(5869))/v(3348)
v(3368)=(Fnew(4)*v(5870)+Fnew(1)*v(5871)+Fnew(7)*v(5872))/v(3348)
v(3367)=(Fnew(4)*v(5873)+Fnew(1)*v(5874)+Fnew(7)*v(5875))/v(3348)
v(3366)=(Fnew(4)*v(5876)+Fnew(1)*v(5877)+Fnew(7)*v(5878))/v(3348)
v(3365)=(Fnew(4)*v(5879)+Fnew(1)*v(5880)+Fnew(7)*v(5881))/v(3348)
v(3364)=(Fnew(4)*v(5882)+Fnew(1)*v(5883)+Fnew(7)*v(5884))/v(3348)
v(3363)=(Fnew(4)*v(5885)+Fnew(1)*v(5886)+Fnew(7)*v(5887))/v(3348)
v(3362)=(Fnew(4)*v(5888)+Fnew(1)*v(5889)+Fnew(7)*v(5890))/v(3348)
v(3361)=(Fnew(4)*v(5891)+Fnew(1)*v(5892)+Fnew(7)*v(5893))/v(3348)
v(979)=v(306)/v(3348)
v(978)=v(304)/v(3348)
v(977)=v(305)/v(3348)
v(976)=v(302)/v(3348)
v(975)=v(301)/v(3348)
v(974)=v(300)/v(3348)
v(973)=v(310)/v(3348)
v(972)=v(308)/v(3348)
v(971)=v(309)/v(3348)
v(297)=(Fnew(4)*v(308)+Fnew(1)*v(309)+Fnew(7)*v(310))/v(3348)
v(5960)=2d0*v(297)
v(986)=v(5960)*v(973)
v(995)=-v(986)/3d0
v(983)=v(5960)*v(972)
v(992)=-v(983)/3d0
v(980)=v(5960)*v(971)
v(989)=-v(980)/3d0
v(298)=(Fnew(2)*v(300)+Fnew(5)*v(301)+Fnew(8)*v(302))/v(3348)
v(5961)=2d0*v(298)
v(1005)=v(5961)*v(976)
v(1014)=-v(1005)/3d0
v(1002)=v(5961)*v(975)
v(1011)=-v(1002)/3d0
v(999)=v(5961)*v(974)
v(1008)=-v(999)/3d0
v(299)=(Fnew(6)*v(304)+Fnew(3)*v(305)+Fnew(9)*v(306))/v(3348)
v(5962)=2d0*v(299)
v(1024)=v(5962)*v(979)
v(1033)=-v(1024)/3d0
v(1021)=v(5962)*v(978)
v(1030)=-v(1021)/3d0
v(1018)=v(5962)*v(977)
v(1027)=-v(1018)/3d0
v(303)=(Fnew(4)*v(300)+Fnew(7)*v(301)+Fnew(1)*v(302))/v(3348)
v(5963)=2d0*v(303)
v(1040)=v(303)*v(973)+v(297)*v(975)
v(1037)=v(303)*v(972)+v(297)*v(974)
v(1034)=v(303)*v(971)+v(297)*v(976)
v(1004)=v(5963)*v(975)
v(1013)=-v(1004)/3d0
v(1001)=v(5963)*v(974)
v(1010)=-v(1001)/3d0
v(998)=v(5963)*v(976)
v(1007)=-v(998)/3d0
v(307)=(Fnew(8)*v(304)+Fnew(5)*v(305)+Fnew(2)*v(306))/v(3348)
v(5964)=2d0*v(307)
v(1068)=v(307)*v(976)+v(298)*v(978)
v(1065)=v(307)*v(975)+v(298)*v(977)
v(1062)=v(307)*v(974)+v(298)*v(979)
v(1023)=v(5964)*v(978)
v(1032)=-v(1023)/3d0
v(1020)=v(5964)*v(977)
v(1029)=-v(1020)/3d0
v(1017)=v(5964)*v(979)
v(1026)=-v(1017)/3d0
v(311)=(Fnew(9)*v(308)+Fnew(6)*v(309)+Fnew(3)*v(310))/v(3348)
v(5965)=2d0*v(311)
v(1096)=v(299)*v(972)+v(311)*v(979)
v(1093)=v(299)*v(971)+v(311)*v(978)
v(1090)=v(299)*v(973)+v(311)*v(977)
v(988)=v(5965)*v(972)
v(997)=-v(988)/3d0
v(985)=v(5965)*v(971)
v(994)=-v(985)/3d0
v(982)=v(5965)*v(973)
v(991)=-v(982)/3d0
v(312)=(Fnew(1)*v(304)+Fnew(7)*v(305)+Fnew(4)*v(306))/v(3348)
v(5966)=2d0*v(312)
v(3514)=2d0*(v(299)*v(3393)+v(307)*v(3415)+v(312)*v(3437))
v(3525)=-v(3514)/3d0
v(3513)=2d0*(v(299)*v(3392)+v(307)*v(3414)+v(312)*v(3436))
v(3524)=-v(3513)/3d0
v(3512)=2d0*(v(299)*v(3391)+v(307)*v(3413)+v(312)*v(3435))
v(3523)=-v(3512)/3d0
v(3511)=2d0*(v(299)*v(3390)+v(307)*v(3412)+v(312)*v(3434))
v(3522)=-v(3511)/3d0
v(3510)=2d0*(v(299)*v(3389)+v(307)*v(3411)+v(312)*v(3433))
v(3521)=-v(3510)/3d0
v(3509)=2d0*(v(299)*v(3388)+v(307)*v(3410)+v(312)*v(3432))
v(3520)=-v(3509)/3d0
v(3508)=2d0*(v(299)*v(3387)+v(307)*v(3409)+v(312)*v(3431))
v(3519)=-v(3508)/3d0
v(3507)=2d0*(v(299)*v(3386)+v(307)*v(3408)+v(312)*v(3430))
v(3518)=-v(3507)/3d0
v(3506)=2d0*(v(299)*v(3385)+v(307)*v(3407)+v(312)*v(3429))
v(3517)=-v(3506)/3d0
v(3505)=2d0*(v(299)*v(3384)+v(307)*v(3406)+v(312)*v(3428))
v(3516)=-v(3505)/3d0
v(3504)=2d0*(v(299)*v(3383)+v(307)*v(3405)+v(312)*v(3427))
v(3515)=-v(3504)/3d0
v(1094)=v(312)*v(973)+v(297)*v(977)
v(1091)=v(312)*v(972)+v(297)*v(979)
v(1088)=v(312)*v(971)+v(297)*v(978)
v(1067)=v(312)*v(975)+v(303)*v(977)
v(1064)=v(312)*v(974)+v(303)*v(979)
v(1061)=v(312)*v(976)+v(303)*v(978)
v(1022)=v(5966)*v(977)
v(1031)=-v(1022)/3d0
v(1019)=v(5966)*v(979)
v(1028)=-v(1019)/3d0
v(1016)=v(5966)*v(978)
v(1025)=-v(1016)/3d0
v(313)=(Fnew(2)*v(308)+Fnew(8)*v(309)+Fnew(5)*v(310))/v(3348)
v(5967)=2d0*v(313)
v(3602)=v(312)*v(3371)+v(311)*v(3393)+v(313)*v(3415)+v(299)*v(3426)+v(297)*v(3437)+v(307)*v(3448)
v(3601)=v(312)*v(3370)+v(311)*v(3392)+v(313)*v(3414)+v(299)*v(3425)+v(297)*v(3436)+v(307)*v(3447)
v(3600)=v(312)*v(3369)+v(311)*v(3391)+v(313)*v(3413)+v(299)*v(3424)+v(297)*v(3435)+v(307)*v(3446)
v(3599)=v(312)*v(3368)+v(311)*v(3390)+v(313)*v(3412)+v(299)*v(3423)+v(297)*v(3434)+v(307)*v(3445)
v(3598)=v(312)*v(3367)+v(311)*v(3389)+v(313)*v(3411)+v(299)*v(3422)+v(297)*v(3433)+v(307)*v(3444)
v(3597)=v(312)*v(3366)+v(311)*v(3388)+v(313)*v(3410)+v(299)*v(3421)+v(297)*v(3432)+v(307)*v(3443)
v(3596)=v(312)*v(3365)+v(311)*v(3387)+v(313)*v(3409)+v(299)*v(3420)+v(297)*v(3431)+v(307)*v(3442)
v(3595)=v(312)*v(3364)+v(311)*v(3386)+v(313)*v(3408)+v(299)*v(3419)+v(297)*v(3430)+v(307)*v(3441)
v(3594)=v(312)*v(3363)+v(311)*v(3385)+v(313)*v(3407)+v(299)*v(3418)+v(297)*v(3429)+v(307)*v(3440)
v(3593)=v(312)*v(3362)+v(311)*v(3384)+v(313)*v(3406)+v(299)*v(3417)+v(297)*v(3428)+v(307)*v(3439)
v(3592)=v(312)*v(3361)+v(311)*v(3383)+v(313)*v(3405)+v(299)*v(3416)+v(297)*v(3427)+v(307)*v(3438)
v(3470)=2d0*(v(297)*v(3371)+v(311)*v(3426)+v(313)*v(3448))
v(3481)=-v(3470)/3d0
v(3469)=2d0*(v(297)*v(3370)+v(311)*v(3425)+v(313)*v(3447))
v(3480)=-v(3469)/3d0
v(3468)=2d0*(v(297)*v(3369)+v(311)*v(3424)+v(313)*v(3446))
v(3479)=-v(3468)/3d0
v(3467)=2d0*(v(297)*v(3368)+v(311)*v(3423)+v(313)*v(3445))
v(3478)=-v(3467)/3d0
v(3466)=2d0*(v(297)*v(3367)+v(311)*v(3422)+v(313)*v(3444))
v(3477)=-v(3466)/3d0
v(3465)=2d0*(v(297)*v(3366)+v(311)*v(3421)+v(313)*v(3443))
v(3476)=-v(3465)/3d0
v(3464)=2d0*(v(297)*v(3365)+v(311)*v(3420)+v(313)*v(3442))
v(3475)=-v(3464)/3d0
v(3463)=2d0*(v(297)*v(3364)+v(311)*v(3419)+v(313)*v(3441))
v(3474)=-v(3463)/3d0
v(3462)=2d0*(v(297)*v(3363)+v(311)*v(3418)+v(313)*v(3440))
v(3473)=-v(3462)/3d0
v(3461)=2d0*(v(297)*v(3362)+v(311)*v(3417)+v(313)*v(3439))
v(3472)=-v(3461)/3d0
v(3460)=2d0*(v(297)*v(3361)+v(311)*v(3416)+v(313)*v(3438))
v(3471)=-v(3460)/3d0
v(1095)=v(307)*v(971)+v(313)*v(978)
v(1092)=v(307)*v(973)+v(313)*v(977)
v(1089)=v(307)*v(972)+v(313)*v(979)
v(1041)=v(298)*v(971)+v(313)*v(976)
v(1038)=v(298)*v(973)+v(313)*v(975)
v(1035)=v(298)*v(972)+v(313)*v(974)
v(987)=v(5967)*v(971)
v(996)=-v(987)/3d0
v(984)=v(5967)*v(973)
v(993)=-v(984)/3d0
v(981)=v(5967)*v(972)
v(990)=-v(981)/3d0
v(314)=(Fnew(9)*v(300)+Fnew(3)*v(301)+Fnew(6)*v(302))/v(3348)
v(5968)=2d0*v(314)
v(3569)=v(307)*v(3382)+v(314)*v(3393)+v(312)*v(3404)+v(298)*v(3415)+v(303)*v(3437)+v(299)*v(3459)
v(3568)=v(307)*v(3381)+v(314)*v(3392)+v(312)*v(3403)+v(298)*v(3414)+v(303)*v(3436)+v(299)*v(3458)
v(3567)=v(307)*v(3380)+v(314)*v(3391)+v(312)*v(3402)+v(298)*v(3413)+v(303)*v(3435)+v(299)*v(3457)
v(3566)=v(307)*v(3379)+v(314)*v(3390)+v(312)*v(3401)+v(298)*v(3412)+v(303)*v(3434)+v(299)*v(3456)
v(3565)=v(307)*v(3378)+v(314)*v(3389)+v(312)*v(3400)+v(298)*v(3411)+v(303)*v(3433)+v(299)*v(3455)
v(3564)=v(307)*v(3377)+v(314)*v(3388)+v(312)*v(3399)+v(298)*v(3410)+v(303)*v(3432)+v(299)*v(3454)
v(3563)=v(307)*v(3376)+v(314)*v(3387)+v(312)*v(3398)+v(298)*v(3409)+v(303)*v(3431)+v(299)*v(3453)
v(3562)=v(307)*v(3375)+v(314)*v(3386)+v(312)*v(3397)+v(298)*v(3408)+v(303)*v(3430)+v(299)*v(3452)
v(3561)=v(307)*v(3374)+v(314)*v(3385)+v(312)*v(3396)+v(298)*v(3407)+v(303)*v(3429)+v(299)*v(3451)
v(3560)=v(307)*v(3373)+v(314)*v(3384)+v(312)*v(3395)+v(298)*v(3406)+v(303)*v(3428)+v(299)*v(3450)
v(3559)=v(307)*v(3372)+v(314)*v(3383)+v(312)*v(3394)+v(298)*v(3405)+v(303)*v(3427)+v(299)*v(3449)
v(3536)=v(303)*v(3371)+v(313)*v(3382)+v(297)*v(3404)+v(314)*v(3426)+v(298)*v(3448)+v(311)*v(3459)
v(3535)=v(303)*v(3370)+v(313)*v(3381)+v(297)*v(3403)+v(314)*v(3425)+v(298)*v(3447)+v(311)*v(3458)
v(3534)=v(303)*v(3369)+v(313)*v(3380)+v(297)*v(3402)+v(314)*v(3424)+v(298)*v(3446)+v(311)*v(3457)
v(3533)=v(303)*v(3368)+v(313)*v(3379)+v(297)*v(3401)+v(314)*v(3423)+v(298)*v(3445)+v(311)*v(3456)
v(3532)=v(303)*v(3367)+v(313)*v(3378)+v(297)*v(3400)+v(314)*v(3422)+v(298)*v(3444)+v(311)*v(3455)
v(3531)=v(303)*v(3366)+v(313)*v(3377)+v(297)*v(3399)+v(314)*v(3421)+v(298)*v(3443)+v(311)*v(3454)
v(3530)=v(303)*v(3365)+v(313)*v(3376)+v(297)*v(3398)+v(314)*v(3420)+v(298)*v(3442)+v(311)*v(3453)
v(3529)=v(303)*v(3364)+v(313)*v(3375)+v(297)*v(3397)+v(314)*v(3419)+v(298)*v(3441)+v(311)*v(3452)
v(3528)=v(303)*v(3363)+v(313)*v(3374)+v(297)*v(3396)+v(314)*v(3418)+v(298)*v(3440)+v(311)*v(3451)
v(3527)=v(303)*v(3362)+v(313)*v(3373)+v(297)*v(3395)+v(314)*v(3417)+v(298)*v(3439)+v(311)*v(3450)
v(3526)=v(303)*v(3361)+v(313)*v(3372)+v(297)*v(3394)+v(314)*v(3416)+v(298)*v(3438)+v(311)*v(3449)
v(3492)=2d0*(v(298)*v(3382)+v(303)*v(3404)+v(314)*v(3459))
v(3503)=-v(3492)/3d0
v(3491)=2d0*(v(298)*v(3381)+v(303)*v(3403)+v(314)*v(3458))
v(3502)=-v(3491)/3d0
v(3490)=2d0*(v(298)*v(3380)+v(303)*v(3402)+v(314)*v(3457))
v(3501)=-v(3490)/3d0
v(3489)=2d0*(v(298)*v(3379)+v(303)*v(3401)+v(314)*v(3456))
v(3500)=-v(3489)/3d0
v(3488)=2d0*(v(298)*v(3378)+v(303)*v(3400)+v(314)*v(3455))
v(3499)=-v(3488)/3d0
v(3487)=2d0*(v(298)*v(3377)+v(303)*v(3399)+v(314)*v(3454))
v(3498)=-v(3487)/3d0
v(3486)=2d0*(v(298)*v(3376)+v(303)*v(3398)+v(314)*v(3453))
v(3497)=-v(3486)/3d0
v(3485)=2d0*(v(298)*v(3375)+v(303)*v(3397)+v(314)*v(3452))
v(3496)=-v(3485)/3d0
v(3484)=2d0*(v(298)*v(3374)+v(303)*v(3396)+v(314)*v(3451))
v(3495)=-v(3484)/3d0
v(3483)=2d0*(v(298)*v(3373)+v(303)*v(3395)+v(314)*v(3450))
v(3494)=-v(3483)/3d0
v(3482)=2d0*(v(298)*v(3372)+v(303)*v(3394)+v(314)*v(3449))
v(3493)=-v(3482)/3d0
v(1069)=v(299)*v(974)+v(314)*v(979)
v(1066)=v(299)*v(976)+v(314)*v(978)
v(1063)=v(299)*v(975)+v(314)*v(977)
v(1042)=v(314)*v(972)+v(311)*v(974)
v(1039)=v(314)*v(971)+v(311)*v(976)
v(1036)=v(314)*v(973)+v(311)*v(975)
v(1006)=v(5968)*v(974)
v(1015)=-v(1006)/3d0
v(1003)=v(5968)*v(976)
v(1012)=-v(1003)/3d0
v(1000)=v(5968)*v(975)
v(1009)=-v(1000)/3d0
v(315)=(v(297)*v(297))+(v(311)*v(311))+(v(313)*v(313))
v(335)=-v(315)/3d0
v(316)=(v(298)*v(298))+(v(303)*v(303))+(v(314)*v(314))
v(336)=-v(316)/3d0
v(317)=(v(299)*v(299))+(v(307)*v(307))+(v(312)*v(312))
v(1185)=(2d0/3d0)*v(317)+v(335)+v(336)
v(328)=-v(317)/3d0
v(1195)=(2d0/3d0)*v(316)+v(328)+v(335)
v(1175)=(2d0/3d0)*v(315)+v(328)+v(336)
v(318)=v(297)*v(303)+v(298)*v(313)+v(311)*v(314)
v(5969)=2d0*v(318)
v(3547)=v(3536)*v(5969)
v(3558)=v(316)*v(3470)+v(315)*v(3492)-v(3547)
v(3546)=v(3535)*v(5969)
v(3557)=v(316)*v(3469)+v(315)*v(3491)-v(3546)
v(3545)=v(3534)*v(5969)
v(3556)=v(316)*v(3468)+v(315)*v(3490)-v(3545)
v(3544)=v(3533)*v(5969)
v(3555)=v(316)*v(3467)+v(315)*v(3489)-v(3544)
v(3543)=v(3532)*v(5969)
v(3554)=v(316)*v(3466)+v(315)*v(3488)-v(3543)
v(3542)=v(3531)*v(5969)
v(3553)=v(316)*v(3465)+v(315)*v(3487)-v(3542)
v(3541)=v(3530)*v(5969)
v(3552)=v(316)*v(3464)+v(315)*v(3486)-v(3541)
v(3540)=v(3529)*v(5969)
v(3551)=v(316)*v(3463)+v(315)*v(3485)-v(3540)
v(3539)=v(3528)*v(5969)
v(3550)=v(316)*v(3462)+v(315)*v(3484)-v(3539)
v(3538)=v(3527)*v(5969)
v(3549)=v(316)*v(3461)+v(315)*v(3483)-v(3538)
v(3537)=v(3526)*v(5969)
v(3548)=v(316)*v(3460)+v(315)*v(3482)-v(3537)
v(1051)=v(1042)*v(5969)
v(1060)=-v(1051)+v(1006)*v(315)+v(316)*v(988)
v(1050)=v(1041)*v(5969)
v(1059)=-v(1050)+v(1005)*v(315)+v(316)*v(987)
v(1049)=v(1040)*v(5969)
v(1058)=-v(1049)+v(1004)*v(315)+v(316)*v(986)
v(1048)=v(1039)*v(5969)
v(1057)=-v(1048)+v(1003)*v(315)+v(316)*v(985)
v(1047)=v(1038)*v(5969)
v(1056)=-v(1047)+v(1002)*v(315)+v(316)*v(984)
v(1046)=v(1037)*v(5969)
v(1055)=-v(1046)+v(1001)*v(315)+v(316)*v(983)
v(1045)=v(1036)*v(5969)
v(1054)=-v(1045)+v(1000)*v(315)+v(316)*v(982)
v(1044)=v(1035)*v(5969)
v(1053)=-v(1044)+v(316)*v(981)+v(315)*v(999)
v(1043)=v(1034)*v(5969)
v(1052)=-v(1043)+v(316)*v(980)+v(315)*v(998)
v(334)=(v(318)*v(318))
v(350)=v(315)*v(316)-v(334)
v(319)=v(298)*v(307)+v(303)*v(312)+v(299)*v(314)
v(5993)=v(319)*v(3592)
v(5991)=v(319)*v(3593)
v(5989)=v(319)*v(3594)
v(5987)=v(319)*v(3595)
v(5985)=v(319)*v(3596)
v(5983)=v(319)*v(3597)
v(5981)=v(319)*v(3598)
v(5979)=v(319)*v(3599)
v(5977)=v(319)*v(3600)
v(5975)=v(319)*v(3601)
v(5973)=v(319)*v(3602)
v(5970)=2d0*v(319)
v(3580)=v(3569)*v(5970)
v(3591)=v(317)*v(3492)+v(316)*v(3514)-v(3580)
v(3579)=v(3568)*v(5970)
v(3590)=v(317)*v(3491)+v(316)*v(3513)-v(3579)
v(3578)=v(3567)*v(5970)
v(3589)=v(317)*v(3490)+v(316)*v(3512)-v(3578)
v(3577)=v(3566)*v(5970)
v(3588)=v(317)*v(3489)+v(316)*v(3511)-v(3577)
v(3576)=v(3565)*v(5970)
v(3587)=v(317)*v(3488)+v(316)*v(3510)-v(3576)
v(3575)=v(3564)*v(5970)
v(3586)=v(317)*v(3487)+v(316)*v(3509)-v(3575)
v(3574)=v(3563)*v(5970)
v(3585)=v(317)*v(3486)+v(316)*v(3508)-v(3574)
v(3573)=v(3562)*v(5970)
v(3584)=v(317)*v(3485)+v(316)*v(3507)-v(3573)
v(3572)=v(3561)*v(5970)
v(3583)=v(317)*v(3484)+v(316)*v(3506)-v(3572)
v(3571)=v(3560)*v(5970)
v(3582)=v(317)*v(3483)+v(316)*v(3505)-v(3571)
v(3570)=v(3559)*v(5970)
v(3581)=v(317)*v(3482)+v(316)*v(3504)-v(3570)
v(1145)=v(318)*v(5970)
v(1078)=v(1069)*v(5970)
v(1087)=-v(1078)+v(1024)*v(316)+v(1006)*v(317)
v(1077)=v(1068)*v(5970)
v(1086)=-v(1077)+v(1023)*v(316)+v(1005)*v(317)
v(1076)=v(1067)*v(5970)
v(1085)=-v(1076)+v(1022)*v(316)+v(1004)*v(317)
v(1075)=v(1066)*v(5970)
v(1084)=-v(1075)+v(1021)*v(316)+v(1003)*v(317)
v(1074)=v(1065)*v(5970)
v(1083)=-v(1074)+v(1020)*v(316)+v(1002)*v(317)
v(1073)=v(1064)*v(5970)
v(1082)=-v(1073)+v(1019)*v(316)+v(1001)*v(317)
v(1072)=v(1063)*v(5970)
v(1081)=-v(1072)+v(1018)*v(316)+v(1000)*v(317)
v(1071)=v(1062)*v(5970)
v(1080)=-v(1071)+v(1017)*v(316)+v(317)*v(999)
v(1070)=v(1061)*v(5970)
v(1079)=-v(1070)+v(1016)*v(316)+v(317)*v(998)
v(322)=(v(319)*v(319))
v(339)=v(316)*v(317)-v(322)
v(320)=v(299)*v(311)+v(297)*v(312)+v(307)*v(313)
v(5992)=v(320)*v(3559)
v(5990)=v(320)*v(3560)
v(5988)=v(320)*v(3561)
v(5986)=v(320)*v(3562)
v(5984)=v(320)*v(3563)
v(5982)=v(320)*v(3564)
v(5980)=v(320)*v(3565)
v(5978)=v(320)*v(3566)
v(5976)=v(320)*v(3567)
v(5974)=v(320)*v(3568)
v(5972)=v(320)*v(3569)
v(5971)=2d0*v(320)
v(3646)=v(3602)*v(5971)
v(3657)=v(317)*v(3470)+v(315)*v(3514)-v(3646)
v(3645)=v(3601)*v(5971)
v(3656)=v(317)*v(3469)+v(315)*v(3513)-v(3645)
v(3644)=v(3600)*v(5971)
v(3655)=v(317)*v(3468)+v(315)*v(3512)-v(3644)
v(3643)=v(3599)*v(5971)
v(3654)=v(317)*v(3467)+v(315)*v(3511)-v(3643)
v(3642)=v(3598)*v(5971)
v(3653)=v(317)*v(3466)+v(315)*v(3510)-v(3642)
v(3641)=v(3597)*v(5971)
v(3652)=v(317)*v(3465)+v(315)*v(3509)-v(3641)
v(3640)=v(3596)*v(5971)
v(3651)=v(317)*v(3464)+v(315)*v(3508)-v(3640)
v(3639)=v(3595)*v(5971)
v(3650)=v(317)*v(3463)+v(315)*v(3507)-v(3639)
v(3638)=v(3594)*v(5971)
v(3649)=v(317)*v(3462)+v(315)*v(3506)-v(3638)
v(3637)=v(3593)*v(5971)
v(3648)=v(317)*v(3461)+v(315)*v(3505)-v(3637)
v(3636)=v(3592)*v(5971)
v(3647)=v(317)*v(3460)+v(315)*v(3504)-v(3636)
v(3635)=-(v(318)*v(3514))-v(317)*v(3536)+v(5972)+v(5973)
v(3634)=-(v(318)*v(3513))-v(317)*v(3535)+v(5974)+v(5975)
v(3633)=-(v(318)*v(3512))-v(317)*v(3534)+v(5976)+v(5977)
v(3632)=-(v(318)*v(3511))-v(317)*v(3533)+v(5978)+v(5979)
v(3631)=-(v(318)*v(3510))-v(317)*v(3532)+v(5980)+v(5981)
v(3630)=-(v(318)*v(3509))-v(317)*v(3531)+v(5982)+v(5983)
v(3629)=-(v(318)*v(3508))-v(317)*v(3530)+v(5984)+v(5985)
v(3628)=-(v(318)*v(3507))-v(317)*v(3529)+v(5986)+v(5987)
v(3627)=-(v(318)*v(3506))-v(317)*v(3528)+v(5988)+v(5989)
v(3626)=-(v(318)*v(3505))-v(317)*v(3527)+v(5990)+v(5991)
v(3625)=-(v(318)*v(3504))-v(317)*v(3526)+v(5992)+v(5993)
v(3624)=-(v(319)*v(3470))+v(320)*v(3536)-v(315)*v(3569)+v(318)*v(3602)
v(3623)=-(v(319)*v(3469))+v(320)*v(3535)-v(315)*v(3568)+v(318)*v(3601)
v(3622)=-(v(319)*v(3468))+v(320)*v(3534)-v(315)*v(3567)+v(318)*v(3600)
v(3621)=-(v(319)*v(3467))+v(320)*v(3533)-v(315)*v(3566)+v(318)*v(3599)
v(3620)=-(v(319)*v(3466))+v(320)*v(3532)-v(315)*v(3565)+v(318)*v(3598)
v(3619)=-(v(319)*v(3465))+v(320)*v(3531)-v(315)*v(3564)+v(318)*v(3597)
v(3618)=-(v(319)*v(3464))+v(320)*v(3530)-v(315)*v(3563)+v(318)*v(3596)
v(3617)=-(v(319)*v(3463))+v(320)*v(3529)-v(315)*v(3562)+v(318)*v(3595)
v(3616)=-(v(319)*v(3462))+v(320)*v(3528)-v(315)*v(3561)+v(318)*v(3594)
v(3615)=-(v(319)*v(3461))+v(320)*v(3527)-v(315)*v(3560)+v(318)*v(3593)
v(3614)=-(v(319)*v(3460))+v(320)*v(3526)-v(315)*v(3559)+v(318)*v(3592)
v(3613)=-(v(320)*v(3492))+v(319)*v(3536)+v(318)*v(3569)-v(316)*v(3602)
v(3612)=-(v(320)*v(3491))+v(319)*v(3535)+v(318)*v(3568)-v(316)*v(3601)
v(3611)=-(v(320)*v(3490))+v(319)*v(3534)+v(318)*v(3567)-v(316)*v(3600)
v(3610)=-(v(320)*v(3489))+v(319)*v(3533)+v(318)*v(3566)-v(316)*v(3599)
v(3609)=-(v(320)*v(3488))+v(319)*v(3532)+v(318)*v(3565)-v(316)*v(3598)
v(3608)=-(v(320)*v(3487))+v(319)*v(3531)+v(318)*v(3564)-v(316)*v(3597)
v(3607)=-(v(320)*v(3486))+v(319)*v(3530)+v(318)*v(3563)-v(316)*v(3596)
v(3606)=-(v(320)*v(3485))+v(319)*v(3529)+v(318)*v(3562)-v(316)*v(3595)
v(3605)=-(v(320)*v(3484))+v(319)*v(3528)+v(318)*v(3561)-v(316)*v(3594)
v(3604)=-(v(320)*v(3483))+v(319)*v(3527)+v(318)*v(3560)-v(316)*v(3593)
v(3603)=-(v(320)*v(3482))+v(319)*v(3526)+v(318)*v(3559)-v(316)*v(3592)
v(1144)=v(318)*v(5971)
v(1142)=v(319)*v(5971)
v(1132)=v(1096)*v(5971)
v(1141)=-v(1132)+v(1024)*v(315)+v(317)*v(988)
v(1131)=v(1095)*v(5971)
v(1140)=-v(1131)+v(1023)*v(315)+v(317)*v(987)
v(1130)=v(1094)*v(5971)
v(1139)=-v(1130)+v(1022)*v(315)+v(317)*v(986)
v(1129)=v(1093)*v(5971)
v(1138)=-v(1129)+v(1021)*v(315)+v(317)*v(985)
v(1128)=v(1092)*v(5971)
v(1137)=-v(1128)+v(1020)*v(315)+v(317)*v(984)
v(1127)=v(1091)*v(5971)
v(1136)=-v(1127)+v(1019)*v(315)+v(317)*v(983)
v(1126)=v(1090)*v(5971)
v(1135)=-v(1126)+v(1018)*v(315)+v(317)*v(982)
v(1125)=v(1089)*v(5971)
v(1134)=-v(1125)+v(1017)*v(315)+v(317)*v(981)
v(1124)=v(1088)*v(5971)
v(1133)=-v(1124)+v(1016)*v(315)+v(317)*v(980)
v(1123)=-(v(1042)*v(317))-v(1024)*v(318)+v(1096)*v(319)+v(1069)*v(320)
v(1122)=-(v(1041)*v(317))-v(1023)*v(318)+v(1095)*v(319)+v(1068)*v(320)
v(1121)=-(v(1040)*v(317))-v(1022)*v(318)+v(1094)*v(319)+v(1067)*v(320)
v(1120)=-(v(1039)*v(317))-v(1021)*v(318)+v(1093)*v(319)+v(1066)*v(320)
v(1119)=-(v(1038)*v(317))-v(1020)*v(318)+v(1092)*v(319)+v(1065)*v(320)
v(1118)=-(v(1037)*v(317))-v(1019)*v(318)+v(1091)*v(319)+v(1064)*v(320)
v(1117)=-(v(1036)*v(317))-v(1018)*v(318)+v(1090)*v(319)+v(1063)*v(320)
v(1116)=-(v(1035)*v(317))-v(1017)*v(318)+v(1089)*v(319)+v(1062)*v(320)
v(1115)=-(v(1034)*v(317))-v(1016)*v(318)+v(1088)*v(319)+v(1061)*v(320)
v(1114)=-(v(1069)*v(315))+v(1096)*v(318)+v(1042)*v(320)-v(319)*v(988)
v(1113)=-(v(1068)*v(315))+v(1095)*v(318)+v(1041)*v(320)-v(319)*v(987)
v(1112)=-(v(1067)*v(315))+v(1094)*v(318)+v(1040)*v(320)-v(319)*v(986)
v(1111)=-(v(1066)*v(315))+v(1093)*v(318)+v(1039)*v(320)-v(319)*v(985)
v(1110)=-(v(1065)*v(315))+v(1092)*v(318)+v(1038)*v(320)-v(319)*v(984)
v(1109)=-(v(1064)*v(315))+v(1091)*v(318)+v(1037)*v(320)-v(319)*v(983)
v(1108)=-(v(1063)*v(315))+v(1090)*v(318)+v(1036)*v(320)-v(319)*v(982)
v(1107)=-(v(1062)*v(315))+v(1089)*v(318)+v(1035)*v(320)-v(319)*v(981)
v(1106)=-(v(1061)*v(315))+v(1088)*v(318)+v(1034)*v(320)-v(319)*v(980)
v(1105)=-(v(1096)*v(316))+v(1069)*v(318)+v(1042)*v(319)-v(1006)*v(320)
v(1104)=-(v(1095)*v(316))+v(1068)*v(318)+v(1041)*v(319)-v(1005)*v(320)
v(1103)=-(v(1094)*v(316))+v(1067)*v(318)+v(1040)*v(319)-v(1004)*v(320)
v(1102)=-(v(1093)*v(316))+v(1066)*v(318)+v(1039)*v(319)-v(1003)*v(320)
v(1101)=-(v(1092)*v(316))+v(1065)*v(318)+v(1038)*v(319)-v(1002)*v(320)
v(1100)=-(v(1091)*v(316))+v(1064)*v(318)+v(1037)*v(319)-v(1001)*v(320)
v(1099)=-(v(1090)*v(316))+v(1063)*v(318)+v(1036)*v(319)-v(1000)*v(320)
v(1098)=-(v(1089)*v(316))+v(1062)*v(318)+v(1035)*v(319)-v(320)*v(999)
v(1097)=-(v(1088)*v(316))+v(1061)*v(318)+v(1034)*v(319)-v(320)*v(998)
v(351)=v(318)*v(319)-v(316)*v(320)
v(346)=-(v(315)*v(319))+v(318)*v(320)
v(341)=-(v(317)*v(318))+v(319)*v(320)
v(326)=(v(320)*v(320))
v(3679)=-(v(322)*v(3470))-v(326)*v(3492)+v(350)*v(3514)+v(1142)*v(3536)+v(317)*v(3558)-v(315)*v(3580)-v(316)*v(3646)&
&+2d0*v(318)*(v(5972)+v(5973))
v(3677)=-(v(322)*v(3469))-v(326)*v(3491)+v(350)*v(3513)+v(1142)*v(3535)+v(317)*v(3557)-v(315)*v(3579)-v(316)*v(3645)&
&+2d0*v(318)*(v(5974)+v(5975))
v(3675)=-(v(322)*v(3468))-v(326)*v(3490)+v(350)*v(3512)+v(1142)*v(3534)+v(317)*v(3556)-v(315)*v(3578)-v(316)*v(3644)&
&+2d0*v(318)*(v(5976)+v(5977))
v(3673)=-(v(322)*v(3467))-v(326)*v(3489)+v(350)*v(3511)+v(1142)*v(3533)+v(317)*v(3555)-v(315)*v(3577)-v(316)*v(3643)&
&+2d0*v(318)*(v(5978)+v(5979))
v(3671)=-(v(322)*v(3466))-v(326)*v(3488)+v(350)*v(3510)+v(1142)*v(3532)+v(317)*v(3554)-v(315)*v(3576)-v(316)*v(3642)&
&+2d0*v(318)*(v(5980)+v(5981))
v(3669)=-(v(322)*v(3465))-v(326)*v(3487)+v(350)*v(3509)+v(1142)*v(3531)+v(317)*v(3553)-v(315)*v(3575)-v(316)*v(3641)&
&+2d0*v(318)*(v(5982)+v(5983))
v(3667)=-(v(322)*v(3464))-v(326)*v(3486)+v(350)*v(3508)+v(1142)*v(3530)+v(317)*v(3552)-v(315)*v(3574)-v(316)*v(3640)&
&+2d0*v(318)*(v(5984)+v(5985))
v(3665)=-(v(322)*v(3463))-v(326)*v(3485)+v(350)*v(3507)+v(1142)*v(3529)+v(317)*v(3551)-v(315)*v(3573)-v(316)*v(3639)&
&+2d0*v(318)*(v(5986)+v(5987))
v(3663)=-(v(322)*v(3462))-v(326)*v(3484)+v(350)*v(3506)+v(1142)*v(3528)+v(317)*v(3550)-v(315)*v(3572)-v(316)*v(3638)&
&+2d0*v(318)*(v(5988)+v(5989))
v(3661)=-(v(322)*v(3461))-v(326)*v(3483)+v(350)*v(3505)+v(1142)*v(3527)+v(317)*v(3549)-v(315)*v(3571)-v(316)*v(3637)&
&+2d0*v(318)*(v(5990)+v(5991))
v(3659)=-(v(322)*v(3460))-v(326)*v(3482)+v(350)*v(3504)+v(1142)*v(3526)+v(317)*v(3548)-v(315)*v(3570)-v(316)*v(3636)&
&+2d0*v(318)*(v(5992)+v(5993))
v(1153)=v(1042)*v(1142)+v(1069)*v(1144)+v(1096)*v(1145)-v(1078)*v(315)-v(1132)*v(316)+v(1060)*v(317)-v(1006)*v(326)+v&
&(1024)*v(350)-v(322)*v(988)
v(1152)=v(1041)*v(1142)+v(1068)*v(1144)+v(1095)*v(1145)-v(1077)*v(315)-v(1131)*v(316)+v(1059)*v(317)-v(1005)*v(326)+v&
&(1023)*v(350)-v(322)*v(987)
v(1151)=v(1040)*v(1142)+v(1067)*v(1144)+v(1094)*v(1145)-v(1076)*v(315)-v(1130)*v(316)+v(1058)*v(317)-v(1004)*v(326)+v&
&(1022)*v(350)-v(322)*v(986)
v(1150)=v(1039)*v(1142)+v(1066)*v(1144)+v(1093)*v(1145)-v(1075)*v(315)-v(1129)*v(316)+v(1057)*v(317)-v(1003)*v(326)+v&
&(1021)*v(350)-v(322)*v(985)
v(1149)=v(1038)*v(1142)+v(1065)*v(1144)+v(1092)*v(1145)-v(1074)*v(315)-v(1128)*v(316)+v(1056)*v(317)-v(1002)*v(326)+v&
&(1020)*v(350)-v(322)*v(984)
v(1148)=v(1037)*v(1142)+v(1064)*v(1144)+v(1091)*v(1145)-v(1073)*v(315)-v(1127)*v(316)+v(1055)*v(317)-v(1001)*v(326)+v&
&(1019)*v(350)-v(322)*v(983)
v(1147)=v(1036)*v(1142)+v(1063)*v(1144)+v(1090)*v(1145)-v(1072)*v(315)-v(1126)*v(316)+v(1054)*v(317)-v(1000)*v(326)+v&
&(1018)*v(350)-v(322)*v(982)
v(1146)=v(1035)*v(1142)+v(1062)*v(1144)+v(1089)*v(1145)-v(1071)*v(315)-v(1125)*v(316)+v(1053)*v(317)+v(1017)*v(350)-v&
&(322)*v(981)-v(326)*v(999)
v(1143)=v(1034)*v(1142)+v(1061)*v(1144)+v(1088)*v(1145)-v(1070)*v(315)-v(1124)*v(316)+v(1052)*v(317)+v(1016)*v(350)-v&
&(322)*v(980)-v(326)*v(998)
v(345)=v(315)*v(317)-v(326)
v(323)=v(1142)*v(318)-v(315)*v(322)-v(316)*v(326)+v(317)*v(350)
v(6030)=v(341)/v(323)
v(5997)=sqrt(v(323))
v(3680)=1d0/v(5997)
v(5996)=mpar(2)*(1d0-v(3680)/2d0)
v(5994)=-(mpar(2)*((-2d0)+v(3680)))/2d0
v(3702)=v(3679)*v(5994)
v(3700)=v(3677)*v(5994)
v(3698)=v(3675)*v(5994)
v(3696)=v(3673)*v(5994)
v(3694)=v(3671)*v(5994)
v(3692)=v(3669)*v(5994)
v(3690)=v(3667)*v(5994)
v(3688)=v(3665)*v(5994)
v(3686)=v(3663)*v(5994)
v(3684)=v(3661)*v(5994)
v(3682)=v(3659)*v(5994)
v(1216)=1d0/v(323)**0.23333333333333334d1
v(3801)=(-4d0/3d0)*v(1216)*v(3679)
v(3800)=(-4d0/3d0)*v(1216)*v(3677)
v(3799)=(-4d0/3d0)*v(1216)*v(3675)
v(3798)=(-4d0/3d0)*v(1216)*v(3673)
v(3797)=(-4d0/3d0)*v(1216)*v(3671)
v(3796)=(-4d0/3d0)*v(1216)*v(3669)
v(3795)=(-4d0/3d0)*v(1216)*v(3667)
v(3794)=(-4d0/3d0)*v(1216)*v(3665)
v(3793)=(-4d0/3d0)*v(1216)*v(3663)
v(3792)=(-4d0/3d0)*v(1216)*v(3661)
v(3791)=(-4d0/3d0)*v(1216)*v(3659)
v(1224)=(-4d0/3d0)*v(1153)*v(1216)
v(1223)=(-4d0/3d0)*v(1152)*v(1216)
v(1222)=(-4d0/3d0)*v(1151)*v(1216)
v(1221)=(-4d0/3d0)*v(1150)*v(1216)
v(1220)=(-4d0/3d0)*v(1149)*v(1216)
v(1219)=(-4d0/3d0)*v(1148)*v(1216)
v(1218)=(-4d0/3d0)*v(1147)*v(1216)
v(1217)=(-4d0/3d0)*v(1146)*v(1216)
v(1215)=(-4d0/3d0)*v(1143)*v(1216)
v(1206)=1d0/v(323)**2
v(3790)=-(v(1206)*v(3679))
v(3789)=-(v(1206)*v(3677))
v(3788)=-(v(1206)*v(3675))
v(3787)=-(v(1206)*v(3673))
v(3786)=-(v(1206)*v(3671))
v(3785)=-(v(1206)*v(3669))
v(3784)=-(v(1206)*v(3667))
v(3783)=-(v(1206)*v(3665))
v(3782)=-(v(1206)*v(3663))
v(3781)=-(v(1206)*v(3661))
v(3780)=-(v(1206)*v(3659))
v(1214)=-(v(1153)*v(1206))
v(1213)=-(v(1152)*v(1206))
v(1212)=-(v(1151)*v(1206))
v(1211)=-(v(1150)*v(1206))
v(1210)=-(v(1149)*v(1206))
v(1209)=-(v(1148)*v(1206))
v(1208)=-(v(1147)*v(1206))
v(1207)=-(v(1146)*v(1206))
v(1205)=-(v(1143)*v(1206))
v(1165)=1d0/v(323)**0.13333333333333333d1
v(6026)=mpar(1)*v(1165)
v(5995)=-v(1165)/3d0
v(3713)=v(3679)*v(5995)
v(3712)=v(3677)*v(5995)
v(3711)=v(3675)*v(5995)
v(3710)=v(3673)*v(5995)
v(3709)=v(3671)*v(5995)
v(3708)=v(3669)*v(5995)
v(3707)=v(3667)*v(5995)
v(3706)=v(3665)*v(5995)
v(3705)=v(3663)*v(5995)
v(3704)=v(3661)*v(5995)
v(3703)=v(3659)*v(5995)
v(1174)=v(1153)*v(5995)
v(1173)=v(1152)*v(5995)
v(1172)=v(1151)*v(5995)
v(1171)=v(1150)*v(5995)
v(1170)=v(1149)*v(5995)
v(1169)=v(1148)*v(5995)
v(1168)=v(1147)*v(5995)
v(1167)=v(1146)*v(5995)
v(1166)=v(1143)*v(5995)
v(1164)=v(1153)*v(5996)
v(1163)=v(1152)*v(5996)
v(1162)=v(1151)*v(5996)
v(1161)=v(1150)*v(5996)
v(1160)=v(1149)*v(5996)
v(1159)=v(1148)*v(5996)
v(1158)=v(1147)*v(5996)
v(1157)=v(1146)*v(5996)
v(1155)=v(1143)*v(5996)
v(330)=mpar(2)*(v(323)-v(5997))
v(329)=1d0/v(323)**0.3333333333333333d0
v(6025)=mpar(1)*v(329)
v(6024)=mpar(1)*(v(1166)*v(1195)+v(329)*(v(1025)+v(989)+(2d0/3d0)*v(998)))
v(6023)=mpar(1)*(v(1166)*v(1185)+v(329)*(v(1007)+(2d0/3d0)*v(1016)+v(989)))
v(6022)=mpar(1)*(v(1166)*v(1175)+v(329)*(v(1007)+v(1025)+(2d0/3d0)*v(980)))
v(6021)=mpar(1)*(v(1167)*v(1195)+v(329)*(v(1026)+v(990)+(2d0/3d0)*v(999)))
v(6020)=mpar(1)*(v(1167)*v(1185)+v(329)*(v(1008)+(2d0/3d0)*v(1017)+v(990)))
v(6019)=mpar(1)*(v(1167)*v(1175)+v(329)*(v(1008)+v(1026)+(2d0/3d0)*v(981)))
v(6018)=mpar(1)*(v(1168)*v(1195)+v(329)*((2d0/3d0)*v(1000)+v(1027)+v(991)))
v(6017)=mpar(1)*(v(1168)*v(1185)+v(329)*(v(1009)+(2d0/3d0)*v(1018)+v(991)))
v(6016)=mpar(1)*(v(1168)*v(1175)+v(329)*(v(1009)+v(1027)+(2d0/3d0)*v(982)))
v(6015)=mpar(1)*(v(1169)*v(1195)+v(329)*((2d0/3d0)*v(1001)+v(1028)+v(992)))
v(6014)=mpar(1)*(v(1169)*v(1185)+v(329)*(v(1010)+(2d0/3d0)*v(1019)+v(992)))
v(6013)=mpar(1)*(v(1169)*v(1175)+v(329)*(v(1010)+v(1028)+(2d0/3d0)*v(983)))
v(6012)=mpar(1)*(v(1170)*v(1195)+v(329)*((2d0/3d0)*v(1002)+v(1029)+v(993)))
v(6011)=mpar(1)*(v(1170)*v(1185)+v(329)*(v(1011)+(2d0/3d0)*v(1020)+v(993)))
v(6010)=mpar(1)*(v(1170)*v(1175)+v(329)*(v(1011)+v(1029)+(2d0/3d0)*v(984)))
v(6009)=mpar(1)*(v(1171)*v(1195)+v(329)*((2d0/3d0)*v(1003)+v(1030)+v(994)))
v(6008)=mpar(1)*(v(1171)*v(1185)+v(329)*(v(1012)+(2d0/3d0)*v(1021)+v(994)))
v(6007)=mpar(1)*(v(1171)*v(1175)+v(329)*(v(1012)+v(1030)+(2d0/3d0)*v(985)))
v(6006)=mpar(1)*(v(1172)*v(1195)+v(329)*((2d0/3d0)*v(1004)+v(1031)+v(995)))
v(6005)=mpar(1)*(v(1172)*v(1185)+v(329)*(v(1013)+(2d0/3d0)*v(1022)+v(995)))
v(6004)=mpar(1)*(v(1172)*v(1175)+v(329)*(v(1013)+v(1031)+(2d0/3d0)*v(986)))
v(6003)=mpar(1)*(v(1173)*v(1195)+v(329)*((2d0/3d0)*v(1005)+v(1032)+v(996)))
v(6002)=mpar(1)*(v(1173)*v(1185)+v(329)*(v(1014)+(2d0/3d0)*v(1023)+v(996)))
v(6001)=mpar(1)*(v(1173)*v(1175)+v(329)*(v(1014)+v(1032)+(2d0/3d0)*v(987)))
v(6000)=mpar(1)*(v(1174)*v(1195)+v(329)*((2d0/3d0)*v(1006)+v(1033)+v(997)))
v(5999)=mpar(1)*(v(1174)*v(1185)+v(329)*(v(1015)+(2d0/3d0)*v(1024)+v(997)))
v(5998)=mpar(1)*(v(1174)*v(1175)+v(329)*(v(1015)+v(1033)+(2d0/3d0)*v(988)))
v(3779)=v(3702)+mpar(1)*(v(329)*(v(3481)+(2d0/3d0)*v(3492)+v(3525))+v(1195)*v(3713))
v(3777)=v(3700)+mpar(1)*(v(329)*(v(3480)+(2d0/3d0)*v(3491)+v(3524))+v(1195)*v(3712))
v(3775)=v(3698)+mpar(1)*(v(329)*(v(3479)+(2d0/3d0)*v(3490)+v(3523))+v(1195)*v(3711))
v(3773)=v(3696)+mpar(1)*(v(329)*(v(3478)+(2d0/3d0)*v(3489)+v(3522))+v(1195)*v(3710))
v(3771)=v(3694)+mpar(1)*(v(329)*(v(3477)+(2d0/3d0)*v(3488)+v(3521))+v(1195)*v(3709))
v(3769)=v(3692)+mpar(1)*(v(329)*(v(3476)+(2d0/3d0)*v(3487)+v(3520))+v(1195)*v(3708))
v(3767)=v(3690)+mpar(1)*(v(329)*(v(3475)+(2d0/3d0)*v(3486)+v(3519))+v(1195)*v(3707))
v(3765)=v(3688)+mpar(1)*(v(329)*(v(3474)+(2d0/3d0)*v(3485)+v(3518))+v(1195)*v(3706))
v(3763)=v(3686)+mpar(1)*(v(329)*(v(3473)+(2d0/3d0)*v(3484)+v(3517))+v(1195)*v(3705))
v(3761)=v(3684)+mpar(1)*(v(329)*(v(3472)+(2d0/3d0)*v(3483)+v(3516))+v(1195)*v(3704))
v(3759)=v(3682)+mpar(1)*(v(329)*(v(3471)+(2d0/3d0)*v(3482)+v(3515))+v(1195)*v(3703))
v(3757)=v(3702)+mpar(1)*(v(329)*(v(3481)+v(3503)+(2d0/3d0)*v(3514))+v(1185)*v(3713))
v(3755)=v(3700)+mpar(1)*(v(329)*(v(3480)+v(3502)+(2d0/3d0)*v(3513))+v(1185)*v(3712))
v(3753)=v(3698)+mpar(1)*(v(329)*(v(3479)+v(3501)+(2d0/3d0)*v(3512))+v(1185)*v(3711))
v(3751)=v(3696)+mpar(1)*(v(329)*(v(3478)+v(3500)+(2d0/3d0)*v(3511))+v(1185)*v(3710))
v(3749)=v(3694)+mpar(1)*(v(329)*(v(3477)+v(3499)+(2d0/3d0)*v(3510))+v(1185)*v(3709))
v(3747)=v(3692)+mpar(1)*(v(329)*(v(3476)+v(3498)+(2d0/3d0)*v(3509))+v(1185)*v(3708))
v(3745)=v(3690)+mpar(1)*(v(329)*(v(3475)+v(3497)+(2d0/3d0)*v(3508))+v(1185)*v(3707))
v(3743)=v(3688)+mpar(1)*(v(329)*(v(3474)+v(3496)+(2d0/3d0)*v(3507))+v(1185)*v(3706))
v(3741)=v(3686)+mpar(1)*(v(329)*(v(3473)+v(3495)+(2d0/3d0)*v(3506))+v(1185)*v(3705))
v(3739)=v(3684)+mpar(1)*(v(329)*(v(3472)+v(3494)+(2d0/3d0)*v(3505))+v(1185)*v(3704))
v(3737)=v(3682)+mpar(1)*(v(329)*(v(3471)+v(3493)+(2d0/3d0)*v(3504))+v(1185)*v(3703))
v(3735)=v(3702)+mpar(1)*(v(329)*((2d0/3d0)*v(3470)+v(3503)+v(3525))+v(1175)*v(3713))
v(3733)=v(3700)+mpar(1)*(v(329)*((2d0/3d0)*v(3469)+v(3502)+v(3524))+v(1175)*v(3712))
v(3731)=v(3698)+mpar(1)*(v(329)*((2d0/3d0)*v(3468)+v(3501)+v(3523))+v(1175)*v(3711))
v(3729)=v(3696)+mpar(1)*(v(329)*((2d0/3d0)*v(3467)+v(3500)+v(3522))+v(1175)*v(3710))
v(3727)=v(3694)+mpar(1)*(v(329)*((2d0/3d0)*v(3466)+v(3499)+v(3521))+v(1175)*v(3709))
v(3725)=v(3692)+mpar(1)*(v(329)*((2d0/3d0)*v(3465)+v(3498)+v(3520))+v(1175)*v(3708))
v(3723)=v(3690)+mpar(1)*(v(329)*((2d0/3d0)*v(3464)+v(3497)+v(3519))+v(1175)*v(3707))
v(3721)=v(3688)+mpar(1)*(v(329)*((2d0/3d0)*v(3463)+v(3496)+v(3518))+v(1175)*v(3706))
v(3719)=v(3686)+mpar(1)*(v(329)*((2d0/3d0)*v(3462)+v(3495)+v(3517))+v(1175)*v(3705))
v(3717)=v(3684)+mpar(1)*(v(329)*((2d0/3d0)*v(3461)+v(3494)+v(3516))+v(1175)*v(3704))
v(3715)=v(3682)+mpar(1)*(v(329)*((2d0/3d0)*v(3460)+v(3493)+v(3515))+v(1175)*v(3703))
v(1204)=v(1164)+v(6000)
v(1203)=v(1163)+v(6003)
v(1202)=v(1162)+v(6006)
v(1201)=v(1161)+v(6009)
v(1200)=v(1160)+v(6012)
v(1199)=v(1159)+v(6015)
v(1198)=v(1158)+v(6018)
v(1197)=v(1157)+v(6021)
v(1196)=v(1155)+v(6024)
v(1194)=v(1164)+v(5999)
v(1193)=v(1163)+v(6002)
v(1192)=v(1162)+v(6005)
v(1191)=v(1161)+v(6008)
v(1190)=v(1160)+v(6011)
v(1189)=v(1159)+v(6014)
v(1188)=v(1158)+v(6017)
v(1187)=v(1157)+v(6020)
v(1186)=v(1155)+v(6023)
v(1184)=v(1164)+v(5998)
v(1183)=v(1163)+v(6001)
v(1182)=v(1162)+v(6004)
v(1181)=v(1161)+v(6007)
v(1180)=v(1160)+v(6010)
v(1179)=v(1159)+v(6013)
v(1178)=v(1158)+v(6016)
v(1177)=v(1157)+v(6019)
v(1176)=v(1155)+v(6022)
v(352)=v(330)+v(1175)*v(6025)
v(6032)=v(339)*v(352)
v(6029)=v(351)*v(352)
v(654)=-v(352)/3d0
v(360)=v(352)-x(2)-x(7)
v(364)=-v(360)/3d0
v(347)=v(330)+v(1185)*v(6025)
v(6028)=v(347)*v(350)
v(6027)=v(346)*v(347)
v(651)=-v(347)/3d0
v(363)=-v(347)+v(5542)+v(5550)
v(359)=v(363)/3d0
v(342)=v(330)+v(1195)*v(6025)
v(6031)=v(342)*v(345)
v(653)=-v(342)/3d0
v(358)=-v(342)+x(3)+x(8)
v(362)=v(358)/3d0
v(3845)=mpar(1)*(v(1165)*v(3536)+v(318)*v(3801))
v(3844)=mpar(1)*(v(1165)*v(3535)+v(318)*v(3800))
v(3843)=mpar(1)*(v(1165)*v(3534)+v(318)*v(3799))
v(3842)=mpar(1)*(v(1165)*v(3533)+v(318)*v(3798))
v(3841)=mpar(1)*(v(1165)*v(3532)+v(318)*v(3797))
v(3840)=mpar(1)*(v(1165)*v(3531)+v(318)*v(3796))
v(3839)=mpar(1)*(v(1165)*v(3530)+v(318)*v(3795))
v(3838)=mpar(1)*(v(1165)*v(3529)+v(318)*v(3794))
v(3837)=mpar(1)*(v(1165)*v(3528)+v(318)*v(3793))
v(3836)=mpar(1)*(v(1165)*v(3527)+v(318)*v(3792))
v(3835)=mpar(1)*(v(1165)*v(3526)+v(318)*v(3791))
v(3834)=mpar(1)*(v(1165)*v(3613)+v(351)*v(3801))
v(3833)=mpar(1)*(v(1165)*v(3612)+v(351)*v(3800))
v(3832)=mpar(1)*(v(1165)*v(3611)+v(351)*v(3799))
v(3831)=mpar(1)*(v(1165)*v(3610)+v(351)*v(3798))
v(3830)=mpar(1)*(v(1165)*v(3609)+v(351)*v(3797))
v(3829)=mpar(1)*(v(1165)*v(3608)+v(351)*v(3796))
v(3828)=mpar(1)*(v(1165)*v(3607)+v(351)*v(3795))
v(3827)=mpar(1)*(v(1165)*v(3606)+v(351)*v(3794))
v(3826)=mpar(1)*(v(1165)*v(3605)+v(351)*v(3793))
v(3825)=mpar(1)*(v(1165)*v(3604)+v(351)*v(3792))
v(3824)=mpar(1)*(v(1165)*v(3603)+v(351)*v(3791))
v(3823)=mpar(1)*(v(1165)*v(3569)+v(319)*v(3801))
v(3822)=mpar(1)*(v(1165)*v(3568)+v(319)*v(3800))
v(3821)=mpar(1)*(v(1165)*v(3567)+v(319)*v(3799))
v(3820)=mpar(1)*(v(1165)*v(3566)+v(319)*v(3798))
v(3819)=mpar(1)*(v(1165)*v(3565)+v(319)*v(3797))
v(3818)=mpar(1)*(v(1165)*v(3564)+v(319)*v(3796))
v(3817)=mpar(1)*(v(1165)*v(3563)+v(319)*v(3795))
v(3816)=mpar(1)*(v(1165)*v(3562)+v(319)*v(3794))
v(3815)=mpar(1)*(v(1165)*v(3561)+v(319)*v(3793))
v(3814)=mpar(1)*(v(1165)*v(3560)+v(319)*v(3792))
v(3813)=mpar(1)*(v(1165)*v(3559)+v(319)*v(3791))
v(3812)=mpar(1)*(v(1165)*v(3602)+v(320)*v(3801))
v(3811)=mpar(1)*(v(1165)*v(3601)+v(320)*v(3800))
v(3810)=mpar(1)*(v(1165)*v(3600)+v(320)*v(3799))
v(3809)=mpar(1)*(v(1165)*v(3599)+v(320)*v(3798))
v(3808)=mpar(1)*(v(1165)*v(3598)+v(320)*v(3797))
v(3807)=mpar(1)*(v(1165)*v(3597)+v(320)*v(3796))
v(3806)=mpar(1)*(v(1165)*v(3596)+v(320)*v(3795))
v(3805)=mpar(1)*(v(1165)*v(3595)+v(320)*v(3794))
v(3804)=mpar(1)*(v(1165)*v(3594)+v(320)*v(3793))
v(3803)=mpar(1)*(v(1165)*v(3593)+v(320)*v(3792))
v(3802)=mpar(1)*(v(1165)*v(3592)+v(320)*v(3791))
v(1260)=mpar(1)*(v(1042)*v(1165)+v(1224)*v(318))
v(1259)=mpar(1)*(v(1041)*v(1165)+v(1223)*v(318))
v(1258)=mpar(1)*(v(1040)*v(1165)+v(1222)*v(318))
v(1257)=mpar(1)*(v(1039)*v(1165)+v(1221)*v(318))
v(1256)=mpar(1)*(v(1038)*v(1165)+v(1220)*v(318))
v(1255)=mpar(1)*(v(1037)*v(1165)+v(1219)*v(318))
v(1254)=mpar(1)*(v(1036)*v(1165)+v(1218)*v(318))
v(1253)=mpar(1)*(v(1035)*v(1165)+v(1217)*v(318))
v(1252)=mpar(1)*(v(1034)*v(1165)+v(1215)*v(318))
v(1251)=mpar(1)*(v(1105)*v(1165)+v(1224)*v(351))
v(1250)=mpar(1)*(v(1104)*v(1165)+v(1223)*v(351))
v(1249)=mpar(1)*(v(1103)*v(1165)+v(1222)*v(351))
v(1248)=mpar(1)*(v(1102)*v(1165)+v(1221)*v(351))
v(1247)=mpar(1)*(v(1101)*v(1165)+v(1220)*v(351))
v(1246)=mpar(1)*(v(1100)*v(1165)+v(1219)*v(351))
v(1245)=mpar(1)*(v(1099)*v(1165)+v(1218)*v(351))
v(1244)=mpar(1)*(v(1098)*v(1165)+v(1217)*v(351))
v(1243)=mpar(1)*(v(1097)*v(1165)+v(1215)*v(351))
v(1242)=mpar(1)*(v(1069)*v(1165)+v(1224)*v(319))
v(1241)=mpar(1)*(v(1068)*v(1165)+v(1223)*v(319))
v(1240)=mpar(1)*(v(1067)*v(1165)+v(1222)*v(319))
v(1239)=mpar(1)*(v(1066)*v(1165)+v(1221)*v(319))
v(1238)=mpar(1)*(v(1065)*v(1165)+v(1220)*v(319))
v(1237)=mpar(1)*(v(1064)*v(1165)+v(1219)*v(319))
v(1236)=mpar(1)*(v(1063)*v(1165)+v(1218)*v(319))
v(1235)=mpar(1)*(v(1062)*v(1165)+v(1217)*v(319))
v(1234)=mpar(1)*(v(1061)*v(1165)+v(1215)*v(319))
v(1233)=mpar(1)*(v(1096)*v(1165)+v(1224)*v(320))
v(1232)=mpar(1)*(v(1095)*v(1165)+v(1223)*v(320))
v(1231)=mpar(1)*(v(1094)*v(1165)+v(1222)*v(320))
v(1230)=mpar(1)*(v(1093)*v(1165)+v(1221)*v(320))
v(1229)=mpar(1)*(v(1092)*v(1165)+v(1220)*v(320))
v(1228)=mpar(1)*(v(1091)*v(1165)+v(1219)*v(320))
v(1227)=mpar(1)*(v(1090)*v(1165)+v(1218)*v(320))
v(1226)=mpar(1)*(v(1089)*v(1165)+v(1217)*v(320))
v(1225)=mpar(1)*(v(1088)*v(1165)+v(1215)*v(320))
v(349)=v(320)*v(6026)
v(344)=v(319)*v(6026)
v(3933)=v(349)*v(3635)+v(344)*v(3657)+(v(347)*v(3624)+v(346)*v(3757))/v(323)+v(341)*v(3812)+v(345)*v(3823)+v(3790)*v&
&(6027)
v(3932)=v(349)*v(3634)+v(344)*v(3656)+(v(347)*v(3623)+v(346)*v(3755))/v(323)+v(341)*v(3811)+v(345)*v(3822)+v(3789)*v&
&(6027)
v(3931)=v(349)*v(3633)+v(344)*v(3655)+(v(347)*v(3622)+v(346)*v(3753))/v(323)+v(341)*v(3810)+v(345)*v(3821)+v(3788)*v&
&(6027)
v(3930)=v(349)*v(3632)+v(344)*v(3654)+(v(347)*v(3621)+v(346)*v(3751))/v(323)+v(341)*v(3809)+v(345)*v(3820)+v(3787)*v&
&(6027)
v(3929)=v(349)*v(3631)+v(344)*v(3653)+(v(347)*v(3620)+v(346)*v(3749))/v(323)+v(341)*v(3808)+v(345)*v(3819)+v(3786)*v&
&(6027)
v(3928)=v(349)*v(3630)+v(344)*v(3652)+(v(347)*v(3619)+v(346)*v(3747))/v(323)+v(341)*v(3807)+v(345)*v(3818)+v(3785)*v&
&(6027)
v(3927)=v(349)*v(3629)+v(344)*v(3651)+(v(347)*v(3618)+v(346)*v(3745))/v(323)+v(341)*v(3806)+v(345)*v(3817)+v(3784)*v&
&(6027)
v(3926)=v(349)*v(3628)+v(344)*v(3650)+(v(347)*v(3617)+v(346)*v(3743))/v(323)+v(341)*v(3805)+v(345)*v(3816)+v(3783)*v&
&(6027)
v(3925)=v(349)*v(3627)+v(344)*v(3649)+(v(347)*v(3616)+v(346)*v(3741))/v(323)+v(341)*v(3804)+v(345)*v(3815)+v(3782)*v&
&(6027)
v(3924)=v(349)*v(3626)+v(344)*v(3648)+(v(347)*v(3615)+v(346)*v(3739))/v(323)+v(341)*v(3803)+v(345)*v(3814)+v(3781)*v&
&(6027)
v(3923)=v(349)*v(3625)+v(344)*v(3647)+(v(347)*v(3614)+v(346)*v(3737))/v(323)+v(341)*v(3802)+v(345)*v(3813)+v(3780)*v&
&(6027)
v(3856)=v(344)*v(3624)+v(346)*v(3823)
v(3855)=v(344)*v(3623)+v(346)*v(3822)
v(3854)=v(344)*v(3622)+v(346)*v(3821)
v(3853)=v(344)*v(3621)+v(346)*v(3820)
v(3852)=v(344)*v(3620)+v(346)*v(3819)
v(3851)=v(344)*v(3619)+v(346)*v(3818)
v(3850)=v(344)*v(3618)+v(346)*v(3817)
v(3849)=v(344)*v(3617)+v(346)*v(3816)
v(3848)=v(344)*v(3616)+v(346)*v(3815)
v(3847)=v(344)*v(3615)+v(346)*v(3814)
v(3846)=v(344)*v(3614)+v(346)*v(3813)
v(1332)=v(1233)*v(341)+v(1141)*v(344)+v(1242)*v(345)+(v(1194)*v(346)+v(1114)*v(347))/v(323)+v(1123)*v(349)+v(1214)*v&
&(6027)
v(1331)=v(1232)*v(341)+v(1140)*v(344)+v(1241)*v(345)+(v(1193)*v(346)+v(1113)*v(347))/v(323)+v(1122)*v(349)+v(1213)*v&
&(6027)
v(1330)=v(1231)*v(341)+v(1139)*v(344)+v(1240)*v(345)+(v(1192)*v(346)+v(1112)*v(347))/v(323)+v(1121)*v(349)+v(1212)*v&
&(6027)
v(1329)=v(1230)*v(341)+v(1138)*v(344)+v(1239)*v(345)+(v(1191)*v(346)+v(1111)*v(347))/v(323)+v(1120)*v(349)+v(1211)*v&
&(6027)
v(1328)=v(1229)*v(341)+v(1137)*v(344)+v(1238)*v(345)+(v(1190)*v(346)+v(1110)*v(347))/v(323)+v(1119)*v(349)+v(1210)*v&
&(6027)
v(1327)=v(1228)*v(341)+v(1136)*v(344)+v(1237)*v(345)+(v(1189)*v(346)+v(1109)*v(347))/v(323)+v(1118)*v(349)+v(1209)*v&
&(6027)
v(1326)=v(1227)*v(341)+v(1135)*v(344)+v(1236)*v(345)+(v(1188)*v(346)+v(1108)*v(347))/v(323)+v(1117)*v(349)+v(1208)*v&
&(6027)
v(1325)=v(1226)*v(341)+v(1134)*v(344)+v(1235)*v(345)+(v(1187)*v(346)+v(1107)*v(347))/v(323)+v(1116)*v(349)+v(1207)*v&
&(6027)
v(1324)=v(1225)*v(341)+v(1133)*v(344)+v(1234)*v(345)+(v(1186)*v(346)+v(1106)*v(347))/v(323)+v(1115)*v(349)+v(1205)*v&
&(6027)
v(1269)=v(1114)*v(344)+v(1242)*v(346)
v(1268)=v(1113)*v(344)+v(1241)*v(346)
v(1267)=v(1112)*v(344)+v(1240)*v(346)
v(1266)=v(1111)*v(344)+v(1239)*v(346)
v(1265)=v(1110)*v(344)+v(1238)*v(346)
v(1264)=v(1109)*v(344)+v(1237)*v(346)
v(1263)=v(1108)*v(344)+v(1236)*v(346)
v(1262)=v(1107)*v(344)+v(1235)*v(346)
v(1261)=v(1106)*v(344)+v(1234)*v(346)
v(340)=v(351)*v(6026)
v(3867)=v(340)*v(3602)+v(320)*v(3834)
v(3911)=(v(347)*v(3558)+v(350)*v(3757))/v(323)+v(3856)+v(3867)+v(3790)*v(6028)
v(3866)=v(340)*v(3601)+v(320)*v(3833)
v(3910)=(v(347)*v(3557)+v(350)*v(3755))/v(323)+v(3855)+v(3866)+v(3789)*v(6028)
v(3865)=v(340)*v(3600)+v(320)*v(3832)
v(3909)=(v(347)*v(3556)+v(350)*v(3753))/v(323)+v(3854)+v(3865)+v(3788)*v(6028)
v(3864)=v(340)*v(3599)+v(320)*v(3831)
v(3908)=(v(347)*v(3555)+v(350)*v(3751))/v(323)+v(3853)+v(3864)+v(3787)*v(6028)
v(3863)=v(340)*v(3598)+v(320)*v(3830)
v(3907)=(v(347)*v(3554)+v(350)*v(3749))/v(323)+v(3852)+v(3863)+v(3786)*v(6028)
v(3862)=v(340)*v(3597)+v(320)*v(3829)
v(3906)=(v(347)*v(3553)+v(350)*v(3747))/v(323)+v(3851)+v(3862)+v(3785)*v(6028)
v(3861)=v(340)*v(3596)+v(320)*v(3828)
v(3905)=(v(347)*v(3552)+v(350)*v(3745))/v(323)+v(3850)+v(3861)+v(3784)*v(6028)
v(3860)=v(340)*v(3595)+v(320)*v(3827)
v(3904)=(v(347)*v(3551)+v(350)*v(3743))/v(323)+v(3849)+v(3860)+v(3783)*v(6028)
v(3859)=v(340)*v(3594)+v(320)*v(3826)
v(3903)=(v(347)*v(3550)+v(350)*v(3741))/v(323)+v(3848)+v(3859)+v(3782)*v(6028)
v(3858)=v(340)*v(3593)+v(320)*v(3825)
v(3902)=(v(347)*v(3549)+v(350)*v(3739))/v(323)+v(3847)+v(3858)+v(3781)*v(6028)
v(3857)=v(340)*v(3592)+v(320)*v(3824)
v(3901)=(v(347)*v(3548)+v(350)*v(3737))/v(323)+v(3846)+v(3857)+v(3780)*v(6028)
v(1278)=v(1251)*v(320)+v(1096)*v(340)
v(1314)=v(1269)+v(1278)+(v(1060)*v(347)+v(1194)*v(350))/v(323)+v(1214)*v(6028)
v(1277)=v(1250)*v(320)+v(1095)*v(340)
v(1313)=v(1268)+v(1277)+(v(1059)*v(347)+v(1193)*v(350))/v(323)+v(1213)*v(6028)
v(1276)=v(1249)*v(320)+v(1094)*v(340)
v(1312)=v(1267)+v(1276)+(v(1058)*v(347)+v(1192)*v(350))/v(323)+v(1212)*v(6028)
v(1275)=v(1248)*v(320)+v(1093)*v(340)
v(1311)=v(1266)+v(1275)+(v(1057)*v(347)+v(1191)*v(350))/v(323)+v(1211)*v(6028)
v(1274)=v(1247)*v(320)+v(1092)*v(340)
v(1310)=v(1265)+v(1274)+(v(1056)*v(347)+v(1190)*v(350))/v(323)+v(1210)*v(6028)
v(1273)=v(1246)*v(320)+v(1091)*v(340)
v(1309)=v(1264)+v(1273)+(v(1055)*v(347)+v(1189)*v(350))/v(323)+v(1209)*v(6028)
v(1272)=v(1245)*v(320)+v(1090)*v(340)
v(1308)=v(1263)+v(1272)+(v(1054)*v(347)+v(1188)*v(350))/v(323)+v(1208)*v(6028)
v(1271)=v(1244)*v(320)+v(1089)*v(340)
v(1307)=v(1262)+v(1271)+(v(1053)*v(347)+v(1187)*v(350))/v(323)+v(1207)*v(6028)
v(1270)=v(1243)*v(320)+v(1088)*v(340)
v(1306)=v(1261)+v(1270)+(v(1052)*v(347)+v(1186)*v(350))/v(323)+v(1205)*v(6028)
v(338)=v(318)*v(6026)
v(3977)=v(349)*v(3558)+v(338)*v(3624)+(v(352)*v(3613)+v(351)*v(3735))/v(323)+v(350)*v(3812)+v(346)*v(3845)+v(3790)*v&
&(6029)
v(3976)=v(349)*v(3557)+v(338)*v(3623)+(v(352)*v(3612)+v(351)*v(3733))/v(323)+v(350)*v(3811)+v(346)*v(3844)+v(3789)*v&
&(6029)
v(3975)=v(349)*v(3556)+v(338)*v(3622)+(v(352)*v(3611)+v(351)*v(3731))/v(323)+v(350)*v(3810)+v(346)*v(3843)+v(3788)*v&
&(6029)
v(3974)=v(349)*v(3555)+v(338)*v(3621)+(v(352)*v(3610)+v(351)*v(3729))/v(323)+v(350)*v(3809)+v(346)*v(3842)+v(3787)*v&
&(6029)
v(3973)=v(349)*v(3554)+v(338)*v(3620)+(v(352)*v(3609)+v(351)*v(3727))/v(323)+v(350)*v(3808)+v(346)*v(3841)+v(3786)*v&
&(6029)
v(3972)=v(349)*v(3553)+v(338)*v(3619)+(v(352)*v(3608)+v(351)*v(3725))/v(323)+v(350)*v(3807)+v(346)*v(3840)+v(3785)*v&
&(6029)
v(3971)=v(349)*v(3552)+v(338)*v(3618)+(v(352)*v(3607)+v(351)*v(3723))/v(323)+v(350)*v(3806)+v(346)*v(3839)+v(3784)*v&
&(6029)
v(3970)=v(349)*v(3551)+v(338)*v(3617)+(v(352)*v(3606)+v(351)*v(3721))/v(323)+v(350)*v(3805)+v(346)*v(3838)+v(3783)*v&
&(6029)
v(3969)=v(349)*v(3550)+v(338)*v(3616)+(v(352)*v(3605)+v(351)*v(3719))/v(323)+v(350)*v(3804)+v(346)*v(3837)+v(3782)*v&
&(6029)
v(3968)=v(349)*v(3549)+v(338)*v(3615)+(v(352)*v(3604)+v(351)*v(3717))/v(323)+v(350)*v(3803)+v(346)*v(3836)+v(3781)*v&
&(6029)
v(3967)=v(349)*v(3548)+v(338)*v(3614)+(v(352)*v(3603)+v(351)*v(3715))/v(323)+v(350)*v(3802)+v(346)*v(3835)+v(3780)*v&
&(6029)
v(3922)=v(340)*v(3569)+v(338)*v(3591)+v(342)*(v(3635)/v(323)+v(341)*v(3790))+v(319)*v(3834)+v(339)*v(3845)+v(3779)*v&
&(6030)
v(3921)=v(340)*v(3568)+v(338)*v(3590)+v(342)*(v(3634)/v(323)+v(341)*v(3789))+v(319)*v(3833)+v(339)*v(3844)+v(3777)*v&
&(6030)
v(3920)=v(340)*v(3567)+v(338)*v(3589)+v(342)*(v(3633)/v(323)+v(341)*v(3788))+v(319)*v(3832)+v(339)*v(3843)+v(3775)*v&
&(6030)
v(3919)=v(340)*v(3566)+v(338)*v(3588)+v(342)*(v(3632)/v(323)+v(341)*v(3787))+v(319)*v(3831)+v(339)*v(3842)+v(3773)*v&
&(6030)
v(3918)=v(340)*v(3565)+v(338)*v(3587)+v(342)*(v(3631)/v(323)+v(341)*v(3786))+v(319)*v(3830)+v(339)*v(3841)+v(3771)*v&
&(6030)
v(3917)=v(340)*v(3564)+v(338)*v(3586)+v(342)*(v(3630)/v(323)+v(341)*v(3785))+v(319)*v(3829)+v(339)*v(3840)+v(3769)*v&
&(6030)
v(3916)=v(340)*v(3563)+v(338)*v(3585)+v(342)*(v(3629)/v(323)+v(341)*v(3784))+v(319)*v(3828)+v(339)*v(3839)+v(3767)*v&
&(6030)
v(3915)=v(340)*v(3562)+v(338)*v(3584)+v(342)*(v(3628)/v(323)+v(341)*v(3783))+v(319)*v(3827)+v(339)*v(3838)+v(3765)*v&
&(6030)
v(3914)=v(340)*v(3561)+v(338)*v(3583)+v(342)*(v(3627)/v(323)+v(341)*v(3782))+v(319)*v(3826)+v(339)*v(3837)+v(3763)*v&
&(6030)
v(3913)=v(340)*v(3560)+v(338)*v(3582)+v(342)*(v(3626)/v(323)+v(341)*v(3781))+v(319)*v(3825)+v(339)*v(3836)+v(3761)*v&
&(6030)
v(3912)=v(340)*v(3559)+v(338)*v(3581)+v(342)*(v(3625)/v(323)+v(341)*v(3780))+v(319)*v(3824)+v(339)*v(3835)+v(3759)*v&
&(6030)
v(3878)=v(338)*v(3635)+v(341)*v(3845)
v(3900)=(v(342)*v(3657)+v(345)*v(3779))/v(323)+v(3856)+v(3878)+v(3790)*v(6031)
v(3889)=(v(352)*v(3591)+v(339)*v(3735))/v(323)+v(3867)+v(3878)+v(3790)*v(6032)
v(3877)=v(338)*v(3634)+v(341)*v(3844)
v(3899)=(v(342)*v(3656)+v(345)*v(3777))/v(323)+v(3855)+v(3877)+v(3789)*v(6031)
v(3888)=(v(352)*v(3590)+v(339)*v(3733))/v(323)+v(3866)+v(3877)+v(3789)*v(6032)
v(3876)=v(338)*v(3633)+v(341)*v(3843)
v(3898)=(v(342)*v(3655)+v(345)*v(3775))/v(323)+v(3854)+v(3876)+v(3788)*v(6031)
v(3887)=(v(352)*v(3589)+v(339)*v(3731))/v(323)+v(3865)+v(3876)+v(3788)*v(6032)
v(3875)=v(338)*v(3632)+v(341)*v(3842)
v(3897)=(v(342)*v(3654)+v(345)*v(3773))/v(323)+v(3853)+v(3875)+v(3787)*v(6031)
v(3886)=(v(352)*v(3588)+v(339)*v(3729))/v(323)+v(3864)+v(3875)+v(3787)*v(6032)
v(3874)=v(338)*v(3631)+v(341)*v(3841)
v(3896)=(v(342)*v(3653)+v(345)*v(3771))/v(323)+v(3852)+v(3874)+v(3786)*v(6031)
v(3885)=(v(352)*v(3587)+v(339)*v(3727))/v(323)+v(3863)+v(3874)+v(3786)*v(6032)
v(3873)=v(338)*v(3630)+v(341)*v(3840)
v(3895)=(v(342)*v(3652)+v(345)*v(3769))/v(323)+v(3851)+v(3873)+v(3785)*v(6031)
v(3884)=(v(352)*v(3586)+v(339)*v(3725))/v(323)+v(3862)+v(3873)+v(3785)*v(6032)
v(3872)=v(338)*v(3629)+v(341)*v(3839)
v(3894)=(v(342)*v(3651)+v(345)*v(3767))/v(323)+v(3850)+v(3872)+v(3784)*v(6031)
v(3883)=(v(352)*v(3585)+v(339)*v(3723))/v(323)+v(3861)+v(3872)+v(3784)*v(6032)
v(3871)=v(338)*v(3628)+v(341)*v(3838)
v(3893)=(v(342)*v(3650)+v(345)*v(3765))/v(323)+v(3849)+v(3871)+v(3783)*v(6031)
v(3882)=(v(352)*v(3584)+v(339)*v(3721))/v(323)+v(3860)+v(3871)+v(3783)*v(6032)
v(3870)=v(338)*v(3627)+v(341)*v(3837)
v(3892)=(v(342)*v(3649)+v(345)*v(3763))/v(323)+v(3848)+v(3870)+v(3782)*v(6031)
v(3881)=(v(352)*v(3583)+v(339)*v(3719))/v(323)+v(3859)+v(3870)+v(3782)*v(6032)
v(3869)=v(338)*v(3626)+v(341)*v(3836)
v(3891)=(v(342)*v(3648)+v(345)*v(3761))/v(323)+v(3847)+v(3869)+v(3781)*v(6031)
v(3880)=(v(352)*v(3582)+v(339)*v(3717))/v(323)+v(3858)+v(3869)+v(3781)*v(6032)
v(3868)=v(338)*v(3625)+v(341)*v(3835)
v(3890)=(v(342)*v(3647)+v(345)*v(3759))/v(323)+v(3846)+v(3868)+v(3780)*v(6031)
v(3879)=(v(352)*v(3581)+v(339)*v(3715))/v(323)+v(3857)+v(3868)+v(3780)*v(6032)
v(1371)=v(1114)*v(338)+v(1260)*v(346)+v(1060)*v(349)+v(1233)*v(350)+(v(1184)*v(351)+v(1105)*v(352))/v(323)+v(1214)*v&
&(6029)
v(1422)=v(1332)*v(298)+v(1314)*v(307)+v(1371)*v(313)
v(1389)=v(1371)*v(297)+v(1332)*v(303)+v(1314)*v(312)
v(1370)=v(1113)*v(338)+v(1259)*v(346)+v(1059)*v(349)+v(1232)*v(350)+(v(1183)*v(351)+v(1104)*v(352))/v(323)+v(1213)*v&
&(6029)
v(1399)=v(1313)*v(299)+v(1370)*v(311)+v(1331)*v(314)
v(1388)=v(1370)*v(297)+v(1331)*v(303)+v(1313)*v(312)
v(1369)=v(1112)*v(338)+v(1258)*v(346)+v(1058)*v(349)+v(1231)*v(350)+(v(1182)*v(351)+v(1103)*v(352))/v(323)+v(1212)*v&
&(6029)
v(1420)=v(1330)*v(298)+v(1312)*v(307)+v(1369)*v(313)
v(1398)=v(1312)*v(299)+v(1369)*v(311)+v(1330)*v(314)
v(1368)=v(1111)*v(338)+v(1257)*v(346)+v(1057)*v(349)+v(1230)*v(350)+(v(1181)*v(351)+v(1102)*v(352))/v(323)+v(1211)*v&
&(6029)
v(1419)=v(1329)*v(298)+v(1311)*v(307)+v(1368)*v(313)
v(1386)=v(1368)*v(297)+v(1329)*v(303)+v(1311)*v(312)
v(1367)=v(1110)*v(338)+v(1256)*v(346)+v(1056)*v(349)+v(1229)*v(350)+(v(1180)*v(351)+v(1101)*v(352))/v(323)+v(1210)*v&
&(6029)
v(1395)=v(1310)*v(299)+v(1367)*v(311)+v(1328)*v(314)
v(1385)=v(1367)*v(297)+v(1328)*v(303)+v(1310)*v(312)
v(1366)=v(1109)*v(338)+v(1255)*v(346)+v(1055)*v(349)+v(1228)*v(350)+(v(1179)*v(351)+v(1100)*v(352))/v(323)+v(1209)*v&
&(6029)
v(1417)=v(1327)*v(298)+v(1309)*v(307)+v(1366)*v(313)
v(1394)=v(1309)*v(299)+v(1366)*v(311)+v(1327)*v(314)
v(1365)=v(1108)*v(338)+v(1254)*v(346)+v(1054)*v(349)+v(1227)*v(350)+(v(1178)*v(351)+v(1099)*v(352))/v(323)+v(1208)*v&
&(6029)
v(1416)=v(1326)*v(298)+v(1308)*v(307)+v(1365)*v(313)
v(1383)=v(1365)*v(297)+v(1326)*v(303)+v(1308)*v(312)
v(1364)=v(1107)*v(338)+v(1253)*v(346)+v(1053)*v(349)+v(1226)*v(350)+(v(1177)*v(351)+v(1098)*v(352))/v(323)+v(1207)*v&
&(6029)
v(1391)=v(1307)*v(299)+v(1364)*v(311)+v(1325)*v(314)
v(1382)=v(1364)*v(297)+v(1325)*v(303)+v(1307)*v(312)
v(1363)=v(1106)*v(338)+v(1252)*v(346)+v(1052)*v(349)+v(1225)*v(350)+(v(1176)*v(351)+v(1097)*v(352))/v(323)+v(1205)*v&
&(6029)
v(1414)=v(1324)*v(298)+v(1306)*v(307)+v(1363)*v(313)
v(1390)=v(1306)*v(299)+v(1363)*v(311)+v(1324)*v(314)
v(1323)=v(1251)*v(319)+v(1087)*v(338)+v(1260)*v(339)+v(1069)*v(340)+(v(1123)/v(323)+v(1214)*v(341))*v(342)+v(1204)*v&
&(6030)
v(1322)=v(1250)*v(319)+v(1086)*v(338)+v(1259)*v(339)+v(1068)*v(340)+(v(1122)/v(323)+v(1213)*v(341))*v(342)+v(1203)*v&
&(6030)
v(1321)=v(1249)*v(319)+v(1085)*v(338)+v(1258)*v(339)+v(1067)*v(340)+(v(1121)/v(323)+v(1212)*v(341))*v(342)+v(1202)*v&
&(6030)
v(1320)=v(1248)*v(319)+v(1084)*v(338)+v(1257)*v(339)+v(1066)*v(340)+(v(1120)/v(323)+v(1211)*v(341))*v(342)+v(1201)*v&
&(6030)
v(1319)=v(1247)*v(319)+v(1083)*v(338)+v(1256)*v(339)+v(1065)*v(340)+(v(1119)/v(323)+v(1210)*v(341))*v(342)+v(1200)*v&
&(6030)
v(1318)=v(1246)*v(319)+v(1082)*v(338)+v(1255)*v(339)+v(1064)*v(340)+(v(1118)/v(323)+v(1209)*v(341))*v(342)+v(1199)*v&
&(6030)
v(1317)=v(1245)*v(319)+v(1081)*v(338)+v(1254)*v(339)+v(1063)*v(340)+(v(1117)/v(323)+v(1208)*v(341))*v(342)+v(1198)*v&
&(6030)
v(1316)=v(1244)*v(319)+v(1080)*v(338)+v(1253)*v(339)+v(1062)*v(340)+(v(1116)/v(323)+v(1207)*v(341))*v(342)+v(1197)*v&
&(6030)
v(1315)=v(1243)*v(319)+v(1079)*v(338)+v(1252)*v(339)+v(1061)*v(340)+(v(1115)/v(323)+v(1205)*v(341))*v(342)+v(1196)*v&
&(6030)
v(1287)=v(1123)*v(338)+v(1260)*v(341)
v(1305)=v(1269)+v(1287)+(v(1141)*v(342)+v(1204)*v(345))/v(323)+v(1214)*v(6031)
v(1362)=v(1305)*v(298)+v(1332)*v(307)+v(1323)*v(313)
v(1341)=v(1323)*v(297)+v(1305)*v(303)+v(1332)*v(312)
v(1296)=v(1278)+v(1287)+(v(1184)*v(339)+v(1087)*v(352))/v(323)+v(1214)*v(6032)
v(1431)=v(1323)*v(298)+v(1371)*v(307)+v(1296)*v(313)
v(1380)=v(1296)*v(297)+v(1323)*v(303)+v(1371)*v(312)
v(1286)=v(1122)*v(338)+v(1259)*v(341)
v(1304)=v(1268)+v(1286)+(v(1140)*v(342)+v(1203)*v(345))/v(323)+v(1213)*v(6031)
v(1351)=v(1331)*v(299)+v(1322)*v(311)+v(1304)*v(314)
v(1340)=v(1322)*v(297)+v(1304)*v(303)+v(1331)*v(312)
v(1295)=v(1277)+v(1286)+(v(1183)*v(339)+v(1086)*v(352))/v(323)+v(1213)*v(6032)
v(1411)=v(1370)*v(299)+v(1295)*v(311)+v(1322)*v(314)
v(1379)=v(1295)*v(297)+v(1322)*v(303)+v(1370)*v(312)
v(1285)=v(1121)*v(338)+v(1258)*v(341)
v(1303)=v(1267)+v(1285)+(v(1139)*v(342)+v(1202)*v(345))/v(323)+v(1212)*v(6031)
v(1360)=v(1303)*v(298)+v(1330)*v(307)+v(1321)*v(313)
v(1350)=v(1330)*v(299)+v(1321)*v(311)+v(1303)*v(314)
v(1294)=v(1276)+v(1285)+(v(1182)*v(339)+v(1085)*v(352))/v(323)+v(1212)*v(6032)
v(1429)=v(1321)*v(298)+v(1369)*v(307)+v(1294)*v(313)
v(1410)=v(1369)*v(299)+v(1294)*v(311)+v(1321)*v(314)
v(1284)=v(1120)*v(338)+v(1257)*v(341)
v(1302)=v(1266)+v(1284)+(v(1138)*v(342)+v(1201)*v(345))/v(323)+v(1211)*v(6031)
v(1359)=v(1302)*v(298)+v(1329)*v(307)+v(1320)*v(313)
v(1338)=v(1320)*v(297)+v(1302)*v(303)+v(1329)*v(312)
v(1293)=v(1275)+v(1284)+(v(1181)*v(339)+v(1084)*v(352))/v(323)+v(1211)*v(6032)
v(1428)=v(1320)*v(298)+v(1368)*v(307)+v(1293)*v(313)
v(1377)=v(1293)*v(297)+v(1320)*v(303)+v(1368)*v(312)
v(1283)=v(1119)*v(338)+v(1256)*v(341)
v(1301)=v(1265)+v(1283)+(v(1137)*v(342)+v(1200)*v(345))/v(323)+v(1210)*v(6031)
v(1347)=v(1328)*v(299)+v(1319)*v(311)+v(1301)*v(314)
v(1337)=v(1319)*v(297)+v(1301)*v(303)+v(1328)*v(312)
v(1292)=v(1274)+v(1283)+(v(1180)*v(339)+v(1083)*v(352))/v(323)+v(1210)*v(6032)
v(1407)=v(1367)*v(299)+v(1292)*v(311)+v(1319)*v(314)
v(1376)=v(1292)*v(297)+v(1319)*v(303)+v(1367)*v(312)
v(1282)=v(1118)*v(338)+v(1255)*v(341)
v(1300)=v(1264)+v(1282)+(v(1136)*v(342)+v(1199)*v(345))/v(323)+v(1209)*v(6031)
v(1357)=v(1300)*v(298)+v(1327)*v(307)+v(1318)*v(313)
v(1346)=v(1327)*v(299)+v(1318)*v(311)+v(1300)*v(314)
v(1291)=v(1273)+v(1282)+(v(1179)*v(339)+v(1082)*v(352))/v(323)+v(1209)*v(6032)
v(1426)=v(1318)*v(298)+v(1366)*v(307)+v(1291)*v(313)
v(1406)=v(1366)*v(299)+v(1291)*v(311)+v(1318)*v(314)
v(1281)=v(1117)*v(338)+v(1254)*v(341)
v(1299)=v(1263)+v(1281)+(v(1135)*v(342)+v(1198)*v(345))/v(323)+v(1208)*v(6031)
v(1356)=v(1299)*v(298)+v(1326)*v(307)+v(1317)*v(313)
v(1335)=v(1317)*v(297)+v(1299)*v(303)+v(1326)*v(312)
v(1290)=v(1272)+v(1281)+(v(1178)*v(339)+v(1081)*v(352))/v(323)+v(1208)*v(6032)
v(1425)=v(1317)*v(298)+v(1365)*v(307)+v(1290)*v(313)
v(1374)=v(1290)*v(297)+v(1317)*v(303)+v(1365)*v(312)
v(1280)=v(1116)*v(338)+v(1253)*v(341)
v(1298)=v(1262)+v(1280)+(v(1134)*v(342)+v(1197)*v(345))/v(323)+v(1207)*v(6031)
v(1343)=v(1325)*v(299)+v(1316)*v(311)+v(1298)*v(314)
v(1334)=v(1316)*v(297)+v(1298)*v(303)+v(1325)*v(312)
v(1289)=v(1271)+v(1280)+(v(1177)*v(339)+v(1080)*v(352))/v(323)+v(1207)*v(6032)
v(1403)=v(1364)*v(299)+v(1289)*v(311)+v(1316)*v(314)
v(1373)=v(1289)*v(297)+v(1316)*v(303)+v(1364)*v(312)
v(1279)=v(1115)*v(338)+v(1252)*v(341)
v(1297)=v(1261)+v(1279)+(v(1133)*v(342)+v(1196)*v(345))/v(323)+v(1205)*v(6031)
v(1354)=v(1297)*v(298)+v(1324)*v(307)+v(1315)*v(313)
v(1342)=v(1324)*v(299)+v(1315)*v(311)+v(1297)*v(314)
v(1288)=v(1270)+v(1279)+(v(1176)*v(339)+v(1079)*v(352))/v(323)+v(1205)*v(6032)
v(1423)=v(1315)*v(298)+v(1363)*v(307)+v(1288)*v(313)
v(1402)=v(1363)*v(299)+v(1288)*v(311)+v(1315)*v(314)
v(333)=v(344)*v(346)
v(332)=v(320)*v(340)
v(325)=v(338)*v(341)
v(324)=v(325)+v(332)+v(6032)/v(323)
v(331)=v(325)+v(333)+v(6031)/v(323)
v(337)=v(332)+v(333)+v(6028)/v(323)
v(343)=v(338)*v(339)+v(319)*v(340)+v(342)*v(6030)
v(348)=v(344)*v(345)+v(341)*v(349)+v(6027)/v(323)
v(4190)=v(1323)*v(315)+v(1305)*v(318)+v(1332)*v(320)+v(1042)*v(331)+v(1096)*v(348)+v(343)*v(988)
v(4189)=v(1322)*v(315)+v(1304)*v(318)+v(1331)*v(320)+v(1041)*v(331)+v(1095)*v(348)+v(343)*v(987)
v(4188)=v(1321)*v(315)+v(1303)*v(318)+v(1330)*v(320)+v(1040)*v(331)+v(1094)*v(348)+v(343)*v(986)
v(4187)=v(1320)*v(315)+v(1302)*v(318)+v(1329)*v(320)+v(1039)*v(331)+v(1093)*v(348)+v(343)*v(985)
v(4186)=v(1319)*v(315)+v(1301)*v(318)+v(1328)*v(320)+v(1038)*v(331)+v(1092)*v(348)+v(343)*v(984)
v(4185)=v(1318)*v(315)+v(1300)*v(318)+v(1327)*v(320)+v(1037)*v(331)+v(1091)*v(348)+v(343)*v(983)
v(4184)=v(1317)*v(315)+v(1299)*v(318)+v(1326)*v(320)+v(1036)*v(331)+v(1090)*v(348)+v(343)*v(982)
v(4183)=v(1316)*v(315)+v(1298)*v(318)+v(1325)*v(320)+v(1035)*v(331)+v(1089)*v(348)+v(343)*v(981)
v(4182)=v(1315)*v(315)+v(1297)*v(318)+v(1324)*v(320)+v(1034)*v(331)+v(1088)*v(348)+v(343)*v(980)
v(3966)=v(331)*v(3382)+v(343)*v(3448)+v(3415)*v(348)+v(298)*v(3900)+v(313)*v(3922)+v(307)*v(3933)
v(3965)=v(331)*v(3381)+v(343)*v(3447)+v(3414)*v(348)+v(298)*v(3899)+v(313)*v(3921)+v(307)*v(3932)
v(3964)=v(331)*v(3380)+v(343)*v(3446)+v(3413)*v(348)+v(298)*v(3898)+v(313)*v(3920)+v(307)*v(3931)
v(3963)=v(331)*v(3379)+v(343)*v(3445)+v(3412)*v(348)+v(298)*v(3897)+v(313)*v(3919)+v(307)*v(3930)
v(3962)=v(331)*v(3378)+v(343)*v(3444)+v(3411)*v(348)+v(298)*v(3896)+v(313)*v(3918)+v(307)*v(3929)
v(3961)=v(331)*v(3377)+v(343)*v(3443)+v(3410)*v(348)+v(298)*v(3895)+v(313)*v(3917)+v(307)*v(3928)
v(3960)=v(331)*v(3376)+v(343)*v(3442)+v(3409)*v(348)+v(298)*v(3894)+v(313)*v(3916)+v(307)*v(3927)
v(3959)=v(331)*v(3375)+v(343)*v(3441)+v(3408)*v(348)+v(298)*v(3893)+v(313)*v(3915)+v(307)*v(3926)
v(3958)=v(331)*v(3374)+v(343)*v(3440)+v(3407)*v(348)+v(298)*v(3892)+v(313)*v(3914)+v(307)*v(3925)
v(3957)=v(331)*v(3373)+v(343)*v(3439)+v(3406)*v(348)+v(298)*v(3891)+v(313)*v(3913)+v(307)*v(3924)
v(3956)=v(331)*v(3372)+v(343)*v(3438)+v(3405)*v(348)+v(298)*v(3890)+v(313)*v(3912)+v(307)*v(3923)
v(3955)=v(3426)*v(343)+v(331)*v(3459)+v(3393)*v(348)+v(314)*v(3900)+v(311)*v(3922)+v(299)*v(3933)
v(3954)=v(3425)*v(343)+v(331)*v(3458)+v(3392)*v(348)+v(314)*v(3899)+v(311)*v(3921)+v(299)*v(3932)
v(3953)=v(3424)*v(343)+v(331)*v(3457)+v(3391)*v(348)+v(314)*v(3898)+v(311)*v(3920)+v(299)*v(3931)
v(3952)=v(3423)*v(343)+v(331)*v(3456)+v(3390)*v(348)+v(314)*v(3897)+v(311)*v(3919)+v(299)*v(3930)
v(3951)=v(3422)*v(343)+v(331)*v(3455)+v(3389)*v(348)+v(314)*v(3896)+v(311)*v(3918)+v(299)*v(3929)
v(3950)=v(3421)*v(343)+v(331)*v(3454)+v(3388)*v(348)+v(314)*v(3895)+v(311)*v(3917)+v(299)*v(3928)
v(3949)=v(3420)*v(343)+v(331)*v(3453)+v(3387)*v(348)+v(314)*v(3894)+v(311)*v(3916)+v(299)*v(3927)
v(3948)=v(3419)*v(343)+v(331)*v(3452)+v(3386)*v(348)+v(314)*v(3893)+v(311)*v(3915)+v(299)*v(3926)
v(3947)=v(3418)*v(343)+v(331)*v(3451)+v(3385)*v(348)+v(314)*v(3892)+v(311)*v(3914)+v(299)*v(3925)
v(3946)=v(3417)*v(343)+v(331)*v(3450)+v(3384)*v(348)+v(314)*v(3891)+v(311)*v(3913)+v(299)*v(3924)
v(3945)=v(3416)*v(343)+v(331)*v(3449)+v(3383)*v(348)+v(314)*v(3890)+v(311)*v(3912)+v(299)*v(3923)
v(3944)=v(331)*v(3404)+v(3371)*v(343)+v(3437)*v(348)+v(303)*v(3900)+v(297)*v(3922)+v(312)*v(3933)
v(3943)=v(331)*v(3403)+v(3370)*v(343)+v(3436)*v(348)+v(303)*v(3899)+v(297)*v(3921)+v(312)*v(3932)
v(3942)=v(331)*v(3402)+v(3369)*v(343)+v(3435)*v(348)+v(303)*v(3898)+v(297)*v(3920)+v(312)*v(3931)
v(3941)=v(331)*v(3401)+v(3368)*v(343)+v(3434)*v(348)+v(303)*v(3897)+v(297)*v(3919)+v(312)*v(3930)
v(3940)=v(331)*v(3400)+v(3367)*v(343)+v(3433)*v(348)+v(303)*v(3896)+v(297)*v(3918)+v(312)*v(3929)
v(3939)=v(331)*v(3399)+v(3366)*v(343)+v(3432)*v(348)+v(303)*v(3895)+v(297)*v(3917)+v(312)*v(3928)
v(3938)=v(331)*v(3398)+v(3365)*v(343)+v(3431)*v(348)+v(303)*v(3894)+v(297)*v(3916)+v(312)*v(3927)
v(3937)=v(331)*v(3397)+v(3364)*v(343)+v(3430)*v(348)+v(303)*v(3893)+v(297)*v(3915)+v(312)*v(3926)
v(3936)=v(331)*v(3396)+v(3363)*v(343)+v(3429)*v(348)+v(303)*v(3892)+v(297)*v(3914)+v(312)*v(3925)
v(3935)=v(331)*v(3395)+v(3362)*v(343)+v(3428)*v(348)+v(303)*v(3891)+v(297)*v(3913)+v(312)*v(3924)
v(3934)=v(331)*v(3394)+v(3361)*v(343)+v(3427)*v(348)+v(303)*v(3890)+v(297)*v(3912)+v(312)*v(3923)
v(1352)=v(343)*v(972)+v(331)*v(974)+v(348)*v(979)
v(1355)=v(1352)+v(1298)*v(298)+v(1325)*v(307)+v(1316)*v(313)
v(1353)=v(1352)+v(1332)*v(299)+v(1323)*v(311)+v(1305)*v(314)
v(1348)=v(343)*v(971)+v(331)*v(976)+v(348)*v(978)
v(1361)=v(1348)+v(1304)*v(298)+v(1331)*v(307)+v(1322)*v(313)
v(1349)=v(1348)+v(1329)*v(299)+v(1320)*v(311)+v(1302)*v(314)
v(1344)=v(343)*v(973)+v(331)*v(975)+v(348)*v(977)
v(1358)=v(1344)+v(1301)*v(298)+v(1328)*v(307)+v(1319)*v(313)
v(1345)=v(1344)+v(1326)*v(299)+v(1317)*v(311)+v(1299)*v(314)
v(1339)=v(1344)+v(1321)*v(297)+v(1303)*v(303)+v(1330)*v(312)
v(1336)=v(1352)+v(1318)*v(297)+v(1300)*v(303)+v(1327)*v(312)
v(1333)=v(1348)+v(1315)*v(297)+v(1297)*v(303)+v(1324)*v(312)
v(960)=v(303)*v(331)+v(297)*v(343)+v(312)*v(348)
v(956)=v(314)*v(331)+v(311)*v(343)+v(299)*v(348)
v(952)=v(298)*v(331)+v(313)*v(343)+v(307)*v(348)
v(353)=v(338)*v(346)+v(349)*v(350)+v(6029)/v(323)
v(4208)=v(1371)*v(317)+v(1323)*v(319)+v(1296)*v(320)+v(1096)*v(324)+v(1069)*v(343)+v(1024)*v(353)
v(4207)=v(1370)*v(317)+v(1322)*v(319)+v(1295)*v(320)+v(1095)*v(324)+v(1068)*v(343)+v(1023)*v(353)
v(4206)=v(1369)*v(317)+v(1321)*v(319)+v(1294)*v(320)+v(1094)*v(324)+v(1067)*v(343)+v(1022)*v(353)
v(4205)=v(1368)*v(317)+v(1320)*v(319)+v(1293)*v(320)+v(1093)*v(324)+v(1066)*v(343)+v(1021)*v(353)
v(4204)=v(1367)*v(317)+v(1319)*v(319)+v(1292)*v(320)+v(1092)*v(324)+v(1065)*v(343)+v(1020)*v(353)
v(4203)=v(1366)*v(317)+v(1318)*v(319)+v(1291)*v(320)+v(1091)*v(324)+v(1064)*v(343)+v(1019)*v(353)
v(4202)=v(1365)*v(317)+v(1317)*v(319)+v(1290)*v(320)+v(1090)*v(324)+v(1063)*v(343)+v(1018)*v(353)
v(4201)=v(1364)*v(317)+v(1316)*v(319)+v(1289)*v(320)+v(1089)*v(324)+v(1062)*v(343)+v(1017)*v(353)
v(4200)=v(1363)*v(317)+v(1315)*v(319)+v(1288)*v(320)+v(1088)*v(324)+v(1061)*v(343)+v(1016)*v(353)
v(4199)=v(1332)*v(316)+v(1371)*v(318)+v(1314)*v(319)+v(1069)*v(337)+v(1006)*v(348)+v(1042)*v(353)
v(4198)=v(1331)*v(316)+v(1370)*v(318)+v(1313)*v(319)+v(1068)*v(337)+v(1005)*v(348)+v(1041)*v(353)
v(4197)=v(1330)*v(316)+v(1369)*v(318)+v(1312)*v(319)+v(1067)*v(337)+v(1004)*v(348)+v(1040)*v(353)
v(4196)=v(1329)*v(316)+v(1368)*v(318)+v(1311)*v(319)+v(1066)*v(337)+v(1003)*v(348)+v(1039)*v(353)
v(4195)=v(1328)*v(316)+v(1367)*v(318)+v(1310)*v(319)+v(1065)*v(337)+v(1002)*v(348)+v(1038)*v(353)
v(4194)=v(1327)*v(316)+v(1366)*v(318)+v(1309)*v(319)+v(1064)*v(337)+v(1001)*v(348)+v(1037)*v(353)
v(4193)=v(1326)*v(316)+v(1365)*v(318)+v(1308)*v(319)+v(1063)*v(337)+v(1000)*v(348)+v(1036)*v(353)
v(4192)=v(1325)*v(316)+v(1364)*v(318)+v(1307)*v(319)+v(1062)*v(337)+v(1035)*v(353)+v(348)*v(999)
v(4191)=v(1324)*v(316)+v(1363)*v(318)+v(1306)*v(319)+v(1061)*v(337)+v(1034)*v(353)+v(348)*v(998)
v(4043)=v(3382)*v(343)+v(324)*v(3448)+v(3415)*v(353)+v(313)*v(3889)+v(298)*v(3922)+v(307)*v(3977)
v(4042)=v(3381)*v(343)+v(324)*v(3447)+v(3414)*v(353)+v(313)*v(3888)+v(298)*v(3921)+v(307)*v(3976)
v(4041)=v(3380)*v(343)+v(324)*v(3446)+v(3413)*v(353)+v(313)*v(3887)+v(298)*v(3920)+v(307)*v(3975)
v(4040)=v(3379)*v(343)+v(324)*v(3445)+v(3412)*v(353)+v(313)*v(3886)+v(298)*v(3919)+v(307)*v(3974)
v(4039)=v(3378)*v(343)+v(324)*v(3444)+v(3411)*v(353)+v(313)*v(3885)+v(298)*v(3918)+v(307)*v(3973)
v(4038)=v(3377)*v(343)+v(324)*v(3443)+v(3410)*v(353)+v(313)*v(3884)+v(298)*v(3917)+v(307)*v(3972)
v(4037)=v(3376)*v(343)+v(324)*v(3442)+v(3409)*v(353)+v(313)*v(3883)+v(298)*v(3916)+v(307)*v(3971)
v(4036)=v(3375)*v(343)+v(324)*v(3441)+v(3408)*v(353)+v(313)*v(3882)+v(298)*v(3915)+v(307)*v(3970)
v(4035)=v(3374)*v(343)+v(324)*v(3440)+v(3407)*v(353)+v(313)*v(3881)+v(298)*v(3914)+v(307)*v(3969)
v(4034)=v(3373)*v(343)+v(324)*v(3439)+v(3406)*v(353)+v(313)*v(3880)+v(298)*v(3913)+v(307)*v(3968)
v(4033)=v(3372)*v(343)+v(324)*v(3438)+v(3405)*v(353)+v(313)*v(3879)+v(298)*v(3912)+v(307)*v(3967)
v(4032)=v(337)*v(3415)+v(3382)*v(348)+v(3448)*v(353)+v(307)*v(3911)+v(298)*v(3933)+v(313)*v(3977)
v(4031)=v(337)*v(3414)+v(3381)*v(348)+v(3447)*v(353)+v(307)*v(3910)+v(298)*v(3932)+v(313)*v(3976)
v(4030)=v(337)*v(3413)+v(3380)*v(348)+v(3446)*v(353)+v(307)*v(3909)+v(298)*v(3931)+v(313)*v(3975)
v(4029)=v(337)*v(3412)+v(3379)*v(348)+v(3445)*v(353)+v(307)*v(3908)+v(298)*v(3930)+v(313)*v(3974)
v(4028)=v(337)*v(3411)+v(3378)*v(348)+v(3444)*v(353)+v(307)*v(3907)+v(298)*v(3929)+v(313)*v(3973)
v(4027)=v(337)*v(3410)+v(3377)*v(348)+v(3443)*v(353)+v(307)*v(3906)+v(298)*v(3928)+v(313)*v(3972)
v(4026)=v(337)*v(3409)+v(3376)*v(348)+v(3442)*v(353)+v(307)*v(3905)+v(298)*v(3927)+v(313)*v(3971)
v(4025)=v(337)*v(3408)+v(3375)*v(348)+v(3441)*v(353)+v(307)*v(3904)+v(298)*v(3926)+v(313)*v(3970)
v(4024)=v(337)*v(3407)+v(3374)*v(348)+v(3440)*v(353)+v(307)*v(3903)+v(298)*v(3925)+v(313)*v(3969)
v(4023)=v(337)*v(3406)+v(3373)*v(348)+v(3439)*v(353)+v(307)*v(3902)+v(298)*v(3924)+v(313)*v(3968)
v(4022)=v(337)*v(3405)+v(3372)*v(348)+v(3438)*v(353)+v(307)*v(3901)+v(298)*v(3923)+v(313)*v(3967)
v(4021)=v(324)*v(3426)+v(343)*v(3459)+v(3393)*v(353)+v(311)*v(3889)+v(314)*v(3922)+v(299)*v(3977)
v(4020)=v(324)*v(3425)+v(343)*v(3458)+v(3392)*v(353)+v(311)*v(3888)+v(314)*v(3921)+v(299)*v(3976)
v(4019)=v(324)*v(3424)+v(343)*v(3457)+v(3391)*v(353)+v(311)*v(3887)+v(314)*v(3920)+v(299)*v(3975)
v(4018)=v(324)*v(3423)+v(343)*v(3456)+v(3390)*v(353)+v(311)*v(3886)+v(314)*v(3919)+v(299)*v(3974)
v(4017)=v(324)*v(3422)+v(343)*v(3455)+v(3389)*v(353)+v(311)*v(3885)+v(314)*v(3918)+v(299)*v(3973)
v(4016)=v(324)*v(3421)+v(343)*v(3454)+v(3388)*v(353)+v(311)*v(3884)+v(314)*v(3917)+v(299)*v(3972)
v(4015)=v(324)*v(3420)+v(343)*v(3453)+v(3387)*v(353)+v(311)*v(3883)+v(314)*v(3916)+v(299)*v(3971)
v(4014)=v(324)*v(3419)+v(343)*v(3452)+v(3386)*v(353)+v(311)*v(3882)+v(314)*v(3915)+v(299)*v(3970)
v(4013)=v(324)*v(3418)+v(343)*v(3451)+v(3385)*v(353)+v(311)*v(3881)+v(314)*v(3914)+v(299)*v(3969)
v(4012)=v(324)*v(3417)+v(343)*v(3450)+v(3384)*v(353)+v(311)*v(3880)+v(314)*v(3913)+v(299)*v(3968)
v(4011)=v(324)*v(3416)+v(343)*v(3449)+v(3383)*v(353)+v(311)*v(3879)+v(314)*v(3912)+v(299)*v(3967)
v(4010)=v(337)*v(3393)+v(3459)*v(348)+v(3426)*v(353)+v(299)*v(3911)+v(314)*v(3933)+v(311)*v(3977)
v(4009)=v(337)*v(3392)+v(3458)*v(348)+v(3425)*v(353)+v(299)*v(3910)+v(314)*v(3932)+v(311)*v(3976)
v(4008)=v(337)*v(3391)+v(3457)*v(348)+v(3424)*v(353)+v(299)*v(3909)+v(314)*v(3931)+v(311)*v(3975)
v(4007)=v(337)*v(3390)+v(3456)*v(348)+v(3423)*v(353)+v(299)*v(3908)+v(314)*v(3930)+v(311)*v(3974)
v(4006)=v(337)*v(3389)+v(3455)*v(348)+v(3422)*v(353)+v(299)*v(3907)+v(314)*v(3929)+v(311)*v(3973)
v(4005)=v(337)*v(3388)+v(3454)*v(348)+v(3421)*v(353)+v(299)*v(3906)+v(314)*v(3928)+v(311)*v(3972)
v(4004)=v(337)*v(3387)+v(3453)*v(348)+v(3420)*v(353)+v(299)*v(3905)+v(314)*v(3927)+v(311)*v(3971)
v(4003)=v(337)*v(3386)+v(3452)*v(348)+v(3419)*v(353)+v(299)*v(3904)+v(314)*v(3926)+v(311)*v(3970)
v(4002)=v(337)*v(3385)+v(3451)*v(348)+v(3418)*v(353)+v(299)*v(3903)+v(314)*v(3925)+v(311)*v(3969)
v(4001)=v(337)*v(3384)+v(3450)*v(348)+v(3417)*v(353)+v(299)*v(3902)+v(314)*v(3924)+v(311)*v(3968)
v(4000)=v(337)*v(3383)+v(3449)*v(348)+v(3416)*v(353)+v(299)*v(3901)+v(314)*v(3923)+v(311)*v(3967)
v(3999)=v(337)*v(3437)+v(3404)*v(348)+v(3371)*v(353)+v(312)*v(3911)+v(303)*v(3933)+v(297)*v(3977)
v(3998)=v(337)*v(3436)+v(3403)*v(348)+v(3370)*v(353)+v(312)*v(3910)+v(303)*v(3932)+v(297)*v(3976)
v(3997)=v(337)*v(3435)+v(3402)*v(348)+v(3369)*v(353)+v(312)*v(3909)+v(303)*v(3931)+v(297)*v(3975)
v(3996)=v(337)*v(3434)+v(3401)*v(348)+v(3368)*v(353)+v(312)*v(3908)+v(303)*v(3930)+v(297)*v(3974)
v(3995)=v(337)*v(3433)+v(3400)*v(348)+v(3367)*v(353)+v(312)*v(3907)+v(303)*v(3929)+v(297)*v(3973)
v(3994)=v(337)*v(3432)+v(3399)*v(348)+v(3366)*v(353)+v(312)*v(3906)+v(303)*v(3928)+v(297)*v(3972)
v(3993)=v(337)*v(3431)+v(3398)*v(348)+v(3365)*v(353)+v(312)*v(3905)+v(303)*v(3927)+v(297)*v(3971)
v(3992)=v(337)*v(3430)+v(3397)*v(348)+v(3364)*v(353)+v(312)*v(3904)+v(303)*v(3926)+v(297)*v(3970)
v(3991)=v(337)*v(3429)+v(3396)*v(348)+v(3363)*v(353)+v(312)*v(3903)+v(303)*v(3925)+v(297)*v(3969)
v(3990)=v(337)*v(3428)+v(3395)*v(348)+v(3362)*v(353)+v(312)*v(3902)+v(303)*v(3924)+v(297)*v(3968)
v(3989)=v(337)*v(3427)+v(3394)*v(348)+v(3361)*v(353)+v(312)*v(3901)+v(303)*v(3923)+v(297)*v(3967)
v(3988)=v(324)*v(3371)+v(3404)*v(343)+v(3437)*v(353)+v(297)*v(3889)+v(303)*v(3922)+v(312)*v(3977)
v(3987)=v(324)*v(3370)+v(3403)*v(343)+v(3436)*v(353)+v(297)*v(3888)+v(303)*v(3921)+v(312)*v(3976)
v(3986)=v(324)*v(3369)+v(3402)*v(343)+v(3435)*v(353)+v(297)*v(3887)+v(303)*v(3920)+v(312)*v(3975)
v(3985)=v(324)*v(3368)+v(3401)*v(343)+v(3434)*v(353)+v(297)*v(3886)+v(303)*v(3919)+v(312)*v(3974)
v(3984)=v(324)*v(3367)+v(3400)*v(343)+v(3433)*v(353)+v(297)*v(3885)+v(303)*v(3918)+v(312)*v(3973)
v(3983)=v(324)*v(3366)+v(3399)*v(343)+v(3432)*v(353)+v(297)*v(3884)+v(303)*v(3917)+v(312)*v(3972)
v(3982)=v(324)*v(3365)+v(3398)*v(343)+v(3431)*v(353)+v(297)*v(3883)+v(303)*v(3916)+v(312)*v(3971)
v(3981)=v(324)*v(3364)+v(3397)*v(343)+v(3430)*v(353)+v(297)*v(3882)+v(303)*v(3915)+v(312)*v(3970)
v(3980)=v(324)*v(3363)+v(3396)*v(343)+v(3429)*v(353)+v(297)*v(3881)+v(303)*v(3914)+v(312)*v(3969)
v(3979)=v(324)*v(3362)+v(3395)*v(343)+v(3428)*v(353)+v(297)*v(3880)+v(303)*v(3913)+v(312)*v(3968)
v(3978)=v(324)*v(3361)+v(3394)*v(343)+v(3427)*v(353)+v(297)*v(3879)+v(303)*v(3912)+v(312)*v(3967)
v(1412)=v(324)*v(972)+v(343)*v(974)+v(353)*v(979)
v(1424)=v(1412)+v(1316)*v(298)+v(1364)*v(307)+v(1289)*v(313)
v(1413)=v(1412)+v(1371)*v(299)+v(1296)*v(311)+v(1323)*v(314)
v(1408)=v(324)*v(971)+v(343)*v(976)+v(353)*v(978)
v(1430)=v(1408)+v(1322)*v(298)+v(1370)*v(307)+v(1295)*v(313)
v(1409)=v(1408)+v(1368)*v(299)+v(1293)*v(311)+v(1320)*v(314)
v(1404)=v(324)*v(973)+v(343)*v(975)+v(353)*v(977)
v(1427)=v(1404)+v(1319)*v(298)+v(1367)*v(307)+v(1292)*v(313)
v(1405)=v(1404)+v(1365)*v(299)+v(1290)*v(311)+v(1317)*v(314)
v(1400)=v(353)*v(972)+v(348)*v(974)+v(337)*v(979)
v(1415)=v(1400)+v(1325)*v(298)+v(1307)*v(307)+v(1364)*v(313)
v(1401)=v(1400)+v(1314)*v(299)+v(1371)*v(311)+v(1332)*v(314)
v(1396)=v(353)*v(971)+v(348)*v(976)+v(337)*v(978)
v(1421)=v(1396)+v(1331)*v(298)+v(1313)*v(307)+v(1370)*v(313)
v(1397)=v(1396)+v(1311)*v(299)+v(1368)*v(311)+v(1329)*v(314)
v(1392)=v(353)*v(973)+v(348)*v(975)+v(337)*v(977)
v(1418)=v(1392)+v(1328)*v(298)+v(1310)*v(307)+v(1367)*v(313)
v(1393)=v(1392)+v(1308)*v(299)+v(1365)*v(311)+v(1326)*v(314)
v(1387)=v(1392)+v(1369)*v(297)+v(1330)*v(303)+v(1312)*v(312)
v(1384)=v(1400)+v(1366)*v(297)+v(1327)*v(303)+v(1309)*v(312)
v(1381)=v(1396)+v(1363)*v(297)+v(1324)*v(303)+v(1306)*v(312)
v(1378)=v(1404)+v(1294)*v(297)+v(1321)*v(303)+v(1369)*v(312)
v(1375)=v(1412)+v(1291)*v(297)+v(1318)*v(303)+v(1366)*v(312)
v(1372)=v(1408)+v(1288)*v(297)+v(1315)*v(303)+v(1363)*v(312)
v(962)=v(297)*v(324)+v(303)*v(343)+v(312)*v(353)
v(961)=v(312)*v(337)+v(303)*v(348)+v(297)*v(353)
v(1493)=v(962)*v(972)+v(960)*v(974)+v(961)*v(979)
v(1471)=v(962)*v(973)+v(960)*v(975)+v(961)*v(977)
v(1469)=v(962)*v(971)+v(960)*v(976)+v(961)*v(978)
v(958)=v(299)*v(337)+v(314)*v(348)+v(311)*v(353)
v(957)=v(311)*v(324)+v(314)*v(343)+v(299)*v(353)
v(1489)=v(957)*v(972)+v(956)*v(974)+v(958)*v(979)
v(1484)=v(957)*v(971)+v(956)*v(976)+v(958)*v(978)
v(1461)=v(957)*v(973)+v(956)*v(975)+v(958)*v(977)
v(954)=v(307)*v(337)+v(298)*v(348)+v(313)*v(353)
v(953)=v(313)*v(324)+v(298)*v(343)+v(307)*v(353)
v(1480)=v(953)*v(971)+v(952)*v(976)+v(954)*v(978)
v(1475)=v(953)*v(973)+v(952)*v(975)+v(954)*v(977)
v(1453)=v(953)*v(972)+v(952)*v(974)+v(954)*v(979)
v(354)=v(318)*v(331)+v(315)*v(343)+v(320)*v(348)
v(355)=v(319)*v(337)+v(316)*v(348)+v(318)*v(353)
v(356)=v(320)*v(324)+v(319)*v(343)+v(317)*v(353)
v(357)=v(359)+(2d0/3d0)*v(360)+v(362)
v(361)=(-2d0/3d0)*v(358)+v(359)+v(364)
v(365)=v(362)+(-2d0/3d0)*v(363)+v(364)
v(366)=v(354)-x(4)-x(9)
v(367)=v(355)-x(11)-x(6)
v(368)=v(356)-x(10)-x(5)
v(375)=sqrt(v(369)+v(370)+v(371)+2d0*v(372)+2d0*v(373)+2d0*v(374))
v(6033)=v(5515)/v(375)
v(4244)=v(6033)*(v(223)*v(5998)+v(228)*v(5999)+v(227)*v(6000)+v(4190)*v(6034)+v(4199)*v(6035)+v(4208)*v(6036))
v(4243)=v(6033)*(v(223)*v(6001)+v(228)*v(6002)+v(227)*v(6003)+v(4189)*v(6034)+v(4198)*v(6035)+v(4207)*v(6036))
v(4242)=v(6033)*(v(223)*v(6004)+v(228)*v(6005)+v(227)*v(6006)+v(4188)*v(6034)+v(4197)*v(6035)+v(4206)*v(6036))
v(4241)=v(6033)*(v(223)*v(6007)+v(228)*v(6008)+v(227)*v(6009)+v(4187)*v(6034)+v(4196)*v(6035)+v(4205)*v(6036))
v(4240)=v(6033)*(v(223)*v(6010)+v(228)*v(6011)+v(227)*v(6012)+v(4186)*v(6034)+v(4195)*v(6035)+v(4204)*v(6036))
v(4239)=v(6033)*(v(223)*v(6013)+v(228)*v(6014)+v(227)*v(6015)+v(4185)*v(6034)+v(4194)*v(6035)+v(4203)*v(6036))
v(4238)=v(6033)*(v(223)*v(6016)+v(228)*v(6017)+v(227)*v(6018)+v(4184)*v(6034)+v(4193)*v(6035)+v(4202)*v(6036))
v(4237)=v(6033)*(v(223)*v(6019)+v(228)*v(6020)+v(227)*v(6021)+v(4183)*v(6034)+v(4192)*v(6035)+v(4201)*v(6036))
v(4236)=v(6033)*(v(223)*v(6022)+v(228)*v(6023)+v(227)*v(6024)+v(4182)*v(6034)+v(4191)*v(6035)+v(4200)*v(6036))
v(387)=v(6033)*(v(228)*v(5550)+v(6036)*x(10)+v(6035)*x(11)+v(223)*x(7)+v(227)*x(8)+v(6034)*x(9))
v(378)=v(6033)*(v(223)*v(357)+v(227)*v(361)+v(228)*v(365)+v(366)*v(6034)+v(367)*v(6035)+v(368)*v(6036))
v(377)=0.15d1*mpar(8)*v(375)
v(4318)=(v(377)*v(4208)+v(231)*v(4244))*v(6037)
v(4317)=(v(377)*v(4207)+v(231)*v(4243))*v(6037)
v(4316)=(v(377)*v(4206)+v(231)*v(4242))*v(6037)
v(4315)=(v(377)*v(4205)+v(231)*v(4241))*v(6037)
v(4314)=(v(377)*v(4204)+v(231)*v(4240))*v(6037)
v(4313)=(v(377)*v(4203)+v(231)*v(4239))*v(6037)
v(4312)=(v(377)*v(4202)+v(231)*v(4238))*v(6037)
v(4311)=(v(377)*v(4201)+v(231)*v(4237))*v(6037)
v(4310)=(v(377)*v(4200)+v(231)*v(4236))*v(6037)
v(4299)=(v(377)*v(4199)+v(230)*v(4244))*v(6037)
v(4298)=(v(377)*v(4198)+v(230)*v(4243))*v(6037)
v(4297)=(v(377)*v(4197)+v(230)*v(4242))*v(6037)
v(4296)=(v(377)*v(4196)+v(230)*v(4241))*v(6037)
v(4295)=(v(377)*v(4195)+v(230)*v(4240))*v(6037)
v(4294)=(v(377)*v(4194)+v(230)*v(4239))*v(6037)
v(4293)=(v(377)*v(4193)+v(230)*v(4238))*v(6037)
v(4292)=(v(377)*v(4192)+v(230)*v(4237))*v(6037)
v(4291)=(v(377)*v(4191)+v(230)*v(4236))*v(6037)
v(4280)=(v(377)*v(4190)+v(229)*v(4244))*v(6037)
v(4279)=(v(377)*v(4189)+v(229)*v(4243))*v(6037)
v(4278)=(v(377)*v(4188)+v(229)*v(4242))*v(6037)
v(4277)=(v(377)*v(4187)+v(229)*v(4241))*v(6037)
v(4276)=(v(377)*v(4186)+v(229)*v(4240))*v(6037)
v(4275)=(v(377)*v(4185)+v(229)*v(4239))*v(6037)
v(4274)=(v(377)*v(4184)+v(229)*v(4238))*v(6037)
v(4273)=(v(377)*v(4183)+v(229)*v(4237))*v(6037)
v(4272)=(v(377)*v(4182)+v(229)*v(4236))*v(6037)
v(4271)=(v(228)*v(4244)+v(377)*v(5999))*v(6037)
v(4270)=(v(228)*v(4243)+v(377)*v(6002))*v(6037)
v(4269)=(v(228)*v(4242)+v(377)*v(6005))*v(6037)
v(4268)=(v(228)*v(4241)+v(377)*v(6008))*v(6037)
v(4267)=(v(228)*v(4240)+v(377)*v(6011))*v(6037)
v(4266)=(v(228)*v(4239)+v(377)*v(6014))*v(6037)
v(4265)=(v(228)*v(4238)+v(377)*v(6017))*v(6037)
v(4264)=(v(228)*v(4237)+v(377)*v(6020))*v(6037)
v(4263)=(v(228)*v(4236)+v(377)*v(6023))*v(6037)
v(4262)=(v(227)*v(4244)+v(377)*v(6000))*v(6037)
v(4261)=(v(227)*v(4243)+v(377)*v(6003))*v(6037)
v(4260)=(v(227)*v(4242)+v(377)*v(6006))*v(6037)
v(4259)=(v(227)*v(4241)+v(377)*v(6009))*v(6037)
v(4258)=(v(227)*v(4240)+v(377)*v(6012))*v(6037)
v(4257)=(v(227)*v(4239)+v(377)*v(6015))*v(6037)
v(4256)=(v(227)*v(4238)+v(377)*v(6018))*v(6037)
v(4255)=(v(227)*v(4237)+v(377)*v(6021))*v(6037)
v(4254)=(v(227)*v(4236)+v(377)*v(6024))*v(6037)
v(4253)=(v(223)*v(4244)+v(377)*v(5998))*v(6037)
v(4252)=(v(223)*v(4243)+v(377)*v(6001))*v(6037)
v(4251)=(v(223)*v(4242)+v(377)*v(6004))*v(6037)
v(4250)=(v(223)*v(4241)+v(377)*v(6007))*v(6037)
v(4249)=(v(223)*v(4240)+v(377)*v(6010))*v(6037)
v(4248)=(v(223)*v(4239)+v(377)*v(6013))*v(6037)
v(4247)=(v(223)*v(4238)+v(377)*v(6016))*v(6037)
v(4246)=(v(223)*v(4237)+v(377)*v(6019))*v(6037)
v(4245)=(v(223)*v(4236)+v(377)*v(6022))*v(6037)
v(376)=-v(223)+(v(357)*v(377)+v(223)*v(378))*v(6037)
v(6044)=v(376)*v(5541)
v(4384)=v(376)*v(5807)
v(379)=-v(227)+(v(361)*v(377)+v(227)*v(378))*v(6037)
v(6048)=v(379)*v(5541)
v(6039)=v(376)+v(379)
v(4610)=v(379)*v(5807)
v(380)=-v(228)+(v(365)*v(377)+v(228)*v(378))*v(6037)
v(6052)=v(380)*v(5541)
v(6040)=v(379)+v(380)
v(6038)=v(376)+v(380)
v(4755)=v(380)*v(5807)
v(381)=-v(229)+(v(366)*v(377)+v(229)*v(378))*v(6037)
v(6043)=v(381)*v(5541)
v(4282)=v(381)*v(5807)
v(4290)=v(4280)*v(4282)
v(4289)=v(4279)*v(4282)
v(4288)=v(4278)*v(4282)
v(4287)=v(4277)*v(4282)
v(4286)=v(4276)*v(4282)
v(4285)=v(4275)*v(4282)
v(4284)=v(4274)*v(4282)
v(4283)=v(4273)*v(4282)
v(4281)=v(4272)*v(4282)
v(410)=v(232)*(v(381)*v(381))
v(382)=-v(230)+(v(367)*v(377)+v(230)*v(378))*v(6037)
v(6047)=v(382)*v(5541)
v(4301)=v(382)*v(5807)
v(4309)=v(4299)*v(4301)
v(4618)=v(4290)+v(4309)+v(4262)*v(4610)
v(4308)=v(4298)*v(4301)
v(4617)=v(4289)+v(4308)+v(4261)*v(4610)
v(4307)=v(4297)*v(4301)
v(4616)=v(4288)+v(4307)+v(4260)*v(4610)
v(4306)=v(4296)*v(4301)
v(4615)=v(4287)+v(4306)+v(4259)*v(4610)
v(4305)=v(4295)*v(4301)
v(4614)=v(4286)+v(4305)+v(4258)*v(4610)
v(4304)=v(4294)*v(4301)
v(4613)=v(4285)+v(4304)+v(4257)*v(4610)
v(4303)=v(4293)*v(4301)
v(4612)=v(4284)+v(4303)+v(4256)*v(4610)
v(4302)=v(4292)*v(4301)
v(4611)=v(4283)+v(4302)+v(4255)*v(4610)
v(4300)=v(4291)*v(4301)
v(4609)=v(4281)+v(4300)+v(4254)*v(4610)
v(427)=v(232)*(v(382)*v(382))
v(383)=-v(231)+(v(368)*v(377)+v(231)*v(378))*v(6037)
v(6042)=v(383)*v(5541)
v(4373)=v(232)*(v(383)*(v(4253)+v(4271))+v(382)*v(4280)+v(381)*v(4299)+v(4318)*v(6038))
v(4372)=v(232)*(v(383)*(v(4252)+v(4270))+v(382)*v(4279)+v(381)*v(4298)+v(4317)*v(6038))
v(4371)=v(232)*(v(383)*(v(4251)+v(4269))+v(382)*v(4278)+v(381)*v(4297)+v(4316)*v(6038))
v(4370)=v(232)*(v(383)*(v(4250)+v(4268))+v(382)*v(4277)+v(381)*v(4296)+v(4315)*v(6038))
v(4369)=v(232)*(v(383)*(v(4249)+v(4267))+v(382)*v(4276)+v(381)*v(4295)+v(4314)*v(6038))
v(4368)=v(232)*(v(383)*(v(4248)+v(4266))+v(382)*v(4275)+v(381)*v(4294)+v(4313)*v(6038))
v(4367)=v(232)*(v(383)*(v(4247)+v(4265))+v(382)*v(4274)+v(381)*v(4293)+v(4312)*v(6038))
v(4366)=v(232)*(v(383)*(v(4246)+v(4264))+v(382)*v(4273)+v(381)*v(4292)+v(4311)*v(6038))
v(4365)=v(232)*(v(383)*(v(4245)+v(4263))+v(382)*v(4272)+v(381)*v(4291)+v(4310)*v(6038))
v(4355)=v(232)*(v(381)*(v(4253)+v(4262))+v(383)*v(4299)+v(382)*v(4318)+v(4280)*v(6039))
v(4354)=v(232)*(v(381)*(v(4252)+v(4261))+v(383)*v(4298)+v(382)*v(4317)+v(4279)*v(6039))
v(4353)=v(232)*(v(381)*(v(4251)+v(4260))+v(383)*v(4297)+v(382)*v(4316)+v(4278)*v(6039))
v(4352)=v(232)*(v(381)*(v(4250)+v(4259))+v(383)*v(4296)+v(382)*v(4315)+v(4277)*v(6039))
v(4351)=v(232)*(v(381)*(v(4249)+v(4258))+v(383)*v(4295)+v(382)*v(4314)+v(4276)*v(6039))
v(4350)=v(232)*(v(381)*(v(4248)+v(4257))+v(383)*v(4294)+v(382)*v(4313)+v(4275)*v(6039))
v(4349)=v(232)*(v(381)*(v(4247)+v(4256))+v(383)*v(4293)+v(382)*v(4312)+v(4274)*v(6039))
v(4348)=v(232)*(v(381)*(v(4246)+v(4255))+v(383)*v(4292)+v(382)*v(4311)+v(4273)*v(6039))
v(4347)=v(232)*(v(381)*(v(4245)+v(4254))+v(383)*v(4291)+v(382)*v(4310)+v(4272)*v(6039))
v(4337)=v(232)*(v(382)*(v(4262)+v(4271))+v(383)*v(4280)+v(381)*v(4318)+v(4299)*v(6040))
v(4336)=v(232)*(v(382)*(v(4261)+v(4270))+v(383)*v(4279)+v(381)*v(4317)+v(4298)*v(6040))
v(4335)=v(232)*(v(382)*(v(4260)+v(4269))+v(383)*v(4278)+v(381)*v(4316)+v(4297)*v(6040))
v(4334)=v(232)*(v(382)*(v(4259)+v(4268))+v(383)*v(4277)+v(381)*v(4315)+v(4296)*v(6040))
v(4333)=v(232)*(v(382)*(v(4258)+v(4267))+v(383)*v(4276)+v(381)*v(4314)+v(4295)*v(6040))
v(4332)=v(232)*(v(382)*(v(4257)+v(4266))+v(383)*v(4275)+v(381)*v(4313)+v(4294)*v(6040))
v(4331)=v(232)*(v(382)*(v(4256)+v(4265))+v(383)*v(4274)+v(381)*v(4312)+v(4293)*v(6040))
v(4330)=v(232)*(v(382)*(v(4255)+v(4264))+v(383)*v(4273)+v(381)*v(4311)+v(4292)*v(6040))
v(4329)=v(232)*(v(382)*(v(4254)+v(4263))+v(383)*v(4272)+v(381)*v(4310)+v(4291)*v(6040))
v(4320)=v(383)*v(5807)
v(4328)=v(4318)*v(4320)
v(4763)=v(4309)+v(4328)+v(4271)*v(4755)
v(4392)=v(4290)+v(4328)+v(4253)*v(4384)
v(4327)=v(4317)*v(4320)
v(4762)=v(4308)+v(4327)+v(4270)*v(4755)
v(4391)=v(4289)+v(4327)+v(4252)*v(4384)
v(4326)=v(4316)*v(4320)
v(4761)=v(4307)+v(4326)+v(4269)*v(4755)
v(4390)=v(4288)+v(4326)+v(4251)*v(4384)
v(4325)=v(4315)*v(4320)
v(4760)=v(4306)+v(4325)+v(4268)*v(4755)
v(4389)=v(4287)+v(4325)+v(4250)*v(4384)
v(4324)=v(4314)*v(4320)
v(4759)=v(4305)+v(4324)+v(4267)*v(4755)
v(4388)=v(4286)+v(4324)+v(4249)*v(4384)
v(4323)=v(4313)*v(4320)
v(4758)=v(4304)+v(4323)+v(4266)*v(4755)
v(4387)=v(4285)+v(4323)+v(4248)*v(4384)
v(4322)=v(4312)*v(4320)
v(4757)=v(4303)+v(4322)+v(4265)*v(4755)
v(4386)=v(4284)+v(4322)+v(4247)*v(4384)
v(4321)=v(4311)*v(4320)
v(4756)=v(4302)+v(4321)+v(4264)*v(4755)
v(4385)=v(4283)+v(4321)+v(4246)*v(4384)
v(4319)=v(4310)*v(4320)
v(4754)=v(4300)+v(4319)+v(4263)*v(4755)
v(4383)=v(4281)+v(4319)+v(4245)*v(4384)
v(428)=v(232)*(v(383)*v(383))
v(415)=v(232)*(v(381)*v(383)+v(382)*v(6040))
v(4346)=(v(415)*v(4299)+v(382)*v(4337))*v(5541)
v(4345)=(v(415)*v(4298)+v(382)*v(4336))*v(5541)
v(4344)=(v(415)*v(4297)+v(382)*v(4335))*v(5541)
v(4343)=(v(415)*v(4296)+v(382)*v(4334))*v(5541)
v(4342)=(v(415)*v(4295)+v(382)*v(4333))*v(5541)
v(4341)=(v(415)*v(4294)+v(382)*v(4332))*v(5541)
v(4340)=(v(415)*v(4293)+v(382)*v(4331))*v(5541)
v(4339)=(v(415)*v(4292)+v(382)*v(4330))*v(5541)
v(4338)=(v(415)*v(4291)+v(382)*v(4329))*v(5541)
v(431)=v(415)*v(6047)
v(396)=v(232)*(v(382)*v(383)+v(381)*v(6039))
v(4364)=(v(396)*v(4280)+v(381)*v(4355))*v(5541)
v(4363)=(v(396)*v(4279)+v(381)*v(4354))*v(5541)
v(4362)=(v(396)*v(4278)+v(381)*v(4353))*v(5541)
v(4361)=(v(396)*v(4277)+v(381)*v(4352))*v(5541)
v(4360)=(v(396)*v(4276)+v(381)*v(4351))*v(5541)
v(4359)=(v(396)*v(4275)+v(381)*v(4350))*v(5541)
v(4358)=(v(396)*v(4274)+v(381)*v(4349))*v(5541)
v(4357)=(v(396)*v(4273)+v(381)*v(4348))*v(5541)
v(4356)=(v(396)*v(4272)+v(381)*v(4347))*v(5541)
v(412)=v(396)*v(6043)
v(395)=v(232)*(v(381)*v(382)+v(383)*v(6038))
v(4382)=(v(395)*v(4318)+v(383)*v(4373))*v(5541)
v(4381)=(v(395)*v(4317)+v(383)*v(4372))*v(5541)
v(4380)=(v(395)*v(4316)+v(383)*v(4371))*v(5541)
v(4379)=(v(395)*v(4315)+v(383)*v(4370))*v(5541)
v(4378)=(v(395)*v(4314)+v(383)*v(4369))*v(5541)
v(4377)=(v(395)*v(4313)+v(383)*v(4368))*v(5541)
v(4376)=(v(395)*v(4312)+v(383)*v(4367))*v(5541)
v(4375)=(v(395)*v(4311)+v(383)*v(4366))*v(5541)
v(4374)=(v(395)*v(4310)+v(383)*v(4365))*v(5541)
v(430)=v(395)*v(6042)
v(386)=-v(223)+v(6041)*(v(223)*v(387)+v(377)*x(7))
v(6064)=v(386)*v(5541)
v(388)=-v(227)+v(6041)*(v(227)*v(387)+v(377)*x(8))
v(6067)=v(388)*v(5541)
v(389)=-v(228)+(v(228)*v(387)+v(377)*v(5550))*v(6041)
v(6070)=v(389)*v(5541)
v(390)=-v(229)+v(6041)*(v(229)*v(387)+v(377)*x(9))
v(6063)=v(390)*v(5541)
v(473)=v(232)*(v(390)*v(390))
v(391)=-v(230)+v(6041)*(v(230)*v(387)+v(377)*x(11))
v(6066)=v(391)*v(5541)
v(490)=v(232)*(v(391)*v(391))
v(392)=-v(231)+v(6041)*(v(231)*v(387)+v(377)*x(10))
v(6062)=v(392)*v(5541)
v(491)=v(232)*(v(392)*v(392))
v(478)=v(232)*((v(388)+v(389))*v(391)+v(390)*v(392))
v(494)=v(478)*v(6066)
v(459)=v(232)*((v(386)+v(388))*v(390)+v(391)*v(392))
v(475)=v(459)*v(6063)
v(458)=v(232)*(v(390)*v(391)+(v(386)+v(389))*v(392))
v(493)=v(458)*v(6062)
v(393)=v(232)*(v(376)*v(376))+v(410)+v(428)
v(4437)=v(4364)+v(4382)+(v(393)*v(4253)+v(376)*v(4392))*v(5541)
v(4436)=v(4363)+v(4381)+(v(393)*v(4252)+v(376)*v(4391))*v(5541)
v(4435)=v(4362)+v(4380)+(v(393)*v(4251)+v(376)*v(4390))*v(5541)
v(4434)=v(4361)+v(4379)+(v(393)*v(4250)+v(376)*v(4389))*v(5541)
v(4433)=v(4360)+v(4378)+(v(393)*v(4249)+v(376)*v(4388))*v(5541)
v(4432)=v(4359)+v(4377)+(v(393)*v(4248)+v(376)*v(4387))*v(5541)
v(4431)=v(4358)+v(4376)+(v(393)*v(4247)+v(376)*v(4386))*v(5541)
v(4430)=v(4357)+v(4375)+(v(393)*v(4246)+v(376)*v(4385))*v(5541)
v(4429)=v(4356)+v(4374)+(v(393)*v(4245)+v(376)*v(4383))*v(5541)
v(4419)=(v(396)*v(4262)+v(393)*v(4280)+v(395)*v(4299)+v(379)*v(4355)+v(382)*v(4373)+v(381)*v(4392))*v(5541)
v(4418)=(v(396)*v(4261)+v(393)*v(4279)+v(395)*v(4298)+v(379)*v(4354)+v(382)*v(4372)+v(381)*v(4391))*v(5541)
v(4417)=(v(396)*v(4260)+v(393)*v(4278)+v(395)*v(4297)+v(379)*v(4353)+v(382)*v(4371)+v(381)*v(4390))*v(5541)
v(4416)=(v(396)*v(4259)+v(393)*v(4277)+v(395)*v(4296)+v(379)*v(4352)+v(382)*v(4370)+v(381)*v(4389))*v(5541)
v(4415)=(v(396)*v(4258)+v(393)*v(4276)+v(395)*v(4295)+v(379)*v(4351)+v(382)*v(4369)+v(381)*v(4388))*v(5541)
v(4414)=(v(396)*v(4257)+v(393)*v(4275)+v(395)*v(4294)+v(379)*v(4350)+v(382)*v(4368)+v(381)*v(4387))*v(5541)
v(4413)=(v(396)*v(4256)+v(393)*v(4274)+v(395)*v(4293)+v(379)*v(4349)+v(382)*v(4367)+v(381)*v(4386))*v(5541)
v(4412)=(v(396)*v(4255)+v(393)*v(4273)+v(395)*v(4292)+v(379)*v(4348)+v(382)*v(4366)+v(381)*v(4385))*v(5541)
v(4411)=(v(396)*v(4254)+v(393)*v(4272)+v(395)*v(4291)+v(379)*v(4347)+v(382)*v(4365)+v(381)*v(4383))*v(5541)
v(4401)=(v(395)*v(4271)+v(396)*v(4299)+v(393)*v(4318)+v(382)*v(4355)+v(380)*v(4373)+v(383)*v(4392))*v(5541)
v(4400)=(v(395)*v(4270)+v(396)*v(4298)+v(393)*v(4317)+v(382)*v(4354)+v(380)*v(4372)+v(383)*v(4391))*v(5541)
v(4399)=(v(395)*v(4269)+v(396)*v(4297)+v(393)*v(4316)+v(382)*v(4353)+v(380)*v(4371)+v(383)*v(4390))*v(5541)
v(4398)=(v(395)*v(4268)+v(396)*v(4296)+v(393)*v(4315)+v(382)*v(4352)+v(380)*v(4370)+v(383)*v(4389))*v(5541)
v(4397)=(v(395)*v(4267)+v(396)*v(4295)+v(393)*v(4314)+v(382)*v(4351)+v(380)*v(4369)+v(383)*v(4388))*v(5541)
v(4396)=(v(395)*v(4266)+v(396)*v(4294)+v(393)*v(4313)+v(382)*v(4350)+v(380)*v(4368)+v(383)*v(4387))*v(5541)
v(4395)=(v(395)*v(4265)+v(396)*v(4293)+v(393)*v(4312)+v(382)*v(4349)+v(380)*v(4367)+v(383)*v(4386))*v(5541)
v(4394)=(v(395)*v(4264)+v(396)*v(4292)+v(393)*v(4311)+v(382)*v(4348)+v(380)*v(4366)+v(383)*v(4385))*v(5541)
v(4393)=(v(395)*v(4263)+v(396)*v(4291)+v(393)*v(4310)+v(382)*v(4347)+v(380)*v(4365)+v(383)*v(4383))*v(5541)
v(399)=(v(383)*v(393)+v(380)*v(395)+v(382)*v(396))*v(5541)
v(4410)=(v(399)*v(4318)+v(383)*v(4401))*v(5541)
v(4409)=(v(399)*v(4317)+v(383)*v(4400))*v(5541)
v(4408)=(v(399)*v(4316)+v(383)*v(4399))*v(5541)
v(4407)=(v(399)*v(4315)+v(383)*v(4398))*v(5541)
v(4406)=(v(399)*v(4314)+v(383)*v(4397))*v(5541)
v(4405)=(v(399)*v(4313)+v(383)*v(4396))*v(5541)
v(4404)=(v(399)*v(4312)+v(383)*v(4395))*v(5541)
v(4403)=(v(399)*v(4311)+v(383)*v(4394))*v(5541)
v(4402)=(v(399)*v(4310)+v(383)*v(4393))*v(5541)
v(434)=v(399)*v(6042)
v(398)=(v(381)*v(393)+v(382)*v(395)+v(379)*v(396))*v(5541)
v(4428)=(v(398)*v(4280)+v(381)*v(4419))*v(5541)
v(4427)=(v(398)*v(4279)+v(381)*v(4418))*v(5541)
v(4426)=(v(398)*v(4278)+v(381)*v(4417))*v(5541)
v(4425)=(v(398)*v(4277)+v(381)*v(4416))*v(5541)
v(4424)=(v(398)*v(4276)+v(381)*v(4415))*v(5541)
v(4423)=(v(398)*v(4275)+v(381)*v(4414))*v(5541)
v(4422)=(v(398)*v(4274)+v(381)*v(4413))*v(5541)
v(4421)=(v(398)*v(4273)+v(381)*v(4412))*v(5541)
v(4420)=(v(398)*v(4272)+v(381)*v(4411))*v(5541)
v(414)=v(398)*v(6043)
v(394)=v(412)+v(430)+v(393)*v(6044)
v(4482)=v(4410)+v(4428)+(v(394)*v(4253)+v(376)*v(4437))*v(5541)
v(4481)=v(4409)+v(4427)+(v(394)*v(4252)+v(376)*v(4436))*v(5541)
v(4480)=v(4408)+v(4426)+(v(394)*v(4251)+v(376)*v(4435))*v(5541)
v(4479)=v(4407)+v(4425)+(v(394)*v(4250)+v(376)*v(4434))*v(5541)
v(4478)=v(4406)+v(4424)+(v(394)*v(4249)+v(376)*v(4433))*v(5541)
v(4477)=v(4405)+v(4423)+(v(394)*v(4248)+v(376)*v(4432))*v(5541)
v(4476)=v(4404)+v(4422)+(v(394)*v(4247)+v(376)*v(4431))*v(5541)
v(4475)=v(4403)+v(4421)+(v(394)*v(4246)+v(376)*v(4430))*v(5541)
v(4474)=v(4402)+v(4420)+(v(394)*v(4245)+v(376)*v(4429))*v(5541)
v(4464)=(v(399)*v(4271)+v(398)*v(4299)+v(394)*v(4318)+v(380)*v(4401)+v(382)*v(4419)+v(383)*v(4437))*v(5541)
v(4463)=(v(399)*v(4270)+v(398)*v(4298)+v(394)*v(4317)+v(380)*v(4400)+v(382)*v(4418)+v(383)*v(4436))*v(5541)
v(4462)=(v(399)*v(4269)+v(398)*v(4297)+v(394)*v(4316)+v(380)*v(4399)+v(382)*v(4417)+v(383)*v(4435))*v(5541)
v(4461)=(v(399)*v(4268)+v(398)*v(4296)+v(394)*v(4315)+v(380)*v(4398)+v(382)*v(4416)+v(383)*v(4434))*v(5541)
v(4460)=(v(399)*v(4267)+v(398)*v(4295)+v(394)*v(4314)+v(380)*v(4397)+v(382)*v(4415)+v(383)*v(4433))*v(5541)
v(4459)=(v(399)*v(4266)+v(398)*v(4294)+v(394)*v(4313)+v(380)*v(4396)+v(382)*v(4414)+v(383)*v(4432))*v(5541)
v(4458)=(v(399)*v(4265)+v(398)*v(4293)+v(394)*v(4312)+v(380)*v(4395)+v(382)*v(4413)+v(383)*v(4431))*v(5541)
v(4457)=(v(399)*v(4264)+v(398)*v(4292)+v(394)*v(4311)+v(380)*v(4394)+v(382)*v(4412)+v(383)*v(4430))*v(5541)
v(4456)=(v(399)*v(4263)+v(398)*v(4291)+v(394)*v(4310)+v(380)*v(4393)+v(382)*v(4411)+v(383)*v(4429))*v(5541)
v(4446)=(v(398)*v(4262)+v(394)*v(4280)+v(399)*v(4299)+v(382)*v(4401)+v(379)*v(4419)+v(381)*v(4437))*v(5541)
v(4445)=(v(398)*v(4261)+v(394)*v(4279)+v(399)*v(4298)+v(382)*v(4400)+v(379)*v(4418)+v(381)*v(4436))*v(5541)
v(4444)=(v(398)*v(4260)+v(394)*v(4278)+v(399)*v(4297)+v(382)*v(4399)+v(379)*v(4417)+v(381)*v(4435))*v(5541)
v(4443)=(v(398)*v(4259)+v(394)*v(4277)+v(399)*v(4296)+v(382)*v(4398)+v(379)*v(4416)+v(381)*v(4434))*v(5541)
v(4442)=(v(398)*v(4258)+v(394)*v(4276)+v(399)*v(4295)+v(382)*v(4397)+v(379)*v(4415)+v(381)*v(4433))*v(5541)
v(4441)=(v(398)*v(4257)+v(394)*v(4275)+v(399)*v(4294)+v(382)*v(4396)+v(379)*v(4414)+v(381)*v(4432))*v(5541)
v(4440)=(v(398)*v(4256)+v(394)*v(4274)+v(399)*v(4293)+v(382)*v(4395)+v(379)*v(4413)+v(381)*v(4431))*v(5541)
v(4439)=(v(398)*v(4255)+v(394)*v(4273)+v(399)*v(4292)+v(382)*v(4394)+v(379)*v(4412)+v(381)*v(4430))*v(5541)
v(4438)=(v(398)*v(4254)+v(394)*v(4272)+v(399)*v(4291)+v(382)*v(4393)+v(379)*v(4411)+v(381)*v(4429))*v(5541)
v(402)=(v(381)*v(394)+v(379)*v(398)+v(382)*v(399))*v(5541)
v(4455)=(v(402)*v(4280)+v(381)*v(4446))*v(5541)
v(4454)=(v(402)*v(4279)+v(381)*v(4445))*v(5541)
v(4453)=(v(402)*v(4278)+v(381)*v(4444))*v(5541)
v(4452)=(v(402)*v(4277)+v(381)*v(4443))*v(5541)
v(4451)=(v(402)*v(4276)+v(381)*v(4442))*v(5541)
v(4450)=(v(402)*v(4275)+v(381)*v(4441))*v(5541)
v(4449)=(v(402)*v(4274)+v(381)*v(4440))*v(5541)
v(4448)=(v(402)*v(4273)+v(381)*v(4439))*v(5541)
v(4447)=(v(402)*v(4272)+v(381)*v(4438))*v(5541)
v(418)=v(402)*v(6043)
v(401)=(v(383)*v(394)+v(382)*v(398)+v(380)*v(399))*v(5541)
v(4473)=(v(401)*v(4318)+v(383)*v(4464))*v(5541)
v(4472)=(v(401)*v(4317)+v(383)*v(4463))*v(5541)
v(4471)=(v(401)*v(4316)+v(383)*v(4462))*v(5541)
v(4470)=(v(401)*v(4315)+v(383)*v(4461))*v(5541)
v(4469)=(v(401)*v(4314)+v(383)*v(4460))*v(5541)
v(4468)=(v(401)*v(4313)+v(383)*v(4459))*v(5541)
v(4467)=(v(401)*v(4312)+v(383)*v(4458))*v(5541)
v(4466)=(v(401)*v(4311)+v(383)*v(4457))*v(5541)
v(4465)=(v(401)*v(4310)+v(383)*v(4456))*v(5541)
v(436)=v(401)*v(6042)
v(397)=v(414)+v(434)+v(394)*v(6044)
v(4527)=v(4455)+v(4473)+(v(397)*v(4253)+v(376)*v(4482))*v(5541)
v(4526)=v(4454)+v(4472)+(v(397)*v(4252)+v(376)*v(4481))*v(5541)
v(4525)=v(4453)+v(4471)+(v(397)*v(4251)+v(376)*v(4480))*v(5541)
v(4524)=v(4452)+v(4470)+(v(397)*v(4250)+v(376)*v(4479))*v(5541)
v(4523)=v(4451)+v(4469)+(v(397)*v(4249)+v(376)*v(4478))*v(5541)
v(4522)=v(4450)+v(4468)+(v(397)*v(4248)+v(376)*v(4477))*v(5541)
v(4521)=v(4449)+v(4467)+(v(397)*v(4247)+v(376)*v(4476))*v(5541)
v(4520)=v(4448)+v(4466)+(v(397)*v(4246)+v(376)*v(4475))*v(5541)
v(4519)=v(4447)+v(4465)+(v(397)*v(4245)+v(376)*v(4474))*v(5541)
v(4509)=(v(402)*v(4262)+v(397)*v(4280)+v(401)*v(4299)+v(379)*v(4446)+v(382)*v(4464)+v(381)*v(4482))*v(5541)
v(4508)=(v(402)*v(4261)+v(397)*v(4279)+v(401)*v(4298)+v(379)*v(4445)+v(382)*v(4463)+v(381)*v(4481))*v(5541)
v(4507)=(v(402)*v(4260)+v(397)*v(4278)+v(401)*v(4297)+v(379)*v(4444)+v(382)*v(4462)+v(381)*v(4480))*v(5541)
v(4506)=(v(402)*v(4259)+v(397)*v(4277)+v(401)*v(4296)+v(379)*v(4443)+v(382)*v(4461)+v(381)*v(4479))*v(5541)
v(4505)=(v(402)*v(4258)+v(397)*v(4276)+v(401)*v(4295)+v(379)*v(4442)+v(382)*v(4460)+v(381)*v(4478))*v(5541)
v(4504)=(v(402)*v(4257)+v(397)*v(4275)+v(401)*v(4294)+v(379)*v(4441)+v(382)*v(4459)+v(381)*v(4477))*v(5541)
v(4503)=(v(402)*v(4256)+v(397)*v(4274)+v(401)*v(4293)+v(379)*v(4440)+v(382)*v(4458)+v(381)*v(4476))*v(5541)
v(4502)=(v(402)*v(4255)+v(397)*v(4273)+v(401)*v(4292)+v(379)*v(4439)+v(382)*v(4457)+v(381)*v(4475))*v(5541)
v(4501)=(v(402)*v(4254)+v(397)*v(4272)+v(401)*v(4291)+v(379)*v(4438)+v(382)*v(4456)+v(381)*v(4474))*v(5541)
v(4491)=(v(401)*v(4271)+v(402)*v(4299)+v(397)*v(4318)+v(382)*v(4446)+v(380)*v(4464)+v(383)*v(4482))*v(5541)
v(4490)=(v(401)*v(4270)+v(402)*v(4298)+v(397)*v(4317)+v(382)*v(4445)+v(380)*v(4463)+v(383)*v(4481))*v(5541)
v(4489)=(v(401)*v(4269)+v(402)*v(4297)+v(397)*v(4316)+v(382)*v(4444)+v(380)*v(4462)+v(383)*v(4480))*v(5541)
v(4488)=(v(401)*v(4268)+v(402)*v(4296)+v(397)*v(4315)+v(382)*v(4443)+v(380)*v(4461)+v(383)*v(4479))*v(5541)
v(4487)=(v(401)*v(4267)+v(402)*v(4295)+v(397)*v(4314)+v(382)*v(4442)+v(380)*v(4460)+v(383)*v(4478))*v(5541)
v(4486)=(v(401)*v(4266)+v(402)*v(4294)+v(397)*v(4313)+v(382)*v(4441)+v(380)*v(4459)+v(383)*v(4477))*v(5541)
v(4485)=(v(401)*v(4265)+v(402)*v(4293)+v(397)*v(4312)+v(382)*v(4440)+v(380)*v(4458)+v(383)*v(4476))*v(5541)
v(4484)=(v(401)*v(4264)+v(402)*v(4292)+v(397)*v(4311)+v(382)*v(4439)+v(380)*v(4457)+v(383)*v(4475))*v(5541)
v(4483)=(v(401)*v(4263)+v(402)*v(4291)+v(397)*v(4310)+v(382)*v(4438)+v(380)*v(4456)+v(383)*v(4474))*v(5541)
v(405)=(v(383)*v(397)+v(380)*v(401)+v(382)*v(402))*v(5541)
v(4500)=(v(405)*v(4318)+v(383)*v(4491))*v(5541)
v(4499)=(v(405)*v(4317)+v(383)*v(4490))*v(5541)
v(4498)=(v(405)*v(4316)+v(383)*v(4489))*v(5541)
v(4497)=(v(405)*v(4315)+v(383)*v(4488))*v(5541)
v(4496)=(v(405)*v(4314)+v(383)*v(4487))*v(5541)
v(4495)=(v(405)*v(4313)+v(383)*v(4486))*v(5541)
v(4494)=(v(405)*v(4312)+v(383)*v(4485))*v(5541)
v(4493)=(v(405)*v(4311)+v(383)*v(4484))*v(5541)
v(4492)=(v(405)*v(4310)+v(383)*v(4483))*v(5541)
v(440)=v(405)*v(6042)
v(404)=(v(381)*v(397)+v(382)*v(401)+v(379)*v(402))*v(5541)
v(4518)=(v(404)*v(4280)+v(381)*v(4509))*v(5541)
v(4517)=(v(404)*v(4279)+v(381)*v(4508))*v(5541)
v(4516)=(v(404)*v(4278)+v(381)*v(4507))*v(5541)
v(4515)=(v(404)*v(4277)+v(381)*v(4506))*v(5541)
v(4514)=(v(404)*v(4276)+v(381)*v(4505))*v(5541)
v(4513)=(v(404)*v(4275)+v(381)*v(4504))*v(5541)
v(4512)=(v(404)*v(4274)+v(381)*v(4503))*v(5541)
v(4511)=(v(404)*v(4273)+v(381)*v(4502))*v(5541)
v(4510)=(v(404)*v(4272)+v(381)*v(4501))*v(5541)
v(420)=v(404)*v(6043)
v(400)=v(418)+v(436)+v(397)*v(6044)
v(4563)=(v(404)*v(4262)+v(400)*v(4280)+v(405)*v(4299)+v(382)*v(4491)+v(379)*v(4509)+v(381)*v(4527))*v(5541)
v(4562)=(v(404)*v(4261)+v(400)*v(4279)+v(405)*v(4298)+v(382)*v(4490)+v(379)*v(4508)+v(381)*v(4526))*v(5541)
v(4561)=(v(404)*v(4260)+v(400)*v(4278)+v(405)*v(4297)+v(382)*v(4489)+v(379)*v(4507)+v(381)*v(4525))*v(5541)
v(4560)=(v(404)*v(4259)+v(400)*v(4277)+v(405)*v(4296)+v(382)*v(4488)+v(379)*v(4506)+v(381)*v(4524))*v(5541)
v(4559)=(v(404)*v(4258)+v(400)*v(4276)+v(405)*v(4295)+v(382)*v(4487)+v(379)*v(4505)+v(381)*v(4523))*v(5541)
v(4558)=(v(404)*v(4257)+v(400)*v(4275)+v(405)*v(4294)+v(382)*v(4486)+v(379)*v(4504)+v(381)*v(4522))*v(5541)
v(4557)=(v(404)*v(4256)+v(400)*v(4274)+v(405)*v(4293)+v(382)*v(4485)+v(379)*v(4503)+v(381)*v(4521))*v(5541)
v(4556)=(v(404)*v(4255)+v(400)*v(4273)+v(405)*v(4292)+v(382)*v(4484)+v(379)*v(4502)+v(381)*v(4520))*v(5541)
v(4555)=(v(404)*v(4254)+v(400)*v(4272)+v(405)*v(4291)+v(382)*v(4483)+v(379)*v(4501)+v(381)*v(4519))*v(5541)
v(4545)=(v(405)*v(4271)+v(404)*v(4299)+v(400)*v(4318)+v(380)*v(4491)+v(382)*v(4509)+v(383)*v(4527))*v(5541)
v(4544)=(v(405)*v(4270)+v(404)*v(4298)+v(400)*v(4317)+v(380)*v(4490)+v(382)*v(4508)+v(383)*v(4526))*v(5541)
v(4543)=(v(405)*v(4269)+v(404)*v(4297)+v(400)*v(4316)+v(380)*v(4489)+v(382)*v(4507)+v(383)*v(4525))*v(5541)
v(4542)=(v(405)*v(4268)+v(404)*v(4296)+v(400)*v(4315)+v(380)*v(4488)+v(382)*v(4506)+v(383)*v(4524))*v(5541)
v(4541)=(v(405)*v(4267)+v(404)*v(4295)+v(400)*v(4314)+v(380)*v(4487)+v(382)*v(4505)+v(383)*v(4523))*v(5541)
v(4540)=(v(405)*v(4266)+v(404)*v(4294)+v(400)*v(4313)+v(380)*v(4486)+v(382)*v(4504)+v(383)*v(4522))*v(5541)
v(4539)=(v(405)*v(4265)+v(404)*v(4293)+v(400)*v(4312)+v(380)*v(4485)+v(382)*v(4503)+v(383)*v(4521))*v(5541)
v(4538)=(v(405)*v(4264)+v(404)*v(4292)+v(400)*v(4311)+v(380)*v(4484)+v(382)*v(4502)+v(383)*v(4520))*v(5541)
v(4537)=(v(405)*v(4263)+v(404)*v(4291)+v(400)*v(4310)+v(380)*v(4483)+v(382)*v(4501)+v(383)*v(4519))*v(5541)
v(4536)=v(4500)+v(4518)+(v(400)*v(4253)+v(376)*v(4527))*v(5541)
v(4535)=v(4499)+v(4517)+(v(400)*v(4252)+v(376)*v(4526))*v(5541)
v(4534)=v(4498)+v(4516)+(v(400)*v(4251)+v(376)*v(4525))*v(5541)
v(4533)=v(4497)+v(4515)+(v(400)*v(4250)+v(376)*v(4524))*v(5541)
v(4532)=v(4496)+v(4514)+(v(400)*v(4249)+v(376)*v(4523))*v(5541)
v(4531)=v(4495)+v(4513)+(v(400)*v(4248)+v(376)*v(4522))*v(5541)
v(4530)=v(4494)+v(4512)+(v(400)*v(4247)+v(376)*v(4521))*v(5541)
v(4529)=v(4493)+v(4511)+(v(400)*v(4246)+v(376)*v(4520))*v(5541)
v(4528)=v(4492)+v(4510)+(v(400)*v(4245)+v(376)*v(4519))*v(5541)
v(403)=v(420)+v(440)+v(400)*v(6044)
v(6045)=5040d0+v(403)
v(406)=(v(383)*v(400)+v(382)*v(404)+v(380)*v(405))*v(5541)
v(4554)=(v(406)*v(4318)+v(383)*v(4545))*v(5541)
v(4553)=(v(406)*v(4317)+v(383)*v(4544))*v(5541)
v(4552)=(v(406)*v(4316)+v(383)*v(4543))*v(5541)
v(4551)=(v(406)*v(4315)+v(383)*v(4542))*v(5541)
v(4550)=(v(406)*v(4314)+v(383)*v(4541))*v(5541)
v(4549)=(v(406)*v(4313)+v(383)*v(4540))*v(5541)
v(4548)=(v(406)*v(4312)+v(383)*v(4539))*v(5541)
v(4547)=(v(406)*v(4311)+v(383)*v(4538))*v(5541)
v(4546)=(v(406)*v(4310)+v(383)*v(4537))*v(5541)
v(442)=v(406)*v(6042)
v(407)=(v(381)*v(400)+v(379)*v(404)+v(382)*v(405))*v(5541)
v(4599)=(7d0*(360d0*v(4355)+120d0*v(4419)+30d0*v(4446)+6d0*v(4509)+v(4563))+v(5541)*(v(407)*v(4262)+v(406)*v(4299)+v&
&(381)*v(4536)+v(382)*v(4545)+v(379)*v(4563)+v(4280)*v(6045)))/5040d0
v(4598)=(7d0*(360d0*v(4354)+120d0*v(4418)+30d0*v(4445)+6d0*v(4508)+v(4562))+v(5541)*(v(407)*v(4261)+v(406)*v(4298)+v&
&(381)*v(4535)+v(382)*v(4544)+v(379)*v(4562)+v(4279)*v(6045)))/5040d0
v(4597)=(7d0*(360d0*v(4353)+120d0*v(4417)+30d0*v(4444)+6d0*v(4507)+v(4561))+v(5541)*(v(407)*v(4260)+v(406)*v(4297)+v&
&(381)*v(4534)+v(382)*v(4543)+v(379)*v(4561)+v(4278)*v(6045)))/5040d0
v(4596)=(7d0*(360d0*v(4352)+120d0*v(4416)+30d0*v(4443)+6d0*v(4506)+v(4560))+v(5541)*(v(407)*v(4259)+v(406)*v(4296)+v&
&(381)*v(4533)+v(382)*v(4542)+v(379)*v(4560)+v(4277)*v(6045)))/5040d0
v(4595)=(7d0*(360d0*v(4351)+120d0*v(4415)+30d0*v(4442)+6d0*v(4505)+v(4559))+v(5541)*(v(407)*v(4258)+v(406)*v(4295)+v&
&(381)*v(4532)+v(382)*v(4541)+v(379)*v(4559)+v(4276)*v(6045)))/5040d0
v(4594)=(7d0*(360d0*v(4350)+120d0*v(4414)+30d0*v(4441)+6d0*v(4504)+v(4558))+v(5541)*(v(407)*v(4257)+v(406)*v(4294)+v&
&(381)*v(4531)+v(382)*v(4540)+v(379)*v(4558)+v(4275)*v(6045)))/5040d0
v(4593)=(7d0*(360d0*v(4349)+120d0*v(4413)+30d0*v(4440)+6d0*v(4503)+v(4557))+v(5541)*(v(407)*v(4256)+v(406)*v(4293)+v&
&(381)*v(4530)+v(382)*v(4539)+v(379)*v(4557)+v(4274)*v(6045)))/5040d0
v(4592)=(7d0*(360d0*v(4348)+120d0*v(4412)+30d0*v(4439)+6d0*v(4502)+v(4556))+v(5541)*(v(407)*v(4255)+v(406)*v(4292)+v&
&(381)*v(4529)+v(382)*v(4538)+v(379)*v(4556)+v(4273)*v(6045)))/5040d0
v(4591)=(7d0*(360d0*v(4347)+120d0*v(4411)+30d0*v(4438)+6d0*v(4501)+v(4555))+v(5541)*(v(407)*v(4254)+v(406)*v(4291)+v&
&(381)*v(4528)+v(382)*v(4537)+v(379)*v(4555)+v(4272)*v(6045)))/5040d0
v(4581)=(v(407)*v(4280)+v(381)*v(4563))*v(5541)
v(4590)=(2520d0*v(4392)+840d0*v(4437)+210d0*v(4482)+42d0*v(4527)+7d0*v(4536)+v(4554)+v(4581)+v(5541)*(v(376)*v(4536)+v&
&(4253)*v(6045)))/5040d0
v(4580)=(v(407)*v(4279)+v(381)*v(4562))*v(5541)
v(4589)=(2520d0*v(4391)+840d0*v(4436)+210d0*v(4481)+42d0*v(4526)+7d0*v(4535)+v(4553)+v(4580)+v(5541)*(v(376)*v(4535)+v&
&(4252)*v(6045)))/5040d0
v(4579)=(v(407)*v(4278)+v(381)*v(4561))*v(5541)
v(4588)=(2520d0*v(4390)+840d0*v(4435)+210d0*v(4480)+42d0*v(4525)+7d0*v(4534)+v(4552)+v(4579)+v(5541)*(v(376)*v(4534)+v&
&(4251)*v(6045)))/5040d0
v(4578)=(v(407)*v(4277)+v(381)*v(4560))*v(5541)
v(4587)=(2520d0*v(4389)+840d0*v(4434)+210d0*v(4479)+42d0*v(4524)+7d0*v(4533)+v(4551)+v(4578)+v(5541)*(v(376)*v(4533)+v&
&(4250)*v(6045)))/5040d0
v(4577)=(v(407)*v(4276)+v(381)*v(4559))*v(5541)
v(4586)=(2520d0*v(4388)+840d0*v(4433)+210d0*v(4478)+42d0*v(4523)+7d0*v(4532)+v(4550)+v(4577)+v(5541)*(v(376)*v(4532)+v&
&(4249)*v(6045)))/5040d0
v(4576)=(v(407)*v(4275)+v(381)*v(4558))*v(5541)
v(4585)=(2520d0*v(4387)+840d0*v(4432)+210d0*v(4477)+42d0*v(4522)+7d0*v(4531)+v(4549)+v(4576)+v(5541)*(v(376)*v(4531)+v&
&(4248)*v(6045)))/5040d0
v(4575)=(v(407)*v(4274)+v(381)*v(4557))*v(5541)
v(4584)=(2520d0*v(4386)+840d0*v(4431)+210d0*v(4476)+42d0*v(4521)+7d0*v(4530)+v(4548)+v(4575)+v(5541)*(v(376)*v(4530)+v&
&(4247)*v(6045)))/5040d0
v(4574)=(v(407)*v(4273)+v(381)*v(4556))*v(5541)
v(4583)=(2520d0*v(4385)+840d0*v(4430)+210d0*v(4475)+42d0*v(4520)+7d0*v(4529)+v(4547)+v(4574)+v(5541)*(v(376)*v(4529)+v&
&(4246)*v(6045)))/5040d0
v(4573)=(v(407)*v(4272)+v(381)*v(4555))*v(5541)
v(4582)=(2520d0*v(4383)+840d0*v(4429)+210d0*v(4474)+42d0*v(4519)+7d0*v(4528)+v(4546)+v(4573)+v(5541)*(v(376)*v(4528)+v&
&(4245)*v(6045)))/5040d0
v(4572)=(7d0*(360d0*v(4373)+120d0*v(4401)+30d0*v(4464)+6d0*v(4491)+v(4545))+(v(406)*v(4271)+v(407)*v(4299)+5040d0*v&
&(4318)+v(403)*v(4318)+v(383)*v(4536)+v(380)*v(4545)+v(382)*v(4563))*v(5541))/5040d0
v(4853)=statev(17)*v(4590)+statev(15)*v(4599)+v(4572)*v(5527)
v(4826)=statev(19)*v(4572)+statev(14)*v(4590)+v(4599)*v(5526)
v(4608)=statev(16)*v(4572)+statev(18)*v(4599)+v(4590)*v(5525)
v(4571)=(7d0*(360d0*v(4372)+120d0*v(4400)+30d0*v(4463)+6d0*v(4490)+v(4544))+(v(406)*v(4270)+v(407)*v(4298)+5040d0*v&
&(4317)+v(403)*v(4317)+v(383)*v(4535)+v(380)*v(4544)+v(382)*v(4562))*v(5541))/5040d0
v(4852)=statev(17)*v(4589)+statev(15)*v(4598)+v(4571)*v(5527)
v(4825)=statev(19)*v(4571)+statev(14)*v(4589)+v(4598)*v(5526)
v(4607)=statev(16)*v(4571)+statev(18)*v(4598)+v(4589)*v(5525)
v(4570)=(7d0*(360d0*v(4371)+120d0*v(4399)+30d0*v(4462)+6d0*v(4489)+v(4543))+(v(406)*v(4269)+v(407)*v(4297)+5040d0*v&
&(4316)+v(403)*v(4316)+v(383)*v(4534)+v(380)*v(4543)+v(382)*v(4561))*v(5541))/5040d0
v(4851)=statev(17)*v(4588)+statev(15)*v(4597)+v(4570)*v(5527)
v(4824)=statev(19)*v(4570)+statev(14)*v(4588)+v(4597)*v(5526)
v(4606)=statev(16)*v(4570)+statev(18)*v(4597)+v(4588)*v(5525)
v(4569)=(7d0*(360d0*v(4370)+120d0*v(4398)+30d0*v(4461)+6d0*v(4488)+v(4542))+(v(406)*v(4268)+v(407)*v(4296)+5040d0*v&
&(4315)+v(403)*v(4315)+v(383)*v(4533)+v(380)*v(4542)+v(382)*v(4560))*v(5541))/5040d0
v(4850)=statev(17)*v(4587)+statev(15)*v(4596)+v(4569)*v(5527)
v(4823)=statev(19)*v(4569)+statev(14)*v(4587)+v(4596)*v(5526)
v(4605)=statev(16)*v(4569)+statev(18)*v(4596)+v(4587)*v(5525)
v(4568)=(7d0*(360d0*v(4369)+120d0*v(4397)+30d0*v(4460)+6d0*v(4487)+v(4541))+(v(406)*v(4267)+v(407)*v(4295)+5040d0*v&
&(4314)+v(403)*v(4314)+v(383)*v(4532)+v(380)*v(4541)+v(382)*v(4559))*v(5541))/5040d0
v(4849)=statev(17)*v(4586)+statev(15)*v(4595)+v(4568)*v(5527)
v(4822)=statev(19)*v(4568)+statev(14)*v(4586)+v(4595)*v(5526)
v(4604)=statev(16)*v(4568)+statev(18)*v(4595)+v(4586)*v(5525)
v(4567)=(7d0*(360d0*v(4368)+120d0*v(4396)+30d0*v(4459)+6d0*v(4486)+v(4540))+(v(406)*v(4266)+v(407)*v(4294)+5040d0*v&
&(4313)+v(403)*v(4313)+v(383)*v(4531)+v(380)*v(4540)+v(382)*v(4558))*v(5541))/5040d0
v(4848)=statev(17)*v(4585)+statev(15)*v(4594)+v(4567)*v(5527)
v(4821)=statev(19)*v(4567)+statev(14)*v(4585)+v(4594)*v(5526)
v(4603)=statev(16)*v(4567)+statev(18)*v(4594)+v(4585)*v(5525)
v(4566)=(7d0*(360d0*v(4367)+120d0*v(4395)+30d0*v(4458)+6d0*v(4485)+v(4539))+(v(406)*v(4265)+v(407)*v(4293)+5040d0*v&
&(4312)+v(403)*v(4312)+v(383)*v(4530)+v(380)*v(4539)+v(382)*v(4557))*v(5541))/5040d0
v(4847)=statev(17)*v(4584)+statev(15)*v(4593)+v(4566)*v(5527)
v(4820)=statev(19)*v(4566)+statev(14)*v(4584)+v(4593)*v(5526)
v(4602)=statev(16)*v(4566)+statev(18)*v(4593)+v(4584)*v(5525)
v(4565)=(7d0*(360d0*v(4366)+120d0*v(4394)+30d0*v(4457)+6d0*v(4484)+v(4538))+(v(406)*v(4264)+v(407)*v(4292)+5040d0*v&
&(4311)+v(403)*v(4311)+v(383)*v(4529)+v(380)*v(4538)+v(382)*v(4556))*v(5541))/5040d0
v(4846)=statev(17)*v(4583)+statev(15)*v(4592)+v(4565)*v(5527)
v(4819)=statev(19)*v(4565)+statev(14)*v(4583)+v(4592)*v(5526)
v(4601)=statev(16)*v(4565)+statev(18)*v(4592)+v(4583)*v(5525)
v(4564)=(7d0*(360d0*v(4365)+120d0*v(4393)+30d0*v(4456)+6d0*v(4483)+v(4537))+(v(406)*v(4263)+v(407)*v(4291)+5040d0*v&
&(4310)+v(403)*v(4310)+v(383)*v(4528)+v(380)*v(4537)+v(382)*v(4555))*v(5541))/5040d0
v(4845)=statev(17)*v(4582)+statev(15)*v(4591)+v(4564)*v(5527)
v(4818)=statev(19)*v(4564)+statev(14)*v(4582)+v(4591)*v(5526)
v(4600)=statev(16)*v(4564)+statev(18)*v(4591)+v(4582)*v(5525)
v(445)=(7d0*(360d0*v(395)+120d0*v(399)+30d0*v(401)+6d0*v(405)+v(406))+v(5541)*(v(380)*v(406)+v(382)*v(407)+v(383)*v&
&(6045)))/5040d0
v(425)=v(407)*v(6043)
v(6050)=5040d0+v(425)
v(447)=(2520d0*v(393)+840d0*v(394)+210d0*v(397)+42d0*v(400)+7d0*v(403)+v(442)+v(6044)*v(6045)+v(6050))/5040d0
v(409)=(7d0*(360d0*v(396)+120d0*v(398)+30d0*v(402)+6d0*v(404)+v(407))+v(5541)*(v(382)*v(406)+v(379)*v(407)+v(381)*v&
&(6045)))/5040d0
v(408)=statev(18)*v(409)+statev(16)*v(445)+v(447)*v(5525)
v(6046)=2d0*v(408)
v(5079)=v(4608)*v(6046)
v(5078)=v(4607)*v(6046)
v(5077)=v(4606)*v(6046)
v(5076)=v(4605)*v(6046)
v(5075)=v(4604)*v(6046)
v(5074)=v(4603)*v(6046)
v(5073)=v(4602)*v(6046)
v(5072)=v(4601)*v(6046)
v(5071)=v(4600)*v(6046)
v(411)=v(232)*(v(379)*v(379))+v(410)+v(427)
v(4645)=v(4346)+v(4364)+(v(411)*v(4262)+v(379)*v(4618))*v(5541)
v(4644)=v(4345)+v(4363)+(v(411)*v(4261)+v(379)*v(4617))*v(5541)
v(4643)=v(4344)+v(4362)+(v(411)*v(4260)+v(379)*v(4616))*v(5541)
v(4642)=v(4343)+v(4361)+(v(411)*v(4259)+v(379)*v(4615))*v(5541)
v(4641)=v(4342)+v(4360)+(v(411)*v(4258)+v(379)*v(4614))*v(5541)
v(4640)=v(4341)+v(4359)+(v(411)*v(4257)+v(379)*v(4613))*v(5541)
v(4639)=v(4340)+v(4358)+(v(411)*v(4256)+v(379)*v(4612))*v(5541)
v(4638)=v(4339)+v(4357)+(v(411)*v(4255)+v(379)*v(4611))*v(5541)
v(4637)=v(4338)+v(4356)+(v(411)*v(4254)+v(379)*v(4609))*v(5541)
v(4627)=(v(415)*v(4271)+v(411)*v(4299)+v(396)*v(4318)+v(380)*v(4337)+v(383)*v(4355)+v(382)*v(4618))*v(5541)
v(4626)=(v(415)*v(4270)+v(411)*v(4298)+v(396)*v(4317)+v(380)*v(4336)+v(383)*v(4354)+v(382)*v(4617))*v(5541)
v(4625)=(v(415)*v(4269)+v(411)*v(4297)+v(396)*v(4316)+v(380)*v(4335)+v(383)*v(4353)+v(382)*v(4616))*v(5541)
v(4624)=(v(415)*v(4268)+v(411)*v(4296)+v(396)*v(4315)+v(380)*v(4334)+v(383)*v(4352)+v(382)*v(4615))*v(5541)
v(4623)=(v(415)*v(4267)+v(411)*v(4295)+v(396)*v(4314)+v(380)*v(4333)+v(383)*v(4351)+v(382)*v(4614))*v(5541)
v(4622)=(v(415)*v(4266)+v(411)*v(4294)+v(396)*v(4313)+v(380)*v(4332)+v(383)*v(4350)+v(382)*v(4613))*v(5541)
v(4621)=(v(415)*v(4265)+v(411)*v(4293)+v(396)*v(4312)+v(380)*v(4331)+v(383)*v(4349)+v(382)*v(4612))*v(5541)
v(4620)=(v(415)*v(4264)+v(411)*v(4292)+v(396)*v(4311)+v(380)*v(4330)+v(383)*v(4348)+v(382)*v(4611))*v(5541)
v(4619)=(v(415)*v(4263)+v(411)*v(4291)+v(396)*v(4310)+v(380)*v(4329)+v(383)*v(4347)+v(382)*v(4609))*v(5541)
v(417)=(v(383)*v(396)+v(382)*v(411)+v(380)*v(415))*v(5541)
v(4636)=(v(417)*v(4299)+v(382)*v(4627))*v(5541)
v(4635)=(v(417)*v(4298)+v(382)*v(4626))*v(5541)
v(4634)=(v(417)*v(4297)+v(382)*v(4625))*v(5541)
v(4633)=(v(417)*v(4296)+v(382)*v(4624))*v(5541)
v(4632)=(v(417)*v(4295)+v(382)*v(4623))*v(5541)
v(4631)=(v(417)*v(4294)+v(382)*v(4622))*v(5541)
v(4630)=(v(417)*v(4293)+v(382)*v(4621))*v(5541)
v(4629)=(v(417)*v(4292)+v(382)*v(4620))*v(5541)
v(4628)=(v(417)*v(4291)+v(382)*v(4619))*v(5541)
v(433)=v(417)*v(6047)
v(413)=v(412)+v(431)+v(411)*v(6048)
v(4672)=v(4428)+v(4636)+(v(413)*v(4262)+v(379)*v(4645))*v(5541)
v(4671)=v(4427)+v(4635)+(v(413)*v(4261)+v(379)*v(4644))*v(5541)
v(4670)=v(4426)+v(4634)+(v(413)*v(4260)+v(379)*v(4643))*v(5541)
v(4669)=v(4425)+v(4633)+(v(413)*v(4259)+v(379)*v(4642))*v(5541)
v(4668)=v(4424)+v(4632)+(v(413)*v(4258)+v(379)*v(4641))*v(5541)
v(4667)=v(4423)+v(4631)+(v(413)*v(4257)+v(379)*v(4640))*v(5541)
v(4666)=v(4422)+v(4630)+(v(413)*v(4256)+v(379)*v(4639))*v(5541)
v(4665)=v(4421)+v(4629)+(v(413)*v(4255)+v(379)*v(4638))*v(5541)
v(4664)=v(4420)+v(4628)+(v(413)*v(4254)+v(379)*v(4637))*v(5541)
v(4654)=(v(417)*v(4271)+v(413)*v(4299)+v(398)*v(4318)+v(383)*v(4419)+v(380)*v(4627)+v(382)*v(4645))*v(5541)
v(4653)=(v(417)*v(4270)+v(413)*v(4298)+v(398)*v(4317)+v(383)*v(4418)+v(380)*v(4626)+v(382)*v(4644))*v(5541)
v(4652)=(v(417)*v(4269)+v(413)*v(4297)+v(398)*v(4316)+v(383)*v(4417)+v(380)*v(4625)+v(382)*v(4643))*v(5541)
v(4651)=(v(417)*v(4268)+v(413)*v(4296)+v(398)*v(4315)+v(383)*v(4416)+v(380)*v(4624)+v(382)*v(4642))*v(5541)
v(4650)=(v(417)*v(4267)+v(413)*v(4295)+v(398)*v(4314)+v(383)*v(4415)+v(380)*v(4623)+v(382)*v(4641))*v(5541)
v(4649)=(v(417)*v(4266)+v(413)*v(4294)+v(398)*v(4313)+v(383)*v(4414)+v(380)*v(4622)+v(382)*v(4640))*v(5541)
v(4648)=(v(417)*v(4265)+v(413)*v(4293)+v(398)*v(4312)+v(383)*v(4413)+v(380)*v(4621)+v(382)*v(4639))*v(5541)
v(4647)=(v(417)*v(4264)+v(413)*v(4292)+v(398)*v(4311)+v(383)*v(4412)+v(380)*v(4620)+v(382)*v(4638))*v(5541)
v(4646)=(v(417)*v(4263)+v(413)*v(4291)+v(398)*v(4310)+v(383)*v(4411)+v(380)*v(4619)+v(382)*v(4637))*v(5541)
v(421)=(v(383)*v(398)+v(382)*v(413)+v(380)*v(417))*v(5541)
v(4663)=(v(421)*v(4299)+v(382)*v(4654))*v(5541)
v(4662)=(v(421)*v(4298)+v(382)*v(4653))*v(5541)
v(4661)=(v(421)*v(4297)+v(382)*v(4652))*v(5541)
v(4660)=(v(421)*v(4296)+v(382)*v(4651))*v(5541)
v(4659)=(v(421)*v(4295)+v(382)*v(4650))*v(5541)
v(4658)=(v(421)*v(4294)+v(382)*v(4649))*v(5541)
v(4657)=(v(421)*v(4293)+v(382)*v(4648))*v(5541)
v(4656)=(v(421)*v(4292)+v(382)*v(4647))*v(5541)
v(4655)=(v(421)*v(4291)+v(382)*v(4646))*v(5541)
v(437)=v(421)*v(6047)
v(416)=v(414)+v(433)+v(413)*v(6048)
v(4699)=v(4455)+v(4663)+(v(416)*v(4262)+v(379)*v(4672))*v(5541)
v(4698)=v(4454)+v(4662)+(v(416)*v(4261)+v(379)*v(4671))*v(5541)
v(4697)=v(4453)+v(4661)+(v(416)*v(4260)+v(379)*v(4670))*v(5541)
v(4696)=v(4452)+v(4660)+(v(416)*v(4259)+v(379)*v(4669))*v(5541)
v(4695)=v(4451)+v(4659)+(v(416)*v(4258)+v(379)*v(4668))*v(5541)
v(4694)=v(4450)+v(4658)+(v(416)*v(4257)+v(379)*v(4667))*v(5541)
v(4693)=v(4449)+v(4657)+(v(416)*v(4256)+v(379)*v(4666))*v(5541)
v(4692)=v(4448)+v(4656)+(v(416)*v(4255)+v(379)*v(4665))*v(5541)
v(4691)=v(4447)+v(4655)+(v(416)*v(4254)+v(379)*v(4664))*v(5541)
v(4681)=(v(421)*v(4271)+v(416)*v(4299)+v(402)*v(4318)+v(383)*v(4446)+v(380)*v(4654)+v(382)*v(4672))*v(5541)
v(4680)=(v(421)*v(4270)+v(416)*v(4298)+v(402)*v(4317)+v(383)*v(4445)+v(380)*v(4653)+v(382)*v(4671))*v(5541)
v(4679)=(v(421)*v(4269)+v(416)*v(4297)+v(402)*v(4316)+v(383)*v(4444)+v(380)*v(4652)+v(382)*v(4670))*v(5541)
v(4678)=(v(421)*v(4268)+v(416)*v(4296)+v(402)*v(4315)+v(383)*v(4443)+v(380)*v(4651)+v(382)*v(4669))*v(5541)
v(4677)=(v(421)*v(4267)+v(416)*v(4295)+v(402)*v(4314)+v(383)*v(4442)+v(380)*v(4650)+v(382)*v(4668))*v(5541)
v(4676)=(v(421)*v(4266)+v(416)*v(4294)+v(402)*v(4313)+v(383)*v(4441)+v(380)*v(4649)+v(382)*v(4667))*v(5541)
v(4675)=(v(421)*v(4265)+v(416)*v(4293)+v(402)*v(4312)+v(383)*v(4440)+v(380)*v(4648)+v(382)*v(4666))*v(5541)
v(4674)=(v(421)*v(4264)+v(416)*v(4292)+v(402)*v(4311)+v(383)*v(4439)+v(380)*v(4647)+v(382)*v(4665))*v(5541)
v(4673)=(v(421)*v(4263)+v(416)*v(4291)+v(402)*v(4310)+v(383)*v(4438)+v(380)*v(4646)+v(382)*v(4664))*v(5541)
v(423)=(v(383)*v(402)+v(382)*v(416)+v(380)*v(421))*v(5541)
v(4690)=(v(423)*v(4299)+v(382)*v(4681))*v(5541)
v(4689)=(v(423)*v(4298)+v(382)*v(4680))*v(5541)
v(4688)=(v(423)*v(4297)+v(382)*v(4679))*v(5541)
v(4687)=(v(423)*v(4296)+v(382)*v(4678))*v(5541)
v(4686)=(v(423)*v(4295)+v(382)*v(4677))*v(5541)
v(4685)=(v(423)*v(4294)+v(382)*v(4676))*v(5541)
v(4684)=(v(423)*v(4293)+v(382)*v(4675))*v(5541)
v(4683)=(v(423)*v(4292)+v(382)*v(4674))*v(5541)
v(4682)=(v(423)*v(4291)+v(382)*v(4673))*v(5541)
v(439)=v(423)*v(6047)
v(419)=v(418)+v(437)+v(416)*v(6048)
v(4717)=(v(423)*v(4271)+v(419)*v(4299)+v(404)*v(4318)+v(383)*v(4509)+v(380)*v(4681)+v(382)*v(4699))*v(5541)
v(4716)=(v(423)*v(4270)+v(419)*v(4298)+v(404)*v(4317)+v(383)*v(4508)+v(380)*v(4680)+v(382)*v(4698))*v(5541)
v(4715)=(v(423)*v(4269)+v(419)*v(4297)+v(404)*v(4316)+v(383)*v(4507)+v(380)*v(4679)+v(382)*v(4697))*v(5541)
v(4714)=(v(423)*v(4268)+v(419)*v(4296)+v(404)*v(4315)+v(383)*v(4506)+v(380)*v(4678)+v(382)*v(4696))*v(5541)
v(4713)=(v(423)*v(4267)+v(419)*v(4295)+v(404)*v(4314)+v(383)*v(4505)+v(380)*v(4677)+v(382)*v(4695))*v(5541)
v(4712)=(v(423)*v(4266)+v(419)*v(4294)+v(404)*v(4313)+v(383)*v(4504)+v(380)*v(4676)+v(382)*v(4694))*v(5541)
v(4711)=(v(423)*v(4265)+v(419)*v(4293)+v(404)*v(4312)+v(383)*v(4503)+v(380)*v(4675)+v(382)*v(4693))*v(5541)
v(4710)=(v(423)*v(4264)+v(419)*v(4292)+v(404)*v(4311)+v(383)*v(4502)+v(380)*v(4674)+v(382)*v(4692))*v(5541)
v(4709)=(v(423)*v(4263)+v(419)*v(4291)+v(404)*v(4310)+v(383)*v(4501)+v(380)*v(4673)+v(382)*v(4691))*v(5541)
v(4708)=v(4518)+v(4690)+(v(419)*v(4262)+v(379)*v(4699))*v(5541)
v(4707)=v(4517)+v(4689)+(v(419)*v(4261)+v(379)*v(4698))*v(5541)
v(4706)=v(4516)+v(4688)+(v(419)*v(4260)+v(379)*v(4697))*v(5541)
v(4705)=v(4515)+v(4687)+(v(419)*v(4259)+v(379)*v(4696))*v(5541)
v(4704)=v(4514)+v(4686)+(v(419)*v(4258)+v(379)*v(4695))*v(5541)
v(4703)=v(4513)+v(4685)+(v(419)*v(4257)+v(379)*v(4694))*v(5541)
v(4702)=v(4512)+v(4684)+(v(419)*v(4256)+v(379)*v(4693))*v(5541)
v(4701)=v(4511)+v(4683)+(v(419)*v(4255)+v(379)*v(4692))*v(5541)
v(4700)=v(4510)+v(4682)+(v(419)*v(4254)+v(379)*v(4691))*v(5541)
v(422)=v(420)+v(439)+v(419)*v(6048)
v(6049)=5040d0+v(422)
v(424)=(v(383)*v(404)+v(382)*v(419)+v(380)*v(423))*v(5541)
v(4735)=(v(424)*v(4299)+v(382)*v(4717))*v(5541)
v(4744)=(v(4581)+2520d0*v(4618)+840d0*v(4645)+210d0*v(4672)+42d0*v(4699)+7d0*v(4708)+v(4735)+v(5541)*(v(379)*v(4708)+v&
&(4262)*v(6049)))/5040d0
v(4734)=(v(424)*v(4298)+v(382)*v(4716))*v(5541)
v(4743)=(v(4580)+2520d0*v(4617)+840d0*v(4644)+210d0*v(4671)+42d0*v(4698)+7d0*v(4707)+v(4734)+v(5541)*(v(379)*v(4707)+v&
&(4261)*v(6049)))/5040d0
v(4733)=(v(424)*v(4297)+v(382)*v(4715))*v(5541)
v(4742)=(v(4579)+2520d0*v(4616)+840d0*v(4643)+210d0*v(4670)+42d0*v(4697)+7d0*v(4706)+v(4733)+v(5541)*(v(379)*v(4706)+v&
&(4260)*v(6049)))/5040d0
v(4732)=(v(424)*v(4296)+v(382)*v(4714))*v(5541)
v(4741)=(v(4578)+2520d0*v(4615)+840d0*v(4642)+210d0*v(4669)+42d0*v(4696)+7d0*v(4705)+v(4732)+v(5541)*(v(379)*v(4705)+v&
&(4259)*v(6049)))/5040d0
v(4731)=(v(424)*v(4295)+v(382)*v(4713))*v(5541)
v(4740)=(v(4577)+2520d0*v(4614)+840d0*v(4641)+210d0*v(4668)+42d0*v(4695)+7d0*v(4704)+v(4731)+v(5541)*(v(379)*v(4704)+v&
&(4258)*v(6049)))/5040d0
v(4730)=(v(424)*v(4294)+v(382)*v(4712))*v(5541)
v(4739)=(v(4576)+2520d0*v(4613)+840d0*v(4640)+210d0*v(4667)+42d0*v(4694)+7d0*v(4703)+v(4730)+v(5541)*(v(379)*v(4703)+v&
&(4257)*v(6049)))/5040d0
v(4729)=(v(424)*v(4293)+v(382)*v(4711))*v(5541)
v(4738)=(v(4575)+2520d0*v(4612)+840d0*v(4639)+210d0*v(4666)+42d0*v(4693)+7d0*v(4702)+v(4729)+v(5541)*(v(379)*v(4702)+v&
&(4256)*v(6049)))/5040d0
v(4728)=(v(424)*v(4292)+v(382)*v(4710))*v(5541)
v(4737)=(v(4574)+2520d0*v(4611)+840d0*v(4638)+210d0*v(4665)+42d0*v(4692)+7d0*v(4701)+v(4728)+v(5541)*(v(379)*v(4701)+v&
&(4255)*v(6049)))/5040d0
v(4727)=(v(424)*v(4291)+v(382)*v(4709))*v(5541)
v(4736)=(v(4573)+2520d0*v(4609)+840d0*v(4637)+210d0*v(4664)+42d0*v(4691)+7d0*v(4700)+v(4727)+v(5541)*(v(379)*v(4700)+v&
&(4254)*v(6049)))/5040d0
v(4726)=(7d0*(360d0*v(4337)+120d0*v(4627)+30d0*v(4654)+6d0*v(4681)+v(4717))+v(5541)*(v(424)*v(4271)+v(407)*v(4318)+v&
&(383)*v(4563)+v(382)*v(4708)+v(380)*v(4717)+v(4299)*v(6049)))/5040d0
v(4880)=statev(16)*v(4726)+statev(18)*v(4744)+v(4599)*v(5525)
v(6076)=v(408)*v(4880)
v(6338)=(-2d0)*v(6076)
v(4835)=statev(17)*v(4599)+statev(15)*v(4744)+v(4726)*v(5527)
v(4753)=statev(14)*v(4599)+statev(19)*v(4726)+v(4744)*v(5526)
v(4725)=(7d0*(360d0*v(4336)+120d0*v(4626)+30d0*v(4653)+6d0*v(4680)+v(4716))+v(5541)*(v(424)*v(4270)+v(407)*v(4317)+v&
&(383)*v(4562)+v(382)*v(4707)+v(380)*v(4716)+v(4298)*v(6049)))/5040d0
v(4879)=statev(16)*v(4725)+statev(18)*v(4743)+v(4598)*v(5525)
v(6082)=v(408)*v(4879)
v(6344)=(-2d0)*v(6082)
v(4834)=statev(17)*v(4598)+statev(15)*v(4743)+v(4725)*v(5527)
v(4752)=statev(14)*v(4598)+statev(19)*v(4725)+v(4743)*v(5526)
v(4724)=(7d0*(360d0*v(4335)+120d0*v(4625)+30d0*v(4652)+6d0*v(4679)+v(4715))+v(5541)*(v(424)*v(4269)+v(407)*v(4316)+v&
&(383)*v(4561)+v(382)*v(4706)+v(380)*v(4715)+v(4297)*v(6049)))/5040d0
v(4878)=statev(16)*v(4724)+statev(18)*v(4742)+v(4597)*v(5525)
v(6088)=v(408)*v(4878)
v(6348)=(-2d0)*v(6088)
v(4833)=statev(17)*v(4597)+statev(15)*v(4742)+v(4724)*v(5527)
v(4751)=statev(14)*v(4597)+statev(19)*v(4724)+v(4742)*v(5526)
v(4723)=(7d0*(360d0*v(4334)+120d0*v(4624)+30d0*v(4651)+6d0*v(4678)+v(4714))+v(5541)*(v(424)*v(4268)+v(407)*v(4315)+v&
&(383)*v(4560)+v(382)*v(4705)+v(380)*v(4714)+v(4296)*v(6049)))/5040d0
v(4877)=statev(16)*v(4723)+statev(18)*v(4741)+v(4596)*v(5525)
v(6091)=v(408)*v(4877)
v(6352)=(-2d0)*v(6091)
v(4832)=statev(17)*v(4596)+statev(15)*v(4741)+v(4723)*v(5527)
v(4750)=statev(14)*v(4596)+statev(19)*v(4723)+v(4741)*v(5526)
v(4722)=(7d0*(360d0*v(4333)+120d0*v(4623)+30d0*v(4650)+6d0*v(4677)+v(4713))+v(5541)*(v(424)*v(4267)+v(407)*v(4314)+v&
&(383)*v(4559)+v(382)*v(4704)+v(380)*v(4713)+v(4295)*v(6049)))/5040d0
v(4876)=statev(16)*v(4722)+statev(18)*v(4740)+v(4595)*v(5525)
v(6094)=v(408)*v(4876)
v(6356)=(-2d0)*v(6094)
v(4831)=statev(17)*v(4595)+statev(15)*v(4740)+v(4722)*v(5527)
v(4749)=statev(14)*v(4595)+statev(19)*v(4722)+v(4740)*v(5526)
v(4721)=(7d0*(360d0*v(4332)+120d0*v(4622)+30d0*v(4649)+6d0*v(4676)+v(4712))+v(5541)*(v(424)*v(4266)+v(407)*v(4313)+v&
&(383)*v(4558)+v(382)*v(4703)+v(380)*v(4712)+v(4294)*v(6049)))/5040d0
v(4875)=statev(16)*v(4721)+statev(18)*v(4739)+v(4594)*v(5525)
v(6097)=v(408)*v(4875)
v(6360)=(-2d0)*v(6097)
v(4830)=statev(17)*v(4594)+statev(15)*v(4739)+v(4721)*v(5527)
v(4748)=statev(14)*v(4594)+statev(19)*v(4721)+v(4739)*v(5526)
v(4720)=(7d0*(360d0*v(4331)+120d0*v(4621)+30d0*v(4648)+6d0*v(4675)+v(4711))+v(5541)*(v(424)*v(4265)+v(407)*v(4312)+v&
&(383)*v(4557)+v(382)*v(4702)+v(380)*v(4711)+v(4293)*v(6049)))/5040d0
v(4874)=statev(16)*v(4720)+statev(18)*v(4738)+v(4593)*v(5525)
v(6100)=v(408)*v(4874)
v(6364)=(-2d0)*v(6100)
v(4829)=statev(17)*v(4593)+statev(15)*v(4738)+v(4720)*v(5527)
v(4747)=statev(14)*v(4593)+statev(19)*v(4720)+v(4738)*v(5526)
v(4719)=(7d0*(360d0*v(4330)+120d0*v(4620)+30d0*v(4647)+6d0*v(4674)+v(4710))+v(5541)*(v(424)*v(4264)+v(407)*v(4311)+v&
&(383)*v(4556)+v(382)*v(4701)+v(380)*v(4710)+v(4292)*v(6049)))/5040d0
v(4873)=statev(16)*v(4719)+statev(18)*v(4737)+v(4592)*v(5525)
v(6103)=v(408)*v(4873)
v(6368)=(-2d0)*v(6103)
v(4828)=statev(17)*v(4592)+statev(15)*v(4737)+v(4719)*v(5527)
v(4746)=statev(14)*v(4592)+statev(19)*v(4719)+v(4737)*v(5526)
v(4718)=(7d0*(360d0*v(4329)+120d0*v(4619)+30d0*v(4646)+6d0*v(4673)+v(4709))+v(5541)*(v(424)*v(4263)+v(407)*v(4310)+v&
&(383)*v(4555)+v(382)*v(4700)+v(380)*v(4709)+v(4291)*v(6049)))/5040d0
v(4872)=statev(16)*v(4718)+statev(18)*v(4736)+v(4591)*v(5525)
v(6106)=v(408)*v(4872)
v(6372)=(-2d0)*v(6106)
v(4827)=statev(17)*v(4591)+statev(15)*v(4736)+v(4718)*v(5527)
v(4745)=statev(14)*v(4591)+statev(19)*v(4718)+v(4736)*v(5526)
v(444)=(7d0*(360d0*v(415)+120d0*v(417)+30d0*v(421)+6d0*v(423)+v(424))+v(5541)*(v(383)*v(407)+v(380)*v(424)+v(382)*v&
&(6049)))/5040d0
v(443)=v(424)*v(6047)
v(449)=(2520d0*v(411)+840d0*v(413)+210d0*v(416)+42d0*v(419)+7d0*v(422)+v(443)+v(6048)*v(6049)+v(6050))/5040d0
v(426)=statev(14)*v(409)+statev(19)*v(444)+v(449)*v(5526)
v(6373)=v(426)*v(4818)
v(6369)=v(426)*v(4819)
v(6365)=v(426)*v(4820)
v(6361)=v(426)*v(4821)
v(6357)=v(426)*v(4822)
v(6353)=v(426)*v(4823)
v(6349)=v(426)*v(4824)
v(6345)=v(426)*v(4825)
v(6339)=v(426)*v(4826)
v(6334)=v(426)*v(4600)+v(408)*v(4745)
v(6333)=-(v(426)*v(4845))
v(6327)=v(426)*v(4601)+v(408)*v(4746)
v(6326)=-(v(426)*v(4846))
v(6320)=v(426)*v(4602)+v(408)*v(4747)
v(6319)=-(v(426)*v(4847))
v(6313)=v(426)*v(4603)+v(408)*v(4748)
v(6312)=-(v(426)*v(4848))
v(6306)=v(426)*v(4604)+v(408)*v(4749)
v(6305)=-(v(426)*v(4849))
v(6299)=v(426)*v(4605)+v(408)*v(4750)
v(6298)=-(v(426)*v(4850))
v(6292)=v(426)*v(4606)+v(408)*v(4751)
v(6291)=-(v(426)*v(4851))
v(6281)=v(426)*v(4607)+v(408)*v(4752)
v(6280)=-(v(426)*v(4852))
v(6274)=v(408)*v(426)
v(6269)=v(426)*v(4608)+v(408)*v(4753)
v(6268)=-(v(426)*v(4853))
v(6051)=2d0*v(426)
v(5043)=v(4753)*v(6051)
v(5042)=v(4752)*v(6051)
v(5041)=v(4751)*v(6051)
v(5040)=v(4750)*v(6051)
v(5039)=v(4749)*v(6051)
v(5038)=v(4748)*v(6051)
v(5037)=v(4747)*v(6051)
v(5036)=v(4746)*v(6051)
v(5035)=v(4745)*v(6051)
v(429)=v(232)*(v(380)*v(380))+v(427)+v(428)
v(4772)=v(4346)+v(4382)+(v(4271)*v(429)+v(380)*v(4763))*v(5541)
v(4771)=v(4345)+v(4381)+(v(4270)*v(429)+v(380)*v(4762))*v(5541)
v(4770)=v(4344)+v(4380)+(v(4269)*v(429)+v(380)*v(4761))*v(5541)
v(4769)=v(4343)+v(4379)+(v(4268)*v(429)+v(380)*v(4760))*v(5541)
v(4768)=v(4342)+v(4378)+(v(4267)*v(429)+v(380)*v(4759))*v(5541)
v(4767)=v(4341)+v(4377)+(v(4266)*v(429)+v(380)*v(4758))*v(5541)
v(4766)=v(4340)+v(4376)+(v(4265)*v(429)+v(380)*v(4757))*v(5541)
v(4765)=v(4339)+v(4375)+(v(4264)*v(429)+v(380)*v(4756))*v(5541)
v(4764)=v(4338)+v(4374)+(v(4263)*v(429)+v(380)*v(4754))*v(5541)
v(432)=v(430)+v(431)+v(429)*v(6052)
v(4781)=v(4410)+v(4636)+(v(4271)*v(432)+v(380)*v(4772))*v(5541)
v(4780)=v(4409)+v(4635)+(v(4270)*v(432)+v(380)*v(4771))*v(5541)
v(4779)=v(4408)+v(4634)+(v(4269)*v(432)+v(380)*v(4770))*v(5541)
v(4778)=v(4407)+v(4633)+(v(4268)*v(432)+v(380)*v(4769))*v(5541)
v(4777)=v(4406)+v(4632)+(v(4267)*v(432)+v(380)*v(4768))*v(5541)
v(4776)=v(4405)+v(4631)+(v(4266)*v(432)+v(380)*v(4767))*v(5541)
v(4775)=v(4404)+v(4630)+(v(4265)*v(432)+v(380)*v(4766))*v(5541)
v(4774)=v(4403)+v(4629)+(v(4264)*v(432)+v(380)*v(4765))*v(5541)
v(4773)=v(4402)+v(4628)+(v(4263)*v(432)+v(380)*v(4764))*v(5541)
v(435)=v(433)+v(434)+v(432)*v(6052)
v(4790)=v(4473)+v(4663)+(v(4271)*v(435)+v(380)*v(4781))*v(5541)
v(4789)=v(4472)+v(4662)+(v(4270)*v(435)+v(380)*v(4780))*v(5541)
v(4788)=v(4471)+v(4661)+(v(4269)*v(435)+v(380)*v(4779))*v(5541)
v(4787)=v(4470)+v(4660)+(v(4268)*v(435)+v(380)*v(4778))*v(5541)
v(4786)=v(4469)+v(4659)+(v(4267)*v(435)+v(380)*v(4777))*v(5541)
v(4785)=v(4468)+v(4658)+(v(4266)*v(435)+v(380)*v(4776))*v(5541)
v(4784)=v(4467)+v(4657)+(v(4265)*v(435)+v(380)*v(4775))*v(5541)
v(4783)=v(4466)+v(4656)+(v(4264)*v(435)+v(380)*v(4774))*v(5541)
v(4782)=v(4465)+v(4655)+(v(4263)*v(435)+v(380)*v(4773))*v(5541)
v(438)=v(436)+v(437)+v(435)*v(6052)
v(4799)=v(4500)+v(4690)+(v(4271)*v(438)+v(380)*v(4790))*v(5541)
v(4798)=v(4499)+v(4689)+(v(4270)*v(438)+v(380)*v(4789))*v(5541)
v(4797)=v(4498)+v(4688)+(v(4269)*v(438)+v(380)*v(4788))*v(5541)
v(4796)=v(4497)+v(4687)+(v(4268)*v(438)+v(380)*v(4787))*v(5541)
v(4795)=v(4496)+v(4686)+(v(4267)*v(438)+v(380)*v(4786))*v(5541)
v(4794)=v(4495)+v(4685)+(v(4266)*v(438)+v(380)*v(4785))*v(5541)
v(4793)=v(4494)+v(4684)+(v(4265)*v(438)+v(380)*v(4784))*v(5541)
v(4792)=v(4493)+v(4683)+(v(4264)*v(438)+v(380)*v(4783))*v(5541)
v(4791)=v(4492)+v(4682)+(v(4263)*v(438)+v(380)*v(4782))*v(5541)
v(441)=v(439)+v(440)+v(438)*v(6052)
v(6053)=5040d0+v(441)
v(4808)=(v(4554)+v(4735)+2520d0*v(4763)+840d0*v(4772)+210d0*v(4781)+42d0*v(4790)+7d0*v(4799)+v(5541)*(v(380)*v(4799)+v&
&(4271)*v(6053)))/5040d0
v(4916)=statev(14)*v(4572)+statev(19)*v(4808)+v(4726)*v(5526)
v(6151)=v(426)*v(4916)
v(6152)=(-2d0)*v(6151)
v(4844)=statev(18)*v(4726)+statev(16)*v(4808)+v(4572)*v(5525)
v(6213)=v(408)*v(4844)
v(4817)=statev(17)*v(4572)+statev(15)*v(4726)+v(4808)*v(5527)
v(4807)=(v(4553)+v(4734)+2520d0*v(4762)+840d0*v(4771)+210d0*v(4780)+42d0*v(4789)+7d0*v(4798)+v(5541)*(v(380)*v(4798)+v&
&(4270)*v(6053)))/5040d0
v(4915)=statev(14)*v(4571)+statev(19)*v(4807)+v(4725)*v(5526)
v(6161)=v(426)*v(4915)
v(6162)=(-2d0)*v(6161)
v(4843)=statev(18)*v(4725)+statev(16)*v(4807)+v(4571)*v(5525)
v(6220)=v(408)*v(4843)
v(4816)=statev(17)*v(4571)+statev(15)*v(4725)+v(4807)*v(5527)
v(4806)=(v(4552)+v(4733)+2520d0*v(4761)+840d0*v(4770)+210d0*v(4779)+42d0*v(4788)+7d0*v(4797)+v(5541)*(v(380)*v(4797)+v&
&(4269)*v(6053)))/5040d0
v(4914)=statev(14)*v(4570)+statev(19)*v(4806)+v(4724)*v(5526)
v(6168)=v(426)*v(4914)
v(6169)=(-2d0)*v(6168)
v(4842)=statev(18)*v(4724)+statev(16)*v(4806)+v(4570)*v(5525)
v(6227)=v(408)*v(4842)
v(4815)=statev(17)*v(4570)+statev(15)*v(4724)+v(4806)*v(5527)
v(4805)=(v(4551)+v(4732)+2520d0*v(4760)+840d0*v(4769)+210d0*v(4778)+42d0*v(4787)+7d0*v(4796)+v(5541)*(v(380)*v(4796)+v&
&(4268)*v(6053)))/5040d0
v(4913)=statev(14)*v(4569)+statev(19)*v(4805)+v(4723)*v(5526)
v(6174)=v(426)*v(4913)
v(6175)=(-2d0)*v(6174)
v(4841)=statev(18)*v(4723)+statev(16)*v(4805)+v(4569)*v(5525)
v(6233)=v(408)*v(4841)
v(4814)=statev(17)*v(4569)+statev(15)*v(4723)+v(4805)*v(5527)
v(4804)=(v(4550)+v(4731)+2520d0*v(4759)+840d0*v(4768)+210d0*v(4777)+42d0*v(4786)+7d0*v(4795)+v(5541)*(v(380)*v(4795)+v&
&(4267)*v(6053)))/5040d0
v(4912)=statev(14)*v(4568)+statev(19)*v(4804)+v(4722)*v(5526)
v(6180)=v(426)*v(4912)
v(6181)=(-2d0)*v(6180)
v(4840)=statev(18)*v(4722)+statev(16)*v(4804)+v(4568)*v(5525)
v(6239)=v(408)*v(4840)
v(4813)=statev(17)*v(4568)+statev(15)*v(4722)+v(4804)*v(5527)
v(4803)=(v(4549)+v(4730)+2520d0*v(4758)+840d0*v(4767)+210d0*v(4776)+42d0*v(4785)+7d0*v(4794)+v(5541)*(v(380)*v(4794)+v&
&(4266)*v(6053)))/5040d0
v(4911)=statev(14)*v(4567)+statev(19)*v(4803)+v(4721)*v(5526)
v(6186)=v(426)*v(4911)
v(6187)=(-2d0)*v(6186)
v(4839)=statev(18)*v(4721)+statev(16)*v(4803)+v(4567)*v(5525)
v(6245)=v(408)*v(4839)
v(4812)=statev(17)*v(4567)+statev(15)*v(4721)+v(4803)*v(5527)
v(4802)=(v(4548)+v(4729)+2520d0*v(4757)+840d0*v(4766)+210d0*v(4775)+42d0*v(4784)+7d0*v(4793)+v(5541)*(v(380)*v(4793)+v&
&(4265)*v(6053)))/5040d0
v(4910)=statev(14)*v(4566)+statev(19)*v(4802)+v(4720)*v(5526)
v(6192)=v(426)*v(4910)
v(6193)=(-2d0)*v(6192)
v(4838)=statev(18)*v(4720)+statev(16)*v(4802)+v(4566)*v(5525)
v(6251)=v(408)*v(4838)
v(4811)=statev(17)*v(4566)+statev(15)*v(4720)+v(4802)*v(5527)
v(4801)=(v(4547)+v(4728)+2520d0*v(4756)+840d0*v(4765)+210d0*v(4774)+42d0*v(4783)+7d0*v(4792)+v(5541)*(v(380)*v(4792)+v&
&(4264)*v(6053)))/5040d0
v(4909)=statev(14)*v(4565)+statev(19)*v(4801)+v(4719)*v(5526)
v(6198)=v(426)*v(4909)
v(6199)=(-2d0)*v(6198)
v(4837)=statev(18)*v(4719)+statev(16)*v(4801)+v(4565)*v(5525)
v(6257)=v(408)*v(4837)
v(4810)=statev(17)*v(4565)+statev(15)*v(4719)+v(4801)*v(5527)
v(4800)=(v(4546)+v(4727)+2520d0*v(4754)+840d0*v(4764)+210d0*v(4773)+42d0*v(4782)+7d0*v(4791)+v(5541)*(v(380)*v(4791)+v&
&(4263)*v(6053)))/5040d0
v(4908)=statev(14)*v(4564)+statev(19)*v(4800)+v(4718)*v(5526)
v(6204)=v(426)*v(4908)
v(6205)=(-2d0)*v(6204)
v(4836)=statev(18)*v(4718)+statev(16)*v(4800)+v(4564)*v(5525)
v(6263)=v(408)*v(4836)
v(4809)=statev(17)*v(4564)+statev(15)*v(4718)+v(4800)*v(5527)
v(451)=(5040d0+2520d0*v(429)+840d0*v(432)+210d0*v(435)+42d0*v(438)+7d0*v(441)+v(442)+v(443)+v(6052)*v(6053))/5040d0
v(446)=statev(15)*v(444)+statev(17)*v(445)+v(451)*v(5527)
v(6207)=v(446)*v(4827)
v(6201)=v(446)*v(4828)
v(6195)=v(446)*v(4829)
v(6189)=v(446)*v(4830)
v(6183)=v(446)*v(4831)
v(6177)=v(446)*v(4832)
v(6171)=v(446)*v(4833)
v(6164)=v(446)*v(4834)
v(6154)=v(446)*v(4835)
v(6054)=2d0*v(446)
v(6259)=-(v(4845)*v(6054))
v(6253)=-(v(4846)*v(6054))
v(6247)=-(v(4847)*v(6054))
v(6241)=-(v(4848)*v(6054))
v(6235)=-(v(4849)*v(6054))
v(6229)=-(v(4850)*v(6054))
v(6223)=-(v(4851)*v(6054))
v(6216)=-(v(4852)*v(6054))
v(6209)=-(v(4853)*v(6054))
v(5115)=v(4817)*v(6054)
v(5114)=v(4816)*v(6054)
v(5113)=v(4815)*v(6054)
v(5112)=v(4814)*v(6054)
v(5111)=v(4813)*v(6054)
v(5110)=v(4812)*v(6054)
v(5109)=v(4811)*v(6054)
v(5108)=v(4810)*v(6054)
v(5107)=v(4809)*v(6054)
v(448)=statev(19)*v(445)+statev(14)*v(447)+v(409)*v(5526)
v(6336)=-(v(448)*v(4872))
v(6329)=-(v(448)*v(4873))
v(6322)=-(v(448)*v(4874))
v(6315)=-(v(448)*v(4875))
v(6308)=-(v(448)*v(4876))
v(6301)=-(v(448)*v(4877))
v(6294)=-(v(448)*v(4878))
v(6283)=-(v(448)*v(4879))
v(6271)=-(v(448)*v(4880))
v(6260)=v(448)*v(4908)
v(6261)=(-2d0)*v(6260)
v(6254)=v(448)*v(4909)
v(6255)=(-2d0)*v(6254)
v(6248)=v(448)*v(4910)
v(6249)=(-2d0)*v(6248)
v(6242)=v(448)*v(4911)
v(6243)=(-2d0)*v(6242)
v(6236)=v(448)*v(4912)
v(6237)=(-2d0)*v(6236)
v(6230)=v(448)*v(4913)
v(6231)=(-2d0)*v(6230)
v(6224)=v(448)*v(4914)
v(6225)=(-2d0)*v(6224)
v(6217)=v(448)*v(4915)
v(6218)=(-2d0)*v(6217)
v(6210)=v(448)*v(4916)
v(6211)=(-2d0)*v(6210)
v(6108)=v(426)*v(448)
v(6105)=v(448)*v(4745)+v(6373)
v(6144)=v(6105)+v(6106)
v(6102)=v(448)*v(4746)+v(6369)
v(6141)=v(6102)+v(6103)
v(6099)=v(448)*v(4747)+v(6365)
v(6138)=v(6099)+v(6100)
v(6096)=v(448)*v(4748)+v(6361)
v(6135)=v(6096)+v(6097)
v(6093)=v(448)*v(4749)+v(6357)
v(6132)=v(6093)+v(6094)
v(6090)=v(448)*v(4750)+v(6353)
v(6129)=v(6090)+v(6091)
v(6087)=v(448)*v(4751)+v(6349)
v(6126)=v(6087)+v(6088)
v(6081)=v(448)*v(4752)+v(6345)
v(6120)=v(6081)+v(6082)
v(6075)=v(448)*v(4753)+v(6339)
v(6115)=v(6075)+v(6076)
v(6055)=2d0*v(448)
v(6374)=-(v(4745)*v(6055))-2d0*v(6373)
v(6370)=-(v(4746)*v(6055))-2d0*v(6369)
v(6366)=-(v(4747)*v(6055))-2d0*v(6365)
v(6362)=-(v(4748)*v(6055))-2d0*v(6361)
v(6358)=-(v(4749)*v(6055))-2d0*v(6357)
v(6354)=-(v(4750)*v(6055))-2d0*v(6353)
v(6350)=-(v(4751)*v(6055))-2d0*v(6349)
v(6346)=-(v(4752)*v(6055))-2d0*v(6345)
v(6340)=-(v(4753)*v(6055))-2d0*v(6339)
v(5097)=v(4826)*v(6055)
v(5096)=v(4825)*v(6055)
v(5095)=v(4824)*v(6055)
v(5094)=v(4823)*v(6055)
v(5093)=v(4822)*v(6055)
v(5092)=v(4821)*v(6055)
v(5091)=v(4820)*v(6055)
v(5090)=v(4819)*v(6055)
v(5089)=v(4818)*v(6055)
v(450)=statev(17)*v(409)+statev(15)*v(449)+v(444)*v(5527)
v(6331)=v(450)*v(4818)+v(448)*v(4827)
v(6324)=v(450)*v(4819)+v(448)*v(4828)
v(6317)=v(450)*v(4820)+v(448)*v(4829)
v(6310)=v(450)*v(4821)+v(448)*v(4830)
v(6303)=v(450)*v(4822)+v(448)*v(4831)
v(6296)=v(450)*v(4823)+v(448)*v(4832)
v(6289)=v(450)*v(4824)+v(448)*v(4833)
v(6278)=v(450)*v(4825)+v(448)*v(4834)
v(6272)=v(448)*v(450)
v(6266)=v(450)*v(4826)+v(448)*v(4835)
v(6206)=v(450)*v(4809)
v(6208)=(-2d0)*(v(6206)+v(6207))
v(6200)=v(450)*v(4810)
v(6202)=(-2d0)*(v(6200)+v(6201))
v(6194)=v(450)*v(4811)
v(6196)=(-2d0)*(v(6194)+v(6195))
v(6188)=v(450)*v(4812)
v(6190)=(-2d0)*(v(6188)+v(6189))
v(6182)=v(450)*v(4813)
v(6184)=(-2d0)*(v(6182)+v(6183))
v(6176)=v(450)*v(4814)
v(6178)=(-2d0)*(v(6176)+v(6177))
v(6170)=v(450)*v(4815)
v(6172)=(-2d0)*(v(6170)+v(6171))
v(6163)=v(450)*v(4816)
v(6165)=(-2d0)*(v(6163)+v(6164))
v(6156)=v(446)*v(450)
v(6153)=v(450)*v(4817)
v(6155)=(-2d0)*(v(6153)+v(6154))
v(6145)=v(450)*v(4845)
v(6142)=v(450)*v(4846)
v(6139)=v(450)*v(4847)
v(6136)=v(450)*v(4848)
v(6133)=v(450)*v(4849)
v(6130)=v(450)*v(4850)
v(6127)=v(450)*v(4851)
v(6121)=v(450)*v(4852)
v(6116)=v(450)*v(4853)
v(6056)=2d0*v(450)
v(6371)=-(v(4845)*v(6056))
v(6367)=-(v(4846)*v(6056))
v(6363)=-(v(4847)*v(6056))
v(6359)=-(v(4848)*v(6056))
v(6355)=-(v(4849)*v(6056))
v(6351)=-(v(4850)*v(6056))
v(6347)=-(v(4851)*v(6056))
v(6343)=-(v(4852)*v(6056))
v(6337)=-(v(4853)*v(6056))
v(5052)=v(4835)*v(6056)
v(5051)=v(4834)*v(6056)
v(5050)=v(4833)*v(6056)
v(5049)=v(4832)*v(6056)
v(5048)=v(4831)*v(6056)
v(5047)=v(4830)*v(6056)
v(5046)=v(4829)*v(6056)
v(5045)=v(4828)*v(6056)
v(5044)=v(4827)*v(6056)
v(452)=statev(18)*v(444)+statev(16)*v(451)+v(445)*v(5525)
v(6262)=v(452)*v(4600)
v(6330)=v(6260)+v(6262)+v(6263)
v(6264)=(-2d0)*(v(6262)+v(6263))
v(6256)=v(452)*v(4601)
v(6323)=v(6254)+v(6256)+v(6257)
v(6258)=(-2d0)*(v(6256)+v(6257))
v(6250)=v(452)*v(4602)
v(6316)=v(6248)+v(6250)+v(6251)
v(6252)=(-2d0)*(v(6250)+v(6251))
v(6244)=v(452)*v(4603)
v(6309)=v(6242)+v(6244)+v(6245)
v(6246)=(-2d0)*(v(6244)+v(6245))
v(6238)=v(452)*v(4604)
v(6302)=v(6236)+v(6238)+v(6239)
v(6240)=(-2d0)*(v(6238)+v(6239))
v(6232)=v(452)*v(4605)
v(6295)=v(6230)+v(6232)+v(6233)
v(6234)=(-2d0)*(v(6232)+v(6233))
v(6226)=v(452)*v(4606)
v(6288)=v(6224)+v(6226)+v(6227)
v(6228)=(-2d0)*(v(6226)+v(6227))
v(6219)=v(452)*v(4607)
v(6277)=v(6217)+v(6219)+v(6220)
v(6221)=(-2d0)*(v(6219)+v(6220))
v(6215)=v(408)*v(452)
v(6212)=v(452)*v(4608)
v(6265)=v(6210)+v(6212)+v(6213)
v(6214)=(-2d0)*(v(6212)+v(6213))
v(6057)=2d0*v(452)
v(6203)=-(v(4872)*v(6057))
v(6197)=-(v(4873)*v(6057))
v(6191)=-(v(4874)*v(6057))
v(6185)=-(v(4875)*v(6057))
v(6179)=-(v(4876)*v(6057))
v(6173)=-(v(4877)*v(6057))
v(6167)=-(v(4878)*v(6057))
v(6160)=-(v(4879)*v(6057))
v(6150)=-(v(4880)*v(6057))
v(5133)=v(4844)*v(6057)
v(5132)=v(4843)*v(6057)
v(5131)=v(4842)*v(6057)
v(5130)=v(4841)*v(6057)
v(5129)=v(4840)*v(6057)
v(5128)=v(4839)*v(6057)
v(5127)=v(4838)*v(6057)
v(5126)=v(4837)*v(6057)
v(5125)=v(4836)*v(6057)
v(453)=statev(15)*v(409)+statev(17)*v(447)+v(445)*v(5527)
v(6332)=-(v(453)*v(4745))
v(6325)=-(v(453)*v(4746))
v(6318)=-(v(453)*v(4747))
v(6311)=-(v(453)*v(4748))
v(6304)=-(v(453)*v(4749))
v(6297)=-(v(453)*v(4750))
v(6290)=-(v(453)*v(4751))
v(6279)=-(v(453)*v(4752))
v(6276)=v(446)*v(453)+v(6215)
v(6273)=-(v(426)*v(453))
v(6284)=v(6272)-v(6273)
v(6267)=-(v(453)*v(4753))
v(6111)=v(450)*v(453)
v(6107)=v(453)*v(4827)+v(6145)
v(6104)=v(453)*v(4828)+v(6142)
v(6101)=v(453)*v(4829)+v(6139)
v(6098)=v(453)*v(4830)+v(6136)
v(6095)=v(453)*v(4831)+v(6133)
v(6092)=v(453)*v(4832)+v(6130)
v(6089)=v(453)*v(4833)+v(6127)
v(6083)=v(453)*v(4834)+v(6121)
v(6079)=v(453)*v(4835)+v(6116)
v(6078)=v(6108)+v(6111)
v(6058)=2d0*v(453)
v(6341)=-(v(426)*v(6055))-v(450)*v(6058)
v(6222)=-(v(446)*v(6058))-2d0*v(6215)
v(5088)=v(4853)*v(6058)
v(5087)=v(4852)*v(6058)
v(5086)=v(4851)*v(6058)
v(5085)=v(4850)*v(6058)
v(5084)=v(4849)*v(6058)
v(5083)=v(4848)*v(6058)
v(5082)=v(4847)*v(6058)
v(5081)=v(4846)*v(6058)
v(5080)=v(4845)*v(6058)
v(4871)=v(446)*v(4608)+v(408)*v(4817)-v(453)*v(4844)-v(452)*v(4853)
v(4870)=v(446)*v(4607)+v(408)*v(4816)-v(453)*v(4843)-v(452)*v(4852)
v(4869)=v(446)*v(4606)+v(408)*v(4815)-v(453)*v(4842)-v(452)*v(4851)
v(4868)=v(446)*v(4605)+v(408)*v(4814)-v(453)*v(4841)-v(452)*v(4850)
v(4867)=v(446)*v(4604)+v(408)*v(4813)-v(453)*v(4840)-v(452)*v(4849)
v(4866)=v(446)*v(4603)+v(408)*v(4812)-v(453)*v(4839)-v(452)*v(4848)
v(4865)=v(446)*v(4602)+v(408)*v(4811)-v(453)*v(4838)-v(452)*v(4847)
v(4864)=v(446)*v(4601)+v(408)*v(4810)-v(453)*v(4837)-v(452)*v(4846)
v(4863)=v(446)*v(4600)+v(408)*v(4809)-v(453)*v(4836)-v(452)*v(4845)
v(4862)=v(6266)+v(6267)+v(6268)
v(4861)=v(6278)+v(6279)+v(6280)
v(4860)=v(6289)+v(6290)+v(6291)
v(4859)=v(6296)+v(6297)+v(6298)
v(4858)=v(6303)+v(6304)+v(6305)
v(4857)=v(6310)+v(6311)+v(6312)
v(4856)=v(6317)+v(6318)+v(6319)
v(4855)=v(6324)+v(6325)+v(6326)
v(4854)=v(6331)+v(6332)+v(6333)
v(552)=v(6272)+v(6273)
v(4972)=(v(552)*v(552))
v(545)=v(408)*v(446)-v(452)*v(453)
v(5005)=(v(545)*v(545))
v(454)=statev(16)*v(444)+statev(18)*v(449)+v(409)*v(5525)
v(6335)=-(v(454)*v(4818))
v(6328)=-(v(454)*v(4819))
v(6321)=-(v(454)*v(4820))
v(6314)=-(v(454)*v(4821))
v(6307)=-(v(454)*v(4822))
v(6300)=-(v(454)*v(4823))
v(6293)=-(v(454)*v(4824))
v(6282)=-(v(454)*v(4825))
v(6275)=-(v(448)*v(454))
v(6285)=v(6274)-v(6275)
v(6270)=-(v(454)*v(4826))
v(6146)=v(454)*v(4600)
v(6143)=v(454)*v(4601)
v(6140)=v(454)*v(4602)
v(6137)=v(454)*v(4603)
v(6134)=v(454)*v(4604)
v(6131)=v(454)*v(4605)
v(6128)=v(454)*v(4606)
v(6122)=v(454)*v(4607)
v(6118)=v(454)*v(4608)
v(6109)=v(408)*v(454)
v(6149)=v(6109)+v(6111)
v(6114)=v(6108)+v(6109)
v(6059)=2d0*v(454)
v(6166)=-(v(452)*v(6059))-2d0*v(6156)
v(5061)=v(4880)*v(6059)
v(5060)=v(4879)*v(6059)
v(5059)=v(4878)*v(6059)
v(5058)=v(4877)*v(6059)
v(5057)=v(4876)*v(6059)
v(5056)=v(4875)*v(6059)
v(5055)=v(4874)*v(6059)
v(5054)=v(4873)*v(6059)
v(5053)=v(4872)*v(6059)
v(4907)=-(v(454)*v(4817))+v(452)*v(4835)+v(450)*v(4844)-v(446)*v(4880)
v(4906)=-(v(454)*v(4816))+v(452)*v(4834)+v(450)*v(4843)-v(446)*v(4879)
v(4905)=-(v(454)*v(4815))+v(452)*v(4833)+v(450)*v(4842)-v(446)*v(4878)
v(4904)=-(v(454)*v(4814))+v(452)*v(4832)+v(450)*v(4841)-v(446)*v(4877)
v(4903)=-(v(454)*v(4813))+v(452)*v(4831)+v(450)*v(4840)-v(446)*v(4876)
v(4902)=-(v(454)*v(4812))+v(452)*v(4830)+v(450)*v(4839)-v(446)*v(4875)
v(4901)=-(v(454)*v(4811))+v(452)*v(4829)+v(450)*v(4838)-v(446)*v(4874)
v(4900)=-(v(454)*v(4810))+v(452)*v(4828)+v(450)*v(4837)-v(446)*v(4873)
v(4899)=-(v(454)*v(4809))+v(452)*v(4827)+v(450)*v(4836)-v(446)*v(4872)
v(4898)=-(v(450)*v(4608))-v(408)*v(4835)+v(454)*v(4853)+v(453)*v(4880)
v(4897)=-(v(450)*v(4607))-v(408)*v(4834)+v(454)*v(4852)+v(453)*v(4879)
v(4896)=-(v(450)*v(4606))-v(408)*v(4833)+v(454)*v(4851)+v(453)*v(4878)
v(4895)=-(v(450)*v(4605))-v(408)*v(4832)+v(454)*v(4850)+v(453)*v(4877)
v(4894)=-(v(450)*v(4604))-v(408)*v(4831)+v(454)*v(4849)+v(453)*v(4876)
v(4893)=-(v(450)*v(4603))-v(408)*v(4830)+v(454)*v(4848)+v(453)*v(4875)
v(4892)=-(v(450)*v(4602))-v(408)*v(4829)+v(454)*v(4847)+v(453)*v(4874)
v(4891)=-(v(450)*v(4601))-v(408)*v(4828)+v(454)*v(4846)+v(453)*v(4873)
v(4890)=-(v(450)*v(4600))-v(408)*v(4827)+v(454)*v(4845)+v(453)*v(4872)
v(4889)=v(6269)+v(6270)+v(6271)
v(4888)=v(6281)+v(6282)+v(6283)
v(4887)=v(6292)+v(6293)+v(6294)
v(4886)=v(6299)+v(6300)+v(6301)
v(4885)=v(6306)+v(6307)+v(6308)
v(4884)=v(6313)+v(6314)+v(6315)
v(4883)=v(6320)+v(6321)+v(6322)
v(4882)=v(6327)+v(6328)+v(6329)
v(4881)=v(6334)+v(6335)+v(6336)
v(554)=v(6274)+v(6275)
v(4974)=(v(554)*v(554))
v(553)=-(v(408)*v(450))+v(453)*v(454)
v(4973)=(v(553)*v(553))
v(6073)=-v(4972)-v(4973)-v(4974)
v(546)=v(450)*v(452)-v(446)*v(454)
v(4984)=(v(546)*v(546))
v(455)=statev(14)*v(445)+statev(19)*v(451)+v(444)*v(5526)
v(6123)=v(448)*v(455)+v(6215)
v(6084)=v(426)*v(455)+v(6156)
v(6060)=2d0*v(455)
v(5124)=v(4916)*v(6060)
v(5123)=v(4915)*v(6060)
v(5122)=v(4914)*v(6060)
v(5121)=v(4913)*v(6060)
v(5120)=v(4912)*v(6060)
v(5119)=v(4911)*v(6060)
v(5118)=v(4910)*v(6060)
v(5117)=v(4909)*v(6060)
v(5116)=v(4908)*v(6060)
v(4961)=v(452)*v(4862)+v(446)*v(4889)+v(455)*v(4898)+v(4844)*v(552)+v(4916)*v(553)+v(4817)*v(554)
v(4960)=v(452)*v(4861)+v(446)*v(4888)+v(455)*v(4897)+v(4843)*v(552)+v(4915)*v(553)+v(4816)*v(554)
v(4959)=v(452)*v(4860)+v(446)*v(4887)+v(455)*v(4896)+v(4842)*v(552)+v(4914)*v(553)+v(4815)*v(554)
v(4958)=v(452)*v(4859)+v(446)*v(4886)+v(455)*v(4895)+v(4841)*v(552)+v(4913)*v(553)+v(4814)*v(554)
v(4957)=v(452)*v(4858)+v(446)*v(4885)+v(455)*v(4894)+v(4840)*v(552)+v(4912)*v(553)+v(4813)*v(554)
v(4956)=v(452)*v(4857)+v(446)*v(4884)+v(455)*v(4893)+v(4839)*v(552)+v(4911)*v(553)+v(4812)*v(554)
v(4955)=v(452)*v(4856)+v(446)*v(4883)+v(455)*v(4892)+v(4838)*v(552)+v(4910)*v(553)+v(4811)*v(554)
v(4954)=v(452)*v(4855)+v(446)*v(4882)+v(455)*v(4891)+v(4837)*v(552)+v(4909)*v(553)+v(4810)*v(554)
v(4953)=v(452)*v(4854)+v(446)*v(4881)+v(455)*v(4890)+v(4836)*v(552)+v(4908)*v(553)+v(4809)*v(554)
v(4952)=-(v(455)*v(4608))+v(452)*v(4826)+v(448)*v(4844)-v(408)*v(4916)
v(4951)=-(v(455)*v(4607))+v(452)*v(4825)+v(448)*v(4843)-v(408)*v(4915)
v(4950)=-(v(455)*v(4606))+v(452)*v(4824)+v(448)*v(4842)-v(408)*v(4914)
v(4949)=-(v(455)*v(4605))+v(452)*v(4823)+v(448)*v(4841)-v(408)*v(4913)
v(4948)=-(v(455)*v(4604))+v(452)*v(4822)+v(448)*v(4840)-v(408)*v(4912)
v(4947)=-(v(455)*v(4603))+v(452)*v(4821)+v(448)*v(4839)-v(408)*v(4911)
v(4946)=-(v(455)*v(4602))+v(452)*v(4820)+v(448)*v(4838)-v(408)*v(4910)
v(4945)=-(v(455)*v(4601))+v(452)*v(4819)+v(448)*v(4837)-v(408)*v(4909)
v(4944)=-(v(455)*v(4600))+v(452)*v(4818)+v(448)*v(4836)-v(408)*v(4908)
v(4943)=-(v(452)*v(4753))-v(426)*v(4844)+v(455)*v(4880)+v(454)*v(4916)
v(4942)=-(v(452)*v(4752))-v(426)*v(4843)+v(455)*v(4879)+v(454)*v(4915)
v(4941)=-(v(452)*v(4751))-v(426)*v(4842)+v(455)*v(4878)+v(454)*v(4914)
v(4940)=-(v(452)*v(4750))-v(426)*v(4841)+v(455)*v(4877)+v(454)*v(4913)
v(4939)=-(v(452)*v(4749))-v(426)*v(4840)+v(455)*v(4876)+v(454)*v(4912)
v(4938)=-(v(452)*v(4748))-v(426)*v(4839)+v(455)*v(4875)+v(454)*v(4911)
v(4937)=-(v(452)*v(4747))-v(426)*v(4838)+v(455)*v(4874)+v(454)*v(4910)
v(4936)=-(v(452)*v(4746))-v(426)*v(4837)+v(455)*v(4873)+v(454)*v(4909)
v(4935)=-(v(452)*v(4745))-v(426)*v(4836)+v(455)*v(4872)+v(454)*v(4908)
v(4934)=v(446)*v(4753)+v(426)*v(4817)-v(455)*v(4835)-v(450)*v(4916)
v(4933)=v(446)*v(4752)+v(426)*v(4816)-v(455)*v(4834)-v(450)*v(4915)
v(4932)=v(446)*v(4751)+v(426)*v(4815)-v(455)*v(4833)-v(450)*v(4914)
v(4931)=v(446)*v(4750)+v(426)*v(4814)-v(455)*v(4832)-v(450)*v(4913)
v(4930)=v(446)*v(4749)+v(426)*v(4813)-v(455)*v(4831)-v(450)*v(4912)
v(4929)=v(446)*v(4748)+v(426)*v(4812)-v(455)*v(4830)-v(450)*v(4911)
v(4928)=v(446)*v(4747)+v(426)*v(4811)-v(455)*v(4829)-v(450)*v(4910)
v(4927)=v(446)*v(4746)+v(426)*v(4810)-v(455)*v(4828)-v(450)*v(4909)
v(4926)=v(446)*v(4745)+v(426)*v(4809)-v(455)*v(4827)-v(450)*v(4908)
v(4925)=-(v(448)*v(4817))-v(446)*v(4826)+v(455)*v(4853)+v(453)*v(4916)
v(4924)=-(v(448)*v(4816))-v(446)*v(4825)+v(455)*v(4852)+v(453)*v(4915)
v(4923)=-(v(448)*v(4815))-v(446)*v(4824)+v(455)*v(4851)+v(453)*v(4914)
v(4922)=-(v(448)*v(4814))-v(446)*v(4823)+v(455)*v(4850)+v(453)*v(4913)
v(4921)=-(v(448)*v(4813))-v(446)*v(4822)+v(455)*v(4849)+v(453)*v(4912)
v(4920)=-(v(448)*v(4812))-v(446)*v(4821)+v(455)*v(4848)+v(453)*v(4911)
v(4919)=-(v(448)*v(4811))-v(446)*v(4820)+v(455)*v(4847)+v(453)*v(4910)
v(4918)=-(v(448)*v(4810))-v(446)*v(4819)+v(455)*v(4846)+v(453)*v(4909)
v(4917)=-(v(448)*v(4809))-v(446)*v(4818)+v(455)*v(4845)+v(453)*v(4908)
v(550)=-(v(446)*v(448))+v(453)*v(455)
v(5007)=(v(550)*v(550))
v(549)=v(426)*v(446)-v(450)*v(455)
v(4986)=(v(549)*v(549))
v(548)=-(v(426)*v(452))+v(454)*v(455)
v(6375)=v(549)*v(552)+v(546)*v(553)+v(548)*v(554)
v(4985)=(v(548)*v(548))
v(6072)=v(4984)+v(4985)+v(4986)
v(547)=v(448)*v(452)-v(408)*v(455)
v(6377)=v(545)*v(546)+v(547)*v(548)+v(549)*v(550)
v(6376)=v(550)*v(552)+v(545)*v(553)+v(547)*v(554)
v(5006)=(v(547)*v(547))
v(6071)=-v(5005)-v(5006)-v(5007)
v(520)=v(452)*v(552)+v(455)*v(553)+v(446)*v(554)
v(5163)=1d0/v(520)**6
v(4963)=1d0/v(520)**3
v(6061)=(-2d0)*v(4963)
v(4971)=v(4961)*v(6061)
v(4970)=v(4960)*v(6061)
v(4969)=v(4959)*v(6061)
v(4968)=v(4958)*v(6061)
v(4967)=v(4957)*v(6061)
v(4966)=v(4956)*v(6061)
v(4965)=v(4955)*v(6061)
v(4964)=v(4954)*v(6061)
v(4962)=v(4953)*v(6061)
v(456)=v(232)*(v(386)*v(386))+v(473)+v(491)
v(462)=(v(392)*v(456)+v(389)*v(458)+v(391)*v(459))*v(5541)
v(497)=v(462)*v(6062)
v(461)=(v(390)*v(456)+v(391)*v(458)+v(388)*v(459))*v(5541)
v(477)=v(461)*v(6063)
v(457)=v(475)+v(493)+v(456)*v(6064)
v(465)=(v(390)*v(457)+v(388)*v(461)+v(391)*v(462))*v(5541)
v(481)=v(465)*v(6063)
v(464)=(v(392)*v(457)+v(391)*v(461)+v(389)*v(462))*v(5541)
v(499)=v(464)*v(6062)
v(460)=v(477)+v(497)+v(457)*v(6064)
v(468)=(v(392)*v(460)+v(389)*v(464)+v(391)*v(465))*v(5541)
v(503)=v(468)*v(6062)
v(467)=(v(390)*v(460)+v(391)*v(464)+v(388)*v(465))*v(5541)
v(483)=v(467)*v(6063)
v(463)=v(481)+v(499)+v(460)*v(6064)
v(466)=v(483)+v(503)+v(463)*v(6064)
v(6065)=5040d0+v(466)
v(469)=(v(392)*v(463)+v(391)*v(467)+v(389)*v(468))*v(5541)
v(505)=v(469)*v(6062)
v(470)=(v(390)*v(463)+v(388)*v(467)+v(391)*v(468))*v(5541)
v(508)=(7d0*(360d0*v(458)+120d0*v(462)+30d0*v(464)+6d0*v(468)+v(469))+v(5541)*(v(389)*v(469)+v(391)*v(470)+v(392)*v&
&(6065)))/5040d0
v(488)=v(470)*v(6063)
v(6068)=5040d0+v(488)
v(510)=(2520d0*v(456)+840d0*v(457)+210d0*v(460)+42d0*v(463)+7d0*v(466)+v(505)+v(6064)*v(6065)+v(6068))/5040d0
v(472)=(7d0*(360d0*v(459)+120d0*v(461)+30d0*v(465)+6d0*v(467)+v(470))+v(5541)*(v(391)*v(469)+v(388)*v(470)+v(390)*v&
&(6065)))/5040d0
v(471)=statev(27)*v(472)+statev(25)*v(508)+v(510)*v(5528)
v(474)=v(232)*(v(388)*v(388))+v(473)+v(490)
v(480)=(v(392)*v(459)+v(391)*v(474)+v(389)*v(478))*v(5541)
v(496)=v(480)*v(6066)
v(476)=v(475)+v(494)+v(474)*v(6067)
v(484)=(v(392)*v(461)+v(391)*v(476)+v(389)*v(480))*v(5541)
v(500)=v(484)*v(6066)
v(479)=v(477)+v(496)+v(476)*v(6067)
v(486)=(v(392)*v(465)+v(391)*v(479)+v(389)*v(484))*v(5541)
v(502)=v(486)*v(6066)
v(482)=v(481)+v(500)+v(479)*v(6067)
v(485)=v(483)+v(502)+v(482)*v(6067)
v(6069)=5040d0+v(485)
v(487)=(v(392)*v(467)+v(391)*v(482)+v(389)*v(486))*v(5541)
v(507)=(7d0*(360d0*v(478)+120d0*v(480)+30d0*v(484)+6d0*v(486)+v(487))+v(5541)*(v(392)*v(470)+v(389)*v(487)+v(391)*v&
&(6069)))/5040d0
v(506)=v(487)*v(6066)
v(512)=(2520d0*v(474)+840d0*v(476)+210d0*v(479)+42d0*v(482)+7d0*v(485)+v(506)+v(6068)+v(6067)*v(6069))/5040d0
v(489)=statev(23)*v(472)+statev(28)*v(507)+v(512)*v(5529)
v(492)=v(232)*(v(389)*v(389))+v(490)+v(491)
v(495)=v(493)+v(494)+v(492)*v(6070)
v(498)=v(496)+v(497)+v(495)*v(6070)
v(501)=v(499)+v(500)+v(498)*v(6070)
v(504)=v(502)+v(503)+v(501)*v(6070)
v(514)=(5040d0+2520d0*v(492)+840d0*v(495)+210d0*v(498)+42d0*v(501)+7d0*v(504)+v(505)+v(506)+(5040d0+v(504))*v(6070))&
&/5040d0
v(509)=statev(24)*v(507)+statev(26)*v(508)+v(514)*v(5530)
v(511)=statev(28)*v(508)+statev(23)*v(510)+v(472)*v(5529)
v(513)=statev(26)*v(472)+statev(24)*v(512)+v(507)*v(5530)
v(515)=statev(27)*v(507)+statev(25)*v(514)+v(508)*v(5528)
v(516)=statev(24)*v(472)+statev(26)*v(510)+v(508)*v(5530)
v(577)=v(511)*v(513)-v(489)*v(516)
v(568)=v(471)*v(509)-v(515)*v(516)
v(517)=statev(25)*v(507)+statev(27)*v(512)+v(472)*v(5528)
v(576)=v(471)*v(489)-v(511)*v(517)
v(575)=-(v(471)*v(513))+v(516)*v(517)
v(569)=v(513)*v(515)-v(509)*v(517)
v(518)=statev(23)*v(508)+statev(28)*v(514)+v(507)*v(5529)
v(573)=-(v(489)*v(515))+v(517)*v(518)
v(572)=v(511)*v(515)-v(471)*v(518)
v(571)=-(v(509)*v(511))+v(516)*v(518)
v(570)=v(489)*v(509)-v(513)*v(518)
v(519)=1d0/v(520)**2
v(5274)=v(519)*v(6375)
v(5255)=v(519)*v(6376)
v(5236)=v(519)*v(6377)
v(5016)=v(519)*((-2d0)*v(4871)*v(545)-2d0*v(4952)*v(547)-2d0*v(4925)*v(550))+v(4971)*v(6071)
v(5025)=v(5016)/3d0
v(5015)=v(519)*((-2d0)*v(4870)*v(545)-2d0*v(4951)*v(547)-2d0*v(4924)*v(550))+v(4970)*v(6071)
v(5024)=v(5015)/3d0
v(5014)=v(519)*((-2d0)*v(4869)*v(545)-2d0*v(4950)*v(547)-2d0*v(4923)*v(550))+v(4969)*v(6071)
v(5023)=v(5014)/3d0
v(5013)=v(519)*((-2d0)*v(4868)*v(545)-2d0*v(4949)*v(547)-2d0*v(4922)*v(550))+v(4968)*v(6071)
v(5022)=v(5013)/3d0
v(5012)=v(519)*((-2d0)*v(4867)*v(545)-2d0*v(4948)*v(547)-2d0*v(4921)*v(550))+v(4967)*v(6071)
v(5021)=v(5012)/3d0
v(5011)=v(519)*((-2d0)*v(4866)*v(545)-2d0*v(4947)*v(547)-2d0*v(4920)*v(550))+v(4966)*v(6071)
v(5020)=v(5011)/3d0
v(5010)=v(519)*((-2d0)*v(4865)*v(545)-2d0*v(4946)*v(547)-2d0*v(4919)*v(550))+v(4965)*v(6071)
v(5019)=v(5010)/3d0
v(5009)=v(519)*((-2d0)*v(4864)*v(545)-2d0*v(4945)*v(547)-2d0*v(4918)*v(550))+v(4964)*v(6071)
v(5018)=v(5009)/3d0
v(5008)=v(519)*((-2d0)*v(4863)*v(545)-2d0*v(4944)*v(547)-2d0*v(4917)*v(550))+v(4962)*v(6071)
v(5017)=v(5008)/3d0
v(4995)=v(519)*(2d0*v(4907)*v(546)+2d0*v(4943)*v(548)+2d0*v(4934)*v(549))+v(4971)*v(6072)
v(5004)=-v(4995)/3d0
v(4994)=v(519)*(2d0*v(4906)*v(546)+2d0*v(4942)*v(548)+2d0*v(4933)*v(549))+v(4970)*v(6072)
v(5003)=-v(4994)/3d0
v(4993)=v(519)*(2d0*v(4905)*v(546)+2d0*v(4941)*v(548)+2d0*v(4932)*v(549))+v(4969)*v(6072)
v(5002)=-v(4993)/3d0
v(4992)=v(519)*(2d0*v(4904)*v(546)+2d0*v(4940)*v(548)+2d0*v(4931)*v(549))+v(4968)*v(6072)
v(5001)=-v(4992)/3d0
v(4991)=v(519)*(2d0*v(4903)*v(546)+2d0*v(4939)*v(548)+2d0*v(4930)*v(549))+v(4967)*v(6072)
v(5000)=-v(4991)/3d0
v(4990)=v(519)*(2d0*v(4902)*v(546)+2d0*v(4938)*v(548)+2d0*v(4929)*v(549))+v(4966)*v(6072)
v(4999)=-v(4990)/3d0
v(4989)=v(519)*(2d0*v(4901)*v(546)+2d0*v(4937)*v(548)+2d0*v(4928)*v(549))+v(4965)*v(6072)
v(4998)=-v(4989)/3d0
v(4988)=v(519)*(2d0*v(4900)*v(546)+2d0*v(4936)*v(548)+2d0*v(4927)*v(549))+v(4964)*v(6072)
v(4997)=-v(4988)/3d0
v(4987)=v(519)*(2d0*v(4899)*v(546)+2d0*v(4935)*v(548)+2d0*v(4926)*v(549))+v(4962)*v(6072)
v(4996)=-v(4987)/3d0
v(4983)=v(519)*((-2d0)*v(4862)*v(552)-2d0*v(4898)*v(553)-2d0*v(4889)*v(554))+v(4971)*v(6073)
v(5034)=v(4983)/3d0
v(4982)=v(519)*((-2d0)*v(4861)*v(552)-2d0*v(4897)*v(553)-2d0*v(4888)*v(554))+v(4970)*v(6073)
v(5033)=v(4982)/3d0
v(4981)=v(519)*((-2d0)*v(4860)*v(552)-2d0*v(4896)*v(553)-2d0*v(4887)*v(554))+v(4969)*v(6073)
v(5032)=v(4981)/3d0
v(4980)=v(519)*((-2d0)*v(4859)*v(552)-2d0*v(4895)*v(553)-2d0*v(4886)*v(554))+v(4968)*v(6073)
v(5031)=v(4980)/3d0
v(4979)=v(519)*((-2d0)*v(4858)*v(552)-2d0*v(4894)*v(553)-2d0*v(4885)*v(554))+v(4967)*v(6073)
v(5030)=v(4979)/3d0
v(4978)=v(519)*((-2d0)*v(4857)*v(552)-2d0*v(4893)*v(553)-2d0*v(4884)*v(554))+v(4966)*v(6073)
v(5029)=v(4978)/3d0
v(4977)=v(519)*((-2d0)*v(4856)*v(552)-2d0*v(4892)*v(553)-2d0*v(4883)*v(554))+v(4965)*v(6073)
v(5028)=v(4977)/3d0
v(4976)=v(519)*((-2d0)*v(4855)*v(552)-2d0*v(4891)*v(553)-2d0*v(4882)*v(554))+v(4964)*v(6073)
v(5027)=v(4976)/3d0
v(4975)=v(519)*((-2d0)*v(4854)*v(552)-2d0*v(4890)*v(553)-2d0*v(4881)*v(554))+v(4962)*v(6073)
v(5026)=v(4975)/3d0
v(541)=v(519)*v(6073)
v(538)=v(519)*v(6072)
v(543)=-v(538)/3d0
v(537)=v(519)*v(6071)
v(542)=v(537)/3d0
v(5217)=(-2d0/3d0)*v(541)+v(542)+v(543)
v(536)=v(541)/3d0
v(5198)=v(536)+(-2d0/3d0)*v(537)+v(543)
v(5179)=v(536)+(2d0/3d0)*v(538)+v(542)
v(521)=(v(426)*v(426))
v(522)=(v(450)*v(450))
v(6074)=-v(521)-v(522)
v(523)=(v(454)*v(454))
v(6080)=-v(522)-v(523)
v(6112)=v(448)*v(6080)
v(6086)=v(426)*v(450)*v(453)+v(6112)
v(6077)=-v(521)-v(523)
v(6110)=v(453)*v(6077)
v(6085)=v(426)*v(448)*v(450)+v(6110)
v(5070)=v(408)*v(4844)*v(6074)+v(452)*(v(408)*(-v(5043)-v(5052))+v(4608)*v(6074)+v(4880)*v(6078))+v(455)*(v(450)*v(453&
&)*v(4753)+v(448)*(-v(5052)-v(5061))+v(426)*(v(6076)+v(6079))+v(4826)*v(6080))+v(4817)*v(6085)+v(4916)*v(6086)+v(446)*(v&
&(426)*v(448)*v(4835)+v(453)*(-v(5043)-v(5061))+v(4853)*v(6077)+v(450)*v(6115))+v(454)*(v(4844)*v(6078)+v(452)*(v(6075)&
&+v(6079))+v(4608)*v(6084)+v(408)*(v(455)*v(4753)+v(6151)+v(6153)+v(6154)))
v(5069)=v(408)*v(4843)*v(6074)+v(452)*(v(408)*(-v(5042)-v(5051))+v(4607)*v(6074)+v(4879)*v(6078))+v(455)*(v(450)*v(453&
&)*v(4752)+v(448)*(-v(5051)-v(5060))+v(4825)*v(6080)+v(426)*(v(6082)+v(6083)))+v(4816)*v(6085)+v(4915)*v(6086)+v(446)*(v&
&(426)*v(448)*v(4834)+v(453)*(-v(5042)-v(5060))+v(4852)*v(6077)+v(450)*v(6120))+v(454)*(v(4843)*v(6078)+v(452)*(v(6081)&
&+v(6083))+v(4607)*v(6084)+v(408)*(v(455)*v(4752)+v(6161)+v(6163)+v(6164)))
v(5068)=v(408)*v(4842)*v(6074)+v(452)*(v(408)*(-v(5041)-v(5050))+v(4606)*v(6074)+v(4878)*v(6078))+v(4815)*v(6085)+v&
&(4914)*v(6086)+v(455)*(v(450)*v(453)*v(4751)+v(448)*(-v(5050)-v(5059))+v(4824)*v(6080)+v(426)*(v(6088)+v(6089)))+v(446&
&)*(v(426)*v(448)*v(4833)+v(453)*(-v(5041)-v(5059))+v(4851)*v(6077)+v(450)*v(6126))+v(454)*(v(4842)*v(6078)+v(4606)*v&
&(6084)+v(452)*(v(6087)+v(6089))+v(408)*(v(455)*v(4751)+v(6168)+v(6170)+v(6171)))
v(5067)=v(408)*v(4841)*v(6074)+v(452)*(v(408)*(-v(5040)-v(5049))+v(4605)*v(6074)+v(4877)*v(6078))+v(4814)*v(6085)+v&
&(4913)*v(6086)+v(455)*(v(450)*v(453)*v(4750)+v(448)*(-v(5049)-v(5058))+v(4823)*v(6080)+v(426)*(v(6091)+v(6092)))+v(446&
&)*(v(426)*v(448)*v(4832)+v(453)*(-v(5040)-v(5058))+v(4850)*v(6077)+v(450)*v(6129))+v(454)*(v(4841)*v(6078)+v(4605)*v&
&(6084)+v(452)*(v(6090)+v(6092))+v(408)*(v(455)*v(4750)+v(6174)+v(6176)+v(6177)))
v(5066)=v(408)*v(4840)*v(6074)+v(452)*(v(408)*(-v(5039)-v(5048))+v(4604)*v(6074)+v(4876)*v(6078))+v(4813)*v(6085)+v&
&(4912)*v(6086)+v(455)*(v(450)*v(453)*v(4749)+v(448)*(-v(5048)-v(5057))+v(4822)*v(6080)+v(426)*(v(6094)+v(6095)))+v(446&
&)*(v(426)*v(448)*v(4831)+v(453)*(-v(5039)-v(5057))+v(4849)*v(6077)+v(450)*v(6132))+v(454)*(v(4840)*v(6078)+v(4604)*v&
&(6084)+v(452)*(v(6093)+v(6095))+v(408)*(v(455)*v(4749)+v(6180)+v(6182)+v(6183)))
v(5065)=v(408)*v(4839)*v(6074)+v(452)*(v(408)*(-v(5038)-v(5047))+v(4603)*v(6074)+v(4875)*v(6078))+v(4812)*v(6085)+v&
&(4911)*v(6086)+v(455)*(v(450)*v(453)*v(4748)+v(448)*(-v(5047)-v(5056))+v(4821)*v(6080)+v(426)*(v(6097)+v(6098)))+v(446&
&)*(v(426)*v(448)*v(4830)+v(453)*(-v(5038)-v(5056))+v(4848)*v(6077)+v(450)*v(6135))+v(454)*(v(4839)*v(6078)+v(4603)*v&
&(6084)+v(452)*(v(6096)+v(6098))+v(408)*(v(455)*v(4748)+v(6186)+v(6188)+v(6189)))
v(5064)=v(408)*v(4838)*v(6074)+v(452)*(v(408)*(-v(5037)-v(5046))+v(4602)*v(6074)+v(4874)*v(6078))+v(4811)*v(6085)+v&
&(4910)*v(6086)+v(455)*(v(450)*v(453)*v(4747)+v(448)*(-v(5046)-v(5055))+v(4820)*v(6080)+v(426)*(v(6100)+v(6101)))+v(446&
&)*(v(426)*v(448)*v(4829)+v(453)*(-v(5037)-v(5055))+v(4847)*v(6077)+v(450)*v(6138))+v(454)*(v(4838)*v(6078)+v(4602)*v&
&(6084)+v(452)*(v(6099)+v(6101))+v(408)*(v(455)*v(4747)+v(6192)+v(6194)+v(6195)))
v(5063)=v(408)*v(4837)*v(6074)+v(452)*(v(408)*(-v(5036)-v(5045))+v(4601)*v(6074)+v(4873)*v(6078))+v(4810)*v(6085)+v&
&(4909)*v(6086)+v(455)*(v(450)*v(453)*v(4746)+v(448)*(-v(5045)-v(5054))+v(4819)*v(6080)+v(426)*(v(6103)+v(6104)))+v(446&
&)*(v(426)*v(448)*v(4828)+v(453)*(-v(5036)-v(5054))+v(4846)*v(6077)+v(450)*v(6141))+v(454)*(v(4837)*v(6078)+v(4601)*v&
&(6084)+v(452)*(v(6102)+v(6104))+v(408)*(v(455)*v(4746)+v(6198)+v(6200)+v(6201)))
v(5062)=v(408)*v(4836)*v(6074)+v(452)*(v(408)*(-v(5035)-v(5044))+v(4600)*v(6074)+v(4872)*v(6078))+v(4809)*v(6085)+v&
&(4908)*v(6086)+v(455)*(v(450)*v(453)*v(4745)+v(448)*(-v(5044)-v(5053))+v(4818)*v(6080)+v(426)*(v(6106)+v(6107)))+v(446&
&)*(v(426)*v(448)*v(4827)+v(453)*(-v(5035)-v(5053))+v(4845)*v(6077)+v(450)*v(6144))+v(454)*(v(4836)*v(6078)+v(4600)*v&
&(6084)+v(452)*(v(6105)+v(6107))+v(408)*(v(455)*v(4745)+v(6204)+v(6206)+v(6207)))
v(524)=v(452)*(v(408)*v(6074)+v(454)*v(6078))+v(446)*(v(6110)+v(450)*v(6114))+v(455)*(v(6112)+v(426)*v(6149))
v(525)=(v(408)*v(408))
v(526)=(v(453)*v(453))
v(6119)=-v(525)-v(526)
v(6148)=v(426)*v(6119)
v(6125)=v(408)*v(448)*v(454)+v(6148)
v(527)=(v(448)*v(448))
v(6117)=-v(526)-v(527)
v(6147)=v(454)*v(6117)
v(6124)=v(408)*v(426)*v(448)+v(6147)
v(6113)=-v(525)-v(527)
v(5167)=(-2d0)*v(426)*v(448)*v(450)*v(453)-v(525)*v(6074)-v(526)*v(6077)-v(527)*v(6080)+v(408)*v(454)*v(6341)
v(5106)=v(450)*v(4817)*v(6113)+v(446)*(v(450)*(-v(5079)-v(5097))+v(4835)*v(6113)+v(4853)*v(6114))+v(452)*(v(426)*v(448&
&)*v(4608)+v(454)*(-v(5088)-v(5097))+v(408)*(v(6075)+v(6116))+v(4880)*v(6117))+v(455)*(v(408)*v(454)*v(4826)+v(426)*(-v&
&(5079)-v(5088))+v(448)*(v(6076)+v(6116)+v(6118))+v(4753)*v(6119))+v(4844)*v(6124)+v(4916)*v(6125)+v(453)*(v(4817)*v&
&(6114)+v(446)*(v(6115)+v(6118))+v(4835)*v(6123)+v(450)*(v(455)*v(4826)+v(6265)))
v(5105)=v(450)*v(4816)*v(6113)+v(446)*(v(450)*(-v(5078)-v(5096))+v(4834)*v(6113)+v(4852)*v(6114))+v(452)*(v(426)*v(448&
&)*v(4607)+v(454)*(-v(5087)-v(5096))+v(4879)*v(6117)+v(408)*(v(6081)+v(6121)))+v(455)*(v(408)*v(454)*v(4825)+v(426)*(-v&
&(5078)-v(5087))+v(4752)*v(6119)+v(448)*(v(6082)+v(6121)+v(6122)))+v(4843)*v(6124)+v(4915)*v(6125)+v(453)*(v(4816)*v&
&(6114)+v(446)*(v(6120)+v(6122))+v(4834)*v(6123)+v(450)*(v(455)*v(4825)+v(6277)))
v(5104)=v(450)*v(4815)*v(6113)+v(446)*(v(450)*(-v(5077)-v(5095))+v(4833)*v(6113)+v(4851)*v(6114))+v(4842)*v(6124)+v&
&(4914)*v(6125)+v(452)*(v(426)*v(448)*v(4606)+v(454)*(-v(5086)-v(5095))+v(4878)*v(6117)+v(408)*(v(6087)+v(6127)))+v(455&
&)*(v(408)*v(454)*v(4824)+v(426)*(-v(5077)-v(5086))+v(4751)*v(6119)+v(448)*(v(6088)+v(6127)+v(6128)))+v(453)*(v(4815)*v&
&(6114)+v(4833)*v(6123)+v(446)*(v(6126)+v(6128))+v(450)*(v(455)*v(4824)+v(6288)))
v(5103)=v(450)*v(4814)*v(6113)+v(446)*(v(450)*(-v(5076)-v(5094))+v(4832)*v(6113)+v(4850)*v(6114))+v(4841)*v(6124)+v&
&(4913)*v(6125)+v(452)*(v(426)*v(448)*v(4605)+v(454)*(-v(5085)-v(5094))+v(4877)*v(6117)+v(408)*(v(6090)+v(6130)))+v(455&
&)*(v(408)*v(454)*v(4823)+v(426)*(-v(5076)-v(5085))+v(4750)*v(6119)+v(448)*(v(6091)+v(6130)+v(6131)))+v(453)*(v(4814)*v&
&(6114)+v(4832)*v(6123)+v(446)*(v(6129)+v(6131))+v(450)*(v(455)*v(4823)+v(6295)))
v(5102)=v(450)*v(4813)*v(6113)+v(446)*(v(450)*(-v(5075)-v(5093))+v(4831)*v(6113)+v(4849)*v(6114))+v(4840)*v(6124)+v&
&(4912)*v(6125)+v(452)*(v(426)*v(448)*v(4604)+v(454)*(-v(5084)-v(5093))+v(4876)*v(6117)+v(408)*(v(6093)+v(6133)))+v(455&
&)*(v(408)*v(454)*v(4822)+v(426)*(-v(5075)-v(5084))+v(4749)*v(6119)+v(448)*(v(6094)+v(6133)+v(6134)))+v(453)*(v(4813)*v&
&(6114)+v(4831)*v(6123)+v(446)*(v(6132)+v(6134))+v(450)*(v(455)*v(4822)+v(6302)))
v(5101)=v(450)*v(4812)*v(6113)+v(446)*(v(450)*(-v(5074)-v(5092))+v(4830)*v(6113)+v(4848)*v(6114))+v(4839)*v(6124)+v&
&(4911)*v(6125)+v(452)*(v(426)*v(448)*v(4603)+v(454)*(-v(5083)-v(5092))+v(4875)*v(6117)+v(408)*(v(6096)+v(6136)))+v(455&
&)*(v(408)*v(454)*v(4821)+v(426)*(-v(5074)-v(5083))+v(4748)*v(6119)+v(448)*(v(6097)+v(6136)+v(6137)))+v(453)*(v(4812)*v&
&(6114)+v(4830)*v(6123)+v(446)*(v(6135)+v(6137))+v(450)*(v(455)*v(4821)+v(6309)))
v(5100)=v(450)*v(4811)*v(6113)+v(446)*(v(450)*(-v(5073)-v(5091))+v(4829)*v(6113)+v(4847)*v(6114))+v(4838)*v(6124)+v&
&(4910)*v(6125)+v(452)*(v(426)*v(448)*v(4602)+v(454)*(-v(5082)-v(5091))+v(4874)*v(6117)+v(408)*(v(6099)+v(6139)))+v(455&
&)*(v(408)*v(454)*v(4820)+v(426)*(-v(5073)-v(5082))+v(4747)*v(6119)+v(448)*(v(6100)+v(6139)+v(6140)))+v(453)*(v(4811)*v&
&(6114)+v(4829)*v(6123)+v(446)*(v(6138)+v(6140))+v(450)*(v(455)*v(4820)+v(6316)))
v(5099)=v(450)*v(4810)*v(6113)+v(446)*(v(450)*(-v(5072)-v(5090))+v(4828)*v(6113)+v(4846)*v(6114))+v(4837)*v(6124)+v&
&(4909)*v(6125)+v(452)*(v(426)*v(448)*v(4601)+v(454)*(-v(5081)-v(5090))+v(4873)*v(6117)+v(408)*(v(6102)+v(6142)))+v(455&
&)*(v(408)*v(454)*v(4819)+v(426)*(-v(5072)-v(5081))+v(4746)*v(6119)+v(448)*(v(6103)+v(6142)+v(6143)))+v(453)*(v(4810)*v&
&(6114)+v(4828)*v(6123)+v(446)*(v(6141)+v(6143))+v(450)*(v(455)*v(4819)+v(6323)))
v(5098)=v(450)*v(4809)*v(6113)+v(446)*(v(450)*(-v(5071)-v(5089))+v(4827)*v(6113)+v(4845)*v(6114))+v(4836)*v(6124)+v&
&(4908)*v(6125)+v(452)*(v(426)*v(448)*v(4600)+v(454)*(-v(5080)-v(5089))+v(4872)*v(6117)+v(408)*(v(6105)+v(6145)))+v(455&
&)*(v(408)*v(454)*v(4818)+v(426)*(-v(5071)-v(5080))+v(4745)*v(6119)+v(448)*(v(6106)+v(6145)+v(6146)))+v(453)*(v(4809)*v&
&(6114)+v(4827)*v(6123)+v(446)*(v(6144)+v(6146))+v(450)*(v(455)*v(4818)+v(6330)))
v(528)=v(446)*(v(450)*v(6113)+v(453)*v(6114))+v(452)*(v(408)*v(6078)+v(6147))+v(455)*(v(6148)+v(448)*v(6149))
v(529)=(v(446)*v(446))
v(530)=(v(455)*v(455))
v(6157)=v(529)+v(530)
v(6287)=v(446)*v(452)*v(453)-v(408)*v(6157)
v(531)=(v(452)*v(452))
v(6159)=v(530)+v(531)
v(6286)=v(408)*v(446)*v(452)-v(453)*v(6159)
v(6158)=v(529)+v(531)
v(5160)=-(v(5133)*v(6074))-v(5115)*v(6077)-v(5124)*v(6080)+v(446)*v(450)*(v(6150)+v(6152))+v(454)*((-2d0)*v(446)*v(450&
&)*v(4844)+v(452)*(v(6152)+v(6155)))+v(5061)*v(6157)+v(5043)*v(6158)+v(5052)*v(6159)+v(455)*(v(426)*(-(v(4844)*v(6059))&
&+v(6150)+v(6155))+v(4753)*v(6166))
v(5159)=-(v(5132)*v(6074))-v(5114)*v(6077)-v(5123)*v(6080)+v(5060)*v(6157)+v(5042)*v(6158)+v(5051)*v(6159)+v(446)*v(450&
&)*(v(6160)+v(6162))+v(454)*((-2d0)*v(446)*v(450)*v(4843)+v(452)*(v(6162)+v(6165)))+v(455)*(v(426)*(-(v(4843)*v(6059))+v&
&(6160)+v(6165))+v(4752)*v(6166))
v(5158)=-(v(5131)*v(6074))-v(5113)*v(6077)-v(5122)*v(6080)+v(5059)*v(6157)+v(5041)*v(6158)+v(5050)*v(6159)+v(446)*v(450&
&)*(v(6167)+v(6169))+v(455)*(v(4751)*v(6166)+v(426)*(-(v(4842)*v(6059))+v(6167)+v(6172)))+v(454)*((-2d0)*v(446)*v(450)*v&
&(4842)+v(452)*(v(6169)+v(6172)))
v(5157)=-(v(5130)*v(6074))-v(5112)*v(6077)-v(5121)*v(6080)+v(5058)*v(6157)+v(5040)*v(6158)+v(5049)*v(6159)+v(446)*v(450&
&)*(v(6173)+v(6175))+v(455)*(v(4750)*v(6166)+v(426)*(-(v(4841)*v(6059))+v(6173)+v(6178)))+v(454)*((-2d0)*v(446)*v(450)*v&
&(4841)+v(452)*(v(6175)+v(6178)))
v(5156)=-(v(5129)*v(6074))-v(5111)*v(6077)-v(5120)*v(6080)+v(5057)*v(6157)+v(5039)*v(6158)+v(5048)*v(6159)+v(446)*v(450&
&)*(v(6179)+v(6181))+v(455)*(v(4749)*v(6166)+v(426)*(-(v(4840)*v(6059))+v(6179)+v(6184)))+v(454)*((-2d0)*v(446)*v(450)*v&
&(4840)+v(452)*(v(6181)+v(6184)))
v(5155)=-(v(5128)*v(6074))-v(5110)*v(6077)-v(5119)*v(6080)+v(5056)*v(6157)+v(5038)*v(6158)+v(5047)*v(6159)+v(446)*v(450&
&)*(v(6185)+v(6187))+v(455)*(v(4748)*v(6166)+v(426)*(-(v(4839)*v(6059))+v(6185)+v(6190)))+v(454)*((-2d0)*v(446)*v(450)*v&
&(4839)+v(452)*(v(6187)+v(6190)))
v(5154)=-(v(5127)*v(6074))-v(5109)*v(6077)-v(5118)*v(6080)+v(5055)*v(6157)+v(5037)*v(6158)+v(5046)*v(6159)+v(446)*v(450&
&)*(v(6191)+v(6193))+v(455)*(v(4747)*v(6166)+v(426)*(-(v(4838)*v(6059))+v(6191)+v(6196)))+v(454)*((-2d0)*v(446)*v(450)*v&
&(4838)+v(452)*(v(6193)+v(6196)))
v(5153)=-(v(5126)*v(6074))-v(5108)*v(6077)-v(5117)*v(6080)+v(5054)*v(6157)+v(5036)*v(6158)+v(5045)*v(6159)+v(446)*v(450&
&)*(v(6197)+v(6199))+v(455)*(v(4746)*v(6166)+v(426)*(-(v(4837)*v(6059))+v(6197)+v(6202)))+v(454)*((-2d0)*v(446)*v(450)*v&
&(4837)+v(452)*(v(6199)+v(6202)))
v(5152)=-(v(5125)*v(6074))-v(5107)*v(6077)-v(5116)*v(6080)+v(5053)*v(6157)+v(5035)*v(6158)+v(5044)*v(6159)+v(446)*v(450&
&)*(v(6203)+v(6205))+v(455)*(v(4745)*v(6166)+v(426)*(-(v(4836)*v(6059))+v(6203)+v(6208)))+v(454)*((-2d0)*v(446)*v(450)*v&
&(4836)+v(452)*(v(6205)+v(6208)))
v(5151)=-(v(5115)*v(6113))-v(5133)*v(6117)-v(5124)*v(6119)+v(5079)*v(6157)+v(5097)*v(6158)+v(5088)*v(6159)+v(408)*v(452&
&)*(v(6209)+v(6211))+v(453)*((-2d0)*v(408)*v(452)*v(4817)+v(446)*(v(6211)+v(6214)))+v(455)*(v(448)*(-(v(4817)*v(6058))+v&
&(6209)+v(6214))+v(4826)*v(6222))
v(5150)=-(v(5114)*v(6113))-v(5132)*v(6117)-v(5123)*v(6119)+v(5078)*v(6157)+v(5096)*v(6158)+v(5087)*v(6159)+v(408)*v(452&
&)*(v(6216)+v(6218))+v(453)*((-2d0)*v(408)*v(452)*v(4816)+v(446)*(v(6218)+v(6221)))+v(455)*(v(448)*(-(v(4816)*v(6058))+v&
&(6216)+v(6221))+v(4825)*v(6222))
v(5149)=-(v(5113)*v(6113))-v(5131)*v(6117)-v(5122)*v(6119)+v(5077)*v(6157)+v(5095)*v(6158)+v(5086)*v(6159)+v(408)*v(452&
&)*(v(6223)+v(6225))+v(455)*(v(4824)*v(6222)+v(448)*(-(v(4815)*v(6058))+v(6223)+v(6228)))+v(453)*((-2d0)*v(408)*v(452)*v&
&(4815)+v(446)*(v(6225)+v(6228)))
v(5148)=-(v(5112)*v(6113))-v(5130)*v(6117)-v(5121)*v(6119)+v(5076)*v(6157)+v(5094)*v(6158)+v(5085)*v(6159)+v(408)*v(452&
&)*(v(6229)+v(6231))+v(455)*(v(4823)*v(6222)+v(448)*(-(v(4814)*v(6058))+v(6229)+v(6234)))+v(453)*((-2d0)*v(408)*v(452)*v&
&(4814)+v(446)*(v(6231)+v(6234)))
v(5147)=-(v(5111)*v(6113))-v(5129)*v(6117)-v(5120)*v(6119)+v(5075)*v(6157)+v(5093)*v(6158)+v(5084)*v(6159)+v(408)*v(452&
&)*(v(6235)+v(6237))+v(455)*(v(4822)*v(6222)+v(448)*(-(v(4813)*v(6058))+v(6235)+v(6240)))+v(453)*((-2d0)*v(408)*v(452)*v&
&(4813)+v(446)*(v(6237)+v(6240)))
v(5146)=-(v(5110)*v(6113))-v(5128)*v(6117)-v(5119)*v(6119)+v(5074)*v(6157)+v(5092)*v(6158)+v(5083)*v(6159)+v(408)*v(452&
&)*(v(6241)+v(6243))+v(455)*(v(4821)*v(6222)+v(448)*(-(v(4812)*v(6058))+v(6241)+v(6246)))+v(453)*((-2d0)*v(408)*v(452)*v&
&(4812)+v(446)*(v(6243)+v(6246)))
v(5145)=-(v(5109)*v(6113))-v(5127)*v(6117)-v(5118)*v(6119)+v(5073)*v(6157)+v(5091)*v(6158)+v(5082)*v(6159)+v(408)*v(452&
&)*(v(6247)+v(6249))+v(455)*(v(4820)*v(6222)+v(448)*(-(v(4811)*v(6058))+v(6247)+v(6252)))+v(453)*((-2d0)*v(408)*v(452)*v&
&(4811)+v(446)*(v(6249)+v(6252)))
v(5144)=-(v(5108)*v(6113))-v(5126)*v(6117)-v(5117)*v(6119)+v(5072)*v(6157)+v(5090)*v(6158)+v(5081)*v(6159)+v(408)*v(452&
&)*(v(6253)+v(6255))+v(455)*(v(4819)*v(6222)+v(448)*(-(v(4810)*v(6058))+v(6253)+v(6258)))+v(453)*((-2d0)*v(408)*v(452)*v&
&(4810)+v(446)*(v(6255)+v(6258)))
v(5143)=-(v(5107)*v(6113))-v(5125)*v(6117)-v(5116)*v(6119)+v(5071)*v(6157)+v(5089)*v(6158)+v(5080)*v(6159)+v(408)*v(452&
&)*(v(6259)+v(6261))+v(455)*(v(4818)*v(6222)+v(448)*(-(v(4809)*v(6058))+v(6259)+v(6264)))+v(453)*((-2d0)*v(408)*v(452)*v&
&(4809)+v(446)*(v(6261)+v(6264)))
v(5142)=-(v(448)*v(4753)*v(6158))+v(454)*(v(446)*v(453)*v(4844)+v(408)*(-v(5115)-v(5124))-v(4608)*v(6157)+v(452)*(v(453&
&)*v(4817)+v(446)*v(4853)+v(6210)))+v(450)*(v(408)*v(452)*v(4817)+v(453)*(-v(5124)-v(5133))-v(4853)*v(6159)+v(446)*v&
&(6265))+v(426)*(v(448)*(-v(5115)-v(5133))-v(4826)*v(6158)+v(4916)*v(6276))+v(455)*(v(446)*(v(6266)-v(6267)-v(6268))+v&
&(452)*(v(6269)-v(6270)-v(6271))+v(4817)*v(6284)+v(4844)*v(6285))+v(4835)*v(6286)+v(4880)*v(6287)
v(5141)=-(v(448)*v(4752)*v(6158))+v(454)*(v(446)*v(453)*v(4843)+v(408)*(-v(5114)-v(5123))-v(4607)*v(6157)+v(452)*(v(453&
&)*v(4816)+v(446)*v(4852)+v(6217)))+v(426)*(v(448)*(-v(5114)-v(5132))-v(4825)*v(6158)+v(4915)*v(6276))+v(450)*(v(408)*v&
&(452)*v(4816)+v(453)*(-v(5123)-v(5132))-v(4852)*v(6159)+v(446)*v(6277))+v(455)*(v(446)*(v(6278)-v(6279)-v(6280))+v(452&
&)*(v(6281)-v(6282)-v(6283))+v(4816)*v(6284)+v(4843)*v(6285))+v(4834)*v(6286)+v(4879)*v(6287)
v(5140)=-(v(448)*v(4751)*v(6158))+v(454)*(v(446)*v(453)*v(4842)+v(408)*(-v(5113)-v(5122))-v(4606)*v(6157)+v(452)*(v(453&
&)*v(4815)+v(446)*v(4851)+v(6224)))+v(426)*(v(448)*(-v(5113)-v(5131))-v(4824)*v(6158)+v(4914)*v(6276))+v(4833)*v(6286)+v&
&(4878)*v(6287)+v(450)*(v(408)*v(452)*v(4815)+v(453)*(-v(5122)-v(5131))-v(4851)*v(6159)+v(446)*v(6288))+v(455)*(v(4815&
&)*v(6284)+v(4842)*v(6285)+v(446)*(v(6289)-v(6290)-v(6291))+v(452)*(v(6292)-v(6293)-v(6294)))
v(5139)=-(v(448)*v(4750)*v(6158))+v(454)*(v(446)*v(453)*v(4841)+v(408)*(-v(5112)-v(5121))-v(4605)*v(6157)+v(452)*(v(453&
&)*v(4814)+v(446)*v(4850)+v(6230)))+v(426)*(v(448)*(-v(5112)-v(5130))-v(4823)*v(6158)+v(4913)*v(6276))+v(4832)*v(6286)+v&
&(4877)*v(6287)+v(450)*(v(408)*v(452)*v(4814)+v(453)*(-v(5121)-v(5130))-v(4850)*v(6159)+v(446)*v(6295))+v(455)*(v(4814&
&)*v(6284)+v(4841)*v(6285)+v(446)*(v(6296)-v(6297)-v(6298))+v(452)*(v(6299)-v(6300)-v(6301)))
v(5138)=-(v(448)*v(4749)*v(6158))+v(454)*(v(446)*v(453)*v(4840)+v(408)*(-v(5111)-v(5120))-v(4604)*v(6157)+v(452)*(v(453&
&)*v(4813)+v(446)*v(4849)+v(6236)))+v(426)*(v(448)*(-v(5111)-v(5129))-v(4822)*v(6158)+v(4912)*v(6276))+v(4831)*v(6286)+v&
&(4876)*v(6287)+v(450)*(v(408)*v(452)*v(4813)+v(453)*(-v(5120)-v(5129))-v(4849)*v(6159)+v(446)*v(6302))+v(455)*(v(4813&
&)*v(6284)+v(4840)*v(6285)+v(446)*(v(6303)-v(6304)-v(6305))+v(452)*(v(6306)-v(6307)-v(6308)))
v(5137)=-(v(448)*v(4748)*v(6158))+v(454)*(v(446)*v(453)*v(4839)+v(408)*(-v(5110)-v(5119))-v(4603)*v(6157)+v(452)*(v(453&
&)*v(4812)+v(446)*v(4848)+v(6242)))+v(426)*(v(448)*(-v(5110)-v(5128))-v(4821)*v(6158)+v(4911)*v(6276))+v(4830)*v(6286)+v&
&(4875)*v(6287)+v(450)*(v(408)*v(452)*v(4812)+v(453)*(-v(5119)-v(5128))-v(4848)*v(6159)+v(446)*v(6309))+v(455)*(v(4812&
&)*v(6284)+v(4839)*v(6285)+v(446)*(v(6310)-v(6311)-v(6312))+v(452)*(v(6313)-v(6314)-v(6315)))
v(5136)=-(v(448)*v(4747)*v(6158))+v(454)*(v(446)*v(453)*v(4838)+v(408)*(-v(5109)-v(5118))-v(4602)*v(6157)+v(452)*(v(453&
&)*v(4811)+v(446)*v(4847)+v(6248)))+v(426)*(v(448)*(-v(5109)-v(5127))-v(4820)*v(6158)+v(4910)*v(6276))+v(4829)*v(6286)+v&
&(4874)*v(6287)+v(450)*(v(408)*v(452)*v(4811)+v(453)*(-v(5118)-v(5127))-v(4847)*v(6159)+v(446)*v(6316))+v(455)*(v(4811&
&)*v(6284)+v(4838)*v(6285)+v(446)*(v(6317)-v(6318)-v(6319))+v(452)*(v(6320)-v(6321)-v(6322)))
v(5135)=-(v(448)*v(4746)*v(6158))+v(454)*(v(446)*v(453)*v(4837)+v(408)*(-v(5108)-v(5117))-v(4601)*v(6157)+v(452)*(v(453&
&)*v(4810)+v(446)*v(4846)+v(6254)))+v(426)*(v(448)*(-v(5108)-v(5126))-v(4819)*v(6158)+v(4909)*v(6276))+v(4828)*v(6286)+v&
&(4873)*v(6287)+v(450)*(v(408)*v(452)*v(4810)+v(453)*(-v(5117)-v(5126))-v(4846)*v(6159)+v(446)*v(6323))+v(455)*(v(4810&
&)*v(6284)+v(4837)*v(6285)+v(446)*(v(6324)-v(6325)-v(6326))+v(452)*(v(6327)-v(6328)-v(6329)))
v(5134)=-(v(448)*v(4745)*v(6158))+v(454)*(v(446)*v(453)*v(4836)+v(408)*(-v(5107)-v(5116))-v(4600)*v(6157)+v(452)*(v(453&
&)*v(4809)+v(446)*v(4845)+v(6260)))+v(426)*(v(448)*(-v(5107)-v(5125))-v(4818)*v(6158)+v(4908)*v(6276))+v(4827)*v(6286)+v&
&(4872)*v(6287)+v(450)*(v(408)*v(452)*v(4809)+v(453)*(-v(5116)-v(5125))-v(4845)*v(6159)+v(446)*v(6330))+v(455)*(v(4809&
&)*v(6284)+v(4836)*v(6285)+v(446)*(v(6331)-v(6332)-v(6333))+v(452)*(v(6334)-v(6335)-v(6336)))
v(532)=-(v(426)*v(448)*v(6158))+v(455)*(v(446)*v(6284)+v(452)*v(6285))+v(450)*v(6286)+v(454)*v(6287)
v(533)=(-2d0)*v(408)*v(446)*v(452)*v(453)-v(529)*v(6113)-v(531)*v(6117)-v(530)*v(6119)+v(448)*v(455)*v(6222)
v(5165)=v(528)*v(532)-v(524)*v(533)
v(534)=(-2d0)*v(446)*v(450)*v(452)*v(454)-v(531)*v(6074)-v(529)*v(6077)-v(530)*v(6080)+v(426)*v(455)*v(6166)
v(5166)=-(v(524)*v(532))+v(528)*v(534)
v(5164)=-(v(532)*v(532))+v(533)*v(534)
v(5162)=v(5164)*v(5167)+v(5165)*v(524)-v(5166)*v(528)
v(5170)=((-6d0)*v(5162))/v(520)**7
v(5161)=v(5162)*v(5163)
v(5169)=1d0/v(5161)**0.13333333333333333d1
v(6342)=-v(5169)/3d0
v(5178)=(v(4961)*v(5170)+v(5163)*(v(5070)*v(5165)-v(5106)*v(5166)+v(524)*(-(v(5151)*v(524))+v(5142)*v(528)+v(5106)*v&
&(532)-v(5070)*v(533))-v(528)*(-(v(5142)*v(524))+v(5160)*v(528)-v(5070)*v(532)+v(5106)*v(534))+v(5167)*((-2d0)*v(5142)*v&
&(532)+v(5160)*v(533)+v(5151)*v(534))+v(5164)*(-(v(5079)*v(6074))-v(5088)*v(6077)-v(5097)*v(6080)-v(5052)*v(6113)-v(5061&
&)*v(6117)-v(5043)*v(6119)+v(426)*v(448)*(v(6337)+v(6338))+v(453)*((-2d0)*v(426)*v(448)*v(4835)+v(450)*(v(6338)+v(6340))&
&)+v(454)*(v(408)*(-(v(4835)*v(6058))+v(6337)+v(6340))+v(4608)*v(6341)))))*v(6342)
v(5177)=v(6342)*(v(4960)*v(5170)+v(5163)*(v(5069)*v(5165)-v(5105)*v(5166)+v(524)*(-(v(5150)*v(524))+v(5141)*v(528)+v&
&(5105)*v(532)-v(5069)*v(533))-v(528)*(-(v(5141)*v(524))+v(5159)*v(528)-v(5069)*v(532)+v(5105)*v(534))+v(5167)*((-2d0)*v&
&(5141)*v(532)+v(5159)*v(533)+v(5150)*v(534))+v(5164)*(-(v(5078)*v(6074))-v(5087)*v(6077)-v(5096)*v(6080)-v(5051)*v(6113&
&)-v(5060)*v(6117)-v(5042)*v(6119)+v(426)*v(448)*(v(6343)+v(6344))+v(454)*(v(4607)*v(6341)+v(408)*(-(v(4834)*v(6058))+v&
&(6343)+v(6346)))+v(453)*((-2d0)*v(426)*v(448)*v(4834)+v(450)*(v(6344)+v(6346))))))
v(5176)=v(6342)*(v(4959)*v(5170)+v(5163)*(v(5068)*v(5165)-v(5104)*v(5166)+v(524)*(-(v(5149)*v(524))+v(5140)*v(528)+v&
&(5104)*v(532)-v(5068)*v(533))-v(528)*(-(v(5140)*v(524))+v(5158)*v(528)-v(5068)*v(532)+v(5104)*v(534))+v(5167)*((-2d0)*v&
&(5140)*v(532)+v(5158)*v(533)+v(5149)*v(534))+v(5164)*(-(v(5077)*v(6074))-v(5086)*v(6077)-v(5095)*v(6080)-v(5050)*v(6113&
&)-v(5059)*v(6117)-v(5041)*v(6119)+v(426)*v(448)*(v(6347)+v(6348))+v(454)*(v(4606)*v(6341)+v(408)*(-(v(4833)*v(6058))+v&
&(6347)+v(6350)))+v(453)*((-2d0)*v(426)*v(448)*v(4833)+v(450)*(v(6348)+v(6350))))))
v(5175)=v(6342)*(v(4958)*v(5170)+v(5163)*(v(5067)*v(5165)-v(5103)*v(5166)+v(524)*(-(v(5148)*v(524))+v(5139)*v(528)+v&
&(5103)*v(532)-v(5067)*v(533))-v(528)*(-(v(5139)*v(524))+v(5157)*v(528)-v(5067)*v(532)+v(5103)*v(534))+v(5167)*((-2d0)*v&
&(5139)*v(532)+v(5157)*v(533)+v(5148)*v(534))+v(5164)*(-(v(5076)*v(6074))-v(5085)*v(6077)-v(5094)*v(6080)-v(5049)*v(6113&
&)-v(5058)*v(6117)-v(5040)*v(6119)+v(426)*v(448)*(v(6351)+v(6352))+v(454)*(v(4605)*v(6341)+v(408)*(-(v(4832)*v(6058))+v&
&(6351)+v(6354)))+v(453)*((-2d0)*v(426)*v(448)*v(4832)+v(450)*(v(6352)+v(6354))))))
v(5174)=v(6342)*(v(4957)*v(5170)+v(5163)*(v(5066)*v(5165)-v(5102)*v(5166)+v(524)*(-(v(5147)*v(524))+v(5138)*v(528)+v&
&(5102)*v(532)-v(5066)*v(533))-v(528)*(-(v(5138)*v(524))+v(5156)*v(528)-v(5066)*v(532)+v(5102)*v(534))+v(5167)*((-2d0)*v&
&(5138)*v(532)+v(5156)*v(533)+v(5147)*v(534))+v(5164)*(-(v(5075)*v(6074))-v(5084)*v(6077)-v(5093)*v(6080)-v(5048)*v(6113&
&)-v(5057)*v(6117)-v(5039)*v(6119)+v(426)*v(448)*(v(6355)+v(6356))+v(454)*(v(4604)*v(6341)+v(408)*(-(v(4831)*v(6058))+v&
&(6355)+v(6358)))+v(453)*((-2d0)*v(426)*v(448)*v(4831)+v(450)*(v(6356)+v(6358))))))
v(5173)=v(6342)*(v(4956)*v(5170)+v(5163)*(v(5065)*v(5165)-v(5101)*v(5166)+v(524)*(-(v(5146)*v(524))+v(5137)*v(528)+v&
&(5101)*v(532)-v(5065)*v(533))-v(528)*(-(v(5137)*v(524))+v(5155)*v(528)-v(5065)*v(532)+v(5101)*v(534))+v(5167)*((-2d0)*v&
&(5137)*v(532)+v(5155)*v(533)+v(5146)*v(534))+v(5164)*(-(v(5074)*v(6074))-v(5083)*v(6077)-v(5092)*v(6080)-v(5047)*v(6113&
&)-v(5056)*v(6117)-v(5038)*v(6119)+v(426)*v(448)*(v(6359)+v(6360))+v(454)*(v(4603)*v(6341)+v(408)*(-(v(4830)*v(6058))+v&
&(6359)+v(6362)))+v(453)*((-2d0)*v(426)*v(448)*v(4830)+v(450)*(v(6360)+v(6362))))))
v(5172)=v(6342)*(v(4955)*v(5170)+v(5163)*(v(5064)*v(5165)-v(5100)*v(5166)+v(524)*(-(v(5145)*v(524))+v(5136)*v(528)+v&
&(5100)*v(532)-v(5064)*v(533))-v(528)*(-(v(5136)*v(524))+v(5154)*v(528)-v(5064)*v(532)+v(5100)*v(534))+v(5167)*((-2d0)*v&
&(5136)*v(532)+v(5154)*v(533)+v(5145)*v(534))+v(5164)*(-(v(5073)*v(6074))-v(5082)*v(6077)-v(5091)*v(6080)-v(5046)*v(6113&
&)-v(5055)*v(6117)-v(5037)*v(6119)+v(426)*v(448)*(v(6363)+v(6364))+v(454)*(v(4602)*v(6341)+v(408)*(-(v(4829)*v(6058))+v&
&(6363)+v(6366)))+v(453)*((-2d0)*v(426)*v(448)*v(4829)+v(450)*(v(6364)+v(6366))))))
v(5171)=v(6342)*(v(4954)*v(5170)+v(5163)*(v(5063)*v(5165)-v(5099)*v(5166)+v(524)*(-(v(5144)*v(524))+v(5135)*v(528)+v&
&(5099)*v(532)-v(5063)*v(533))-v(528)*(-(v(5135)*v(524))+v(5153)*v(528)-v(5063)*v(532)+v(5099)*v(534))+v(5167)*((-2d0)*v&
&(5135)*v(532)+v(5153)*v(533)+v(5144)*v(534))+v(5164)*(-(v(5072)*v(6074))-v(5081)*v(6077)-v(5090)*v(6080)-v(5045)*v(6113&
&)-v(5054)*v(6117)-v(5036)*v(6119)+v(426)*v(448)*(v(6367)+v(6368))+v(454)*(v(4601)*v(6341)+v(408)*(-(v(4828)*v(6058))+v&
&(6367)+v(6370)))+v(453)*((-2d0)*v(426)*v(448)*v(4828)+v(450)*(v(6368)+v(6370))))))
v(5168)=v(6342)*(v(4953)*v(5170)+v(5163)*(v(5062)*v(5165)-v(5098)*v(5166)+v(524)*(-(v(5143)*v(524))+v(5134)*v(528)+v&
&(5098)*v(532)-v(5062)*v(533))-v(528)*(-(v(5134)*v(524))+v(5152)*v(528)-v(5062)*v(532)+v(5098)*v(534))+v(5167)*((-2d0)*v&
&(5134)*v(532)+v(5152)*v(533)+v(5143)*v(534))+v(5164)*(-(v(5071)*v(6074))-v(5080)*v(6077)-v(5089)*v(6080)-v(5044)*v(6113&
&)-v(5053)*v(6117)-v(5035)*v(6119)+v(426)*v(448)*(v(6371)+v(6372))+v(454)*(v(4600)*v(6341)+v(408)*(-(v(4827)*v(6058))+v&
&(6371)+v(6374)))+v(453)*((-2d0)*v(426)*v(448)*v(4827)+v(450)*(v(6372)+v(6374))))))
v(539)=1d0/v(5161)**0.3333333333333333d0
v(6390)=-(mpar(9)*v(539))
v(5292)=v(4208)+mpar(9)*(-(v(5178)*v(5274))-v(539)*(v(519)*(v(4898)*v(546)+v(4889)*v(548)+v(4862)*v(549)+v(4934)*v(552)&
&+v(4907)*v(553)+v(4943)*v(554))+v(4971)*v(6375)))
v(6397)=2d0*v(5292)
v(5290)=v(4207)+mpar(9)*(-(v(5177)*v(5274))-v(539)*(v(519)*(v(4897)*v(546)+v(4888)*v(548)+v(4861)*v(549)+v(4933)*v(552)&
&+v(4906)*v(553)+v(4942)*v(554))+v(4970)*v(6375)))
v(6401)=2d0*v(5290)
v(5288)=v(4206)+mpar(9)*(-(v(5176)*v(5274))-v(539)*(v(519)*(v(4896)*v(546)+v(4887)*v(548)+v(4860)*v(549)+v(4932)*v(552)&
&+v(4905)*v(553)+v(4941)*v(554))+v(4969)*v(6375)))
v(6404)=2d0*v(5288)
v(5286)=v(4205)+mpar(9)*(-(v(5175)*v(5274))-v(539)*(v(519)*(v(4895)*v(546)+v(4886)*v(548)+v(4859)*v(549)+v(4931)*v(552)&
&+v(4904)*v(553)+v(4940)*v(554))+v(4968)*v(6375)))
v(6407)=2d0*v(5286)
v(5284)=v(4204)+mpar(9)*(-(v(5174)*v(5274))-v(539)*(v(519)*(v(4894)*v(546)+v(4885)*v(548)+v(4858)*v(549)+v(4930)*v(552)&
&+v(4903)*v(553)+v(4939)*v(554))+v(4967)*v(6375)))
v(6410)=2d0*v(5284)
v(5282)=v(4203)+mpar(9)*(-(v(5173)*v(5274))-v(539)*(v(519)*(v(4893)*v(546)+v(4884)*v(548)+v(4857)*v(549)+v(4929)*v(552)&
&+v(4902)*v(553)+v(4938)*v(554))+v(4966)*v(6375)))
v(6413)=2d0*v(5282)
v(5280)=v(4202)+mpar(9)*(-(v(5172)*v(5274))-v(539)*(v(519)*(v(4892)*v(546)+v(4883)*v(548)+v(4856)*v(549)+v(4928)*v(552)&
&+v(4901)*v(553)+v(4937)*v(554))+v(4965)*v(6375)))
v(6416)=2d0*v(5280)
v(5278)=v(4201)+mpar(9)*(-(v(5171)*v(5274))-v(539)*(v(519)*(v(4891)*v(546)+v(4882)*v(548)+v(4855)*v(549)+v(4927)*v(552)&
&+v(4900)*v(553)+v(4936)*v(554))+v(4964)*v(6375)))
v(6419)=2d0*v(5278)
v(5276)=v(4200)+mpar(9)*(-(v(5168)*v(5274))-v(539)*(v(519)*(v(4890)*v(546)+v(4881)*v(548)+v(4854)*v(549)+v(4926)*v(552)&
&+v(4899)*v(553)+v(4935)*v(554))+v(4962)*v(6375)))
v(6422)=2d0*v(5276)
v(5273)=v(4199)+mpar(9)*(-(v(5178)*v(5255))-v(539)*(v(519)*(v(4898)*v(545)+v(4889)*v(547)+v(4862)*v(550)+v(4925)*v(552)&
&+v(4871)*v(553)+v(4952)*v(554))+v(4971)*v(6376)))
v(6396)=2d0*v(5273)
v(5271)=v(4198)+mpar(9)*(-(v(5177)*v(5255))-v(539)*(v(519)*(v(4897)*v(545)+v(4888)*v(547)+v(4861)*v(550)+v(4924)*v(552)&
&+v(4870)*v(553)+v(4951)*v(554))+v(4970)*v(6376)))
v(6400)=2d0*v(5271)
v(5269)=v(4197)+mpar(9)*(-(v(5176)*v(5255))-v(539)*(v(519)*(v(4896)*v(545)+v(4887)*v(547)+v(4860)*v(550)+v(4923)*v(552)&
&+v(4869)*v(553)+v(4950)*v(554))+v(4969)*v(6376)))
v(6403)=2d0*v(5269)
v(5267)=v(4196)+mpar(9)*(-(v(5175)*v(5255))-v(539)*(v(519)*(v(4895)*v(545)+v(4886)*v(547)+v(4859)*v(550)+v(4922)*v(552)&
&+v(4868)*v(553)+v(4949)*v(554))+v(4968)*v(6376)))
v(6406)=2d0*v(5267)
v(5265)=v(4195)+mpar(9)*(-(v(5174)*v(5255))-v(539)*(v(519)*(v(4894)*v(545)+v(4885)*v(547)+v(4858)*v(550)+v(4921)*v(552)&
&+v(4867)*v(553)+v(4948)*v(554))+v(4967)*v(6376)))
v(6409)=2d0*v(5265)
v(5263)=v(4194)+mpar(9)*(-(v(5173)*v(5255))-v(539)*(v(519)*(v(4893)*v(545)+v(4884)*v(547)+v(4857)*v(550)+v(4920)*v(552)&
&+v(4866)*v(553)+v(4947)*v(554))+v(4966)*v(6376)))
v(6412)=2d0*v(5263)
v(5261)=v(4193)+mpar(9)*(-(v(5172)*v(5255))-v(539)*(v(519)*(v(4892)*v(545)+v(4883)*v(547)+v(4856)*v(550)+v(4919)*v(552)&
&+v(4865)*v(553)+v(4946)*v(554))+v(4965)*v(6376)))
v(6415)=2d0*v(5261)
v(5259)=v(4192)+mpar(9)*(-(v(5171)*v(5255))-v(539)*(v(519)*(v(4891)*v(545)+v(4882)*v(547)+v(4855)*v(550)+v(4918)*v(552)&
&+v(4864)*v(553)+v(4945)*v(554))+v(4964)*v(6376)))
v(6418)=2d0*v(5259)
v(5257)=v(4191)+mpar(9)*(-(v(5168)*v(5255))-v(539)*(v(519)*(v(4890)*v(545)+v(4881)*v(547)+v(4854)*v(550)+v(4917)*v(552)&
&+v(4863)*v(553)+v(4944)*v(554))+v(4962)*v(6376)))
v(6421)=2d0*v(5257)
v(5254)=v(4190)+mpar(9)*(-(v(5178)*v(5236))-v(539)*(v(519)*(v(4907)*v(545)+v(4871)*v(546)+v(4943)*v(547)+v(4952)*v(548)&
&+v(4925)*v(549)+v(4934)*v(550))+v(4971)*v(6377)))
v(6395)=2d0*v(5254)
v(5252)=v(4189)+mpar(9)*(-(v(5177)*v(5236))-v(539)*(v(519)*(v(4906)*v(545)+v(4870)*v(546)+v(4942)*v(547)+v(4951)*v(548)&
&+v(4924)*v(549)+v(4933)*v(550))+v(4970)*v(6377)))
v(6399)=2d0*v(5252)
v(5250)=v(4188)+mpar(9)*(-(v(5176)*v(5236))-v(539)*(v(519)*(v(4905)*v(545)+v(4869)*v(546)+v(4941)*v(547)+v(4950)*v(548)&
&+v(4923)*v(549)+v(4932)*v(550))+v(4969)*v(6377)))
v(6402)=2d0*v(5250)
v(5248)=v(4187)+mpar(9)*(-(v(5175)*v(5236))-v(539)*(v(519)*(v(4904)*v(545)+v(4868)*v(546)+v(4940)*v(547)+v(4949)*v(548)&
&+v(4922)*v(549)+v(4931)*v(550))+v(4968)*v(6377)))
v(6405)=2d0*v(5248)
v(5246)=v(4186)+mpar(9)*(-(v(5174)*v(5236))-v(539)*(v(519)*(v(4903)*v(545)+v(4867)*v(546)+v(4939)*v(547)+v(4948)*v(548)&
&+v(4921)*v(549)+v(4930)*v(550))+v(4967)*v(6377)))
v(6408)=2d0*v(5246)
v(5244)=v(4185)+mpar(9)*(-(v(5173)*v(5236))-v(539)*(v(519)*(v(4902)*v(545)+v(4866)*v(546)+v(4938)*v(547)+v(4947)*v(548)&
&+v(4920)*v(549)+v(4929)*v(550))+v(4966)*v(6377)))
v(6411)=2d0*v(5244)
v(5242)=v(4184)+mpar(9)*(-(v(5172)*v(5236))-v(539)*(v(519)*(v(4901)*v(545)+v(4865)*v(546)+v(4937)*v(547)+v(4946)*v(548)&
&+v(4919)*v(549)+v(4928)*v(550))+v(4965)*v(6377)))
v(6414)=2d0*v(5242)
v(5240)=v(4183)+mpar(9)*(-(v(5171)*v(5236))-v(539)*(v(519)*(v(4900)*v(545)+v(4864)*v(546)+v(4936)*v(547)+v(4945)*v(548)&
&+v(4918)*v(549)+v(4927)*v(550))+v(4964)*v(6377)))
v(6417)=2d0*v(5240)
v(5238)=v(4182)+mpar(9)*(-(v(5168)*v(5236))-v(539)*(v(519)*(v(4899)*v(545)+v(4863)*v(546)+v(4935)*v(547)+v(4944)*v(548)&
&+v(4917)*v(549)+v(4926)*v(550))+v(4962)*v(6377)))
v(6420)=2d0*v(5238)
v(5235)=mpar(9)*(-(v(5178)*v(5217))-((-2d0/3d0)*v(4983)+v(5004)+v(5025))*v(539))+v(5999)
v(5233)=mpar(9)*(-(v(5177)*v(5217))-((-2d0/3d0)*v(4982)+v(5003)+v(5024))*v(539))+v(6002)
v(5231)=mpar(9)*(-(v(5176)*v(5217))-((-2d0/3d0)*v(4981)+v(5002)+v(5023))*v(539))+v(6005)
v(5229)=mpar(9)*(-(v(5175)*v(5217))-((-2d0/3d0)*v(4980)+v(5001)+v(5022))*v(539))+v(6008)
v(5227)=mpar(9)*(-(v(5174)*v(5217))-((-2d0/3d0)*v(4979)+v(5000)+v(5021))*v(539))+v(6011)
v(5225)=mpar(9)*(-(v(5173)*v(5217))-((-2d0/3d0)*v(4978)+v(4999)+v(5020))*v(539))+v(6014)
v(5223)=mpar(9)*(-(v(5172)*v(5217))-((-2d0/3d0)*v(4977)+v(4998)+v(5019))*v(539))+v(6017)
v(5221)=mpar(9)*(-(v(5171)*v(5217))-((-2d0/3d0)*v(4976)+v(4997)+v(5018))*v(539))+v(6020)
v(5219)=mpar(9)*(-(v(5168)*v(5217))-((-2d0/3d0)*v(4975)+v(4996)+v(5017))*v(539))+v(6023)
v(5216)=mpar(9)*(-(v(5178)*v(5198))-(v(5004)+(-2d0/3d0)*v(5016)+v(5034))*v(539))+v(6000)
v(5214)=mpar(9)*(-(v(5177)*v(5198))-(v(5003)+(-2d0/3d0)*v(5015)+v(5033))*v(539))+v(6003)
v(5212)=mpar(9)*(-(v(5176)*v(5198))-(v(5002)+(-2d0/3d0)*v(5014)+v(5032))*v(539))+v(6006)
v(5210)=mpar(9)*(-(v(5175)*v(5198))-(v(5001)+(-2d0/3d0)*v(5013)+v(5031))*v(539))+v(6009)
v(5208)=mpar(9)*(-(v(5174)*v(5198))-(v(5000)+(-2d0/3d0)*v(5012)+v(5030))*v(539))+v(6012)
v(5206)=mpar(9)*(-(v(5173)*v(5198))-(v(4999)+(-2d0/3d0)*v(5011)+v(5029))*v(539))+v(6015)
v(5204)=mpar(9)*(-(v(5172)*v(5198))-(v(4998)+(-2d0/3d0)*v(5010)+v(5028))*v(539))+v(6018)
v(5202)=mpar(9)*(-(v(5171)*v(5198))-(v(4997)+(-2d0/3d0)*v(5009)+v(5027))*v(539))+v(6021)
v(5200)=mpar(9)*(-(v(5168)*v(5198))-(v(4996)+(-2d0/3d0)*v(5008)+v(5026))*v(539))+v(6024)
v(5197)=mpar(9)*(-(v(5178)*v(5179))-((2d0/3d0)*v(4995)+v(5025)+v(5034))*v(539))+v(5998)
v(5195)=mpar(9)*(-(v(5177)*v(5179))-((2d0/3d0)*v(4994)+v(5024)+v(5033))*v(539))+v(6001)
v(5193)=mpar(9)*(-(v(5176)*v(5179))-((2d0/3d0)*v(4993)+v(5023)+v(5032))*v(539))+v(6004)
v(5191)=mpar(9)*(-(v(5175)*v(5179))-((2d0/3d0)*v(4992)+v(5022)+v(5031))*v(539))+v(6007)
v(5189)=mpar(9)*(-(v(5174)*v(5179))-((2d0/3d0)*v(4991)+v(5021)+v(5030))*v(539))+v(6010)
v(5187)=mpar(9)*(-(v(5173)*v(5179))-((2d0/3d0)*v(4990)+v(5020)+v(5029))*v(539))+v(6013)
v(5185)=mpar(9)*(-(v(5172)*v(5179))-((2d0/3d0)*v(4989)+v(5019)+v(5028))*v(539))+v(6016)
v(5183)=mpar(9)*(-(v(5171)*v(5179))-((2d0/3d0)*v(4988)+v(5018)+v(5027))*v(539))+v(6019)
v(5181)=mpar(9)*(-(v(5168)*v(5179))-((2d0/3d0)*v(4987)+v(5017)+v(5026))*v(539))+v(6022)
v(557)=1d0/(v(518)*v(575)+v(509)*v(576)+v(515)*v(577))**2
v(564)=-(v(557)*((v(575)*v(575))+(v(576)*v(576))+(v(577)*v(577))))
v(562)=1d0/v(557)**0.3333333333333333d0
v(6389)=-(mpar(11)*v(562))
v(6391)=v(557)*v(6389)
v(561)=v(557)*((v(569)*v(569))+(v(570)*v(570))+(v(573)*v(573)))
v(566)=-v(561)/3d0
v(560)=-(v(557)*((v(568)*v(568))+(v(571)*v(571))+(v(572)*v(572))))
v(565)=v(560)/3d0
v(559)=v(564)/3d0
v(580)=-v(117)+v(6378)
v(6382)=v(5541)*v(580)
v(581)=-v(119)+v(6379)*x(13)
v(6385)=v(5541)*v(581)
v(582)=-v(120)+v(5551)*v(6379)
v(6388)=v(5541)*v(582)
v(583)=-v(121)+v(6379)*x(14)
v(6381)=v(5541)*v(583)
v(603)=v(232)*(v(583)*v(583))
v(584)=-v(122)+v(6379)*x(16)
v(6384)=v(5541)*v(584)
v(620)=v(232)*(v(584)*v(584))
v(585)=-v(123)+v(6379)*x(15)
v(6380)=v(5541)*v(585)
v(621)=v(232)*(v(585)*v(585))
v(608)=v(232)*(-(v(580)*v(584))+v(583)*v(585))
v(624)=v(608)*v(6384)
v(589)=v(232)*(-(v(582)*v(583))+v(584)*v(585))
v(605)=v(589)*v(6381)
v(588)=v(232)*(v(583)*v(584)-v(581)*v(585))
v(623)=v(588)*v(6380)
v(586)=v(232)*(v(580)*v(580))+v(603)+v(621)
v(592)=v(5541)*(v(585)*v(586)+v(582)*v(588)+v(584)*v(589))
v(627)=v(592)*v(6380)
v(591)=v(5541)*(v(583)*v(586)+v(584)*v(588)+v(581)*v(589))
v(607)=v(591)*v(6381)
v(587)=v(605)+v(623)+v(586)*v(6382)
v(595)=v(5541)*(v(583)*v(587)+v(581)*v(591)+v(584)*v(592))
v(611)=v(595)*v(6381)
v(594)=v(5541)*(v(585)*v(587)+v(584)*v(591)+v(582)*v(592))
v(629)=v(594)*v(6380)
v(590)=v(607)+v(627)+v(587)*v(6382)
v(598)=v(5541)*(v(585)*v(590)+v(582)*v(594)+v(584)*v(595))
v(633)=v(598)*v(6380)
v(597)=v(5541)*(v(583)*v(590)+v(584)*v(594)+v(581)*v(595))
v(613)=v(597)*v(6381)
v(593)=v(611)+v(629)+v(590)*v(6382)
v(596)=v(613)+v(633)+v(593)*v(6382)
v(6383)=5040d0+v(596)
v(599)=v(5541)*(v(585)*v(593)+v(584)*v(597)+v(582)*v(598))
v(635)=v(599)*v(6380)
v(600)=v(5541)*(v(583)*v(593)+v(581)*v(597)+v(584)*v(598))
v(638)=(7d0*(360d0*v(588)+120d0*v(592)+30d0*v(594)+6d0*v(598)+v(599))+v(5541)*(v(582)*v(599)+v(584)*v(600)+v(585)*v&
&(6383)))/5040d0
v(618)=v(600)*v(6381)
v(6386)=5040d0+v(618)
v(640)=(2520d0*v(586)+840d0*v(587)+210d0*v(590)+42d0*v(593)+7d0*v(596)+v(635)+v(6382)*v(6383)+v(6386))/5040d0
v(602)=(7d0*(360d0*v(589)+120d0*v(591)+30d0*v(595)+6d0*v(597)+v(600))+v(5541)*(v(584)*v(599)+v(581)*v(600)+v(583)*v&
&(6383)))/5040d0
v(604)=v(232)*(v(581)*v(581))+v(603)+v(620)
v(610)=v(5541)*(v(585)*v(589)+v(584)*v(604)+v(582)*v(608))
v(626)=v(610)*v(6384)
v(606)=v(605)+v(624)+v(604)*v(6385)
v(614)=v(5541)*(v(585)*v(591)+v(584)*v(606)+v(582)*v(610))
v(630)=v(614)*v(6384)
v(609)=v(607)+v(626)+v(606)*v(6385)
v(616)=v(5541)*(v(585)*v(595)+v(584)*v(609)+v(582)*v(614))
v(632)=v(616)*v(6384)
v(612)=v(611)+v(630)+v(609)*v(6385)
v(615)=v(613)+v(632)+v(612)*v(6385)
v(6387)=5040d0+v(615)
v(617)=v(5541)*(v(585)*v(597)+v(584)*v(612)+v(582)*v(616))
v(637)=(7d0*(360d0*v(608)+120d0*v(610)+30d0*v(614)+6d0*v(616)+v(617))+v(5541)*(v(585)*v(600)+v(582)*v(617)+v(584)*v&
&(6387)))/5040d0
v(636)=v(617)*v(6384)
v(642)=(2520d0*v(604)+840d0*v(606)+210d0*v(609)+42d0*v(612)+7d0*v(615)+v(636)+v(6386)+v(6385)*v(6387))/5040d0
v(622)=v(232)*(v(582)*v(582))+v(620)+v(621)
v(625)=v(623)+v(624)+v(622)*v(6388)
v(628)=v(626)+v(627)+v(625)*v(6388)
v(631)=v(629)+v(630)+v(628)*v(6388)
v(634)=v(632)+v(633)+v(631)*v(6388)
v(644)=(5040d0+2520d0*v(622)+840d0*v(625)+210d0*v(628)+42d0*v(631)+7d0*v(634)+v(635)+v(636)+(5040d0+v(634))*v(6388))&
&/5040d0
v(650)=(2d0/3d0)*v(352)+(v(559)+(2d0/3d0)*v(561)+v(565))*v(6389)+v(5179)*v(6390)+v(651)+v(653)
v(652)=(2d0/3d0)*v(342)+(v(559)+(-2d0/3d0)*v(560)+v(566))*v(6389)+v(5198)*v(6390)+v(651)+v(654)
v(655)=(2d0/3d0)*v(347)+((-2d0/3d0)*v(564)+v(565)+v(566))*v(6389)+v(5217)*v(6390)+v(653)+v(654)
v(656)=v(354)+v(5236)*v(6390)+(v(568)*v(569)+v(570)*v(571)+v(572)*v(573))*v(6391)
v(6394)=2d0*v(656)
v(657)=v(355)+v(5255)*v(6390)+(v(568)*v(575)+v(572)*v(576)+v(571)*v(577))*v(6391)
v(6393)=2d0*v(657)
v(658)=v(356)+v(5274)*v(6390)+(v(569)*v(575)+v(573)*v(576)+v(570)*v(577))*v(6391)
v(6392)=2d0*v(658)
v(5299)=v(214)*v(6392)+v(169)*v(650)+v(183)*v(652)+v(191)*v(655)+v(2353)*v(656)+v(2357)*v(657)
v(5298)=v(207)*v(6392)+v(205)*v(6393)+v(168)*v(650)+v(181)*v(652)+v(190)*v(655)+v(2356)*v(656)
v(5297)=v(199)*v(6392)+v(198)*v(6393)+v(196)*v(6394)+v(167)*v(650)+v(178)*v(652)+v(187)*v(655)
v(5296)=v(191)*v(6392)+v(190)*v(6393)+v(187)*v(6394)+v(166)*v(650)+v(174)*v(652)+v(186)*v(655)
v(5295)=v(183)*v(6392)+v(181)*v(6393)+v(178)*v(6394)+v(161)*v(650)+v(172)*v(652)+v(174)*v(655)
v(5294)=v(169)*v(6392)+v(168)*v(6393)+v(167)*v(6394)+v(156)*v(650)+v(161)*v(652)+v(166)*v(655)
v(5301)=1d0/sqrt(v(5299)*v(6392)+v(5298)*v(6393)+v(5297)*v(6394)+v(5294)*v(650)+v(5295)*v(652)+v(5296)*v(655))
v(6398)=v(5301)/2d0
v(5309)=v(6398)*(v(5197)*v(5294)+v(5216)*v(5295)+v(5235)*v(5296)+v(5297)*v(6395)+v(6394)*(v(167)*v(5197)+v(178)*v(5216)&
&+v(187)*v(5235)+v(2356)*v(5273)+v(2353)*v(5292)+v(196)*v(6395))+v(5298)*v(6396)+v(6393)*(v(168)*v(5197)+v(181)*v(5216)&
&+v(190)*v(5235)+v(2356)*v(5254)+v(2357)*v(5292)+v(205)*v(6396))+v(5299)*v(6397)+v(6392)*(v(169)*v(5197)+v(183)*v(5216)&
&+v(191)*v(5235)+v(2353)*v(5254)+v(2357)*v(5273)+v(214)*v(6397))+(v(156)*v(5197)+v(161)*v(5216)+v(166)*v(5235)+v(167)*v&
&(6395)+v(168)*v(6396)+v(169)*v(6397))*v(650)+(v(161)*v(5197)+v(172)*v(5216)+v(174)*v(5235)+v(178)*v(6395)+v(181)*v(6396&
&)+v(183)*v(6397))*v(652)+(v(166)*v(5197)+v(174)*v(5216)+v(186)*v(5235)+v(187)*v(6395)+v(190)*v(6396)+v(191)*v(6397))*v&
&(655))
v(5308)=v(6398)*(v(5195)*v(5294)+v(5214)*v(5295)+v(5233)*v(5296)+v(5297)*v(6399)+v(6394)*(v(167)*v(5195)+v(178)*v(5214)&
&+v(187)*v(5233)+v(2356)*v(5271)+v(2353)*v(5290)+v(196)*v(6399))+v(5298)*v(6400)+v(6393)*(v(168)*v(5195)+v(181)*v(5214)&
&+v(190)*v(5233)+v(2356)*v(5252)+v(2357)*v(5290)+v(205)*v(6400))+v(5299)*v(6401)+v(6392)*(v(169)*v(5195)+v(183)*v(5214)&
&+v(191)*v(5233)+v(2353)*v(5252)+v(2357)*v(5271)+v(214)*v(6401))+(v(156)*v(5195)+v(161)*v(5214)+v(166)*v(5233)+v(167)*v&
&(6399)+v(168)*v(6400)+v(169)*v(6401))*v(650)+(v(161)*v(5195)+v(172)*v(5214)+v(174)*v(5233)+v(178)*v(6399)+v(181)*v(6400&
&)+v(183)*v(6401))*v(652)+(v(166)*v(5195)+v(174)*v(5214)+v(186)*v(5233)+v(187)*v(6399)+v(190)*v(6400)+v(191)*v(6401))*v&
&(655))
v(5307)=v(6398)*(v(5193)*v(5294)+v(5212)*v(5295)+v(5231)*v(5296)+v(5297)*v(6402)+v(5298)*v(6403)+v(5299)*v(6404)+v(6394&
&)*(v(167)*v(5193)+v(178)*v(5212)+v(187)*v(5231)+v(196)*v(6402)+v(198)*v(6403)+v(199)*v(6404))+v(6393)*(v(168)*v(5193)+v&
&(181)*v(5212)+v(190)*v(5231)+v(198)*v(6402)+v(205)*v(6403)+v(207)*v(6404))+v(6392)*(v(169)*v(5193)+v(183)*v(5212)+v(191&
&)*v(5231)+v(199)*v(6402)+v(207)*v(6403)+v(214)*v(6404))+(v(156)*v(5193)+v(161)*v(5212)+v(166)*v(5231)+v(167)*v(6402)+v&
&(168)*v(6403)+v(169)*v(6404))*v(650)+(v(161)*v(5193)+v(172)*v(5212)+v(174)*v(5231)+v(178)*v(6402)+v(181)*v(6403)+v(183&
&)*v(6404))*v(652)+(v(166)*v(5193)+v(174)*v(5212)+v(186)*v(5231)+v(187)*v(6402)+v(190)*v(6403)+v(191)*v(6404))*v(655))
v(5306)=v(6398)*(v(5191)*v(5294)+v(5210)*v(5295)+v(5229)*v(5296)+v(5297)*v(6405)+v(6394)*(v(167)*v(5191)+v(178)*v(5210)&
&+v(187)*v(5229)+v(2356)*v(5267)+v(2353)*v(5286)+v(196)*v(6405))+v(5298)*v(6406)+v(6393)*(v(168)*v(5191)+v(181)*v(5210)&
&+v(190)*v(5229)+v(2356)*v(5248)+v(2357)*v(5286)+v(205)*v(6406))+v(5299)*v(6407)+v(6392)*(v(169)*v(5191)+v(183)*v(5210)&
&+v(191)*v(5229)+v(2353)*v(5248)+v(2357)*v(5267)+v(214)*v(6407))+(v(156)*v(5191)+v(161)*v(5210)+v(166)*v(5229)+v(167)*v&
&(6405)+v(168)*v(6406)+v(169)*v(6407))*v(650)+(v(161)*v(5191)+v(172)*v(5210)+v(174)*v(5229)+v(178)*v(6405)+v(181)*v(6406&
&)+v(183)*v(6407))*v(652)+(v(166)*v(5191)+v(174)*v(5210)+v(186)*v(5229)+v(187)*v(6405)+v(190)*v(6406)+v(191)*v(6407))*v&
&(655))
v(5305)=v(6398)*(v(5189)*v(5294)+v(5208)*v(5295)+v(5227)*v(5296)+v(5297)*v(6408)+v(6394)*(v(167)*v(5189)+v(178)*v(5208)&
&+v(187)*v(5227)+v(2356)*v(5265)+v(2353)*v(5284)+v(196)*v(6408))+v(5298)*v(6409)+v(6393)*(v(168)*v(5189)+v(181)*v(5208)&
&+v(190)*v(5227)+v(2356)*v(5246)+v(2357)*v(5284)+v(205)*v(6409))+v(5299)*v(6410)+v(6392)*(v(169)*v(5189)+v(183)*v(5208)&
&+v(191)*v(5227)+v(2353)*v(5246)+v(2357)*v(5265)+v(214)*v(6410))+(v(156)*v(5189)+v(161)*v(5208)+v(166)*v(5227)+v(167)*v&
&(6408)+v(168)*v(6409)+v(169)*v(6410))*v(650)+(v(161)*v(5189)+v(172)*v(5208)+v(174)*v(5227)+v(178)*v(6408)+v(181)*v(6409&
&)+v(183)*v(6410))*v(652)+(v(166)*v(5189)+v(174)*v(5208)+v(186)*v(5227)+v(187)*v(6408)+v(190)*v(6409)+v(191)*v(6410))*v&
&(655))
v(5304)=v(6398)*(v(5187)*v(5294)+v(5206)*v(5295)+v(5225)*v(5296)+v(5297)*v(6411)+v(6394)*(v(167)*v(5187)+v(178)*v(5206)&
&+v(187)*v(5225)+v(2356)*v(5263)+v(2353)*v(5282)+v(196)*v(6411))+v(5298)*v(6412)+v(6393)*(v(168)*v(5187)+v(181)*v(5206)&
&+v(190)*v(5225)+v(2356)*v(5244)+v(2357)*v(5282)+v(205)*v(6412))+v(5299)*v(6413)+v(6392)*(v(169)*v(5187)+v(183)*v(5206)&
&+v(191)*v(5225)+v(2353)*v(5244)+v(2357)*v(5263)+v(214)*v(6413))+(v(156)*v(5187)+v(161)*v(5206)+v(166)*v(5225)+v(167)*v&
&(6411)+v(168)*v(6412)+v(169)*v(6413))*v(650)+(v(161)*v(5187)+v(172)*v(5206)+v(174)*v(5225)+v(178)*v(6411)+v(181)*v(6412&
&)+v(183)*v(6413))*v(652)+(v(166)*v(5187)+v(174)*v(5206)+v(186)*v(5225)+v(187)*v(6411)+v(190)*v(6412)+v(191)*v(6413))*v&
&(655))
v(5303)=v(6398)*(v(5185)*v(5294)+v(5204)*v(5295)+v(5223)*v(5296)+v(5297)*v(6414)+v(6394)*(v(167)*v(5185)+v(178)*v(5204)&
&+v(187)*v(5223)+v(2356)*v(5261)+v(2353)*v(5280)+v(196)*v(6414))+v(5298)*v(6415)+v(6393)*(v(168)*v(5185)+v(181)*v(5204)&
&+v(190)*v(5223)+v(2356)*v(5242)+v(2357)*v(5280)+v(205)*v(6415))+v(5299)*v(6416)+v(6392)*(v(169)*v(5185)+v(183)*v(5204)&
&+v(191)*v(5223)+v(2353)*v(5242)+v(2357)*v(5261)+v(214)*v(6416))+(v(156)*v(5185)+v(161)*v(5204)+v(166)*v(5223)+v(167)*v&
&(6414)+v(168)*v(6415)+v(169)*v(6416))*v(650)+(v(161)*v(5185)+v(172)*v(5204)+v(174)*v(5223)+v(178)*v(6414)+v(181)*v(6415&
&)+v(183)*v(6416))*v(652)+(v(166)*v(5185)+v(174)*v(5204)+v(186)*v(5223)+v(187)*v(6414)+v(190)*v(6415)+v(191)*v(6416))*v&
&(655))
v(5302)=v(6398)*(v(5183)*v(5294)+v(5202)*v(5295)+v(5221)*v(5296)+v(5297)*v(6417)+v(6394)*(v(167)*v(5183)+v(178)*v(5202)&
&+v(187)*v(5221)+v(2356)*v(5259)+v(2353)*v(5278)+v(196)*v(6417))+v(5298)*v(6418)+v(6393)*(v(168)*v(5183)+v(181)*v(5202)&
&+v(190)*v(5221)+v(2356)*v(5240)+v(2357)*v(5278)+v(205)*v(6418))+v(5299)*v(6419)+v(6392)*(v(169)*v(5183)+v(183)*v(5202)&
&+v(191)*v(5221)+v(2353)*v(5240)+v(2357)*v(5259)+v(214)*v(6419))+(v(156)*v(5183)+v(161)*v(5202)+v(166)*v(5221)+v(167)*v&
&(6417)+v(168)*v(6418)+v(169)*v(6419))*v(650)+(v(161)*v(5183)+v(172)*v(5202)+v(174)*v(5221)+v(178)*v(6417)+v(181)*v(6418&
&)+v(183)*v(6419))*v(652)+(v(166)*v(5183)+v(174)*v(5202)+v(186)*v(5221)+v(187)*v(6417)+v(190)*v(6418)+v(191)*v(6419))*v&
&(655))
v(5300)=v(6398)*(v(5181)*v(5294)+v(5200)*v(5295)+v(5219)*v(5296)+v(5297)*v(6420)+v(6394)*(v(167)*v(5181)+v(178)*v(5200)&
&+v(187)*v(5219)+v(2356)*v(5257)+v(2353)*v(5276)+v(196)*v(6420))+v(5298)*v(6421)+v(6393)*(v(168)*v(5181)+v(181)*v(5200)&
&+v(190)*v(5219)+v(2356)*v(5238)+v(2357)*v(5276)+v(205)*v(6421))+v(5299)*v(6422)+v(6392)*(v(169)*v(5181)+v(183)*v(5200)&
&+v(191)*v(5219)+v(2353)*v(5238)+v(2357)*v(5257)+v(214)*v(6422))+(v(156)*v(5181)+v(161)*v(5200)+v(166)*v(5219)+v(167)*v&
&(6420)+v(168)*v(6421)+v(169)*v(6422))*v(650)+(v(161)*v(5181)+v(172)*v(5200)+v(174)*v(5219)+v(178)*v(6420)+v(181)*v(6421&
&)+v(183)*v(6422))*v(652)+(v(166)*v(5181)+v(174)*v(5200)+v(186)*v(5219)+v(187)*v(6420)+v(190)*v(6421)+v(191)*v(6422))*v&
&(655))
v(5415)=Jinv(1,2)*v(5197)+Jinv(1,3)*v(5216)+Jinv(1,4)*v(5254)+Jinv(1,6)*v(5273)+Jinv(1,5)*v(5292)-Jinv(1,1)*v(5309)
v(5403)=Jinv(1,2)*v(5195)+Jinv(1,3)*v(5214)+Jinv(1,4)*v(5252)+Jinv(1,6)*v(5271)+Jinv(1,5)*v(5290)-Jinv(1,1)*v(5308)
v(5391)=Jinv(1,2)*v(5193)+Jinv(1,3)*v(5212)+Jinv(1,4)*v(5250)+Jinv(1,6)*v(5269)+Jinv(1,5)*v(5288)-Jinv(1,1)*v(5307)
v(5379)=Jinv(1,2)*v(5191)+Jinv(1,3)*v(5210)+Jinv(1,4)*v(5248)+Jinv(1,6)*v(5267)+Jinv(1,5)*v(5286)-Jinv(1,1)*v(5306)
v(5367)=Jinv(1,2)*v(5189)+Jinv(1,3)*v(5208)+Jinv(1,4)*v(5246)+Jinv(1,6)*v(5265)+Jinv(1,5)*v(5284)-Jinv(1,1)*v(5305)
v(5355)=Jinv(1,2)*v(5187)+Jinv(1,3)*v(5206)+Jinv(1,4)*v(5244)+Jinv(1,6)*v(5263)+Jinv(1,5)*v(5282)-Jinv(1,1)*v(5304)
v(5343)=Jinv(1,2)*v(5185)+Jinv(1,3)*v(5204)+Jinv(1,4)*v(5242)+Jinv(1,6)*v(5261)+Jinv(1,5)*v(5280)-Jinv(1,1)*v(5303)
v(5331)=Jinv(1,2)*v(5183)+Jinv(1,3)*v(5202)+Jinv(1,4)*v(5240)+Jinv(1,6)*v(5259)+Jinv(1,5)*v(5278)-Jinv(1,1)*v(5302)
v(5319)=Jinv(1,2)*v(5181)+Jinv(1,3)*v(5200)+Jinv(1,4)*v(5238)+Jinv(1,6)*v(5257)+Jinv(1,5)*v(5276)-Jinv(1,1)*v(5300)
v(5416)=Jinv(2,2)*v(5197)+Jinv(2,3)*v(5216)+Jinv(2,4)*v(5254)+Jinv(2,6)*v(5273)+Jinv(2,5)*v(5292)-Jinv(2,1)*v(5309)
v(5404)=Jinv(2,2)*v(5195)+Jinv(2,3)*v(5214)+Jinv(2,4)*v(5252)+Jinv(2,6)*v(5271)+Jinv(2,5)*v(5290)-Jinv(2,1)*v(5308)
v(5392)=Jinv(2,2)*v(5193)+Jinv(2,3)*v(5212)+Jinv(2,4)*v(5250)+Jinv(2,6)*v(5269)+Jinv(2,5)*v(5288)-Jinv(2,1)*v(5307)
v(5380)=Jinv(2,2)*v(5191)+Jinv(2,3)*v(5210)+Jinv(2,4)*v(5248)+Jinv(2,6)*v(5267)+Jinv(2,5)*v(5286)-Jinv(2,1)*v(5306)
v(5368)=Jinv(2,2)*v(5189)+Jinv(2,3)*v(5208)+Jinv(2,4)*v(5246)+Jinv(2,6)*v(5265)+Jinv(2,5)*v(5284)-Jinv(2,1)*v(5305)
v(5356)=Jinv(2,2)*v(5187)+Jinv(2,3)*v(5206)+Jinv(2,4)*v(5244)+Jinv(2,6)*v(5263)+Jinv(2,5)*v(5282)-Jinv(2,1)*v(5304)
v(5344)=Jinv(2,2)*v(5185)+Jinv(2,3)*v(5204)+Jinv(2,4)*v(5242)+Jinv(2,6)*v(5261)+Jinv(2,5)*v(5280)-Jinv(2,1)*v(5303)
v(5332)=Jinv(2,2)*v(5183)+Jinv(2,3)*v(5202)+Jinv(2,4)*v(5240)+Jinv(2,6)*v(5259)+Jinv(2,5)*v(5278)-Jinv(2,1)*v(5302)
v(5320)=Jinv(2,2)*v(5181)+Jinv(2,3)*v(5200)+Jinv(2,4)*v(5238)+Jinv(2,6)*v(5257)+Jinv(2,5)*v(5276)-Jinv(2,1)*v(5300)
v(5417)=Jinv(3,2)*v(5197)+Jinv(3,3)*v(5216)+Jinv(3,4)*v(5254)+Jinv(3,6)*v(5273)+Jinv(3,5)*v(5292)-Jinv(3,1)*v(5309)
v(5405)=Jinv(3,2)*v(5195)+Jinv(3,3)*v(5214)+Jinv(3,4)*v(5252)+Jinv(3,6)*v(5271)+Jinv(3,5)*v(5290)-Jinv(3,1)*v(5308)
v(5393)=Jinv(3,2)*v(5193)+Jinv(3,3)*v(5212)+Jinv(3,4)*v(5250)+Jinv(3,6)*v(5269)+Jinv(3,5)*v(5288)-Jinv(3,1)*v(5307)
v(5381)=Jinv(3,2)*v(5191)+Jinv(3,3)*v(5210)+Jinv(3,4)*v(5248)+Jinv(3,6)*v(5267)+Jinv(3,5)*v(5286)-Jinv(3,1)*v(5306)
v(5369)=Jinv(3,2)*v(5189)+Jinv(3,3)*v(5208)+Jinv(3,4)*v(5246)+Jinv(3,6)*v(5265)+Jinv(3,5)*v(5284)-Jinv(3,1)*v(5305)
v(5357)=Jinv(3,2)*v(5187)+Jinv(3,3)*v(5206)+Jinv(3,4)*v(5244)+Jinv(3,6)*v(5263)+Jinv(3,5)*v(5282)-Jinv(3,1)*v(5304)
v(5345)=Jinv(3,2)*v(5185)+Jinv(3,3)*v(5204)+Jinv(3,4)*v(5242)+Jinv(3,6)*v(5261)+Jinv(3,5)*v(5280)-Jinv(3,1)*v(5303)
v(5333)=Jinv(3,2)*v(5183)+Jinv(3,3)*v(5202)+Jinv(3,4)*v(5240)+Jinv(3,6)*v(5259)+Jinv(3,5)*v(5278)-Jinv(3,1)*v(5302)
v(5321)=Jinv(3,2)*v(5181)+Jinv(3,3)*v(5200)+Jinv(3,4)*v(5238)+Jinv(3,6)*v(5257)+Jinv(3,5)*v(5276)-Jinv(3,1)*v(5300)
v(5418)=Jinv(4,2)*v(5197)+Jinv(4,3)*v(5216)+Jinv(4,4)*v(5254)+Jinv(4,6)*v(5273)+Jinv(4,5)*v(5292)-Jinv(4,1)*v(5309)
v(5406)=Jinv(4,2)*v(5195)+Jinv(4,3)*v(5214)+Jinv(4,4)*v(5252)+Jinv(4,6)*v(5271)+Jinv(4,5)*v(5290)-Jinv(4,1)*v(5308)
v(5394)=Jinv(4,2)*v(5193)+Jinv(4,3)*v(5212)+Jinv(4,4)*v(5250)+Jinv(4,6)*v(5269)+Jinv(4,5)*v(5288)-Jinv(4,1)*v(5307)
v(5382)=Jinv(4,2)*v(5191)+Jinv(4,3)*v(5210)+Jinv(4,4)*v(5248)+Jinv(4,6)*v(5267)+Jinv(4,5)*v(5286)-Jinv(4,1)*v(5306)
v(5370)=Jinv(4,2)*v(5189)+Jinv(4,3)*v(5208)+Jinv(4,4)*v(5246)+Jinv(4,6)*v(5265)+Jinv(4,5)*v(5284)-Jinv(4,1)*v(5305)
v(5358)=Jinv(4,2)*v(5187)+Jinv(4,3)*v(5206)+Jinv(4,4)*v(5244)+Jinv(4,6)*v(5263)+Jinv(4,5)*v(5282)-Jinv(4,1)*v(5304)
v(5346)=Jinv(4,2)*v(5185)+Jinv(4,3)*v(5204)+Jinv(4,4)*v(5242)+Jinv(4,6)*v(5261)+Jinv(4,5)*v(5280)-Jinv(4,1)*v(5303)
v(5334)=Jinv(4,2)*v(5183)+Jinv(4,3)*v(5202)+Jinv(4,4)*v(5240)+Jinv(4,6)*v(5259)+Jinv(4,5)*v(5278)-Jinv(4,1)*v(5302)
v(5322)=Jinv(4,2)*v(5181)+Jinv(4,3)*v(5200)+Jinv(4,4)*v(5238)+Jinv(4,6)*v(5257)+Jinv(4,5)*v(5276)-Jinv(4,1)*v(5300)
v(5419)=Jinv(5,2)*v(5197)+Jinv(5,3)*v(5216)+Jinv(5,4)*v(5254)+Jinv(5,6)*v(5273)+Jinv(5,5)*v(5292)-Jinv(5,1)*v(5309)
v(5407)=Jinv(5,2)*v(5195)+Jinv(5,3)*v(5214)+Jinv(5,4)*v(5252)+Jinv(5,6)*v(5271)+Jinv(5,5)*v(5290)-Jinv(5,1)*v(5308)
v(5395)=Jinv(5,2)*v(5193)+Jinv(5,3)*v(5212)+Jinv(5,4)*v(5250)+Jinv(5,6)*v(5269)+Jinv(5,5)*v(5288)-Jinv(5,1)*v(5307)
v(5383)=Jinv(5,2)*v(5191)+Jinv(5,3)*v(5210)+Jinv(5,4)*v(5248)+Jinv(5,6)*v(5267)+Jinv(5,5)*v(5286)-Jinv(5,1)*v(5306)
v(5371)=Jinv(5,2)*v(5189)+Jinv(5,3)*v(5208)+Jinv(5,4)*v(5246)+Jinv(5,6)*v(5265)+Jinv(5,5)*v(5284)-Jinv(5,1)*v(5305)
v(5359)=Jinv(5,2)*v(5187)+Jinv(5,3)*v(5206)+Jinv(5,4)*v(5244)+Jinv(5,6)*v(5263)+Jinv(5,5)*v(5282)-Jinv(5,1)*v(5304)
v(5347)=Jinv(5,2)*v(5185)+Jinv(5,3)*v(5204)+Jinv(5,4)*v(5242)+Jinv(5,6)*v(5261)+Jinv(5,5)*v(5280)-Jinv(5,1)*v(5303)
v(5335)=Jinv(5,2)*v(5183)+Jinv(5,3)*v(5202)+Jinv(5,4)*v(5240)+Jinv(5,6)*v(5259)+Jinv(5,5)*v(5278)-Jinv(5,1)*v(5302)
v(5323)=Jinv(5,2)*v(5181)+Jinv(5,3)*v(5200)+Jinv(5,4)*v(5238)+Jinv(5,6)*v(5257)+Jinv(5,5)*v(5276)-Jinv(5,1)*v(5300)
v(5420)=Jinv(6,2)*v(5197)+Jinv(6,3)*v(5216)+Jinv(6,4)*v(5254)+Jinv(6,6)*v(5273)+Jinv(6,5)*v(5292)-Jinv(6,1)*v(5309)
v(5408)=Jinv(6,2)*v(5195)+Jinv(6,3)*v(5214)+Jinv(6,4)*v(5252)+Jinv(6,6)*v(5271)+Jinv(6,5)*v(5290)-Jinv(6,1)*v(5308)
v(5396)=Jinv(6,2)*v(5193)+Jinv(6,3)*v(5212)+Jinv(6,4)*v(5250)+Jinv(6,6)*v(5269)+Jinv(6,5)*v(5288)-Jinv(6,1)*v(5307)
v(5384)=Jinv(6,2)*v(5191)+Jinv(6,3)*v(5210)+Jinv(6,4)*v(5248)+Jinv(6,6)*v(5267)+Jinv(6,5)*v(5286)-Jinv(6,1)*v(5306)
v(5372)=Jinv(6,2)*v(5189)+Jinv(6,3)*v(5208)+Jinv(6,4)*v(5246)+Jinv(6,6)*v(5265)+Jinv(6,5)*v(5284)-Jinv(6,1)*v(5305)
v(5360)=Jinv(6,2)*v(5187)+Jinv(6,3)*v(5206)+Jinv(6,4)*v(5244)+Jinv(6,6)*v(5263)+Jinv(6,5)*v(5282)-Jinv(6,1)*v(5304)
v(5348)=Jinv(6,2)*v(5185)+Jinv(6,3)*v(5204)+Jinv(6,4)*v(5242)+Jinv(6,6)*v(5261)+Jinv(6,5)*v(5280)-Jinv(6,1)*v(5303)
v(5336)=Jinv(6,2)*v(5183)+Jinv(6,3)*v(5202)+Jinv(6,4)*v(5240)+Jinv(6,6)*v(5259)+Jinv(6,5)*v(5278)-Jinv(6,1)*v(5302)
v(5324)=Jinv(6,2)*v(5181)+Jinv(6,3)*v(5200)+Jinv(6,4)*v(5238)+Jinv(6,6)*v(5257)+Jinv(6,5)*v(5276)-Jinv(6,1)*v(5300)
v(5421)=Jinv(12,2)*v(5197)+Jinv(12,3)*v(5216)+Jinv(12,4)*v(5254)+Jinv(12,6)*v(5273)+Jinv(12,5)*v(5292)-Jinv(12,1)*v&
&(5309)
v(5409)=Jinv(12,2)*v(5195)+Jinv(12,3)*v(5214)+Jinv(12,4)*v(5252)+Jinv(12,6)*v(5271)+Jinv(12,5)*v(5290)-Jinv(12,1)*v&
&(5308)
v(5397)=Jinv(12,2)*v(5193)+Jinv(12,3)*v(5212)+Jinv(12,4)*v(5250)+Jinv(12,6)*v(5269)+Jinv(12,5)*v(5288)-Jinv(12,1)*v&
&(5307)
v(5385)=Jinv(12,2)*v(5191)+Jinv(12,3)*v(5210)+Jinv(12,4)*v(5248)+Jinv(12,6)*v(5267)+Jinv(12,5)*v(5286)-Jinv(12,1)*v&
&(5306)
v(5373)=Jinv(12,2)*v(5189)+Jinv(12,3)*v(5208)+Jinv(12,4)*v(5246)+Jinv(12,6)*v(5265)+Jinv(12,5)*v(5284)-Jinv(12,1)*v&
&(5305)
v(5361)=Jinv(12,2)*v(5187)+Jinv(12,3)*v(5206)+Jinv(12,4)*v(5244)+Jinv(12,6)*v(5263)+Jinv(12,5)*v(5282)-Jinv(12,1)*v&
&(5304)
v(5349)=Jinv(12,2)*v(5185)+Jinv(12,3)*v(5204)+Jinv(12,4)*v(5242)+Jinv(12,6)*v(5261)+Jinv(12,5)*v(5280)-Jinv(12,1)*v&
&(5303)
v(5337)=Jinv(12,2)*v(5183)+Jinv(12,3)*v(5202)+Jinv(12,4)*v(5240)+Jinv(12,6)*v(5259)+Jinv(12,5)*v(5278)-Jinv(12,1)*v&
&(5302)
v(5325)=Jinv(12,2)*v(5181)+Jinv(12,3)*v(5200)+Jinv(12,4)*v(5238)+Jinv(12,6)*v(5257)+Jinv(12,5)*v(5276)-Jinv(12,1)*v&
&(5300)
v(5422)=Jinv(13,2)*v(5197)+Jinv(13,3)*v(5216)+Jinv(13,4)*v(5254)+Jinv(13,6)*v(5273)+Jinv(13,5)*v(5292)-Jinv(13,1)*v&
&(5309)
v(5410)=Jinv(13,2)*v(5195)+Jinv(13,3)*v(5214)+Jinv(13,4)*v(5252)+Jinv(13,6)*v(5271)+Jinv(13,5)*v(5290)-Jinv(13,1)*v&
&(5308)
v(5398)=Jinv(13,2)*v(5193)+Jinv(13,3)*v(5212)+Jinv(13,4)*v(5250)+Jinv(13,6)*v(5269)+Jinv(13,5)*v(5288)-Jinv(13,1)*v&
&(5307)
v(5386)=Jinv(13,2)*v(5191)+Jinv(13,3)*v(5210)+Jinv(13,4)*v(5248)+Jinv(13,6)*v(5267)+Jinv(13,5)*v(5286)-Jinv(13,1)*v&
&(5306)
v(5374)=Jinv(13,2)*v(5189)+Jinv(13,3)*v(5208)+Jinv(13,4)*v(5246)+Jinv(13,6)*v(5265)+Jinv(13,5)*v(5284)-Jinv(13,1)*v&
&(5305)
v(5362)=Jinv(13,2)*v(5187)+Jinv(13,3)*v(5206)+Jinv(13,4)*v(5244)+Jinv(13,6)*v(5263)+Jinv(13,5)*v(5282)-Jinv(13,1)*v&
&(5304)
v(5350)=Jinv(13,2)*v(5185)+Jinv(13,3)*v(5204)+Jinv(13,4)*v(5242)+Jinv(13,6)*v(5261)+Jinv(13,5)*v(5280)-Jinv(13,1)*v&
&(5303)
v(5338)=Jinv(13,2)*v(5183)+Jinv(13,3)*v(5202)+Jinv(13,4)*v(5240)+Jinv(13,6)*v(5259)+Jinv(13,5)*v(5278)-Jinv(13,1)*v&
&(5302)
v(5326)=Jinv(13,2)*v(5181)+Jinv(13,3)*v(5200)+Jinv(13,4)*v(5238)+Jinv(13,6)*v(5257)+Jinv(13,5)*v(5276)-Jinv(13,1)*v&
&(5300)
v(5423)=Jinv(14,2)*v(5197)+Jinv(14,3)*v(5216)+Jinv(14,4)*v(5254)+Jinv(14,6)*v(5273)+Jinv(14,5)*v(5292)-Jinv(14,1)*v&
&(5309)
v(5411)=Jinv(14,2)*v(5195)+Jinv(14,3)*v(5214)+Jinv(14,4)*v(5252)+Jinv(14,6)*v(5271)+Jinv(14,5)*v(5290)-Jinv(14,1)*v&
&(5308)
v(5399)=Jinv(14,2)*v(5193)+Jinv(14,3)*v(5212)+Jinv(14,4)*v(5250)+Jinv(14,6)*v(5269)+Jinv(14,5)*v(5288)-Jinv(14,1)*v&
&(5307)
v(5387)=Jinv(14,2)*v(5191)+Jinv(14,3)*v(5210)+Jinv(14,4)*v(5248)+Jinv(14,6)*v(5267)+Jinv(14,5)*v(5286)-Jinv(14,1)*v&
&(5306)
v(5375)=Jinv(14,2)*v(5189)+Jinv(14,3)*v(5208)+Jinv(14,4)*v(5246)+Jinv(14,6)*v(5265)+Jinv(14,5)*v(5284)-Jinv(14,1)*v&
&(5305)
v(5363)=Jinv(14,2)*v(5187)+Jinv(14,3)*v(5206)+Jinv(14,4)*v(5244)+Jinv(14,6)*v(5263)+Jinv(14,5)*v(5282)-Jinv(14,1)*v&
&(5304)
v(5351)=Jinv(14,2)*v(5185)+Jinv(14,3)*v(5204)+Jinv(14,4)*v(5242)+Jinv(14,6)*v(5261)+Jinv(14,5)*v(5280)-Jinv(14,1)*v&
&(5303)
v(5339)=Jinv(14,2)*v(5183)+Jinv(14,3)*v(5202)+Jinv(14,4)*v(5240)+Jinv(14,6)*v(5259)+Jinv(14,5)*v(5278)-Jinv(14,1)*v&
&(5302)
v(5327)=Jinv(14,2)*v(5181)+Jinv(14,3)*v(5200)+Jinv(14,4)*v(5238)+Jinv(14,6)*v(5257)+Jinv(14,5)*v(5276)-Jinv(14,1)*v&
&(5300)
v(5424)=Jinv(15,2)*v(5197)+Jinv(15,3)*v(5216)+Jinv(15,4)*v(5254)+Jinv(15,6)*v(5273)+Jinv(15,5)*v(5292)-Jinv(15,1)*v&
&(5309)
v(5412)=Jinv(15,2)*v(5195)+Jinv(15,3)*v(5214)+Jinv(15,4)*v(5252)+Jinv(15,6)*v(5271)+Jinv(15,5)*v(5290)-Jinv(15,1)*v&
&(5308)
v(5400)=Jinv(15,2)*v(5193)+Jinv(15,3)*v(5212)+Jinv(15,4)*v(5250)+Jinv(15,6)*v(5269)+Jinv(15,5)*v(5288)-Jinv(15,1)*v&
&(5307)
v(5388)=Jinv(15,2)*v(5191)+Jinv(15,3)*v(5210)+Jinv(15,4)*v(5248)+Jinv(15,6)*v(5267)+Jinv(15,5)*v(5286)-Jinv(15,1)*v&
&(5306)
v(5376)=Jinv(15,2)*v(5189)+Jinv(15,3)*v(5208)+Jinv(15,4)*v(5246)+Jinv(15,6)*v(5265)+Jinv(15,5)*v(5284)-Jinv(15,1)*v&
&(5305)
v(5364)=Jinv(15,2)*v(5187)+Jinv(15,3)*v(5206)+Jinv(15,4)*v(5244)+Jinv(15,6)*v(5263)+Jinv(15,5)*v(5282)-Jinv(15,1)*v&
&(5304)
v(5352)=Jinv(15,2)*v(5185)+Jinv(15,3)*v(5204)+Jinv(15,4)*v(5242)+Jinv(15,6)*v(5261)+Jinv(15,5)*v(5280)-Jinv(15,1)*v&
&(5303)
v(5340)=Jinv(15,2)*v(5183)+Jinv(15,3)*v(5202)+Jinv(15,4)*v(5240)+Jinv(15,6)*v(5259)+Jinv(15,5)*v(5278)-Jinv(15,1)*v&
&(5302)
v(5328)=Jinv(15,2)*v(5181)+Jinv(15,3)*v(5200)+Jinv(15,4)*v(5238)+Jinv(15,6)*v(5257)+Jinv(15,5)*v(5276)-Jinv(15,1)*v&
&(5300)
v(5425)=Jinv(16,2)*v(5197)+Jinv(16,3)*v(5216)+Jinv(16,4)*v(5254)+Jinv(16,6)*v(5273)+Jinv(16,5)*v(5292)-Jinv(16,1)*v&
&(5309)
v(5413)=Jinv(16,2)*v(5195)+Jinv(16,3)*v(5214)+Jinv(16,4)*v(5252)+Jinv(16,6)*v(5271)+Jinv(16,5)*v(5290)-Jinv(16,1)*v&
&(5308)
v(5401)=Jinv(16,2)*v(5193)+Jinv(16,3)*v(5212)+Jinv(16,4)*v(5250)+Jinv(16,6)*v(5269)+Jinv(16,5)*v(5288)-Jinv(16,1)*v&
&(5307)
v(5389)=Jinv(16,2)*v(5191)+Jinv(16,3)*v(5210)+Jinv(16,4)*v(5248)+Jinv(16,6)*v(5267)+Jinv(16,5)*v(5286)-Jinv(16,1)*v&
&(5306)
v(5377)=Jinv(16,2)*v(5189)+Jinv(16,3)*v(5208)+Jinv(16,4)*v(5246)+Jinv(16,6)*v(5265)+Jinv(16,5)*v(5284)-Jinv(16,1)*v&
&(5305)
v(5365)=Jinv(16,2)*v(5187)+Jinv(16,3)*v(5206)+Jinv(16,4)*v(5244)+Jinv(16,6)*v(5263)+Jinv(16,5)*v(5282)-Jinv(16,1)*v&
&(5304)
v(5353)=Jinv(16,2)*v(5185)+Jinv(16,3)*v(5204)+Jinv(16,4)*v(5242)+Jinv(16,6)*v(5261)+Jinv(16,5)*v(5280)-Jinv(16,1)*v&
&(5303)
v(5341)=Jinv(16,2)*v(5183)+Jinv(16,3)*v(5202)+Jinv(16,4)*v(5240)+Jinv(16,6)*v(5259)+Jinv(16,5)*v(5278)-Jinv(16,1)*v&
&(5302)
v(5329)=Jinv(16,2)*v(5181)+Jinv(16,3)*v(5200)+Jinv(16,4)*v(5238)+Jinv(16,6)*v(5257)+Jinv(16,5)*v(5276)-Jinv(16,1)*v&
&(5300)
v(4044)=v(303)*v(3934)+v(297)*v(3978)+v(312)*v(3989)+v(3394)*v(960)+v(3427)*v(961)+v(3361)*v(962)
v(4045)=v(298)*v(3956)+v(307)*v(4022)+v(313)*v(4033)+v(3372)*v(952)+v(3438)*v(953)+v(3405)*v(954)
v(4046)=v(314)*v(3945)+v(299)*v(4000)+v(311)*v(4011)+v(3449)*v(956)+v(3416)*v(957)+v(3383)*v(958)
v(4047)=v(303)*v(3956)+v(312)*v(4022)+v(297)*v(4033)+v(3394)*v(952)+v(3361)*v(953)+v(3427)*v(954)
v(4048)=v(298)*v(3945)+v(307)*v(4000)+v(313)*v(4011)+v(3372)*v(956)+v(3438)*v(957)+v(3405)*v(958)
v(4049)=v(314)*v(3934)+v(311)*v(3978)+v(299)*v(3989)+v(3449)*v(960)+v(3383)*v(961)+v(3416)*v(962)
v(4050)=v(303)*v(3935)+v(297)*v(3979)+v(312)*v(3990)+v(3395)*v(960)+v(3428)*v(961)+v(3362)*v(962)
v(4051)=v(298)*v(3957)+v(307)*v(4023)+v(313)*v(4034)+v(3373)*v(952)+v(3439)*v(953)+v(3406)*v(954)
v(4052)=v(314)*v(3946)+v(299)*v(4001)+v(311)*v(4012)+v(3450)*v(956)+v(3417)*v(957)+v(3384)*v(958)
v(4053)=v(303)*v(3957)+v(312)*v(4023)+v(297)*v(4034)+v(3395)*v(952)+v(3362)*v(953)+v(3428)*v(954)
v(4054)=v(298)*v(3946)+v(307)*v(4001)+v(313)*v(4012)+v(3373)*v(956)+v(3439)*v(957)+v(3406)*v(958)
v(4055)=v(314)*v(3935)+v(311)*v(3979)+v(299)*v(3990)+v(3450)*v(960)+v(3384)*v(961)+v(3417)*v(962)
v(4056)=v(303)*v(3936)+v(297)*v(3980)+v(312)*v(3991)+v(3396)*v(960)+v(3429)*v(961)+v(3363)*v(962)
v(4057)=v(298)*v(3958)+v(307)*v(4024)+v(313)*v(4035)+v(3374)*v(952)+v(3440)*v(953)+v(3407)*v(954)
v(4058)=v(314)*v(3947)+v(299)*v(4002)+v(311)*v(4013)+v(3451)*v(956)+v(3418)*v(957)+v(3385)*v(958)
v(4059)=v(303)*v(3958)+v(312)*v(4024)+v(297)*v(4035)+v(3396)*v(952)+v(3363)*v(953)+v(3429)*v(954)
v(4060)=v(298)*v(3947)+v(307)*v(4002)+v(313)*v(4013)+v(3374)*v(956)+v(3440)*v(957)+v(3407)*v(958)
v(4061)=v(314)*v(3936)+v(311)*v(3980)+v(299)*v(3991)+v(3451)*v(960)+v(3385)*v(961)+v(3418)*v(962)
v(4062)=v(303)*v(3937)+v(297)*v(3981)+v(312)*v(3992)+v(3397)*v(960)+v(3430)*v(961)+v(3364)*v(962)
v(4063)=v(298)*v(3959)+v(307)*v(4025)+v(313)*v(4036)+v(3375)*v(952)+v(3441)*v(953)+v(3408)*v(954)
v(4064)=v(314)*v(3948)+v(299)*v(4003)+v(311)*v(4014)+v(3452)*v(956)+v(3419)*v(957)+v(3386)*v(958)
v(4065)=v(303)*v(3959)+v(312)*v(4025)+v(297)*v(4036)+v(3397)*v(952)+v(3364)*v(953)+v(3430)*v(954)
v(4066)=v(298)*v(3948)+v(307)*v(4003)+v(313)*v(4014)+v(3375)*v(956)+v(3441)*v(957)+v(3408)*v(958)
v(4067)=v(314)*v(3937)+v(311)*v(3981)+v(299)*v(3992)+v(3452)*v(960)+v(3386)*v(961)+v(3419)*v(962)
v(4068)=v(303)*v(3938)+v(297)*v(3982)+v(312)*v(3993)+v(3398)*v(960)+v(3431)*v(961)+v(3365)*v(962)
v(4069)=v(298)*v(3960)+v(307)*v(4026)+v(313)*v(4037)+v(3376)*v(952)+v(3442)*v(953)+v(3409)*v(954)
v(4070)=v(314)*v(3949)+v(299)*v(4004)+v(311)*v(4015)+v(3453)*v(956)+v(3420)*v(957)+v(3387)*v(958)
v(4071)=v(303)*v(3960)+v(312)*v(4026)+v(297)*v(4037)+v(3398)*v(952)+v(3365)*v(953)+v(3431)*v(954)
v(4072)=v(298)*v(3949)+v(307)*v(4004)+v(313)*v(4015)+v(3376)*v(956)+v(3442)*v(957)+v(3409)*v(958)
v(4073)=v(314)*v(3938)+v(311)*v(3982)+v(299)*v(3993)+v(3453)*v(960)+v(3387)*v(961)+v(3420)*v(962)
v(4074)=v(303)*v(3939)+v(297)*v(3983)+v(312)*v(3994)+v(3399)*v(960)+v(3432)*v(961)+v(3366)*v(962)
v(4075)=v(298)*v(3961)+v(307)*v(4027)+v(313)*v(4038)+v(3377)*v(952)+v(3443)*v(953)+v(3410)*v(954)
v(4076)=v(314)*v(3950)+v(299)*v(4005)+v(311)*v(4016)+v(3454)*v(956)+v(3421)*v(957)+v(3388)*v(958)
v(4077)=v(303)*v(3961)+v(312)*v(4027)+v(297)*v(4038)+v(3399)*v(952)+v(3366)*v(953)+v(3432)*v(954)
v(4078)=v(298)*v(3950)+v(307)*v(4005)+v(313)*v(4016)+v(3377)*v(956)+v(3443)*v(957)+v(3410)*v(958)
v(4079)=v(314)*v(3939)+v(311)*v(3983)+v(299)*v(3994)+v(3454)*v(960)+v(3388)*v(961)+v(3421)*v(962)
v(4080)=v(303)*v(3940)+v(297)*v(3984)+v(312)*v(3995)+v(3400)*v(960)+v(3433)*v(961)+v(3367)*v(962)
v(4081)=v(298)*v(3962)+v(307)*v(4028)+v(313)*v(4039)+v(3378)*v(952)+v(3444)*v(953)+v(3411)*v(954)
v(4082)=v(314)*v(3951)+v(299)*v(4006)+v(311)*v(4017)+v(3455)*v(956)+v(3422)*v(957)+v(3389)*v(958)
v(4083)=v(303)*v(3962)+v(312)*v(4028)+v(297)*v(4039)+v(3400)*v(952)+v(3367)*v(953)+v(3433)*v(954)
v(4084)=v(298)*v(3951)+v(307)*v(4006)+v(313)*v(4017)+v(3378)*v(956)+v(3444)*v(957)+v(3411)*v(958)
v(4085)=v(314)*v(3940)+v(311)*v(3984)+v(299)*v(3995)+v(3455)*v(960)+v(3389)*v(961)+v(3422)*v(962)
v(4086)=v(303)*v(3941)+v(297)*v(3985)+v(312)*v(3996)+v(3401)*v(960)+v(3434)*v(961)+v(3368)*v(962)
v(4087)=v(298)*v(3963)+v(307)*v(4029)+v(313)*v(4040)+v(3379)*v(952)+v(3445)*v(953)+v(3412)*v(954)
v(4088)=v(314)*v(3952)+v(299)*v(4007)+v(311)*v(4018)+v(3456)*v(956)+v(3423)*v(957)+v(3390)*v(958)
v(4089)=v(303)*v(3963)+v(312)*v(4029)+v(297)*v(4040)+v(3401)*v(952)+v(3368)*v(953)+v(3434)*v(954)
v(4090)=v(298)*v(3952)+v(307)*v(4007)+v(313)*v(4018)+v(3379)*v(956)+v(3445)*v(957)+v(3412)*v(958)
v(4091)=v(314)*v(3941)+v(311)*v(3985)+v(299)*v(3996)+v(3456)*v(960)+v(3390)*v(961)+v(3423)*v(962)
v(4092)=v(303)*v(3942)+v(297)*v(3986)+v(312)*v(3997)+v(3402)*v(960)+v(3435)*v(961)+v(3369)*v(962)
v(4093)=v(298)*v(3964)+v(307)*v(4030)+v(313)*v(4041)+v(3380)*v(952)+v(3446)*v(953)+v(3413)*v(954)
v(4094)=v(314)*v(3953)+v(299)*v(4008)+v(311)*v(4019)+v(3457)*v(956)+v(3424)*v(957)+v(3391)*v(958)
v(4095)=v(303)*v(3964)+v(312)*v(4030)+v(297)*v(4041)+v(3402)*v(952)+v(3369)*v(953)+v(3435)*v(954)
v(4096)=v(298)*v(3953)+v(307)*v(4008)+v(313)*v(4019)+v(3380)*v(956)+v(3446)*v(957)+v(3413)*v(958)
v(4097)=v(314)*v(3942)+v(311)*v(3986)+v(299)*v(3997)+v(3457)*v(960)+v(3391)*v(961)+v(3424)*v(962)
v(4098)=v(303)*v(3943)+v(297)*v(3987)+v(312)*v(3998)+v(3403)*v(960)+v(3436)*v(961)+v(3370)*v(962)
v(4099)=v(298)*v(3965)+v(307)*v(4031)+v(313)*v(4042)+v(3381)*v(952)+v(3447)*v(953)+v(3414)*v(954)
v(4100)=v(314)*v(3954)+v(299)*v(4009)+v(311)*v(4020)+v(3458)*v(956)+v(3425)*v(957)+v(3392)*v(958)
v(4101)=v(303)*v(3965)+v(312)*v(4031)+v(297)*v(4042)+v(3403)*v(952)+v(3370)*v(953)+v(3436)*v(954)
v(4102)=v(298)*v(3954)+v(307)*v(4009)+v(313)*v(4020)+v(3381)*v(956)+v(3447)*v(957)+v(3414)*v(958)
v(4103)=v(314)*v(3943)+v(311)*v(3987)+v(299)*v(3998)+v(3458)*v(960)+v(3392)*v(961)+v(3425)*v(962)
v(4104)=v(303)*v(3944)+v(297)*v(3988)+v(312)*v(3999)+v(3404)*v(960)+v(3437)*v(961)+v(3371)*v(962)
v(4105)=v(298)*v(3966)+v(307)*v(4032)+v(313)*v(4043)+v(3382)*v(952)+v(3448)*v(953)+v(3415)*v(954)
v(4106)=v(314)*v(3955)+v(299)*v(4010)+v(311)*v(4021)+v(3459)*v(956)+v(3426)*v(957)+v(3393)*v(958)
v(4107)=v(303)*v(3966)+v(312)*v(4032)+v(297)*v(4043)+v(3404)*v(952)+v(3371)*v(953)+v(3437)*v(954)
v(4108)=v(298)*v(3955)+v(307)*v(4010)+v(313)*v(4021)+v(3382)*v(956)+v(3448)*v(957)+v(3415)*v(958)
v(4109)=v(314)*v(3944)+v(311)*v(3988)+v(299)*v(3999)+v(3459)*v(960)+v(3393)*v(961)+v(3426)*v(962)
v(5310)=v(1469)+v(1372)*v(297)+v(1333)*v(303)+v(1381)*v(312)+v(4044)*v(5319)+v(4050)*v(5320)+v(4056)*v(5321)+v(4062)*v&
&(5322)+v(4068)*v(5323)+v(4074)*v(5324)+v(4080)*v(5325)+v(4086)*v(5326)+v(4092)*v(5327)+v(4098)*v(5328)+v(4104)*v(5329)
v(5311)=v(1373)*v(297)+v(1334)*v(303)+v(1382)*v(312)+v(4044)*v(5331)+v(4050)*v(5332)+v(4056)*v(5333)+v(4062)*v(5334)+v&
&(4068)*v(5335)+v(4074)*v(5336)+v(4080)*v(5337)+v(4086)*v(5338)+v(4092)*v(5339)+v(4098)*v(5340)+v(4104)*v(5341)
v(5312)=v(1374)*v(297)+v(1335)*v(303)+v(1383)*v(312)+v(4044)*v(5343)+v(4050)*v(5344)+v(4056)*v(5345)+v(4062)*v(5346)+v&
&(4068)*v(5347)+v(4074)*v(5348)+v(4080)*v(5349)+v(4086)*v(5350)+v(4092)*v(5351)+v(4098)*v(5352)+v(4104)*v(5353)
v(5313)=v(1493)+v(1375)*v(297)+v(1336)*v(303)+v(1384)*v(312)+v(4044)*v(5355)+v(4050)*v(5356)+v(4056)*v(5357)+v(4062)*v&
&(5358)+v(4068)*v(5359)+v(4074)*v(5360)+v(4080)*v(5361)+v(4086)*v(5362)+v(4092)*v(5363)+v(4098)*v(5364)+v(4104)*v(5365)
v(5314)=v(1376)*v(297)+v(1337)*v(303)+v(1385)*v(312)+v(4044)*v(5367)+v(4050)*v(5368)+v(4056)*v(5369)+v(4062)*v(5370)+v&
&(4068)*v(5371)+v(4074)*v(5372)+v(4080)*v(5373)+v(4086)*v(5374)+v(4092)*v(5375)+v(4098)*v(5376)+v(4104)*v(5377)
v(5315)=v(1377)*v(297)+v(1338)*v(303)+v(1386)*v(312)+v(4044)*v(5379)+v(4050)*v(5380)+v(4056)*v(5381)+v(4062)*v(5382)+v&
&(4068)*v(5383)+v(4074)*v(5384)+v(4080)*v(5385)+v(4086)*v(5386)+v(4092)*v(5387)+v(4098)*v(5388)+v(4104)*v(5389)
v(5316)=v(1471)+v(1378)*v(297)+v(1339)*v(303)+v(1387)*v(312)+v(4044)*v(5391)+v(4050)*v(5392)+v(4056)*v(5393)+v(4062)*v&
&(5394)+v(4068)*v(5395)+v(4074)*v(5396)+v(4080)*v(5397)+v(4086)*v(5398)+v(4092)*v(5399)+v(4098)*v(5400)+v(4104)*v(5401)
v(5317)=v(1379)*v(297)+v(1340)*v(303)+v(1388)*v(312)+v(4044)*v(5403)+v(4050)*v(5404)+v(4056)*v(5405)+v(4062)*v(5406)+v&
&(4068)*v(5407)+v(4074)*v(5408)+v(4080)*v(5409)+v(4086)*v(5410)+v(4092)*v(5411)+v(4098)*v(5412)+v(4104)*v(5413)
v(5318)=v(1380)*v(297)+v(1341)*v(303)+v(1389)*v(312)+v(4044)*v(5415)+v(4050)*v(5416)+v(4056)*v(5417)+v(4062)*v(5418)+v&
&(4068)*v(5419)+v(4074)*v(5420)+v(4080)*v(5421)+v(4086)*v(5422)+v(4092)*v(5423)+v(4098)*v(5424)+v(4104)*v(5425)
v(5330)=v(1354)*v(298)+v(1414)*v(307)+v(1423)*v(313)+v(4045)*v(5319)+v(4051)*v(5320)+v(4057)*v(5321)+v(4063)*v(5322)+v&
&(4069)*v(5323)+v(4075)*v(5324)+v(4081)*v(5325)+v(4087)*v(5326)+v(4093)*v(5327)+v(4099)*v(5328)+v(4105)*v(5329)
v(5342)=v(1453)+v(1355)*v(298)+v(1415)*v(307)+v(1424)*v(313)+v(4045)*v(5331)+v(4051)*v(5332)+v(4057)*v(5333)+v(4063)*v&
&(5334)+v(4069)*v(5335)+v(4075)*v(5336)+v(4081)*v(5337)+v(4087)*v(5338)+v(4093)*v(5339)+v(4099)*v(5340)+v(4105)*v(5341)
v(5354)=v(1356)*v(298)+v(1416)*v(307)+v(1425)*v(313)+v(4045)*v(5343)+v(4051)*v(5344)+v(4057)*v(5345)+v(4063)*v(5346)+v&
&(4069)*v(5347)+v(4075)*v(5348)+v(4081)*v(5349)+v(4087)*v(5350)+v(4093)*v(5351)+v(4099)*v(5352)+v(4105)*v(5353)
v(5366)=v(1357)*v(298)+v(1417)*v(307)+v(1426)*v(313)+v(4045)*v(5355)+v(4051)*v(5356)+v(4057)*v(5357)+v(4063)*v(5358)+v&
&(4069)*v(5359)+v(4075)*v(5360)+v(4081)*v(5361)+v(4087)*v(5362)+v(4093)*v(5363)+v(4099)*v(5364)+v(4105)*v(5365)
v(5378)=v(1475)+v(1358)*v(298)+v(1418)*v(307)+v(1427)*v(313)+v(4045)*v(5367)+v(4051)*v(5368)+v(4057)*v(5369)+v(4063)*v&
&(5370)+v(4069)*v(5371)+v(4075)*v(5372)+v(4081)*v(5373)+v(4087)*v(5374)+v(4093)*v(5375)+v(4099)*v(5376)+v(4105)*v(5377)
v(5390)=v(1359)*v(298)+v(1419)*v(307)+v(1428)*v(313)+v(4045)*v(5379)+v(4051)*v(5380)+v(4057)*v(5381)+v(4063)*v(5382)+v&
&(4069)*v(5383)+v(4075)*v(5384)+v(4081)*v(5385)+v(4087)*v(5386)+v(4093)*v(5387)+v(4099)*v(5388)+v(4105)*v(5389)
v(5402)=v(1360)*v(298)+v(1420)*v(307)+v(1429)*v(313)+v(4045)*v(5391)+v(4051)*v(5392)+v(4057)*v(5393)+v(4063)*v(5394)+v&
&(4069)*v(5395)+v(4075)*v(5396)+v(4081)*v(5397)+v(4087)*v(5398)+v(4093)*v(5399)+v(4099)*v(5400)+v(4105)*v(5401)
v(5414)=v(1480)+v(1361)*v(298)+v(1421)*v(307)+v(1430)*v(313)+v(4045)*v(5403)+v(4051)*v(5404)+v(4057)*v(5405)+v(4063)*v&
&(5406)+v(4069)*v(5407)+v(4075)*v(5408)+v(4081)*v(5409)+v(4087)*v(5410)+v(4093)*v(5411)+v(4099)*v(5412)+v(4105)*v(5413)
v(5426)=v(1362)*v(298)+v(1422)*v(307)+v(1431)*v(313)+v(4045)*v(5415)+v(4051)*v(5416)+v(4057)*v(5417)+v(4063)*v(5418)+v&
&(4069)*v(5419)+v(4075)*v(5420)+v(4081)*v(5421)+v(4087)*v(5422)+v(4093)*v(5423)+v(4099)*v(5424)+v(4105)*v(5425)
v(5427)=v(1390)*v(299)+v(1402)*v(311)+v(1342)*v(314)+v(4046)*v(5319)+v(4052)*v(5320)+v(4058)*v(5321)+v(4064)*v(5322)+v&
&(4070)*v(5323)+v(4076)*v(5324)+v(4082)*v(5325)+v(4088)*v(5326)+v(4094)*v(5327)+v(4100)*v(5328)+v(4106)*v(5329)
v(5428)=v(1391)*v(299)+v(1403)*v(311)+v(1343)*v(314)+v(4046)*v(5331)+v(4052)*v(5332)+v(4058)*v(5333)+v(4064)*v(5334)+v&
&(4070)*v(5335)+v(4076)*v(5336)+v(4082)*v(5337)+v(4088)*v(5338)+v(4094)*v(5339)+v(4100)*v(5340)+v(4106)*v(5341)
v(5429)=v(1461)+v(1393)*v(299)+v(1405)*v(311)+v(1345)*v(314)+v(4046)*v(5343)+v(4052)*v(5344)+v(4058)*v(5345)+v(4064)*v&
&(5346)+v(4070)*v(5347)+v(4076)*v(5348)+v(4082)*v(5349)+v(4088)*v(5350)+v(4094)*v(5351)+v(4100)*v(5352)+v(4106)*v(5353)
v(5430)=v(1394)*v(299)+v(1406)*v(311)+v(1346)*v(314)+v(4046)*v(5355)+v(4052)*v(5356)+v(4058)*v(5357)+v(4064)*v(5358)+v&
&(4070)*v(5359)+v(4076)*v(5360)+v(4082)*v(5361)+v(4088)*v(5362)+v(4094)*v(5363)+v(4100)*v(5364)+v(4106)*v(5365)
v(5431)=v(1395)*v(299)+v(1407)*v(311)+v(1347)*v(314)+v(4046)*v(5367)+v(4052)*v(5368)+v(4058)*v(5369)+v(4064)*v(5370)+v&
&(4070)*v(5371)+v(4076)*v(5372)+v(4082)*v(5373)+v(4088)*v(5374)+v(4094)*v(5375)+v(4100)*v(5376)+v(4106)*v(5377)
v(5432)=v(1484)+v(1397)*v(299)+v(1409)*v(311)+v(1349)*v(314)+v(4046)*v(5379)+v(4052)*v(5380)+v(4058)*v(5381)+v(4064)*v&
&(5382)+v(4070)*v(5383)+v(4076)*v(5384)+v(4082)*v(5385)+v(4088)*v(5386)+v(4094)*v(5387)+v(4100)*v(5388)+v(4106)*v(5389)
v(5433)=v(1398)*v(299)+v(1410)*v(311)+v(1350)*v(314)+v(4046)*v(5391)+v(4052)*v(5392)+v(4058)*v(5393)+v(4064)*v(5394)+v&
&(4070)*v(5395)+v(4076)*v(5396)+v(4082)*v(5397)+v(4088)*v(5398)+v(4094)*v(5399)+v(4100)*v(5400)+v(4106)*v(5401)
v(5434)=v(1399)*v(299)+v(1411)*v(311)+v(1351)*v(314)+v(4046)*v(5403)+v(4052)*v(5404)+v(4058)*v(5405)+v(4064)*v(5406)+v&
&(4070)*v(5407)+v(4076)*v(5408)+v(4082)*v(5409)+v(4088)*v(5410)+v(4094)*v(5411)+v(4100)*v(5412)+v(4106)*v(5413)
v(5435)=v(1489)+v(1401)*v(299)+v(1413)*v(311)+v(1353)*v(314)+v(4046)*v(5415)+v(4052)*v(5416)+v(4058)*v(5417)+v(4064)*v&
&(5418)+v(4070)*v(5419)+v(4076)*v(5420)+v(4082)*v(5421)+v(4088)*v(5422)+v(4094)*v(5423)+v(4100)*v(5424)+v(4106)*v(5425)
v(5436)=v(1480)+v(1423)*v(297)+v(1354)*v(303)+v(1414)*v(312)+v(4047)*v(5319)+v(4053)*v(5320)+v(4059)*v(5321)+v(4065)*v&
&(5322)+v(4071)*v(5323)+v(4077)*v(5324)+v(4083)*v(5325)+v(4089)*v(5326)+v(4095)*v(5327)+v(4101)*v(5328)+v(4107)*v(5329)
v(5437)=v(1424)*v(297)+v(1355)*v(303)+v(1415)*v(312)+v(4047)*v(5331)+v(4053)*v(5332)+v(4059)*v(5333)+v(4065)*v(5334)+v&
&(4071)*v(5335)+v(4077)*v(5336)+v(4083)*v(5337)+v(4089)*v(5338)+v(4095)*v(5339)+v(4101)*v(5340)+v(4107)*v(5341)
v(5438)=v(1425)*v(297)+v(1356)*v(303)+v(1416)*v(312)+v(4047)*v(5343)+v(4053)*v(5344)+v(4059)*v(5345)+v(4065)*v(5346)+v&
&(4071)*v(5347)+v(4077)*v(5348)+v(4083)*v(5349)+v(4089)*v(5350)+v(4095)*v(5351)+v(4101)*v(5352)+v(4107)*v(5353)
v(5439)=v(1453)+v(1426)*v(297)+v(1357)*v(303)+v(1417)*v(312)+v(4047)*v(5355)+v(4053)*v(5356)+v(4059)*v(5357)+v(4065)*v&
&(5358)+v(4071)*v(5359)+v(4077)*v(5360)+v(4083)*v(5361)+v(4089)*v(5362)+v(4095)*v(5363)+v(4101)*v(5364)+v(4107)*v(5365)
v(5440)=v(1427)*v(297)+v(1358)*v(303)+v(1418)*v(312)+v(4047)*v(5367)+v(4053)*v(5368)+v(4059)*v(5369)+v(4065)*v(5370)+v&
&(4071)*v(5371)+v(4077)*v(5372)+v(4083)*v(5373)+v(4089)*v(5374)+v(4095)*v(5375)+v(4101)*v(5376)+v(4107)*v(5377)
v(5441)=v(1428)*v(297)+v(1359)*v(303)+v(1419)*v(312)+v(4047)*v(5379)+v(4053)*v(5380)+v(4059)*v(5381)+v(4065)*v(5382)+v&
&(4071)*v(5383)+v(4077)*v(5384)+v(4083)*v(5385)+v(4089)*v(5386)+v(4095)*v(5387)+v(4101)*v(5388)+v(4107)*v(5389)
v(5442)=v(1475)+v(1429)*v(297)+v(1360)*v(303)+v(1420)*v(312)+v(4047)*v(5391)+v(4053)*v(5392)+v(4059)*v(5393)+v(4065)*v&
&(5394)+v(4071)*v(5395)+v(4077)*v(5396)+v(4083)*v(5397)+v(4089)*v(5398)+v(4095)*v(5399)+v(4101)*v(5400)+v(4107)*v(5401)
v(5443)=v(1430)*v(297)+v(1361)*v(303)+v(1421)*v(312)+v(4047)*v(5403)+v(4053)*v(5404)+v(4059)*v(5405)+v(4065)*v(5406)+v&
&(4071)*v(5407)+v(4077)*v(5408)+v(4083)*v(5409)+v(4089)*v(5410)+v(4095)*v(5411)+v(4101)*v(5412)+v(4107)*v(5413)
v(5444)=v(1431)*v(297)+v(1362)*v(303)+v(1422)*v(312)+v(4047)*v(5415)+v(4053)*v(5416)+v(4059)*v(5417)+v(4065)*v(5418)+v&
&(4071)*v(5419)+v(4077)*v(5420)+v(4083)*v(5421)+v(4089)*v(5422)+v(4095)*v(5423)+v(4101)*v(5424)+v(4107)*v(5425)
v(5445)=v(1342)*v(298)+v(1390)*v(307)+v(1402)*v(313)+v(4048)*v(5319)+v(4054)*v(5320)+v(4060)*v(5321)+v(4066)*v(5322)+v&
&(4072)*v(5323)+v(4078)*v(5324)+v(4084)*v(5325)+v(4090)*v(5326)+v(4096)*v(5327)+v(4102)*v(5328)+v(4108)*v(5329)
v(5446)=v(1489)+v(1343)*v(298)+v(1391)*v(307)+v(1403)*v(313)+v(4048)*v(5331)+v(4054)*v(5332)+v(4060)*v(5333)+v(4066)*v&
&(5334)+v(4072)*v(5335)+v(4078)*v(5336)+v(4084)*v(5337)+v(4090)*v(5338)+v(4096)*v(5339)+v(4102)*v(5340)+v(4108)*v(5341)
v(5447)=v(1345)*v(298)+v(1393)*v(307)+v(1405)*v(313)+v(4048)*v(5343)+v(4054)*v(5344)+v(4060)*v(5345)+v(4066)*v(5346)+v&
&(4072)*v(5347)+v(4078)*v(5348)+v(4084)*v(5349)+v(4090)*v(5350)+v(4096)*v(5351)+v(4102)*v(5352)+v(4108)*v(5353)
v(5448)=v(1346)*v(298)+v(1394)*v(307)+v(1406)*v(313)+v(4048)*v(5355)+v(4054)*v(5356)+v(4060)*v(5357)+v(4066)*v(5358)+v&
&(4072)*v(5359)+v(4078)*v(5360)+v(4084)*v(5361)+v(4090)*v(5362)+v(4096)*v(5363)+v(4102)*v(5364)+v(4108)*v(5365)
v(5449)=v(1461)+v(1347)*v(298)+v(1395)*v(307)+v(1407)*v(313)+v(4048)*v(5367)+v(4054)*v(5368)+v(4060)*v(5369)+v(4066)*v&
&(5370)+v(4072)*v(5371)+v(4078)*v(5372)+v(4084)*v(5373)+v(4090)*v(5374)+v(4096)*v(5375)+v(4102)*v(5376)+v(4108)*v(5377)
v(5450)=v(1349)*v(298)+v(1397)*v(307)+v(1409)*v(313)+v(4048)*v(5379)+v(4054)*v(5380)+v(4060)*v(5381)+v(4066)*v(5382)+v&
&(4072)*v(5383)+v(4078)*v(5384)+v(4084)*v(5385)+v(4090)*v(5386)+v(4096)*v(5387)+v(4102)*v(5388)+v(4108)*v(5389)
v(5451)=v(1350)*v(298)+v(1398)*v(307)+v(1410)*v(313)+v(4048)*v(5391)+v(4054)*v(5392)+v(4060)*v(5393)+v(4066)*v(5394)+v&
&(4072)*v(5395)+v(4078)*v(5396)+v(4084)*v(5397)+v(4090)*v(5398)+v(4096)*v(5399)+v(4102)*v(5400)+v(4108)*v(5401)
v(5452)=v(1484)+v(1351)*v(298)+v(1399)*v(307)+v(1411)*v(313)+v(4048)*v(5403)+v(4054)*v(5404)+v(4060)*v(5405)+v(4066)*v&
&(5406)+v(4072)*v(5407)+v(4078)*v(5408)+v(4084)*v(5409)+v(4090)*v(5410)+v(4096)*v(5411)+v(4102)*v(5412)+v(4108)*v(5413)
v(5453)=v(1353)*v(298)+v(1401)*v(307)+v(1413)*v(313)+v(4048)*v(5415)+v(4054)*v(5416)+v(4060)*v(5417)+v(4066)*v(5418)+v&
&(4072)*v(5419)+v(4078)*v(5420)+v(4084)*v(5421)+v(4090)*v(5422)+v(4096)*v(5423)+v(4102)*v(5424)+v(4108)*v(5425)
v(5454)=v(1381)*v(299)+v(1372)*v(311)+v(1333)*v(314)+v(4049)*v(5319)+v(4055)*v(5320)+v(4061)*v(5321)+v(4067)*v(5322)+v&
&(4073)*v(5323)+v(4079)*v(5324)+v(4085)*v(5325)+v(4091)*v(5326)+v(4097)*v(5327)+v(4103)*v(5328)+v(4109)*v(5329)
v(5455)=v(1382)*v(299)+v(1373)*v(311)+v(1334)*v(314)+v(4049)*v(5331)+v(4055)*v(5332)+v(4061)*v(5333)+v(4067)*v(5334)+v&
&(4073)*v(5335)+v(4079)*v(5336)+v(4085)*v(5337)+v(4091)*v(5338)+v(4097)*v(5339)+v(4103)*v(5340)+v(4109)*v(5341)
v(5456)=v(1471)+v(1383)*v(299)+v(1374)*v(311)+v(1335)*v(314)+v(4049)*v(5343)+v(4055)*v(5344)+v(4061)*v(5345)+v(4067)*v&
&(5346)+v(4073)*v(5347)+v(4079)*v(5348)+v(4085)*v(5349)+v(4091)*v(5350)+v(4097)*v(5351)+v(4103)*v(5352)+v(4109)*v(5353)
v(5457)=v(1384)*v(299)+v(1375)*v(311)+v(1336)*v(314)+v(4049)*v(5355)+v(4055)*v(5356)+v(4061)*v(5357)+v(4067)*v(5358)+v&
&(4073)*v(5359)+v(4079)*v(5360)+v(4085)*v(5361)+v(4091)*v(5362)+v(4097)*v(5363)+v(4103)*v(5364)+v(4109)*v(5365)
v(5458)=v(1385)*v(299)+v(1376)*v(311)+v(1337)*v(314)+v(4049)*v(5367)+v(4055)*v(5368)+v(4061)*v(5369)+v(4067)*v(5370)+v&
&(4073)*v(5371)+v(4079)*v(5372)+v(4085)*v(5373)+v(4091)*v(5374)+v(4097)*v(5375)+v(4103)*v(5376)+v(4109)*v(5377)
v(5459)=v(1469)+v(1386)*v(299)+v(1377)*v(311)+v(1338)*v(314)+v(4049)*v(5379)+v(4055)*v(5380)+v(4061)*v(5381)+v(4067)*v&
&(5382)+v(4073)*v(5383)+v(4079)*v(5384)+v(4085)*v(5385)+v(4091)*v(5386)+v(4097)*v(5387)+v(4103)*v(5388)+v(4109)*v(5389)
v(5460)=v(1387)*v(299)+v(1378)*v(311)+v(1339)*v(314)+v(4049)*v(5391)+v(4055)*v(5392)+v(4061)*v(5393)+v(4067)*v(5394)+v&
&(4073)*v(5395)+v(4079)*v(5396)+v(4085)*v(5397)+v(4091)*v(5398)+v(4097)*v(5399)+v(4103)*v(5400)+v(4109)*v(5401)
v(5461)=v(1388)*v(299)+v(1379)*v(311)+v(1340)*v(314)+v(4049)*v(5403)+v(4055)*v(5404)+v(4061)*v(5405)+v(4067)*v(5406)+v&
&(4073)*v(5407)+v(4079)*v(5408)+v(4085)*v(5409)+v(4091)*v(5410)+v(4097)*v(5411)+v(4103)*v(5412)+v(4109)*v(5413)
v(5462)=v(1493)+v(1389)*v(299)+v(1380)*v(311)+v(1341)*v(314)+v(4049)*v(5415)+v(4055)*v(5416)+v(4061)*v(5417)+v(4067)*v&
&(5418)+v(4073)*v(5419)+v(4079)*v(5420)+v(4085)*v(5421)+v(4091)*v(5422)+v(4097)*v(5423)+v(4103)*v(5424)+v(4109)*v(5425)
sigma(1)=v(5555)*(v(303)*v(960)+v(312)*v(961)+v(297)*v(962))
sigma(2)=v(5555)*(v(298)*v(952)+v(313)*v(953)+v(307)*v(954))
sigma(3)=v(5555)*(v(314)*v(956)+v(311)*v(957)+v(299)*v(958))
sigma(4)=v(5555)*(v(303)*v(952)+v(297)*v(953)+v(312)*v(954))
sigma(5)=v(5555)*(v(314)*v(960)+v(299)*v(961)+v(311)*v(962))
sigma(6)=v(5555)*(v(298)*v(956)+v(313)*v(957)+v(307)*v(958))
ddsdde(1,1)=(Fnew(1)*v(5310)+Fnew(4)*v(5313)+Fnew(7)*v(5316))*v(5555)
ddsdde(1,2)=(Fnew(2)*v(5311)+Fnew(5)*v(5314)+Fnew(8)*v(5317))*v(5555)
ddsdde(1,3)=(Fnew(3)*v(5312)+Fnew(6)*v(5315)+Fnew(9)*v(5318))*v(5555)
ddsdde(1,4)=2d0*(Fnew(8)*v(5310)+Fnew(4)*v(5311)+Fnew(2)*v(5313)+Fnew(7)*v(5314)+Fnew(5)*v(5316)+Fnew(1)*v(5317))*v&
&(6423)
ddsdde(1,5)=2d0*(Fnew(6)*v(5310)+Fnew(7)*v(5312)+Fnew(9)*v(5313)+Fnew(1)*v(5315)+Fnew(3)*v(5316)+Fnew(4)*v(5318))*v&
&(6423)
ddsdde(1,6)=2d0*(Fnew(9)*v(5311)+Fnew(5)*v(5312)+Fnew(3)*v(5314)+Fnew(8)*v(5315)+Fnew(6)*v(5317)+Fnew(2)*v(5318))*v&
&(6423)
ddsdde(2,1)=(Fnew(1)*v(5330)+Fnew(4)*v(5366)+Fnew(7)*v(5402))*v(5555)
ddsdde(2,2)=(Fnew(2)*v(5342)+Fnew(5)*v(5378)+Fnew(8)*v(5414))*v(5555)
ddsdde(2,3)=(Fnew(3)*v(5354)+Fnew(6)*v(5390)+Fnew(9)*v(5426))*v(5555)
ddsdde(2,4)=2d0*(Fnew(8)*v(5330)+Fnew(4)*v(5342)+Fnew(2)*v(5366)+Fnew(7)*v(5378)+Fnew(5)*v(5402)+Fnew(1)*v(5414))*v&
&(6423)
ddsdde(2,5)=2d0*(Fnew(6)*v(5330)+Fnew(7)*v(5354)+Fnew(9)*v(5366)+Fnew(1)*v(5390)+Fnew(3)*v(5402)+Fnew(4)*v(5426))*v&
&(6423)
ddsdde(2,6)=2d0*(Fnew(9)*v(5342)+Fnew(5)*v(5354)+Fnew(3)*v(5378)+Fnew(8)*v(5390)+Fnew(6)*v(5414)+Fnew(2)*v(5426))*v&
&(6423)
ddsdde(3,1)=(Fnew(1)*v(5427)+Fnew(4)*v(5430)+Fnew(7)*v(5433))*v(5555)
ddsdde(3,2)=(Fnew(2)*v(5428)+Fnew(5)*v(5431)+Fnew(8)*v(5434))*v(5555)
ddsdde(3,3)=(Fnew(3)*v(5429)+Fnew(6)*v(5432)+Fnew(9)*v(5435))*v(5555)
ddsdde(3,4)=2d0*(Fnew(8)*v(5427)+Fnew(4)*v(5428)+Fnew(2)*v(5430)+Fnew(7)*v(5431)+Fnew(5)*v(5433)+Fnew(1)*v(5434))*v&
&(6423)
ddsdde(3,5)=2d0*(Fnew(6)*v(5427)+Fnew(7)*v(5429)+Fnew(9)*v(5430)+Fnew(1)*v(5432)+Fnew(3)*v(5433)+Fnew(4)*v(5435))*v&
&(6423)
ddsdde(3,6)=2d0*(Fnew(9)*v(5428)+Fnew(5)*v(5429)+Fnew(3)*v(5431)+Fnew(8)*v(5432)+Fnew(6)*v(5434)+Fnew(2)*v(5435))*v&
&(6423)
ddsdde(4,1)=(Fnew(1)*v(5436)+Fnew(4)*v(5439)+Fnew(7)*v(5442))*v(5555)
ddsdde(4,2)=(Fnew(2)*v(5437)+Fnew(5)*v(5440)+Fnew(8)*v(5443))*v(5555)
ddsdde(4,3)=(Fnew(3)*v(5438)+Fnew(6)*v(5441)+Fnew(9)*v(5444))*v(5555)
ddsdde(4,4)=2d0*(Fnew(8)*v(5436)+Fnew(4)*v(5437)+Fnew(2)*v(5439)+Fnew(7)*v(5440)+Fnew(5)*v(5442)+Fnew(1)*v(5443))*v&
&(6423)
ddsdde(4,5)=2d0*(Fnew(6)*v(5436)+Fnew(7)*v(5438)+Fnew(9)*v(5439)+Fnew(1)*v(5441)+Fnew(3)*v(5442)+Fnew(4)*v(5444))*v&
&(6423)
ddsdde(4,6)=2d0*(Fnew(9)*v(5437)+Fnew(5)*v(5438)+Fnew(3)*v(5440)+Fnew(8)*v(5441)+Fnew(6)*v(5443)+Fnew(2)*v(5444))*v&
&(6423)
ddsdde(5,1)=(Fnew(1)*v(5454)+Fnew(4)*v(5457)+Fnew(7)*v(5460))*v(5555)
ddsdde(5,2)=(Fnew(2)*v(5455)+Fnew(5)*v(5458)+Fnew(8)*v(5461))*v(5555)
ddsdde(5,3)=(Fnew(3)*v(5456)+Fnew(6)*v(5459)+Fnew(9)*v(5462))*v(5555)
ddsdde(5,4)=2d0*(Fnew(8)*v(5454)+Fnew(4)*v(5455)+Fnew(2)*v(5457)+Fnew(7)*v(5458)+Fnew(5)*v(5460)+Fnew(1)*v(5461))*v&
&(6423)
ddsdde(5,5)=2d0*(Fnew(6)*v(5454)+Fnew(7)*v(5456)+Fnew(9)*v(5457)+Fnew(1)*v(5459)+Fnew(3)*v(5460)+Fnew(4)*v(5462))*v&
&(6423)
ddsdde(5,6)=2d0*(Fnew(9)*v(5455)+Fnew(5)*v(5456)+Fnew(3)*v(5458)+Fnew(8)*v(5459)+Fnew(6)*v(5461)+Fnew(2)*v(5462))*v&
&(6423)
ddsdde(6,1)=(Fnew(1)*v(5445)+Fnew(4)*v(5448)+Fnew(7)*v(5451))*v(5555)
ddsdde(6,2)=(Fnew(2)*v(5446)+Fnew(5)*v(5449)+Fnew(8)*v(5452))*v(5555)
ddsdde(6,3)=(Fnew(3)*v(5447)+Fnew(6)*v(5450)+Fnew(9)*v(5453))*v(5555)
ddsdde(6,4)=2d0*(Fnew(8)*v(5445)+Fnew(4)*v(5446)+Fnew(2)*v(5448)+Fnew(7)*v(5449)+Fnew(5)*v(5451)+Fnew(1)*v(5452))*v&
&(6423)
ddsdde(6,5)=2d0*(Fnew(6)*v(5445)+Fnew(7)*v(5447)+Fnew(9)*v(5448)+Fnew(1)*v(5450)+Fnew(3)*v(5451)+Fnew(4)*v(5453))*v&
&(6423)
ddsdde(6,6)=2d0*(Fnew(9)*v(5446)+Fnew(5)*v(5447)+Fnew(3)*v(5449)+Fnew(8)*v(5450)+Fnew(6)*v(5452)+Fnew(2)*v(5453))*v&
&(6423)
statevNew(1)=(-1d0)+v(248)
statevNew(2)=(-1d0)+v(266)
statevNew(3)=(-1d0)+v(286)
statevNew(4)=v(288)
statevNew(5)=v(290)
statevNew(6)=v(292)
statevNew(7)=v(293)
statevNew(8)=v(294)
statevNew(9)=v(295)
statevNew(10)=statev(10)+v(5541)
statevNew(11)=(-1d0)+v(408)
statevNew(12)=(-1d0)+v(426)
statevNew(13)=(-1d0)+v(446)
statevNew(14)=v(448)
statevNew(15)=v(450)
statevNew(16)=v(452)
statevNew(17)=v(453)
statevNew(18)=v(454)
statevNew(19)=v(455)
statevNew(20)=(-1d0)+v(471)
statevNew(21)=(-1d0)+v(489)
statevNew(22)=(-1d0)+v(509)
statevNew(23)=v(511)
statevNew(24)=v(513)
statevNew(25)=v(515)
statevNew(26)=v(516)
statevNew(27)=v(517)
statevNew(28)=v(518)
statevNew(29)=v(125)
statevNew(30)=v(128)
statevNew(31)=v(130)
statevNew(32)=v(132)
statevNew(33)=v(134)
statevNew(34)=v(136)
statevNew(35)=v(138)
statevNew(36)=v(140)
statevNew(37)=v(141)
statevNew(38)=v(142)
statevNew(39)=v(143)
statevNew(40)=v(145)
statevNew(41)=v(146)
statevNew(42)=v(147)
statevNew(43)=v(148)
statevNew(44)=v(149)
statevNew(45)=v(150)
statevNew(46)=v(151)
statevNew(47)=v(152)
statevNew(48)=v(153)
statevNew(49)=v(154)
statevNew(50)=(-1d0)+statev(57)*v(602)+statev(55)*v(638)+v(5534)*v(640)
statevNew(51)=(-1d0)+statev(53)*v(602)+statev(58)*v(637)+v(5535)*v(642)
statevNew(52)=(-1d0)+statev(54)*v(637)+statev(56)*v(638)+v(5536)*v(644)
statevNew(53)=v(5535)*v(602)+statev(58)*v(638)+statev(53)*v(640)
statevNew(54)=statev(56)*v(602)+v(5536)*v(637)+statev(54)*v(642)
statevNew(55)=statev(57)*v(637)+v(5534)*v(638)+statev(55)*v(644)
statevNew(56)=statev(54)*v(602)+v(5536)*v(638)+statev(56)*v(640)
statevNew(57)=v(5534)*v(602)+statev(55)*v(637)+statev(57)*v(642)
statevNew(58)=v(5535)*v(637)+statev(53)*v(638)+statev(58)*v(644)
END SUBROUTINE
end module acegen_mod
|
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|
!
! CalculiX - A 3-dimensional finite element program
! Copyright (C) 1998-2021 Guido Dhondt
!
! This program is free software; you can redistribute it and/or
! modify it under the terms of the GNU General Public License as
! published by the Free Software Foundation(version 2);
!
!
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with this program; if not, write to the Free Software
! Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
!
subroutine extrapolateshell(yi,yn,ipkon,inum,kon,lakon,nfield,nk,
& ne,mi,ndim,orab,ielorien,co,iorienloc,cflag,
& ielmat,thicke,ielprop,prop,iflag)
!
! extrapolates field values at the integration points to the
! nodes for user-defined shell elements
!
! iflag=-1: NEG-position
! iflag=0: MID-position
! iflag=1: POS-position
!
implicit none
!
character*1 cflag
character*8 lakon(*)
!
integer ipkon(*),inum(*),kon(*),mi(*),ne,iorienloc,nfield,nk,i,j,
& ndim,ielorien(mi(3),*),ielmat(mi(3),*),ielprop(*),iflag
!
real*8 yi(ndim,mi(1),*),yn(nfield,*),orab(7,*),co(3,*),prop(*),
& thicke(mi(3),*)
!
do i=1,nk
inum(i)=0
enddo
!
do i=1,nk
do j=1,nfield
yn(j,i)=0.d0
enddo
enddo
!
do i=1,ne
!
if(ipkon(i).lt.0) cycle
!
if(lakon(i)(1:4).eq.'US45') then
call extrapolateshell_us45(yi,yn,ipkon,inum,kon,lakon,
& nfield,nk,ne,mi,ndim,orab,ielorien,co,iorienloc,cflag,
& ielmat,thicke,ielprop,prop,i,iflag)
elseif(lakon(i)(1:3).eq.'US3') then
call extrapolateshell_us3(yi,yn,ipkon,inum,kon,lakon,
& nfield,nk,ne,mi,ndim,orab,ielorien,co,iorienloc,cflag,
& ielmat,thicke,ielprop,prop,i,iflag)
else
cycle
endif
!
enddo
!
! taking the mean of nodal contributions coming from different
! elements having the node in common
!
do i=1,nk
if(inum(i).gt.0) then
do j=1,nfield
yn(j,i)=yn(j,i)/inum(i)
enddo
endif
enddo
!
return
end
|
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|
from numpy.core.fromnumeric import transpose
import torch
import torch.nn as nn
import torchvision.models
import torchvision.transforms as tranforms
import cv2
from PIL import Image
import numpy as np
from torchvision.transforms import transforms
import random
import os
gaussain_t = transforms.Compose([
transforms.ToPILImage(),
transforms.GaussianBlur(kernel_size=51, sigma=10),
])
inpainting_t = transforms.Compose([
transforms.ToPILImage(),
])
toPIL_t = transforms.Compose([
transforms.ToPILImage(),
])
toTensor = tranforms.Compose([
tranforms.ToTensor(),
])
def preprocessing(imgs, datadir, using_mask=True):
mask_path = datadir + '/images_8_mask2'
mask_imgs = [os.path.join(mask_path, f) for f in sorted(os.listdir(mask_path))]
masks = []
i_train = [i for i in range(imgs.shape[0])]
for i in i_train:
if(i % 8 == 0):
i_train.remove(i)
#i_train.remove(1)
for i in range(imgs.shape[0]):
image = torch.Tensor(imgs[i])
image = image.permute((2,0,1))
mask = torch.ones_like(image)
if i in i_train:
if using_mask == True:
m_img = Image.open(mask_imgs[i])
m_img = toTensor(m_img).cuda()
mask = m_img[:3, :, :]
image = image * mask
image = toPIL_t(image)
else:
mask = torch.ones_like(image)
mask_h, mask_w = int(image.shape[1] / 4), int(image.shape[2] / 4)
x = random.randint(0, int(image.shape[1] - image.shape[1]/4))
y = random.randint(0, int(image.shape[2] - image.shape[2]/4))
mask[:, x:x+mask_h, y:mask_w+y] = 0
image = image * mask
image = toPIL_t(image)
else:
print("Not in training set")
image = toPIL_t(image)
reverse_t = transforms.ToTensor()
print('save png')
image.save('./preprocess/preprcessed_{}.png'.format(i))
image = reverse_t(image).permute((1, 2, 0)).numpy()
print(image.shape)
imgs[i] = image
masks.append(torch.Tensor(mask).unsqueeze(0))
masks = torch.cat(masks, 0).permute(0, 2, 3, 1)
return imgs, masks
|
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|
module ThreadsXBenchmarks
import JSON
using ArgCheck: @argcheck
using BangBang
using InteractiveUtils: versioninfo
using Logging: current_logger
using ThreadsX
const setup_terminalloggers = """
let Logging =
Base.require(Base.PkgId(Base.UUID(0x56ddb016857b54e1b83ddb4d58db5568), "Logging")),
TerminalLoggers = Base.require(Base.PkgId(
Base.UUID(0x5d786b921e484d6f91516b4477ca9bed),
"TerminalLoggers",
))
Logging.global_logger(TerminalLoggers.TerminalLogger())
end
"""
is_using_terminal_logger() =
Base.PkgId(parentmodule(typeof(current_logger()))).uuid ==
Base.UUID(0x5d786b921e484d6f91516b4477ca9bed)
function runscript(
script::AbstractString,
ARGS::AbstractVector{<:AbstractString};
env = nothing,
)
@argcheck isfile(script)
code = """
$(Base.load_path_setup_code())
$(is_using_terminal_logger() ? setup_terminalloggers : "")
let script = popfirst!(ARGS)
@eval Base PROGRAM_FILE = \$script
include(script)
end
"""
cmd = `$(Base.julia_cmd()) --startup-file=no`
if Base.have_color
cmd = `$cmd --color=yes`
end
cmd = `$cmd -e $code $script $ARGS`
if env !== nothing
fullenv = copy(ENV)
for (k, v) in env
fullenv[k] = convert(String, v)
end
cmd = setenv(cmd, fullenv)
end
run(cmd)
end
function physical_cores()
lines = split(read(`lscpu --parse`, String), "\n", keepempty = false)
rows = [map(strip, split(ln, ",")) for ln in lines if !startswith(ln, "#")]
return length(Set(r[2] for r in rows))
end
function run_nthreads(
outdir::AbstractString;
nthreads_range::AbstractVector{<:Integer} = 1:physical_cores(),
)
@info "Measuring scaling with respect to number of threads"
mkpath(outdir)
open(versioninfo, joinpath(outdir, "versioninfo.txt"), write = true)
scriptdir = joinpath(@__DIR__, "scripts")
@info "Running: `scaling_nthreads_baseline.jl`"
runscript(
joinpath(scriptdir, "scaling_nthreads_baseline.jl"),
[joinpath(outdir, "scaling_nthreads_baseline")],
env = ["JULIA_NUM_THREADS" => "1"],
)
for nthreads in nthreads_range
outputstem = joinpath(outdir, "scaling_nthreads-$nthreads")
@info "Running: `scaling_nthreads_target.jl` with $nthreads thread(s)"
runscript(
joinpath(scriptdir, "scaling_nthreads_target.jl"),
[outputstem];
env = ["JULIA_NUM_THREADS" => string(nthreads)],
)
end
return
end
function run_datasize(outdir::AbstractString; nthreads::Integer = physical_cores())
@info "Measuring scaling with respect to data size"
mkpath(outdir)
open(versioninfo, joinpath(outdir, "versioninfo.txt"), write = true)
@info "Running: `scaling_datasize.jl`"
scriptdir = joinpath(@__DIR__, "scripts")
runscript(
joinpath(scriptdir, "scaling_datasize.jl"),
[joinpath(outdir, "scaling_datasize")],
env = ["JULIA_NUM_THREADS" => string(nthreads)],
)
return
end
function run_all(
outdir::AbstractString;
nthreads_range::AbstractVector{<:Integer} = 1:physical_cores(),
default_nthreads::Integer = maximum(nthreads_range),
)
run_nthreads(outdir; nthreads_range = nthreads_range)
# run_datasize(outdir; nthreads = default_nthreads)
return
end
include("loading.jl")
end # module
|
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|
import torch
import os
import random
from torch.utils.data import Dataset
from PIL import Image
import numpy as np
import glob
# ==================================================================#
# == RafD
# ==================================================================#
class RafD(Dataset):
def __init__(self,
image_size,
mode_data,
transform,
mode,
shuffling=False,
verbose=False,
**kwargs):
self.transform = transform
self.image_size = image_size
self.shuffling = shuffling
self.name = 'RafD'
self.verbose = verbose
data_root = os.path.join('data', 'RafD', '{}')
data_root = data_root.format(
'faces') if mode_data == 'faces' else data_root.format('data')
self.lines = sorted(
glob.glob(os.path.abspath(os.path.join(data_root, '*.jpg'))))
self.mode = 'train' if mode == 'train' else 'test'
self.lines = self.get_subjects(self.lines, mode)
if self.verbose:
print('Start preprocessing %s: %s!' % (self.name, mode))
random.seed(1234)
self.preprocess()
if self.verbose:
print('Finished preprocessing %s: %s (%d)!' % (self.name, mode,
self.num_data))
def preprocess(self):
self.selected_attrs = [
'neutral', 'angry', 'contemptuous', 'disgusted', 'fearful',
'happy', 'sad', 'surprised'
]
self.idx2cls = {
idx: key
for idx, key in enumerate(self.selected_attrs)
}
self.cls2idx = {
key: idx
for idx, key in enumerate(self.selected_attrs)
}
self.filenames = []
self.labels = []
lines = self.lines
if self.shuffling:
random.shuffle(lines)
for i, line in enumerate(lines):
_class = os.path.basename(line).split('_')[-2]
pose = int(
os.path.basename(line).split('_')[0].replace('Rafd', ''))
if pose == 0 or pose == 180:
continue
label = []
for value in self.selected_attrs:
if _class == value:
label.append(1)
else:
label.append(0)
self.filenames.append(line)
self.labels.append(label)
self.num_data = len(self.filenames)
def get_data(self):
return self.filenames, self.labels
def __getitem__(self, index):
image = Image.open(self.filenames[index]).convert('RGB')
label = self.labels[index]
return self.transform(image), torch.FloatTensor(
label), self.filenames[index]
def __len__(self):
return self.num_data
def shuffle(self, seed):
random.seed(seed)
random.shuffle(self.filenames)
random.seed(seed)
random.shuffle(self.labels)
def get_subjects(self, lines, mode='train'):
subjects = sorted(
list(
set([os.path.basename(line).split('_')[1] for line in lines])))
split = 10 # 90-10
new_lines = []
if mode == 'train':
mode_subjects = subjects[:9 * len(subjects) // split]
else:
mode_subjects = subjects[9 * len(subjects) // split:]
for line in lines:
subject = os.path.basename(line).split('_')[1]
if subject in mode_subjects:
new_lines.append(line)
return new_lines
def train_inception(batch_size, shuffling=False, num_workers=4, **kwargs):
from torchvision.models import inception_v3
from misc.utils import to_var, to_cuda, to_data
from torchvision import transforms
from torch.utils.data import DataLoader
import torch.nn.functional as F
import torch
import torch.nn as nn
import tqdm
metadata_path = os.path.join('data', 'RafD', 'normal')
# inception Norm
image_size = 299
transform = []
window = int(image_size / 10)
transform += [
transforms.Resize((image_size + window, image_size + window),
interpolation=Image.ANTIALIAS)
]
transform += [
transforms.RandomResizedCrop(
image_size, scale=(0.7, 1.0), ratio=(0.8, 1.2))
]
transform += [transforms.RandomHorizontalFlip()]
transform += [transforms.ToTensor()]
transform = transforms.Compose(transform)
dataset_train = RafD(
image_size,
metadata_path,
transform,
'train',
shuffling=True,
**kwargs)
dataset_test = RafD(
image_size,
metadata_path,
transform,
'test',
shuffling=False,
**kwargs)
train_loader = DataLoader(
dataset=dataset_train,
batch_size=batch_size,
shuffle=False,
num_workers=num_workers)
test_loader = DataLoader(
dataset=dataset_test,
batch_size=batch_size,
shuffle=False,
num_workers=num_workers)
num_labels = len(train_loader.dataset.labels[0])
n_epochs = 100
net = inception_v3(pretrained=True, transform_input=True)
net.aux_logits = False
num_ftrs = net.fc.in_features
net.fc = nn.Linear(num_ftrs, num_labels)
net_save = metadata_path + '/inception_v3/{}.pth'
if not os.path.isdir(os.path.dirname(net_save)):
os.makedirs(os.path.dirname(net_save))
print("Model will be saved at: " + net_save)
optimizer = torch.optim.RMSprop(net.parameters(), lr=1e-5)
# loss = F.cross_entropy(output, target)
to_cuda(net)
for epoch in range(n_epochs):
LOSS = {'train': [], 'test': []}
OUTPUT = {'train': [], 'test': []}
LABEL = {'train': [], 'test': []}
net.eval()
for i, (data, label, files) in tqdm.tqdm(
enumerate(test_loader),
total=len(test_loader),
desc='Validating Inception V3 | RafD'):
data = to_var(data, volatile=True)
label = to_var(torch.max(label, dim=1)[1], volatile=True)
out = net(data)
loss = F.cross_entropy(out, label)
# ipdb.set_trace()
LOSS['test'].append(to_data(loss, cpu=True)[0])
OUTPUT['test'].extend(
to_data(F.softmax(out, dim=1).max(1)[1], cpu=True).tolist())
LABEL['test'].extend(to_data(label, cpu=True).tolist())
acc_test = (np.array(OUTPUT['test']) == np.array(LABEL['test'])).mean()
print('[Test] Loss: {:.4f} Acc: {:.4f}'.format(
np.array(LOSS['test']).mean(), acc_test))
net.train()
for i, (data, label, files) in tqdm.tqdm(
enumerate(train_loader),
total=len(train_loader),
desc='[{}/{}] Train Inception V3 | RafD'.format(
str(epoch).zfill(5),
str(n_epochs).zfill(5))):
# ipdb.set_trace()
data = to_var(data)
label = to_var(torch.max(label, dim=1)[1])
out = net(data)
# ipdb.set_trace()
loss = F.cross_entropy(out, label)
optimizer.zero_grad()
loss.backward()
optimizer.step()
LOSS['train'].append(to_data(loss, cpu=True)[0])
OUTPUT['train'].extend(
to_data(F.softmax(out, dim=1).max(1)[1], cpu=True).tolist())
LABEL['train'].extend(to_data(label, cpu=True).tolist())
acc_train = (np.array(OUTPUT['train']) == np.array(
LABEL['train'])).mean()
print('[Train] Loss: {:.4f} Acc: {:.4f}'.format(
np.array(LOSS['train']).mean(), acc_train))
torch.save(net.state_dict(), net_save.format(str(epoch).zfill(5)))
train_loader.dataset.shuffle(epoch)
|
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|
"""
@author: hugonnet
get table of glacier number and areas for Table S2
"""
import os
import pandas as pd
import numpy as np
df=pd.read_csv('/home/atom/data/validation/Hugonnet_2020/dhdt_int_HR.csv')
list_sites = list(set(list(df.site)))
nb_gla = []
area_gla = []
for site in list_sites:
nb_gla.append(len(df[df.site==site]))
area_gla.append(np.nansum(df[df.site==site].area.values/1000000))
df_out = pd.DataFrame()
df_out['site']=list_sites
df_out['nb_gla']=nb_gla
df_out['area']=area_gla
df_out.to_csv('/home/atom/ongoing/work_worldwide/tables/table_hr_dem_nb.csv')
|
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|
[STATEMENT]
lemma emeasure_count_space_density_singleton:
assumes "x \<in> A" "has_density M (count_space A) f"
shows "emeasure M {x} = f x"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
1. emeasure M {x} = f x
[PROOF STEP]
proof-
[PROOF STATE]
proof (state)
goal (1 subgoal):
1. emeasure M {x} = f x
[PROOF STEP]
from has_densityD[OF assms(2)]
[PROOF STATE]
proof (chain)
picking this:
f \<in> borel_measurable (count_space A)
M = density (count_space A) f
space (count_space A) \<noteq> {}
[PROOF STEP]
have nonneg: "\<And>x. x \<in> A \<Longrightarrow> f x \<ge> 0"
[PROOF STATE]
proof (prove)
using this:
f \<in> borel_measurable (count_space A)
M = density (count_space A) f
space (count_space A) \<noteq> {}
goal (1 subgoal):
1. \<And>x. x \<in> A \<Longrightarrow> 0 \<le> f x
[PROOF STEP]
by simp
[PROOF STATE]
proof (state)
this:
?x \<in> A \<Longrightarrow> 0 \<le> f ?x
goal (1 subgoal):
1. emeasure M {x} = f x
[PROOF STEP]
from assms
[PROOF STATE]
proof (chain)
picking this:
x \<in> A
has_density M (count_space A) f
[PROOF STEP]
have M: "M = density (count_space A) f"
[PROOF STATE]
proof (prove)
using this:
x \<in> A
has_density M (count_space A) f
goal (1 subgoal):
1. M = density (count_space A) f
[PROOF STEP]
by (intro has_densityD)
[PROOF STATE]
proof (state)
this:
M = density (count_space A) f
goal (1 subgoal):
1. emeasure M {x} = f x
[PROOF STEP]
from assms
[PROOF STATE]
proof (chain)
picking this:
x \<in> A
has_density M (count_space A) f
[PROOF STEP]
have "emeasure M {x} = \<integral>\<^sup>+y. f y * indicator {x} y \<partial>count_space A"
[PROOF STATE]
proof (prove)
using this:
x \<in> A
has_density M (count_space A) f
goal (1 subgoal):
1. emeasure M {x} = set_nn_integral (count_space A) {x} f
[PROOF STEP]
by (simp add: M emeasure_density)
[PROOF STATE]
proof (state)
this:
emeasure M {x} = set_nn_integral (count_space A) {x} f
goal (1 subgoal):
1. emeasure M {x} = f x
[PROOF STEP]
also
[PROOF STATE]
proof (state)
this:
emeasure M {x} = set_nn_integral (count_space A) {x} f
goal (1 subgoal):
1. emeasure M {x} = f x
[PROOF STEP]
from assms and nonneg
[PROOF STATE]
proof (chain)
picking this:
x \<in> A
has_density M (count_space A) f
?x \<in> A \<Longrightarrow> 0 \<le> f ?x
[PROOF STEP]
have "... = f x"
[PROOF STATE]
proof (prove)
using this:
x \<in> A
has_density M (count_space A) f
?x \<in> A \<Longrightarrow> 0 \<le> f ?x
goal (1 subgoal):
1. set_nn_integral (count_space A) {x} f = f x
[PROOF STEP]
by (subst nn_integral_indicator_singleton) auto
[PROOF STATE]
proof (state)
this:
set_nn_integral (count_space A) {x} f = f x
goal (1 subgoal):
1. emeasure M {x} = f x
[PROOF STEP]
finally
[PROOF STATE]
proof (chain)
picking this:
emeasure M {x} = f x
[PROOF STEP]
show ?thesis
[PROOF STATE]
proof (prove)
using this:
emeasure M {x} = f x
goal (1 subgoal):
1. emeasure M {x} = f x
[PROOF STEP]
.
[PROOF STATE]
proof (state)
this:
emeasure M {x} = f x
goal:
No subgoals!
[PROOF STEP]
qed
|
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|
# --------------
# Importing header files
import numpy as np
# Path of the file has been stored in variable called 'path'
#New record
new_record = [[50, 9, 4, 1, 0, 0, 40, 0]]
#Code starts here
data = np.genfromtxt(path, delimiter=",", skip_header=1)
census = np.concatenate([data,new_record], axis=0)
# --------------
#Code starts here
age = census[:,0]
max_age = age.max(axis=0)
min_age = age.min(axis=0)
age_mean = age.mean()
age_std = np.std(age)
# --------------
#Code starts here
race_0 = census[census[:,2]==0]
race_1 = census[census[:,2]==1]
race_2 = census[census[:,2]==2]
race_3 = census[census[:,2]==3]
race_4 = census[census[:,2]==4]
len_0 = len(race_0)
len_1 = len(race_1)
len_2 = len(race_2)
len_3 = len(race_3)
len_4 = len(race_4)
print("Race_0: ",len_0)
print("Race_1: ",len_1)
print("Race_2: ",len_2)
print("Race_3: ",len_3)
print("Race_4: ",len_4)
race_list=[len_0, len_1, len_2, len_3, len_4]
minority_race = race_list.index(min(race_list))
# --------------
#Code starts here
#Finding Senior citizens
senior_citizens = census[census[:,0]>60]
#Summing Work Hours
working_hours = senior_citizens[:,6]
working_hours_sum = working_hours.sum(axis=0)
#No of senior citizens
senior_citizens_len = len(senior_citizens)
#Average working hours
avg_working_hours = working_hours_sum/senior_citizens_len
print(avg_working_hours)
# --------------
#Code starts here
high = census[census[:,1]>10]
low = census[census[:,1]<=10]
avg_pay_high = high[:,7].mean()
avg_pay_low = low[:,7].mean()
|
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|
import numpy as np
import tensorflow as tf
from yadlt.models.autoencoders import stacked_denoising_autoencoder
from yadlt.utils import datasets, utilities
# #################### #
# Flags definition #
# #################### #
flags = tf.app.flags
FLAGS = flags.FLAGS
# Global configuration
flags.DEFINE_string('dataset', 'mnist', 'Which dataset to use. ["mnist", "cifar10", "custom"]')
flags.DEFINE_string('train_dataset', '', 'Path to train set .npy file.')
flags.DEFINE_string('train_labels', '', 'Path to train labels .npy file.')
flags.DEFINE_string('valid_dataset', '', 'Path to valid set .npy file.')
flags.DEFINE_string('valid_labels', '', 'Path to valid labels .npy file.')
flags.DEFINE_string('test_dataset', '', 'Path to test set .npy file.')
flags.DEFINE_string('test_labels', '', 'Path to test labels .npy file.')
flags.DEFINE_string('cifar_dir', '', 'Path to the cifar 10 dataset directory.')
flags.DEFINE_boolean('do_pretrain', True, 'Whether or not doing unsupervised pretraining.')
flags.DEFINE_string('save_predictions', '', 'Path to a .npy file to save predictions of the model.')
flags.DEFINE_string('save_layers_output_test', '', 'Path to a .npy file to save test set output from all the layers of the model.')
flags.DEFINE_string('save_layers_output_train', '', 'Path to a .npy file to save train set output from all the layers of the model.')
flags.DEFINE_integer('seed', -1, 'Seed for the random generators (>= 0). Useful for testing hyperparameters.')
flags.DEFINE_string('name', 'sdae', 'Name for the model.')
flags.DEFINE_float('momentum', 0.5, 'Momentum parameter.')
# Supervised fine tuning parameters
flags.DEFINE_string('finetune_loss_func', 'softmax_cross_entropy', 'Last Layer Loss function. ["softmax_cross_entropy", "mse"]')
flags.DEFINE_integer('finetune_num_epochs', 30, 'Number of epochs for the fine-tuning phase.')
flags.DEFINE_float('finetune_learning_rate', 0.001, 'Learning rate for the fine-tuning phase.')
flags.DEFINE_string('finetune_act_func', 'relu', 'Activation function for the fine-tuning phase. ["sigmoid, "tanh", "relu"]')
flags.DEFINE_float('finetune_dropout', 1, 'Dropout parameter.')
flags.DEFINE_string('finetune_opt', 'sgd', '["sgd", "adagrad", "momentum", "adam"]')
flags.DEFINE_integer('finetune_batch_size', 20, 'Size of each mini-batch for the fine-tuning phase.')
# Autoencoder layers specific parameters
flags.DEFINE_string('dae_layers', '256,', 'Comma-separated values for the layers in the sdae.')
flags.DEFINE_string('dae_regcoef', '5e-4,', 'Regularization parameter for the autoencoders. If 0, no regularization.')
flags.DEFINE_string('dae_enc_act_func', 'sigmoid,', 'Activation function for the encoder. ["sigmoid", "tanh"]')
flags.DEFINE_string('dae_dec_act_func', 'none,', 'Activation function for the decoder. ["sigmoid", "tanh", "none"]')
flags.DEFINE_string('dae_loss_func', 'mse,', 'Loss function. ["mse" or "cross_entropy"]')
flags.DEFINE_string('dae_opt', 'sgd,', '["sgd", "ada_grad", "momentum", "adam"]')
flags.DEFINE_string('dae_learning_rate', '0.01,', 'Initial learning rate.')
flags.DEFINE_string('dae_num_epochs', '10,', 'Number of epochs.')
flags.DEFINE_string('dae_batch_size', '10,', 'Size of each mini-batch.')
flags.DEFINE_string('dae_corr_type', 'none,', 'Type of input corruption. ["none", "masking", "salt_and_pepper"]')
flags.DEFINE_string('dae_corr_frac', '0.0,', 'Fraction of the input to corrupt.')
# Conversion of Autoencoder layers parameters from string to their specific type
dae_layers = utilities.flag_to_list(FLAGS.dae_layers, 'int')
dae_enc_act_func = utilities.flag_to_list(FLAGS.dae_enc_act_func, 'str')
dae_dec_act_func = utilities.flag_to_list(FLAGS.dae_dec_act_func, 'str')
dae_opt = utilities.flag_to_list(FLAGS.dae_opt, 'str')
dae_loss_func = utilities.flag_to_list(FLAGS.dae_loss_func, 'str')
dae_learning_rate = utilities.flag_to_list(FLAGS.dae_learning_rate, 'float')
dae_regcoef = utilities.flag_to_list(FLAGS.dae_regcoef, 'float')
dae_corr_type = utilities.flag_to_list(FLAGS.dae_corr_type, 'str')
dae_corr_frac = utilities.flag_to_list(FLAGS.dae_corr_frac, 'float')
dae_num_epochs = utilities.flag_to_list(FLAGS.dae_num_epochs, 'int')
dae_batch_size = utilities.flag_to_list(FLAGS.dae_batch_size, 'int')
# Parameters validation
assert all([0. <= cf <= 1. for cf in dae_corr_frac])
assert all([ct in ['masking', 'salt_and_pepper', 'none'] for ct in dae_corr_type])
assert FLAGS.dataset in ['mnist', 'cifar10', 'custom']
assert len(dae_layers) > 0
assert all([af in ['sigmoid', 'tanh'] for af in dae_enc_act_func])
assert all([af in ['sigmoid', 'tanh', 'none'] for af in dae_dec_act_func])
if __name__ == '__main__':
utilities.random_seed_np_tf(FLAGS.seed)
if FLAGS.dataset == 'mnist':
# ################# #
# MNIST Dataset #
# ################# #
trX, trY, vlX, vlY, teX, teY = datasets.load_mnist_dataset(mode='supervised')
elif FLAGS.dataset == 'cifar10':
# ################### #
# Cifar10 Dataset #
# ################### #
trX, trY, teX, teY = datasets.load_cifar10_dataset(FLAGS.cifar_dir, mode='supervised')
# Validation set is the first half of the test set
vlX = teX[:5000]
vlY = teY[:5000]
elif FLAGS.dataset == 'custom':
# ################## #
# Custom Dataset #
# ################## #
def load_from_np(dataset_path):
if dataset_path != '':
return np.load(dataset_path)
else:
return None
trX, trY = load_from_np(FLAGS.train_dataset), load_from_np(FLAGS.train_labels)
vlX, vlY = load_from_np(FLAGS.valid_dataset), load_from_np(FLAGS.valid_labels)
teX, teY = load_from_np(FLAGS.test_dataset), load_from_np(FLAGS.test_labels)
else:
trX = None
trY = None
vlX = None
vlY = None
teX = None
teY = None
# Create the object
sdae = None
dae_enc_act_func = [utilities.str2actfunc(af) for af in dae_enc_act_func]
dae_dec_act_func = [utilities.str2actfunc(af) for af in dae_dec_act_func]
finetune_act_func = utilities.str2actfunc(FLAGS.finetune_act_func)
sdae = stacked_denoising_autoencoder.StackedDenoisingAutoencoder(
do_pretrain=FLAGS.do_pretrain, name=FLAGS.name,
layers=dae_layers, finetune_loss_func=FLAGS.finetune_loss_func,
finetune_learning_rate=FLAGS.finetune_learning_rate, finetune_num_epochs=FLAGS.finetune_num_epochs,
finetune_opt=FLAGS.finetune_opt, finetune_batch_size=FLAGS.finetune_batch_size,
finetune_dropout=FLAGS.finetune_dropout,
enc_act_func=dae_enc_act_func, dec_act_func=dae_dec_act_func,
corr_type=dae_corr_type, corr_frac=dae_corr_frac, regcoef=dae_regcoef,
loss_func=dae_loss_func, opt=dae_opt,
learning_rate=dae_learning_rate, momentum=FLAGS.momentum,
num_epochs=dae_num_epochs, batch_size=dae_batch_size,
finetune_act_func=finetune_act_func)
# Fit the model (unsupervised pretraining)
if FLAGS.do_pretrain:
encoded_X, encoded_vX = sdae.pretrain(trX, vlX)
# Supervised finetuning
sdae.fit(trX, trY, vlX, vlY)
# Compute the accuracy of the model
print('Test set accuracy: {}'.format(sdae.score(teX, teY)))
# Save the predictions of the model
if FLAGS.save_predictions:
print('Saving the predictions for the test set...')
np.save(FLAGS.save_predictions, sdae.predict(teX))
def save_layers_output(which_set):
if which_set == 'train':
trout = sdae.get_layers_output(trX)
for i, o in enumerate(trout):
np.save(FLAGS.save_layers_output_train + '-layer-' + str(i + 1) + '-train', o)
elif which_set == 'test':
teout = sdae.get_layers_output(teX)
for i, o in enumerate(teout):
np.save(FLAGS.save_layers_output_test + '-layer-' + str(i + 1) + '-test', o)
# Save output from each layer of the model
if FLAGS.save_layers_output_test:
print('Saving the output of each layer for the test set')
save_layers_output('test')
# Save output from each layer of the model
if FLAGS.save_layers_output_train:
print('Saving the output of each layer for the train set')
save_layers_output('train')
|
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|
"""Contains example usage of the features in the OpticSim.jl package."""
module Examples
using ..OpticSim
using ..OpticSim.Vis
# using ..OpticSim.GlassCat use this if you want to type SCHOTT.N_BK7 rather than OpticSim.GlassCat.SCHOTT.N_BK7
using StaticArrays
using DataFrames
using Images
using Unitful
using Plots
using LinearAlgebra
# Create a geometric hemisphere
function hemisphere()::CSGTree
sph = Sphere(10.0)
pln = Plane(0.0, 0.0, -1.0, 0.0, 0.0, 0.0)
csgintersection(sph, pln)() #csg operations create a csggenerator which instantiates the csg tree after applying a rigid body transformation. This allows you to make as many instances of the object as you want with different transformations. We just want the CSGTree object rather than a generator.
end
# Create an optical hemisphere that has optical material properties so it will reflect and refract light. In the previous example the hemisphere object had optical properties of OpticSim.GlassCat.Air, which is the default optical interface, so it won't refract or reflect light.
function opticalhemisphere()::CSGOpticalSystem
sph = Sphere(10.0, interface = FresnelInterface{Float64}(OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air))
pln = Plane(0.0, 0.0, -1.0, 0.0, 0.0, 0.0, interface = FresnelInterface{Float64}(OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air))
assy = LensAssembly{Float64}(csgintersection(sph, pln)())
return CSGOpticalSystem(assy, Rectangle(1.0, 1.0, SVector{3,Float64}(0.0, 0.0, 1.0), SVector{3,Float64}(0.0, 0.0, -11.0)))
end
#! format: off
cooketriplet(::Type{T} = Float64, detpix::Int = 1000) where {T<:Real} = AxisymmetricOpticalSystem{T}(
DataFrame(Surface = [:Object, 1, 2, 3, :Stop, 5, 6, :Image],
Radius = [Inf, 26.777, 66.604, -35.571, 35.571, 35.571, -26.777, Inf],
OptimizeRadius = [false,true,true,true,true,true,true,false],
Thickness = [Inf, 4.0, 2.0, 4.0, 2.0, 4.0, 44.748, missing],
OptimizeThickness = [false,true,true,true,true,true,true,false],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_SK16, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_SF2, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_SK16, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf, 8.580, 7.513, 7.054, 6.033, 7.003, 7.506, 15.0]), detpix, detpix)
export cooketriplet
#no longer works
cooketripletlensonly(::Type{T} = Float64) where {T<:Real} = AxisymmetricLens{T}(
DataFrame(Surface = [:Object, 1, 2, 3, :Stop, 5, 6, :Image],
Radius = [Inf, 26.777, 66.604, -35.571, 35.571, 35.571, -26.777, Inf],
OptimizeRadius = [false,true,true,true,true,true,true,false],
Thickness = [Inf, 4.0, 2.0, 4.0, 2.0, 4.0, 44.748, missing],
OptimizeThickness = [false,true,true,true,true,true,true,false],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_SK16, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_SF2, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_SK16, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf, 8.580, 7.513, 7.054, 6.033, 7.003, 7.506, 15.0]))
export cooketripletlensonly
cooketripletfirstelement(::Type{T} = Float64) where {T<:Real} = AxisymmetricOpticalSystem(
DataFrame(Surface = [:Object, 1, 2, :Image],
Radius = [Inf, -35.571, 35.571, Inf],
Thickness = [Inf, 4.0, 44.748, missing],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_SK16, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf, 7.054, 6.033, 15.0]))
convexplano(::Type{T} = Float64) where {T<:Real} = AxisymmetricOpticalSystem{T}(
DataFrame(Surface = [:Object, 1, 2, :Image],
Radius = [Inf, 60.0, Inf, Inf],
Thickness = [Inf, 10.0, 57.8, missing],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf, 9.0, 9.0, 15.0]))
doubleconvex(frontradius::T,rearradius::T) where{T<:Real} =
AxisymmetricOpticalSystem{T}(
DataFrame(Surface = [:Object, 1, 2, :Image],
Radius = [T(Inf64), frontradius, rearradius, T(Inf64)],
OptimizeRadius = [false,true,true,false],
Thickness = [T(Inf64), T(10.0), T(57.8), missing],
OptimizeThickness = [false,false,false,false],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, missing],
SemiDiameter = [T(Inf64), T(9.0), T(9.0), T(15.0)]))
doubleconvexconic(::Type{T} = Float64) where {T<:Real} =
AxisymmetricOpticalSystem{T}(
DataFrame(Surface = [:Object, 1, 2, :Image],
Radius = [Inf64, 60, -60, Inf64],
OptimizeRadius = [false,true,true,false],
Thickness = [Inf64, 10.0, 57.8, missing],
OptimizeThickness = [false,false,false,false],
Conic = [missing, 0.01, 0.01, missing],
OptimizeConic = [false, true, true, false],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf64, 9.0, 9.0, 15.0]))
doubleconvexlensonly(frontradius::T,rearradius::T) where{T<:Real} =
AxisymmetricLens{T}(
DataFrame(Surface = [:Object, 1, 2, :Image],
Radius = [T(Inf64), frontradius, rearradius, T(Inf64)],
OptimizeRadius = [false,true,true,false],
Thickness = [T(Inf64), T(10.0), T(57.8), missing],
OptimizeThickness = [false,false,false,false],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, missing],
SemiDiameter = [T(Inf64), T(9.0), T(9.0), T(15.0)]))
export doubleconvexlensonly
doubleconvexprescription() = DataFrame(
Surface = [:Object, 1, 2, :Image],
Radius = [Inf64, 60, -60, Inf64],
OptimizeRadius = [false,true,true,false],
Thickness = [Inf64, 10.0, 57.8, missing],
OptimizeThickness = [false,true,true,false],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf64, 9.0, 9.0, 15.0])
doubleconvex(::Type{T} = Float64; temperature::Unitful.Temperature = OpticSim.GlassCat.TEMP_REF_UNITFUL, pressure::T = T(OpticSim.GlassCat.PRESSURE_REF)) where {T<:Real} = AxisymmetricOpticalSystem{T}(doubleconvexprescription(),temperature = temperature, pressure = pressure)
doubleconcave(::Type{T} = Float64) where {T<:Real} = AxisymmetricOpticalSystem{T}(
DataFrame(Surface = [:Object, 1, 2, :Image],
Radius = [Inf64, -41.0, 41.0, Inf64],
Thickness = [Inf64, 10.0, 57.8, missing],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf64, 9.0, 9.0, 15.0]))
planoconcaverefl(::Type{T} = Float64) where {T<:Real} = AxisymmetricOpticalSystem{T}(
DataFrame(Surface = [:Object, 1, 2, :Image],
Radius = [Inf64, Inf64, -41.0, Inf64],
Thickness = [Inf64, 10.0, -57.8, missing],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf64, 9.0, 9.0, 25.0],
Reflectance = [missing, missing, 1.0, missing]))
concaveplano(::Type{T} = Float64) where {T<:Real} = AxisymmetricOpticalSystem{T}(
DataFrame(Surface = [:Object, 1, 2, :Image],
Radius = [Inf64, -41.0, Inf64, Inf64],
Thickness = [Inf64, 10.0, 57.8, missing],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf64, 9.0, 9.0, 15.0]))
planoplano(::Type{T} = Float64) where {T<:Real} = AxisymmetricOpticalSystem{T}(
DataFrame(Surface = [:Object, 1, 2, :Image],
Radius = [Inf64, Inf64, Inf64, Inf64],
Thickness = [Inf64, 10.0, 57.8, missing],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf64, 9.0, 9.0, 15.0]))
#! format: on
end #module SphericalLenses
function autodrawrays(lens::AxisymmetricOpticalSystem = cooketriplet(), angle = 10; kwargs...)
f1 = HexapolarField(lens, collimated = true, wavelength = 0.45, sourcenum = 1)
Vis.drawtracerays(lens, raygenerator = f1, test = true, trackallrays = true, colorbysourcenum = true; kwargs...)
f2 = HexapolarField(lens, collimated = true, wavelength = 0.45, sourceangle = angle / 180 * π, sourcenum = 2)
Vis.drawtracerays!(lens, raygenerator = f2, test = true, trackallrays = true, colorbysourcenum = true; kwargs...)
end
function autospotdiag(lens::AxisymmetricOpticalSystem = cooketriplet(); kwargs...)
f1 = HexapolarField(lens, collimated = true, wavelength = 0.45, sourcenum = 1)
f2 = HexapolarField(lens, collimated = true, wavelength = 0.45, sourceangle = 5 / 180 * π, sourcenum = 2)
f3 = HexapolarField(lens, collimated = true, wavelength = 0.45, sourceangle = 10 / 180 * π, sourcenum = 3)
Vis.spotdiaggrid(lens, [f1, f2, f3]; kwargs...)
end
# Display the spot diagram of a simple cooketriplet lens
function hexapolarspotdiagramexample(lens = cooketriplet(), numrings::Int = 5, angle = 0.0)
Vis.spotdiag(lens, samples = numrings, sourceangle = angle)
end
function cartesiangridspotdiagramexample(lens = cooketriplet(), numsamples::Int = 5, angle = 0.0)
Vis.spotdiag(lens, hexapolar = false, samples = numsamples, sourceangle = angle)
end
function SchmidtCassegrainTelescope()
# glass entrance lens on telescope
topsurf = Plane(SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, 0.0), interface = FresnelInterface{Float64}(OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air), vishalfsizeu = 12.00075, vishalfsizev = 12.00075)
botsurf = AcceleratedParametricSurface(ZernikeSurface(12.00075, radius = -1.14659768e+4, aspherics = [(4, 3.68090959e-7), (6, 2.73643352e-11), (8, 3.20036892e-14)]), 17, interface = FresnelInterface{Float64}(OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air))
coverlens = csgintersection(leaf(Cylinder(12.00075, 1.4)), csgintersection(leaf(topsurf), leaf(botsurf, RigidBodyTransform(OpticSim.rotmatd(0, 180, 0), SVector(0.0, 0.0, -0.65)))))
# big mirror with a hole in it
bigmirror = ConicLens(OpticSim.GlassCat.SCHOTT.N_BK7, -72.65, -95.2773500000134, 0.077235, Inf, 0.0, 0.2, 12.18263, frontsurfacereflectance = 1.0)
bigmirror = csgdifference(bigmirror, leaf(Cylinder(4.0, 0.3, interface = opaqueinterface()), translation(0.0, 0.0, -72.75)))
# small mirror supported on a spider
smallmirror = SphericalLens(OpticSim.GlassCat.SCHOTT.N_BK7, -40.65, Inf, -49.6845, 1.13365, 4.3223859, backsurfacereflectance = 1.0)
obscuration1 = Circle(4.5, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, -40.649), interface = opaqueinterface())
obscurations2 = Spider(3, 0.5, 12.0, SVector(0.0, 0.0, -40.65))
# put it together with the detector
la = LensAssembly(coverlens(), bigmirror(), smallmirror(), obscuration1, obscurations2...)
det = Circle(3.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, -92.4542988), interface = opaqueinterface())
return CSGOpticalSystem(la, det)
end
drawSchmidt(; kwargs...) = Vis.drawtracerays(SchmidtCassegrainTelescope(), raygenerator = UniformOpticalSource(CollimatedSource(GridRectOriginPoints(5, 5, 10.0, 10.0, position = SVector(0.0, 0.0, 20.0))), 0.55), trackallrays = true, colorbynhits = true, test = true, numdivisions = 100; kwargs...)
function prism_refraction()
# build the triangular prism
int = FresnelInterface{Float64}(OpticSim.GlassCat.SCHOTT.N_SF14, OpticSim.GlassCat.Air)
s = 2.0
prism = csgintersection(leaf(Plane(SVector(0.0, -1.0, 0.0), SVector(0.0, -s, 0.0), interface = int, vishalfsizeu = 2 * s, vishalfsizev = 2 * s)), csgintersection(Plane(SVector(0.0, sind(30), cosd(30)), SVector(0.0, s * sind(30), s * cosd(30)), interface = int, vishalfsizeu = 2 * s, vishalfsizev = 2 * s), Plane(SVector(0.0, sind(30), -cosd(30)), SVector(0.0, s * sind(30), -s * cosd(30)), interface = int, vishalfsizeu = 2 * s, vishalfsizev = 2 * s)))
sys = CSGOpticalSystem(LensAssembly(prism()), Rectangle(15.0, 15.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, -20.0), interface = opaqueinterface()))
# create some 'white' light
rays = Vector{OpticalRay{Float64,3}}(undef, 0)
for i in 0:7
λ = ((i / 7) * 200 + 450) / 1000
r = OpticalRay(SVector(0.0, -3.0, 10.0), SVector(0.0, 0.5, -1.0), 1.0, λ)
push!(rays, r)
end
raygen = RayListSource(rays)
# draw the result
Vis.drawtracerays(sys, raygenerator = raygen, test = true, trackallrays = true)
end
function zoom_lens(pos = 1)
if pos == 0
stop = 2.89
zoom = 9.48
dist = 4.46970613
elseif pos == 1
stop = 3.99
zoom = 4.48
dist = 21.21
else
stop = 4.90
zoom = 2.00
dist = 43.81
end
#! format: off
return AxisymmetricOpticalSystem{Float64}(
DataFrame(Surface = [:Object, :Stop, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, :Image],
Radius = [Inf64, Inf64, -1.6202203499676E+01, -4.8875855327468E+01, 1.5666614444619E+01, -4.2955326460481E+01, 1.0869565217391E+02, 2.3623907394283E+01, -1.6059097478722E+01, -4.2553191489362E+02, -3.5435861091425E+01, -1.4146272457208E+01, -2.5125628140704E+02, -2.2502250225023E+01, -1.0583130489999E+01, -4.4444444444444E+01, Inf64],
Aspherics = [missing, missing, missing, missing, missing, [(4, 1.03860000000E-04), (6, 1.42090000000E-07), (8, -8.84950000000E-09), (10, 1.24770000000E-10), (12, -1.03670000000E-12), (14, 3.65560000000E-15)], missing, missing, [(4, 4.27210000000E-05), (6, 1.24840000000E-07), (8, 9.70790000000E-09), (10, -1.84440000000E-10), (12, 1.86440000000E-12), (14, -7.79750000000E-15)], [(4, 1.13390000000E-04), (6, 4.81650000000E-07), (8, 1.87780000000E-08), (10, -5.75710000000E-10), (12, 8.99940000000E-12), (14, -4.67680000000E-14)], missing, missing, missing, missing, missing, missing, missing],
Thickness = [Inf64, 0.0, 5.18, 0.10, 4.40, 0.16, 1.0, 4.96, zoom, 4.04, 1.35, 1.0, 2.80, 3.0, 1.22, dist, missing],
Material = [OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, OpticSim.GlassCat.OHARA.S_LAH66, OpticSim.GlassCat.Air, OpticSim.GlassCat.NIKON.LLF6, OpticSim.GlassCat.Air, OpticSim.GlassCat.OHARA.S_TIH6, OpticSim.GlassCat.OHARA.S_FSL5, OpticSim.GlassCat.Air, OpticSim.GlassCat.OHARA.S_FSL5, OpticSim.GlassCat.Air, OpticSim.GlassCat.OHARA.S_LAL8, OpticSim.GlassCat.SCHOTT.S_FL4, OpticSim.GlassCat.Air, OpticSim.GlassCat.OHARA.S_LAH66, OpticSim.GlassCat.Air, missing],
SemiDiameter = [Inf64, stop, 3.85433218451, 3.85433218451, 4.36304692871, 4.36304692871, 4.72505505439, 4.72505505439, 4.72505505439, 4.45240784026, 4.45240784026, 4.50974054117, 4.50974054117, 4.50974054117, 4.76271114409, 4.76271114409, 15.0]))
#! format: on
end
function fresnel(convex = true; kwargs...)
lens = FresnelLens(OpticSim.GlassCat.SCHOTT.N_BK7, 0.0, convex ? 15.0 : -15.0, 1.0, 8.0, 0.8, conic = 0.1)
sys = CSGOpticalSystem(LensAssembly(lens()), Rectangle(15.0, 15.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, -25.0), interface = opaqueinterface()))
Vis.drawtracerays(sys; test = true, trackallrays = true, numdivisions = 30, kwargs...)
end
function grating(; period = 1.0, θ = 0.0, λ = 0.55, kwargs...)
int = ThinGratingInterface(SVector(0.0, 1.0, 0.0), period, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, minorder = -2, maxorder = 2, reflectance = [0.0, 0.0, 0.1, 0.0, 0.0], transmission = [0.05, 0.1, 0.4, 0.1, 0.05])
grating = ThinGratingSurface(Rectangle(5.0, 5.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, 0.0)), int)
back = Rectangle(30.0, 30.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, 25.0))
sys = CSGOpticalSystem(LensAssembly(grating, back), Rectangle(30.0, 30.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, -25.0), interface = opaqueinterface()))
Vis.drawtracerays(sys; raygenerator = UniformOpticalSource(CollimatedSource(OriginPoint{Float64}(100, position = SVector(0.0, 0.0, 10.0), direction = SVector(0.0, sind(θ), -cosd(θ)))), λ), trackallrays = true, rayfilter = nothing, kwargs...)
end
function reflgrating(; period = 1.0, θ = 0.0, λ = 0.55, kwargs...)
int = ThinGratingInterface(SVector(0.0, 1.0, 0.0), period, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, minorder = -2, maxorder = 2, transmission = [0.0, 0.0, 0.1, 0.0, 0.0], reflectance = [0.05, 0.1, 0.4, 0.1, 0.05])
grating = ThinGratingSurface(Rectangle(5.0, 5.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, 0.0)), int)
back = Rectangle(30.0, 30.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, -25.0))
sys = CSGOpticalSystem(LensAssembly(grating, back), Rectangle(30.0, 30.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, 25.0), interface = opaqueinterface()))
Vis.drawtracerays(sys; raygenerator = UniformOpticalSource(CollimatedSource(OriginPoint{Float64}(100, position = SVector(0.0, 0.0, 10.0), direction = SVector(0.0, sind(θ), -cosd(θ)))), λ), trackallrays = true, rayfilter = nothing, kwargs...)
end
function HOE(refl = false, firstorderonly = false; kwargs...)
rect = Rectangle(5.0, 5.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, 0.0))
if refl
int = HologramInterface(SVector(0.0, -10.0, 20.0), ConvergingBeam, SVector(0.0, 0.0, -200), ConvergingBeam, 0.55, 9.0, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, 0.05, !firstorderonly)
else
int = HologramInterface(SVector(0.0, -10.0, -20.0), ConvergingBeam, SVector(0.0, 0.0, -200), ConvergingBeam, 0.55, 5.0, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, 0.05, !firstorderonly)
end
obj = HologramSurface(rect, int)
back = Rectangle(50.0, 50.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, 25.0))
sys = CSGOpticalSystem(LensAssembly(obj, back), Rectangle(50.0, 50.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, -25.0), interface = opaqueinterface()))
Vis.drawtracerays(sys; raygenerator = UniformOpticalSource(GridSource(OriginPoint{Float64}(10, position = SVector(0.0, 0.0, 10.0), direction = SVector(0.0, 0.0, -1.0)), 1, 15, 0.0, π / 6), 0.55), trackallrays = true, rayfilter = nothing, kwargs...)
end
function HOEfocus(; kwargs...)
rect = Rectangle(5.0, 5.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, 0.0))
int = HologramInterface(SVector(0.0, -3.0, -20.0), ConvergingBeam, SVector(0.0, 0.0, -1.0), CollimatedBeam, 0.55, 9.0, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, 0.05, false)
obj = HologramSurface(rect, int)
sys = CSGOpticalSystem(LensAssembly(obj), Rectangle(10.0, 10.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, -25.0), interface = opaqueinterface()))
Vis.drawtracerays(sys; raygenerator = UniformOpticalSource(CollimatedSource(GridRectOriginPoints(5, 5, 3.0, 3.0, position = SVector(0.0, 0.0, 10.0), direction = SVector(0.0, 0.0, -1.0))), 0.55), trackallrays = true, rayfilter = nothing, test = true, kwargs...)
end
function HOEcollimate(; kwargs...)
rect = Rectangle(5.0, 5.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, 0.0))
int = HologramInterface(SVector(0.1, -0.05, -1.0), CollimatedBeam, SVector(0.0, 0.0, 10), DivergingBeam, 0.55, 9.0, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, 0.05, false)
obj = HologramSurface(rect, int)
sys = CSGOpticalSystem(LensAssembly(obj), Rectangle(10.0, 10.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, -25.0), interface = opaqueinterface()))
Vis.drawtracerays(sys; raygenerator = UniformOpticalSource(GridSource(OriginPoint{Float64}(1, position = SVector(0.0, 0.0, 10.0), direction = SVector(0.0, 0.0, -1.0)), 5, 5, π / 4, π / 4), 0.55), trackallrays = true, rayfilter = nothing, test = true, kwargs...)
end
function eyetrackHOE(nrays = 5000, det = false, showhead = true, zeroorder = false; kwargs...)
# TODO update for new specs from Chris
hoehalfwidth = 50.0 #25.0
hoehalfheight = 50.0 #22.5
hoecenter = SVector(-8.0 - 25.0, 0.0, -10.0 - 25.0)
rect = Rectangle(hoehalfheight, hoehalfwidth, SVector(0.0, 1.0, 0.0), hoecenter)
er = 15.0
cornea_rad = 7.85
corneavertex = SVector(0.0, er, 0.0)
sourceloc = SVector(-33.0, er, 0.0)
camloc = SVector(20.0, 3.0, -11.0)
camdir = corneavertex - camloc
camdir_norm = normalize(camdir)
interfaces = []
# offset = SVector(-5.0, 10.0, -10.0)
# for θ in 0:(π / 6):(2π)
# ledloc = SVector(20 * cos(θ) + offset[1], 0 + offset[2], 15 * sin(θ) + offset[3])
# int = HologramInterface(ledloc, ConvergingBeam, sourceloc, DivergingBeam, 0.78, 100.0, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, 0.05, zeroorder)
# push!(interfaces, int)
# end
dirs = [SVector(0.7713, 0.6350, -0.0437), SVector(0.5667, 0.8111, -0.1445), SVector(0.3400, 0.9349, -0.1017), SVector(0.1492, 0.9878, 0.0445), SVector(0.0249, 0.9686, 0.2474), SVector(-0.0184, 0.8855, 0.4643), SVector(0.0254, 0.7537, 0.6567), SVector(0.1548, 0.5964, 0.7876), SVector(0.3570, 0.4462, 0.8207), SVector(0.5959, 0.3470, 0.7242), SVector(0.7976, 0.3449, 0.4948), SVector(0.8680, 0.4555, 0.1978)]
for d in dirs
int = HologramInterface(normalize(d), CollimatedBeam, sourceloc, DivergingBeam, 0.78, 100.0, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, 0.05, zeroorder)
# int = HologramInterface(corneavertex - 10 * d, ConvergingBeam, sourceloc, DivergingBeam, 0.78, 100.0, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, 0.05, zeroorder)
push!(interfaces, int)
end
mint = MultiHologramInterface(interfaces...)
obj = MultiHologramSurface(rect, mint)
cornea = leaf(Sphere(cornea_rad, interface = FresnelInterface{Float64}(OpticSim.GlassCat.EYE.CORNEA, OpticSim.GlassCat.Air, reflectance = 1.0, transmission = 0.0)), translation(0.0, er + cornea_rad, 0.0))()
# cam settings
fnum = 2.0
fov = 80
sensorrad = 1.0
barrellength = sensorrad / tand(fov / 2)
aprad = barrellength / fnum / 2
camrad = max(sensorrad, aprad)
camap = Annulus(aprad, camrad, camdir_norm, camloc)
distfromcamtoeye = norm(camdir)
focallength = 1 / (1 / distfromcamtoeye + 1 / barrellength)
camlens = ParaxialLensEllipse(focallength, aprad, aprad, -camdir_norm, camloc)
barrelloc = camloc - barrellength / 2 * camdir_norm
barreltop = Plane(camdir_norm, camloc)
barrelbot = Plane(-camdir_norm, camloc - 3 * barrellength * camdir_norm)
barrelrot = OpticSim.rotmatbetween(SVector(0.0, 0.0, 1.0), camdir_norm)
cambarrel = csgintersection(barrelbot, csgintersection(barreltop, leaf(Cylinder(camrad, barrellength, interface = opaqueinterface(Float64)), RigidBodyTransform(barrelrot, barrelloc))))()
camdet = Circle(sensorrad, camdir_norm, camloc - barrellength * camdir_norm, interface = opaqueinterface(Float64))
# sourceleft = hoecenter[1] + hoehalfwidth - sourceloc[1]
# sourceright = hoecenter[1] - hoehalfwidth - sourceloc[1]
# sourceleftθ = atan(sourceleft, sourceloc[2])
# sourcerightθ = atan(sourceright, sourceloc[2])
# midθ = (sourceleftθ + sourcerightθ) / 2
# sourcedir = normalize(SVector(er * tan(midθ), -er, 0.0))
# sourceextentθ = abs(midθ - sourcerightθ)
# source = CosineOpticalSource(RandomSource(OriginPoint{Float64}(1, position = sourceloc, direction = sourcedir), nrays, sourceextentθ), 1.0, 0.78)
rays = Vector{OpticalRay{Float64,3}}(undef, nrays)
@simd for i in 1:nrays
p = point(rect, rand() * 2 - 1, rand() * 2 - 1)
rays[i] = OpticalRay(sourceloc, p - sourceloc, 1.0, 0.78)
end
source = RayListSource(rays)
sys = CSGOpticalSystem(LensAssembly(obj, cornea, camlens, cambarrel, camap), camdet, 800, 800)
if det
Vis.show(OpticSim.traceMT(sys, source))
else
Vis.drawtracerays(sys; raygenerator = source, trackallrays = true, kwargs...)
# for θ in 0:(π / 6):(2π)
# ledloc = SVector(20 * cos(θ) + offset[1], 0 + offset[2], 15 * sin(θ) + offset[3])
# Vis.draw!(leaf(Sphere(1.0), translation(ledloc...)), color = :red)
# end
for d in dirs
# Vis.draw!(leaf(Sphere(1.0), translation((corneavertex - 10 * d)...)), color = :red)
Vis.draw!((corneavertex - 50 * d, corneavertex), color = :red)
end
if showhead
Vis.draw!(joinpath(@__DIR__, "../../OBJ/glasses.obj"), scale = 100.0, transform = RigidBodyTransform(OpticSim.rotmatd(90, 0, 0), [27.0, 45.0, -8.0]), color = :black)
Vis.draw!(joinpath(@__DIR__, "../../OBJ/femalehead.obj"), scale = 13.0, transform = RigidBodyTransform(OpticSim.rotmatd(0, 0, 180), [27.0, 105.0, -148.0]), color = :white)
end
Vis.display()
end
end
function multiHOE(; kwargs...)
rect = Rectangle(5.0, 5.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, 0.0))
int1 = HologramInterface(SVector(-5.0, 0.0, -20.0), ConvergingBeam, SVector(0.0, -1.0, -1.0), CollimatedBeam, 0.55, 100.0, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, 0.05, false)
int2 = HologramInterface(SVector(5.0, 0.0, -20.0), ConvergingBeam, SVector(0.0, 1.0, -1.0), CollimatedBeam, 0.55, 100.0, OpticSim.GlassCat.Air, OpticSim.GlassCat.SCHOTT.N_BK7, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, OpticSim.GlassCat.Air, 0.05, false)
mint = MultiHologramInterface(int1, int2)
obj = MultiHologramSurface(rect, mint)
sys = CSGOpticalSystem(LensAssembly(obj), Rectangle(10.0, 10.0, SVector(0.0, 0.0, 1.0), SVector(0.0, 0.0, -20.0), interface = opaqueinterface()))
s1 = UniformOpticalSource(CollimatedSource(RandomRectOriginPoints(500, 3.0, 3.0, position = SVector(0.0, 3.0, 3.0), direction = SVector(0.0, -1.0, -1.0))), 0.55, sourcenum = 1)
s2 = UniformOpticalSource(CollimatedSource(RandomRectOriginPoints(500, 3.0, 3.0, position = SVector(0.0, -3.0, 3.0), direction = SVector(0.0, 1.0, -1.0))), 0.55, sourcenum = 2)
s3 = UniformOpticalSource(CollimatedSource(RandomRectOriginPoints(500, 3.0, 3.0, position = SVector(0.0, 0.0, 3.0), direction = SVector(0.0, 0.0, -1.0))), 0.55, sourcenum = 3)
Vis.drawtracerays(sys; raygenerator = s1, trackallrays = true, colorbysourcenum = true, rayfilter = nothing, kwargs...)
Vis.drawtracerays!(sys; raygenerator = s2, trackallrays = true, colorbysourcenum = true, rayfilter = nothing, drawgen = true, kwargs...)
Vis.drawtracerays!(sys; raygenerator = s3, trackallrays = true, colorbysourcenum = true, rayfilter = nothing, drawgen = true, kwargs...)
end
export Examples
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|
import sys
import numpy as np
import optlang
import pytest
from cobra.util.solver import linear_reaction_coefficients
from numpy.testing._private.utils import assert_almost_equal
from optlang.util import solve_with_glpsol
from .load_test_model import build_test_model
@pytest.fixture
def tfa_model():
return build_test_model()
def test_num_cons_vars(tfa_model):
# tfa_model = build_core_model()
num_cons = 2 * 3 * (
len(tfa_model.reactions) - len(tfa_model.Exclude_reactions)
) + len(tfa_model.metabolites)
num_vars = (
2 * (len(tfa_model.metabolites))
+ 4 * (len(tfa_model.reactions) - len(tfa_model.Exclude_reactions))
+ 2 * len(tfa_model.reactions)
)
assert num_cons == len(tfa_model.constraints)
assert num_vars == len(tfa_model.variables)
def test_solver_instances(tfa_model):
if optlang.available_solvers["GUROBI"]:
tfa_model.solver = "gurobi"
assert tfa_model.gurobi_interface
elif optlang.available_solvers["CPLEX"]:
tfa_model.solver = "cplex"
assert tfa_model.cplex_interface
else:
pass
def test_optimization(tfa_model):
solution = tfa_model.optimize()
assert_almost_equal(abs(solution.objective_value), 0.8739, decimal=3)
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|
import numpy as np
import networkx as nx
def distance_partition(g):
'''
input: NetworkX graph g. Assumption: g is a maximal connected subgraph of RH Graph.
output: list of sets of nodes: partition
partition[0] = {soln_states}
partition[i] = {states | soln_dist(states) = i , i integer g.t.e to 0}
'''
partition = {}
partition[0] = set([x for x in g.nodes() if 5 == x[1] ])
remaining_nodes = set(g.nodes())
remaining_nodes.difference_update(partition[0])
i = 1
while remaining_nodes:
partition[i] = set()
for x in partition[i-1]:
nbrs = set(g.neighbors(x) )
remaining_nodes.difference_update(nbrs)
# delete from neighbors thos in partition[i-2] and partition[i-1]
nbrs.difference_update(partition[i-1])
#!!! TDODO - consider ...perhaps an explicit construciton of the dist = 1 set to bootsrap the iteration makes more sense.
if i > 1:
nbrs.difference_update(partition[i-2])
partition[i].update(nbrs)
i=i+1
return partition
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|
import s_discrete
open_locale classical
noncomputable def s_finset {s : ℕ} (s_ne_zero : s ≠ 0) : finset ℝ :=
begin
let numerators : finset ℕ := finset.range s,
let div_by_s_fn : ℕ ↪ ℝ :=
begin
let div_by_s_fn : ℕ → ℝ := λ numerator, ↑numerator / ↑s,
have div_by_s_fn_injective : function.injective div_by_s_fn :=
begin
intros num1 num2 num1_div_by_s_eq_num2_div_by_s,
dsimp[div_by_s_fn] at num1_div_by_s_eq_num2_div_by_s,
have s_cast_ne_zero : (s : ℝ) ≠ 0 := by exact_mod_cast s_ne_zero,
have mul_div_cancel_fact1 := mul_div_cancel' (num1 : ℝ) s_cast_ne_zero,
have mul_div_cancel_fact2 := mul_div_cancel' (num2 : ℝ) s_cast_ne_zero,
replace num1_div_by_s_eq_num2_div_by_s : (s : ℝ) * ((num1 : ℝ) / (s : ℝ)) = (s : ℝ) * ((num2 : ℝ) / (s : ℝ)) :=
by rw num1_div_by_s_eq_num2_div_by_s,
rw [mul_div_cancel_fact1, mul_div_cancel_fact2] at num1_div_by_s_eq_num2_div_by_s,
exact_mod_cast num1_div_by_s_eq_num2_div_by_s,
end,
exact {to_fun := div_by_s_fn, inj' := div_by_s_fn_injective},
end,
exact finset.map div_by_s_fn numerators,
end
lemma s_finset_card {s : ℕ} (s_ne_zero : s ≠ 0) : (s_finset s_ne_zero).card = s :=
by {rw s_finset, simp only [finset.card_range, finset.card_map],}
lemma s_finset_range {s : ℕ} {s_ne_zero : s ≠ 0} {a : ℝ} (a_in_s_finset : a ∈ s_finset s_ne_zero) : 0 ≤ a ∧ a < 1 :=
begin
rw s_finset at a_in_s_finset,
simp only [exists_prop, finset.mem_map, function.embedding.coe_fn_mk, finset.mem_range] at a_in_s_finset,
rcases a_in_s_finset with ⟨a_num, a_num_lt_s, a_num_div_s_eq_a⟩,
have zero_le_s : 0 ≤ s := nat.zero_le s,
have cast_zero_le_s : (0 : ℝ) ≤ ↑s := by {exact_mod_cast zero_le_s},
have cast_zero_lt_s : (0 : ℝ) < ↑s :=
begin
cases eq_or_lt_of_le cast_zero_le_s with zero_eq_s zero_lt_s,
{ exfalso,
symmetry' at zero_eq_s,
have s_eq_zero : s = 0 := by {exact_mod_cast zero_eq_s},
exact s_ne_zero s_eq_zero,
},
exact zero_lt_s,
end,
have zero_le_a : 0 ≤ a :=
begin
have zero_le_a_num : 0 ≤ a_num := nat.zero_le a_num,
have cast_zero_le_a_num : (0 : ℝ) ≤ ↑a_num := by {exact_mod_cast zero_le_a_num},
rw ← a_num_div_s_eq_a,
exact div_nonneg cast_zero_le_a_num cast_zero_le_s,
end,
have a_lt_one : a < 1 :=
by {rw [← a_num_div_s_eq_a, div_lt_one cast_zero_lt_s], exact_mod_cast a_num_lt_s},
exact ⟨zero_le_a, a_lt_one⟩,
end
lemma s_finset_distinct_mod_one {s : ℕ} {s_ne_zero : s ≠ 0} {a : ℝ} {b : ℝ} (a_ne_b : a ≠ b) (a_in_s_finset : a ∈ s_finset s_ne_zero)
(b_in_s_finset : b ∈ s_finset s_ne_zero) : ne_mod_one a b :=
begin
rcases s_finset_range a_in_s_finset with ⟨zero_le_a, a_lt_one⟩,
rcases s_finset_range b_in_s_finset with ⟨zero_le_b, b_lt_one⟩,
rintro ⟨a_floor, b_floor, y, zero_le_y, y_lt_one, a_eq_a_floor_add_y, b_eq_b_floor_add_y⟩,
rcases eq_or_lt_or_gt a_floor b_floor with a_floor_eq_b_floor | a_floor_lt_b_floor | a_floor_gt_b_floor,
{ rw [a_floor_eq_b_floor, ← b_eq_b_floor_add_y] at a_eq_a_floor_add_y,
exact a_ne_b a_eq_a_floor_add_y,
},
{ have a_floor_add_one_le_b_floor := int.add_one_le_of_lt a_floor_lt_b_floor,
have cast_a_floor_add_one_le_b_floor : (↑a_floor : ℝ) + 1 ≤ ↑b_floor := by {exact_mod_cast a_floor_add_one_le_b_floor},
rw a_eq_a_floor_add_y at zero_le_a a_lt_one,
rw b_eq_b_floor_add_y at zero_le_b b_lt_one,
clear_except cast_a_floor_add_one_le_b_floor zero_le_a a_lt_one zero_le_b b_lt_one,
linarith,
},
rw gt at a_floor_gt_b_floor,
have b_floor_add_one_le_a_floor := int.add_one_le_of_lt a_floor_gt_b_floor,
have cast_a_floor_add_one_le_b_floor : (↑b_floor : ℝ) + 1 ≤ ↑a_floor := by {exact_mod_cast b_floor_add_one_le_a_floor},
rw a_eq_a_floor_add_y at zero_le_a a_lt_one,
rw b_eq_b_floor_add_y at zero_le_b b_lt_one,
clear_except cast_a_floor_add_one_le_b_floor zero_le_a a_lt_one zero_le_b b_lt_one,
linarith,
end
lemma inductive_replacement_lemma_helper2 {d : ℕ} {s : ℕ} (s_ne_zero : s ≠ 0) (i : fin d) (T : set (point d))
(T_is_tiling : is_tiling T) (T_faceshare_free : tiling_faceshare_free T) (T_is_periodic : is_periodic T_is_tiling)
(coords_before_i_handled : ∀ p : point d, p ∈ T → ∀ j : fin d, j.val < i.val →
∃ s_val ∈ s_finset s_ne_zero, eq_mod_one (vector.nth p j) s_val) :
∀ coords_left : ℕ, ∀ coords : finset ℝ, ∀ goal_finset : finset ℝ, goal_finset ⊆ s_finset s_ne_zero →
(∀ coord ∈ coords, ∀ s_val ∈ s_finset s_ne_zero, ne_mod_one coord s_val) →
(∀ p ∈ T, ∀ goal_val ∈ goal_finset, ne_mod_one (vector.nth p i) goal_val) →
coords_left = coords.card → coords.card ≤ goal_finset.card →
∃ T_shifted : set (point d), ∃ T_shifted_is_tiling : is_tiling T_shifted, tiling_faceshare_free T_shifted ∧ is_periodic T_shifted_is_tiling ∧
(∀ p : point d, p ∈ T_shifted → ∀ j : fin d, j.val < i.val → ∃ s_val ∈ s_finset s_ne_zero, eq_mod_one (vector.nth p j) s_val) ∧
(∀ p : point d, p ∈ T_shifted → (∀ coord ∈ coords, ne_mod_one (vector.nth p i) coord)
∧ ((∃ goal_val ∈ goal_finset, eq_mod_one (vector.nth p i) goal_val) ∨ p ∈ T)) ∧
(∀ p : point d, p ∈ T_shifted → ∀ j : fin d, j.val > i.val → ∃ p' ∈ T, vector.nth p j = vector.nth p' j) :=
begin
intro coords_left,
induction coords_left with coords_left_pred ih,
{ intros coords goal_finset goal_finset_subset_s_finset coords_inter_s_finset_empty T_disjoint_goal_finset coords_empty
coords_card_le_goal_finset_card,
use [T, T_is_tiling, T_faceshare_free, T_is_periodic],
split, exact coords_before_i_handled, --T_shifted_property_before_i
split,
{ intros p p_in_T,--Prove T_shifted_property_at_i
split,
{ intros coord coord_in_coords,
exfalso, --Derive contradiction between coord_in_coords and coords_empty
symmetry' at coords_empty,
rw finset.card_eq_zero at coords_empty,
rw coords_empty at coord_in_coords,
exact finset.not_mem_empty coord coord_in_coords,
},
right, exact p_in_T,
},
intros p p_in_T j j_val_gt_i_val, --Prove T_shifted_property_after_i
use [p, p_in_T],
},
intros coords goal_finset goal_finset_subset_s_finset coords_disjoint_s_fisnet T_disjoint_goal_finset coords_left_def
coords_card_le_goal_finset_card,
let coords_list : list ℝ := finset.sort has_le.le coords,
let goal_list : list ℝ := finset.sort has_le.le goal_finset,
have coords_list_def : coords_list = finset.sort has_le.le coords := by refl,
have goal_list_def : goal_list = finset.sort has_le.le goal_finset := by refl,
cases finset.sort has_le.le coords with last_coord rest_coords,
{ exfalso, --coords_left_def says coords.card > 0, so it is impossible that coords_list = list.nil
have coords_list_length_eq_coords_card : coords_list.length = coords.card := finset.length_sort real.has_le.le,
rw [← coords_list_length_eq_coords_card, coords_list_def, list.length] at coords_left_def,
exact nat.succ_ne_zero coords_left_pred coords_left_def,
},
cases finset.sort has_le.le goal_finset with last_goal rest_goal_list,
{ exfalso, --coords.card ≤ goal_finset.card and coords.card > 0, so it is impossible that goal_list = list.nil
have goal_finset_card_eq_goal_list_length : goal_list.length = goal_finset.card := finset.length_sort real.has_le.le,
rw [← goal_finset_card_eq_goal_list_length, goal_list_def, list.length, ← coords_left_def] at coords_card_le_goal_finset_card,
exact nat.not_succ_le_zero coords_left_pred coords_card_le_goal_finset_card,
},
have last_goal_in_goal_finset : last_goal ∈ goal_finset :=
begin
rw ← finset.mem_sort real.has_le.le,
change last_goal ∈ goal_list,
rw goal_list_def,
simp only [list.mem_cons_iff, true_or, eq_self_iff_true],
end,
have last_goal_in_s_finset := finset.mem_of_subset goal_finset_subset_s_finset last_goal_in_goal_finset,
let rest_coords_finset : finset ℝ := rest_coords.to_finset,
let rest_goal_finset : finset ℝ := rest_goal_list.to_finset,
have rest_goal_finset_subset_goal_finset : rest_goal_finset ⊆ goal_finset :=
begin
dsimp[rest_goal_finset],
rw finset.subset_iff,
intros rest_goal_val rest_goal_val_in_rest_goal_finset,
rw list.mem_to_finset at rest_goal_val_in_rest_goal_finset,
rw ← finset.mem_sort real.has_le.le,
change rest_goal_val ∈ goal_list,
rw [goal_list_def, list.mem_cons_iff],
right,
exact rest_goal_val_in_rest_goal_finset,
end,
have rest_goal_finset_subset_s_finset : rest_goal_finset ⊆ s_finset s_ne_zero :=
finset.subset.trans rest_goal_finset_subset_goal_finset goal_finset_subset_s_finset,
have rest_coords_finset_subset_coords : rest_coords_finset ⊆ coords :=
begin
dsimp[rest_coords_finset],
rw finset.subset_iff,
intros coord coord_in_rest_coords,
rw list.mem_to_finset at coord_in_rest_coords,
rw ← finset.mem_sort real.has_le.le,
change coord ∈ coords_list,
rw [coords_list_def, list.mem_cons_iff],
right,
exact coord_in_rest_coords,
end,
have rest_coords_finset_disjoint_s_finset :
∀ (coord : ℝ), coord ∈ rest_coords_finset → ∀ (s_val : ℝ), s_val ∈ s_finset s_ne_zero → ne_mod_one coord s_val :=
begin
intros coord coord_in_rest_coords_finset s_val s_val_in_s_finset,
have coord_in_coords := finset.mem_of_subset rest_coords_finset_subset_coords coord_in_rest_coords_finset,
exact coords_disjoint_s_fisnet coord coord_in_coords s_val s_val_in_s_finset,
end,
have rest_coords_nodup : rest_coords.nodup :=
begin
rw list.nodup,
have coords_list_nodup : coords_list.nodup := finset.sort_nodup real.has_le.le coords,
rw [list.nodup, coords_list_def, list.pairwise_cons] at coords_list_nodup,
exact coords_list_nodup.2,
end,
have rest_coords_card : coords_left_pred = rest_coords_finset.card :=
begin
dsimp[rest_coords_finset],
have coords_list_length : coords_list.length = rest_coords.length + 1 :=
by {rw coords_list_def, exact list.length_cons last_coord rest_coords},
have coords_list_length_eq_coords_card : coords_list.length = coords.card :=
by {dsimp[coords_list], apply finset.length_sort},
rw ← coords_left_def at coords_list_length_eq_coords_card,
rw list.to_finset_card_of_nodup rest_coords_nodup,
clear_except coords_list_length coords_list_length_eq_coords_card,
omega,
end,
have T_disjoint_rest_goal_finset :
∀ (p : vector ℝ d), p ∈ T → ∀ (goal_val : ℝ), goal_val ∈ rest_goal_finset → ne_mod_one (p.nth i) goal_val :=
begin
intros p p_in_T goal_val goal_val_in_rest_goal_finset,
have goal_val_in_goal_finset := finset.mem_of_subset rest_goal_finset_subset_goal_finset goal_val_in_rest_goal_finset,
exact T_disjoint_goal_finset p p_in_T goal_val goal_val_in_goal_finset,
end,
have rest_coords_card_le_rest_goal_finset_card : rest_coords_finset.card ≤ rest_goal_finset.card :=
begin
rw ← rest_coords_card,
rw [← coords_left_def, nat.succ_eq_add_one] at coords_card_le_goal_finset_card,
have coords_left_pred_le_goal_finset_card_sub_one : coords_left_pred ≤ goal_finset.card - 1 :=
by {clear_except coords_card_le_goal_finset_card, omega},
have goal_finset_card : goal_finset.card = rest_goal_finset.card + 1 :=
begin
rw ← finset.length_sort real.has_le.le,
change goal_list.length = rest_goal_finset.card + 1,
dsimp[rest_goal_finset],
have rest_goal_list_nodup : rest_goal_list.nodup :=
begin
have goal_list_nodup : goal_list.nodup := finset.sort_nodup has_le.le goal_finset,
rw [goal_list_def, list.nodup, list.pairwise_cons, ← list.nodup] at goal_list_nodup,
exact goal_list_nodup.2,
end,
rw [goal_list_def, list.length_cons, list.to_finset_card_of_nodup rest_goal_list_nodup],
end,
rw goal_finset_card at coords_left_pred_le_goal_finset_card_sub_one,
simp only [nat.add_succ_sub_one, add_zero] at coords_left_pred_le_goal_finset_card_sub_one,
exact coords_left_pred_le_goal_finset_card_sub_one,
end,
rcases ih rest_coords_finset rest_goal_finset rest_goal_finset_subset_s_finset rest_coords_finset_disjoint_s_finset
T_disjoint_rest_goal_finset rest_coords_card rest_coords_card_le_rest_goal_finset_card with
⟨T_shifted_prev, T_shifted_prev_is_tiling, T_shifted_prev_faceshare_free, T_shifted_prev_is_periodic, T_shifted_prev_property_before_i,
T_shifted_prev_property_at_i, T_shifted_prev_property_after_i⟩,
let T_shifted := shift_tiling T_shifted_prev i last_coord (last_goal - last_coord),
rcases replacement_lemma d T_shifted_prev T_shifted_prev_is_tiling last_coord (last_goal - last_coord) i with
⟨T_shifted_is_tiling, T_shifted_prev_faceshare_free_implication⟩,
use [T_shifted, T_shifted_is_tiling],
have last_goal_not_in_T_shifted_prev :
(∀ (t : point d), t ∈ T_shifted_prev → ne_mod_one (vector.nth t i) (last_coord + (last_goal - last_coord))) :=
begin
intros t t_in_T_shifted_prev,
simp only [add_sub_cancel'_right],
rcases T_shifted_prev_property_at_i t t_in_T_shifted_prev with
⟨t_ne_mod_one_rest_coords, ⟨goal_val, goal_val_in_rest_goal_finset, t_eq_goal_val_mod_one⟩ | t_in_T⟩,
{ have goal_val_ne_last_goal : goal_val ≠ last_goal :=
begin
have goal_list_nodup : goal_list.nodup := finset.sort_nodup real.has_le.le goal_finset,
rw [list.nodup, goal_list_def, list.pairwise_cons] at goal_list_nodup,
rcases goal_list_nodup with ⟨last_goal_not_in_rest_goal_list, rest_goal_list_nodup⟩,
dsimp[rest_goal_finset] at goal_val_in_rest_goal_finset,
rw list.mem_to_finset at goal_val_in_rest_goal_finset,
symmetry,
exact last_goal_not_in_rest_goal_list goal_val goal_val_in_rest_goal_finset,
end,
have goal_val_in_s_finset : goal_val ∈ s_finset s_ne_zero :=
finset.mem_of_subset rest_goal_finset_subset_s_finset goal_val_in_rest_goal_finset,
have goal_val_ne_last_goal_mod_one := s_finset_distinct_mod_one goal_val_ne_last_goal goal_val_in_s_finset last_goal_in_s_finset,
intro t_eq_last_goal_mod_one,
replace t_eq_goal_val_mod_one := eq_mod_one_symmetric t_eq_goal_val_mod_one,
exact goal_val_ne_last_goal_mod_one (eq_mod_one_transitive t_eq_goal_val_mod_one t_eq_last_goal_mod_one),
},
exact T_disjoint_goal_finset t t_in_T last_goal last_goal_in_goal_finset,
end,
have T_shifted_faceshare_free := T_shifted_prev_faceshare_free_implication T_shifted_prev_faceshare_free last_goal_not_in_T_shifted_prev,
split, exact T_shifted_faceshare_free,
split,
exact shifted_periodic_tiling_still_periodic T_shifted_prev_is_tiling T_shifted_prev_is_periodic i last_coord (last_goal - last_coord) T_shifted_is_tiling,
split,
{ intros p p_in_T_shifted j j_val_lt_i_val, --Prove T_shifted_property_before_i
dsimp[T_shifted] at p_in_T_shifted,
rw shift_tiling at p_in_T_shifted,
simp only [exists_prop, set.mem_union_eq, set.mem_set_of_eq] at p_in_T_shifted,
rcases p_in_T_shifted with
⟨p_in_T_shifted_prev, p_ne_last_coord_mod_one⟩ | ⟨p_prev, p_prev_in_T_shifted_prev, p_def, p_prev_eq_last_coord_mod_one⟩,
exact T_shifted_prev_property_before_i p p_in_T_shifted_prev j j_val_lt_i_val,
rw [scaled_basis_vector, add_vectors] at p_def,
simp only [vector.nth_of_fn] at p_def,
rw p_def,
simp only [vector.nth_of_fn],
have i_ne_j : i ≠ j :=
by {intro i_eq_j, rw i_eq_j at j_val_lt_i_val, exact lt_irrefl j.val j_val_lt_i_val},
rw [if_neg i_ne_j, add_zero],
exact T_shifted_prev_property_before_i p_prev p_prev_in_T_shifted_prev j j_val_lt_i_val,
},
split,
{ intros p p_in_T_shifted, --Prove T_shifted_property_at_i
dsimp[T_shifted] at p_in_T_shifted,
rw shift_tiling at p_in_T_shifted,
simp only [exists_prop, set.mem_union_eq, set.mem_set_of_eq] at p_in_T_shifted,
rcases p_in_T_shifted with
⟨p_in_T_shifted_prev, p_ne_last_coord_mod_one⟩ | ⟨p_prev, p_prev_in_T_shifted_prev, p_def, p_prev_eq_last_coord_mod_one⟩,
{ rcases T_shifted_prev_property_at_i p p_in_T_shifted_prev with ⟨p_ne_rest_coords_mod_one, T_shifted_second_property_at_i⟩,
split,
{ intros coord coord_in_coords,
by_cases coord_in_rest_coords_finset : coord ∈ rest_coords_finset,
exact p_ne_rest_coords_mod_one coord coord_in_rest_coords_finset,
rename coord_in_rest_coords_finset coord_not_in_rest_coords_finset,
have coord_in_coords_list : coord ∈ coords_list := by {rw finset.mem_sort, exact coord_in_coords},
rw [coords_list_def, list.mem_cons_eq] at coord_in_coords_list,
cases coord_in_coords_list with coord_eq_last_coord coord_in_rest_coords,
{ rw coord_eq_last_coord,
exact p_ne_last_coord_mod_one,
},
have coord_in_rest_coords_finset : coord ∈ rest_coords_finset := by {rw list.mem_to_finset, exact coord_in_rest_coords},
exact p_ne_rest_coords_mod_one coord coord_in_rest_coords_finset,
},
rcases T_shifted_second_property_at_i with
⟨goal_val, goal_val_in_rest_goal_finset, p_eq_goal_val_mod_one⟩ | p_in_T,
{ left,
have goal_val_in_goal_finset := finset.mem_of_subset rest_goal_finset_subset_goal_finset goal_val_in_rest_goal_finset,
use [goal_val, goal_val_in_goal_finset, p_eq_goal_val_mod_one],
},
right,
exact p_in_T,
},
split,
{ intros coord coord_in_coords p_eq_coord_mod_one,
rw [p_def, scaled_basis_vector, add_vectors] at p_eq_coord_mod_one,
simp only [if_true, eq_self_iff_true, vector.nth_of_fn] at p_eq_coord_mod_one,
replace p_eq_coord_mod_one := subst_summand_eq_mod_one p_prev_eq_last_coord_mod_one p_eq_coord_mod_one,
simp only [add_sub_cancel'_right] at p_eq_coord_mod_one,
exact coords_disjoint_s_fisnet coord coord_in_coords last_goal last_goal_in_s_finset (eq_mod_one_symmetric p_eq_coord_mod_one),
},
left,
use [last_goal, last_goal_in_goal_finset],
rw [p_def, scaled_basis_vector, add_vectors],
simp only [if_true, eq_self_iff_true, vector.nth_of_fn],
apply subst_summand_eq_mod_one (eq_mod_one_symmetric p_prev_eq_last_coord_mod_one),
simp only [add_sub_cancel'_right],
exact eq_mod_one_reflexive last_goal,
},
intros p p_in_T_shifted j j_val_gt_i_val, --Prove T_shifted_property_after_i
dsimp[T_shifted] at p_in_T_shifted,
rw shift_tiling at p_in_T_shifted,
simp only [exists_prop, set.mem_union_eq, set.mem_set_of_eq] at p_in_T_shifted,
rcases p_in_T_shifted with
⟨p_in_T_shifted_prev, p_ne_last_coord_mod_one⟩ | ⟨p_prev, p_prev_in_T_shifted_prev, p_def, p_prev_eq_last_coord_mod_one⟩,
exact T_shifted_prev_property_after_i p p_in_T_shifted_prev j j_val_gt_i_val,
rw [scaled_basis_vector, add_vectors] at p_def,
simp only [vector.nth_of_fn] at p_def,
rw p_def,
simp only [vector.nth_of_fn],
have i_ne_j : i ≠ j :=
by {intro i_eq_j, rw i_eq_j at j_val_gt_i_val, exact gt_irrefl j.val j_val_gt_i_val},
rw [if_neg i_ne_j, add_zero],
exact T_shifted_prev_property_after_i p_prev p_prev_in_T_shifted_prev j j_val_gt_i_val,
end
lemma inductive_replacement_lemma_helper1 {d : ℕ} {s : ℕ} (d_ne_zero : d ≠ 0) (s_ne_zero : s ≠ 0) (i : fin d) (T : set (point d))
(T_is_tiling : is_tiling T) (T_faceshare_free : tiling_faceshare_free T) (T_is_periodic : is_periodic T_is_tiling) (T_is_s_discrete : is_s_discrete s T)
(coords_before_i_handled : ∀ p : point d, p ∈ T → ∀ j : fin d, j.val < i.val →
∃ s_val ∈ s_finset s_ne_zero, eq_mod_one (vector.nth p j) s_val) :
∃ T_shifted : set (point d), ∃ T_shifted_is_tiling : is_tiling T_shifted, tiling_faceshare_free T_shifted ∧
is_periodic T_shifted_is_tiling ∧ is_s_discrete s T_shifted ∧
∀ p : point d, p ∈ T_shifted → ∀ j : fin d, j.val ≤ i.val → ∃ s_val ∈ s_finset s_ne_zero, eq_mod_one (vector.nth p j) s_val :=
begin
rcases T_is_s_discrete i with ⟨coords, coords_card_le_s, ⟨coords_distinct_mod_one, T_is_s_discrete'⟩⟩,
let goal_finset := {s_val ∈ s_finset s_ne_zero | ∀ coord ∈ coords, ne_mod_one coord s_val},
let coords_inter_s_finset := {coord ∈ coords | ∃ s_val ∈ s_finset s_ne_zero, eq_mod_one coord s_val},
have coords_inter_goal_subset_of_coords : coords_inter_s_finset ⊆ coords :=
by {dsimp[coords_inter_s_finset], simp only [finset.filter_subset]},
have goal_finset_subset_s_finset : goal_finset ⊆ s_finset s_ne_zero :=
by {dsimp[goal_finset], apply finset.filter_subset},
have coords_to_handle_disjoint_s_finset :
∀ (coord : ℝ), coord ∈ coords \ coords_inter_s_finset → ∀ (s_val : ℝ), s_val ∈ s_finset s_ne_zero → ne_mod_one coord s_val :=
begin
intros coord coord_in_coords_remaining s_val s_val_in_s_finset,
dsimp[coords_inter_s_finset, goal_finset] at coord_in_coords_remaining,
simp only [not_exists, and_imp, not_and, finset.mem_sdiff, finset.mem_filter] at coord_in_coords_remaining,
cases coord_in_coords_remaining with coord_in_coords coord_in_coords_imp,
exact coord_in_coords_imp coord_in_coords s_val s_val_in_s_finset,
end,
have T_disjoint_goal_finset :
∀ (p : vector ℝ d), p ∈ T → ∀ (goal_val : ℝ), goal_val ∈ goal_finset → ne_mod_one (p.nth i) goal_val :=
begin
intros p p_in_T goal_val goal_val_in_goal_finset p_eq_goal_val_mod_one,
dsimp[goal_finset] at goal_val_in_goal_finset,
simp only [finset.mem_filter] at goal_val_in_goal_finset,
cases goal_val_in_goal_finset with goal_val_in_s_finset goal_val_not_in_T,
rcases T_is_s_discrete' p p_in_T with ⟨coord, coord_in_coords, p_eq_coord_mod_one⟩,
replace p_eq_coord_mod_one := eq_mod_one_symmetric p_eq_coord_mod_one,
have coord_eq_goal_val_mod_one := eq_mod_one_transitive p_eq_coord_mod_one p_eq_goal_val_mod_one,
exact goal_val_not_in_T coord coord_in_coords coord_eq_goal_val_mod_one,
end,
have coords_to_handle_card_le_goal_finset_card : (coords \ coords_inter_s_finset).card ≤ goal_finset.card :=
begin
rw finset.card_sdiff,
{ simp only [tsub_le_iff_right],
have goal_finset_card_add_coord_inter_s_card_eq_s_card : goal_finset.card + coords_inter_s_finset.card = (s_finset s_ne_zero).card :=
begin
let s_finset_filter_fn := (λ s_val : ℝ, ∀ (coord : ℝ), coord ∈ coords → ne_mod_one coord s_val),
have s_finset_filter_fn_decidable : decidable_pred s_finset_filter_fn :=
(λ s_val, classical.prop_decidable (s_finset_filter_fn s_val)),
let s_finset_filter_fn_neg := (λ s_val : ℝ, ∃ coord ∈ coords, eq_mod_one coord s_val),
have not_s_finset_filter_fn_neg_eq_f_finset_filter_fn_neg : not ∘ s_finset_filter_fn = s_finset_filter_fn_neg :=
begin
apply funext,
intro s_val,
dsimp[s_finset_filter_fn, s_finset_filter_fn_neg],
simp only [exists_prop, eq_iff_iff, not_forall],
split,
{ rintro ⟨coord, coord_in_coords, coord_eq_s_val_mod_one⟩,
use [coord, coord_in_coords],
rw [ne_mod_one, not_not] at coord_eq_s_val_mod_one,
exact coord_eq_s_val_mod_one,
},
rintro ⟨coord, coord_in_coords, coord_eq_s_val_mod_one⟩,
use [coord, coord_in_coords],
end,
rw ← @finset.filter_card_add_filter_neg_card_eq_card ℝ (s_finset s_ne_zero) s_finset_filter_fn s_finset_filter_fn_decidable,
have goal_finset_eq_s_finset_filtered :
goal_finset = @finset.filter ℝ s_finset_filter_fn s_finset_filter_fn_decidable (s_finset s_ne_zero) :=
begin
dsimp[goal_finset, s_finset_filter_fn],
apply finset.filter_congr_decidable,
end,
rw goal_finset_eq_s_finset_filtered,
simp only [add_right_inj],
let f : ℝ → ℝ :=
(λ coord : ℝ,
begin
by_cases h : ∃ s_val ∈ s_finset s_ne_zero, eq_mod_one coord s_val,
exact classical.some h,
exact (-1 : ℝ),
end
),
convert_to coords_inter_s_finset.card = (finset.image f coords_inter_s_finset).card,
{ have finset_card_eq_self_card : ∀ s : finset ℝ, ∀ s' : finset ℝ, s = s' → s.card = s'.card :=
by {intros s s' s_eq_s', rw s_eq_s'},
apply finset_card_eq_self_card,
apply finset.ext,
intro s_val,
split,
{ intro s_val_in_filtered_set,
conv at s_val_in_filtered_set
begin
find (not ∘ s_finset_filter_fn) {rw not_s_finset_filter_fn_neg_eq_f_finset_filter_fn_neg}
end,
dsimp[s_finset_filter_fn_neg] at s_val_in_filtered_set,
simp only [exists_prop, finset.mem_filter] at s_val_in_filtered_set,
rcases s_val_in_filtered_set with ⟨s_val_in_s_finset, ⟨coord, coord_in_coords, coord_eq_s_val_mod_one⟩⟩,
rw finset.mem_image,
use coord,
split,
{ dsimp[coords_inter_s_finset],
simp only [exists_prop, finset.mem_filter],
use [coord_in_coords, s_val, s_val_in_s_finset, coord_eq_s_val_mod_one],
},
dsimp[f],
have if_cond_true : ∃ (s_val : ℝ) (H : s_val ∈ s_finset s_ne_zero), eq_mod_one coord s_val :=
⟨s_val, s_val_in_s_finset, coord_eq_s_val_mod_one⟩,
convert_to classical.some if_cond_true = s_val, apply dif_pos,
rcases classical.some_spec if_cond_true with ⟨classical_some_in_s_finset, coord_eq_classical_some_mod_one⟩,
by_contra classical_some_ne_s_val,
have classical_some_eq_s_val_mod_one : eq_mod_one (classical.some if_cond_true) s_val :=
eq_mod_one_transitive (eq_mod_one_symmetric coord_eq_classical_some_mod_one) coord_eq_s_val_mod_one,
exact s_finset_distinct_mod_one classical_some_ne_s_val classical_some_in_s_finset s_val_in_s_finset
classical_some_eq_s_val_mod_one,
},
intro s_val_in_image,
conv
begin
find (not ∘ s_finset_filter_fn) {rw not_s_finset_filter_fn_neg_eq_f_finset_filter_fn_neg}
end,
dsimp[s_finset_filter_fn_neg],
simp only [exists_prop, finset.mem_filter],
dsimp[f] at s_val_in_image,
rw finset.mem_image at s_val_in_image,
simp only [exists_prop] at s_val_in_image,
rcases s_val_in_image with ⟨coord, coord_in_coords_inter_s_finset, classical_some_eq_s_val⟩,
by_cases if_cond : ∃ (s_val : ℝ), s_val ∈ s_finset s_ne_zero ∧ eq_mod_one coord s_val,
{ rename if_cond if_cond_true,
rw dif_pos if_cond_true at classical_some_eq_s_val,
rcases classical.some_spec if_cond_true with ⟨classical_some_in_s_finset, coord_eq_classical_some_mod_one⟩,
rw ← classical_some_eq_s_val,
have coord_in_coords : coord ∈ coords :=
begin
dsimp[coords_inter_s_finset] at coord_in_coords_inter_s_finset,
rw finset.mem_filter at coord_in_coords_inter_s_finset,
cases coord_in_coords_inter_s_finset with coord_in_coords _,
exact coord_in_coords,
end,
exact ⟨classical_some_in_s_finset, ⟨coord, coord_in_coords, coord_eq_classical_some_mod_one⟩⟩,
},
rename if_cond if_cond_false,
exfalso, --Derive contradiction from if_cond_false
dsimp[coords_inter_s_finset] at coord_in_coords_inter_s_finset,
rw finset.mem_filter at coord_in_coords_inter_s_finset,
cases coord_in_coords_inter_s_finset with _ if_cond_true,
have if_cond_true' : ∃ s_val : ℝ, s_val ∈ s_finset s_ne_zero ∧ eq_mod_one coord s_val :=
begin
rcases if_cond_true with ⟨s_val, s_val_in_s_finset, coord_eq_s_val_mod_one⟩,
use s_val,
exact ⟨s_val_in_s_finset, coord_eq_s_val_mod_one⟩,
end,
exact if_cond_false if_cond_true',
},
symmetry,
rw finset.card_image_eq_iff_inj_on,
rw set.inj_on,
intros coord1 coord1_in_coords_inter_s_finset coord2 coord2_in_coords_inter_s_finset f_coord1_eq_f_coord2,
rw finset.mem_coe at coord1_in_coords_inter_s_finset coord2_in_coords_inter_s_finset,
dsimp[coords_inter_s_finset] at coord1_in_coords_inter_s_finset coord2_in_coords_inter_s_finset,
simp only [exists_prop, finset.mem_filter] at coord1_in_coords_inter_s_finset coord2_in_coords_inter_s_finset,
rcases coord1_in_coords_inter_s_finset with
⟨coord1_in_coords, ⟨coord1_s_val, coord1_s_val_in_s_finset, coord1_eq_coord1_s_val_mod_one⟩⟩,
rcases coord2_in_coords_inter_s_finset with
⟨coord2_in_coords, ⟨coord2_s_val, coord2_s_val_in_s_finset, coord2_eq_coord2_s_val_mod_one⟩⟩,
dsimp[f] at f_coord1_eq_f_coord2,
have exists_s_val_eq_coord1_mod_one : ∃ (s_val : ℝ) (H : s_val ∈ s_finset s_ne_zero), eq_mod_one coord1 s_val :=
⟨coord1_s_val, coord1_s_val_in_s_finset, coord1_eq_coord1_s_val_mod_one⟩,
have exists_s_val_eq_coord2_mod_one : ∃ (s_val : ℝ) (H : s_val ∈ s_finset s_ne_zero), eq_mod_one coord2 s_val :=
⟨coord2_s_val, coord2_s_val_in_s_finset, coord2_eq_coord2_s_val_mod_one⟩,
rw [dif_pos exists_s_val_eq_coord1_mod_one, dif_pos exists_s_val_eq_coord2_mod_one] at f_coord1_eq_f_coord2,
rcases classical.some_spec exists_s_val_eq_coord1_mod_one with
⟨classical_some1_in_s_finset, coord1_eq_classical_some1_mod_one⟩,
rcases classical.some_spec exists_s_val_eq_coord2_mod_one with
⟨classical_some2_in_s_finset, coord2_eq_classical_some2_mod_one⟩,
rw f_coord1_eq_f_coord2 at coord1_eq_classical_some1_mod_one,
have coord1_eq_coord2_mod_one : eq_mod_one coord1 coord2 :=
eq_mod_one_transitive coord1_eq_classical_some1_mod_one (eq_mod_one_symmetric coord2_eq_classical_some2_mod_one),
by_contra coord1_ne_coord2,
exact coords_distinct_mod_one coord1 coord1_in_coords coord2 coord2_in_coords coord1_ne_coord2 coord1_eq_coord2_mod_one,
end,
rw [goal_finset_card_add_coord_inter_s_card_eq_s_card, s_finset_card s_ne_zero],
exact coords_card_le_s,
},
apply finset.filter_subset,
end,
rcases inductive_replacement_lemma_helper2 s_ne_zero i T T_is_tiling T_faceshare_free T_is_periodic coords_before_i_handled
(coords \ coords_inter_s_finset).card (coords \ coords_inter_s_finset) goal_finset goal_finset_subset_s_finset
coords_to_handle_disjoint_s_finset T_disjoint_goal_finset (by refl) coords_to_handle_card_le_goal_finset_card with
⟨T_shifted, T_shifted_is_tiling, T_shifted_faceshare_free, T_shifted_is_periodic, T_shifted_property_before_i, T_shifted_property_at_i,
T_shifted_property_after_i⟩,
use [T_shifted, T_shifted_is_tiling],
split, exact T_shifted_faceshare_free,
split, exact T_shifted_is_periodic,
split,
{ rw is_s_discrete,
intro j,
have j_eq_or_lt_or_gt_i := nat_eq_or_lt_or_gt j.val i.val,
rcases j_eq_or_lt_or_gt_i with j_val_eq_i_val | j_val_lt_i_val | j_val_gt_i_val,
{ use s_finset s_ne_zero,
split,
{ apply le_of_eq,
exact s_finset_card s_ne_zero,
},
split,
{ intros coord1 coord1_in_s_finset coord2 coord2_in_s_finset coord1_ne_coord2,
exact s_finset_distinct_mod_one coord1_ne_coord2 coord1_in_s_finset coord2_in_s_finset,
},
intros t t_in_T_shifted,
have j_eq_i := fin.eq_of_veq j_val_eq_i_val,
rw j_eq_i,
cases T_shifted_property_at_i t t_in_T_shifted with coords_not_in_T_shifted T_shifted_has_goal,
by_contra goal_false,
cases T_shifted_has_goal with goal t_in_T,
{ simp only [not_exists, exists_prop, not_and] at goal_false,
rcases goal with ⟨goal_val, goal_val_in_goal_finset, t_eq_goal_val_mod_one⟩,
have goal_val_in_s_finset := finset.mem_of_subset goal_finset_subset_s_finset goal_val_in_goal_finset,
exact goal_false goal_val goal_val_in_s_finset t_eq_goal_val_mod_one,
},
rcases T_is_s_discrete' t t_in_T with ⟨coord, coord_in_coords, t_eq_mod_one_coord⟩,
have coord_in_coords_to_handle : coord ∈ coords \ coords_inter_s_finset :=
begin
dsimp[coords_inter_s_finset],
simp only [not_exists, exists_prop, not_and, finset.mem_sdiff, finset.mem_filter],
split, exact coord_in_coords,
intros coord_in_coords goal_val goal_val_in_goal_finset coord_eq_goal_val_mod_one,
have t_eq_goal_val_mod_one := eq_mod_one_transitive t_eq_mod_one_coord coord_eq_goal_val_mod_one,
simp only [not_exists, exists_prop, not_and] at goal_false,
exact goal_false goal_val goal_val_in_goal_finset t_eq_goal_val_mod_one,
end,
exact coords_not_in_T_shifted coord coord_in_coords_to_handle t_eq_mod_one_coord,
},
{ use s_finset s_ne_zero,
split,
{ apply le_of_eq,
exact s_finset_card s_ne_zero,
},
split,
{ intros coord1 coord1_in_s_finset coord2 coord2_in_s_finset coord1_ne_coord2,
exact s_finset_distinct_mod_one coord1_ne_coord2 coord1_in_s_finset coord2_in_s_finset,
},
intros t t_in_T_shifted,
exact T_shifted_property_before_i t t_in_T_shifted j j_val_lt_i_val,
},
rcases T_is_s_discrete j with ⟨coords, coords_card_le_s, ⟨coords_distinct_mod_one, t_in_T_imp_t_j_in_coords⟩⟩,
use [coords, coords_card_le_s],
split, exact coords_distinct_mod_one,
intros t t_in_T_shifted,
rcases T_shifted_property_after_i t t_in_T_shifted j j_val_gt_i_val with ⟨t', t'_in_T, t_eq_t'_at_j⟩,
rw t_eq_t'_at_j,
exact t_in_T_imp_t_j_in_coords t' t'_in_T,
},
intros p p_in_T_shifted j j_val_le_i,
cases lt_or_eq_of_le j_val_le_i with j_val_lt_i_val j_val_eq_i_val,
exact T_shifted_property_before_i p p_in_T_shifted j j_val_lt_i_val,
have j_eq_i : j = i := fin.eq_of_veq j_val_eq_i_val,
rw j_eq_i,
replace T_shifted_property_at_i := T_shifted_property_at_i p p_in_T_shifted,
cases T_shifted_property_at_i with T_shifted_shifts_all_bad_coords T_shifted_coords_all_in_goal_finset,
by_contra p_coord_not_in_goal_finset, --Derive contradiction between p_coord_not_in_goal_finset and T_shifted_property_at_i
cases T_shifted_coords_all_in_goal_finset with T_shifted_coords_all_in_goal_finset p_in_T,
{ rcases T_shifted_coords_all_in_goal_finset with ⟨goal_val, goal_val_in_goal_finset, p_eq_goal_val_mod_one⟩,
simp only [not_exists, exists_prop, not_and] at p_coord_not_in_goal_finset,
have goal_val_in_s_finset := finset.mem_of_subset goal_finset_subset_s_finset goal_val_in_goal_finset,
exact p_coord_not_in_goal_finset goal_val goal_val_in_s_finset p_eq_goal_val_mod_one,
},
have p_i_in_coords : ∃ coord ∈ coords, eq_mod_one (vector.nth p i) coord := T_is_s_discrete' p p_in_T,
rcases p_i_in_coords with ⟨coord, coord_in_coords, p_i_eq_coords_mod_one⟩,
by_cases coord_in_goal_finset : coord ∈ goal_finset,
{ simp only [not_exists, exists_prop, not_and] at p_coord_not_in_goal_finset,
have coord_in_s_finset := finset.mem_of_subset goal_finset_subset_s_finset coord_in_goal_finset,
exact p_coord_not_in_goal_finset coord coord_in_s_finset p_i_eq_coords_mod_one,
},
rename coord_in_goal_finset coord_not_in_goal_finset,
have coord_in_coords_to_handle : coord ∈ coords \ coords_inter_s_finset :=
begin
dsimp[coords_inter_s_finset],
simp only [not_exists, exists_prop, not_and, finset.mem_sdiff, finset.mem_filter],
split, exact coord_in_coords,
intros coord_in_coords goal_val goal_val_in_goal_finset coord_eq_goal_val_mod_one,
have p_eq_goal_val_mod_one := eq_mod_one_transitive p_i_eq_coords_mod_one coord_eq_goal_val_mod_one,
simp only [not_exists, exists_prop, not_and] at p_coord_not_in_goal_finset,
exact p_coord_not_in_goal_finset goal_val goal_val_in_goal_finset p_eq_goal_val_mod_one,
end,
exact T_shifted_shifts_all_bad_coords coord coord_in_coords_to_handle p_i_eq_coords_mod_one,
end
lemma inductive_replacement_lemma {d : ℕ} {s : ℕ} (d_ne_zero : d ≠ 0) (s_ne_zero : s ≠ 0) (T : set (point d))
(T_is_tiling : is_tiling T) (T_faceshare_free : tiling_faceshare_free T) (T_is_periodic: is_periodic T_is_tiling) (T_is_s_discrete : is_s_discrete s T) :
∃ T_shifted : set (point d), ∃ T_shifted_is_tiling : is_tiling T_shifted, tiling_faceshare_free T_shifted ∧ is_periodic T_shifted_is_tiling ∧
(∀ i : fin d, ∀ p : point d, p ∈ T_shifted → ∃ s_val ∈ s_finset s_ne_zero, eq_mod_one (vector.nth p i) s_val) :=
begin
let d_sub_one : fin d := ⟨d - 1, nat.pred_lt d_ne_zero⟩,
have inductive_replacement_lemma_helper_fact : ∀ i : fin d, i.val < d →
∃ T_shifted : set (point d), ∃ T_shifted_is_tiling : is_tiling T_shifted, tiling_faceshare_free T_shifted ∧
is_periodic T_shifted_is_tiling ∧ is_s_discrete s T_shifted ∧
∀ p : point d, p ∈ T_shifted → ∀ j : fin d, j.val ≤ i.val → ∃ s_val ∈ s_finset s_ne_zero, eq_mod_one (vector.nth p j) s_val :=
begin
intro i,
induction i.val,
{ intro zero_lt_d,
have coords_before_zero_handled : ∀ p : point d, p ∈ T → ∀ j : fin d, j.val < 0 →
∃ s_val ∈ s_finset s_ne_zero, eq_mod_one (vector.nth p j) s_val :=
by {intros p p_in_T j j_lt_zero, exfalso, clear_except j_lt_zero, linarith,},
exact inductive_replacement_lemma_helper1 d_ne_zero s_ne_zero ⟨0, zero_lt_d⟩ T T_is_tiling T_faceshare_free
T_is_periodic T_is_s_discrete coords_before_zero_handled,
},
intro n_succ_lt_d,
have n_lt_d : n < d := nat.lt_of_succ_lt n_succ_lt_d,
rcases ih n_lt_d with
⟨T_shifted_prev, T_shifted_prev_is_tiling, T_shifted_prev_faceshare_free, T_shifted_prev_is_periodic, T_shifted_prev_s_discrete,
T_shifted_prev_coord_property⟩,
have coords_before_n_succ_handled :
∀ p : point d, p ∈ T_shifted_prev → ∀ j : fin d, j.val < n.succ → ∃ s_val ∈ s_finset s_ne_zero, eq_mod_one (vector.nth p j) s_val :=
begin
intros p p_in_T_shifted_prev j j_lt_n_succ,
have j_le_n := nat.le_of_lt_succ j_lt_n_succ,
exact T_shifted_prev_coord_property p p_in_T_shifted_prev j j_le_n,
end,
exact inductive_replacement_lemma_helper1 d_ne_zero s_ne_zero ⟨n.succ, n_succ_lt_d⟩ T_shifted_prev T_shifted_prev_is_tiling
T_shifted_prev_faceshare_free T_shifted_prev_is_periodic T_shifted_prev_s_discrete coords_before_n_succ_handled,
end,
rcases inductive_replacement_lemma_helper_fact d_sub_one (nat.pred_lt d_ne_zero) with
⟨T_shifted, T_shifted_is_tiling, T_shifted_faceshare_free, T_shifted_is_periodic, T_shifted_s_discrete, T_shifted_only_uses_goal_coordinates⟩,
use [T_shifted, T_shifted_is_tiling, T_shifted_faceshare_free, T_shifted_is_periodic],
intros i p p_in_T_shifted,
have i_val_le_d_sub_one_val : i.val ≤ d_sub_one.val :=
begin
have i_val_lt_d := i.property,
dsimp only[d_sub_one],
exact nat.le_pred_of_lt i_val_lt_d,
end,
exact T_shifted_only_uses_goal_coordinates p p_in_T_shifted i i_val_le_d_sub_one_val,
end
lemma goal_clique_with_info_map_fn_yields_fin_double_s_vector {d s : ℕ} (d_ne_zero : d ≠ 0) (s_ne_zero : s ≠ 0) (T : set (point d)) (T_is_tiling : is_tiling T)
(T_faceshare_free : tiling_faceshare_free T) (T_is_periodic : is_periodic T_is_tiling) (T_is_s_discrete : is_s_discrete s T) (T_shifted : set (point d))
(T_shifted_is_tiling : is_tiling T_shifted) (T_shifted_faceshare_free : tiling_faceshare_free T_shifted)
(T_shifted_contains_only_s_points :
∀ (i : fin d) (p : point d), p ∈ T_shifted → (∃ (s_val : ℝ) (H : s_val ∈ s_finset s_ne_zero), eq_mod_one (vector.nth p i) s_val))
(core_points_finset :
finset {p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)})
(core_points_finset_card : core_points_finset.card = 2 ^ d)
(core_points_finset_property :
∀ (p : point d) (h : ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)),
(⟨p, h⟩ : {p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)}) ∈ core_points_finset)
(p : {p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)}) :
∃ fin_double_s_vector : vector (fin (2*s)) d, ∀ i : fin d, ↑(fin_double_s_vector.nth i).val = ↑s * (((point_to_corner T_shifted_is_tiling p).val).nth i) + s - 1 :=
begin
let p_corner := (point_to_corner T_shifted_is_tiling ↑p).val,
have p_corner_def : p_corner = (point_to_corner T_shifted_is_tiling ↑p).val := by refl,
have p_corner_property := (point_to_corner T_shifted_is_tiling ↑p).property,
rw ← p_corner_def at p_corner_property,
rw ← p_corner_def,
rcases p_corner_property with ⟨p_corner_in_T_shifted, p_in_p_corner, p_corner_unique⟩,
rw cube at p_in_p_corner,
simp only [set.mem_set_of_eq] at p_in_p_corner,
rw in_cube at p_in_p_corner,
have each_coord_is_nat : ∀ i : fin d, ∃ n : ℕ, ↑n = ↑s * vector.nth p_corner i + ↑s - 1 :=
begin
intro i,
rcases T_shifted_contains_only_s_points i p_corner p_corner_in_T_shifted with ⟨s_val, s_val_in_s_finset, p_corner_eq_s_val_mod_one⟩,
rcases s_finset_range s_val_in_s_finset with ⟨zero_le_s_val, s_val_lt_one⟩,
replace p_in_p_corner := p_in_p_corner i,
rcases p_in_p_corner with ⟨p_corner_le_p, p_lt_p_corner_add_one⟩,
cases p.property i with p_property unnecessary,
clear unnecessary,
cases p_property i.property with p_eq_zero p_eq_one,
{ simp only [subtype.val_eq_coe] at p_eq_zero,
rw p_eq_zero at p_corner_le_p p_lt_p_corner_add_one,
rcases p_corner_eq_s_val_mod_one with ⟨p_corner_floor, zero, y, zero_le_y, y_lt_one, p_corner_def, s_val_def⟩,
have zero_eq_zero : zero = 0 :=
begin
rw s_val_def at zero_le_s_val s_val_lt_one,
clear_except zero_le_s_val s_val_lt_one zero_le_y y_lt_one,
rcases eq_or_lt_or_gt zero 0 with zero_eq_zero | zero_lt_zero | zero_gt_zero,
exact zero_eq_zero,
{ have zero_le_neg_one : zero ≤ -1 := by omega,
have cast_zero_le_neg_one : ↑zero ≤ (-1 : ℝ) := by exact_mod_cast zero_le_neg_one,
linarith,
},
have zero_ge_one : zero ≥ 1 := by omega,
have cast_zero_ge_one : ↑zero ≥ (1 : ℝ) := by exact_mod_cast zero_ge_one,
linarith,
end,
have cast_zero_eq_zero : ↑zero = (0 : ℝ) := by exact_mod_cast zero_eq_zero,
rw [cast_zero_eq_zero, zero_add] at s_val_def,
rw ← s_val_def at p_corner_def,
by_cases s_val_eq_zero : s_val = 0,
{ rw [s_val_eq_zero, add_zero] at p_corner_def,
use s * int.to_nat(p_corner_floor) + s - 1,
have zero_le_p_corner_floor : 0 ≤ p_corner_floor :=
begin
clear_except p_corner_def p_lt_p_corner_add_one p_corner_le_p,
rw p_corner_def at p_lt_p_corner_add_one p_corner_le_p,
have h1 : p_corner_floor ≤ 0 := by exact_mod_cast p_corner_le_p,
have h2 : 0 < p_corner_floor + 1 := by exact_mod_cast p_lt_p_corner_add_one,
omega,
end,
have p_corner_floor_to_nat_eq_self : ↑p_corner_floor.to_nat = p_corner_floor := int.to_nat_of_nonneg zero_le_p_corner_floor,
have cast_p_corner_floor_to_nat_eq_self : ↑p_corner_floor.to_nat = (↑p_corner_floor : ℝ) :=
by exact_mod_cast p_corner_floor_to_nat_eq_self,
have one_le_s : 1 ≤ s :=
begin
rcases nat_eq_or_lt_or_gt s 0 with s_eq_zero | s_lt_zero | s_gt_zero,
{ exfalso,
exact s_ne_zero s_eq_zero,
},
{ exfalso,
exact nat.not_lt_zero s s_lt_zero,
},
clear_except s_gt_zero,
have zero_lt_s : 0 < s := by linarith,
omega,
end,
rw [nat.add_sub_assoc one_le_s, nat.cast_add (s * p_corner_floor.to_nat) (s - 1), nat.cast_sub one_le_s, nat.cast_mul,
cast_p_corner_floor_to_nat_eq_self, p_corner_def, ← add_sub_assoc, nat.cast_one],
},
rename s_val_eq_zero s_val_ne_zero,
rcases s_finset_range s_val_in_s_finset with ⟨zero_le_s_val, s_val_lt_one⟩,
rw s_finset at s_val_in_s_finset,
simp only [exists_prop, finset.mem_map, function.embedding.coe_fn_mk, finset.mem_range] at s_val_in_s_finset,
rcases s_val_in_s_finset with ⟨s_val_num, s_val_num_lt_s, s_val_num_div_s_eq_s_val⟩,
use s_val_num - 1,
rcases nat_eq_or_lt_or_gt s_val_num 0 with s_val_num_eq_zero | s_val_num_lt_zero | s_val_num_gt_zero,
{ exfalso,
rw s_val_num_eq_zero at s_val_num_div_s_eq_s_val,
simp only [zero_div, nat.cast_zero] at s_val_num_div_s_eq_s_val,
symmetry' at s_val_num_div_s_eq_s_val,
exact s_val_ne_zero s_val_num_div_s_eq_s_val,
},
{ exfalso,
clear_except s_val_num_lt_zero,
linarith,
},
have one_le_s_val_num : 1 ≤ s_val_num := by {clear_except s_val_num_gt_zero, omega},
have cast_s_ne_zero : ↑s ≠ (0 : ℝ) := by exact_mod_cast s_ne_zero,
have p_corner_floor_eq_neg_one : p_corner_floor = -1 :=
begin
rcases eq_or_lt_or_gt p_corner_floor (-1) with p_corner_floor_eq_neg_one | p_corner_floor_lt_neg_one | p_corner_floor_gt_neg_one,
exact p_corner_floor_eq_neg_one,
{ have p_corner_floor_le_neg_two : p_corner_floor ≤ -2 := by {clear_except p_corner_floor_lt_neg_one, omega},
have cast_p_corner_floor_le_neg_two : ↑p_corner_floor ≤ (-2 : ℝ) := by exact_mod_cast p_corner_floor_le_neg_two,
linarith,
},
have zero_le_p_corner_floor : 0 ≤ p_corner_floor := by {clear_except p_corner_floor_gt_neg_one, omega},
have cast_zero_le_p_corner_floor : (0 : ℝ) ≤ ↑p_corner_floor := by exact_mod_cast zero_le_p_corner_floor,
have zero_ne_s_val : 0 ≠ s_val := by {intro zero_eq_s_val, symmetry' at zero_eq_s_val, exact s_val_ne_zero zero_eq_s_val},
have zero_lt_s_val : 0 < s_val := lt_of_le_of_ne zero_le_s_val zero_ne_s_val,
linarith,
end,
have cast_p_corner_floor_eq_neg_one : ↑p_corner_floor = (-1 : ℝ) := by exact_mod_cast p_corner_floor_eq_neg_one,
rw ← s_val_num_div_s_eq_s_val at p_corner_def,
rw [nat.cast_sub one_le_s_val_num, p_corner_def, mul_add, mul_div_of_ne_zero ↑s_val_num cast_s_ne_zero, cast_p_corner_floor_eq_neg_one],
simp only [nat.cast_one, mul_neg, mul_one, neg_add_cancel_comm],
},
simp only [subtype.val_eq_coe] at p_eq_one,
rw p_eq_one at p_corner_le_p p_lt_p_corner_add_one,
rcases p_corner_eq_s_val_mod_one with ⟨p_corner_floor, zero, y, zero_le_y, y_lt_one, p_corner_def, s_val_def⟩,
have zero_eq_zero : zero = 0 :=
begin
rw s_val_def at zero_le_s_val s_val_lt_one,
clear_except zero_le_s_val s_val_lt_one zero_le_y y_lt_one,
rcases eq_or_lt_or_gt zero 0 with zero_eq_zero | zero_lt_zero | zero_gt_zero,
exact zero_eq_zero,
{ have zero_le_neg_one : zero ≤ -1 := by omega,
have cast_zero_le_neg_one : ↑zero ≤ (-1 : ℝ) := by exact_mod_cast zero_le_neg_one,
linarith,
},
have zero_ge_one : zero ≥ 1 := by omega,
have cast_zero_ge_one : ↑zero ≥ (1 : ℝ) := by exact_mod_cast zero_ge_one,
linarith,
end,
have cast_zero_eq_zero : ↑zero = (0 : ℝ) := by exact_mod_cast zero_eq_zero,
rw [cast_zero_eq_zero, zero_add] at s_val_def,
rw ← s_val_def at p_corner_def,
by_cases s_val_eq_zero : s_val = 0,
{ rw [s_val_eq_zero, add_zero] at p_corner_def,
use s * int.to_nat(p_corner_floor) + s - 1,
have one_le_p_corner_floor : 1 ≤ p_corner_floor :=
begin
clear_except p_corner_def p_lt_p_corner_add_one,
rw p_corner_def at p_lt_p_corner_add_one,
have h : 1 < p_corner_floor + 1 := by exact_mod_cast p_lt_p_corner_add_one,
omega,
end,
have zero_le_p_corner_floor : 0 ≤ p_corner_floor := by linarith,
have p_corner_floor_to_nat_eq_self : ↑p_corner_floor.to_nat = p_corner_floor := int.to_nat_of_nonneg zero_le_p_corner_floor,
have cast_p_corner_floor_to_nat_eq_self : ↑p_corner_floor.to_nat = (↑p_corner_floor : ℝ) :=
by exact_mod_cast p_corner_floor_to_nat_eq_self,
have one_le_s : 1 ≤ s :=
begin
rcases nat_eq_or_lt_or_gt s 0 with s_eq_zero | s_lt_zero | s_gt_zero,
{ exfalso,
exact s_ne_zero s_eq_zero,
},
{ exfalso,
exact nat.not_lt_zero s s_lt_zero,
},
clear_except s_gt_zero,
have zero_lt_s : 0 < s := by linarith,
omega,
end,
rw [nat.add_sub_assoc one_le_s, nat.cast_add (s * p_corner_floor.to_nat) (s - 1), nat.cast_sub one_le_s, nat.cast_mul,
cast_p_corner_floor_to_nat_eq_self, p_corner_def, ← add_sub_assoc, nat.cast_one],
},
rename s_val_eq_zero s_val_ne_zero,
rcases s_finset_range s_val_in_s_finset with ⟨zero_le_s_val, s_val_lt_one⟩,
rw s_finset at s_val_in_s_finset,
simp only [exists_prop, finset.mem_map, function.embedding.coe_fn_mk, finset.mem_range] at s_val_in_s_finset,
rcases s_val_in_s_finset with ⟨s_val_num, s_val_num_lt_s, s_val_num_div_s_eq_s_val⟩,
use ↑s_val_num + ↑s - 1,
rcases nat_eq_or_lt_or_gt s_val_num 0 with s_val_num_eq_zero | s_val_num_lt_zero | s_val_num_gt_zero,
{ exfalso,
rw s_val_num_eq_zero at s_val_num_div_s_eq_s_val,
simp only [zero_div, nat.cast_zero] at s_val_num_div_s_eq_s_val,
symmetry' at s_val_num_div_s_eq_s_val,
exact s_val_ne_zero s_val_num_div_s_eq_s_val,
},
{ exfalso,
clear_except s_val_num_lt_zero,
linarith,
},
have one_le_s_val_num : 1 ≤ s_val_num := by {clear_except s_val_num_gt_zero, omega},
have one_le_s_add_s_val_num : 1 ≤ ↑s_val_num + ↑s := by linarith,
have cast_s_ne_zero : ↑s ≠ (0 : ℝ) := by exact_mod_cast s_ne_zero,
have p_corner_floor_eq_zero : p_corner_floor = 0 :=
begin
rcases eq_or_lt_or_gt p_corner_floor 0 with p_corner_floor_eq_zero | p_corner_floor_lt_zero | p_corner_floor_gt_zero,
exact p_corner_floor_eq_zero,
{ have p_corner_floor_le_neg_one : p_corner_floor ≤ -1 := by {clear_except p_corner_floor_lt_zero, omega},
have cast_p_corner_floor_le_neg_one : ↑p_corner_floor ≤ (-1 : ℝ) := by exact_mod_cast p_corner_floor_le_neg_one,
linarith,
},
have one_le_p_corner_floor : 1 ≤ p_corner_floor := by {clear_except p_corner_floor_gt_zero, omega},
have cast_one_le_p_corner_floor : (1 : ℝ) ≤ ↑p_corner_floor := by exact_mod_cast one_le_p_corner_floor,
have zero_ne_s_val : 0 ≠ s_val := by {intro zero_eq_s_val, symmetry' at zero_eq_s_val, exact s_val_ne_zero zero_eq_s_val},
have zero_lt_s_val : 0 < s_val := lt_of_le_of_ne zero_le_s_val zero_ne_s_val,
linarith,
end,
have cast_p_corner_floor_eq_zero : ↑p_corner_floor = (0 : ℝ) := by exact_mod_cast p_corner_floor_eq_zero,
rw ← s_val_num_div_s_eq_s_val at p_corner_def,
rw [nat.cast_sub one_le_s_add_s_val_num, p_corner_def, mul_add, mul_div_of_ne_zero ↑s_val_num cast_s_ne_zero, cast_p_corner_floor_eq_zero],
simp only [nat.cast_id, nat.cast_add, zero_add, nat.cast_one, mul_zero],
end,
have each_coord_lt_double_s : ∀ i : fin d, classical.some (each_coord_is_nat i) < 2 * s :=
begin
intro i,
have cast_goal : ↑(classical.some (each_coord_is_nat i)) < (2 : ℝ) * ↑s :=
begin
rw classical.some_spec (each_coord_is_nat i),
replace p_in_p_corner := p_in_p_corner i,
rcases p_in_p_corner with ⟨p_corner_le_p, p_lt_p_corner_add_one⟩,
have p_le_one : vector.nth (↑p : point d) i ≤ (1 : ℝ) :=
begin
cases p.property i with p_property unneeded,
simp only [subtype.val_eq_coe] at p_property,
cases p_property i.property with p_eq_zero p_eq_one,
{ rw p_eq_zero,
linarith,
},
rw p_eq_one,
end,
have p_corner_le_one : vector.nth p_corner i ≤ 1 := by linarith,
have zero_le_p : (0 : ℝ) ≤ vector.nth (↑p : point d) i :=
begin
cases p.property i with p_property unneeded,
simp only [subtype.val_eq_coe] at p_property,
cases p_property i.property with p_eq_zero p_eq_one,
rw p_eq_zero,
rw p_eq_one,
linarith,
end,
have neg_one_le_p_corner : -1 ≤ vector.nth p_corner i := by linarith,
have zero_le_cast_s : (0 : ℝ) ≤ ↑s := by exact_mod_cast (zero_le s),
have goal_sans_sub_one : ↑s * vector.nth p_corner i + ↑s ≤ 2 * ↑s :=
begin
rw mul_comm (2 : ℝ) ↑s,
convert_to ↑s * vector.nth p_corner i + ↑s * 1 ≤ ↑s * 2, rw mul_one,
rw ← mul_add,
apply mul_le_mul, exact le_refl ↑s, linarith, linarith, exact zero_le_cast_s,
end,
clear_except goal_sans_sub_one,
linarith,
end,
exact_mod_cast cast_goal,
end,
use vector.of_fn (λ i, ⟨classical.some (each_coord_is_nat i), each_coord_lt_double_s i⟩),
intro i,
simp only [vector.nth_of_fn],
rw classical.some_spec (each_coord_is_nat i),
end
noncomputable def build_goal_clique_with_info_map_fn {d s : ℕ} (d_ne_zero : d ≠ 0) (s_ne_zero : s ≠ 0) (T : set (point d)) (T_is_tiling : is_tiling T)
(T_faceshare_free : tiling_faceshare_free T) (T_is_periodic : is_periodic T_is_tiling) (T_is_s_discrete : is_s_discrete s T) (T_shifted : set (point d))
(T_shifted_is_tiling : is_tiling T_shifted) (T_shifted_faceshare_free : tiling_faceshare_free T_shifted)
(T_shifted_contains_only_s_points :
∀ (i : fin d) (p : point d), p ∈ T_shifted → (∃ (s_val : ℝ) (H : s_val ∈ s_finset s_ne_zero), eq_mod_one (vector.nth p i) s_val))
(core_points_finset :
finset {p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)})
(core_points_finset_card : core_points_finset.card = 2 ^ d)
(core_points_finset_property :
∀ (p : point d) (h : ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)),
(⟨p, h⟩ : {p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)}) ∈ core_points_finset) :
{p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)} →
{v : vector (fin (2*s)) d // ∃ p : point d, is_core_point p ∧ ∃ p_corner ∈ T_shifted,
p ∈ cube p_corner ∧ (∀ alt_corner : point d, alt_corner ∈ T_shifted → p ∈ cube alt_corner → alt_corner = p_corner) ∧
(∀ i : fin d, ↑s * (vector.nth p_corner i) + ↑s - 1 = (vector.nth v i).val)} :=
begin
intro p,
use classical.some
(goal_clique_with_info_map_fn_yields_fin_double_s_vector d_ne_zero s_ne_zero T T_is_tiling T_faceshare_free T_is_periodic T_is_s_discrete T_shifted
T_shifted_is_tiling T_shifted_faceshare_free T_shifted_contains_only_s_points core_points_finset core_points_finset_card
core_points_finset_property p),
let res := classical.some
(goal_clique_with_info_map_fn_yields_fin_double_s_vector d_ne_zero s_ne_zero T T_is_tiling T_faceshare_free T_is_periodic T_is_s_discrete T_shifted
T_shifted_is_tiling T_shifted_faceshare_free T_shifted_contains_only_s_points core_points_finset core_points_finset_card
core_points_finset_property p),
have res_def : res = classical.some
(goal_clique_with_info_map_fn_yields_fin_double_s_vector d_ne_zero s_ne_zero T T_is_tiling T_faceshare_free T_is_periodic T_is_s_discrete T_shifted
T_shifted_is_tiling T_shifted_faceshare_free T_shifted_contains_only_s_points core_points_finset core_points_finset_card
core_points_finset_property p) := by refl,
rw ← res_def,
have res_property := classical.some_spec
(goal_clique_with_info_map_fn_yields_fin_double_s_vector d_ne_zero s_ne_zero T T_is_tiling T_faceshare_free T_is_periodic T_is_s_discrete T_shifted
T_shifted_is_tiling T_shifted_faceshare_free T_shifted_contains_only_s_points core_points_finset core_points_finset_card
core_points_finset_property p),
rw ← res_def at res_property,
let p_corner := (point_to_corner T_shifted_is_tiling p).val,
have p_corner_def : p_corner = (point_to_corner T_shifted_is_tiling p).val := by refl,
have p_corner_property := (point_to_corner T_shifted_is_tiling p).property,
rw ← p_corner_def at p_corner_property,
rcases p_corner_property with ⟨p_corner_in_T_shifted, p_in_p_corner, p_corner_unique⟩,
use [p.val, (λ i, (and.elim_left (p.property i)) i.property), p_corner, p_corner_in_T_shifted, p_in_p_corner, p_corner_unique],
intro i,
symmetry,
exact res_property i,
end
lemma periodic_tiling_implies_clique_helper {d s : ℕ} (d_ne_zero : d ≠ 0) (s_ne_zero : s ≠ 0) (T : set (point d)) (T_is_tiling : is_tiling T)
(T_faceshare_free : tiling_faceshare_free T) (T_is_periodic : is_periodic T_is_tiling) (T_is_s_discrete : is_s_discrete s T)
(T_shifted : set (point d)) (T_shifted_is_tiling : is_tiling T_shifted) (T_shifted_faceshare_free : tiling_faceshare_free T_shifted)
(T_shifted_is_periodic : is_periodic T_shifted_is_tiling)
(T_shifted_contains_only_s_points :
∀ (i : fin d) (p : point d), p ∈ T_shifted → (∃ (s_val : ℝ) (H : s_val ∈ s_finset s_ne_zero), eq_mod_one (vector.nth p i) s_val))
(core_points_finset :
finset {p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)})
(core_points_finset_card : core_points_finset.card = 2 ^ d)
(core_points_finset_property :
∀ (p : point d) (h : ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)),
(⟨p, h⟩ : {p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)})
∈ core_points_finset)
(goal_clique_with_info_map :
{p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)} ↪
{v : vector (fin (2*s)) d // ∃ (p : point d), is_core_point p ∧ ∃ (p_corner : point d) (H : p_corner ∈ T_shifted), p ∈ cube p_corner ∧
(∀ (alt_corner : point d), alt_corner ∈ T_shifted → p ∈ cube alt_corner → alt_corner = p_corner) ∧
∀ (i : fin d), ↑s * vector.nth p_corner i + ↑s - 1 = ↑((v.nth i).val)})
(v1 v2 : vector (fin (2 * s)) d) (v1_ne_v2 : v1 ≠ v2) (v1' : vector (fin (2 * s)) d) (core_point1 : point d)
(core_point1_is_core_point : is_core_point core_point1) (core_point1_corner : point d)
(core_point1_corner_in_T_shifted : core_point1_corner ∈ T_shifted) (core_point1_in_core_point1_corner : core_point1 ∈ cube core_point1_corner)
(core_point1_corner_unique :
∀ (alt_corner : point d), alt_corner ∈ T_shifted → core_point1 ∈ cube alt_corner → alt_corner = core_point1_corner)
(v2' : vector (fin (2 * s)) d) (core_point2 : point d) (core_point2_is_core_point : is_core_point core_point2) (core_point2_corner : point d)
(core_point2_corner_in_T_shifted : core_point2_corner ∈ T_shifted) (core_point2_in_core_point2_corner : core_point2 ∈ cube core_point2_corner)
(core_point2_corner_unique : ∀ (alt_corner : point d), alt_corner ∈ T_shifted → core_point2 ∈ cube alt_corner → alt_corner = core_point2_corner)
(v2_def : v2' = v2) (v1_def : v1' = v1)
(core_point1_corner_v1'_relationship : ∀ (i : fin d), ↑s * vector.nth core_point1_corner i + ↑s - 1 = ↑(↑(v1.nth i) : ℕ))
(core_point2_corner_v2'_relationship : ∀ (i : fin d), ↑s * vector.nth core_point2_corner i + ↑s - 1 = ↑(↑(v2.nth i) : ℕ))
(v1_not_adj_v2 :
(∀ (x : fin d), ↑(v1.nth x) = ↑(v2.nth x) + s → ∀ (x_1 : fin d), ¬v1.nth x_1 = v2.nth x_1 → x = x_1) ∧
∀ (x : fin d), ↑(v2.nth x) = ↑(v1.nth x) + s → ∀ (x_1 : fin d), ¬v2.nth x_1 = v1.nth x_1 → x = x_1)
(v1_not_adj_v2_hyp_false : ¬∃ (i : fin d), ↑(v1.nth i) = ↑(v2.nth i) + s ∨ ↑(v2.nth i) = ↑(v1.nth i) + s) :
let goal_clique_with_info : finset
{v : vector (fin (2*s)) d // ∃ (p : point d),
is_core_point p ∧
∃ (p_corner : point d) (H : p_corner ∈ T_shifted),
p ∈ cube p_corner ∧
(∀ (alt_corner : point d),
alt_corner ∈ T_shifted →
p ∈ cube alt_corner → alt_corner = p_corner) ∧
∀ (i : fin d),
↑s * vector.nth p_corner i + ↑s - 1 =
↑((v.nth i).val)} :=
finset.map goal_clique_with_info_map core_points_finset
in false :=
begin
intros goal_clique_with_info,
simp only [not_exists] at v1_not_adj_v2_hyp_false,
have core_point1_corner_ne_core_point2_corner_add_or_sub_1 :
∀ i : fin d, core_point1_corner.nth i ≠ core_point2_corner.nth i + 1 ∧ core_point2_corner.nth i ≠ core_point1_corner.nth i + 1 :=
begin
intro i,
replace v1_not_adj_v2_hyp_false := v1_not_adj_v2_hyp_false i,
rw not_or_distrib at v1_not_adj_v2_hyp_false,
cases v1_not_adj_v2_hyp_false with v1_ne_v2_add_s v2_ne_v1_add_s,
replace core_point1_corner_v1'_relationship := core_point1_corner_v1'_relationship i,
replace core_point2_corner_v2'_relationship := core_point2_corner_v2'_relationship i,
have real_v1_ne_v2_add_s : (↑(↑(v1.nth i) : ℕ) : ℝ) ≠ (↑(↑(v2.nth i) : ℕ) : ℝ) + ↑s := by exact_mod_cast v1_ne_v2_add_s,
have real_v2_ne_v1_add_s : (↑(↑(v2.nth i) : ℕ) : ℝ) ≠ (↑(↑(v1.nth i) : ℕ) : ℝ) + ↑s := by exact_mod_cast v2_ne_v1_add_s,
rw [← core_point1_corner_v1'_relationship, ← core_point2_corner_v2'_relationship, add_sub_assoc, add_sub_assoc,
add_comm (↑s * vector.nth core_point1_corner i) (↑s - 1),
add_comm (↑s * vector.nth core_point2_corner i) (↑s - 1),
add_assoc] at real_v1_ne_v2_add_s real_v2_ne_v1_add_s,
simp only [ne.def, add_right_inj] at real_v1_ne_v2_add_s real_v2_ne_v1_add_s,
have rw1 : ↑s * vector.nth core_point1_corner i + ↑s = ↑s * vector.nth core_point1_corner i + ↑s * (1 : ℝ) := by rw mul_one,
have rw2 : ↑s * vector.nth core_point2_corner i + ↑s = ↑s * vector.nth core_point2_corner i + ↑s * (1 : ℝ) := by rw mul_one,
rw rw1 at real_v2_ne_v1_add_s,
rw rw2 at real_v1_ne_v2_add_s,
rw ← mul_add at real_v1_ne_v2_add_s real_v2_ne_v1_add_s,
simp only [mul_eq_mul_left_iff, nat.cast_eq_zero] at real_v1_ne_v2_add_s real_v2_ne_v1_add_s,
rw not_or_distrib at real_v1_ne_v2_add_s real_v2_ne_v1_add_s,
exact ⟨real_v1_ne_v2_add_s.1, real_v2_ne_v1_add_s.1⟩,
end,
let z : int_point d := vector.of_fn
(λ i, if(core_point1_corner.nth i < core_point2_corner.nth i + 1 ∧ core_point2_corner.nth i < core_point1_corner.nth i + 1) then 0
else if(core_point2_corner.nth i >= core_point1_corner.nth i + 1) then 1
else -1),
let int_core_point1 : int_point d := vector.of_fn (λ i, if(core_point1.nth i = 0) then 0 else 1),
have int_point_to_point_int_core_point1_eq_core_point1 : int_point_to_point int_core_point1 = core_point1 :=
begin
apply vector.ext,
intro i,
rw int_point_to_point,
dsimp only[int_core_point1],
simp only [vector.nth_of_fn],
cases core_point1_is_core_point i with core_point1_eq_zero core_point1_eq_one,
rw [if_pos core_point1_eq_zero, core_point1_eq_zero], refl,
have core_point1_ne_zero : core_point1.nth i ≠ 0 := by {rw core_point1_eq_one, norm_num},
rw [if_neg core_point1_ne_zero, core_point1_eq_one],
norm_num,
end,
replace T_shifted_is_periodic := T_shifted_is_periodic int_core_point1 z,
let core_point1_add_double_z_corner := (int_point_to_corner T_shifted_is_tiling (add_int_vectors int_core_point1 (double_int_vector z))).val,
have core_point1_add_double_z_corner_def :
core_point1_add_double_z_corner = (int_point_to_corner T_shifted_is_tiling (add_int_vectors int_core_point1 (double_int_vector z))).val := by refl,
have core_point1_add_double_z_corner_property := (int_point_to_corner T_shifted_is_tiling (add_int_vectors int_core_point1 (double_int_vector z))).property,
rw ← core_point1_add_double_z_corner_def at core_point1_add_double_z_corner_property,
rcases core_point1_add_double_z_corner_property with
⟨core_point1_add_double_z_corner_in_T_shifted, core_point1_add_double_z_in_core_point1_add_double_z_corner, core_point1_add_double_z_corner_unique⟩,
let shared_point : point d := vector.of_fn
(λ i, if(core_point2_corner.nth i >= core_point1_add_double_z_corner.nth i) then core_point2_corner.nth i else core_point1_add_double_z_corner.nth i),
rcases T_shifted_is_tiling shared_point with ⟨unique_corner, unique_corner_in_T_shifted, shared_point_in_unique_corner, unique_corner_unique⟩,
have shared_point_in_core_point1_add_double_z_corner : shared_point ∈ cube core_point1_add_double_z_corner :=
begin
rw cube,
simp only [set.mem_set_of_eq],
rw in_cube,
simp only [vector.nth_of_fn, ge_iff_le, not_exists],
intro i,
replace core_point1_corner_ne_core_point2_corner_add_or_sub_1 := core_point1_corner_ne_core_point2_corner_add_or_sub_1 i,
split,
{ by_cases h : vector.nth core_point1_add_double_z_corner i ≤ vector.nth core_point2_corner i,
{ rw if_pos h,
exact h,
},
rw if_neg h,
},
by_cases h : vector.nth core_point1_add_double_z_corner i ≤ vector.nth core_point2_corner i,
{ rw if_pos h,
have int_core_point1_corner_eq_core_point1_corner : ↑(int_point_to_corner T_shifted_is_tiling int_core_point1) = core_point1_corner :=
begin
rw ← subtype.val_eq_coe,
rcases (int_point_to_corner T_shifted_is_tiling int_core_point1).property with
⟨int_core_point1_corner_in_T_shifted, int_core_point1_in_int_core_point1_corner, int_core_point1_corner_unique⟩,
conv at int_core_point1_in_int_core_point1_corner
begin
find (int_point_to_point int_core_point1) {rw int_point_to_point_int_core_point1_eq_core_point1},
end,
exact core_point1_corner_unique (int_point_to_corner T_shifted_is_tiling int_core_point1).val int_core_point1_corner_in_T_shifted
int_core_point1_in_int_core_point1_corner,
end,
rw [core_point1_add_double_z_corner_def, T_shifted_is_periodic, double_int_vector, add_vectors],
conv
begin
find (int_point_to_point _) {rw int_point_to_point},
end,
simp only [subtype.val_eq_coe, vector.nth_of_fn, ge_iff_le, mul_ite, mul_zero, mul_one, mul_neg],
by_cases z_eq_zero : vector.nth core_point1_corner i < vector.nth core_point2_corner i + 1 ∧ vector.nth core_point2_corner i < vector.nth core_point1_corner i + 1,
{ rw [if_pos z_eq_zero, int.cast_zero, add_zero, int_core_point1_corner_eq_core_point1_corner],
exact z_eq_zero.2,
},
rename z_eq_zero z_ne_zero,
rw cube at core_point1_in_core_point1_corner core_point2_in_core_point2_corner,
simp only [set.mem_set_of_eq] at core_point1_in_core_point1_corner core_point2_in_core_point2_corner,
rw in_cube at core_point1_in_core_point1_corner core_point2_in_core_point2_corner,
replace core_point1_in_core_point1_corner := core_point1_in_core_point1_corner i,
replace core_point2_in_core_point2_corner := core_point2_in_core_point2_corner i,
by_cases z_eq_one : vector.nth core_point2_corner i ≥ vector.nth core_point1_corner i + 1,
{ rw [if_neg z_ne_zero, if_pos z_eq_one, int.cast_bit0, int.cast_one, int_core_point1_corner_eq_core_point1_corner],
have core_point2_le_one := le_one_of_is_core_point i core_point2_is_core_point,
have core_point1_ge_zero := ge_zero_of_is_core_point i core_point1_is_core_point,
linarith,
},
rename z_eq_one z_ne_one,
rw [if_neg z_ne_zero, if_neg z_ne_one, int.cast_neg, int.cast_bit0, int.cast_one, int_core_point1_corner_eq_core_point1_corner],
rw [not_and_distrib, not_lt, not_lt] at z_ne_zero,
cases z_ne_zero with core_point2_corner_add_one_le_core_point1_corner core_point1_corner_add_one_le_core_point2_corner,
{ cases lt_or_eq_of_le core_point2_corner_add_one_le_core_point1_corner with goal core_point2_corner_add_one_eq_core_point1_corner,
linarith,
exfalso,
symmetry' at core_point2_corner_add_one_eq_core_point1_corner,
exact core_point1_corner_ne_core_point2_corner_add_or_sub_1.1 core_point2_corner_add_one_eq_core_point1_corner,
},
linarith,
},
rw if_neg h,
norm_num,
end,
have core_point1_add_double_z_corner_eq_unique_corner :=
unique_corner_unique core_point1_add_double_z_corner core_point1_add_double_z_corner_in_T_shifted shared_point_in_core_point1_add_double_z_corner,
have shared_point_in_core_point2_corner : shared_point ∈ cube core_point2_corner :=
begin
rw cube,
simp only [set.mem_set_of_eq],
rw in_cube,
simp only [vector.nth_of_fn, ge_iff_le, not_exists],
intro i,
replace core_point1_corner_ne_core_point2_corner_add_or_sub_1 := core_point1_corner_ne_core_point2_corner_add_or_sub_1 i,
split,
{ by_cases h : vector.nth core_point1_add_double_z_corner i ≤ vector.nth core_point2_corner i,
rw if_pos h,
rw if_neg h,
simp only [not_le] at h,
exact le_of_lt h,
},
by_cases h : vector.nth core_point1_add_double_z_corner i ≤ vector.nth core_point2_corner i,
{ rw if_pos h,
norm_num,
},
rw if_neg h,
have int_core_point1_corner_eq_core_point1_corner : ↑(int_point_to_corner T_shifted_is_tiling int_core_point1) = core_point1_corner :=
begin
rw ← subtype.val_eq_coe,
rcases (int_point_to_corner T_shifted_is_tiling int_core_point1).property with
⟨int_core_point1_corner_in_T_shifted, int_core_point1_in_int_core_point1_corner, int_core_point1_corner_unique⟩,
conv at int_core_point1_in_int_core_point1_corner
begin
find (int_point_to_point int_core_point1) {rw int_point_to_point_int_core_point1_eq_core_point1},
end,
exact core_point1_corner_unique (int_point_to_corner T_shifted_is_tiling int_core_point1).val int_core_point1_corner_in_T_shifted
int_core_point1_in_int_core_point1_corner,
end,
rw [core_point1_add_double_z_corner_def, T_shifted_is_periodic, double_int_vector, add_vectors],
conv
begin
find (int_point_to_point _) {rw int_point_to_point},
end,
simp only [subtype.val_eq_coe, vector.nth_of_fn, ge_iff_le, mul_ite, mul_zero, mul_one, mul_neg],
by_cases z_eq_zero : vector.nth core_point1_corner i < vector.nth core_point2_corner i + 1 ∧ vector.nth core_point2_corner i < vector.nth core_point1_corner i + 1,
{ rw [if_pos z_eq_zero, int.cast_zero, add_zero, int_core_point1_corner_eq_core_point1_corner],
exact z_eq_zero.1,
},
rename z_eq_zero z_ne_zero,
rw cube at core_point1_in_core_point1_corner core_point2_in_core_point2_corner,
simp only [set.mem_set_of_eq] at core_point1_in_core_point1_corner core_point2_in_core_point2_corner,
rw in_cube at core_point1_in_core_point1_corner core_point2_in_core_point2_corner,
replace core_point1_in_core_point1_corner := core_point1_in_core_point1_corner i,
replace core_point2_in_core_point2_corner := core_point2_in_core_point2_corner i,
by_cases z_eq_one : vector.nth core_point2_corner i ≥ vector.nth core_point1_corner i + 1,
{ rw [if_neg z_ne_zero, if_pos z_eq_one, int.cast_bit0, int.cast_one, int_core_point1_corner_eq_core_point1_corner],
rw [not_and_distrib, not_lt, not_lt] at z_ne_zero,
cases z_ne_zero with core_point2_corner_add_one_le_core_point1_corner core_point1_corner_add_one_le_core_point2_corner,
linarith,
cases lt_or_eq_of_le core_point1_corner_add_one_le_core_point2_corner with goal core_point1_corner_add_one_eq_core_point2_corner,
linarith,
exfalso,
symmetry' at core_point1_corner_add_one_eq_core_point2_corner,
exact core_point1_corner_ne_core_point2_corner_add_or_sub_1.2 core_point1_corner_add_one_eq_core_point2_corner,
},
rename z_eq_one z_ne_one,
rw [if_neg z_ne_zero, if_neg z_ne_one, int.cast_neg, int.cast_bit0, int.cast_one, int_core_point1_corner_eq_core_point1_corner],
have core_point2_ge_zero := ge_zero_of_is_core_point i core_point2_is_core_point,
have core_point2_le_one := le_one_of_is_core_point i core_point1_is_core_point,
linarith,
end,
have core_point2_corner_eq_unique_corner :=
unique_corner_unique core_point2_corner core_point2_corner_in_T_shifted shared_point_in_core_point2_corner,
have core_point2_corner_eq_core_point1_add_double_z_corner : core_point2_corner = core_point1_add_double_z_corner :=
by rw [core_point1_add_double_z_corner_eq_unique_corner, core_point2_corner_eq_unique_corner],
by_cases core_point1_eq_core_point2 : core_point1 = core_point2,
{ have v1_eq_v2 : v1 = v2 :=
begin
apply vector.ext,
intro i,
have cast_cast_goal : (↑(↑(v1.nth i) : ℕ) : ℝ) = (↑(↑(v2.nth i) : ℕ) : ℝ) :=
begin
rw [← core_point1_corner_v1'_relationship i, ← core_point2_corner_v2'_relationship i],
simp only [sub_left_inj, add_left_inj, mul_eq_mul_left_iff, nat.cast_eq_zero],
left,
rw core_point1_eq_core_point2 at core_point1_in_core_point1_corner,
rw core_point2_corner_unique core_point1_corner core_point1_corner_in_T_shifted core_point1_in_core_point1_corner,
end,
have cast_goal : (↑(v1.nth i) : ℕ) = (↑(v2.nth i) : ℕ) := by exact_mod_cast cast_cast_goal,
apply fin.eq_of_veq,
simp only [fin.val_eq_coe],
exact_mod_cast cast_goal,
end,
exact v1_ne_v2 v1_eq_v2,
},
have core_point1_ne_core_point2 : ∃ i : fin d, core_point1.nth i ≠ core_point2.nth i :=
begin
by_contra h,
simp only [not_exists_not] at h,
exact core_point1_eq_core_point2 (vector.ext h),
end,
cases core_point1_ne_core_point2 with i core_point1_ne_core_point2,
replace core_point1_is_core_point := core_point1_is_core_point i,
replace core_point2_is_core_point := core_point2_is_core_point i,
rw cube at core_point1_in_core_point1_corner core_point2_in_core_point2_corner core_point1_add_double_z_in_core_point1_add_double_z_corner,
simp only [set.mem_set_of_eq] at core_point1_in_core_point1_corner core_point2_in_core_point2_corner core_point1_add_double_z_in_core_point1_add_double_z_corner,
rw in_cube at core_point1_in_core_point1_corner core_point2_in_core_point2_corner core_point1_add_double_z_in_core_point1_add_double_z_corner,
replace core_point1_in_core_point1_corner := core_point1_in_core_point1_corner i,
replace core_point2_in_core_point2_corner := core_point2_in_core_point2_corner i,
replace core_point1_add_double_z_in_core_point1_add_double_z_corner := core_point1_add_double_z_in_core_point1_add_double_z_corner i,
cases core_point1_in_core_point1_corner with core_point1_corner_le_core_point1 core_point1_lt_core_point1_corner_add_one,
cases core_point2_in_core_point2_corner with core_point2_corner_le_core_point2 core_point2_lt_core_point2_corner_add_one,
rw [int_point_to_point, add_int_vectors, double_int_vector] at core_point1_add_double_z_in_core_point1_add_double_z_corner,
simp only [vector.nth_of_fn, ge_iff_le, mul_ite, mul_zero, mul_one, mul_neg, int.cast_add] at core_point1_add_double_z_in_core_point1_add_double_z_corner,
cases core_point1_is_core_point with core_point1_eq_zero core_point1_eq_one,
{ cases core_point2_is_core_point with core_point2_eq_zero core_point2_eq_one,
{ rw [core_point1_eq_zero, core_point2_eq_zero] at core_point1_ne_core_point2,
exact core_point1_ne_core_point2 (by refl),
},
rw if_pos core_point1_eq_zero at core_point1_add_double_z_in_core_point1_add_double_z_corner,
simp only [int.cast_zero, zero_add] at core_point1_add_double_z_in_core_point1_add_double_z_corner,
rw ← core_point2_corner_eq_core_point1_add_double_z_corner at core_point1_add_double_z_in_core_point1_add_double_z_corner,
by_cases h1 : vector.nth core_point1_corner i < vector.nth core_point2_corner i + 1 ∧ vector.nth core_point2_corner i < vector.nth core_point1_corner i + 1,
{ rw if_pos h1 at core_point1_add_double_z_in_core_point1_add_double_z_corner,
simp only [int.cast_zero] at core_point1_add_double_z_in_core_point1_add_double_z_corner,
linarith,
},
rw if_neg h1 at core_point1_add_double_z_in_core_point1_add_double_z_corner,
by_cases h2 : vector.nth core_point1_corner i + 1 ≤ vector.nth core_point2_corner i,
{ rw if_pos h2 at core_point1_add_double_z_in_core_point1_add_double_z_corner,
simp only [int.cast_bit0, int.cast_one] at core_point1_add_double_z_in_core_point1_add_double_z_corner,
linarith,
},
rw if_neg h2 at core_point1_add_double_z_in_core_point1_add_double_z_corner,
simp only [int.cast_neg, int.cast_bit0, int.cast_one] at core_point1_add_double_z_in_core_point1_add_double_z_corner,
linarith,
},
cases core_point2_is_core_point with core_point2_eq_zero core_point2_eq_one,
{ have core_point1_ne_zero : core_point1.nth i ≠ 0 := by {rw core_point1_eq_one, norm_num},
rw if_neg core_point1_ne_zero at core_point1_add_double_z_in_core_point1_add_double_z_corner,
simp only [int.cast_one] at core_point1_add_double_z_in_core_point1_add_double_z_corner,
rw ← core_point2_corner_eq_core_point1_add_double_z_corner at core_point1_add_double_z_in_core_point1_add_double_z_corner,
by_cases h1 : vector.nth core_point1_corner i < vector.nth core_point2_corner i + 1 ∧ vector.nth core_point2_corner i < vector.nth core_point1_corner i + 1,
{ rw if_pos h1 at core_point1_add_double_z_in_core_point1_add_double_z_corner,
simp only [int.cast_zero, add_zero, lt_add_iff_pos_left] at core_point1_add_double_z_in_core_point1_add_double_z_corner,
linarith,
},
rw if_neg h1 at core_point1_add_double_z_in_core_point1_add_double_z_corner,
by_cases h2 : vector.nth core_point1_corner i + 1 ≤ vector.nth core_point2_corner i,
{ rw if_pos h2 at core_point1_add_double_z_in_core_point1_add_double_z_corner,
simp only [int.cast_bit0, int.cast_one] at core_point1_add_double_z_in_core_point1_add_double_z_corner,
linarith,
},
rw if_neg h2 at core_point1_add_double_z_in_core_point1_add_double_z_corner,
simp only [int.cast_neg, int.cast_bit0, int.cast_one, le_add_neg_iff_add_le, add_neg_lt_iff_le_add'] at core_point1_add_double_z_in_core_point1_add_double_z_corner,
linarith,
},
rw [core_point1_eq_one, core_point2_eq_one] at core_point1_ne_core_point2,
exact core_point1_ne_core_point2 (by refl),
end
theorem periodic_tiling_implies_clique {d : ℕ} {s : ℕ} (d_ne_zero : d ≠ 0) (s_ne_zero : s ≠ 0) :
(∃ (T : set (point d)) (T_is_tiling : is_tiling T), tiling_faceshare_free T ∧ is_periodic T_is_tiling ∧ is_s_discrete s T) →
has_clique (Keller_graph d s) (2 ^ d) :=
begin
rintro ⟨T, T_is_tiling, T_faceshare_free, T_is_periodic, T_is_s_discrete⟩,
rcases inductive_replacement_lemma d_ne_zero s_ne_zero T T_is_tiling T_faceshare_free T_is_periodic T_is_s_discrete with
⟨T_shifted, T_shifted_is_tiling, T_shifted_faceshare_free, T_shifted_is_periodic, T_shifted_contains_only_s_points⟩,
have core_points_finset := build_core_points_finset ⟨d, lt_add_one d⟩,
rcases core_points_finset with ⟨core_points_finset, core_points_finset_card, core_points_finset_property⟩,
have goal_clique_with_info_map :
{p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)} ↪
{v : vector (fin (2*s)) d // ∃ p : point d, is_core_point p ∧ ∃ p_corner ∈ T_shifted,
p ∈ cube p_corner ∧ (∀ alt_corner : point d, alt_corner ∈ T_shifted → p ∈ cube alt_corner → alt_corner = p_corner) ∧
(∀ i : fin d, ↑s * (vector.nth p_corner i) + ↑s - 1 = (vector.nth v i).val)} :=
begin
let goal_clique_with_info_map_fn :
{p : point d // ∀ (j : fin d), (j.val < d → vector.nth p j = 0 ∨ vector.nth p j = 1) ∧ (j.val ≥ d → vector.nth p j = 0)} →
{v : vector (fin (2*s)) d // ∃ p : point d, is_core_point p ∧ ∃ p_corner ∈ T_shifted,
p ∈ cube p_corner ∧ (∀ alt_corner : point d, alt_corner ∈ T_shifted → p ∈ cube alt_corner → alt_corner = p_corner) ∧
(∀ i : fin d, ↑s * (vector.nth p_corner i) + ↑s - 1 = (vector.nth v i).val)} :=
build_goal_clique_with_info_map_fn d_ne_zero s_ne_zero T T_is_tiling T_faceshare_free T_is_periodic T_is_s_discrete T_shifted
T_shifted_is_tiling T_shifted_faceshare_free T_shifted_contains_only_s_points core_points_finset core_points_finset_card
core_points_finset_property,
have goal_clique_with_info_map_fn_injective : function.injective goal_clique_with_info_map_fn :=
begin
rw function.injective,
intros p1 p2 mapped_p1_eq_mapped_p2,
dsimp[goal_clique_with_info_map_fn] at mapped_p1_eq_mapped_p2,
rw build_goal_clique_with_info_map_fn at mapped_p1_eq_mapped_p2,
simp only [subtype.val_eq_coe] at mapped_p1_eq_mapped_p2,
let mapped_p1_statement :=
goal_clique_with_info_map_fn_yields_fin_double_s_vector d_ne_zero s_ne_zero T T_is_tiling T_faceshare_free T_is_periodic T_is_s_discrete T_shifted
T_shifted_is_tiling T_shifted_faceshare_free T_shifted_contains_only_s_points core_points_finset core_points_finset_card
core_points_finset_property p1,
let mapped_p2_statement :=
goal_clique_with_info_map_fn_yields_fin_double_s_vector d_ne_zero s_ne_zero T T_is_tiling T_faceshare_free T_is_periodic T_is_s_discrete T_shifted
T_shifted_is_tiling T_shifted_faceshare_free T_shifted_contains_only_s_points core_points_finset core_points_finset_card
core_points_finset_property p2,
change classical.some mapped_p1_statement = classical.some mapped_p2_statement at mapped_p1_eq_mapped_p2,
let mapped_p1 := classical.some mapped_p1_statement,
have mapped_p1_def : mapped_p1 = classical.some mapped_p1_statement := by refl,
have mapped_p1_property := classical.some_spec mapped_p1_statement,
rw ← mapped_p1_def at mapped_p1_property,
let mapped_p2 := classical.some mapped_p2_statement,
have mapped_p2_def : mapped_p2 = classical.some mapped_p2_statement := by refl,
have mapped_p2_property := classical.some_spec mapped_p2_statement,
rw ← mapped_p2_def at mapped_p2_property,
rw [← mapped_p1_def, ← mapped_p2_def] at mapped_p1_eq_mapped_p2,
let p1_corner := (point_to_corner T_shifted_is_tiling ↑p1).val,
have p1_corner_def : p1_corner = (point_to_corner T_shifted_is_tiling ↑p1).val := by refl,
have p1_corner_property := (point_to_corner T_shifted_is_tiling ↑p1).property,
rw ← p1_corner_def at p1_corner_property,
rcases p1_corner_property with ⟨p1_corner_in_T_shifted, p1_in_p1_corner, p1_corner_unique⟩,
let p2_corner := (point_to_corner T_shifted_is_tiling ↑p2).val,
have p2_corner_def : p2_corner = (point_to_corner T_shifted_is_tiling ↑p2).val := by refl,
have p2_corner_property := (point_to_corner T_shifted_is_tiling ↑p2).property,
rw ← p2_corner_def at p2_corner_property,
rcases p2_corner_property with ⟨p2_corner_in_T_shifted, p2_in_p2_corner, p2_corner_unique⟩,
have p1_corner_eq_p2_corner : p1_corner = p2_corner :=
begin
apply vector.ext,
intro i,
replace mapped_p1_property := mapped_p1_property i,
replace mapped_p2_property := mapped_p2_property i,
rw mapped_p1_eq_mapped_p2 at mapped_p1_property,
rw [mapped_p1_property, ← p1_corner_def, ← p2_corner_def] at mapped_p2_property,
simp only [add_left_inj, mul_eq_mul_left_iff, nat.cast_eq_zero, sub_left_inj, subtype.val_eq_coe] at mapped_p2_property,
cases mapped_p2_property with goal s_eq_zero, exact goal,
exfalso,
exact s_ne_zero s_eq_zero,
end,
apply subtype.ext,
apply vector.ext,
intro i,
by_contra p1_ne_p2_at_i,
rcases p1.property i with ⟨p1_is_core_point, unneeded1⟩,
rcases p2.property i with ⟨p2_is_core_point, unneeded2⟩,
clear unneeded1 unneeded2,
simp only [subtype.val_eq_coe] at p1_is_core_point p2_is_core_point,
replace p1_is_core_point := p1_is_core_point i.property,
replace p2_is_core_point := p2_is_core_point i.property,
rw cube at p1_in_p1_corner p2_in_p2_corner,
simp only [set.mem_set_of_eq] at p1_in_p1_corner p2_in_p2_corner,
rw in_cube at p1_in_p1_corner p2_in_p2_corner,
replace p1_in_p1_corner := p1_in_p1_corner i,
replace p2_in_p2_corner := p2_in_p2_corner i,
rw p1_corner_eq_p2_corner at p1_in_p1_corner,
cases p1_in_p1_corner with p1_corner_le_p1 p1_lt_p1_corner_add_one,
cases p2_in_p2_corner with p2_corner_le_p2 p2_lt_p2_corner_add_one,
cases p1_is_core_point with p1_eq_zero p1_eq_one,
{ cases p2_is_core_point with p2_eq_zero p2_eq_one,
{ rw [p1_eq_zero, p2_eq_zero] at p1_ne_p2_at_i,
exact p1_ne_p2_at_i (by refl),
},
rw p1_eq_zero at p1_corner_le_p1 p1_lt_p1_corner_add_one,
rw p2_eq_one at p2_corner_le_p2 p2_lt_p2_corner_add_one,
linarith,
},
cases p2_is_core_point with p2_eq_zero p2_eq_one,
{ rw p1_eq_one at p1_corner_le_p1 p1_lt_p1_corner_add_one,
rw p2_eq_zero at p2_corner_le_p2 p2_lt_p2_corner_add_one,
linarith,
},
rw [p1_eq_one, p2_eq_one] at p1_ne_p2_at_i,
exact p1_ne_p2_at_i (by refl),
end,
exact {to_fun := goal_clique_with_info_map_fn, inj' := goal_clique_with_info_map_fn_injective},
end,
let goal_clique_with_info := finset.map goal_clique_with_info_map core_points_finset,
have goal_clique_with_info_card : goal_clique_with_info.card = core_points_finset.card := finset.card_map goal_clique_with_info_map,
rw core_points_finset_card at goal_clique_with_info_card,
simp only [] at goal_clique_with_info_card,
let remove_info_map :
{v : vector (fin (2*s)) d // ∃ p : point d, is_core_point p ∧ ∃ p_corner ∈ T_shifted,
p ∈ cube p_corner ∧ (∀ alt_corner : point d, alt_corner ∈ T_shifted → p ∈ cube alt_corner → alt_corner = p_corner) ∧
(∀ i : fin d, ↑s * (vector.nth p_corner i) + ↑s - 1 = (vector.nth v i).val)} ↪ vector (fin (2*s)) d :=
begin
let remove_info_map_fn :
{v : vector (fin (2*s)) d // ∃ p : point d, is_core_point p ∧ ∃ p_corner ∈ T_shifted,
p ∈ cube p_corner ∧ (∀ alt_corner : point d, alt_corner ∈ T_shifted → p ∈ cube alt_corner → alt_corner = p_corner) ∧
(∀ i : fin d, ↑s * (vector.nth p_corner i) + ↑s - 1 = (vector.nth v i).val)} → vector (fin (2*s)) d :=
λ v, v,
have remove_info_map_fn_injective : function.injective remove_info_map_fn :=
by {rw function.injective, dsimp[remove_info_map_fn], simp},
exact {to_fun := remove_info_map_fn, inj' := remove_info_map_fn_injective},
end,
let goal_clique := finset.map remove_info_map goal_clique_with_info,
have goal_clique_card : goal_clique.card = goal_clique_with_info.card := finset.card_map remove_info_map,
rw goal_clique_with_info_card at goal_clique_card,
use [goal_clique, goal_clique_card],
intros v1 v2 v1_in_goal_clique v2_in_goal_clique v1_ne_v2,
rw Keller_graph,
simp only [simple_graph.from_rel_adj, fin.val_eq_coe, exists_and_distrib_left, ne.def],
split, exact v1_ne_v2,
dsimp[goal_clique] at v1_in_goal_clique v2_in_goal_clique,
rw finset.mem_map at v1_in_goal_clique v2_in_goal_clique,
simp only [exists_prop, fin.val_eq_coe, finset.mem_map, ge_iff_le, subtype.exists] at v1_in_goal_clique v2_in_goal_clique,
rcases v1_in_goal_clique with
⟨v1', ⟨core_point1, core_point1_is_core_point, ⟨core_point1_corner, core_point1_corner_in_T_shifted,
core_point1_in_core_point1_corner, core_point1_corner_unique, core_point1_corner_v1'_relationship⟩⟩, redundant, v1_def⟩,
clear redundant,
rcases v2_in_goal_clique with
⟨v2', ⟨core_point2, core_point2_is_core_point, ⟨core_point2_corner, core_point2_corner_in_T_shifted,
core_point2_in_core_point2_corner, core_point2_corner_unique, core_point2_corner_v2'_relationship⟩⟩, redundant, v2_def⟩,
clear redundant,
dsimp[remove_info_map] at v1_def v2_def,
rw v1_def at core_point1_corner_v1'_relationship,
rw v2_def at core_point2_corner_v2'_relationship,
by_contra v1_not_adj_v2,
rw not_or_distrib at v1_not_adj_v2,
simp only [not_exists, not_and, not_not] at v1_not_adj_v2,
by_cases v1_not_adj_v2_hyp : ∃ i : fin d, ↑(v1.nth i) = ↑(v2.nth i) + s ∨ ↑(v2.nth i) = ↑(v1.nth i) + s,
{ replace T_shifted_faceshare_free := T_shifted_faceshare_free core_point1_corner core_point1_corner_in_T_shifted
core_point2_corner core_point2_corner_in_T_shifted,
rw is_facesharing at T_shifted_faceshare_free,
simp only [not_exists, not_and, not_forall] at T_shifted_faceshare_free,
rcases v1_not_adj_v2_hyp with ⟨i, v1_eq_v2_add_s | v2_eq_v1_add_s⟩,
{ replace v1_not_adj_v2 := (and.elim_left v1_not_adj_v2) i v1_eq_v2_add_s,
have core_point_corners_off_by_one : vector.nth core_point1_corner i - vector.nth core_point2_corner i = 1 :=
begin
replace core_point1_corner_v1'_relationship := core_point1_corner_v1'_relationship i,
replace core_point2_corner_v2'_relationship := core_point2_corner_v2'_relationship i,
rw v1_eq_v2_add_s at core_point1_corner_v1'_relationship,
rw fin.coe_eq_val at core_point1_corner_v1'_relationship core_point2_corner_v2'_relationship,
replace core_point1_corner_v1'_relationship :
↑s * vector.nth core_point1_corner i + ↑s - (1 : ℝ) = ↑((v2.nth i).val) + ↑s :=
by exact_mod_cast core_point1_corner_v1'_relationship,
rw ← core_point2_corner_v2'_relationship at core_point1_corner_v1'_relationship,
clear_except core_point1_corner_v1'_relationship s_ne_zero,
rw add_comm (↑s * vector.nth core_point2_corner i + ↑s - 1) ↑s at core_point1_corner_v1'_relationship,
rw [sub_eq_add_neg, sub_eq_add_neg, add_assoc (↑s * vector.nth core_point2_corner i) ↑s (-1), ← add_assoc,
add_assoc (↑s * vector.nth core_point1_corner i) ↑s (-1)] at core_point1_corner_v1'_relationship,
simp only [add_left_inj] at core_point1_corner_v1'_relationship,
have s_times_goal : ↑s * vector.nth core_point1_corner i - ↑s * vector.nth core_point2_corner i = ↑s := by linarith,
rw ← mul_sub_left_distrib at s_times_goal,
have s_times_goal_div_s : ↑s * (vector.nth core_point1_corner i - vector.nth core_point2_corner i) / ↑s = ↑s / ↑s :=
by rw s_times_goal,
have cast_s_ne_zero : ↑s ≠ (0 : ℝ) := by exact_mod_cast s_ne_zero,
rw [mul_div_cancel_left (vector.nth core_point1_corner i - vector.nth core_point2_corner i) cast_s_ne_zero,
div_self cast_s_ne_zero] at s_times_goal_div_s,
exact s_times_goal_div_s,
end,
replace T_shifted_faceshare_free := T_shifted_faceshare_free i (or.inl core_point_corners_off_by_one),
rcases T_shifted_faceshare_free with ⟨j, i_ne_j_and_core_point1_eq_core_point2_at_j⟩,
rw not_or_distrib at i_ne_j_and_core_point1_eq_core_point2_at_j,
cases i_ne_j_and_core_point1_eq_core_point2_at_j with i_ne_j core_point1_corner_ne_core_point2_corner_at_j,
have v1_ne_v2_at_j : v1.nth j ≠ v2.nth j :=
begin
replace core_point1_corner_v1'_relationship := core_point1_corner_v1'_relationship j,
replace core_point2_corner_v2'_relationship := core_point2_corner_v2'_relationship j,
intro v1_eq_v2_at_j,
rcases real_eq_or_lt_or_gt (core_point1_corner.nth j) (core_point2_corner.nth j) with
core_point1_corner_eq_core_point2_corner | core_point1_corner_lt_core_point2_corner |
core_point1_corner_gt_core_point2_corner,
exact core_point1_corner_ne_core_point2_corner_at_j core_point1_corner_eq_core_point2_corner,
{ rw [v1_eq_v2_at_j, ← core_point2_corner_v2'_relationship] at core_point1_corner_v1'_relationship,
simp only [add_left_inj, mul_eq_mul_left_iff, nat.cast_eq_zero, sub_left_inj] at core_point1_corner_v1'_relationship,
cases core_point1_corner_v1'_relationship with core_point1_corner_eq_core_point2_corner s_eq_zero,
{ rw core_point1_corner_eq_core_point2_corner at core_point1_corner_lt_core_point2_corner,
exact lt_irrefl (vector.nth core_point2_corner j) core_point1_corner_lt_core_point2_corner,
},
exact s_ne_zero s_eq_zero,
},
rw [v1_eq_v2_at_j, ← core_point2_corner_v2'_relationship] at core_point1_corner_v1'_relationship,
simp only [add_left_inj, mul_eq_mul_left_iff, nat.cast_eq_zero, sub_left_inj] at core_point1_corner_v1'_relationship,
cases core_point1_corner_v1'_relationship with core_point1_corner_eq_core_point2_corner s_eq_zero,
{ rw core_point1_corner_eq_core_point2_corner at core_point1_corner_gt_core_point2_corner,
exact gt_irrefl (vector.nth core_point2_corner j) core_point1_corner_gt_core_point2_corner,
},
exact s_ne_zero s_eq_zero,
end,
exact i_ne_j (v1_not_adj_v2 j v1_ne_v2_at_j),
}, --Next case is symmetrical to the above case
replace v1_not_adj_v2 := (and.elim_right v1_not_adj_v2) i v2_eq_v1_add_s,
have core_point_corners_off_by_one : vector.nth core_point2_corner i - vector.nth core_point1_corner i = 1 :=
begin
replace core_point1_corner_v1'_relationship := core_point1_corner_v1'_relationship i,
replace core_point2_corner_v2'_relationship := core_point2_corner_v2'_relationship i,
rw v2_eq_v1_add_s at core_point2_corner_v2'_relationship,
rw fin.coe_eq_val at core_point1_corner_v1'_relationship core_point2_corner_v2'_relationship,
replace core_point2_corner_v2'_relationship :
↑s * vector.nth core_point2_corner i + ↑s - (1 : ℝ) = ↑((v1.nth i).val) + ↑s :=
by exact_mod_cast core_point2_corner_v2'_relationship,
rw ← core_point1_corner_v1'_relationship at core_point2_corner_v2'_relationship,
clear_except core_point2_corner_v2'_relationship s_ne_zero,
rw add_comm (↑s * vector.nth core_point1_corner i + ↑s - 1) ↑s at core_point2_corner_v2'_relationship,
rw [sub_eq_add_neg, sub_eq_add_neg, add_assoc (↑s * vector.nth core_point1_corner i) ↑s (-1), ← add_assoc,
add_assoc (↑s * vector.nth core_point2_corner i) ↑s (-1)] at core_point2_corner_v2'_relationship,
simp only [add_left_inj] at core_point2_corner_v2'_relationship,
have s_times_goal : ↑s * vector.nth core_point2_corner i - ↑s * vector.nth core_point1_corner i = ↑s := by linarith,
rw ← mul_sub_left_distrib at s_times_goal,
have s_times_goal_div_s : ↑s * (vector.nth core_point2_corner i - vector.nth core_point1_corner i) / ↑s = ↑s / ↑s :=
by rw s_times_goal,
have cast_s_ne_zero : ↑s ≠ (0 : ℝ) := by exact_mod_cast s_ne_zero,
rw [mul_div_cancel_left (vector.nth core_point2_corner i - vector.nth core_point1_corner i) cast_s_ne_zero,
div_self cast_s_ne_zero] at s_times_goal_div_s,
exact s_times_goal_div_s,
end,
replace T_shifted_faceshare_free := T_shifted_faceshare_free i (or.inr core_point_corners_off_by_one),
rcases T_shifted_faceshare_free with ⟨j, i_ne_j_and_core_point1_eq_core_point2_at_j⟩,
rw not_or_distrib at i_ne_j_and_core_point1_eq_core_point2_at_j,
cases i_ne_j_and_core_point1_eq_core_point2_at_j with i_ne_j core_point1_corner_ne_core_point2_corner_at_j,
have v2_ne_v1_at_j : v2.nth j ≠ v1.nth j :=
begin
replace core_point1_corner_v1'_relationship := core_point1_corner_v1'_relationship j,
replace core_point2_corner_v2'_relationship := core_point2_corner_v2'_relationship j,
intro v2_eq_v1_at_j,
rcases real_eq_or_lt_or_gt (core_point1_corner.nth j) (core_point2_corner.nth j) with
core_point1_corner_eq_core_point2_corner | core_point1_corner_lt_core_point2_corner |
core_point1_corner_gt_core_point2_corner,
exact core_point1_corner_ne_core_point2_corner_at_j core_point1_corner_eq_core_point2_corner,
{ rw [← v2_eq_v1_at_j, ← core_point2_corner_v2'_relationship] at core_point1_corner_v1'_relationship,
simp only [add_left_inj, mul_eq_mul_left_iff, nat.cast_eq_zero, sub_left_inj] at core_point1_corner_v1'_relationship,
cases core_point1_corner_v1'_relationship with core_point1_corner_eq_core_point2_corner s_eq_zero,
{ rw core_point1_corner_eq_core_point2_corner at core_point1_corner_lt_core_point2_corner,
exact lt_irrefl (vector.nth core_point2_corner j) core_point1_corner_lt_core_point2_corner,
},
exact s_ne_zero s_eq_zero,
},
rw [← v2_eq_v1_at_j, ← core_point2_corner_v2'_relationship] at core_point1_corner_v1'_relationship,
simp only [add_left_inj, mul_eq_mul_left_iff, nat.cast_eq_zero, sub_left_inj] at core_point1_corner_v1'_relationship,
cases core_point1_corner_v1'_relationship with core_point1_corner_eq_core_point2_corner s_eq_zero,
{ rw core_point1_corner_eq_core_point2_corner at core_point1_corner_gt_core_point2_corner,
exact gt_irrefl (vector.nth core_point2_corner j) core_point1_corner_gt_core_point2_corner,
},
exact s_ne_zero s_eq_zero,
end,
exact i_ne_j (v1_not_adj_v2 j v2_ne_v1_at_j),
},
rename v1_not_adj_v2_hyp v1_not_adj_v2_hyp_false,
clear' remove_info_map goal_clique goal_clique_card goal_clique_with_info_card,
exact periodic_tiling_implies_clique_helper d_ne_zero s_ne_zero T T_is_tiling T_faceshare_free T_is_periodic T_is_s_discrete T_shifted
T_shifted_is_tiling T_shifted_faceshare_free T_shifted_is_periodic T_shifted_contains_only_s_points core_points_finset core_points_finset_card
core_points_finset_property goal_clique_with_info_map v1 v2 v1_ne_v2 v1' core_point1 core_point1_is_core_point core_point1_corner
core_point1_corner_in_T_shifted core_point1_in_core_point1_corner core_point1_corner_unique v2' core_point2 core_point2_is_core_point
core_point2_corner core_point2_corner_in_T_shifted core_point2_in_core_point2_corner core_point2_corner_unique v2_def v1_def
core_point1_corner_v1'_relationship core_point2_corner_v2'_relationship v1_not_adj_v2 v1_not_adj_v2_hyp_false,
end
lemma clique_nonexistence_implies_Keller_conjecture {d : ℕ} (d_gt_zero : d > 0) :
¬has_clique (Keller_graph d (2^(d-1))) (2^d) → Keller_conjecture d :=
begin
intro h,
apply periodic_reduction d d_gt_zero,
contrapose h,
rw not_not,
rw periodic_Keller_conjecture at h,
simp only [not_forall, not_not, exists_prop, exists_and_distrib_right] at h,
rcases h with ⟨T, ⟨T_is_tiling, T_is_periodic⟩, T_faceshare_free⟩,
have T_is_s_discrete := s_discrete_upper_bound d T T_is_tiling d_gt_zero T_is_periodic,
have d_ne_zero : d ≠ 0 := by linarith,
have two_to_the_d_sub_one_ne_zero : 2^(d - 1) ≠ 0 :=
begin
have two_to_the_d_sub_one_pos : 2^(d - 1) > 0 := by norm_num,
linarith,
end,
apply periodic_tiling_implies_clique d_ne_zero two_to_the_d_sub_one_ne_zero,
use [T, T_is_tiling, T_faceshare_free, T_is_periodic, T_is_s_discrete],
end
|
{"author": "JOSHCLUNE", "repo": "Keller_reduction", "sha": "dc392b3da352fc1ffcfbecb1d4717d05f5faed4a", "save_path": "github-repos/lean/JOSHCLUNE-Keller_reduction", "path": "github-repos/lean/JOSHCLUNE-Keller_reduction/Keller_reduction-dc392b3da352fc1ffcfbecb1d4717d05f5faed4a/src/no_clique_implies_keller.lean"}
|
import os
import copy
import json
import logging
import pymongo
import numpy as np
from torch import set_grad_enabled
from torch import load
from torch import device as D
from pymongo import MongoClient
from collections import defaultdict
from flask import Flask, jsonify, request
from flask_cors import CORS
from poker_env.env import Poker,flatten
import poker_env.datatypes as pdt
from poker_env.config import Config
from models.model_utils import norm_frequencies
from models.networks import OmahaActor,OmahaObsQCritic
"""
API for connecting the Poker Env with Alex's frontend client for baseline testing the trained bot.
"""
class API(object):
def __init__(self):
self.increment_position = {'SB':'BB','BB':'SB'}
self.seed = 1458
self.connect()
self.game_object = pdt.Globals.GameTypeDict[pdt.GameTypes.OMAHAHI]
self.config = Config()
self.env_params = {
'game':pdt.GameTypes.OMAHAHI,
'betsizes': self.game_object.rule_params['betsizes'],
'bet_type': self.game_object.rule_params['bettype'],
'n_players': 2,
'pot':self.game_object.state_params['pot'],
'stacksize': self.game_object.state_params['stacksize'],
'cards_per_player': self.game_object.state_params['cards_per_player'],
'starting_street': self.game_object.starting_street,
'global_mapping':self.config.global_mapping,
'state_mapping':self.config.state_mapping,
'obs_mapping':self.config.obs_mapping,
'shuffle':True
}
self.env = Poker(self.env_params)
self.network_params = self.instantiate_network_params()
self.actor = OmahaActor(self.seed,self.env.state_space,self.env.action_space,self.env.betsize_space,self.network_params)
self.critic = OmahaObsQCritic(self.seed,self.env.state_space,self.env.action_space,self.env.betsize_space,self.network_params)
self.load_model(self.actor,self.config.production_actor)
self.load_model(self.critic,self.config.production_critic)
self.player = {'name':None,'position':'BB'}
self.reset_trajectories()
def reset_trajectories(self):
self.trajectories = defaultdict(lambda:[])
self.trajectory = defaultdict(lambda:{'states':[],'obs':[],'betsize_masks':[],'action_masks':[], 'actions':[],'action_category':[],'action_probs':[],'action_prob':[],'betsize':[],'rewards':[],'value':[]})
def instantiate_network_params(self):
device = 'cpu'
network_params = copy.deepcopy(self.config.network_params)
network_params['maxlen'] = self.config.maxlen
network_params['device'] = device
return network_params
def load_model(self,model,path):
if os.path.isfile(path):
model.load_state_dict(load(path,map_location=D('cpu')))
set_grad_enabled(False)
else:
raise ValueError('File does not exist')
def connect(self):
client = MongoClient('localhost', 27017,maxPoolSize=10000)
self.db = client.baseline
def update_player_name(self,name:str):
"""updates player name"""
self.player['name'] = name
def update_player_position(self,position):
self.player['position'] = position
def insert_model_outputs(self,model_outputs,action_mask):
outputs_json = {
'action':model_outputs['action'],
'action_category':model_outputs['action_category'],
'betsize':model_outputs['betsize'],
'action_prob':model_outputs['action_prob'].detach().numpy().tolist(),
'action_probs':model_outputs['action_probs'].detach().numpy().tolist(),
'value':model_outputs['value'].detach().numpy().tolist(),
'action_mask':action_mask.tolist(),
'player':self.player['name']
}
self.db['bot_data'].insert_one(outputs_json)
def insert_into_db(self,training_data:dict):
"""
stores player data in the player_stats collection.
takes trajectories and inserts them into db for data analysis and learning.
"""
stats_json = {
'game':self.env.game,
'player':self.player['name'],
'reward':training_data[self.player['position']][0]['rewards'][0],
'position':self.player['position'],
}
self.db['player_stats'].insert_one(stats_json)
keys = training_data.keys()
positions = [position for position in keys if position in ['SB','BB']]
for position in positions:
for i,poker_round in enumerate(training_data[position]):
states = poker_round['states']
observations = poker_round['obs']
actions = poker_round['actions']
action_prob = poker_round['action_prob']
action_probs = poker_round['action_probs']
action_categories = poker_round['action_category']
betsize_masks = poker_round['betsize_masks']
action_masks = poker_round['action_masks']
rewards = poker_round['rewards']
betsizes = poker_round['betsize']
values = poker_round['value']
assert(isinstance(rewards,list))
assert(isinstance(actions,list))
assert(isinstance(action_prob,list))
assert(isinstance(action_probs,list))
assert(isinstance(states,list))
assert(isinstance(values,list))
for step,state in enumerate(states):
state_json = {
'game':self.env.game,
'player':self.player['name'],
'poker_round':step,
'state':state.tolist(),
'action_probs':action_probs[step].tolist(),
'action_prob':action_prob[step].tolist(),
'action':actions[step],
'action_category':action_categories[step],
'betsize_mask':betsize_masks[step].tolist(),
'action_mask':action_masks[step].tolist(),
'betsize':betsizes[step],
'reward':rewards[step],
'value':values[step].tolist()
}
self.db['game_data'].insert_one(state_json)
def return_model_outputs(self):
query = {
'player':self.player['name']
}
player_data = self.db['bot_data'].find(query).sort('_id',-1)
action_probs = []
values = []
action_mask = []
for result in player_data:
action_probs.append(np.array(result['action_probs']))
values.append(np.array(result['value']))
action_mask.append(np.array(result['action_mask']))
break
if action_probs:
action_probs = action_probs[0]
values = values[0]
action_mask = action_mask[0]
if np.sum(action_probs) > 0:
action_probs *= action_mask
action_probs /= np.sum(action_probs)
# scale values
if np.max(np.abs(values)) > 0:
values *= action_mask
values /= self.env_params['stacksize'] + self.env_params['pot']
model_outputs = {
'action_probs':action_probs.tolist(),
'q_values':[values.tolist()]
}
else:
model_outputs = {
'action_probs':[0]*self.env.action_space,
'q_values':[0]*self.env.action_space
}
print(model_outputs)
print(action_mask)
return model_outputs
def return_player_stats(self):
"""Returns dict of current player stats against the bot."""
query = {
'player':self.player['name']
}
# projection ={'reward':1,'hand_num':1,'_id':0}
player_data = self.db['player_stats'].find(query)
total_hands = self.db['player_stats'].count_documents(query)
results = []
position_results = {'SB':0,'BB':0}
# total_hands = 0
for result in player_data:
results.append(result['reward'])
position_results[result['position']] += result['reward']
bb_per_hand = sum(results) / total_hands if total_hands > 0 else 0
sb_bb_per_hand = position_results['SB'] / total_hands if total_hands > 0 else 0
bb_bb_per_hand = position_results['BB'] / total_hands if total_hands > 0 else 0
player_stats = {
'results':sum(results),
'bb_per_hand':round(bb_per_hand,2),
'total_hands':total_hands,
'SB':round(sb_bb_per_hand,2),
'BB':round(bb_bb_per_hand,2),
}
return player_stats
def parse_env_outputs(self,state,action_mask,betsize_mask,done):
"""Wraps state and passes to frontend. Can be the dummy last state. In which case hero mappings are reversed."""
reward = state[:,-1][:,self.env.state_mapping['hero_stacksize']] - self.env.starting_stack
# cards go in a list
hero = self.env.players[self.player['position']]
villain = self.env.players[self.increment_position[self.player['position']]]
state_object = {
'history' :state.tolist(),
'betsizes' :self.env.betsizes.tolist(),
'mapping' :self.env.state_mapping,
'current_player' :pdt.Globals.POSITION_MAPPING[self.env.current_player],
'hero_stack' :hero.stack,
'hero_position' :pdt.Globals.POSITION_MAPPING[hero.position],
'hero_cards' :flatten(hero.hand),
'hero_street_total' :hero.street_total,
'pot' :float(state[:,-1][:,self.env.state_mapping['pot']][0]),
'board_cards' :state[:,-1][:,self.env.state_mapping['board']][0].tolist(),
'villain_stack' :villain.stack,
'villain_position' :pdt.Globals.POSITION_MAPPING[villain.position],
'villain_cards' :flatten(villain.hand),
'villain_street_total' :villain.street_total,
'last_action' :int(state[:,-1][:,self.env.state_mapping['last_action']][0]),
'last_betsize' :float(state[:,-1][:,self.env.state_mapping['last_betsize']][0]),
'last_position' :int(state[:,-1][:,self.env.state_mapping['last_position']][0]),
'last_aggressive_action' :int(state[:,-1][:,self.env.state_mapping['last_aggressive_action']][0]),
'last_aggressive_betsize' :float(state[:,-1][:,self.env.state_mapping['last_aggressive_betsize']][0]),
'last_aggressive_position' :int(state[:,-1][:,self.env.state_mapping['last_aggressive_position']][0]),
'done' :done,
'action_mask' :action_mask.tolist(),
'betsize_mask' :betsize_mask.tolist(),
'street' :int(state[:,-1][:,self.env.state_mapping['street']][0]),
'blind' :bool(state[:,-1][:,self.env.state_mapping['blind']][0])
}
outcome_object = {
'player1_reward' :hero.stack - self.env.starting_stack,
'player1_hand' :flatten(hero.hand),
'player2_reward' :villain.stack - self.env.starting_stack,
'player2_hand' :flatten(villain.hand),
'player1_handrank' :hero.handrank,
'player2_handrank' :villain.handrank
}
json_obj = {'state':state_object,'outcome':outcome_object}
return json.dumps(json_obj)
def store_state(self,state,obs,action_mask,betsize_mask):
cur_player = self.env.current_player
self.trajectory[cur_player]['states'].append(copy.copy(state))
self.trajectory[cur_player]['action_masks'].append(copy.copy(action_mask))
self.trajectory[cur_player]['betsize_masks'].append(copy.copy(betsize_mask))
def store_actions(self,actor_outputs):
cur_player = self.env.current_player
self.trajectory[cur_player]['actions'].append(actor_outputs['action'])
self.trajectory[cur_player]['action_category'].append(actor_outputs['action_category'])
self.trajectory[cur_player]['action_prob'].append(actor_outputs['action_prob'])
self.trajectory[cur_player]['action_probs'].append(actor_outputs['action_probs'])
self.trajectory[cur_player]['betsize'].append(actor_outputs['betsize'])
self.trajectory[cur_player]['value'].append(actor_outputs['value'])
def query_bot(self,state,obs,action_mask,betsize_mask,done):
while self.env.current_player != self.player['position'] and not done:
actor_outputs = self.actor(state,action_mask,betsize_mask)
critic_outputs = self.critic(obs)
actor_outputs['value'] = critic_outputs['value']
self.insert_model_outputs(actor_outputs,action_mask)
self.store_actions(actor_outputs)
state,obs,done,action_mask,betsize_mask = self.env.step(actor_outputs)
if not done:
self.store_state(state,obs,action_mask,betsize_mask)
return state,obs,done,action_mask,betsize_mask
def reset(self):
assert self.player['name'] is not None
assert isinstance(self.player['position'],str)
self.reset_trajectories()
self.update_player_position(self.increment_position[self.player['position']])
state,obs,done,action_mask,betsize_mask = self.env.reset()
self.store_state(state,obs,action_mask,betsize_mask)
if self.env.current_player != self.player['position'] and not done:
state,obs,done,action_mask,betsize_mask = self.query_bot(state,obs,action_mask,betsize_mask,done)
assert self.env.current_player == self.player['position']
return self.parse_env_outputs(state,action_mask,betsize_mask,done)
def step(self,action:str,betsize:float):
"""Maps action + betsize -> to a flat action category"""
assert self.player['name'] is not None
assert isinstance(self.player['position'],str)
if isinstance(betsize,str):
betsize = float(betsize)
action_type = pdt.Globals.SERVER_ACTION_DICT[action]
flat_action_category,betsize_category = self.env.convert_to_category(action_type,betsize)
assert isinstance(flat_action_category,int)
player_outputs = {
'action':flat_action_category,
'action_category':action_type,
'betsize':betsize_category,
'action_prob':np.array([0]),
'action_probs':np.zeros(self.env.action_space + self.env.betsize_space - 2),
'value':np.zeros(self.env.action_space + self.env.betsize_space - 2)
}
self.store_actions(player_outputs)
state,obs,done,action_mask,betsize_mask = self.env.step(player_outputs)
if not done:
self.store_state(state,obs,action_mask,betsize_mask)
if self.env.current_player != self.player['position']:
state,obs,done,action_mask,betsize_mask = self.query_bot(state,obs,action_mask,betsize_mask,done)
if done:
rewards = self.env.player_rewards()
for position in self.trajectory.keys():
N = len(self.trajectory[position]['betsize_masks'])
self.trajectory[position]['rewards'] = [rewards[position]] * N
self.trajectories[position].append(self.trajectory[position])
self.insert_into_db(self.trajectories)
return self.parse_env_outputs(state,action_mask,betsize_mask,done)
@property
def current_player(self):
return self.player
# instantiate env
api = API()
app = Flask(__name__)
app.config['CORS_HEADERS'] = 'Content-Type'
cors = CORS(app, resources={r"/api/*": {"origins": "http://localhost:*"}})
cors = CORS(app, resources={r"/api/*": {"origins": "http://71.237.218.23*"}}) # This should be replaced with server public ip
logging.basicConfig(level=logging.DEBUG)
@app.route('/health')
def home():
return 'Server is up and running'
@app.route('/api/player/name',methods=['POST'])
def player():
req_data = json.loads(request.get_data())
api.update_player_name(req_data.get('name'))
return 'Updated Name'
@app.route('/api/player/stats')
def player_stats():
return json.dumps(api.return_player_stats())
@app.route('/api/model/outputs')
def model_outputs():
return json.dumps(api.return_model_outputs())
@app.route('/api/model/load',methods=['POST'])
def load_model():
req_data = json.loads(request.get_data())
api.load_model(req_data.get('path'))
return 'Loaded Model'
@app.route('/api/reset')
def reset():
return api.reset()
@app.route('/api/step', methods=['POST'])
def gen_routes():
log = logging.getLogger(__name__)
log.info(request.get_data())
req_data = json.loads(request.get_data())
action = req_data.get('action')
betsize = req_data.get('betsize')
log.info(f'action {action}')
log.info(f'betsize {betsize}')
return api.step(action,betsize)
if __name__ == '__main__':
app.run(debug=True, port=4000)
|
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|
(* File: Profile_List_Monadic.thy
Copyright 2023 Karlsruhe Institute of Technology (KIT)
*)
\<^marker>\<open>creator "Valentin Springsklee, Karlsruhe Institute of Technology (KIT)"\<close>
section \<open>Refined Profile Evaluation\<close>
theory Profile_List_Monadic
imports "Verified_Voting_Rule_Construction.Profile"
"Verified_Voting_Rule_Construction.Profile_List"
Ballot_Refinement
begin
subsection \<open>Profile Evaluation on List-based Profiles \<close>
fun win_count_l :: "'a Profile_List \<Rightarrow> 'a \<Rightarrow> nat" where
"win_count_l p a = fold (\<lambda>x ac.
if (0 < length x \<and> x!0 = a) then (ac+1) else (ac)) p 0"
fun prefer_count_l :: "'a Profile_List \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> nat" where
"prefer_count_l p a b = fold (\<lambda> x ac. (if (b \<lesssim>\<^sub>x a) then (ac+1) else (ac))) p 0"
fun wins_l :: "'a \<Rightarrow> 'a Profile_List \<Rightarrow> 'a \<Rightarrow> bool" where
"wins_l x p y =
(prefer_count_l p x y > prefer_count_l p y x)"
fun condorcet_winner_l :: "'a set \<Rightarrow> 'a Profile_List \<Rightarrow> 'a \<Rightarrow> bool" where
"condorcet_winner_l A p w =
(finite A \<and> profile_l A p \<and> w \<in> A \<and> (\<forall> x \<in> A - {w} . wins_l w p x))"
subsection \<open> Monadic definition of profile functions \<close>
lemma w_eq_param [sepref_import_param]: "((=), (=)::'a\<Rightarrow>_) \<in> Id \<rightarrow> Id \<rightarrow> Id" by simp
definition "index_mon_inv ballot a \<equiv> (\<lambda> (i, found).
(i \<le> List_Index.index ballot a)
\<and> (found \<longrightarrow> (i = List_Index.index ballot a)))"
(* \<and> (\<not>found \<longrightarrow> (i \<le> List_Index.index ballot a)))"*)
(* low level optimization for pref count *)
definition index_mon :: "'a::{default, heap, hashable} Preference_List
\<Rightarrow> 'a::{default, heap, hashable}
\<Rightarrow> nat nres" where
"index_mon ballot a \<equiv> do {
(i, found) \<leftarrow> WHILET
(\<lambda>(i, found). (i < (length ballot) \<and> \<not>found))
(\<lambda>(i,_). do {
ASSERT (i < (length ballot));
let (c::'a::{default, heap, hashable}) = (ballot ! i);
if (a = c) then
RETURN (i,True)
else
RETURN (i+1,False)
})(0::nat, False);
RETURN (i)
}"
sepref_definition index_sep is "uncurry index_mon" ::
"(arl_assn id_assn)\<^sup>k *\<^sub>a (id_assn)\<^sup>k \<rightarrow>\<^sub>a nat_assn"
unfolding index_mon_def
apply sepref_dbg_keep
done
sepref_register index_mon
declare index_sep.refine[sepref_fr_rules]
lemma isl1_measure: "wf (measure (\<lambda>(i, found). length ballot - i - (if found then 1 else 0)))"
by simp
lemma index_sound:
fixes a:: 'a and l :: "'a list" and i::nat
assumes "i \<le> List_Index.index l a"
shows "(a = l!i) \<longrightarrow> (i = List_Index.index l a)"
by (metis assms(1) index_first le_eq_less_or_eq)
lemma index_mon_correct:
shows "index_mon ballot a \<le> SPEC (\<lambda> r. r = index ballot a)"
unfolding index_mon_def
apply (intro WHILET_rule[where I= "index_mon_inv ballot a" and R="measure (\<lambda>(i, found). length ballot - i - (if found then 1 else 0))"] refine_vcg)
proof (unfold index_mon_inv_def, simp+, safe, auto)
fix aa::nat
assume bound: "aa \<le> List_Index.index ballot (ballot ! aa)"
(*assume range : "aa < length ballot"*)
thus "aa = List_Index.index ballot (ballot ! aa)" by (simp add: index_sound)
next
fix i
assume notnow: "a \<noteq> ballot ! i"
assume notyet: "i \<le> List_Index.index ballot a"
assume ir: "i < length ballot"
from notnow have "i \<noteq> List_Index.index ballot a"
by (metis index_eq_iff ir)
from notyet this show "Suc i \<le> List_Index.index ballot a"
by fastforce
next
assume ir: "List_Index.index ballot a < length ballot"
assume na: "a \<noteq> ballot ! index ballot a"
from ir have "a = ballot ! List_Index.index ballot a"
by (metis index_eq_iff)
from this na show "False" by simp
next
fix aa
assume "aa \<le> List_Index.index ballot a"
and "aa \<noteq> List_Index.index ballot a"
thus "aa < length ballot"
by (metis antisym index_le_size le_neq_implies_less order_trans)
qed
(* TODO: move to IICF Array List *)
lemma index_mon_impl:
shows "(index_mon, mop_list_index) \<in> \<langle>Id\<rangle>list_rel \<rightarrow> Id \<rightarrow> \<langle>nat_rel\<rangle>nres_rel"
apply (intro fun_relI nres_relI)
apply clarsimp
apply (refine_vcg index_mon_correct) by simp
lemma arl_index_nc_correct: "(uncurry index_sep, uncurry mop_list_index)
\<in> (arl_assn id_assn)\<^sup>k *\<^sub>a id_assn\<^sup>k \<rightarrow>\<^sub>a nat_assn"
using index_sep.refine[FCOMP index_mon_impl]
list_rel_id hr_comp_Id2
by metis
(*sepref_decl_impl (ismop) arl_index: arl_index_nc_correct .*)
definition rank_mon :: "'a::{default, heap, hashable} Preference_List
\<Rightarrow> 'a::{default, heap, hashable} \<Rightarrow> nat nres" where
"rank_mon ballot a \<equiv> do {
i \<leftarrow> (index_mon ballot a);
if (i = length ballot) then RETURN 0 else RETURN (i + 1)
}"
lemma rank_mon_correct: "rank_mon ballot a \<le> SPEC (\<lambda> r. r = rank_l ballot a)"
unfolding rank_mon_def
proof (refine_vcg, auto)
assume mem: "a \<in> set ballot"
from this have "List_Index.index ballot a \<noteq> length ballot"
by (simp add: in_set_member index_size_conv)
from this show "index_mon ballot a \<le> SPEC (\<lambda>i. i = List_Index.index ballot a \<and> i \<noteq> length ballot)"
using index_mon_correct
by (metis (mono_tags, lifting) SPEC_cons_rule)
next
assume nmem: "\<not>a \<in> set ballot"
from this have "List_Index.index ballot a = length ballot"
by (simp add: in_set_member)
from this show "index_mon ballot a \<le> RES {length ballot}"
using index_mon_correct
by (metis singleton_conv)
qed
lemma rank_mon_refine:
shows "(rank_mon, (\<lambda> ballot a. RETURN (rank_l ballot a)))\<in> Id \<rightarrow> Id \<rightarrow> \<langle>nat_rel\<rangle>nres_rel"
by (refine_vcg rank_mon_correct, simp)
definition is_less_preferred_than_ref ::
"'a::{default, heap, hashable} \<Rightarrow> 'a Preference_List
\<Rightarrow> 'a
\<Rightarrow> bool nres" ("_ p\<lesssim>\<^sub>_ _" [50, 1000, 51] 50) where
"x p\<lesssim>\<^sub>l y \<equiv> do {
idxx \<leftarrow> index_mon l x;
idxy \<leftarrow> index_mon l y;
RETURN (idxx \<noteq> length l \<and> idxy \<noteq> length l \<and> idxx \<ge> idxy)}"
lemma is_less_preferred_than_ref_refine:
shows "(is_less_preferred_than_ref,
RETURN ooo is_less_preferred_than_l) \<in> Id \<rightarrow> \<langle>Id\<rangle>list_rel \<rightarrow> Id \<rightarrow> \<langle>bool_rel\<rangle>nres_rel"
unfolding is_less_preferred_than_ref_def is_less_preferred_than_l.simps
unfolding comp_apply
by (refine_vcg index_mon_correct, auto)
sepref_definition is_less_preferred_than_sep
is "uncurry2 is_less_preferred_than_ref" ::
"(id_assn\<^sup>k *\<^sub>a (ballot_impl_assn id_assn)\<^sup>k *\<^sub>a id_assn\<^sup>k \<rightarrow>\<^sub>a bool_assn)"
unfolding is_less_preferred_than_ref_def[abs_def]
apply sepref_dbg_keep
done
sepref_register is_less_preferred_than_ref
declare is_less_preferred_than_sep.refine [sepref_fr_rules]
lemmas is_less_preferred_than_sep_correct =
is_less_preferred_than_sep.refine[FCOMP is_less_preferred_than_ref_refine]
text \<open>
win-count, multiple refinement steps
\<close>
definition "wc_invar_fe p0 a \<equiv> \<lambda>(xs,ac).
xs = drop (length p0 - length xs) p0 \<and>
ac = card {i. i < (length p0 - length xs) \<and> above (p0!i) a = {a}}"
definition wc_foreach:: "'a Profile \<Rightarrow> 'a \<Rightarrow> nat nres" where
"wc_foreach p a \<equiv> do {
(xs,ac) \<leftarrow> WHILEIT (wc_invar_fe p a) (FOREACH_cond (\<lambda>_.True))
(FOREACH_body (\<lambda>x (ac).
if (above x a = {a}) then RETURN (ac+1) else RETURN (ac)
)) (p,0);
RETURN ac
}"
lemma wc_foreach_correct:
shows "wc_foreach p a \<le> SPEC (\<lambda> wc. wc = win_count p a)"
unfolding wc_foreach_def wc_invar_fe_def
FOREACH_cond_def FOREACH_body_def
apply (intro WHILEIT_rule[where R="measure (\<lambda>(xs,_). length xs)"] refine_vcg)
apply (safe, simp_all)
apply (metis append_Nil diff_le_self drop_Suc drop_all drop_append length_drop tl_drop)
proof (-)
fix xs:: "'a Profile"
assume headr: "xs = drop (length p - length xs) p"
assume pnemp: "xs \<noteq> []"
from pnemp headr have hdidx: "hd xs = (p!(length p - length xs))"
by (metis drop_eq_Nil hd_drop_conv_nth linorder_not_le)
assume atop: "above (hd xs) a = {a}"
from hdidx this have aba: "above (p!(length p - length xs)) a = {a}" by simp
from this aba have comp: "{i. i \<le> (length p) - length xs \<and> above (p ! i) a = {a}}
= ({i. i < length p - length xs \<and> above (p ! i) a = {a}} \<union>
{(length p - length xs)})"
by fastforce
from headr have "{i. i \<le> (length p) - length xs \<and> above (p ! i) a = {a}}
= {i. i < Suc (length p) - length xs \<and> above (p ! i) a = {a}}"
by (metis Suc_diff_le diff_le_self length_drop less_Suc_eq_le)
from this comp have "{i. i < Suc (length p) - length xs \<and> above (p ! i) a = {a}}
= ({i. i < length p - length xs \<and> above (p ! i) a = {a}} \<union>
{(length p - length xs)})" by simp
from this show
"Suc (card {i. i < (length p) - length xs \<and> above (p ! i) a = {a}}) =
card {i. i < Suc (length p) - length xs \<and> above (p ! i) a = {a}}"
by fastforce
next
fix xs:: "'a Profile"
fix alt:: "'a"
assume headr: "xs = drop (length p - length xs) p"
show "tl xs = drop (Suc (length p) - length xs) p"
by (metis Suc_diff_le diff_le_self drop_Suc headr length_drop tl_drop)
next
fix xs:: "'a Profile"
fix alt:: "'a"
assume headr: "xs = drop (length p - length xs) p"
assume pnemp: "xs \<noteq> []"
from pnemp headr have hdidx: "hd xs = (p!(length p - length xs))"
by (metis drop_eq_Nil hd_drop_conv_nth linorder_not_le)
assume xtop: "alt \<in> above (hd xs) a"
assume xna: "alt \<noteq> a"
from hdidx headr xna xtop show
"card {i. i < (length p) - length xs \<and> above (p ! i) a = {a}} =
card {i. i < Suc (length p) - length xs \<and> above (p ! i) a = {a}}"
by (metis Suc_diff_le diff_le_self insert_absorb insert_iff insert_not_empty length_drop less_Suc_eq )
next
fix xs:: "'a Profile"
fix alt:: "'a"
assume headr: "xs = drop (length p - length xs) p"
from headr show "tl xs = drop (Suc (length p) - length xs) p"
by (metis Suc_diff_le diff_le_self drop_Suc length_drop tl_drop)
next
fix xs:: "'a Profile"
fix alt:: "'a"
assume headr: "xs = drop (length p - length xs) p"
assume pnemp: "xs \<noteq> []"
from pnemp headr have hdidx: "hd xs = (p!(length p - length xs))"
by (metis drop_eq_Nil hd_drop_conv_nth linorder_not_le)
assume xtop: "a \<notin> above (hd xs) a"
from hdidx this have aba: "above (p!(length p - length xs)) a \<noteq> {a}"
by fastforce
from this show
"card {i. i < (length p) - length xs \<and> above (p ! i) a = {a}} =
card {i. i < Suc (length p) - length xs \<and> above (p ! i) a = {a}}"
by (metis Suc_diff_le diff_le_self headr length_drop less_Suc_eq)
qed
schematic_goal wc_code_aux: "RETURN ?wc_code \<le> wc_foreach p a"
unfolding wc_foreach_def FOREACH_body_def FOREACH_cond_def
by (refine_transfer)
concrete_definition win_count_code for p a uses wc_code_aux
thm win_count_code_def
lemma win_count_equiv:
shows "win_count p a = win_count_code p a"
proof -
from order_trans[OF win_count_code.refine wc_foreach_correct]
have "win_count_code p a = win_count p a"
by fastforce
thus ?thesis by simp
qed
lemma carde: assumes prof: "profile A p"
shows "\<forall>ballot \<in> set p. (rank ballot a = 1) = (above ballot a = {a})"
using prof
by (metis above_rank profile_set)
lemma cardei: assumes prof: "profile A p"
shows "\<forall>i < length p. let ballot=(p!i) in ((rank ballot a = 1) = (above ballot a = {a}))"
using prof
by (metis carde nth_mem)
definition "f_inner_rel a \<equiv> (\<lambda>(x::'a Preference_Relation) (ac::nat).
(if (rank x a = 1) then RETURN (ac+1) else RETURN (ac)
))"
definition wc_foreach_rank:: "'a Profile \<Rightarrow> 'a \<Rightarrow> nat nres" where
"wc_foreach_rank p a \<equiv> do {
(xs,ac) \<leftarrow> WHILET (FOREACH_cond (\<lambda>_.True))
(FOREACH_body (f_inner_rel a)) (p,0::nat);
RETURN ac
}"
lemma wc_foreach_rank_refine:
assumes prof: "profile A p"
shows "wc_foreach_rank p a \<le> \<Down> nat_rel (wc_foreach p a)"
unfolding wc_foreach_rank_def wc_foreach_def wc_invar_fe_def FOREACH_body_def FOREACH_cond_def
f_inner_rel_def
apply (refine_vcg)
apply (refine_dref_type) \<comment> \<open>Type-based heuristics to instantiate data
refinement goals\<close>
proof (clarsimp_all simp del: rank.simps)
fix x1:: "'a Profile"
assume x1ne: "x1 \<noteq> []"
assume rest: "x1 = drop (length p - length x1) p"
from x1ne rest show "(rank (hd x1) a = Suc 0) = (above (hd x1) a = {a})" using carde
by (metis One_nat_def in_set_dropD list.set_sel(1) prof rank.simps)
qed
lemma rank_refaux:
assumes prof: "profile A p"
shows "wc_foreach_rank p a \<le> (wc_foreach p a)"
using prof wc_foreach_rank_refine
by (metis refine_IdD)
theorem wc_foreach_rank_correct:
assumes prof: "profile A p"
shows "wc_foreach_rank p a \<le> SPEC (\<lambda> wc. wc = win_count p a)"
using assms ref_two_step[OF wc_foreach_rank_refine wc_foreach_correct]
by fastforce
subsubsection \<open> Data refinement \<close>
text \<open> these auxiliary lemmas illustrate the equivalence of checking the the first
candidate on a non empty ballot. \<close>
lemma top_above:
assumes ne: "length pl > 0"
shows "pl!0 = a \<longleftrightarrow> above_l pl a = [a]"
unfolding above_l_def
proof (simp add: rankdef, safe)
assume mem: "pl ! 0 \<in> set pl"
assume "a = pl ! 0"
have "List_Index.index pl (pl ! 0) = 0"
by (simp add: index_eqI)
from mem this show "take (Suc (List_Index.index pl (pl ! 0))) pl = [pl ! 0]"
by (metis append_Nil index_less_size_conv take0 take_Suc_conv_app_nth)
next
(*assume mem: "List.member pl a"*)
assume "take (Suc (List_Index.index pl a)) pl = [a]"
from this show "pl ! 0 = a"
by (metis append_Cons append_Nil append_take_drop_id hd_conv_nth list.sel(1))
next
assume nm: "\<not> pl ! 0 \<in> set pl"
from this have pl_empty: "pl = []"
by (metis length_greater_0_conv nth_mem)
from ne this pl_empty show "False"
by simp
qed
lemma top_l_above_r:
assumes ballot: "ballot_on A pl"
and ne: "length pl > 0"
shows "pl!0 = a \<longleftrightarrow> above (pl_\<alpha> pl) a = {a}"
proof -
from ne have listeq: "pl!0 = a \<longleftrightarrow> above_l pl a = [a]"
by (simp add: top_above)
from assms have above_abstract: "set (above_l pl a) = above (pl_\<alpha> pl) a"
by (auto simp add: aboveeq)
have list_set: "above_l pl a = [a] \<longleftrightarrow> set (above_l pl a) = {a}"
by (metis above_l_def append_self_conv2 gr0I hd_take id_take_nth_drop insert_not_empty list.sel(1) list.set(1) list.set_sel(1) list.simps(15) listeq ne singleton_iff take_eq_Nil)
from above_abstract listeq this show ?thesis
by (simp)
qed
definition "f_inner_list a \<equiv> (\<lambda>x ac::nat.
(if (rank_l x a = 1) then RETURN (ac+1) else RETURN (ac)))"
definition "wc_list_invar p0 a \<equiv> \<lambda>(i,ac::nat).
0 \<le> i \<and> i \<le> length p0"
definition "wc_list_invar' p0 a \<equiv> \<lambda>(xs,ac).
xs = drop (length p0 - length xs) p0"
lemma innerf_eq:
fixes A:: "'a set" and l :: "'a Preference_List" and a :: 'a
assumes "(l,r) \<in> ballot_rel"
shows "f_inner_list a l n \<le> \<Down> nat_rel (f_inner_rel a r n)"
unfolding f_inner_list_def f_inner_rel_def
apply (refine_vcg)
using assms rankeq unfolding ballot_rel_def
by (metis in_br_conv)
lemma foreachrel:
assumes "(pl, pr) \<in> profile_rel" and "pl \<noteq> []"
shows "(hd pl, hd pr) \<in> (ballot_rel) \<and>
(tl pl, tl pr) \<in> (profile_rel)"
using assms
by (metis list.collapse list_rel_simp(2) list_rel_simp(4))
definition wc_foreach_list_rank :: "'a Profile_List \<Rightarrow> 'a \<Rightarrow> nat nres" where
"wc_foreach_list_rank pl a \<equiv> do {
(xs,ac) \<leftarrow> WHILET (FOREACH_cond (\<lambda>_.True))
(FOREACH_body (f_inner_list a)) (pl,0::nat);
RETURN ac
}"
lemma initrel:
fixes A:: "'a set"
assumes "(pl, pr) \<in> profile_rel"
shows "((pl,0::nat), pr , 0::nat) \<in> ((profile_rel \<times>\<^sub>r nat_rel))"
using assms
by simp
lemma wc_foreach_list_rank_refine:
fixes A:: "'a set"
shows "(wc_foreach_list_rank, wc_foreach_rank) \<in>
profile_rel \<rightarrow> Id \<rightarrow> \<langle>Id\<rangle>nres_rel"
unfolding wc_foreach_list_rank_def wc_foreach_rank_def
FOREACH_cond_def FOREACH_body_def
apply (refine_vcg initrel)
apply (simp add: initrel)
apply refine_dref_type
apply (simp add: refine_rel_defs)
apply blast
apply clarsimp_all
using innerf_eq unfolding ballot_rel_def
apply (metis param_hd refine_IdD)
using foreachrel unfolding ballot_rel_def by (metis)
lemma win_count_list_r_refine_os:
fixes A:: "'a set"
assumes "(pl, pr) \<in> (profile_rel)"
shows "wc_foreach_list_rank pl a \<le> \<Down> Id (wc_foreach_rank pr a)"
unfolding wc_foreach_list_rank_def wc_foreach_rank_def
FOREACH_cond_def FOREACH_body_def
using assms apply (refine_vcg wc_foreach_list_rank_refine initrel)
apply (simp_all only: refine_rel_defs pl_to_pr_\<alpha>_def)
apply refine_dref_type
apply (clarsimp_all, safe)
using innerf_eq unfolding ballot_rel_def
apply (metis (mono_tags, lifting) brI list.rel_sel refine_IdD)
using foreachrel
using list.rel_sel by blast
lemma wc_foreach_list_rank_correct:
assumes "(pl, pr) \<in> profile_rel" and "profile_l A pl"
shows "wc_foreach_list_rank pl a \<le> SPEC (\<lambda> wc. wc = win_count pr a)"
proof (-)
from assms have "profile A pr" using profile_ref
by (metis)
from assms(1) this
show "wc_foreach_list_rank pl a \<le> (SPEC (\<lambda>wc. wc = win_count pr a))"
using ref_two_step[OF win_count_list_r_refine_os wc_foreach_rank_correct] refine_IdD
by (metis)
qed
lemma top_rank1:
assumes ballot: "ballot_on A ballot" and "length ballot > 0"
shows "ballot!0 = a \<longleftrightarrow> rank_l ballot a = 1"
using assms
apply clarsimp
apply safe
apply (simp add: index_eq_iff)
apply (metis nth_index)
by simp
definition wc_foreach_top:: "'a Profile_List \<Rightarrow> 'a \<Rightarrow> nat nres" where
"wc_foreach_top p a \<equiv> do {
(xs::'a Profile_List,ac) \<leftarrow> WHILET (FOREACH_cond (\<lambda>_.True))
(FOREACH_body (\<lambda>x (ac).
if ((length x > 0) \<and> (x!0 = a)) then RETURN (ac+1) else RETURN (ac)
)) (p,0);
RETURN ac
}"
lemma wc_foreach_top_refine_os:
fixes A:: "'a set"
shows "wc_foreach_top pl a \<le> \<Down> Id (wc_foreach_list_rank pl a)"
unfolding wc_foreach_list_rank_def f_inner_list_def wc_foreach_top_def
FOREACH_cond_def FOREACH_body_def
apply (refine_vcg wc_foreach_list_rank_refine initrel)
apply (simp_all only: refine_rel_defs pl_to_pr_\<alpha>_def)
apply refine_dref_type
apply auto
apply (metis gr0I index_first)
by (metis index_eq_iff length_pos_if_in_set)
lemma wc_foreach_top_correct:
assumes "(pl, pr) \<in> profile_rel" and "profile_l A pl"
shows "wc_foreach_top pl a \<le> SPEC (\<lambda> wc. wc = win_count pr a)"
using assms ref_two_step[OF wc_foreach_top_refine_os wc_foreach_list_rank_correct] refine_IdD
by (metis)
definition wc_fold:: "'a Profile_List \<Rightarrow> 'a \<Rightarrow> nat nres"
where "wc_fold l a \<equiv>
nfoldli l (\<lambda>_. True)
(\<lambda>x (ac).
RETURN (if ((length x > 0) \<and> (x!0 = a))then (ac+1) else (ac))
)
(0)"
lemma wc_fold_refine:
shows "wc_fold pl a \<le> \<Down> Id (wc_foreach_top pl a)"
unfolding wc_fold_def wc_foreach_top_def
by (simp add: nfoldli_mono(1) while_eq_nfoldli)
theorem wc_fold_correct:
assumes "(pl, pr) \<in> profile_rel" and "profile_l A pl"
shows "wc_fold pl a \<le> SPEC (\<lambda> wc. wc = win_count pr a)"
using assms ref_two_step[OF wc_fold_refine wc_foreach_top_correct] refine_IdD
by (metis)
lemma nfwcc: "nofail (wc_fold p a)"
unfolding wc_fold_def
apply (induction p rule: rev_induct, simp)
apply simp
by (simp add: pw_bind_nofail)
lemma win_count_l_correct:
shows "(win_count_l, win_count)
\<in> (profile_on_A_rel A) \<rightarrow> Id \<rightarrow> nat_rel"
apply (auto simp del: win_count_l.simps win_count.simps)
apply (rename_tac pl pr)
proof (standard, rename_tac a)
fix pl :: "'a Profile_List"
fix pr :: "'a Profile"
fix a:: 'a
assume prel: "(pl, pr) \<in> (profile_on_A_rel A)"
from prel have profrel: "(pl, pr) \<in> profile_rel" using profile_type_ref by fastforce
from prel have profprop: "profile_l A pl" using profile_prop_list by fastforce
have "RETURN (win_count_l pl a) = (wc_fold pl a)"
unfolding wc_fold_def win_count_l.simps
using fold_eq_nfoldli[where l = pl and f = "(\<lambda>x ac. if (0 < length x \<and> x ! 0 = a)
then ac + 1 else ac)" and s = 0]
by fastforce
from this profrel profprop have meq: "RETURN (win_count_l pl a) = RETURN (win_count pr a)"
using wc_fold_correct[where pl=pl and pr = pr and A = A and a = a]
by (metis mem_Collect_eq nres_order_simps(21))
from meq show "win_count_l pl a = win_count pr a"
by simp
qed
text \<open>
pref count
\<close>
definition pc_foldli:: "'a Profile \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> nat nres" where
"pc_foldli p a b \<equiv>
nfoldli p (\<lambda>_.True)
(\<lambda>x (ac).
if (b \<preceq>\<^sub>x a) then RETURN (ac+1) else RETURN (ac)
) (0::nat)"
lemma pc_foldli_correct:
shows "pc_foldli p a b \<le> SPEC (\<lambda> wc. wc = prefer_count p a b)"
unfolding pc_foldli_def
apply (intro nfoldli_rule[where I="\<lambda> proc xs ac.
ac = card {i::nat. i < length proc \<and> (let r = (p!i) in (b \<preceq>\<^sub>r a))}"] refine_vcg)
proof (clarsimp_all)
fix l1:: "'a Profile"
fix l2:: "'a Profile"
fix x:: "'a Preference_Relation"
assume "p = l1 @ x # l2"
assume blpa: "(b, a) \<in> x"
have pnemp: "l1 @ x # l2 \<noteq> []" by simp
have xatl1: "(l1 @ x # l2) ! (length l1) = x"
by simp
from xatl1 blpa have stone: "{i. i \<le>(length l1) \<and> (b, a) \<in> (l1 @ x # l2) ! i}
= {i. i < length l1 \<and> (b, a) \<in> (l1 @ x # l2) ! i} \<union>
{length l1}"
by fastforce
from this have "{i. i < Suc (length l1) \<and> (b, a) \<in> (l1 @ x # l2) ! i} =
({i. i < length l1 \<and> (b, a) \<in> (l1 @ x # l2) ! i} \<union> {length l1})"
using less_Suc_eq_le
by blast
from this show "Suc(card {i. i < length l1 \<and> (b, a) \<in> (l1 @ x # l2) ! i}) =
card {i. i < Suc (length l1) \<and> (b, a) \<in> (l1 @ x # l2) ! i}"
by fastforce
next
fix l1:: "'a Profile"
fix l2:: "'a Profile"
fix x:: "'a Preference_Relation"
assume "p = l1 @ x # l2"
assume blpa: "(b, a) \<notin> x"
have pnemp: "l1 @ x # l2 \<noteq> []" by simp
have xatl1: "(l1 @ x # l2) ! (length l1) = x"
by simp
from xatl1 blpa have stone: "{i. i < Suc (length l1) \<and> (b, a) \<in> (l1 @ x # l2) ! i}
= {i. i < length l1 \<and> (b, a) \<in> (l1 @ x # l2) ! i}"
using less_Suc_eq_le order_le_less by blast
thus "card {i. i < length l1 \<and> (b, a) \<in> (l1 @ x # l2) ! i} =
card {i. i < Suc (length l1) \<and> (b, a) \<in> (l1 @ x # l2) ! i}"
by fastforce
qed
definition pc_foldli_list:: "'a Profile_List \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> nat nres" where
"pc_foldli_list p a b \<equiv>
nfoldli p (\<lambda>_.True)
(\<lambda> x ac. RETURN (if (b \<lesssim>\<^sub>x a) then (ac+1) else (ac)))
(0::nat)"
lemma pc_fold_monad_eq:
shows "RETURN (prefer_count_l p a b) = pc_foldli_list p a b"
unfolding pc_foldli_list_def
using fold_eq_nfoldli
by fastforce
lemma pc_foldli_list_refine:
shows "(pc_foldli_list, pc_foldli)
\<in> profile_rel \<rightarrow> Id \<rightarrow> Id \<rightarrow> \<langle>nat_rel\<rangle>nres_rel"
unfolding ballot_rel_def
apply (auto simp del : is_less_preferred_than.simps)
apply (rename_tac pl pr a b)
unfolding pc_foldli_list_def pc_foldli_def
apply (refine_vcg nfoldli_rule)
apply (auto simp del : is_less_preferred_than_l.simps is_less_preferred_than.simps)
apply (rename_tac l r)
apply (metis in_br_conv is_less_preferred_than_eq)+
done
lemma pc_foldli_list_correct:
shows "(pc_foldli_list, (\<lambda> p a b. SPEC (\<lambda> wc. wc = prefer_count p a b)))
\<in> profile_rel \<rightarrow> Id \<rightarrow> Id \<rightarrow> \<langle>nat_rel\<rangle>nres_rel"
apply(refine_vcg)
apply (clarsimp_all simp del: prefer_count.simps)
apply (rename_tac pl pr a b)
proof -
fix pl :: "'a Profile_List"
fix pr :: "'a Profile"
fix a :: 'a
fix b :: 'a
assume profr: "(pl, pr) \<in> profile_rel"
note ref_two_step[OF pc_foldli_list_refine[THEN fun_relD, THEN fun_relD,
THEN fun_relD, THEN nres_relD]
pc_foldli_correct, where x5 = pl and p1=pr and x4 = a and a1 = a
and x3 = b and b1 = b]
refine_IdD
from profr this show "pc_foldli_list pl a b \<le> RES {prefer_count pr a b}"
by fastforce
qed
definition prefer_count_monadic_imp:: "'a::{default, heap, hashable} Profile_List
\<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> nat nres" where
"prefer_count_monadic_imp p a b \<equiv>
nfoldli p (\<lambda>_.True) (\<lambda> x ac.
do {
b_less_a \<leftarrow> is_less_preferred_than_ref b x a;
RETURN (if b_less_a then (ac+1) else (ac))
}) (0::nat)"
lemma prefer_count_monadic_imp_refine:
shows "(prefer_count_monadic_imp, pc_foldli_list)
\<in> \<langle>\<langle>Id\<rangle>list_rel\<rangle>list_rel \<rightarrow> Id \<rightarrow> Id \<rightarrow> \<langle>nat_rel\<rangle>nres_rel"
unfolding prefer_count_monadic_imp_def pc_foldli_list_def
apply (refine_vcg is_less_preferred_than_ref_refine)
apply (refine_dref_type)
apply (auto simp del : is_less_preferred_than_l.simps)
proof (rename_tac b a l)
fix a b :: 'a
fix l :: "'a Preference_List"
assume alpb: "a \<lesssim>\<^sub>l b"
note iq = is_less_preferred_than_ref_refine[THEN fun_relD,THEN fun_relD,THEN fun_relD,
THEN nres_relD]
from alpb iq[where x3= a and x'3 =a and x2 = l and x'2 =l and x1 =b and x'1 =b]
show "(a p\<lesssim>\<^sub>l b) \<le> SPEC (\<lambda>b_less_a. b_less_a)"
using conc_trans_additional(6) by fastforce
next
fix a b :: 'a
fix l :: "'a Preference_List"
assume alpb: "\<not> a \<lesssim>\<^sub>l b"
note iq = is_less_preferred_than_ref_refine[THEN fun_relD,THEN fun_relD,THEN fun_relD,
THEN nres_relD]
from alpb iq[where x3= a and x'3 =a and x2 = l and x'2 =l and x1 =b and x'1 =b]
show "(a p\<lesssim>\<^sub>l b) \<le> SPEC (Not)"
using conc_trans_additional(6) by fastforce
qed
theorem prefer_count_monadic_imp_correct:
assumes "(pl, pr) \<in> profile_rel"
shows "prefer_count_monadic_imp pl a b \<le> SPEC (\<lambda> pc. pc = prefer_count pr a b)"
using assms(1) ref_two_step[OF prefer_count_monadic_imp_refine [THEN fun_relD,THEN fun_relD,THEN fun_relD,THEN nres_relD]
pc_foldli_list_correct[THEN fun_relD,THEN fun_relD,THEN fun_relD,THEN nres_relD,THEN refine_IdD],
where x10 = pl and x5 = pl and x'5 = pr] refine_IdD
by (metis list_rel_id IdI)
lemma prefer_count_monadic_correct_rel:
shows "(prefer_count_monadic_imp, RETURN ooo prefer_count)
\<in> profile_rel \<rightarrow> Id \<rightarrow> Id \<rightarrow> \<langle>Id\<rangle>nres_rel"
proof (refine_vcg, clarify, unfold comp_apply, (clarsimp simp del: prefer_count.simps),
rename_tac pl pr a b)
fix a b :: "'a"
fix pr :: "'a Profile"
fix pl :: "'a Profile_List"
assume prel: "(pl, pr) \<in> profile_rel"
then show "prefer_count_monadic_imp pl a b \<le> RETURN (prefer_count pr a b) "
using ref_two_step[OF prefer_count_monadic_imp_refine [THEN fun_relD,THEN fun_relD,THEN fun_relD,THEN nres_relD]
pc_foldli_list_correct[THEN fun_relD,THEN fun_relD,THEN fun_relD,THEN nres_relD,THEN refine_IdD]]
IdI
unfolding SPEC_eq_is_RETURN(2)
by fastforce
qed
sepref_definition prefer_count_sep is
"uncurry2 prefer_count_monadic_imp" :: "(profile_impl_assn id_assn)\<^sup>k *\<^sub>a id_assn\<^sup>k *\<^sub>a id_assn\<^sup>k
\<rightarrow>\<^sub>a nat_assn"
unfolding prefer_count_monadic_imp_def
apply sepref_dbg_keep
done
sepref_register prefer_count_monadic_imp
declare prefer_count_sep.refine [sepref_fr_rules]
definition wins_monadic :: "'a::{default, heap, hashable}
\<Rightarrow> 'a Profile_List \<Rightarrow> 'a \<Rightarrow> bool nres" where
"wins_monadic x p y \<equiv> do {
pxy \<leftarrow> prefer_count_monadic_imp p x y;
pyx \<leftarrow> prefer_count_monadic_imp p y x;
RETURN (pxy > pyx)
}"
lemma prefer_count_l_correct:
shows "(prefer_count_l, prefer_count)
\<in> profile_rel \<rightarrow> Id \<rightarrow> Id \<rightarrow> nat_rel"
apply (auto simp del: prefer_count_l.simps prefer_count.simps)
apply (rename_tac pl pr)
proof (standard, standard, rename_tac a b)
fix pl :: "'a Profile_List"
fix pr :: "'a Profile"
fix a:: 'a and b:: 'a
assume "(pl, pr) \<in> profile_rel"
from this have meq: "RETURN (prefer_count_l pl a b) = RETURN (prefer_count pr a b)"
using pc_fold_monad_eq[where p = pl and a=a and b=b]
pc_foldli_list_correct[THEN fun_relD,THEN fun_relD,THEN fun_relD,THEN nres_relD,
where x3 = pl and x'3=pr and x2 = a and x'2 = a
and x1 = b and x'1 = b]
by (metis (full_types) RETURN_ref_SPECD pair_in_Id_conv)
from meq show "prefer_count_l pl a b = prefer_count pr a b"
by simp
qed
lemma prefer_count_l_eq:
fixes pl :: "'a Profile_List"
fixes pr :: "'a Profile"
assumes prel: "(pl, pr) \<in> profile_rel"
shows "prefer_count_l pl a b = prefer_count pr a b"
using prefer_count_l_correct[THEN fun_relD, THEN fun_relD, THEN fun_relD,
where x2 = pl and x'2 = pr and x1 = a and x'1 = a and x = b and x' = b]
assms by auto
lemma prefer_count_monadic_imp_ref_l:
shows "(prefer_count_monadic_imp, RETURN ooo prefer_count_l)
\<in> \<langle>\<langle>Id\<rangle>list_rel\<rangle>list_rel \<rightarrow> Id \<rightarrow> Id \<rightarrow> \<langle>nat_rel\<rangle>nres_rel"
proof (clarsimp simp del: prefer_count_l.simps, rename_tac pl a b,
refine_vcg, unfold conc_fun_RETURN[symmetric], rule refine_IdI)
fix pl :: "'a Profile_List"
fix a:: 'a and b:: 'a
note pcr = prefer_count_monadic_imp_refine[THEN fun_relD,THEN fun_relD,THEN fun_relD,
THEN nres_relD, THEN refine_IdD]
pc_fold_monad_eq[symmetric]
from this show "prefer_count_monadic_imp pl a b \<le> RETURN (prefer_count_l pl a b)"
using IdI list_rel_id by (metis)
qed
lemma imp_direct_ref:
fixes pl :: "'a::{default, heap, hashable} Profile_List"
fixes a b :: "'a::{default, heap, hashable}"
shows"prefer_count_monadic_imp pl a b \<le> RETURN (prefer_count_l pl a b)"
proof -
have "(pl, pl) \<in> \<langle>\<langle>Id\<rangle>list_rel\<rangle>list_rel" using list_rel_id IdI by simp
thus ?thesis
using prefer_count_monadic_imp_ref_l[THEN fun_relD, THEN fun_relD, THEN fun_relD
,THEN nres_relD, THEN refine_IdD] IdI unfolding comp_def
by metis
qed
lemma wins_monadic_correct:
shows "(wins_monadic, (\<lambda> A p a. SPEC (\<lambda> is_win. is_win = wins A p a))) \<in> Id \<rightarrow> profile_rel \<rightarrow> Id \<rightarrow> \<langle>bool_rel\<rangle>nres_rel"
unfolding wins_monadic_def wins.simps
apply (clarsimp simp del: prefer_count.simps)
apply (refine_vcg prefer_count_monadic_imp_correct)
by (auto)
sepref_definition wins_imp is "uncurry2 wins_monadic" ::
"(nat_assn\<^sup>k *\<^sub>a (profile_impl_assn id_assn)\<^sup>k *\<^sub>a nat_assn\<^sup>k \<rightarrow>\<^sub>a bool_assn )"
unfolding wins_monadic_def
apply sepref_dbg_keep
done
lemma wins_l_correct:
shows "(wins_l, wins)
\<in> Id \<rightarrow> profile_rel \<rightarrow> Id \<rightarrow> bool_rel"
apply(refine_vcg)
proof (clarsimp simp del: prefer_count_l.simps prefer_count.simps, rename_tac a pl pr b, safe)
fix pl :: "'a Profile_List"
fix pr :: "'a Profile"
fix a:: 'a and b:: 'a
assume a1: "(pl, pr) \<in> profile_rel"
assume a2: "prefer_count_l pl b a < prefer_count_l pl a b"
note eq = prefer_count_l_correct[THEN fun_relD,THEN fun_relD,THEN fun_relD,
where x2= pl and x'2=pr]
from eq a1 have "\<forall> alt1 alt2. prefer_count_l pl alt1 alt2 = prefer_count pr alt1 alt2 "
by blast
from a2 this show "prefer_count pr b a < prefer_count pr a b"
by fastforce
next
fix pl :: "'a Profile_List"
fix pr :: "'a Profile"
fix a:: 'a and b:: 'a
assume a1: "(pl, pr) \<in> profile_rel"
assume a2: "prefer_count pr b a < prefer_count pr a b"
note eq = prefer_count_l_correct[THEN fun_relD,THEN fun_relD,THEN fun_relD,
where x2= pl and x'2=pr]
from eq a1 have "\<forall> alt1 alt2. prefer_count_l pl alt1 alt2 = prefer_count pr alt1 alt2 "
by blast
from a2 this show "prefer_count_l pl b a < prefer_count_l pl a b"
by fastforce
qed
lemma wins_monadic_refine:
shows "(wins_monadic, RETURN ooo wins_l) \<in> Id \<rightarrow> \<langle>\<langle>Id\<rangle>list_rel\<rangle>list_rel \<rightarrow> Id \<rightarrow> \<langle>Id\<rangle>nres_rel"
unfolding wins_monadic_def wins_l.simps
proof (clarsimp simp del: prefer_count_l.simps, rule nres_relI, rule refine_IdI,
refine_vcg , unfold SPEC_eq_is_RETURN(1), rename_tac a pl b )
fix pl :: "'a Profile_List"
fix a:: 'a and b:: 'a
note pcab = imp_direct_ref[where pl = pl and a = a and b = b]
note pcba = imp_direct_ref[where pl = pl and a = b and b = a]
have "prefer_count_monadic_imp pl a b
\<le> SPEC (\<lambda>pab. pab = prefer_count_l pl a b)"
using pcab SPEC_eq_is_RETURN(2)[symmetric, where y = "prefer_count_l pl a b"]
by metis
from this pcab pcba show "prefer_count_monadic_imp pl a b
\<le> SPEC (\<lambda>pxy. prefer_count_monadic_imp pl b a \<bind> (\<lambda>pyx. RETURN (pyx < pxy))
\<le> RETURN (prefer_count_l pl b a < prefer_count_l pl a b))"
using bind_rule SPEC_cons_rule SPEC_eq_is_RETURN(1)
by (smt (z3) order_eq_refl specify_left)
qed
lemma condorcet_winner_l_correct:
shows "(condorcet_winner_l, condorcet_winner)
\<in> \<langle>Id\<rangle>set_rel \<rightarrow> profile_rel \<rightarrow> Id \<rightarrow> bool_rel"
apply (refine_vcg)
apply (clarsimp simp del : wins_l.simps wins.simps)
proof (rename_tac A pl pr alt, safe)
fix pl :: "'a Profile_List"
fix pr :: "'a Profile"
fix A:: "'a set" and alt:: 'a
assume a1: "(pl, pr) \<in> profile_rel"
assume a2: "profile_l A pl"
note winc = wins_l_correct[unfolded fref_def, THEN fun_relD, THEN fun_relD,THEN fun_relD,
where x2 = alt and x'2 = alt and x1 = pl and x'1 = pr]
note profr = profile_ref
from a1 a2 profr show "(profile A pr)"
by metis
next
fix pl :: "'a Profile_List"
fix pr :: "'a Profile"
fix A:: "'a set" and alt:: 'a
fix con:: 'a
assume a1: "(pl, pr) \<in> profile_rel"
assume a2: "con \<in> A"
assume a3: "\<not> wins alt pr con"
assume altwins: "\<forall>x\<in>A - {alt}. wins_l alt pl x"
note winc = wins_l_correct[unfolded fref_def, THEN fun_relD, THEN fun_relD,THEN fun_relD,
where x2 = alt and x'2 = alt and x1 = pl and x'1 = pr]
from a1 a3 winc have "\<not> wins_l alt pl con" by blast
from altwins a2 this show "con = alt" by blast
next
fix pl :: "'a Profile_List"
fix pr :: "'a Profile"
fix A:: "'a set" and alt:: 'a
assume a1: "(pl, pr) \<in> profile_rel"
assume a2: "profile A pr"
note winc = wins_l_correct[unfolded fref_def, THEN fun_relD, THEN fun_relD,THEN fun_relD,
where x2 = alt and x'2 = alt and x1 = pl and x'1 = pr]
note profr = profile_ref
from a1 a2 profr show "(profile_l A pl)"
by blast
next
fix pl :: "'a Profile_List"
fix pr :: "'a Profile"
fix A:: "'a set" and alt:: 'a
fix con:: 'a
assume a1: "(pl, pr) \<in> profile_rel"
assume a2: "con \<in> A"
assume a3: "\<not> wins_l alt pl con"
assume altwins: "\<forall>x\<in>A - {alt}. wins alt pr x"
note winc = wins_l_correct[THEN fun_relD, THEN fun_relD,THEN fun_relD,
where x2 = alt and x'2 = alt and x1 = pl and x'1 = pr]
from a1 a3 winc have "\<not> wins alt pr con" by blast
from altwins a2 this show "con = alt" by blast
qed
definition condorcet_winner_monadic :: "'a::{default, heap, hashable} set
\<Rightarrow> 'a Profile_List \<Rightarrow> 'a \<Rightarrow> bool nres" where
"condorcet_winner_monadic A p w \<equiv>
if (w \<in> A) then
FOREACHc A (\<lambda> sigma. sigma = True)
(\<lambda> x b. do {
winswx \<leftarrow> wins_monadic w p x;
RETURN (if (x = w) then True
else ((winswx)))
}) (True)
else RETURN False"
sepref_definition cond_imp is "uncurry2 condorcet_winner_monadic"
:: "(alts_set_impl_assn id_assn)\<^sup>k *\<^sub>a (profile_impl_assn id_assn)\<^sup>k *\<^sub>a id_assn\<^sup>k \<rightarrow>\<^sub>a bool_assn"
unfolding condorcet_winner_monadic_def wins_monadic_def
apply sepref_dbg_keep
done
sepref_register condorcet_winner_monadic
declare cond_imp.refine [sepref_fr_rules]
lemma condorcet_winner_monadic_correct:
fixes A :: "'a::{default, heap, hashable} set"
fixes pl :: "'a::{default, heap, hashable} Profile_List"
and pr :: "'a::{default, heap, hashable} Profile"
assumes prel: "(pl, pr) \<in> profile_rel" and profp: "profile A pr"
assumes fina: "finite A"
shows "condorcet_winner_monadic A pl a
\<le> SPEC (\<lambda> is_win. is_win = condorcet_winner A pr a)"
proof (unfold condorcet_winner_monadic_def RETURN_SPEC_conv FOREACH_def[symmetric]
, auto simp del: condorcet_winner.simps)
assume winner_in: "a \<in> A"
note winsc = wins_monadic_correct[THEN fun_relD,THEN fun_relD,THEN fun_relD,THEN nres_relD, THEN refine_IdD]
from winner_in have " FOREACH\<^sub>C A (\<lambda>sigma. sigma)
(\<lambda>x b. wins_monadic a pl x \<bind> (\<lambda>winswx. RES {if x = a then True else winswx})) True
\<le> SPEC (\<lambda> is_win. is_win = condorcet_winner A pr a)"
apply (refine_vcg FOREACHc_rule [where I =" \<lambda> it b. b =
(\<forall>x\<in>(A - it) - {a}. wins a pr x)"] winsc prel fina profp)
by (auto simp add: winner_in fina profp simp del: wins.simps)
from this show " a \<in> A \<Longrightarrow>
FOREACH\<^sub>C A (\<lambda>sigma. sigma)
(\<lambda>x b. wins_monadic a pl x \<bind> (\<lambda>winswx. RES {if x = a then True else winswx})) True
\<le> RES {condorcet_winner A pr a}" by simp
next
assume aA: "a \<notin> A"
assume condwa: "condorcet_winner A pr a"
from aA condwa show "False" by simp
qed
lemma cond_winner_l_unique:
fixes A:: "'a set"
fixes pl :: "'a Profile_List"
fixes pr :: "'a Profile"
fixes c :: 'a and w :: 'a
assumes
prel: "(pl, pr) \<in> profile_rel" and
winner_c: "condorcet_winner_l A pl c" and
winner_w: "condorcet_winner_l A pl w"
shows "w = c"
using condorcet_winner_l_correct[THEN fun_relD,THEN fun_relD, THEN fun_relD,
where x2 = A and x'2 = A and x1 = pl and x'1 = pr] set_rel_id_simp
cond_winner_unique[where A = A and p = pr and c = c and w = w]
assms by blast
lemma cond_winner_l_unique2:
fixes A:: "'a set"
fixes pl :: "'a Profile_List"
fixes pr :: "'a Profile"
fixes x :: 'a and w :: 'a
assumes
prel: "(pl, pr) \<in> profile_rel" and
winner: "condorcet_winner_l A pl w" and
not_w: "x \<noteq> w"
shows "\<not> condorcet_winner_l A pl x"
using condorcet_winner_l_correct[THEN fun_relD,THEN fun_relD,THEN fun_relD,
where x2 = A and x'2 = A and x1 = pl and x'1 = pr] set_rel_id_simp
cond_winner_unique2[where A = A and p = pr and x = x and w = w]
assms by blast
lemma cond_winner_unique3_l:
fixes A:: "'a set"
fixes pl :: "'a Profile_List"
fixes pr :: "'a Profile"
fixes w :: 'a
assumes
prel: "(pl, pr) \<in> profile_rel" and
wcond: "condorcet_winner_l A pl w"
shows "{a \<in> A. condorcet_winner_l A pl a} = {w}"
using condorcet_winner_l_correct[THEN fun_relD,THEN fun_relD,THEN fun_relD,
where x2 = A and x'2 = A and x1 = pl and x'1 = pr] set_rel_id_simp
cond_winner_unique3[where A = A and p = pr and w = w]
assms by blast
subsubsection \<open>Convert HOL types to heap data structures\<close>
definition convert_list :: "'a::{default, heap} list \<Rightarrow> 'a list nres" where
"convert_list l \<equiv>
nfoldli l (\<lambda> x. True)
(\<lambda> x nl.
RETURN (nl @ [x])) []"
sepref_definition clist is "convert_list" :: "(list_assn id_assn)\<^sup>d
\<rightarrow>\<^sub>a (arl_assn nat_assn)"
unfolding convert_list_def
apply (rewrite in "nfoldli _ _ _ rewrite_HOLE" arl.fold_custom_empty)
by sepref
definition convert_list_to_set :: "'a::{default, heap} list \<Rightarrow> 'a set nres" where
"convert_list_to_set l \<equiv>
nfoldli l (\<lambda> x. True)
(\<lambda> x ns.
RETURN (insert x ns)) {}"
sepref_definition convert_list_to_hash_set is "convert_list_to_set" :: "(list_assn id_assn)\<^sup>d
\<rightarrow>\<^sub>a (hs.assn nat_assn)"
unfolding convert_list_to_set_def
apply (rewrite in "nfoldli _ _ _ rewrite_HOLE" hs.fold_custom_empty)
by sepref
lemma convert_list_correct:
shows "(convert_list, RETURN) \<in> \<langle>Id\<rangle>list_rel \<rightarrow> \<langle>\<langle>Id\<rangle>list_rel\<rangle>nres_rel"
unfolding convert_list_def
apply (clarsimp, intro nres_relI refine_IdI)
apply (refine_vcg nfoldli_rule[where I = "(\<lambda> l1 l2 r.
(r = l1))"])
by auto
lemma convert_list_to_set_correct:
shows "(convert_list_to_set, RETURN o set) \<in> \<langle>Id\<rangle>list_rel \<rightarrow> \<langle>\<langle>Id\<rangle>set_rel\<rangle>nres_rel"
unfolding convert_list_to_set_def
apply (clarsimp, intro nres_relI refine_IdI)
apply (refine_vcg nfoldli_rule[where I = "(\<lambda> l1 l2 r.
(r = set l1))"])
by auto
subsection \<open>Monadic Implementation for Limiting Profiles\<close>
definition limit_profile_l :: "'a::{default, hashable, heap} set \<Rightarrow>
'a Profile_List \<Rightarrow> 'a Profile_List nres" where
"limit_profile_l A p =
nfoldli p (\<lambda>_. True)
(\<lambda> x np. do {
newb \<leftarrow> (limit_monadic A x);
RETURN (op_list_append np newb)}) []"
sepref_register limit_monadic
declare limit_sep.refine [sepref_fr_rules]
sepref_definition limit_profile_sep is "uncurry (limit_profile_l)" ::
"(hs.assn id_assn)\<^sup>k *\<^sub>a (profile_impl_assn id_assn )\<^sup>k \<rightarrow>\<^sub>a (profile_impl_assn id_assn )"
unfolding limit_profile_l_def
apply (rewrite in "nfoldli _ _ _ rewrite_HOLE" HOL_list.fold_custom_empty)
apply sepref_dbg_keep
done
sepref_register limit_profile_l
lemma limitp_correct:
shows "(uncurry limit_profile_l, uncurry (RETURN oo limit_profile)) \<in>
[\<lambda> (A, pl). finite A ]\<^sub>f (\<langle>Id\<rangle>set_rel \<times>\<^sub>r profile_rel) \<rightarrow> \<langle>profile_rel\<rangle>nres_rel"
proof(intro frefI, unfold limit_profile_l_def comp_apply SPEC_eq_is_RETURN(2)[symmetric],
refine_vcg, auto, rename_tac A pl pr)
fix A :: "'a set"
fix pl:: "'a Profile_List"
fix pr :: "'a Profile"
assume fina : "finite A"
assume prel: " (pl, pr) \<in> profile_rel"
show " nfoldli pl (\<lambda>_. True) (\<lambda>x np. limit_monadic A x \<bind> (\<lambda>newb. RES {np @ [newb]})) []
\<le> \<Down> profile_rel (RES {map (limit A) pr})"
apply (refine_vcg limit_monadic_refine nfoldli_rule[where I = "(\<lambda> proc rem r.
r = map (limit_l A) proc)"] )
apply (auto simp add: fina)
unfolding ballot_rel_def well_formed_pl_def relAPP_def in_br_conv
in_br_conv length_map limit_l_sound list_rel_eq_listrel listrel_iff_nth
nth_map prel relAPP_def
apply safe using length_preserving
using prel list_rel_imp_same_length prel apply blast
using limit_eq
apply (metis ballot_rel_def list_rel_imp_same_length map_in_list_rel_conv nth_map
nth_mem prel profile_rel_imp_map_ballots)
using limit_eq
apply (metis ballot_rel_def list_rel_imp_same_length map_in_list_rel_conv nth_map
nth_mem prel profile_rel_imp_map_ballots)
using prel limit_l_sound
by (metis ballot_rel_def map_in_list_rel_conv nth_map nth_mem
profile_rel_imp_map_ballots well_formed_pl_def)
qed
definition "ballot_assn R \<equiv> (hr_comp (ballot_impl_assn R) ballot_rel)"
lemma limit_profile_sep_correct:
shows "(uncurry limit_profile_sep, uncurry (RETURN \<circ>\<circ> limit_profile))
\<in> [\<lambda>(a, b).
finite
a]\<^sub>a (alts_set_impl_assn id_assn)\<^sup>k *\<^sub>a
(list_assn
(ballot_assn id_assn))\<^sup>k \<rightarrow> list_assn
(ballot_assn id_assn)"
using limit_profile_sep.refine[FCOMP limitp_correct] set_rel_id hr_comp_Id2
unfolding ballot_assn_def
by (simp)
declare limit_profile_sep_correct [sepref_fr_rules]
lemma limit_profile_sound_sep:
shows "s \<subseteq> A \<and> finite_profile A p \<Longrightarrow> <(alts_set_impl_assn nat_assn) s hs *
(list_assn (ballot_assn nat_assn)) p hp> limit_profile_sep hs hp
< \<lambda>r. \<exists>\<^sub>Ares. list_assn (ballot_assn nat_assn) p hp *
(list_assn (ballot_assn nat_assn)) res r * \<up> (finite_profile s res) >\<^sub>t"
proof (clarsimp)
assume sA: "s \<subseteq> A"
assume fina: "finite A"
assume prof: "profile A p"
from sA fina have fins: "finite s"
using rev_finite_subset by blast
have postapp: "\<And>x. (\<exists>\<^sub>Axa. alts_set_impl_assn nat_assn s hs *
list_assn (ballot_assn nat_assn) p hp *
list_assn (ballot_assn nat_assn) xa x *
true *
\<up> (xa = map (limit s) p)) \<Longrightarrow>\<^sub>A
( \<exists>\<^sub>Ares. list_assn (ballot_assn nat_assn) p hp *
list_assn (ballot_assn nat_assn) res x * true *
\<up> (finite_profile s res))"
using limit_profile_sound[where S = A and p = p and A = s]
apply sep_auto
using fins apply blast
by (simp add: fina prof sA)
from this fins show "<alts_set_impl_assn nat_assn s hs *
list_assn (ballot_assn nat_assn) p hp>
limit_profile_sep hs hp
<\<lambda>r. \<exists>\<^sub>Ares. list_assn (ballot_assn nat_assn) p hp *
list_assn (ballot_assn nat_assn) res r * true *
\<up> (finite_profile s res)>"
using limit_profile_sep_correct[THEN hfrefD, THEN hn_refineD, of "(s, p)" "(hs, hp)", simplified]
cons_rule[where P = "(alts_set_impl_assn nat_assn) s hs *
(list_assn (ballot_assn nat_assn)) p hp"
and P' = "(alts_set_impl_assn nat_assn) s hs *
(list_assn
(hr_comp (ballot_impl_assn nat_assn)
ballot_rel)) p hp" and Q = "(\<lambda> r. \<exists>\<^sub>Ax. alts_set_impl_assn nat_assn s hs *
list_assn (ballot_assn nat_assn) p hp *
list_assn (ballot_assn nat_assn) x r *
true *
\<up> (x = map (limit s) p))"
and Q' = "\<lambda>r. \<exists>\<^sub>Ares. list_assn (ballot_assn nat_assn) p hp *
list_assn (ballot_assn nat_assn) res r * true *
\<up> (finite_profile s res)"
and c = "limit_profile_sep hs hp"]
using ent_refl
by (simp add: ballot_assn_def)
qed
end
|
{"author": "SpringVaS", "repo": "RefinementOfVotingRules", "sha": "a01e44b062fb43e172dff81cffbf941856c977d8", "save_path": "github-repos/isabelle/SpringVaS-RefinementOfVotingRules", "path": "github-repos/isabelle/SpringVaS-RefinementOfVotingRules/RefinementOfVotingRules-a01e44b062fb43e172dff81cffbf941856c977d8/theories/Compositional_Structures/Basic_Modules/Component_Types/Social_Choice_Types/Profile_List_Monadic.thy"}
|
# Copyright (c) 2021 J.A. Duffek
# Copyright (c) 2000 D.M. Spink
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, see <http://www.gnu.org/licenses/>.
"""
nrbruled(crv1::NURBS1D{I,F},crv2::NURBS1D{I,F}
)::NURBS2D{I,F} where {I<:Integer,F<:AbstractFloat}
Constructs a ruled surface between two NURBS curves. The ruled surface is ruled
along the V direction.
# Arguments:
- `crv1`: First NURBS curve, see [`nrbmak`](@ref).
- `crv2`: Second NURBS curve, see [`nrbmak`](@ref).
# Output:
- `srf`: Ruled NURBS surface.
# Examples:
```julia
julia> srf = nrbruled(crv1,crv2)
```
Construct a ruled surface between a semicircle and a straight line.
```julia
julia> cir = nrbcirc(1.0,[0.0;0.0;0],0.0,1.0*pi);
julia> line = nrbline(vec([-1 0.5 1]),vec([1 0.5 1]));
julia> srf = nrbruled(cir,line);
julia> nrbplot(srf,[20;20]);
```
"""
function nrbruled(crv1::NURBS1D{I,F},crv2::NURBS1D{I,F}
)::NURBS2D{I,F} where {I<:Integer,F<:AbstractFloat}
# ensure both curves have a common degree
d = max(crv1.order,crv2.order);
crv1 = nrbdegelev(crv1, d - crv1.order);
crv2 = nrbdegelev(crv2, d - crv2.order);
# merge the knot vectors, to obtain a common knot vector
k1 = crv1.knots;
k2 = crv2.knots;
ku = unique([k1;k2]);
n = length(ku);
# TODO this is bad, increasing the size without allocating
ka = Vector{F}();
kb = Vector{F}();
for i in 1:n
i1 = sum(x-> x == ku[i],k1);
i2 = sum(x-> x == ku[i],k2);
m = max(i1, i2);
if m-i1>0; append!(ka, fill(ku[i],m-i1)); end #if
if m-i2>0; append!(kb, fill(ku[i],m-i2)); end #if
end # for i
if !(isempty(ka)); crv1 = nrbkntins(crv1, ka); end # if
if !(isempty(kb)); crv2 = nrbkntins(crv2, kb); end # if
coefs = cat(crv1.coefs,crv2.coefs,dims=3);
return nrbmak(coefs, [crv1.knots,vec([0.0 0.0 1.0 1.0])]);
end # nrbruled
|
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|
MODULE bc_variables
implicit none
PRIVATE
PUBLIC :: n_neighbor, fdinfo_send, fdinfo_recv
PUBLIC :: www, sbuf, rbuf
PUBLIC :: TYPE_MAIN, zero, Md
include 'mpif.h'
integer :: n_neighbor(6)
integer,allocatable :: fdinfo_send(:,:,:),fdinfo_recv(:,:,:)
#ifdef _DRSDFT_
integer,parameter :: TYPE_MAIN=MPI_REAL8
real(8),allocatable :: www(:,:,:,:)
real(8),allocatable :: sbuf(:,:,:),rbuf(:,:,:)
real(8),parameter :: zero=0.0d0
#else
integer,parameter :: TYPE_MAIN=MPI_COMPLEX16
complex(8),allocatable :: www(:,:,:,:)
complex(8),allocatable :: sbuf(:,:,:),rbuf(:,:,:)
complex(8),parameter :: zero=(0.d0,0.d0)
#endif
integer :: Md
END MODULE bc_variables
|
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#
# COPYRIGHT:
# The Leginon software is Copyright 2003
# The Scripps Research Institute, La Jolla, CA
# For terms of the license agreement
# see http://ami.scripps.edu/software/leginon-license
#
import calibrator
import calibrationclient
import event
from leginon import leginondata
import node
import gui.wx.MagCalibrator
import time
import libCVwrapper
import numpy
from pyami import arraystats, mrc, affine, msc
import pyami.quietscipy
from scipy import ndimage
class MagCalibrator(calibrator.Calibrator):
'''
'''
panelclass = gui.wx.MagCalibrator.Panel
settingsclass = leginondata.MagCalibratorSettingsData
defaultsettings = calibrator.Calibrator.defaultsettings
defaultsettings.update({
'minsize': 50,
'maxsize': 500,
'pause': 1.0,
'label': '',
'maxthreshold': 60000,
'maxcount': 5000,
'cutoffpercent': 1.0,
'minbright': 100,
'maxbright': 5000,
'mag1': 5000,
'mag2': 6500,
})
def __init__(self, id, session, managerlocation, **kwargs):
calibrator.Calibrator.__init__(self, id, session, managerlocation, **kwargs)
self.start()
def OLDuiStart(self):
mag = self.instrument.tem.Magnification
print 'MAG', mag
mags = self.getMags()
print 'MAGS', mags
magindex = mags.index(mag)
othermag = mags[magindex-1]
self.compareToOtherMag(othermag)
return
print 'MAGINDEX', magindex
if magindex == 0:
print 'already at lowest mag'
return
else:
previousmags = mags[magindex-5:magindex-1]
previousmags.reverse()
print 'PREVIOUSMAGS', previousmags
self.matchMags(previousmags)
def uiStart(self):
mag1 = self.settings['mag1']
mag2 = self.settings['mag2']
self.compareTwoMags(mag1, mag2)
return
mag = self.instrument.tem.Magnification
print 'MAG', mag
mags = self.getMags()
print 'MAGS', mags
magindex = mags.index(mag)
print 'MAGINDEX', magindex
if magindex == 0:
print 'already at lowest mag'
return
steps = self.settings['magsteps']
maglist = mags[magindex-steps:magindex]
maglist.reverse()
self.acquireMags(maglist)
def acquireAcquisitionImageData(self, range=None):
if range is None:
im = self.acquireImage()
else:
im = self.acquireWithinRange(*range)
im = leginondata.AcquisitionImageData(initializer=im)
im['session'] = self.session
mag = im['scope']['magnification']
magstring = '%06d' % (mag,)
label = self.settings['label']
im['filename'] = self.session['name'] + '-' + label + '-' + magstring
im['label'] = label
return im
def acquireMags(self, maglist):
firstim = self.acquireAcquisitionImageData()
firstim.insert(force=True)
print 'FIRST', firstim['image']
limitmin = self.settings['minbright']
limitmax = self.settings['maxbright']
for mag in maglist:
self.logger.info('mag: %s' % (mag,))
self.instrument.tem.Magnification = mag
self.pause()
im = self.acquireAcquisitionImageData(range=(limitmin,limitmax))
im.insert(force=True)
self.logger.info('inserted mag: %s' % (mag,))
def uiTest(self):
imdata = self.acquireImage()
im = imdata['image']
regions = self.findRegions(im)
def pause(self):
pause = self.settings['pause']
time.sleep(pause)
def getMags(self):
mags = self.instrument.tem.Magnifications
return mags
def compareTwoMags(self, mag1, mag2):
minbright = self.settings['minbright']
maxbright = self.settings['maxbright']
## mag1
self.instrument.tem.Magnification = mag1
self.pause()
mag1imdata = self.acquireWithinRange(minbright, maxbright)
## mag2
self.instrument.tem.Magnification = mag2
self.pause()
mag2imdata = self.acquireWithinRange(minbright, maxbright)
mag1im = mag1imdata['image']
mag2im = mag2imdata['image']
## compare
anglestart = -3
angleend = 3
angleinc = 0.25
scaleguess = float(mag2) / mag1
scalestart = scaleguess - 0.08
scaleend = scaleguess + 0.08
scaleinc = 0.02
prebin = 1
result = msc.findRotationScaleShift(mag1im, mag2im, anglestart, angleend, angleinc, scalestart, scaleend, scaleinc, prebin)
if result is None:
self.logger.error('could not determine relation')
return
angle = result[0]
scale = result[1]
shift = result[2]
print 'ANGLE', angle
print 'SCALE', scale
print 'SHIFT', shift
magdata = leginondata.MagnificationComparisonData()
magdata['mag1'] = mag1
magdata['mag2'] = mag2
magdata['rotation'] = angle
magdata['scale'] = scale
magdata['shiftrow'] = shift[0]
magdata['shiftcol'] = shift[1]
magdata.insert(force=True)
def isSaturated(self, im):
thresh = self.settings['threshold']
bins = (thresh,)
result = numpy.histogram(im, bins=bins)
count = result[0][0]
maxcount = self.settings['maxcount']
if count > maxcount:
self.logger.info('Overflow: %s pixels above %s (max allowed: %s)' % (count, thresh, maxcount))
return True
else:
return False
def isUnderexposed(self, im):
thresh = self.settings['threshold']
def brightestStats(self, im, percent):
# look only at the brightest 1% of the pixels
sortedpixels = numpy.sort(im, axis=None)
npixels = len(sortedpixels)
nbrightest = int(percent / 100.0 * npixels)
brightest = sortedpixels[-nbrightest:]
stats = arraystats.all(brightest)
self.logger.info('Top %.1f%% stats: mean: %.1f, std: %.1f, min: %.1f, max: %.1f' % (percent, stats['mean'],stats['std'],stats['min'],stats['max']))
return stats
def acquireWithinRange(self, min, max):
imagedata = self.acquireImage()
stats = self.brightestStats(imagedata['image'], self.settings['cutoffpercent'])
while not (min < stats['mean'] < max):
if stats['mean'] > max:
self.logger.info('too bright')
# assuming we are greater than crossover, increase lens value
i = self.instrument.tem.Intensity
if i < 1.0:
self.logger.info('spreading beam')
self.instrument.tem.Intensity = 1.02 * i
else:
self.logger.info('decreasing exposure time')
t = self.instrument.ccdcamera.ExposureTime
self.instrument.ccdcamera.ExposureTime = t / 2
imagedata = self.acquireImage()
stats = self.brightestStats(imagedata['image'], self.settings['cutoffpercent'])
if stats['mean'] < min:
self.logger.info('not bright enough, condensing beam...')
# assuming we are greater than crossover, decrease lens value
i = self.instrument.tem.Intensity
self.instrument.tem.Intensity = 0.98 * i
imagedata = self.acquireImage()
stats = self.brightestStats(imagedata['image'], self.settings['cutoffpercent'])
return imagedata
def acquireImage(self):
im = calibrator.Calibrator.acquireImage(self)
#im['image'] = ndimage.gaussian_filter(im['image'], 1.2)
return im
def matchMags(self, mags):
# acquire first image at current state
oldimagedata = self.acquireImage()
self.findRegions(oldimagedata['image'])
mrc.write(oldimagedata['image'], 'imref.mrc')
stats = arraystats.all(oldimagedata['image'])
shape = oldimagedata['image'].shape
# determine limits to adjust exposure of other mags
limitmax = 1.5 * stats['mean']
limitmin = 0.5 * stats['mean']
self.logger.info('image1 mean: %f, limits: %f-%f' % (stats['mean'], limitmin, limitmax))
## iterate through mags
runningresult = numpy.identity(3)
for i,mag in enumerate(mags):
self.instrument.tem.Magnification = mag
self.pause()
newimagedata = self.acquireWithinRange(limitmin, limitmax)
self.findRegions(newimagedata['image'])
mrc.write(newimagedata['image'], 'im%02d.mrc' % (i,))
minsize = self.settings['minsize']
maxsize = self.settings['maxsize']
self.logger.info('matchimages')
result = self.matchImages(oldimagedata['image'], newimagedata['image'], minsize, maxsize)
runningresult = numpy.dot(result, runningresult)
self.logger.info('transforms')
final_step = affine.transform(newimagedata['image'], result, shape)
final_all = affine.transform(newimagedata['image'], runningresult, shape)
self.logger.info('writing result mrcs')
mrc.write(final_step, 'trans%02d.mrc' % (i,))
mrc.write(final_all, 'transall%02d.mrc' % (i,))
oldimagedata = newimagedata
# self.getMagDiff(imagedata1, imagedata2, result)
def getMagDiff(self, imdata1, imdata2, matrix):
ccol = imdata1['camera']['dimension']['x'] / 2 - 0.5
crow = imdata1['camera']['dimension']['y'] / 2 - 0.5
center = numpy.array((ccol, crow, 1))
othercenter = numpy.dot(matrix, center)
print 'OTHER', othercenter
def matchImages(self, im1, im2, minsize, maxsize):
result = libCVwrapper.MatchImages(im1, im2, minsize, maxsize, 0, 0, 1, 1)
return result
def findRegions(self, im):
minsize = self.settings['minsize']
maxsize = self.settings['maxsize']
regions, image = libCVwrapper.FindRegions(im, minsize, maxsize, 0, 0, 1, 1)
coords = map(self.regionCenter, regions)
self.setTargets(coords, 'Peak')
return regions
def regionCenter(self, region):
coord = region['regionEllipse'][:2]
coord = coord[1], coord[0]
return coord
|
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|
function mori = parents(mori)
% variants of an orientation relationship
%
% Syntax
%
% ori_parents = ori_child * inv(mori.parents)
%
% Input
% mori - child to parent @orientation relationship
% ori_child - child orientation
%
% Output
% ori_parents - all possible parent @orientation
%
% Example
% % parent symmetry
% cs_fcc = crystalSymmetry('m-3m', [3.6599 3.6599 3.6599], 'mineral', 'Iron fcc');
%
% % child symmetry
% cs_bcc = crystalSymmetry('m-3m', [2.866 2.866 2.866], 'mineral', 'Iron bcc')
%
% % define a bcc child orientation
% ori_bcc = orientation.goss(cs_bcc)
%
% % define Nishiyama Wassermann fcc to bcc orientation relation ship
% NW = orientation.NishiyamaWassermann (cs_fcc,cs_bcc)
%
% % compute a fcc parent orientation related to the bcc child orientation
% ori_fcc = ori_bcc * NW
%
% % compute all symmetrically possible parent orientations
% ori_fcc = unique(ori_bcc.symmetrise * NW)
%
% % same using the function parents
% ori_fcc2 = ori_bcc * NW.parents
%
% See also
% orientation/variants
%
% store child symmetry
CS_child = mori.SS;
% symmetrise only with respect to child symmetry
mori = CS_child * mori;
% ignore all variants symmetrically equivalent
% with respect to the parent symmetry
mori.SS = crystalSymmetry('1');
mori = unique(mori);
mori.SS = CS_child;
|
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|
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Tests for `openclsim` package."""
import pytest
import simpy
import shapely.geometry
import logging
import datetime
import time
import numpy as np
import pandas as pd
from click.testing import CliRunner
from openclsim import core
from openclsim import model
from openclsim import cli
logger = logging.getLogger(__name__)
@pytest.fixture
def env():
simulation_start = datetime.datetime(2019, 1, 1)
my_env = simpy.Environment(initial_time=time.mktime(simulation_start.timetuple()))
my_env.epoch = time.mktime(simulation_start.timetuple())
return my_env
@pytest.fixture
def geometry_a():
return shapely.geometry.Point(0, 0)
@pytest.fixture
def geometry_b():
return shapely.geometry.Point(1, 1)
@pytest.fixture
def locatable_a(geometry_a):
return core.Locatable(geometry_a)
@pytest.fixture
def locatable_b(geometry_b):
return core.Locatable(geometry_b)
@pytest.fixture
def weather_data():
df = pd.read_csv("tests/test_weather.csv")
df.index = df[["Year", "Month", "Day", "Hour"]].apply(
lambda s: datetime.datetime(*s), axis=1
)
df = df.drop(["Year", "Month", "Day", "Hour"], axis=1)
return df
# make a location with metocean data
@pytest.fixture
def LocationWeather():
return type(
"Location with Metocean",
(
core.Identifiable, # Give it a name
core.Log, # Allow logging of all discrete events
core.Locatable, # Add coordinates to extract distance information and visualize
core.HasContainer, # Add information on the material available at the site
core.HasResource, # Add information on serving equipment
core.HasWeather,
), # Add information on metocean data
{},
)
# make a location without metocean data
@pytest.fixture
def Location():
return type(
"Location without Metocean",
(
core.Identifiable, # Give it a name
core.Log, # Allow logging of all discrete events
core.Locatable, # Add coordinates to extract distance information and visualize
core.HasContainer, # Add information on the material available at the site
core.HasResource,
), # Add information on serving equipment
{},
)
# make the processors
@pytest.fixture
def Processor():
return type(
"Processor",
(
core.Identifiable,
core.Processor,
core.LoadingFunction,
core.UnloadingFunction,
core.Log,
core.Locatable,
),
{},
)
# make the movers
@pytest.fixture
def Mover():
return type(
"Mover",
(
core.Identifiable,
core.Movable,
core.Log,
core.HasResource,
core.HasContainer,
core.HasDepthRestriction,
),
{},
)
# Test calculating restrictions
def test_calc_restrictions(
env, geometry_a, Mover, Processor, LocationWeather, weather_data
):
# Initialize the Mover
def compute_draught(draught_empty, draught_full):
return lambda x: x * (draught_full - draught_empty) + draught_empty
data = {
"env": env, # The simpy environment
"name": "Vessel", # Name
"geometry": geometry_a, # Location
"capacity": 7_200, # Capacity of the hopper - "Beunvolume"
"v": 1, # Speed always 1 m/s
"compute_draught": compute_draught(4.0, 7.0), # Variable draught
"waves": [0.5, 1], # Waves with specific ukc
"ukc": [0.75, 1], # UKC corresponding to the waves
"filling": None,
} # The filling degree
mover = Mover(**data)
mover.ActivityID = "Test activity"
data = {
"env": env, # The simpy environment
"name": "Quay Crane", # Name
"geometry": geometry_a, # It starts at the "from site"
"loading_rate": 1, # Loading rate
"unloading_rate": 1,
} # Unloading rate
crane = Processor(**data)
crane.rate = crane.loading
crane.ActivityID = "Test activity"
# Initialize the LocationWeather
data = {
"env": env, # The simpy environment defined in the first cel
"name": "Limited Location", # The name of the site
"geometry": geometry_a, # Location
"capacity": 500_000, # The capacity of the site
"level": 500_000, # The actual volume of the site
"dataframe": weather_data, # The dataframe containing the weather data
"bed": -7,
} # The level of the seabed with respect to CD
location = LocationWeather(**data)
# Test weather data at site
# The bed level is at CD -7, the tide is at CD. thus the water depth is 7 meters
assert location.metocean_data["Water depth"][0] == 7
# The timeseries start is equal to the simulation start
assert location.metocean_data.index[0] == datetime.datetime.fromtimestamp(env.now)
# Test calculated restrictions
mover.calc_depth_restrictions(location, crane)
assert mover.depth_data[location.name][0.5]["Volume"] == 3_600
assert mover.depth_data[location.name][0.5]["Draught"] == 5.5
# Test current draught of the mover (empty)
assert mover.current_draught == 4.0
# Process an amount of 3_600 from the location into the mover
# This takes 3_600 seconds and should be able to start right away
start = env.now
env.process(crane.process(site=location, ship=mover, desired_level=3_600))
env.run()
np.testing.assert_almost_equal(env.now, start + 3_600)
# Step forward to 18:00
def step_forward(env):
yield env.timeout(17 * 3600)
env.process(step_forward(env))
env.run()
# Process an amount of 3_600 from the location into the mover
# This takes 3_600 seconds and cannot start right away due to tide restrictions
start = env.now
assert datetime.datetime.fromtimestamp(env.now) == datetime.datetime(2019, 1, 1, 18)
assert (
location.metocean_data["Water depth"][datetime.datetime(2019, 1, 1, 21)] == 6.5
)
assert mover.container.level / mover.container.capacity in list(
mover.depth_data[location.name].keys()
)
env.process(crane.process(ship=mover, site=location, desired_level=0))
env.run()
# There should be 3 hours of waiting, 1 hour of processing, so time should be start + 4 hours
np.testing.assert_almost_equal(env.now, start + 3_600 + 3 * 3_600)
# Test optimal filling
# Every 4th hour dredging not possible
# sailing 2x 1 hour, dredging + dumping 1 hour, to get cycle with continous "optimal degree at 50%"
|
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|
import pandas
import numpy as np
from typing import List
def read_blosum(fn):
""" Read .txt encoded blosum matrix and return as dictionary of lists.
:param fn:
:return: Blosum embedding: keys are amino acids to embed and values are embedding as list
(similarity ot other amino acids).
"""
blosum_tab = pandas.read_csv(
filepath_or_buffer=fn,
skiprows=2, header=0,
delimiter=" ", skipinitialspace=True,
index_col=0
)
return blosum_tab.to_dict(orient="list")
def encode_as_blosum(
x: List[str],
blosum_embedding: dict
) -> np.ndarray:
""" Embed amino acid sequences in BLOSUM space.
Embedding: one dimension for distance to
- each amino acid
- end-of-sequence char
The entries captured are:
- each amino acid in dictionary
- unobserved amino acids labelled as "*"
- end of sequences positions which receive no penalty (value of zero in each dimension)
- any element in an unobserved peptide: no penalty (value of zero in each dimension)
:param x: Peptide sequences to encode.
:param blosum_embedding: Blosum embedding: keys are amino acids to embed and values are embedding as list
(similarity ot other amino acids).
:return: Peptide sequences in embedding (observations, peptides, sequence positions, embedding dimensions).
"""
dim_obs = len(x)
dim_chains = len(x[0])
dim_pos = np.max([np.max([len(xij) if xij is not None else 0 for xij in xi]) for xi in x]) + 1 # 1 padding
dim_aa = len(next(iter(blosum_embedding.values()))) + 1 # Add end-of-sequence dimension to embedding.
x_encoded = np.zeros([dim_obs, dim_chains, dim_pos, dim_aa])
for i, xi in enumerate(x): # Loop over observations.
for j, xij in enumerate(xi): # Loop over peptides per observation.
if xij is None: # Fill with end-of-sequence chars if peptide was not found.
x_encoded[i, j, :, -1] = 1
else:
for k, aa in enumerate(xij): # Loop over observed sequence positions.
x_encoded[i, j, k, :-1] = blosum_embedding[aa]
# Fill remaining positions as None.
for k in np.arange(len(xij), dim_pos): # Loop over padded remaining sequence positions.
x_encoded[i, j, k, -1] = 1
return x_encoded
def encode_as_onehot(
x: List[str],
dict_aa: dict,
eos_char: str
):
"""
Embed amino acid sequences in one-hot-encodeds space.
Embedding: one dimension for distance to
- each amino acid
- unobserved amino acids ("*" entry in BLOSUM matrix)
The entries captured are:
- each amino acid in dictionary
- end of sequences positions
- any element in an unobserved peptide labeled as "#"
:param x: Peptide sequences to encode.
:param dict_aa: Index of each encoded element in categorical embedding.
:param eos_char: End-of-sequence char.
:return: Peptide sequences in embedding (observations, peptides, sequence positions, embedding dimensions).
"""
dim_obs = len(x)
dim_chains = len(x[0])
dim_pos = np.max([np.max([len(xij) if xij is not None else 0 for xij in xi]) for xi in x]) + 1 # 1 padding
dim_aa = len(dict_aa)
x_encoded = np.zeros([dim_obs, dim_chains, dim_pos, dim_aa])
for i, xi in enumerate(x): # Loop over observations.
for j, xij in enumerate(xi): # Loop over peptides per observation.
if xij is None: # Write missing string if peptide was not found.
pass
else:
for k, aa in enumerate(xij): # Loop over observed sequence positions.
x_encoded[i, j, k, dict_aa[aa]] = 1
# Fill remaining positions as None.
for k in np.arange(len(xij), dim_pos): # Loop over padded remaining sequence positions.
x_encoded[i, j, k, dict_aa[eos_char]] = 1
return x_encoded
|
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|
import unittest
import tensorflow.contrib.keras as keras
import numpy as np
from vixstructure.models import term_structure_to_spread_price, term_structure_to_spread_price_v2
from vixstructure.models import term_structure_to_single_spread_price
from vixstructure.models import mask_output
from vixstructure.data import LongPricesDataset
class TestModels(unittest.TestCase):
def setUp(self):
self.dataset = LongPricesDataset("../../data/8_m_settle.csv", "../../data/expirations.csv")
def test_term_structure_to_spread_price(self):
model = term_structure_to_spread_price(5, 9)
self.assertEqual(len(model.layers), 7)
def test_mask_output_function_for_lambda_layers(self):
input = keras.layers.Input(shape=(9,))
output = keras.layers.Lambda(mask_output)(input)
model = keras.models.Model(inputs=input, outputs=output)
x, y = self.dataset.dataset()
preds = model.predict(x)
self.assertEqual(preds.shape, (2655, 6))
self.assertEqual(np.all(preds, axis=0).sum(), 5)
self.assertEqual(np.all(preds, axis=1).sum(), 2529)
self.assertEqual((preds == 0.).sum(), 126)
def test_term_structure_to_spread_prices_v2(self):
model = term_structure_to_spread_price_v2(5, 9)
x, y = self.dataset.dataset()
preds = model.predict(x)
self.assertEqual(preds.shape, (2655, 6))
self.assertEqual(np.all(preds, axis=0).sum(), 5)
self.assertEqual(np.all(preds, axis=1).sum(), 2529)
def test_term_structure_to_single_spread_price(self):
"""Just test model construction."""
model = term_structure_to_single_spread_price(5, 9)
self.assertEqual([layer.output_shape[1] for layer in model.layers], [8, 9, 9, 9, 9, 9, 1])
for distribution in (layer.kernel_initializer.distribution for layer in model.layers
if isinstance(layer, keras.layers.Dense)):
self.assertEqual(distribution, "uniform")
model_reduced_widths = term_structure_to_single_spread_price(5, 9, reduce_width=True)
self.assertEqual([layer.output_shape[1] for layer in model_reduced_widths.layers], [8, 9, 7, 6, 4, 3, 1])
for distribution in (layer.kernel_initializer.distribution for layer in model_reduced_widths.layers
if isinstance(layer, keras.layers.Dense)):
self.assertEqual(distribution, "uniform")
def test_term_structure_to_single_spread_price_with_selu(self):
model = term_structure_to_single_spread_price(5, 9, activation_function="selu")
self.assertEqual([layer.output_shape[1] for layer in model.layers], [8, 9, 9, 9, 9, 9, 1])
vars = [np.square(layer.kernel_initializer.stddev) for layer in model.layers
if isinstance(layer, keras.layers.Dense)]
self.assertAlmostEqual(1 / vars[0], 8 / 2)
for fst, snd in zip(vars[1:], [9, 9, 9, 9, 9]):
self.assertAlmostEqual(1 / fst, snd)
model_reduced_widths = term_structure_to_single_spread_price(5, 9, reduce_width=True, activation_function="selu")
self.assertEqual([layer.output_shape[1] for layer in model_reduced_widths.layers], [8, 9, 7, 6, 4, 3, 1])
vars_reduced_widths = [np.square(layer.kernel_initializer.stddev) for layer in model_reduced_widths.layers
if isinstance(layer, keras.layers.Dense)]
self.assertAlmostEqual(1 / vars[0], 8 / 2)
for fst, snd in zip(vars_reduced_widths[1:], [9, 7, 6, 4, 3]):
self.assertAlmostEqual(1 / fst, snd)
if __name__ == '__main__':
unittest.main()
|
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|
import gdspy
import numpy as np
from ..core.entity import gen_name
from ..utils import Vector, parse_entry, val
TOLERANCE = 1e-9 # for arcs
print("gdspy_version : ", gdspy.__version__)
class GdsModeler:
gds_object_instances = {}
gds_cells = {}
dict_units = {"km": 1.0e3, "m": 1.0, "cm": 1.0e-2, "mm": 1.0e-3}
# coor_systems = {'Global':[[0,0,0],[1,0]]}
# coor_system = coor_systems['Global']
def __init__(self, unit=1.0e-6, precision=1.0e-9):
self.unit = unit
self.precision = precision
gdspy.current_library = gdspy.GdsLibrary()
@classmethod
def print_instances(cls):
for instance_name in cls.gds_object_instances:
print(instance_name)
def reset_cell(self):
del self.cell
def create_coor_sys(self, coor_sys="chip", rel_coor=None, ref_name="Global"):
# this creates a cell, should not care about the rel_coor
if not (coor_sys in gdspy.current_library.cells.keys()):
cell = gdspy.Cell(coor_sys)
self.gds_cells[coor_sys] = cell
else:
cell = self.gds_cells[coor_sys]
# active cell should be the new cell
self.cell = cell
def set_coor_sys(self, coor_sys):
if coor_sys in self.gds_cells.keys():
self.cell = self.gds_cells[coor_sys]
else:
raise ValueError("%s cell do not exist" % coor_sys)
def copy(self, entity):
new_polygon = gdspy.copy(self.gds_object_instances[entity.name], 0, 0)
new_name = gen_name(entity.name)
self.gds_object_instances[new_name] = new_polygon
self.cell.add(new_polygon)
def rename(self, entity, name):
obj = self.gds_object_instances.pop(entity.name)
self.gds_object_instances[name] = obj
def generate_gds(self, file, max_points):
for instance in self.gds_object_instances.keys():
obj = self.gds_object_instances[instance]
if isinstance(obj, gdspy.Polygon) or isinstance(obj, gdspy.PolygonSet):
self.gds_object_instances[instance] = obj.fracture(
max_points=max_points, precision=1e-9
)
for cell_name in self.gds_cells.keys():
filename = file + "_%s.gds" % cell_name
gdspy.write_gds(filename, cells=[cell_name], unit=1.0, precision=1e-9)
def get_vertices(self, entity):
polygon = self.gds_object_instances[entity.name]
return polygon.polygons[0]
def set_units(self, units="m"):
self.unit = self.dict_units[units]
def box(self, pos, size, **kwargs):
pass
def box_center(self, pos, size, **kwargs):
pass
def polyline(self, points, closed, **kwargs):
# TODO sace of open path
# size is the thickness of the polyline for gds, must be a 2D-list with idential elements
name = kwargs["name"]
layer = kwargs["layer"]
points = parse_entry(points)
# TODO, this is a dirty fixe cause of Vector3D
points_2D = []
for point in points:
points_2D.append([point[0], point[1]])
if closed:
poly1 = gdspy.Polygon(points_2D, layer=layer)
else:
poly1 = gdspy.FlexPath(points_2D, 1e-9, layer=layer)
self.gds_object_instances[name] = poly1
self.cell.add(poly1)
def rect(self, pos, size, **kwargs):
pos, size = parse_entry(pos, size)
name = kwargs["name"]
layer = kwargs["layer"]
# This function neglects the z coordinate
points = [
(pos[0], pos[1]),
(pos[0] + size[0], pos[1] + 0),
(pos[0] + size[0], pos[1] + size[1]),
(pos[0], pos[1] + size[1]),
]
poly1 = gdspy.Polygon(points, layer)
self.gds_object_instances[name] = poly1
self.cell.add(poly1)
def text(self, pos, size, text, angle, horizontal, **kwargs):
pos, size = parse_entry(pos, size)
name = kwargs["name"]
layer = kwargs["layer"]
poly1 = gdspy.Text(text, size, pos, horizontal=horizontal, angle=angle, layer=layer)
self.gds_object_instances[name] = poly1
self.cell.add(poly1)
def rect_center(self, pos, size, **kwargs):
pos, size = parse_entry(pos, size)
corner_pos = [val(p) - val(s) / 2 for p, s in zip(pos, size)]
self.rect(corner_pos, size, **kwargs)
def cylinder(self, pos, radius, height, axis, **kwargs):
pass
def disk(self, pos, radius, axis, number_of_points=None, **kwargs):
pos, radius = parse_entry(pos, radius)
name = kwargs["name"]
layer = kwargs["layer"]
assert axis == "Z", "axis must be 'Z' for the gdsModeler"
round1 = gdspy.Round(
(pos[0], pos[1]),
radius,
layer=layer,
tolerance=TOLERANCE,
number_of_points=number_of_points,
)
self.gds_object_instances[name] = round1
self.cell.add(round1)
def wirebond(self, pos, ori, ymax, ymin, height="0.1mm", **kwargs): # ori should be normed
bond_diam = "20um"
pos, ori, ymax, ymin, heigth, bond_diam = parse_entry(
(pos, ori, ymax, ymin, height, bond_diam)
)
bond1 = pos + ori.orth() * (ymax + 2 * bond_diam)
bond2 = pos + ori.orth() * (ymin - 2 * bond_diam)
self.disk(
bond1,
bond_diam / 2,
"Z",
layer=kwargs["layer"],
name=kwargs["name"] + "a",
number_of_points=6,
)
self.disk(
bond2,
bond_diam / 2,
"Z",
layer=kwargs["layer"],
name=kwargs["name"] + "b",
number_of_points=6,
)
def path(self, points, port, fillet, name="", corner="circular bend"):
# TODO, this is a dirty fixe cause of Vector3D
points_2D = []
for point in points:
points_2D.append([point[0], point[1]])
# use dummy layers to recover the right elements
layers = [ii for ii in range(len(port.widths))]
cable = gdspy.FlexPath(
points_2D,
port.widths,
offset=port.offsets,
corners=corner,
bend_radius=fillet,
gdsii_path=False,
tolerance=TOLERANCE,
layer=layers,
max_points=0,
) # tolerance (meter) is highly important here should be smaller than the smallest dim typ. 100nm
polygons = cable.get_polygons()
names = []
layers = []
for ii in range(len(polygons)):
poly = gdspy.Polygon(polygons[ii])
poly.layers = [port.layers[ii]]
current_name = name + "_" + port.subnames[ii]
names.append(current_name)
layers.append(port.layers[ii])
self.gds_object_instances[current_name] = poly
self.cell.add(poly)
return names, layers
def connect_faces(self, entity1, entity2):
pass
def delete(self, entity):
self.cell.polygons.remove(self.gds_object_instances[entity.name])
self.gds_object_instances.pop(entity.name)
def rename_entity(self, entity, name):
polygon = self.gds_object_instances.pop(entity.name)
self.gds_object_instances[name] = polygon
def unite(self, entities, keep_originals=True):
blank_entity = entities.pop(0)
blank_polygon = self.gds_object_instances.pop(blank_entity.name)
self.cell = self.gds_cells[blank_entity.body.name]
self.cell.polygons.remove(blank_polygon)
tool_polygons = []
for tool_entity in entities:
tool_polygon = self.gds_object_instances[tool_entity.name]
if isinstance(tool_polygon, gdspy.PolygonSet):
for polygon in tool_polygon.polygons:
tool_polygons.append(polygon)
else:
tool_polygons.append(tool_polygon)
# 2 unite operation
tool_polygon_set = gdspy.PolygonSet(tool_polygons, layer=blank_entity.layer)
united = gdspy.boolean(
blank_polygon,
tool_polygon_set,
"or",
precision=TOLERANCE,
max_points=0,
layer=blank_entity.layer,
)
self.gds_object_instances[blank_entity.name] = united
self.cell.add(united)
return blank_entity
def intersect(self, entities):
raise NotImplementedError()
def subtract(self, blank_entities, tool_entities, keep_originals=True):
if isinstance(blank_entities, list):
for blank_entity in blank_entities:
self.subtract(blank_entity, tool_entities, keep_originals=keep_originals)
else:
blank_entity = blank_entities
# 1 We clear the cell of all elements and create lists to store the polygons
blank_polygon = self.gds_object_instances.pop(blank_entity.name)
self.cell = self.gds_cells[
blank_entity.body.name
] # assumes blank and tool are in same body
self.cell.polygons.remove(blank_polygon)
tool_polygons = []
for tool_entity in tool_entities:
tool_polygon = self.gds_object_instances[tool_entity.name]
if isinstance(tool_polygon, gdspy.PolygonSet):
for polygon in tool_polygon.polygons:
tool_polygons.append(polygon)
else:
tool_polygons.append(tool_polygon)
# 2 subtract operation
tool_polygon_set = gdspy.PolygonSet(tool_polygons, layer=blank_entity.layer)
subtracted = gdspy.boolean(
blank_polygon,
tool_polygon_set,
"not",
precision=TOLERANCE,
max_points=0,
layer=blank_entity.layer,
)
if subtracted is not None:
# 3 At last we update the cell and the gds_object_instance
self.gds_object_instances[blank_entity.name] = subtracted
self.cell.add(subtracted)
else:
print(
"Warning: the entity %s was fully \
subtracted"
% blank_entity.name
)
dummy = gdspy.Polygon([[0, 0]])
self.gds_object_instances[blank_entity.name] = dummy
self.cell.add(dummy)
blank_entity.delete()
def assign_material(self, *args, **kwargs):
pass
def assign_perfect_E(self, entity, name=None):
pass
def assign_impedance(self, entities, ResistanceSq, ReactanceSq, name="impedance"):
pass
def assign_perfect_E_faces(self, entity):
pass
def assign_mesh_length(self, entity, length): # , suff = '_mesh'):
pass
def assign_lumped_rlc(self, entity, r, l, c, start, end, name="RLC"):
pass
def assign_waveport(self, *args, **kwargs):
pass
def assign_terminal_auto(self, *args, **kwargs):
pass
def create_object_from_face(self, name):
pass
def fillet(self, entity, radius, vertex_indices=None):
polygon = self.gds_object_instances[entity.name]
if vertex_indices is None:
polygon.fillet(radius, max_points=0)
else:
vertices_number = len(polygon.polygons[0])
radii = [0] * vertices_number
for rad, indices in zip(radius, vertex_indices):
for index in indices:
radii[index] = rad
polygon.fillet([radii], max_points=0, precision=TOLERANCE)
def get_vertex_ids(self, entity):
return None
def sweep_along_vector(self, names, vector):
self._modeler.SweepAlongVector(
self._selections_array(*names),
[
"NAME:VectorSweepParameters",
"DraftAngle:=",
"0deg",
"DraftType:=",
"Round",
"CheckFaceFaceIntersection:=",
False,
"SweepVectorX:=",
vector[0],
"SweepVectorY:=",
vector[1],
"SweepVectorZ:=",
vector[2],
],
)
def thicken_sheet(self, sheet, thickness, bothsides=False):
self._modeler.ThickenSheet(
["NAME:Selections", "Selections:=", sheet, "NewPartsModelFlag:=", "Model"],
[
"NAME:SheetThickenParameters",
"Thickness:=",
thickness,
"BothSides:=",
bothsides,
],
)
def mirrorZ(self, entity):
pass
def translate(self, entities, vector):
"""vector is 3-dimentional but with a z=0 component"""
if not isinstance(entities, list):
entities = [entities]
translation_vector = [vector[0], vector[1]]
for entity in entities:
# if entity!=None:
gds_entity = self.gds_object_instances[entity.name]
gds_entity.translate(*translation_vector)
def rotate(self, entities, angle, center=None):
if center is None:
center = (0, 0)
if not isinstance(entities, list):
entities = [entities]
for entity in entities:
# if entity!=None:
gds_entity = self.gds_object_instances[entity.name]
gds_entity.rotate(angle / 360 * 2 * np.pi, center=(val(center[0]), val(center[1])))
def rect_array(self, pos, size, columns, rows, spacing, origin=(0, 0), **kwargs):
pos, size = parse_entry(pos, size)
name = kwargs["name"]
layer = kwargs["layer"]
points = [
(pos[0], pos[1]),
(pos[0] + size[0], pos[1] + 0),
(pos[0] + size[0], pos[1] + size[1]),
(pos[0], pos[1] + size[1]),
]
poly1 = gdspy.Polygon(points, layer)
self.gds_object_instances[name] = poly1
cell_to_copy = gdspy.Cell("cell_to_copy")
self.gds_cells["cell_to_copy"] = cell_to_copy
cell_to_copy.add(poly1)
spacing = parse_entry(spacing)
cell_array = gdspy.CellArray(cell_to_copy, columns, rows, spacing, origin)
polygon_list = cell_array.get_polygons()
poly2 = gdspy.PolygonSet(polygon_list, layer)
self.cell.add(poly2)
self.gds_object_instances[name] = poly2
|
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|
SUBROUTINE POLATEV2(IPOPT,IGDTNUMI,IGDTMPLI,IGDTLENI, &
IGDTNUMO,IGDTMPLO,IGDTLENO, &
MI,MO,KM,IBI,LI,UI,VI, &
NO,RLAT,RLON,CROT,SROT,IBO,LO,UO,VO,IRET)
!$$$ SUBPROGRAM DOCUMENTATION BLOCK
!
! $Revision: 74685 $
!
! SUBPROGRAM: POLATEV2 INTERPOLATE VECTOR FIELDS (NEIGHBOR)
! PRGMMR: IREDELL ORG: W/NMC23 DATE: 96-04-10
!
! ABSTRACT: THIS SUBPROGRAM PERFORMS NEIGHBOR INTERPOLATION
! FROM ANY GRID TO ANY GRID FOR VECTOR FIELDS.
! OPTIONS ALLOW CHOOSING THE WIDTH OF THE GRID SQUARE
! (IPOPT(1)) TO SEARCH FOR VALID DATA, WHICH DEFAULTS TO 1
! (IF IPOPT(1)=-1). ODD WIDTH SQUARES ARE CENTERED ON
! THE NEAREST INPUT GRID POINT; EVEN WIDTH SQUARES ARE
! CENTERED ON THE NEAREST FOUR INPUT GRID POINTS.
! SQUARES ARE SEARCHED FOR VALID DATA IN A SPIRAL PATTERN
! STARTING FROM THE CENTER. NO SEARCHING IS DONE WHERE
! THE OUTPUT GRID IS OUTSIDE THE INPUT GRID.
! ONLY HORIZONTAL INTERPOLATION IS PERFORMED.
!
! THE INPUT AND OUTPUT GRIDS ARE DEFINED BY THEIR GRIB 2 GRID
! DEFINITION TEMPLATE AS DECODED BY THE NCEP G2 LIBRARY. THE
! CODE RECOGNIZES THE FOLLOWING PROJECTIONS, WHERE
! "IGDTNUMI/O" IS THE GRIB 2 GRID DEFINTION TEMPLATE NUMBER
! FOR THE INPUT AND OUTPUT GRIDS, RESPECTIVELY:
! (IGDTNUMI/O=00) EQUIDISTANT CYLINDRICAL
! (IGDTNUMI/O=01) ROTATED EQUIDISTANT CYLINDRICAL. "E" AND
! NON-"E" STAGGERED
! (IGDTNUMI/O=10) MERCATOR CYLINDRICAL
! (IGDTNUMI/O=20) POLAR STEREOGRAPHIC AZIMUTHAL
! (IGDTNUMI/O=30) LAMBERT CONFORMAL CONICAL
! (IGDTNUMI/O=40) GAUSSIAN CYLINDRICAL
!
! THE INPUT AND OUTPUT VECTORS ARE ROTATED SO THAT THEY ARE
! EITHER RESOLVED RELATIVE TO THE DEFINED GRID
! IN THE DIRECTION OF INCREASING X AND Y COORDINATES
! OR RESOLVED RELATIVE TO EASTERLY AND NORTHERLY DIRECTIONS,
! AS DESIGNATED BY THEIR RESPECTIVE GRID DEFINITION SECTIONS.
!
! AS AN ADDED BONUS THE NUMBER OF OUTPUT GRID POINTS
! AND THEIR LATITUDES AND LONGITUDES ARE ALSO RETURNED
! ALONG WITH THEIR VECTOR ROTATION PARAMETERS.
! ON THE OTHER HAND, THE OUTPUT CAN BE A SET OF STATION POINTS
! IF IGDTNUMO<0, IN WHICH CASE THE NUMBER OF POINTS
! AND THEIR LATITUDES AND LONGITUDES MUST BE INPUT
! ALONG WITH THEIR VECTOR ROTATION PARAMETERS.
!
! INPUT BITMAPS WILL BE INTERPOLATED TO OUTPUT BITMAPS.
! OUTPUT BITMAPS WILL ALSO BE CREATED WHEN THE OUTPUT GRID
! EXTENDS OUTSIDE OF THE DOMAIN OF THE INPUT GRID.
! THE OUTPUT FIELD IS SET TO 0 WHERE THE OUTPUT BITMAP IS OFF.
!
! PROGRAM HISTORY LOG:
! 96-04-10 IREDELL
! 1999-04-08 IREDELL SPLIT IJKGDS INTO TWO PIECES
! 2001-06-18 IREDELL INCLUDE SPIRAL SEARCH OPTION
! 2002-01-17 IREDELL SAVE DATA FROM LAST CALL FOR OPTIMIZATION
! 2006-01-04 GAYNO MINOR BUG FIX
! 2007-10-30 IREDELL SAVE WEIGHTS AND THREAD FOR PERFORMANCE
! 2012-06-26 GAYNO FIX OUT-OF-BOUNDS ERROR. SEE NCEPLIBS
! TICKET #9.
! 2015-01-27 GAYNO REPLACE CALLS TO GDSWIZ WITH NEW MERGED
! ROUTINE GDSWZD.
! 2015-07-13 GAYNO CONVERT TO GRIB 2. REPLACE GRIB 1 KGDS ARRAYS
! WITH GRIB 2 GRID DEFINITION TEMPLATE ARRAYS.
!
! USAGE: CALL POLATEV2(IPOPT,IGDTNUMI,IGDTMPLI,IGDTLENI, &
! IGDTNUMO,IGDTMPLO,IGDTLENO, &
! MI,MO,KM,IBI,LI,UI,VI, &
! NO,RLAT,RLON,CROT,SROT,IBO,LO,UO,VO,IRET)
!
! INPUT ARGUMENT LIST:
! IPOPT - INTEGER (20) INTERPOLATION OPTIONS
! IPOPT(1) IS WIDTH OF SQUARE TO EXAMINE IN SPIRAL SEARCH
! (DEFAULTS TO 1 IF IPOPT(1)=-1)
! IGDTNUMI - INTEGER GRID DEFINITION TEMPLATE NUMBER - INPUT GRID.
! CORRESPONDS TO THE GFLD%IGDTNUM COMPONENT OF THE
! NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE:
! 00 - EQUIDISTANT CYLINDRICAL
! 01 - ROTATED EQUIDISTANT CYLINDRICAL. "E"
! AND NON-"E" STAGGERED
! 10 - MERCATOR CYCLINDRICAL
! 20 - POLAR STEREOGRAPHIC AZIMUTHAL
! 30 - LAMBERT CONFORMAL CONICAL
! 40 - GAUSSIAN EQUIDISTANT CYCLINDRICAL
! IGDTMPLI - INTEGER (IGDTLENI) GRID DEFINITION TEMPLATE ARRAY -
! INPUT GRID. CORRESPONDS TO THE GFLD%IGDTMPL COMPONENT
! OF THE NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE
! (SECTION 3 INFO). SEE COMMENTS IN ROUTINE
! IPOLATEV FOR COMPLETE DEFINITION.
! IGDTLENI - INTEGER NUMBER OF ELEMENTS OF THE GRID DEFINITION
! TEMPLATE ARRAY - INPUT GRID. CORRESPONDS TO THE GFLD%IGDTLEN
! COMPONENT OF THE NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE.
! IGDTNUMO - INTEGER GRID DEFINITION TEMPLATE NUMBER - OUTPUT GRID.
! CORRESPONDS TO THE GFLD%IGDTNUM COMPONENT OF THE
! NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE. IGDTNUMO<0
! MEANS INTERPOLATE TO RANDOM STATION POINTS.
! OTHERWISE, SAME DEFINITION AS "IGDTNUMI".
! IGDTMPLO - INTEGER (IGDTLENO) GRID DEFINITION TEMPLATE ARRAY -
! OUTPUT GRID. CORRESPONDS TO THE GFLD%IGDTMPL COMPONENT
! OF THE NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE.
! (SECTION 3 INFO). SEE COMMENTS IN ROUTINE
! IPOLATEV FOR COMPLETE DEFINITION.
! IGDTLENO - INTEGER NUMBER OF ELEMENTS OF THE GRID DEFINITION
! TEMPLATE ARRAY - OUTPUT GRID. CORRESPONDS TO THE GFLD%IGDTLEN
! COMPONENT OF THE NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE.
! MI - INTEGER SKIP NUMBER BETWEEN INPUT GRID FIELDS IF KM>1
! OR DIMENSION OF INPUT GRID FIELDS IF KM=1
! MO - INTEGER SKIP NUMBER BETWEEN OUTPUT GRID FIELDS IF KM>1
! OR DIMENSION OF OUTPUT GRID FIELDS IF KM=1
! KM - INTEGER NUMBER OF FIELDS TO INTERPOLATE
! IBI - INTEGER (KM) INPUT BITMAP FLAGS
! LI - LOGICAL*1 (MI,KM) INPUT BITMAPS (IF SOME IBI(K)=1)
! UI - REAL (MI,KM) INPUT U-COMPONENT FIELDS TO INTERPOLATE
! VI - REAL (MI,KM) INPUT V-COMPONENT FIELDS TO INTERPOLATE
! RLAT - REAL (MO) OUTPUT LATITUDES IN DEGREES (IF IGDTNUMO<0)
! RLON - REAL (MO) OUTPUT LONGITUDES IN DEGREES (IF IGDTNUMO<0)
! CROT - REAL (MO) VECTOR ROTATION COSINES (IF IGDTNUMO<0)
! SROT - REAL (MO) VECTOR ROTATION SINES (IF IGDTNUMO<0)
! (UGRID=CROT*UEARTH-SROT*VEARTH;
! VGRID=SROT*UEARTH+CROT*VEARTH)
!
! OUTPUT ARGUMENT LIST:
! NO - INTEGER NUMBER OF OUTPUT POINTS (ONLY IF IGDTNUMO>=0)
! RLAT - REAL (MO) OUTPUT LATITUDES IN DEGREES (IF IGDTNUMO>=0)
! RLON - REAL (MO) OUTPUT LONGITUDES IN DEGREES (IF IGDTNUMO>=0)
! CROT - REAL (NO) VECTOR ROTATION COSINES (IF IGDTNUMO>=0)
! SROT - REAL (NO) VECTOR ROTATION SINES (IF IGDTNUMO>=0)
! (UGRID=CROT*UEARTH-SROT*VEARTH;
! VGRID=SROT*UEARTH+CROT*VEARTH)
! IBO - INTEGER (KM) OUTPUT BITMAP FLAGS
! LO - LOGICAL*1 (MO,KM) OUTPUT BITMAPS (ALWAYS OUTPUT)
! UO - REAL (MO,KM) OUTPUT U-COMPONENT FIELDS INTERPOLATED
! VO - REAL (MO,KM) OUTPUT V-COMPONENT FIELDS INTERPOLATED
! IRET - INTEGER RETURN CODE
! 0 SUCCESSFUL INTERPOLATION
! 2 UNRECOGNIZED INPUT GRID OR NO GRID OVERLAP
! 3 UNRECOGNIZED OUTPUT GRID
!
! SUBPROGRAMS CALLED:
! CHECK_GRIDS2V CHECK IF INPUT OR OUTPUT GRIDS HAVE CHANGED
! GDSWZD GRID DESCRIPTION SECTION WIZARD
! IJKGDS0 SET UP PARAMETERS FOR IJKGDS1
! IJKGDS1 RETURN FIELD POSITION FOR A GIVEN GRID POINT
! MOVECT MOVE A VECTOR ALONG A GREAT CIRCLE
! POLFIXV MAKE MULTIPLE POLE VECTOR VALUES CONSISTENT
!
! ATTRIBUTES:
! LANGUAGE: FORTRAN 90
!
!$$$
!
USE GDSWZD_MOD
!
IMPLICIT NONE
!
INTEGER, INTENT(IN ) :: IPOPT(20)
INTEGER, INTENT(IN ) :: IGDTNUMI, IGDTLENI
INTEGER, INTENT(IN ) :: IGDTMPLI(IGDTLENI)
INTEGER, INTENT(IN ) :: IGDTNUMO, IGDTLENO
INTEGER, INTENT(IN ) :: IGDTMPLO(IGDTLENO)
INTEGER, INTENT(IN ) :: IBI(KM),MI,MO,KM
INTEGER, INTENT(INOUT) :: NO
INTEGER, INTENT( OUT) :: IRET, IBO(KM)
!
LOGICAL*1, INTENT(IN ) :: LI(MI,KM)
LOGICAL*1, INTENT( OUT) :: LO(MO,KM)
!
REAL, INTENT(IN ) :: UI(MI,KM),VI(MI,KM)
REAL, INTENT(INOUT) :: CROT(MO),SROT(MO)
REAL, INTENT(INOUT) :: RLAT(MO),RLON(MO)
REAL, INTENT( OUT) :: UO(MO,KM),VO(MO,KM)
!
REAL, PARAMETER :: FILL=-9999.
!
INTEGER :: IJKGDSA(20)
INTEGER :: I1,J1,IXS,JXS,MX
INTEGER :: KXS,KXT,IX,JX,NX
INTEGER :: MSPIRAL,N,K,NK,NV,IJKGDS1
INTEGER, SAVE :: NOX=-1,IRETX=-1
INTEGER, ALLOCATABLE, SAVE :: NXY(:)
!
LOGICAL :: SAME_GRIDI, SAME_GRIDO
!
REAL :: CX,SX,CM,SM,UROT,VROT
REAL :: XPTS(MO),YPTS(MO)
REAL :: CROI(MI),SROI(MI)
REAL :: XPTI(MI),YPTI(MI),RLOI(MI),RLAI(MI)
REAL, ALLOCATABLE, SAVE :: RLATX(:),RLONX(:),XPTSX(:),YPTSX(:)
REAL, ALLOCATABLE, SAVE :: CROTX(:),SROTX(:),CXY(:),SXY(:)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! SET PARAMETERS
IRET=0
MSPIRAL=MAX(IPOPT(1),1)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CALL CHECK_GRIDS2V(IGDTNUMI,IGDTMPLI,IGDTLENI, &
IGDTNUMO,IGDTMPLO,IGDTLENO, &
SAME_GRIDI,SAME_GRIDO)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! SAVE OR SKIP WEIGHT COMPUTATION
IF(IRET.EQ.0.AND.(IGDTNUMO.LT.0.OR..NOT.SAME_GRIDI.OR..NOT.SAME_GRIDO))THEN
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! COMPUTE NUMBER OF OUTPUT POINTS AND THEIR LATITUDES AND LONGITUDES.
IF(IGDTNUMO.GE.0) THEN
CALL GDSWZD(IGDTNUMO,IGDTMPLO,IGDTLENO, 0,MO,FILL,XPTS,YPTS,RLON,RLAT, &
NO,CROT,SROT)
IF(NO.EQ.0) IRET=3
ENDIF
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! LOCATE INPUT POINTS
CALL GDSWZD(IGDTNUMI,IGDTMPLI,IGDTLENI,-1,NO,FILL,XPTS,YPTS,RLON,RLAT,NV)
IF(IRET.EQ.0.AND.NV.EQ.0) IRET=2
CALL GDSWZD(IGDTNUMI,IGDTMPLI,IGDTLENI, 0,MI,FILL,XPTI,YPTI,RLOI,RLAI, &
NV,CROI,SROI)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! ALLOCATE AND SAVE GRID DATA
IF(NOX.NE.NO) THEN
IF(NOX.GE.0) DEALLOCATE(RLATX,RLONX,XPTSX,YPTSX,CROTX,SROTX,NXY,CXY,SXY)
ALLOCATE(RLATX(NO),RLONX(NO),XPTSX(NO),YPTSX(NO), &
CROTX(NO),SROTX(NO),NXY(NO),CXY(NO),SXY(NO))
NOX=NO
ENDIF
IRETX=IRET
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! COMPUTE WEIGHTS
IF(IRET.EQ.0) THEN
CALL IJKGDS0(IGDTNUMI,IGDTMPLI,IGDTLENI,IJKGDSA)
!$OMP PARALLEL DO PRIVATE(N,CM,SM) SCHEDULE(STATIC)
DO N=1,NO
RLONX(N)=RLON(N)
RLATX(N)=RLAT(N)
XPTSX(N)=XPTS(N)
YPTSX(N)=YPTS(N)
CROTX(N)=CROT(N)
SROTX(N)=SROT(N)
IF(XPTS(N).NE.FILL.AND.YPTS(N).NE.FILL) THEN
NXY(N)=IJKGDS1(NINT(XPTS(N)),NINT(YPTS(N)),IJKGDSA)
IF(NXY(N).GT.0) THEN
CALL MOVECT(RLAI(NXY(N)),RLOI(NXY(N)),RLAT(N),RLON(N),CM,SM)
CXY(N)=CM*CROI(NXY(N))+SM*SROI(NXY(N))
SXY(N)=SM*CROI(NXY(N))-CM*SROI(NXY(N))
ENDIF
ELSE
NXY(N)=0
ENDIF
ENDDO
ENDIF
ENDIF
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! INTERPOLATE OVER ALL FIELDS
IF(IRET.EQ.0.AND.IRETX.EQ.0) THEN
IF(IGDTNUMO.GE.0) THEN
NO=NOX
DO N=1,NO
RLON(N)=RLONX(N)
RLAT(N)=RLATX(N)
CROT(N)=CROTX(N)
SROT(N)=SROTX(N)
ENDDO
ENDIF
DO N=1,NO
XPTS(N)=XPTSX(N)
YPTS(N)=YPTSX(N)
ENDDO
!$OMP PARALLEL DO &
!$OMP PRIVATE(NK,K,N,I1,J1,IXS,JXS,MX,KXS,KXT,IX,JX,NX) &
!$OMP PRIVATE(CM,SM,CX,SX,UROT,VROT) SCHEDULE(STATIC)
DO NK=1,NO*KM
K=(NK-1)/NO+1
N=NK-NO*(K-1)
UO(N,K)=0
VO(N,K)=0
LO(N,K)=.FALSE.
IF(NXY(N).GT.0) THEN
IF(IBI(K).EQ.0.OR.LI(NXY(N),K)) THEN
UROT=CXY(N)*UI(NXY(N),K)-SXY(N)*VI(NXY(N),K)
VROT=SXY(N)*UI(NXY(N),K)+CXY(N)*VI(NXY(N),K)
UO(N,K)=CROT(N)*UROT-SROT(N)*VROT
VO(N,K)=SROT(N)*UROT+CROT(N)*VROT
LO(N,K)=.TRUE.
! SPIRAL AROUND UNTIL VALID DATA IS FOUND.
ELSEIF(MSPIRAL.GT.1) THEN
I1=NINT(XPTS(N))
J1=NINT(YPTS(N))
IXS=SIGN(1.,XPTS(N)-I1)
JXS=SIGN(1.,YPTS(N)-J1)
DO MX=2,MSPIRAL**2
KXS=SQRT(4*MX-2.5)
KXT=MX-(KXS**2/4+1)
SELECT CASE(MOD(KXS,4))
CASE(1)
IX=I1-IXS*(KXS/4-KXT)
JX=J1-JXS*KXS/4
CASE(2)
IX=I1+IXS*(1+KXS/4)
JX=J1-JXS*(KXS/4-KXT)
CASE(3)
IX=I1+IXS*(1+KXS/4-KXT)
JX=J1+JXS*(1+KXS/4)
CASE DEFAULT
IX=I1-IXS*KXS/4
JX=J1+JXS*(KXS/4-KXT)
END SELECT
NX=IJKGDS1(IX,JX,IJKGDSA)
IF(NX.GT.0) THEN
IF(LI(NX,K)) THEN
CALL MOVECT(RLAI(NX),RLOI(NX),RLAT(N),RLON(N),CM,SM)
CX=CM*CROI(NX)+SM*SROI(NX)
SX=SM*CROI(NX)-CM*SROI(NX)
UROT=CX*UI(NX,K)-SX*VI(NX,K)
VROT=SX*UI(NX,K)+CX*VI(NX,K)
UO(N,K)=CROT(N)*UROT-SROT(N)*VROT
VO(N,K)=SROT(N)*UROT+CROT(N)*VROT
LO(N,K)=.TRUE.
EXIT
ENDIF
ENDIF
ENDDO
ENDIF
ENDIF
ENDDO
DO K=1,KM
IBO(K)=IBI(K)
IF(.NOT.ALL(LO(1:NO,K))) IBO(K)=1
ENDDO
IF(IGDTNUMO.EQ.0) CALL POLFIXV(NO,MO,KM,RLAT,RLON,IBO,LO,UO,VO)
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ELSE
IF(IRET.EQ.0) IRET=IRETX
IF(IGDTNUMO.GE.0) NO=0
ENDIF
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
END SUBROUTINE POLATEV2
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
SUBROUTINE CHECK_GRIDS2V(IGDTNUMI,IGDTMPLI,IGDTLENI, &
IGDTNUMO,IGDTMPLO,IGDTLENO, &
SAME_GRIDI, SAME_GRIDO)
!$$$ SUBPROGRAM DOCUMENTATION BLOCK
!
! SUBPROGRAM: CHECK_GRIDS2V CHECK GRID INFORMATION
! PRGMMR: GAYNO ORG: W/NMC23 DATE: 2015-07-13
!
! ABSTRACT: DETERMINE WHETHER THE INPUT OR OUTPUT GRID SPECS
! HAVE CHANGED.
!
! PROGRAM HISTORY LOG:
! 2015-07-13 GAYNO INITIAL VERSION
!
! USAGE: CALL CHECK_GRIDS2V(IGDTNUMI,IGDTMPLI,IGDTLENI, &
! IGDTNUMO,IGDTMPLO, &
! IGDTLENO, SAME_GRIDI, SAME_GRIDO)
!
! INPUT ARGUMENT LIST:
! IGDTNUMI - INTEGER GRID DEFINITION TEMPLATE NUMBER - INPUT GRID.
! CORRESPONDS TO THE GFLD%IGDTNUM COMPONENT OF THE
! NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE.
! IGDTMPLI - INTEGER (IGDTLENI) GRID DEFINITION TEMPLATE ARRAY -
! INPUT GRID. CORRESPONDS TO THE GFLD%IGDTMPL COMPONENT
! OF THE NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE.
! IGDTLENI - INTEGER NUMBER OF ELEMENTS OF THE GRID DEFINITION
! TEMPLATE ARRAY - INPUT GRID. CORRESPONDS TO THE GFLD%IGDTLEN
! COMPONENT OF THE NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE.
! IGDTNUMO - INTEGER GRID DEFINITION TEMPLATE NUMBER - OUTPUT GRID.
! CORRESPONDS TO THE GFLD%IGDTNUM COMPONENT OF THE
! NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE.
! IGDTMPLO - INTEGER (IGDTLENO) GRID DEFINITION TEMPLATE ARRAY -
! OUTPUT GRID. CORRESPONDS TO THE GFLD%IGDTMPL COMPONENT
! OF THE NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE.
! IGDTLENO - INTEGER NUMBER OF ELEMENTS OF THE GRID DEFINITION
! TEMPLATE ARRAY - OUTPUT GRID. CORRESPONDS TO THE GFLD%IGDTLEN
! COMPONENT OF THE NCEP G2 LIBRARY GRIDMOD DATA STRUCTURE.
!
! OUTPUT ARGUMENT LIST:
! SAME_GRIDI - WHEN TRUE, THE INPUT GRID HAS NOT CHANGED BETWEEN CALLS.
! SAME_GRIDO - WHEN TRUE, THE OUTPUT GRID HAS NOT CHANGED BETWEEN CALLS.
!
! ATTRIBUTES:
! LANGUAGE: FORTRAN 90
!
!$$$
IMPLICIT NONE
!
INTEGER, INTENT(IN ) :: IGDTNUMI, IGDTLENI
INTEGER, INTENT(IN ) :: IGDTMPLI(IGDTLENI)
INTEGER, INTENT(IN ) :: IGDTNUMO, IGDTLENO
INTEGER, INTENT(IN ) :: IGDTMPLO(IGDTLENO)
!
LOGICAL, INTENT( OUT) :: SAME_GRIDI, SAME_GRIDO
!
INTEGER, SAVE :: IGDTNUMI_SAVE=-9999
INTEGER, SAVE :: IGDTLENI_SAVE=-9999
INTEGER, SAVE :: IGDTMPLI_SAVE(1000)=-9999
INTEGER, SAVE :: IGDTNUMO_SAVE=-9999
INTEGER, SAVE :: IGDTLENO_SAVE=-9999
INTEGER, SAVE :: IGDTMPLO_SAVE(1000)=-9999
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
SAME_GRIDI=.FALSE.
IF(IGDTNUMI==IGDTNUMI_SAVE)THEN
IF(IGDTLENI==IGDTLENI_SAVE)THEN
IF(ALL(IGDTMPLI==IGDTMPLI_SAVE(1:IGDTLENI)))THEN
SAME_GRIDI=.TRUE.
ENDIF
ENDIF
ENDIF
!
IGDTNUMI_SAVE=IGDTNUMI
IGDTLENI_SAVE=IGDTLENI
IGDTMPLI_SAVE(1:IGDTLENI)=IGDTMPLI
IGDTMPLI_SAVE(IGDTLENI+1:1000)=-9999
!
SAME_GRIDO=.FALSE.
IF(IGDTNUMO==IGDTNUMO_SAVE)THEN
IF(IGDTLENO==IGDTLENO_SAVE)THEN
IF(ALL(IGDTMPLO==IGDTMPLO_SAVE(1:IGDTLENO)))THEN
SAME_GRIDO=.TRUE.
ENDIF
ENDIF
ENDIF
!
IGDTNUMO_SAVE=IGDTNUMO
IGDTLENO_SAVE=IGDTLENO
IGDTMPLO_SAVE(1:IGDTLENO)=IGDTMPLO
IGDTMPLO_SAVE(IGDTLENO+1:1000)=-9999
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
END SUBROUTINE CHECK_GRIDS2V
|
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#!/usr/bin/env python3.0
# -*- coding: utf-8 -*-
"""
Created on Tue Aug 22 14:38:25 2017
@author: wangronin & Bas van Stein
"""
import pdb
import subprocess, os, sys
from subprocess import STDOUT, check_output
import numpy as np
import time
import gputil as gp
from mipego import mipego
from mipego.Surrogate import RandomForest
from mipego.SearchSpace import ContinuousSpace, NominalSpace, OrdinalSpace
import re
import traceback
import time
#--------------------------- Configuration settings --------------------------------------
# TODO: implement parallel execution of model
n_step = 110
n_init_sample = 90
verbose = True
save = False
logfile = 'mnist.log'
class obj_func(object):
def __init__(self, program):
self.program = program
def __call__(self, cfg, gpu_no):
print("calling program with gpu "+str(gpu_no))
cmd = ['python3', self.program, '--cfg', str(cfg), str(gpu_no)]
outs = ""
#outputval = 0
outputval = ""
try:
outs = str(check_output(cmd,stderr=STDOUT, timeout=40000))
if os.path.isfile(logfile):
with open(logfile,'a') as f_handle:
f_handle.write(outs)
else:
with open(logfile,'w') as f_handle:
f_handle.write(outs)
outs = outs.split("\\n")
#TODO_CHRIS hacky solution
#outputval = 0
#for i in range(len(outs)-1,1,-1):
for i in range(len(outs)-1,-1,-1):
#if re.match("^\d+?\.\d+?$", outs[-i]) is None:
#CHRIS changed outs[-i] to outs[i]
print(outs[i])
if re.match("^\(\-?\d+\.?\d*\e?\+?\-?\d*\,\s\-?\d+\.?\d*\e?\+?\-?\d*\)$", outs[i]) is None:
#do nothing
a=1
else:
#outputval = -1 * float(outs[-i])
outputval = outs[i]
#if np.isnan(outputval):
# outputval = 0
except subprocess.CalledProcessError as e:
traceback.print_exc()
print (e.output)
except:
print ("Unexpected error:")
traceback.print_exc()
print (outs)
#outputval = 0
#TODO_CHRIS hacky solution
tuple_str1 = ''
tuple_str2 = ''
success = True
i = 1
try:
while outputval[i] != ',':
tuple_str1 += outputval[i]
i += 1
i += 1
while outputval[i] != ')':
tuple_str2 += outputval[i]
i += 1
except:
print("error in receiving answer from gpu " + str(gpu_no))
success = False
try:
tuple = (float(tuple_str1),float(tuple_str2),success)
except:
tuple = (0.0,0.0,False)
#return outputval
return tuple
for it in range(10):
np.random.seed(it)
#define the search space.
objective = obj_func('./all-cnn_bi_mbarrier.py')
real_space = ContinuousSpace([0.0, 4.0],'real_space') * 5
integer_space = OrdinalSpace([0,4],'integer_space') * 5
discrete_space = NominalSpace(['0','1','2','3','4'],'discrete_space') * 5
search_space = real_space * integer_space * discrete_space
print('starting program...')
#available_gpus = gp.getAvailable(limit=2)
available_gpus = gp.getAvailable(limit=5)
#try:
#available_gpus.remove(0)#CHRIS gpu 0 and 5 are differen gpu types on duranium since they are faster, timing will be unreliable, so remove them from list
#except:
#pass
#try:
#available_gpus.remove(5)
#except:
#pass
print(available_gpus)
n_job = max(min(5,len(available_gpus)),1)
# use random forest as the surrogate model
#CHRIS two surrogate models are needed
time_model = RandomForest(levels=search_space.levels,n_estimators=100)
loss_model = RandomForest(levels=search_space.levels,n_estimators=100)
opt = mipego(search_space, objective, time_model, loss_model, ftarget=None,
minimize=True, noisy=False, max_eval=None, max_iter=n_step,
infill='HVI', n_init_sample=n_init_sample, n_point=1, n_job=n_job,
n_restart=None, max_infill_eval=None, wait_iter=3, optimizer='MIES',
log_file=None, data_file=None, verbose=False, random_seed=None,
available_gpus=available_gpus, bi=True,save_name='data_mbarrier_kayfeng_eps_var_alpha_mult_' + str(it),ref_time=None,ref_loss=None,hvi_alpha=0.1)
#ref_time=1000.0,ref_loss=1000.0
incumbent, stop_dict = opt.run()
#print('incumbent #TODO_CHRIS makes no sense for now:')
#for x in incumbent:
# try:
# print(str(x) + ':' + str(incumbent[x]))
# except:
# continue
#print ('stop_dict:')
#for x in stop_dict:
# try:
# print(str(x) + ':' + str(stop_dict[x]))
# except:
# continue
|
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|
function[varargout] = vmoment(varargin)
%VMOMENT Central moment over non-NaN elements along a specfied dimension.
%
% Y=VMOMENT(X,N,DIM) finds the Nth central moment of all non-NaN elements
% of X along dimension DIM.
%
% [Y,NUM]=VMOMENT(X,N,DIM) also outputs the number of non-NaN data points
% NUM, which has the same dimension as X.
%
% [Y1,Y2,...YN]=VMOMENT(X1,X2,...XN,N,DIM) also works.
%
% VMOMENT(X1,X2,...XN,N,DIM); with no output arguments overwrites the
% original input variables.
% __________________________________________________________________
% This is part of JLAB --- type 'help jlab' for more information
% (C) 2001--2020 J.M. Lilly --- type 'help jlab_license' for details
if strcmpi(varargin{1}, '--t')
vmoment_test,return
end
n=varargin{end-1};
ndim=varargin{end};
for i=1:length(varargin)-2
x=varargin{i};
m=vmean(x,ndim);
m=vrep(m,size(x,ndim),ndim);
%previously I had an abs around (x-m), that was incorrect
[varargout{i},numi{i}]=vmean((x-m).^n,ndim);
end
for i=length(varargin)-1:nargout
varargout{i}=numi{i-length(varargin)+2};
end
eval(to_overwrite(nargin-2))
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function[]=vmoment_test
x1=[1 2 3 nan];
x2=x1;
ans1=2/3;
vmoment(x1,x2,2,2);
reporttest('VMOMENT output overwrite', aresame(x1,ans1) && aresame(x2,ans1))
x1=[1 2 3 nan];
ans2=3;
[y1,y2]=vmoment(x1,2,2);
reporttest('VMOMENT moment & num', aresame(y1,ans1) && aresame(y2,ans2))
|
{"author": "jonathanlilly", "repo": "jLab", "sha": "9f32f63e647209bc1cb81c8713deb954857f1919", "save_path": "github-repos/MATLAB/jonathanlilly-jLab", "path": "github-repos/MATLAB/jonathanlilly-jLab/jLab-9f32f63e647209bc1cb81c8713deb954857f1919/jVarfun/vmoment.m"}
|
#!/usr/bin/env python3
'''
Created on Mon Mar 1 02:21:48 2021
@author: skhalil
The script writes the data collected by VNA (.txt) into .s2p format, and
plot the S paramters in frequency domain, and impedance in time domain.
Some manupulation of S parameter indices is done since the data is for 4-point
VNA measurements, where as the skrf library understands it for the 2-point
VNA measurements.
# *.s2p Files format
# Each record contains 1 stimulus value and 4 S-parameters (total of 9 values)
#Stim Real (S11) Imag(S11) Real(S21) Imag(S21) Real(S12) Imag(S12) Real(S22) Imag(S22)
# ==== our file format for vna_0: ====
#!freq RelS11 ImS11 RelS12 ImS12 RelS13 ImS13 RelS14 ImS14
# parameter in file => read from software
# S11 S13 00 01 S11 S12
# ----> ---->
# S12 S14 10 11 S21 S22
# ==== our file format for vna_1: ====
#!freq RelS21 ImS21 RelS22 ImS22 RelS23 ImS23 RelS24 ImS24
# parameter in file => read from software
# S21 S23 00 01 S11 S12
# ----> ---->
# S22 S24 10 11 S21 S22
'''
import csv
import sys, re, os
from pylab import *
import numpy as np
import skrf as rf
import pylab
import pandas as pd
from matplotlib import pyplot as plt
from matplotlib.ticker import AutoMinorLocator
from matplotlib import style
import statistics
from optparse import OptionParser
#rf.stylely()
#print(rf.__version__)
###################
# helper functions
###################
def ensure_dir(file_name):
if not os.path.exists(file_name):
os.mkdir(file_name)
def createLabels(outDir, files):
x_labels=[]
for i in range(len(files)):
ff = str(outDir+"/"+files[i])
label = ff.split('.vna')[0].split('/')[-1:][0]
x_labels.append(label)
return x_labels
def set_axes(ax, title, xmin, xmax, ymin, ymax, nolim):
ax.xaxis.set_minor_locator(AutoMinorLocator(2))
ax.yaxis.set_minor_locator(AutoMinorLocator(2))
ax.grid(True, color='0.8', which='minor')
ax.grid(True, color='0.4', which='major')
ax.set_title(title) # Time domain
if not nolim:
ax.set_xlim((xmin, xmax))
ax.set_ylim((ymin, ymax))
plt.tight_layout()
# https://www.tutorialfor.com/questions-285739.htm
def display_mean_impedance(ax, t1, t2, col):
lines = ax.get_lines()
# Delete all elements of the array (except the last one) correponding to a line drawn in ax.
# This is a brute force way of resetting the line data to the data current line.
if len(lines)>1:
del lines[:-1]
# store the line arrays into list. Every line drawn on the ax is considered as data
Y = [line.get_ydata() for line in lines]
X = [line.get_xdata() for line in lines]
# create a table, and since the list X and Y should have size=1, place the first
# element (array) in pandas table columns t and Z
df = pd.DataFrame()
df['t'] = X[0]
df['Z'] = Y[0]
# get the mean value of Z for a given time difference
Z_mean = df.query('t >=@t1 & t<=@t2').agg({'Z': 'mean'})
print("Mean impedance [{0} ns, {1} ns] = {2:.2f} ohms for {3}".format(t1, t2, Z_mean.values[0], lines[0]))
# plot the average line
x_coor = [t1, t2]
y_coor = [Z_mean, Z_mean]
ax.plot(x_coor, y_coor, color=col, linewidth=1, label='', linestyle='--')
# return mean impedance
return Z_mean.values[0]
def getName(input_string):
match = re.match(r'TP_\w+_\d+', input_string)
name = match.group()
if '1p4' in name:
name = name.replace('1p4', '1.4')
return name
def analyze(createS2p, inDir, inputTxtFiles, cableName, cableLength, t1, t2, outDir, s2pDir, subfile, comp, times=[]):
verbose = False
resultsDir = "results"
files = []
with open(inputTxtFiles, 'r') as fl:
for line in fl.readlines():
files.append(line.strip())
fl.close
if verbose:
print("input file list: {0}".format(inputTxtFiles))
for f in files:
print (" - {0}".format(f))
ensure_dir(s2pDir)
ensure_dir(outDir)
ensure_dir(resultsDir)
############################
# Create the .s2p files
############################
if createS2p:
# convert the .txt files into table with columns corresponding to .s2p format
for f in files:
infile = pd.read_csv(inDir+'/'+f+'.txt', names=['pt','f','s11R','s11I','s12R','s12I','s13R','s13I','s14R','s14I'], delim_whitespace=True, skiprows=1)
infile.dropna(how='all')
pd.set_option("display.max_rows", 5)
fileindex = 0 # this will be increment to upto 9 corresponding to 10 .s2p files
prevF = 0
basename = f.rpartition('.')[0]
if verbose:
print("f: {0}, basename: {1}".format(f, basename))
for i, row in infile.iterrows():
if row['pt'] == 'PARAMETER:':
# new set of points
try:
if not f.closed:
f.close()
except:
pass
filename = s2pDir+'/'+basename+ '_' + str(fileindex)+'.s2p'
fileindex += 1
f = open(filename,'w')
f.write('# GHZ S RI R 50.0\n')
try:
#print (row['f'][1:-1], row['s11R'][1:-1], row['s11I'][1:-1], row['s12R'][1:-1] )
f.write(f"!freq Rel{row['f'][1:-1]} Im{row['f'][1:-1]} Rel{row['s11R'][1:-1]} Im{row['s11R'][1:-1]} Rel{row['s11I'][1:-1]} Im{row['s11I'][1:-1]} Rel{row['s12R'][1:-1]} Im{row['s12R'][1:-1]}\n")
except:
if row['f'][1:-1] == 'SDD':
f.write(f"!freq\tRelS11\tImS11\n")
prevF = 0
try:
if float(row['s11R']) == float(row['s11R']) and float(row['f'])>prevF:
f.write(f"{float(row['f']):.3f}\t{float(row['s11R'])}\t{float(row['s11I'])}\t{float(row['s12R'])}\t{float(row['s12I'])}\t{float(row['s13R'])}\t{float(row['s13I'])}\t{float(row['s14R'])}\t{float(row['s14I'])}\n")
prevF = float(row['f'])
except:
pass
########################
# Plots #
########################
S_ij = ''
if comp == '11' and subfile == '0': S_ij = '11'
elif comp == '12' and subfile == '0': S_ij = '21'
elif comp == '21' and subfile == '1': S_ij = '11'
i = int(S_ij[0])
j = int(S_ij[1])
labels = createLabels(outDir, files)
colors = [
'xkcd:cherry red',
'xkcd:tangerine',
'xkcd:neon green',
'xkcd:azure',
'xkcd:cyan',
'xkcd:neon purple',
'xkcd:coral',
'xkcd:magenta',
'xkcd:goldenrod',
'xkcd:seafoam green',
'xkcd:lavender',
'xkcd:turquoise',
'xkcd:green',
'xkcd:electric blue',
'xkcd:purple',
]
with style.context('seaborn-darkgrid'):
fig0 = plt.figure(figsize=(10,4))
fig0.patch.set_facecolor('xkcd:black')
plt.style.use('dark_background')
ax0=plt.subplot(1,2,1)
ax1=plt.subplot(1,2,2)
ax0.xaxis.set_minor_locator(AutoMinorLocator(2))
ax0.yaxis.set_minor_locator(AutoMinorLocator(2))
ax0.grid(True, color='0.8', which='minor')
ax0.grid(True, color='0.4', which='major')
# write csv file
csv_file = "{0}/{1}.csv".format(resultsDir, cableName)
with open(csv_file, 'w', newline='') as output_csv:
output_writer = csv.writer(output_csv)
titles = ["Channel", "t1", "t2", "Z_mean"]
output_writer.writerow(titles)
for n in range(len(labels)):
# overwrite times if specified
if times:
t1 = times[n][0]
t2 = times[n][1]
label = labels[n]
color = colors[n]
net = rf.Network(s2pDir+'/'+label+'_'+subfile+'.s2p', f_unit='ghz') # 33
## ---Frequency Domain Plots---:
net_dc = net[i,j].extrapolate_to_dc(kind='linear')
net_dc.plot_s_db(label='S'+comp+','+label, ax=ax0, color=color)
# set_axes(ax, title, xmin, xmax, ymin, ymax, nolim)
set_axes(ax0, 'Frequency Domain', 0.0, 6.0e9, -80.0, 10.0, nolim=False)
## ---Time Domain Plots---:
net_dc.plot_z_time_step(pad=0, window='hamming', z0=50, label='TD'+comp+','+label, ax=ax1, color=color)
Z_mean = display_mean_impedance(ax1, t1, t2, color)
# set_axes(ax, title, xmin, xmax, ymin, ymax, nolim)
set_axes(ax1, 'Time Domain', 0.0, 10.0, 0.0, 300.0, nolim=False)
# write to csv file
output_row = [label, t1, t2, round(Z_mean, 2)]
output_writer.writerow(output_row)
if cableName:
cable_ID = cableName
else:
cable_ID = getName(labels[0])
if verbose:
print("labels[0]: {0}, cable_ID: {1}".format(labels[0], cable_ID))
fig0.savefig("{0}/{1}_freq_time_Z_rf_S{2}.png".format(outDir, cable_ID, comp))
#pylab.show()
#input('hold on')
def main():
#######################################
# Options #
#######################################
parser = OptionParser()
parser.add_option('--createS2p', type='int', action='store',
default=1,
dest='createS2p',
help='bool if 1 then create .s2p files, if 0 then they already exist and no need to recreate them')
parser.add_option('--inputDir', metavar='T', type='string', action='store',
default='../example_data',
dest='inputDir',
help='directory with example input files')
parser.add_option('--inputTxtFiles', metavar='F', type='string', action='store',
default = "input_cable_data.txt",
dest='inputTxtFiles',
help='Input txt files')
parser.add_option('--cableName', metavar='T', type='string', action='store',
default='',
dest='cableName',
help='cable name (required for non-standard names)')
parser.add_option('--cableLength', metavar='F', type='string', action='store',
default = "35",
dest='cableLength',
help='cable lenght in cm')
parser.add_option('--t1', metavar='F', type='float', action='store',
default = 0.2,
dest='t1',
help='start time to take the average on the time domain plot')
parser.add_option('--t2', metavar='F', type='float', action='store',
default = 0.4,
dest='t2',
help='stop time to take the average on the time domain plot')
parser.add_option('--outputDir', metavar='T', type='string', action='store',
default='Plots',
dest='outputDir',
help='directory to store plots')
parser.add_option('--outputTouchstone', metavar='T', type='string', action='store',
default='s2pDir',
dest='outputTouchstone',
help='directory to store resulted touch stone files')
parser.add_option('--outputTouchstoneSubFile', metavar='T', type='string', action='store',
default='0',
dest='outputTouchstoneSubFile',
help='subfile to open from one of the 10 created .s2p files')
parser.add_option('--SParamterComp', metavar='T', type='string', action='store',
default='11',
dest='SParamterComp',
help='S-paramter to draw')
(options,args) = parser.parse_args()
createS2p = bool(options.createS2p)
inDir = options.inputDir
inputTxtFiles = options.inputTxtFiles
cableName = options.cableName
cableLength = options.cableLength
t1 = options.t1
t2 = options.t2
outDir = options.outputDir
s2pDir = options.outputTouchstone
subfile = options.outputTouchstoneSubFile
comp = options.SParamterComp
# ========= end: options ============= #
analyze(createS2p, inDir, inputTxtFiles, cableName, cableLength, t1, t2, outDir, s2pDir, subfile, comp)
if __name__ == "__main__":
main()
|
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|
import os
import time
import re
import codecs
import itertools
import numpy as np
import pandas as pd
import tensorflow as tf
import gensim
from gensim import utils
from twtokenize import tokenize
import util
from sklearn.model_selection import train_test_split
from ftfy import fix_text
class streamtwElec(object):
def __init__(self, dirname):
self.i=0
self.dirname = dirname
def __iter__(self):
for fname in os.listdir(self.dirname):
fname = os.path.join(self.dirname, fname)
if not os.path.isfile(fname):
continue
for line in utils.smart_open(fname):
line = line.split('\t')
id = line[1]
if line[2] == 'positive':
sent = 1
elif line[2] == 'negative':
sent = -1
elif line[2] == 'neutral':
sent = 0
senti = sent + 2
target = line[3].lower().strip()
location = line[4]
tw = line[-1].lower().strip()
tw = fix_text(tw.decode('utf-8')).encode('utf-8')
range = []
p = re.compile(r'(?<!\w)({0})(?!\w)'.format(target))
for m in p.finditer(tw.lower()):
range.append([m.start(),m.start()+len(m.group())])
if location != 'nan':
cc = 0
for a, b in enumerate(range):
if b[0]-1 <= int(location) <= b[1]+4:
wh = a
cc=1
if cc==0:
wh = 'nan'
else:
wh = location
if wh == 'nan':
tw=tw.replace(target,' '+target+' ')
tw=tw.replace(''.join(target.split()),' '+'_'.join(target.split())+' ')
tw=tw.replace(target,' '+'_'.join(target.split())+' ')
else:
try:
r = range[wh]
except:
print "Error at processing election data; at line 118 process_data.py!"
tw=tw[:r[0]]+ tw[r[0]:r[1]+2].replace(target, ' '+target+' ') + tw[r[1]+2:]
tw=tw[:r[0]]+ tw[r[0]:r[1]+4].replace(''.join(target.split()),' '+'_'.join(target.split())+' ') + tw[r[1]+4:]
tw=tw[:r[0]]+ tw[r[0]:r[1]+6].replace(target,' '+'_'.join(target.split())+' ') + tw[r[1]+6:]
tweet=tokenize(tw)
yield (tweet,'_'.join(target.split()),senti,id,wh)
class ElectionData:
def __init__(self, batch_size, dynamic_padding=False, preprocessing=False, embedding=True, saved=False, max_length=None):
train = ElectionData.read_data('../data/election-data/training/')
test = ElectionData.read_data('../data/election-data/testing/')
self.batch_size = batch_size
self.dynamic_padding = dynamic_padding
self.train_tweets, self.train_targets, self.train_y = zip(*train)
self.test_tweets, self.test_targets, self.test_y = zip(*test)
self.train_left_tweets = [ElectionData.split_tweet(self.train_tweets[i], self.train_targets[i])[0] for i in range(len(self.train_tweets))]
self.train_right_tweets = [ElectionData.split_tweet(self.train_tweets[i], self.train_targets[i])[1] for i in range(len(self.train_tweets))]
self.test_left_tweets = [ElectionData.split_tweet(self.test_tweets[i], self.test_targets[i])[0] for i in range(len(self.test_tweets))]
self.test_right_tweets = [ElectionData.split_tweet(self.test_tweets[i], self.test_targets[i])[1] for i in range(len(self.test_tweets))]
self.train_tweets = [ElectionData.replace_target(self.train_tweets[i], self.train_targets[i]) for i in range(len(self.train_tweets))]
self.test_tweets = [ElectionData.replace_target(self.test_tweets[i], self.test_targets[i]) for i in range(len(self.test_tweets))]
self.train_targets = [train_target.split('_') for train_target in self.train_targets]
self.test_targets = [test_target.split('_') for test_target in self.test_targets]
# Padding tweets (manually adding '<PAD> tokens')
if not self.dynamic_padding:
self.train_tweets = util.pad_sequences(self.train_tweets, pad_location='RIGHT')
self.test_tweets = util.pad_sequences(self.test_tweets, pad_location='RIGHT')
# Building vocabulary
self.vocab, self.vocab_inv = util.build_vocabulary(self.train_tweets + self.test_tweets)
if embedding:
# Vectorizing tweets - Glove embedding
start = time.clock()
print(' - Loading embedding..')
glove, self.glove_vec, self.glove_shape, glove_vocab = util.gensim_load_vec('../resources/wordemb/glove.twitter.word2vec.27B.100d.txt')
glove_vocab = [token.encode('utf-8') for token in glove_vocab]
self.glove_vocab_dict = {j:i for i, j in enumerate(glove_vocab)}
self.glove_vec = np.append(self.glove_vec, [[0]*self.glove_shape[1]], axis=0)
self.glove_shape = [self.glove_shape[0]+1, self.glove_shape[1]]
print(' - DONE')
print("time taken: %f mins"%((time.clock() - start)/60))
if saved==False:
start = time.clock()
print(' - Matching words-indices')
self.train_x = np.array([[self.glove_vocab_dict[token] if token in glove_vocab else 1193514 for token in tweet] for tweet in self.train_tweets])
self.train_left_x = np.array([[self.glove_vocab_dict[token] if token in glove_vocab else 1193514 for token in tweet] for tweet in self.train_left_tweets])
self.train_right_x = np.array([[self.glove_vocab_dict[token] if token in glove_vocab else 1193514 for token in tweet] for tweet in self.train_right_tweets])
self.test_x = np.array([[self.glove_vocab_dict[token] if token in glove_vocab else 1193514 for token in tweet] for tweet in self.test_tweets])
self.test_left_x = np.array([[self.glove_vocab_dict[token] if token in glove_vocab else 1193514 for token in tweet] for tweet in self.test_left_tweets])
self.test_right_x = np.array([[self.glove_vocab_dict[token] if token in glove_vocab else 1193514 for token in tweet] for tweet in self.test_right_tweets])
self.train_target_x = np.array([[self.glove_vocab_dict[token] if token in glove_vocab else 1193514 for token in target] for target in self.train_targets])
self.test_target_x = np.array([[self.glove_vocab_dict[token] if token in glove_vocab else 1193514 for token in target] for target in self.test_targets])
self.train_y = pd.get_dummies(self.train_y).values.astype(np.int32)
self.train_df = [(self.train_x[i], self.train_left_x[i], self.train_right_x[i], self.train_target_x[i], self.train_y[i])
for i in range(len(self.train_x))]
self.test_df = [(self.test_x[i], self.test_left_x[i], self.test_right_x[i], self.test_target_x[i], self.test_y[i])
for i in range(len(self.test_x))]
train_y = np.array([d[-1] for d in self.train_df])
self.train_df, self.dev_df = self.build_train_dev(train_y) # Dividing to train and dev set
print(' - DONE')
print("time taken: %f mins"%((time.clock() - start)/60))
print(" - Saving data")
np.save('../data/election-data/train_df.npy', self.train_df)
np.save('../data/election-data/dev_df.npy', self.dev_df)
np.save('../data/election-data/test_df.npy', self.test_df)
print(' - DONE')
else:
print(" - Loading data")
self.train_df = np.load('../data/election-data/train_df.npy')
self.dev_df = np.load('../data/election-data/dev_df.npy')
self.test_df = np.load('../data/election-data/test_df.npy')
print(' - DONE')
else:
# Vectorizing tweets - one-hot-vector
self.train_x = np.array([[self.vocab[token] for token in tweet] for tweet in self.train_tweets])
self.test_x = np.array([[self.vocab[token] for token in tweet] for tweet in self.test_tweets])
self.create_batches()
self.reset_batch_pointer()
@staticmethod
def read_data(data_dir):
inputs=streamtwElec(data_dir)
data = []
for i in inputs:
tw = i[0]
target = i[1]
if target=='"long_term_economic"_plans':
target='long_term_economic'
label = i[2]
data.append([tw, target, label])
return data
@staticmethod
def replace_target(tweet, target):
tweet = list(itertools.chain.from_iterable((target.split('_')) if item == target else (item, ) for item in tweet))
return tweet
@staticmethod
def split_tweet(tweet, target):
target_index = tweet.index(target)
left = tweet[0:target_index] + target.split('_')
right = target.split('_') + tweet[target_index+1:]
right = [i for i in reversed(right)]
return left, right
def build_train_dev(self, train_y, dev_size=0.3, random_seed=42):
return train_test_split(
self.train_df,
test_size=dev_size,
random_state=random_seed,
stratify=train_y)
def create_batches(self):
self.train_df = self.shuffle_data(self.train_df) # Randomlise data
#train set:
self.train_x = np.array([d[0] for d in self.train_df])
self.train_size = np.array([len(seq) for seq in self.train_x])
self.train_y = np.array([d[-1] for d in self.train_df])
self.train_left_x = np.array([d[1] for d in self.train_df])
self.train_left_size = np.array([len(seq) for seq in self.train_left_x])
self.train_right_x = np.array([d[2] for d in self.train_df])
self.train_right_size = np.array([len(seq) for seq in self.train_right_x])
self.train_target_x = np.array([d[3] for d in self.train_df])
self.train_x = util.pad_sequences(self.train_x, dynamic_padding=self.dynamic_padding, pad_location='RIGHT') # Padding
self.train_left_x = util.pad_sequences(self.train_left_x, dynamic_padding=self.dynamic_padding, pad_location='RIGHT')
self.train_right_x = util.pad_sequences(self.train_right_x, dynamic_padding=self.dynamic_padding, pad_location='RIGHT')
self.train_x = np.array(self.train_x)
self.train_left_x = np.array(self.train_left_x)
self.train_right_x = np.array(self.train_right_x)
#dev set:
self.dev_x = np.array([d[0] for d in self.dev_df])
self.dev_size = np.array([len(seq) for seq in self.dev_x])
self.dev_y = np.array([d[-1] for d in self.dev_df])
self.dev_left_x = np.array([d[1] for d in self.dev_df])
self.dev_left_size = np.array([len(seq) for seq in self.dev_left_x])
self.dev_right_x = np.array([d[2] for d in self.dev_df])
self.dev_right_size = np.array([len(seq) for seq in self.dev_right_x])
self.dev_target_x = np.array([d[3] for d in self.dev_df])
self.dev_x = util.pad_sequences(self.dev_x, dynamic_padding=self.dynamic_padding, pad_location='RIGHT') # Padding
self.dev_left_x = util.pad_sequences(self.dev_left_x, dynamic_padding=self.dynamic_padding, pad_location='RIGHT')
self.dev_right_x = util.pad_sequences(self.dev_right_x, dynamic_padding=self.dynamic_padding, pad_location='RIGHT')
self.dev_x = np.array(self.dev_x)
self.dev_left_x = np.array(self.dev_left_x)
self.dev_right_x = np.array(self.dev_right_x)
#test set:
self.test_x = np.array([d[0] for d in self.test_df])
self.test_size = np.array([len(seq) for seq in self.test_x])
self.test_y = np.array([d[-1] for d in self.test_df])
self.test_left_x = np.array([d[1] for d in self.test_df])
self.test_left_size = np.array([len(seq) for seq in self.test_left_x])
self.test_right_x = np.array([d[2] for d in self.test_df])
self.test_right_size = np.array([len(seq) for seq in self.test_right_x])
self.test_target_x = np.array([d[3] for d in self.test_df])
self.test_x = util.pad_sequences(self.test_x, dynamic_padding=self.dynamic_padding, pad_location='RIGHT') # Padding
self.test_left_x = util.pad_sequences(self.test_left_x, dynamic_padding=self.dynamic_padding, pad_location='RIGHT')
self.test_right_x = util.pad_sequences(self.test_right_x, dynamic_padding=self.dynamic_padding, pad_location='RIGHT')
self.test_x = np.array(self.test_x)
self.test_left_x = np.array(self.test_left_x)
self.test_right_x = np.array(self.test_right_x)
# Vectorizing labels
# self.train_y = pd.get_dummies(self.train_y).values.astype(np.int32)
# self.dev_y = pd.get_dummies(self.dev_y).values.astype(np.int32)
self.test_y = pd.get_dummies(self.test_y).values.astype(np.int32)
# Creating training batches
self.num_batches = len(self.train_x)//self.batch_size
if self.num_batches==0:
assert False, "Not enough data for the batch size."
self.batch_df = np.array_split(self.train_df, self.num_batches) # Splitting train set into batches based on num_batches
assert np.array([d[-1] for d in self.batch_df[-1]]).shape[1] == 3, "Watch out! All batches must contain 3 labels!"
def next_batch(self):
df = self.batch_df[self.pointer]
x = np.array([d[0] for d in df])
xl = np.array([d[1] for d in df])
xr = np.array([d[2] for d in df])
tar = np.array([d[3] for d in df])
y = np.array([d[-1] for d in df])
# y = pd.get_dummies(y).values.astype(np.int32)
seq_len = [len(seq) for seq in x]
seq_len_l = [len(seq) for seq in xl]
seq_len_r = [len(seq) for seq in xr]
if self.dynamic_padding:
x = np.array(self.pad_minibatches(x, 'RIGHT'))
xl = np.array(self.pad_minibatches(xl, 'RIGHT'))
xr = np.array(self.pad_minibatches(xr, 'RIGHT'))
self.pointer += 1
return x, y, seq_len, xl, seq_len_l, xr, seq_len_r, tar
def reset_batch_pointer(self):
self.train_df = self.shuffle_data(self.train_df)
self.pointer = 0
def pad_minibatches(self, x, pad_location):
x = util.pad_sequences(x, dynamic_padding=self.dynamic_padding, pad_location=pad_location)
return x
@staticmethod
def shuffle_data(a):
a = np.array(a)
p = np.random.permutation(len(a))
return a[p]
|
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|
program decl_all
integer(KIND=8) a
integer :: b, c = -10
real(KIND=4) :: d = -99.34
logical :: e = .true.
real(4) :: arr(10,-1:100), f
integer(2), DIMENSION(1:10,-1:100, 9:10) :: g
end program decl_all
|
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|
import re
import pandas as pd
import numpy as np
from avaml.aggregatedata import PROBLEMS
from avaml.aggregatedata.download import CAUSES, REG_ENG_V4, REGOBS_CLASSES, _camel_to_snake, REGOBS_SCALARS
def coeff(series):
x = np.arange(series.shape[0])
y = series.values
return np.linalg.lstsq(np.vstack([x, np.ones(len(x))]).T, y, rcond=None)[0][0]
def mode(series):
return series.mode().iloc[0]
real_funcs = ['min', 'max', 'mean', 'median', 'std', coeff]
discrete_funcs = real_funcs + [mode]
binary_funcs = ['median', 'mean', coeff]
regobs_discrete_funcs = ['sum', coeff]
regobs_scalar_funcs = ['max', coeff]
real_columns = {
'precip',
'precip_most_exposed',
'temp_freeze_lev',
'temp_lev',
'temp_max',
'temp_min',
'wind_change_speed',
'wind_speed'
}
discrete_columns = {
'danger_level',
'problem_new-loose',
'problem_wet-loose',
'problem_new-slab',
'problem_drift-slab',
'problem_pwl-slab',
'problem_wet-slab',
'problem_glide',
'problem_amount',
}
binary_columns = {
'wind_dir_N',
'wind_dir_NE',
'wind_dir_E',
'wind_dir_SE',
'wind_dir_S',
'wind_dir_SW',
'wind_dir_W',
'wind_dir_NW',
'wind_chg_dir_N',
'wind_chg_dir_NE',
'wind_chg_dir_E',
'wind_chg_dir_SE',
'wind_chg_dir_S',
'wind_chg_dir_SW',
'wind_chg_dir_W',
'wind_chg_dir_NW',
'wind_chg_start_0',
'wind_chg_start_6',
'wind_chg_start_12',
'wind_chg_start_18',
'temp_fl_start_0',
'temp_fl_start_6',
'temp_fl_start_12',
'temp_fl_start_18'
'emergency_warning',
}
for prob in PROBLEMS.values():
discrete_columns = discrete_columns.union({f"problem_{prob}_{attr}" for attr in ['dsize', 'prob', 'trig', 'dist']})
binary_columns = binary_columns.union({f"problem_{prob}_cause_{cause}" for cause in CAUSES.values()})
regobs_discrete_columns = set()
for reg_type, reg_eng in REG_ENG_V4.items():
for reg_class, subclasses in REGOBS_CLASSES[reg_type].items():
reg_class = _camel_to_snake(reg_class)
for subclass in subclasses.values():
subclass = _camel_to_snake(subclass)
for n in range(0, 5):
col = f"regobs_{reg_eng}_{reg_class}_{subclass}_{n}"
regobs_discrete_columns = regobs_discrete_columns.union({col})
regobs_scalar_columns = set()
for reg_type, reg_eng in REG_ENG_V4.items():
for reg_scalar in REGOBS_SCALARS[reg_type].keys():
reg_scalar = _camel_to_snake(reg_scalar)
for n in range(0, 5):
col = f"regobs_{reg_eng}_{reg_scalar}_{n}"
regobs_scalar_columns = regobs_scalar_columns.union({col})
def to_time_parameters(labeled_data):
labeled_data = labeled_data.drop_regions()
data = labeled_data.data
real_groups = data.loc[:, real_columns.intersection(data.columns.get_level_values(0))].T.groupby(level=0)
discrete_groups = data.loc[:, discrete_columns.intersection(data.columns.get_level_values(0))].T.groupby(level=0)
binary_groups = data.loc[:, binary_columns.intersection(data.columns.get_level_values(0))].T.groupby(level=0)
regobs_discrete_groups = data.loc[
:, regobs_discrete_columns.intersection(data.columns.get_level_values(0))
].T.groupby(by=lambda x: x[0][:-1] + str(x[1])).sum()
regobs_discrete_groups = regobs_discrete_groups.groupby(by=lambda x: x[:-2])
regobs_scalar_groups = data.loc[
:, regobs_scalar_columns.intersection(data.columns.get_level_values(0))
].T.groupby(by=lambda x: x[0][:-1] + str(x[1])).max()
regobs_scalar_groups = regobs_scalar_groups.groupby(by=lambda x: x[:-2])
real_groups_params = real_groups.agg(real_funcs).T.unstack()
discrete_groups_params = discrete_groups.agg(discrete_funcs).T.unstack()
binary_groups_params = binary_groups.agg(binary_funcs).T.unstack()
regobs_discrete_groups_params = regobs_discrete_groups.agg(regobs_discrete_funcs).T.unstack()
regobs_scalar_groups_params = regobs_scalar_groups.agg(regobs_scalar_funcs).T.unstack()
return pd.concat([
real_groups_params,
discrete_groups_params,
binary_groups_params,
regobs_discrete_groups_params,
regobs_scalar_groups_params,
], axis=1).sort_index(axis=1)
|
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|
import sys
import os
import logging
import time
import numpy as np
sys.path.append('../../pyNeuIR/')
from pyNeuIR.utils.preprocess import pad_sequences, load_idfs, load_histograms
from pyNeuIR.utils.pairs_generator import PairsGenerator
from pyNeuIR.models.drmm import DRMM, HingeLoss
from pyNeuIR.configs.drmm_config import config
import torch
from torch.autograd import Variable
torch.manual_seed(222)
use_cuda = torch.cuda.device_count() > 0
if use_cuda:
torch.cuda.manual_seed(222)
def get_model_size(model):
return sum([ p.size(0) if len(p.size()) == 1 else p.size(0)*p.size(1) for p in model.parameters()])
def train(trainloader, validationloader, histograms, idfs, save_dir, experiment_name):
global logger
drmm = DRMM(1)
if use_cuda:
drmm = drmm.cuda()
criterion = HingeLoss()
optimizer = torch.optim.Adagrad(drmm.parameters(),lr = 0.001)
logger.info("Start training {} experiment with {} parameters".format(experiment_name, get_model_size(drmm)))
for epoch in range(100):
train_loss = []
time_start = time.time()
for i, data in enumerate(trainloader, 0):
queries, docs_h, docs_l = data
histograms_h = torch.stack([histograms[qid][doc] for qid, doc in zip(queries, docs_h)])
histograms_l = torch.stack([histograms[qid][doc] for qid, doc in zip(queries, docs_l)])
queries_ids = torch.stack([idfs[qid] for qid in queries])
histograms_h = Variable(histograms_h)
histograms_l = Variable(histograms_l)
queries_ids = Variable(queries_ids)
if use_cuda:
histograms_h = histograms_h.cuda()
histograms_l = histograms_l.cuda()
queries_ids = queries_ids.cuda()
score_h = drmm(histograms_h,queries_ids)
score_l = drmm(histograms_l,queries_ids)
optimizer.zero_grad()
loss = criterion(score_h,score_l)
train_loss.append(loss.data)
loss.backward()
optimizer.step()
time_training = time.time() - time_start
validation_loss = validate(drmm, criterion, validationloader, histograms, idfs)
logger.info('Epoch : {}\tTrainingLoss: {}\tValidationLoss: {}\tTime: {}'.format(epoch, np.mean(train_loss).cpu().numpy()[0],
validation_loss.cpu().numpy()[0],time_training))
torch.save(
drmm.state_dict(),
open(os.path.join(
save_dir,
experiment_name + '_epoch_%d' % (epoch) + '.model'), 'wb'
)
)
def validate(drmm, criterion, validationloader, histograms, idfs):
validation_losses = []
for i, data in enumerate(validationloader, 0):
queries, docs_h, docs_l = data
histograms_h = torch.stack([histograms[qid][doc] for qid, doc in zip(queries, docs_h)])
histograms_l = torch.stack([histograms[qid][doc] for qid, doc in zip(queries, docs_l)])
queries_idfs = torch.stack([idfs[qid] for qid in queries])
histograms_h = Variable(histograms_h, requires_grad=False)
histograms_l = Variable(histograms_l, requires_grad=False)
queries_idfs = Variable(queries_idfs, requires_grad=False)
if use_cuda:
histograms_h = histograms_h.cuda()
histograms_l = histograms_l.cuda()
queries_idfs = queries_idfs.cuda()
score_h = drmm(histograms_h,queries_idfs)
score_l = drmm(histograms_l,queries_idfs)
loss = criterion(score_h,score_l)
validation_losses.append(loss.data)
return np.mean(validation_losses)
def main():
train_file = sys.argv[1]
validation_file = sys.argv[2]
histogram_file = sys.argv[3]
save_dir = sys.argv[4]
experiment_name = sys.argv[5]
logging.basicConfig(filename=experiment_name + ".log", level=logging.INFO,
format='%(asctime)s.%(msecs)03d %(levelname)s %(module)s - %(funcName)s: %(message)s', datefmt="%Y-%m-%d %H:%M:%S")
global logger
logger = logging.getLogger(experiment_name)
logger.info("Training from {} and validation from {}.".format(train_file,validation_file))
logger.info("Loading histograms from {}.".format(histogram_file))
histograms = load_histograms(histogram_file,5)
logger.info("Loading ids from {}.".format(config["queries_idfs"]))
idfs = load_idfs(config["queries_idfs"],5)
logger.info("Loading training pairs generator.")
train_generator = PairsGenerator(config["pairs_file"],train_file)
logger.info("Loading validation pairs generator.")
validation_generator = PairsGenerator(config["pairs_file"],validation_file)
trainloader = torch.utils.data.DataLoader(train_generator, batch_size=20, shuffle=True)
validationloader = torch.utils.data.DataLoader(validation_generator, batch_size=len(validation_generator))
train(trainloader, validationloader, histograms, idfs, save_dir, experiment_name)
main()
|
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|
// Group E - Excel Visualization
//
// by Scott Sidoli
//
// 6-15-19
//
// Main.cpp
//
// In this work we use the excel visualization functionality to produce spreadsheet output for the
// four batches. It should be noted that some of the includes need to have the path adjusted to work
// other machines. We describe the four batches, create row labels for the S value and column labels
// are the call/put prices for a given batch. We use an if-else loop inside a for-loop to produce the
// matrix output and then send the output to an excel spreadsheet. We include all our option class
// functionality.
#include "C:\Users\ssido\OneDrive\Desktop\Level9\Level9\Level9Code\Level9Code\UtilitiesDJD\ExcelDriver\ExcelDriverLite.hpp"
#include "C:\Users\ssido\OneDrive\Desktop\Level9\Level9\Level9Code\Level9Code\UtilitiesDJD\ExcelDriver\Utilities.hpp"
#include "C:\Users\ssido\OneDrive\Desktop\Level9\Level9\Level9Code\Level9Code\UtilitiesDJD\VectorsAndMatrices\Vector.hpp"
#include "C:\Users\ssido\OneDrive\Desktop\Level9\Level9\Level9Code\Level9Code\UtilitiesDJD\ExceptionClasses\DatasimException.hpp"
#include <iostream>
#include "EuropeanOption.hpp"
#include "MeshArray.hpp"
#include <boost/tuple/tuple_io.hpp>
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <fstream>
#include <cmath>
#include <boost/numeric/ublas/matrix.hpp>
#include "C:\Users\ssido\OneDrive\Desktop\Level9\Level9\Level9Code\Level9Code\UtilitiesDJD\VectorsAndMatrices\NestedMatrix.hpp"
using NumericMatrix = boost::numeric::ublas::matrix<double>; // using NumericMatrix = NestedMatrix<double>;
using namespace std;
int main()
{
curr_stock_price S_start = (curr_stock_price) 10.0;
curr_stock_price S_end = (curr_stock_price) 50.0;
curr_stock_price S_interval = (curr_stock_price) 1.0;
vector<curr_stock_price> S_array = MeshArray(S_start, S_end, S_interval);
// Batch 1
Time T1 = (Time) 0.25;
Strike_Price K1 = (Strike_Price)65;
Volatility sig1 = (Volatility) 0.30;
rate r1 = (rate) 0.08;
cost_of_carry b1 = (cost_of_carry) 0.08;
curr_stock_price S1 = (curr_stock_price) 60.0;
// Create option and set parameters
EuropeanOption option1;
option1.SetOption(T1, K1, sig1, r1, b1, S1);
// Batch 2
Time T2 = (Time) 1.0;
Strike_Price K2 = (Strike_Price) 100.0;
Volatility sig2 = (Volatility) 0.2;
rate r2 = (rate) 0.00;
cost_of_carry b2 = (cost_of_carry) 0.00;
curr_stock_price S2 = (curr_stock_price) 100.0;
// Create option and set parameters
EuropeanOption option2;
option2.SetOption(T2, K2, sig2, r2, b2, S2);
// Batch 3
Time T3 = (Time) 1.0;
Strike_Price K3 = (Strike_Price) 10.0;
Volatility sig3 = (Volatility) 0.50;
rate r3 = (rate) 0.12;
cost_of_carry b3 = (cost_of_carry) 0.12;
curr_stock_price S3 = (curr_stock_price) 5.0;
// Create option and set parameters
EuropeanOption option3;
option3.SetOption(T3, K3, sig3, r3, b3, S3);
// Batch 4
Time T4 = (Time) 30.0;
Strike_Price K4 = (Strike_Price) 100.0;
Volatility sig4 = (Volatility) 0.30;
rate r4 = (rate) 0.08;
cost_of_carry b4 = (cost_of_carry) 0.08;
curr_stock_price S4 = (curr_stock_price) 100.0;
// Create option and set parameters
EuropeanOption option4;
option4.SetOption(T4, K4, sig4, r4, b4, S4);
// Now we create Row and column labels Rows labeled by S-value, column by Batch num call/put
stringstream ss;
string str;
list<string> rowLabels;
for (unsigned int i = 0; i < S_array.size(); ++i)
{
ss << i + 10;
ss >> str;
rowLabels.push_back(str);
ss.clear();
}
list<string> colLabels{ "Batch 1 Call", "Batch 1 Put", "Batch 2 Call", "Batch 2 Put", "Batch 3 Call", "Batch 3 Put",
"Batch 4 Call", "Batch 4 Put"};
// Now we write the sheet name
string sheetName("Option Prices");
NumericMatrix PriceMatrix(rowLabels.size(), colLabels.size());
for (unsigned int i = 0; i < PriceMatrix.size1(); i++)
{
for (unsigned int j = 0; j < PriceMatrix.size2(); j++)
{
if (j == 0)
{
option1.SetOption(S_array[i]);
PriceMatrix(i, j) = option1.CallPriceEuro();
}
else if ( j == 1)
{
option1.SetOption(S_array[i]);
PriceMatrix(i, j) = option1.PutPriceEuro();
}
else if (j == 2)
{
option2.SetOption(S_array[i]);
PriceMatrix(i, j) = option2.CallPriceEuro();
}
else if (j == 3)
{
option2.SetOption(S_array[i]);
PriceMatrix(i, j) = option2.PutPriceEuro();
}
else if (j == 4)
{
option3.SetOption(S_array[i]);
PriceMatrix(i, j) = option3.CallPriceEuro();
}
else if (j == 5)
{
option3.SetOption(S_array[i]);
PriceMatrix(i, j) = option3.PutPriceEuro();
}
else if (j == 6)
{
option4.SetOption(S_array[i]);
PriceMatrix(i, j) = option4.CallPriceEuro();
}
else if (j == 7)
{
option4.SetOption(S_array[i]);
PriceMatrix(i, j) = option4.PutPriceEuro();
}
}
}
ExcelDriver& excel = ExcelDriver::Instance();
excel.MakeVisible(true);
long row = 1;
long col = 1;
excel.AddMatrix<NumericMatrix>(PriceMatrix, sheetName, rowLabels, colLabels, row, col);
return 0;
}
|
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|
from sklearn.feature_selection import f_regression
import numpy as np
from sklearn import svm
from sklearn import linear_model
import svmcrossvalidate
from array import array
# Main
#f = open("testdata1.txt")
f = open("testdata.txt")
mylist = f.readlines()
testdata = []
for i in range(0, len(mylist), 1):
l = mylist[i].split()
for j in range(0, len(l), 1):
l[j] = float(l[j])
#testdata.append(l)
testdata.append(array('f',l))
f.close()
#print(testdata)
#f = open("traindata1.txt")
f = open("traindata.txt")
mylist = f.readlines()
train = []
for i in range(0, len(mylist), 1):
l = mylist[i].split()
for j in range(0, len(l), 1):
l[j] = float(l[j])
#train.append(l)
train.append(array('f',l))
f.close()
#print(train)
#X is for train data
X = train
#f = open("trueclass1.txt")
f = open("trueclass.txt")
mylist = f.readlines()
trainlabels = []
for i in range(0, len(mylist), 1):
l = mylist[i].split()
for j in range(0, len(l), 1):
l[j] = float(l[j])
trainlabels.append(l[0])
f.close()
y = trainlabels
#print(trainlabels)
#f_output = f_regression(X,y)
f_output = f_regression(X, y, center=True)
#print(f_output[0])
#print(f_output[1])
cols = len(X[0])
indices = []
for i in range(0, cols, 1):
indices.append(i)
fscores = f_output[0]
fscores_dict = {}
for i in range(0, len(f_output[0]), 1):
fscores_dict[i] = fscores[i]
sorted_indices = sorted(indices, key=fscores_dict.__getitem__, reverse=True)
#print(sorted_indices)
print(sorted_indices[:15])
# Reduce both traindata and testdata to top 15 ranked features
newtestdata= []
newtrain = []
rows = len(testdata)
cols = len(testdata[0])
print("**testdata**")
print(rows)
print(cols)
for i in range(0, rows, 1):
l1 = []
for j in range(0, cols, 1):
if (j in sorted_indices[:15]):
l1.append(testdata[i][j])
newtestdata.append(l1)
rows = len(train)
cols = len(train[0])
print("**traindata**")
print(rows)
print(cols)
for i in range(0, rows, 1):
l2 = []
for j in range(0, cols, 1):
if (j in sorted_indices[:15]):
l2.append(train[i][j])
newtrain.append(l2)
#print(newtestdata)
#print(newtrain)
##### Cross-validated linear SVM #####
[bestC,besterror] = svmcrossvalidate.getbestC(newtrain,trainlabels)
print("Best C = ", bestC)
print("Best cross validation error = ", besterror)
# Predict labels of test data
clf = svm.LinearSVC(C=bestC, max_iter=100000)
clf.fit(train,trainlabels)
prediction = clf.predict(testdata)
f = open("testlabel_prediction.txt", 'w')
for i in range(0, len(prediction), 1):
#print("Predict test label:", int(prediction[i]))
f.write(str(int(prediction[i]))+ " " + str(i) + "\n")
f.close()
|
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|
import os
import cv2
import time
import random
import traceback
import subprocess
import numpy as np
import concurrent.futures
from PyQt5.QtCore import QObject, pyqtSignal
# QWidget无法在主线程之外被调用，因此构造一个QObject，使用自定义的信号来触发主线程的槽函数
# 具体可以看：https://stackoverflow.com/questions/2104779/qobject-qplaintextedit-multithreading-issues
# stackoverflow中的回答很好的解释了原因，但是没有给出示例代码。
# 我经过搜索以及研究，做出了解决方案，有同样需求的开发者可以参考本程序。
class UpdateLog(QObject):
# 写入log框信号
update_signal = pyqtSignal()
# 程序出错停止当前执行任务信号
error_stop_signal = pyqtSignal()
# 程序执行完成信号
finish_exec_signal = pyqtSignal()
def __init__(self):
QObject.__init__(self)
def update(self):
self.update_signal.emit()
def error_stop(self):
self.error_stop_signal.emit()
def finish_exec(self):
self.finish_exec_signal.emit()
class Utils():
def __init__(self):
# debug开关（开启后，成功匹配会弹出图片，上面用圈标明了匹配到的坐标点范围）
self.debug = False
# 计数
self.cnt = 0
# 分辨率相关
self.screen_height = 2560
self.screen_width = 1440
self.scale_percentage = 100
# log临时堆栈，输出后会pop掉
self.text = []
# 图像匹配阈值
self.threshold = 0.90
# 停止操作回调
self.stop_callback = False
# wifi_adb默认地址
self.wifi_adb_addr = "192.168.1.239:5555"
# log转发
self.logger = UpdateLog()
# 加载图像资源
def load_res(self):
# 匹配对象的字典
self.res = {}
file_dir = os.path.join(os.getcwd(), "img")
temp_list = os.listdir(file_dir)
for item in temp_list:
self.res[item] = {}
res_path = os.path.join(file_dir, item)
self.res[item]["img"] = cv2.imread(res_path)
# 如果不是原尺寸（1440P），进行对应缩放操作
if self.scale_percentage != 100:
self.res[item]["width"] = int(self.res[item]["img"].shape[1] * self.scale_percentage / 100)
self.res[item]["height"] = int(self.res[item]["img"].shape[0] * self.scale_percentage / 100)
self.res[item]["img"] = cv2.resize(self.res[item]["img"], (self.res[item]["width"], self.res[item]["height"]), interpolation=cv2.INTER_AREA)
else:
self.res[item]["height"], self.res[item]["width"], self.res[item]["channel"] = self.res[item]["img"].shape[::]
# 获取截图
def get_img(self, pop_up_window=False, save_img=False, file_name='screenshot.png'):
image_bytes = self.exec_cmd("adb exec-out screencap -p")
if image_bytes == b'':
self.write_log(f"截图失败！请检查adb是否已经跟手机连接！")
self.error_stop()
else:
self.target_img = cv2.imdecode(np.fromstring(image_bytes, dtype='uint8'), cv2.IMREAD_COLOR)
if save_img:
cv2.imwrite(file_name, self.target_img)
if pop_up_window:
self.show_img()
def show_img(self):
cv2.namedWindow("screenshot", cv2.WINDOW_NORMAL)
cv2.resizeWindow('screenshot', 360, 640)
cv2.imshow("screenshot", self.target_img)
cv2.waitKey(0)
cv2.destroyWindow("screenshot")
# 匹配并获取中心点
def match(self, img_name):
# 从加载好的图像资源中获取数据
find_img = self.res[img_name]["img"]
find_height = self.res[img_name]["height"]
find_width = self.res[img_name]["width"]
# 匹配
try:
result = cv2.matchTemplate(self.target_img, find_img, cv2.TM_CCOEFF_NORMED)
min_val, max_val, min_loc, max_loc = cv2.minMaxLoc(result)
except:
self.write_log(f"OpenCV对比失败！请使用杂项中的截图功能来测试能否正常截图！")
self.error_stop()
print(f"{img_name}最大匹配度：{max_val}")
if max_val < self.threshold:
return False
# 计算位置
self.pointUpLeft = max_loc
self.pointLowRight = (int(max_loc[0] + find_width), int(max_loc[1] + find_height))
self.pointCentre = (int(max_loc[0] + (find_width / 2)), int(max_loc[1] + (find_height / 2)))
if self.debug:
self.draw_circle()
self.write_log(f"匹配到{img_name}，匹配度：{max_val}")
return True
# 匹配多个结果
def multiple_match(self, img_name):
# 用于存放匹配结果
match_res = []
# 从加载好的图像资源中获取数据
find_img = self.res[img_name]["img"]
find_height = self.res[img_name]["height"]
find_width = self.res[img_name]["width"]
# OpenCV匹配多个结果
# https://stackoverflow.com/a/58514954/12766614
try:
result = cv2.matchTemplate(self.target_img, find_img, cv2.TM_CCOEFF_NORMED)
# max_val设置为1，从而能够进入循环
max_val = 1
cnt = 0
while max_val > self.threshold:
min_val, max_val, min_loc, max_loc = cv2.minMaxLoc(result)
if max_val > self.threshold:
# 抹除最大值周围的数值，从而可以在下一次找到其它位置的（第二）最大值
result[max_loc[1]-find_height//2:max_loc[1]+find_height//2+1, max_loc[0]-find_width//2:max_loc[0]+find_width//2+1] = 0
# 计算位置
pointUpLeft = max_loc
pointLowRight = (int(max_loc[0] + find_width), int(max_loc[1] + find_height))
pointCentre = (int(max_loc[0] + (find_width / 2)), int(max_loc[1] + (find_height / 2)))
# image = cv2.rectangle(image, (max_loc[0],max_loc[1]), (max_loc[0]+find_width+1, max_loc[1]+find_height+1), (0,0,0))
# cv2.imwrite(f'output_{cnt}.png', 255*result) 灰阶输出，越亮匹配度越高
cnt += 1
match_res.append(pointCentre)
print(f"{img_name}找到{cnt}个，匹配度：{max_val}")
except:
self.write_log(f"OpenCV对比失败！请使用杂项中的截图功能来测试能否正常截图！")
self.error_stop()
return match_res
# 立即截图，然后匹配，返回boolean
def current_match(self, img_name):
self.get_img()
return self.match(img_name)
# 立即截图，然后匹配多个，返回数组，内含若干匹配成功的tuple
def current_multiple_match(self, img_name):
self.get_img()
return self.multiple_match(img_name)
# 点击（传入坐标）
# 也可以接受比例形式坐标，例如(0.5, 0.5, percentage=True)就是点屏幕中心
# 可以传入randomize=False来禁用坐标的随机偏移
def tap(self, x_coord=None, y_coord=None, percentage=False, randomize=True):
if x_coord is None and y_coord is None:
x_coord, y_coord = self.get_coord(randomize=randomize)
if percentage:
x_coord = int(x_coord * self.screen_width * (self.scale_percentage / 100))
y_coord = int(y_coord * self.screen_height * (self.scale_percentage / 100))
x_coord = self.randomize_coord(x_coord, 5)
y_coord = self.randomize_coord(y_coord, 5)
self.write_log(f"点击坐标：{(x_coord, y_coord)}")
cmd = f"adb shell input tap {x_coord} {y_coord}"
self.exec_cmd(cmd)
# 滑动 / 长按
# 本函数仅用于debug
def swipe(self, fromX=None, fromY=None, toX=None, toY=None, swipe_time=200):
if toX is None and toY is None:
swipe_time = 500
self.write_log(f"长按坐标：{(fromX, fromY)}")
cmd = f"adb shell input swipe {fromX} {fromY} {fromX} {fromY} {swipe_time}"
else:
self.write_log(f"滑动：从{(fromX, fromY)}到{(toX, toY)}")
cmd = f"adb shell input swipe {fromX} {fromY} {toX} {toY} {swipe_time}"
self.exec_cmd(cmd)
# 执行指令
def exec_cmd(self, cmd, new_thread=False, show_output=False):
def do_cmd(cmd):
pipe = subprocess.Popen(cmd, stdin=subprocess.PIPE, stdout=subprocess.PIPE, shell=True)
return pipe.stdout.read()
if new_thread:
if show_output:
self.write_log(f"执行{cmd}")
with concurrent.futures.ThreadPoolExecutor() as executor:
future = executor.submit(do_cmd, cmd)
ret_val = future.result()
else:
if show_output:
self.write_log(f"执行{cmd}")
ret_val = do_cmd(cmd)
if show_output:
self.write_log(ret_val.decode("utf-8"))
return ret_val
# 控制台显示执行次数
def show_cnt(self):
self.write_log(f"已重试{self.cnt}次！")
# adb连接（WIFI）
def adb_connect(self):
self.exec_cmd(f"adb connect {self.wifi_adb_addr}", new_thread=True, show_output=True)
# adb devices（验证设备是否连接）
def adb_devices(self):
self.exec_cmd("adb devices", new_thread=True, show_output=True)
# 查看adb版本
def adb_version(self):
self.exec_cmd("adb --version", new_thread=True, show_output=True)
# 画点（测试用）
def draw_circle(self):
cv2.circle(self.target_img, self.pointUpLeft, 10, (255, 255, 255), 5)
cv2.circle(self.target_img, self.pointCentre, 10, (255, 255, 255), 5)
cv2.circle(self.target_img, self.pointLowRight, 10, (255, 255, 255), 5)
self.show_img()
# 获取匹配到的坐标
def get_coord(self, randomize=True):
x_coord = self.pointCentre[0]
y_coord = self.pointCentre[1]
if randomize:
x_coord = self.randomize_coord(x_coord, 20)
y_coord = self.randomize_coord(y_coord, 15)
return x_coord, y_coord
# 坐标进行随机偏移处理
def randomize_coord(self, coord, diff):
return random.randint(coord - diff, coord + diff)
# 在GUI的文本框内写入log
def write_log(self, text):
self.text.append(text)
self.logger.update()
# 判断文件是否为空
def is_file_empty(self, file_name):
return os.stat(file_name).st_size == 0
# 致命错误时转发到GUI实现停止当前任务
def error_stop(self):
self.stop_callback = False
self.logger.error_stop()
# 等待GUI线程的回调，确保当前任务已经停止
while True:
if self.stop_callback:
self.stop_callback = False
break
def auto_screenshot_on_win(self, mode):
def check_dir(mode):
if not os.path.isdir("homework"):
os.mkdir("homework")
if not os.path.isdir(os.path.join("homework", mode)):
os.mkdir(os.path.join("homework", mode))
if self.ui.checkBox_14.isChecked():
if self.match("stat_button.png"):
self.tap()
name = time.strftime("%Y-%m-%d_%H%M%S", time.localtime()) + ".png"
relative_path = os.path.join("homework", mode, name)
check_dir(mode)
# sleep3秒，确保能截到图，否则游戏内战斗数据有可能还没加载完全
time.sleep(3)
self.get_img(save_img=True, file_name=relative_path)
self.current_match("close_stat_button.png")
self.tap()
self.write_log(f"截图成功，存放在{relative_path}")
# 预设的一些指令组
class Command():
def __init__(self):
self.utils = Utils()
# 指令与执行操作的对应关系
self.func_to_img = {
"click_battle_retry": ["after_battle_retry_button.png", "have_func"],
"click_next_stage": ["next_stage_button.png", "have_func"],
"click_continue": ["continue_button.png", "have_func"],
"click_continue_campaign": ["continue_button.png"],
"no_click_next_stage": ["next_stage_button.png", "have_func"],
"no_click_continue": ["continue_button.png", "have_func"],
"click_battle": ["battle_button.png"],
"click_battle_pause": ["in_battle_pause_button.png"],
"click_battle_exit": ["in_battle_exit_button.png"],
"click_next_team": ["next_team_button.png"],
"click_challenge": ["challenge_button.png"],
"check_boss_stage": ["challenge_boss_button.png"],
"check_bundle_pop_up": ["bundle_pop_up.png", "have_func"],
"click_challenge_boss_fp": ["challenge_boss_fp_button.png"],
"check_level_up": ["level_up.png", "have_func"],
"click_idle_chest": ["idle_chest.png"],
"click_friend_button": ["friend_button.png"],
"click_expand_left_col_button": ["expand_left_col_button.png", "have_func"],
"click_send_heart_button": ["send_heart_button.png"],
"click_close_friend_ui_button": ["ui_return_button.png"],
"click_instant_idle_button": ["instant_idle_button.png"],
"click_instant_idle_free_claim_button": ["instant_idle_free_claim_button.png"],
"click_instant_idle_close_button": ["instant_idle_close_button.png"],
"click_noble_tavern_button": ["noble_tavern_button.png"],
"click_friend_summon_pool": ["friend_summon_pool.png"],
"click_guild_button": ["guild_button.png"],
"click_guild_boss_button": ["guild_boss_button.png"],
"click_arena_button": ["arena_button.png"],
"click_normal_arena_button": ["normal_arena_button.png"],
"click_arena_challenge_button": ["arena_challenge_button.png"],
"click_skip_battle_button": ["skip_battle_button.png"],
"click_bounty_board_button": ["bounty_board_button.png"],
"click_bounty_board_dispatch_all_button": ["bounty_board_dispatch_all_button.png"],
"click_bounty_board_collect_all_button": ["bounty_board_collect_all_button.png"],
"click_bounty_board_confirm_button": ["bounty_board_confirm_button.png"],
"click_tower_button": ["tower_button.png"],
"click_tower_main_button": ["tower_main_button.png"]
}
# 是否杀掉进程
self.stop = False
# 以下坐标会在执行“日常任务”模式时自动初始化
# “领地”、“野外”、“战役”点击坐标
self.ranhorn_coord = None
self.dark_forest_coord = None
self.campaign_coord = None
# exec_func函数默认延迟一秒（延迟太短会导致截图太快，从而反复多点几次）
self.exec_func_delay = 1
# 自动执行符合触发条件的指令
def exec_func(self, cmd_list, exit_cond=None):
afterExecFunc = False
exit_loop_flag = False
if exit_cond:
if "afterExecFunc" in exit_cond:
exit_cond = exit_cond.split("@")[1]
afterExecFunc = True
while True:
if self.stop:
return
self.utils.get_img()
if self.stop:
return
for cmd in cmd_list:
if self.stop:
return
if self.utils.match(self.func_to_img[cmd][0]):
if len(self.func_to_img[cmd]) == 1:
self.utils.tap()
elif self.func_to_img[cmd][1] == "have_func":
cmd_func = "self." + cmd + "()"
exec(cmd_func)
else:
self.utils.write_log("【可能出错了】这不正常，匹配到了图片，但是没有执行任何操作")
# 如果达成退出条件，就会在执行完毕之后退出exec_func函数
if afterExecFunc and exit_cond == cmd:
exit_loop_flag = True
break
if exit_loop_flag:
break
if self.stop:
return
# 防止截图太快重复点击
time.sleep(self.exec_func_delay)
# 主线模式（只重试，过关之后不挑战下一关）
def story_mode_retry_only(self):
self.utils.write_log("开始执行【主线模式（只重试）】！")
self.exec_func([
"click_battle_retry",
"no_click_next_stage",
"click_next_team",
"click_battle"
], exit_cond="afterExecFunc@no_click_next_stage")
self.utils.logger.finish_exec()
# 主线模式（推图）
def story_mode(self):
self.utils.write_log("开始执行【主线模式（推图）】！")
self.exec_func([
"click_battle_retry",
"click_next_stage",
"click_continue_campaign",
"click_next_team",
"click_battle",
"check_boss_stage",
"click_challenge_boss_fp",
"check_bundle_pop_up",
"check_level_up"
])
self.utils.logger.finish_exec()
# 王座之塔模式（只重试，过关之后不挑战下一关）
def tower_mode_retry_only(self):
self.utils.write_log("开始执行【王座之塔模式（只重试）】！")
self.exec_func([
"click_battle_retry",
"no_click_continue",
"click_challenge",
"click_battle"
], exit_cond="afterExecFunc@no_click_continue")
self.utils.logger.finish_exec()
# 王座之塔模式（推塔）
def tower_mode(self):
self.utils.write_log("开始执行【王座之塔模式（推塔）】！")
self.exec_func([
"click_battle_retry",
"click_continue",
"click_battle",
"click_challenge"
])
self.utils.logger.finish_exec()
# 日常任务模式
def daily_mode(self):
self.utils.write_log("开始执行【日常任务模式】！")
# 初始化“领地”、“野外”、“战役”的坐标
if self.ranhorn_coord is None:
self.utils.get_img()
try:
if not self.utils.match("ranhorn_icon.png"):
self.utils.match("ranhorn_icon_chosen.png")
self.ranhorn_coord = self.utils.get_coord()
if not self.utils.match("dark_forest_icon.png"):
self.utils.match("dark_forest_icon_chosen.png")
self.dark_forest_coord = self.utils.get_coord()
if not self.utils.match("campaign_icon.png"):
self.utils.match("campaign_icon_chosen.png")
self.campaign_coord = self.utils.get_coord()
except:
self.utils.write_log("初始化“领地”、“野外”、“战役”的坐标失败，请检查游戏是否在首页")
self.utils.error_stop()
if self.stop:
return
# 获取日常任务勾选信息
mission_list = []
if self.utils.ui.checkBox_2.isChecked():
mission_list.append("daily_challenge_boss")
if self.utils.ui.checkBox_4.isChecked():
mission_list.append("daily_send_heart")
if self.utils.ui.checkBox_5.isChecked():
mission_list.append("daily_instant_idle")
if self.utils.ui.checkBox_6.isChecked():
mission_list.append("daily_summon")
if self.utils.ui.checkBox_7.isChecked():
mission_list.append("daily_guild_boss")
if self.utils.ui.checkBox_8.isChecked():
mission_list.append("daily_arena_battle")
if self.utils.ui.checkBox_9.isChecked():
mission_list.append("daily_bounty_board")
if self.utils.ui.checkBox_10.isChecked():
mission_list.append("daily_tower")
if self.utils.ui.checkBox_11.isChecked():
pass
if self.utils.ui.checkBox_12.isChecked():
pass
if self.utils.ui.checkBox_13.isChecked():
pass
# 箱子会在所有任务开始前后分别领取一次
if self.utils.ui.checkBox_3.isChecked():
self.daily_idle_chest_1st_exec = True
mission_list.insert(0, "daily_idle_chest")
mission_list.append("daily_idle_chest")
# 按照mission list执行每日任务
for mission in mission_list:
if self.stop:
return
func = "self." + mission + "()"
exec(func)
if self.stop:
return
time.sleep(2)
self.utils.write_log("【日常任务】全部完成！")
self.utils.logger.finish_exec()
# 日常任务 - 挑战首领1次（20pts）
def daily_challenge_boss(self):
self.click_campaign_icon()
cmd_list = [
"click_battle_exit",
"click_battle_pause",
"click_battle",
"check_boss_stage",
"click_challenge_boss_fp",
"check_bundle_pop_up",
"check_level_up"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_battle_exit")
self.utils.write_log("【日常任务】完成 - 挑战首领1次（20pts）！")
# 日常任务 - 领取战利品2次（10pts）
def daily_idle_chest(self):
self.click_campaign_icon()
cmd_list = [
"click_idle_chest",
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_idle_chest")
self.utils.tap(0.5, 0.9, percentage=True)
if self.daily_idle_chest_1st_exec:
self.daily_idle_chest_1st_exec = False
self.utils.write_log("【日常任务】领取战利品1次，第2次会在其它日常任务执行完毕后领取！")
else:
self.utils.write_log("【日常任务】完成 - 领取战利品2次（10pts）！")
# 日常任务 - 赠送好友友情点1次（10pts）
def daily_send_heart(self):
self.click_campaign_icon()
cmd_list = [
"click_expand_left_col_button",
"click_friend_button",
"click_send_heart_button"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_send_heart_button")
cmd_list = [
"click_close_friend_ui_button"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_close_friend_ui_button")
self.utils.write_log("【日常任务】完成 - 赠送好友友情点1次（10pts）！")
# 日常任务 - 快速挂机1次（10pts）
def daily_instant_idle(self):
self.click_campaign_icon()
cmd_list = [
"click_instant_idle_button"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_instant_idle_button")
if self.utils.current_match('instant_idle_free_claim_button.png'):
# 点击“免费领取”
self.utils.tap()
# 给予设备足够的反应时间后，点击空白处（屏幕下方）关闭“获得奖励”窗口
time.sleep(1)
self.utils.tap(0.5, 0.9, percentage=True)
self.utils.write_log("【日常任务】完成 - 快速挂机1次（10pts）！")
else:
self.utils.write_log("【日常任务】执行失败 - 快速挂机1次（10pts）！原因：你已经用完免费快速挂机次数")
cmd_list = [
"click_instant_idle_close_button"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_instant_idle_close_button")
# 日常任务 - 在月桂酒馆召唤英雄1次（20pts）
def daily_summon(self):
self.click_ranhorn_icon()
cmd_list = [
"click_noble_tavern_button",
"click_friend_summon_pool"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_friend_summon_pool")
time.sleep(2)
if self.utils.current_match('single_friend_summon_button.png'):
# 单抽一次友情池
self.utils.tap()
# 给予设备足够的反应时间后，点击卡背
retry_cnt = 0
while not self.utils.current_match('summon_card_backside.png'):
time.sleep(2)
retry_cnt += 1
if retry_cnt > 5:
self.utils.error_stop()
self.utils.tap()
# 给予设备足够的反应时间后，点击返回
retry_cnt = 0
while not self.utils.current_match('ui_return_button.png'):
time.sleep(2)
retry_cnt += 1
if retry_cnt > 5:
self.utils.error_stop()
self.utils.tap()
# 等待2秒之后，点击同一位置来关闭“获得奖励”界面
time.sleep(2)
self.utils.tap()
# 等待2秒之后，点击同一位置来关闭抽卡界面
time.sleep(2)
self.utils.tap()
self.utils.write_log("【日常任务】完成 - 在月桂酒馆召唤英雄1次（20pts）！")
else:
self.utils.write_log("【日常任务】执行失败 - 在月桂酒馆召唤英雄1次（20pts）！原因：友情点不够")
# 点击返回，回到主界面
self.utils.match('ui_return_button.png')
self.utils.tap()
# 日常任务 - 参加公会团队狩猎1次（10pts）
def daily_guild_boss(self):
# 通用的公会boss流程
def boss_fight():
while self.utils.current_match('guild_boss_quick_battle_button.png'):
# 点击“扫荡”
self.utils.tap()
# 给予设备足够的反应时间后，点击“扫荡1次”
time.sleep(1)
self.utils.current_match('guild_boss_quick_battle_confirm_button.png')
self.utils.tap()
# 给予设备足够的反应时间后，点击空白处关闭结算界面
time.sleep(2)
while self.utils.current_match('guild_boss_fight_victory.png'):
self.utils.tap(0.2, 0.9, percentage=True, randomize=False)
self.utils.tap(0.2, 0.9, percentage=True, randomize=False)
time.sleep(2)
self.mission_accomplished = True
self.mission_accomplished_cnt += 1
self.mission_accomplished = False
self.mission_accomplished_cnt = 0
self.click_ranhorn_icon()
cmd_list = [
"click_guild_button",
"click_guild_boss_button"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_guild_boss_button")
time.sleep(2)
# 先尝试打哥布林
boss_fight()
if self.mission_accomplished_cnt > 0:
self.utils.write_log(f"【公会Boss】击杀哥布林{self.mission_accomplished_cnt}次！")
self.mission_accomplished_cnt = 0
# 再切到右边尝试打远古剑魂
self.utils.current_match('guild_boss_right_arrow.png')
self.utils.tap()
time.sleep(2)
boss_fight()
if self.mission_accomplished_cnt > 0:
self.utils.write_log(f"【公会Boss】击杀剑魂{self.mission_accomplished_cnt}次！")
self.mission_accomplished_cnt = 0
if self.mission_accomplished:
self.utils.write_log("【日常任务】完成 - 参加公会团队狩猎1次（10pts）！")
else:
self.utils.write_log("【日常任务】执行失败 - 参加公会团队狩猎1次（10pts）！原因：你今天已经打过了")
# 点击返回，回到主界面
while self.utils.current_match('ui_return_button.png'):
self.utils.tap()
time.sleep(2)
# 日常任务 - 参加竞技场挑战1次（20pts）
def daily_arena_battle(self):
self.click_dark_forest_icon()
cmd_list = [
"click_arena_button",
"click_normal_arena_button",
"click_arena_challenge_button"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_arena_challenge_button")
mission_complete = False
time.sleep(2)
# 免费票打完为止
while self.utils.current_match('arena_free_battle_button.png'):
# 寻找y值最大的坐标（最下方的挑战）
res = self.utils.multiple_match('arena_free_battle_button.png')
max_y_idx = 0
if len(res) > 1:
for idx in range(len(res) - 1):
if res[max_y_idx] < res[idx]:
max_y_idx = idx
# 使用免费票
self.utils.tap(res[max_y_idx][0], res[max_y_idx][1], randomize=False)
time.sleep(2)
# 点击战斗
cmd_list = [
"click_skip_battle_button",
"click_battle"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_skip_battle_button")
time.sleep(2)
# 获得奖励界面（点空白处关闭）
self.utils.tap(0.5, 0.9, percentage=True)
time.sleep(2)
# 战斗结算界面（点空白处关闭）
self.utils.tap(0.5, 0.9, percentage=True)
time.sleep(2)
mission_complete = True
# 免费票打完了，回退到主界面
if mission_complete:
self.utils.write_log("【日常任务】完成 - 参加竞技场挑战1次（20pts）！")
else:
self.utils.write_log("【日常任务】执行失败 - 参加竞技场挑战1次（20pts）！原因：已经用完免费票")
# 依次点击空白，返回，返回
self.utils.tap(0.5, 0.9, percentage=True)
time.sleep(2)
self.utils.current_match('ui_return_button.png')
self.utils.tap()
time.sleep(2)
self.utils.tap()
# 日常任务 - 接受3个悬赏任务（10pts）
def daily_bounty_board(self):
self.click_dark_forest_icon()
# 个人悬赏 - 一键领取&派遣
cmd_list = [
"click_bounty_board_button",
"click_bounty_board_collect_all_button",
"click_bounty_board_dispatch_all_button",
"click_bounty_board_confirm_button"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_bounty_board_confirm_button")
time.sleep(1)
# 切换到团队悬赏页面
self.utils.current_match("bounty_board_team_tab.png")
self.utils.tap()
time.sleep(1)
# 团队悬赏 - 一键领取&派遣
cmd_list = [
"click_bounty_board_collect_all_button",
"click_bounty_board_dispatch_all_button",
"click_bounty_board_confirm_button"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_bounty_board_confirm_button")
time.sleep(1)
# 点击返回
self.utils.current_match('ui_return_button.png')
self.utils.tap()
time.sleep(2)
self.utils.write_log("【日常任务】完成 - 接受3个悬赏任务（10pts）！")
# 日常任务 - 挑战王座之塔1次（10pts）
def daily_tower(self):
self.click_dark_forest_icon()
cmd_list = [
"click_battle_exit",
"click_battle_pause",
"click_tower_button",
"click_tower_main_button",
"click_challenge",
"click_battle"
]
self.exec_func(cmd_list, exit_cond="afterExecFunc@click_battle_exit")
time.sleep(1)
# 点击返回，返回
self.utils.current_match('ui_return_button.png')
self.utils.tap()
time.sleep(2)
self.utils.tap()
time.sleep(2)
self.utils.write_log("【日常任务】完成 - 挑战王座之塔1次（10pts）！")
# 点击“领地”
def click_ranhorn_icon(self):
self.utils.tap(self.ranhorn_coord[0], self.ranhorn_coord[1])
# 点击“野外”
def click_dark_forest_icon(self):
self.utils.tap(self.dark_forest_coord[0], self.dark_forest_coord[1])
# 点击“战役”
def click_campaign_icon(self):
self.utils.tap(self.campaign_coord[0], self.campaign_coord[1])
# 点击“再次挑战”
def click_battle_retry(self):
self.utils.cnt += 1
self.utils.show_cnt()
self.utils.tap()
# 点击“下一关”
def click_next_stage(self):
# 挑战成功，重置“重试计数”
self.utils.cnt = 0
self.utils.write_log("【主线模式】恭喜过关！即将自动开始挑战下一关！")
self.utils.auto_screenshot_on_win(mode="main")
self.utils.current_match("next_stage_button.png")
self.utils.tap()
# 只检测，不点击“下一关”
def no_click_next_stage(self):
# 挑战成功，重置“重试计数”
self.utils.cnt = 0
self.utils.write_log("【主线模式】恭喜过关！")
self.utils.auto_screenshot_on_win(mode="main")
# 点击“点击屏幕继续”（用于王座之塔页面）
def click_continue(self):
# 挑战成功，重置“重试计数”
self.utils.cnt = 0
self.utils.write_log("【王座之塔】恭喜过关！即将自动开始挑战下一关！")
self.utils.auto_screenshot_on_win(mode="tower")
self.utils.current_match("continue_button.png")
self.utils.tap()
# 只检测，不点击“点击屏幕继续”（用于王座之塔页面）
def no_click_continue(self):
# 挑战成功，重置“重试计数”
self.utils.cnt = 0
self.utils.write_log("【王座之塔】恭喜过关！")
self.utils.auto_screenshot_on_win(mode="tower")
# 检测限时礼包弹窗
# 如果过关之后弹出限时礼包购买窗口，直接点击屏幕下方关闭
def check_bundle_pop_up(self):
self.utils.tap(0.5, 0.9, percentage=True)
self.utils.write_log("检测到有限时礼包弹窗并自动关闭成功！")
# 检测升级弹窗
# 如果过关之后弹出升级窗口，直接点击屏幕下方关闭
def check_level_up(self):
self.utils.tap(0.5, 0.9, percentage=True)
self.utils.write_log("检测到升级弹窗并自动关闭成功！")
# 点击右侧展开按钮
def click_expand_left_col_button(self):
self.utils.tap(randomize=False)
|
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|
import numpy as np
import openmdao.api as om
class KappaComp(om.ExplicitComponent):
r""" Computes the term kappa in the drag equation:
.. math::
C_D = C_{D0} + \kappa C_{L\alpha} \alpha^2
"""
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
# Inputs
self.add_input('mach', shape=(nn,), desc='Mach number', units=None)
# Outputs
self.add_output(name='kappa', val=np.zeros(nn), desc='induced drag coefficient', units=None)
# Jacobian
ar = np.arange(nn)
self.declare_partials(of='kappa', wrt='mach', rows=ar, cols=ar)
def compute(self, inputs, outputs):
M = inputs['mach']
idx_low = np.where(M < 1.15)[0]
idx_high = np.where(M >= 1.15)[0]
outputs['kappa'][idx_low] = 0.54 + 0.15 * (1.0 + np.tanh((M[idx_low] - 0.9) / 0.06))
outputs['kappa'][idx_high] = 0.54 + 0.15 * (1.0 + np.tanh(0.25 / 0.06)) \
+ 0.14 * (M[idx_high] - 1.15)
def compute_partials(self, inputs, partials):
M = inputs['mach']
idx_low = np.where(M < 1.15)[0]
idx_high = np.where(M >= 1.15)[0]
k = 50.0 / 3.0
tanh = np.tanh(k * (M[idx_low] - 0.9))
sech2 = 1.0 - tanh**2
partials['kappa', 'mach'][idx_low] = 2.5 * sech2
partials['kappa', 'mach'][idx_high] = 0.14
|
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|
From iris.algebra Require Import gmap agree auth.
From iris.proofmode Require Import tactics.
From cap_machine Require Export stdpp_extra region_invariants multiple_updates
region_invariants_revocation region_invariants_static sts.
Require Import stdpp.countable.
Import uPred.
Section heap.
Context {Σ:gFunctors} {memg:memG Σ} {regg:regG Σ}
{stsg : STSG Addr region_type Σ} {heapg : heapG Σ}
`{MonRef: MonRefG (leibnizO _) CapR_rtc Σ}.
Notation STS := (leibnizO (STS_states * STS_rels)).
Notation STS_STD := (leibnizO (STS_std_states Addr region_type)).
Notation WORLD := (prodO STS_STD STS).
Implicit Types W : WORLD.
Lemma related_sts_priv_world_revoked_to_uninit W a w :
(std W) !! a = Some Revoked ->
related_sts_priv_world W (<s[a:=Static {[a:=w]}]s> W).
Proof.
intros Hrev.
split;[|apply related_sts_priv_refl].
split.
- rewrite dom_insert_L. set_solver.
- intros i x y Hx Hy.
destruct (decide (i = a)).
+ simplify_map_eq.
right with Temporary;[left;constructor|].
eright;[|left].
right. constructor.
+ simplify_map_eq. left.
Qed.
Lemma related_sts_priv_world_uninit_to_revoked W a w :
(std W) !! a = Some (Static {[a:=w]}) ->
related_sts_priv_world W (<s[a:=Revoked]s> W).
Proof.
intros Hrev.
split;[|apply related_sts_priv_refl].
split.
- rewrite dom_insert_L. set_solver.
- intros i x y Hx Hy.
destruct (decide (i = a)).
+ simplify_map_eq.
right with Temporary;[left;constructor|].
eright;[|left].
right. constructor.
+ simplify_map_eq. left.
Qed.
Lemma related_sts_pub_world_uninit_to_temporary W a w :
(std W) !! a = Some (Static {[a:=w]}) ->
related_sts_pub_world W (<s[a:=Temporary]s> W).
Proof.
intros Hrev.
split;[|apply related_sts_pub_refl].
split.
- rewrite dom_insert_L. set_solver.
- intros i x y Hx Hy.
destruct (decide (i = a)).
+ simplify_map_eq.
right with Temporary;[|left].
constructor.
+ simplify_map_eq. left.
Qed.
(* Lemma that extracts all temporary addresses in W from a list of addresses l *)
Lemma extract_temps_from_range W (l : list Addr) :
NoDup l ->
∃ l', NoDup l'
∧ Forall (λ (a : Addr), (std W) !! a = Some Temporary <-> a ∈ l') l
∧ Forall (λ (a : Addr), (std W) !! a = Some Temporary) l'.
Proof.
exists (filter (λ a, (std W) !! a = Some Temporary) l).
split.
- apply NoDup_filter. auto.
- split.
+ apply Forall_forall. intros x Hx. split;intros.
* apply elem_of_list_filter. split;auto.
* apply elem_of_list_filter in H0 as [Htemp Hin]. auto.
+ apply Forall_forall. intros x Hx. apply elem_of_list_filter in Hx as [Htemp Hin]. auto.
Qed.
Notation "m1 ∖∖ m2" := (map_difference_het m1 m2) (at level 40, left associativity).
Definition override_uninitialized : (gmap Addr Word) -> STS_STD → STS_STD :=
λ (m : gmap Addr Word) (Wstd : gmap Addr region_type),
(map_imap (λ a w, Some (Static {[a:=w]})) m) ∪ (Wstd ∖∖ m).
Definition override_uninitializedW : (gmap Addr Word) -> WORLD → WORLD :=
λ m W, (override_uninitialized m W.1,W.2).
Notation "m1 >> W" := (override_uninitializedW m1 W) (at level 40, left associativity).
Lemma override_uninitializedW_empty W :
(∅ : gmap Addr Word) >> W = W.
Proof.
rewrite /override_uninitializedW /override_uninitialized difference_het_empty /=.
destruct W. f_equiv. simpl. rewrite left_id_L. auto.
Qed.
Lemma override_uninitializedW_insert W (m : gmap Addr Word) a w :
(<[a:=w]> m) >> W = std_update (m >> W) a (Static {[a:=w]}).
Proof.
rewrite /override_uninitializedW /override_uninitialized difference_het_insert_r /=.
destruct W. rewrite /std_update /=. f_equiv. rewrite map_imap_insert.
rewrite -insert_union_l //.
rewrite map_eq'.
assert (map_imap (λ (a0 : Addr) (w0 : Word), Some (Static {[a0 := w0]})) m ##ₘ o ∖∖ m) as Hdisj.
{ apply map_disjoint_spec. intros i t y Ht Hy.
apply difference_het_lookup_Some in Hy as [_ Hnone].
rewrite map_lookup_imap in Ht. rewrite Hnone /= in Ht. done. }
intros k v. split; intros Hx.
- destruct (decide (a = k));[subst;simplify_map_eq;auto|simplify_map_eq].
apply lookup_union_Some in Hx as [Hx | Hx].
+ apply lookup_union_Some_l. auto.
+ rewrite lookup_delete_ne in Hx;auto. apply lookup_union_Some_r; auto.
+ apply map_disjoint_delete_r. auto.
- destruct (decide (a = k));[subst;simplify_map_eq;auto|simplify_map_eq].
apply lookup_union_Some in Hx as [Hx | Hx].
+ apply lookup_union_Some_l. auto.
+ apply lookup_union_Some_r. apply map_disjoint_delete_r;auto.
rewrite lookup_delete_ne;auto.
+ auto.
Qed.
Lemma override_uninitializedW_commute W (m : gmap Addr Word) :
m >> (revoke W) = revoke (m >> W).
Proof.
induction m using map_ind; [by rewrite !override_uninitializedW_empty|].
rewrite !override_uninitializedW_insert.
rewrite IHm.
rewrite /std_update /revoke /loc /std /=. repeat f_equiv. rewrite map_eq'.
intros k v.
destruct (decide (k = i)).
- subst. rewrite lookup_insert revoke_monotone_lookup_same;rewrite lookup_insert; auto.
- rewrite !lookup_insert_ne //. split; intros.
+ rewrite -(revoke_monotone_lookup (m >> W).1);auto.
rewrite lookup_insert_ne;auto.
+ rewrite -(revoke_monotone_lookup (m >> W).1) in H0;auto.
rewrite lookup_insert_ne;auto.
Qed.
Lemma override_uninitializedW_lookup_some W (m : gmap Addr Word) i w :
m !! i = Some w ->
(m >> W).1 !! i = Some (Static {[i:=w]}).
Proof.
intros Hsome. rewrite /override_uninitializedW /override_uninitialized /=.
apply (lookup_union_Some_l (M:=gmap Addr)). rewrite map_lookup_imap Hsome /=. auto.
Qed.
Lemma override_uninitializedW_lookup_none W (m : gmap Addr Word) i :
m !! i = None ->
(m >> W).1 !! i = W.1 !! i.
Proof.
intros Hnone. rewrite /override_uninitializedW /override_uninitialized /=.
destruct (W.1 !! i) eqn:Hsome.
- apply (lookup_union_Some_r (M:=gmap Addr)).
{ apply map_disjoint_spec. intros j t y Ht Hy.
apply difference_het_lookup_Some in Hy as [_ Hnone'].
rewrite map_lookup_imap /= in Ht. rewrite Hnone' /= in Ht. done. }
apply difference_het_lookup_Some. split;auto.
- apply (lookup_union_None (M:=gmap Addr)).
split.
+ rewrite map_lookup_imap Hnone /=. done.
+ apply difference_het_lookup_None;[|left;auto]. exact Temporary.
Qed.
Lemma override_uninitializedW_lookup_nin W (m : gmap Addr Word) i :
i ∉ (dom (gset Addr) m) -> (m >> W).1 !! i = W.1 !! i.
Proof.
intros Hnin.
apply override_uninitializedW_lookup_none.
apply (not_elem_of_dom (D:=gset Addr)).
auto.
Qed.
Lemma override_uninitializedW_elem_of W (m : gmap Addr Word) i :
i ∈ dom (gset Addr) W.1 -> i ∈ dom (gset Addr) (m >> W).1.
Proof.
intros Hin%elem_of_gmap_dom.
apply elem_of_gmap_dom. destruct (m !! i) eqn:Hsome.
- apply override_uninitializedW_lookup_some with (W:=W) in Hsome. eauto.
- apply override_uninitializedW_lookup_none with (W:=W) in Hsome.
rewrite -Hsome in Hin. eauto.
Qed.
Lemma override_uninitializedW_elem_of_overwritten W (m : gmap Addr Word) i :
i ∈ dom (gset Addr) m -> i ∈ dom (gset Addr) (m >> W).1.
Proof.
intros Hin%elem_of_gmap_dom.
apply elem_of_gmap_dom. destruct Hin as [w Hsome].
apply override_uninitializedW_lookup_some with (W:=W) in Hsome. eauto.
Qed.
Lemma override_uninitializedW_dom W (m : gmap Addr Word) :
dom (gset Addr) W.1 ⊆ dom (gset Addr) (m >> W).1.
Proof.
apply elem_of_subseteq.
intros x Hx.
apply override_uninitializedW_elem_of. auto.
Qed.
Lemma override_uninitializedW_dom' W (m: gmap Addr Word) :
dom (gset Addr) (override_uninitializedW m W).1 =
dom (gset Addr) m ∪ dom (gset Addr) W.1.
Proof.
rewrite /override_uninitializedW /override_uninitialized.
rewrite dom_union_L dom_difference_het.
rewrite dom_map_imap_full. 2: by intros; eauto.
set Dm := dom (gset Addr) m.
set DW := dom (gset Addr) W.1. clearbody Dm DW.
rewrite elem_of_equiv_L. intro x.
rewrite !elem_of_union !elem_of_difference.
split.
- intros [? | [? ?] ]. auto. auto.
- intros [? | ?]. auto. destruct (decide (x ∈ Dm)); auto.
Qed.
Lemma related_sts_priv_world_override_uninitializedW W (m : gmap Addr Word) :
Forall (λ a : Addr, ∃ ρ, (std W) !! a = Some ρ /\ ρ <> Permanent) (elements (dom (gset Addr) m)) →
related_sts_priv_world W (m >> W).
Proof.
induction m using map_ind; intros.
- rewrite override_uninitializedW_empty.
apply related_sts_priv_refl_world.
- rewrite override_uninitializedW_insert.
erewrite dom_insert in H0.
erewrite elements_union_singleton in H0; [|eapply not_elem_of_dom; eauto].
eapply Forall_cons in H0. destruct H0 as [A B].
eapply related_sts_priv_trans_world with (m >> W).
+ eapply IHm. eauto.
+ destruct A as [ρ [A1 A2] ].
split;[|apply related_sts_priv_refl].
split.
* rewrite dom_insert_L. set_solver.
* intros r p q Hp Hq.
destruct (decide (r = i)).
{ subst r. rewrite override_uninitializedW_lookup_nin in Hp; [|eapply not_elem_of_dom; eauto].
rewrite A1 in Hp; inv Hp. rewrite lookup_insert in Hq.
inv Hq. destruct p; try congruence.
- eright. right; constructor.
left.
- eright. left; constructor.
eright. right; constructor.
left.
- eright. left; constructor.
eright. right; constructor.
left. }
{ simplify_map_eq. left. }
Qed.
(* following lemma takes a map of addresses to words, where the addresses are in a revoked state, and makes them
uninitialized *)
Lemma region_revoked_to_uninitialized W m :
(sts_full_world (revoke W)
∗ region (revoke W)
∗ ([∗ map] a↦w ∈ m, ∃ p φ, ⌜∀ Wv : WORLD * Word, Persistent (φ Wv)⌝ ∗ ⌜p ≠ O⌝ ∗ a ↦ₐ[p] w ∗ rel a p φ)
==∗ (sts_full_world (m >> (revoke W))
∗ region (m >> (revoke W))))%I.
Proof.
iIntros "(Hfull & Hr & Hl)".
iInduction (m) as [|a w m] "IH" using map_ind.
- rewrite override_uninitializedW_empty. iFrame. done.
- rewrite override_uninitializedW_insert.
iDestruct (big_sepM_insert with "Hl") as "[Hx Hl]";[apply H|].
iMod ("IH" with "Hfull Hr Hl") as "[Hfull Hr] /=".
iDestruct "Hx" as (p φ Hpers Hne) "[Hx #Hrel]".
rewrite region_eq /region_def.
iDestruct "Hr" as (M Mρ) "(HM & #Hdom & #Hdom' & Hr)".
iDestruct "Hdom" as %Hdom. iDestruct "Hdom'" as %Hdom'.
rewrite rel_eq /rel_def RELS_eq /RELS_def REL_eq /REL_def.
iDestruct "Hrel" as (γpred) "[HR Hsaved]".
iDestruct (reg_in with "[$HM $HR]") as %HMeq.
rewrite HMeq.
iDestruct (big_sepM_delete with "Hr") as "[HX Hr]";[apply lookup_insert|].
iDestruct "HX" as (ρ Hρ) "[Hstate HX]".
iDestruct "HX" as (γpred' p' φ' Heq Hpers') "[#Hsaved' HX]".
inversion Heq;subst.
iDestruct (sts_full_state_std with "Hfull Hstate") as %Hx.
destruct ρ.
{ iDestruct "HX" as (v' Hne') "[Hx' _]".
iDestruct (cap_duplicate_false with "[$Hx $Hx']") as "Hf"; auto. }
{ iDestruct "HX" as (v' Hne') "[Hx' _]".
iDestruct (cap_duplicate_false with "[$Hx $Hx']") as "Hf"; auto. }
2: { iDestruct "HX" as (v' Hx' Hne') "[Hx' _]".
iDestruct (cap_duplicate_false with "[$Hx $Hx']") as "Hf"; auto. }
iDestruct (region_map_delete_nonstatic with "Hr") as "Hr";[rewrite Hρ; auto|].
iDestruct (region_map_insert_singleton (Static {[a:=w]}) with "Hr") as "Hr";[eauto|].
apply (related_sts_priv_world_revoked_to_uninit (m >> revoke W) a w)
in Hx as Hrelated.
iDestruct (monotone_revoke_list_region_def_mono $! Hrelated with "[Hfull] Hr") as "[Hfull Hr]".
{ rewrite override_uninitializedW_commute;auto. }
iMod (sts_update_std _ _ _ (Static {[a:=w]}) with "Hfull Hstate") as "[Hfull Hstate] /=".
iDestruct (big_sepM_delete with "[Hstate Hx $Hr]") as "Hr";[apply lookup_insert|..].
{ iExists (Static {[a:=w]}). iFrame. iSplit;[iPureIntro;apply lookup_insert|].
iExists _,_,_. iFrame "# ∗". repeat iSplit;eauto. iExists _. iFrame.
repeat iSplit;auto;iPureIntro;[apply lookup_singleton|].
intros a' Ha'. apply elem_of_gmap_dom in Ha' as [x Ha'].
destruct (decide (a = a'));[subst;simplify_map_eq;auto|simplify_map_eq].
}
rewrite -HMeq. iModIntro. iSplitL "Hfull".
{ rewrite override_uninitializedW_commute;auto. }
iExists M,(<[a:=Static {[a:=w]}]>Mρ). iFrame. iPureIntro. split.
+ rewrite -Hdom. rewrite dom_insert_L.
assert (a ∈ dom (gset Addr) (m >> (revoke W)).1) as Hin.
{ rewrite Hdom HMeq dom_insert_L. set_solver. }
set_solver.
+ rewrite dom_insert_L -Hdom'. assert (a ∈ dom (gset Addr) Mρ) as Hin;[apply elem_of_gmap_dom;eauto|].
set_solver.
Qed.
(* the following lemma takes some uninitilized states and revokes them. For simplicity we ignore their values *)
(* this lemma is used to revoke the range needed for the local stack frame *)
Lemma region_uninitialized_to_revoked W (l: list Addr) p φ:
NoDup l ->
([∗ list] a ∈ l, ⌜exists w, std W !! a = Some (Static {[a:=w]})⌝ ∗ rel a p φ)
∗ sts_full_world (revoke W)
∗ region (revoke W) ==∗
sts_full_world (std_update_multiple (revoke W) l Revoked)
∗ region (std_update_multiple (revoke W) l Revoked)
∗ ([∗ list] a ∈ l, ∃ v, a ↦ₐ[p] v).
Proof.
iIntros (Hdup) "(Ha & Hsts & Hr)".
iInduction (l) as [|x l] "IH".
- simpl. iFrame. done.
- iDestruct (big_sepL_cons with "Ha") as "[Hx Ha]".
iDestruct "Hx" as "[% Hrelx]". destruct H as [w Hw].
apply NoDup_cons in Hdup as [Hnin Hdup].
iMod ("IH" with "[] Ha Hsts Hr") as "[Hfull [Hr Hx] ] /=";[auto|auto|..].
rewrite region_eq /region_def.
iDestruct "Hr" as (M Mρ) "(HM & #Hdom & #Hdom' & Hr)".
iDestruct "Hdom" as %Hdom. iDestruct "Hdom'" as %Hdom'.
assert (is_Some (M !! x)) as [ρ Hρ].
{ apply elem_of_gmap_dom. rewrite -Hdom. apply elem_of_gmap_dom. apply std_sta_update_multiple_is_Some. eauto.
rewrite /revoke /revoke_std_sta lookup_fmap Hw /=. eauto. }
iDestruct (big_sepM_delete with "Hr") as "[Hw Hr]";[eauto|].
iDestruct "Hw" as (ρ' Hρ') "[Hstate HX]".
iDestruct (sts_full_state_std with "Hfull Hstate") as %Hx.
rewrite std_sta_update_multiple_lookup_same_i in Hx;auto.
rewrite /revoke /revoke_std_sta lookup_fmap Hw /= in Hx. inversion Hx; subst.
iDestruct "HX" as (γpred' p' φ' Heq Hpers') "[#Hsaved' HX]".
iDestruct "HX" as (v Hlookup Hne) "[HX _]".
iDestruct (monotone_revoke_list_region_def_mono with "[] [Hfull] Hr") as "[Hfull Hr]".
{ iPureIntro. apply related_sts_priv_world_uninit_to_revoked with w.
rewrite std_sta_update_multiple_lookup_same_i //.
rewrite /revoke /revoke_std_sta lookup_fmap Hw /=. reflexivity. }
{ rewrite std_update_multiple_revoke_commute. iFrame. auto. }
iMod (sts_update_std _ _ _ (Revoked) with "Hfull Hstate") as "[Hfull Hstate] /=".
iDestruct (region_map_delete_singleton with "Hr") as "Hr";[rewrite Hρ';eauto|].
iDestruct (region_map_insert_nonstatic Revoked with "Hr") as "Hr";[auto|].
iDestruct (big_sepM_delete with "[$Hr Hstate]") as "Hr";[eauto|..].
{ iExists Revoked. iSplit;[rewrite lookup_insert;auto|]. iFrame. iExists _,_,_. repeat iSplit;eauto. }
iFrame.
iSplitL "Hfull".
{ rewrite std_update_multiple_revoke_commute //. }
rewrite RELS_eq/ RELS_def rel_eq /rel_def REL_eq /REL_def.
iDestruct "Hrelx" as (γpred) "[Hrelx Hpredx]".
iDestruct (reg_in with "[$HM $Hrelx]") as %HMeq.
rewrite HMeq in Hρ. rewrite lookup_insert in Hρ. inv Hρ.
inv H0.
iModIntro. iSplitL "HM Hr".
+ iExists M,(<[x:=Revoked]> Mρ). iFrame. repeat iSplit.
++ iPureIntro. rewrite dom_insert_L. rewrite Hdom.
assert (x ∈ dom (gset Addr) M) as Hin. apply elem_of_gmap_dom;eauto.
rewrite HMeq lookup_insert; eauto.
set_solver.
++ iPureIntro. rewrite dom_insert_L. rewrite Hdom'.
assert (x ∈ dom (gset Addr) M) as Hin. apply elem_of_gmap_dom;eauto.
rewrite HMeq lookup_insert; eauto.
set_solver.
+ simplify_map_eq. iExists v. iFrame.
Qed.
Lemma std_update_id W a ρ :
std W !! a = Some ρ -> <s[a:=ρ]s>W = W.
Proof.
intros Hstate. destruct W; simpl in *.
rewrite /std_update /=. f_equiv. rewrite insert_id;auto.
Qed.
(* The following lemma reinstates temporary regions, after they have been uninitialized. The list of previously
uninitialized resources may have turned temporary in the public future world we consider *)
Lemma region_uninitialized_to_temporary_mid_open W W' (m : gmap Addr Word) l :
related_sts_pub_world W W' ->
(∀ a w, m !! a = Some w -> std W !! a = Some Temporary ∨ std W !! a = Some (Static {[a:=w]})) ->
(elements (dom (gset Addr) m)) ## l ->
(□ ([∗ map] a↦w ∈ m, ∃ φ p, ⌜∀ Wv : WORLD * Word, Persistent (φ Wv)⌝
∗ ⌜p ≠ O⌝
∗ ▷ φ (W',w)
∗ rel a p φ
∗ (if pwl p then future_pub_mono φ w
else future_priv_mono φ w))
-∗ open_region_many l W'
-∗ sts_full_world W
==∗
open_region_many l W'
∗ sts_full_world (std_update_multiple W (elements (dom (gset Addr) m)) Temporary))%I.
Proof.
iIntros (Hrelated Hforall Hdisj) "#Hvalid Hr Hsts".
iInduction (m) as [|a w m] "IH" using map_ind.
- rewrite dom_empty_L elements_empty /=. iFrame. done.
- rewrite dom_insert_L.
assert (a ∉ dom (gset Addr) m) as Hnin;[apply not_elem_of_dom;auto|].
assert (a ∉ l) as Hninl.
{ intros Hcontr. apply elem_of_disjoint in Hdisj. apply Hdisj in Hcontr;auto.
rewrite dom_insert_L. rewrite elements_union_singleton;auto. constructor. }
apply elements_union_singleton in Hnin.
apply (std_update_multiple_permutation W _ _ Temporary) in Hnin. rewrite Hnin /=.
iDestruct (big_sepM_delete with "Hvalid") as "[Ha Hvalid_rest]";[apply lookup_insert|].
rewrite delete_insert;auto.
iMod ("IH" with "[] [] Hvalid_rest Hr Hsts") as "[Hr Hsts]".
{ iPureIntro. intros a' w' Ha'. apply Hforall. simplify_map_eq. auto. }
{ iPureIntro. apply elem_of_disjoint. intros x Hm Hx. destruct (decide (a = x));[congruence|].
apply elem_of_disjoint in Hdisj. apply Hdisj in Hx;auto.
rewrite dom_insert_L. rewrite elements_union_singleton;[apply elem_of_cons;right;auto|].
apply not_elem_of_dom. auto.
}
assert (<[a:=w]> m !! a = Some w) as Ha;[apply lookup_insert|].
apply Hforall in Ha as [Htemp | Huninit].
+ rewrite std_update_id. iFrame. done.
rewrite std_sta_update_multiple_lookup_same_i;auto.
intros Hcontr%elem_of_elements%elem_of_gmap_dom. destruct Hcontr. congruence.
+ rewrite open_region_many_eq /open_region_many_def.
iDestruct "Hr" as (M Mρ) "(HM & #Hdom & #Hdom' & Hr)".
iDestruct "Hdom" as %Hdom. iDestruct "Hdom'" as %Hdom'.
assert (is_Some (M !! a)) as [ρ Hρ].
{ apply elem_of_gmap_dom. rewrite -Hdom. destruct Hrelated as [ [Hsub _] _]. apply Hsub.
apply elem_of_gmap_dom. eauto. }
iDestruct (big_sepM_delete with "Hr") as "[Hw Hr]";[rewrite lookup_delete_list_notin;eauto|].
iDestruct "Hw" as (ρ' Hρ') "[Hstate HX]".
iDestruct (sts_full_state_std with "Hsts Hstate") as %Hx.
assert (a ∉ elements (dom (gset Addr) m)) as Hnina.
{ intros Hcontr%elem_of_elements%elem_of_gmap_dom. destruct Hcontr. congruence. }
rewrite std_sta_update_multiple_lookup_same_i in Hx;auto.
rewrite Huninit in Hx;inversion Hx;subst.
iDestruct "HX" as (γpred' p' φ' Heq Hpers') "[#Hsaved' HX]".
iDestruct "HX" as (v Hlookup Hne) "[HX _]".
iMod (sts_update_std _ _ _ Temporary with "Hsts Hstate") as "[Hfull Hstate] /=".
iDestruct (region_map_delete_singleton with "Hr") as "Hr";[rewrite Hρ';eauto|].
iDestruct (region_map_insert_nonstatic Temporary with "Hr") as "Hr";[auto|].
iDestruct "Ha" as (φ p Hpers Hne') "(Hφ & Hrel & Hmono)".
rewrite rel_eq /rel_def. iDestruct "Hrel" as (γpred'') "[HREL Hsaved]".
rewrite REL_eq RELS_eq /REL_def /RELS_def.
iDestruct (reg_in with "[$HM $HREL]") as %Hmeq.
iDestruct (big_sepM_delete with "[$Hr HX Hstate]") as "Hr";[rewrite lookup_delete_list_notin;eauto|..].
{ iExists Temporary. iSplit;[rewrite lookup_insert;auto|]. iFrame.
rewrite Hmeq lookup_insert in Hρ. inversion Hρ.
iExists _,_,_. repeat iSplit;eauto.
iExists _. iFrame "∗ #". simplify_eq. repeat iSplit;eauto. simplify_map_eq. iFrame.
}
iFrame.
iModIntro.
iExists M,(<[a:=Temporary]> Mρ). iFrame. repeat iSplit.
++ iPureIntro. auto.
++ iPureIntro. rewrite dom_insert_L. rewrite Hdom'.
assert (a ∈ dom (gset Addr) M) as Hin. apply elem_of_gmap_dom;eauto.
set_solver.
++ rewrite delete_list_insert;auto.
Qed.
Lemma region_uninitialized_to_temporary_mid W W' (m : gmap Addr Word) :
related_sts_pub_world W W' ->
(∀ a w, m !! a = Some w -> std W !! a = Some Temporary ∨ std W !! a = Some (Static {[a:=w]})) ->
(□ ([∗ map] a↦w ∈ m, ∃ φ p, ⌜∀ Wv : WORLD * Word, Persistent (φ Wv)⌝
∗ ⌜p ≠ O⌝
∗ ▷ φ (W',w)
∗ rel a p φ
∗ (if pwl p then future_pub_mono φ w
else future_priv_mono φ w))
-∗ region W'
-∗ sts_full_world W
==∗
region W'
∗ sts_full_world (std_update_multiple W (elements (dom (gset Addr) m)) Temporary))%I.
Proof.
iIntros (Hrelated HW) "Htemps Hr Hsts".
iDestruct (region_open_nil with "Hr") as "Hr".
iMod (region_uninitialized_to_temporary_mid_open with "Htemps Hr Hsts") as "[Hr Hsts]";auto.
{ apply elem_of_disjoint. intros x Hx Hcontr. inversion Hcontr. }
iDestruct (region_open_nil with "Hr") as "Hr".
iFrame. done.
Qed.
Lemma dom_eq_uninit_to_temporary_region W (m : gmap Addr Word) :
(∀ a, a ∈ dom (gset Addr) m -> std W !! a = Some Temporary ∨ ∃ w, std W !! a = Some (Static {[a:=w]})) ->
dom (gset Addr) W.1 = dom (gset Addr) (std_update_multiple W (elements (dom (gset Addr) m)) Temporary).1.
Proof.
intros Hforall.
apply std_update_multiple_dom_equal. intros i Hin%elem_of_elements.
apply elem_of_gmap_dom. apply Hforall in Hin as [Hx | [w Hx] ];eauto.
Qed.
Lemma related_sts_pub_world_uninit_to_temporary_region W (m : gmap Addr Word) :
(∀ a, a ∈ dom (gset Addr) m -> std W !! a = Some Temporary ∨ ∃ w, std W !! a = Some (Static {[a:=w]})) ->
related_sts_pub_world W (std_update_multiple W (elements (dom (gset Addr) m)) Temporary).
Proof.
intros Hforall.
split;[|rewrite std_update_multiple_loc;apply related_sts_pub_refl].
split.
- rewrite (dom_eq_uninit_to_temporary_region _ m);auto.
- intros i x y Hx Hy.
destruct (decide (i ∈ dom (gset Addr) m)).
+ apply Hforall in e as HW.
rewrite std_sta_update_multiple_lookup_in_i in Hy.
2: { apply elem_of_elements. auto. }
inversion Hy;subst.
destruct HW as [Htemp | [w Huninit] ].
rewrite Hx in Htemp. simplify_eq. left.
rewrite Hx in Huninit. simplify_eq. eright;[|left]. constructor.
+ rewrite std_sta_update_multiple_lookup_same_i in Hy.
2: { intros Hcontr%elem_of_elements. congruence. }
rewrite Hy in Hx. simplify_eq. left.
Qed.
Lemma region_uninitialized_to_temporary W (m : gmap Addr Word) :
(∀ a w, m !! a = Some w -> std W !! a = Some Temporary ∨ std W !! a = Some (Static {[a:=w]})) ->
(□ ([∗ map] a↦w ∈ m, ∃ φ p, ⌜∀ Wv : WORLD * Word, Persistent (φ Wv)⌝
∗ ⌜p ≠ O⌝
∗ ▷ φ ((std_update_multiple W (elements (dom (gset Addr) m)) Temporary),w)
∗ rel a p φ
∗ (if pwl p then future_pub_mono φ w
else future_priv_mono φ w))
-∗ region W
-∗ sts_full_world W
==∗
region (std_update_multiple W (elements (dom (gset Addr) m)) Temporary)
∗ sts_full_world (std_update_multiple W (elements (dom (gset Addr) m)) Temporary))%I.
Proof.
iIntros (Hforall) "#Hvalid Hr Hsts".
iDestruct (region_monotone with "[] [] Hr") as "Hr".
{ iPureIntro. apply dom_eq_uninit_to_temporary_region with (m:=m).
intros a Hin%elem_of_gmap_dom. destruct Hin as [w Hin]. apply Hforall in Hin as [Htemp | Huninit];eauto. }
{ iPureIntro. apply related_sts_pub_world_uninit_to_temporary_region.
intros a Hin%elem_of_gmap_dom. destruct Hin as [w Hin]. apply Hforall in Hin as [Htemp | Huninit];eauto. }
iMod (region_uninitialized_to_temporary_mid with "Hvalid Hr Hsts") as "[Hr Hsts]";[|auto|].
{ apply related_sts_pub_world_uninit_to_temporary_region.
intros a Hin%elem_of_gmap_dom. destruct Hin as [w Hin]. apply Hforall in Hin as [Htemp | Huninit];eauto. }
iModIntro. iFrame.
Qed.
Lemma std_update_elements_app_union {A : Type} W (m1 m2 : gmap Addr A) ρ :
std_update_multiple W (elements (dom (gset Addr) (m1 ∪ m2))) ρ =
std_update_multiple W (elements (dom (gset Addr) m1) ++ elements (dom (gset Addr) m2)) ρ.
Proof.
rewrite (surjective_pairing (std_update_multiple W (elements (dom _ _) ) _)).
erewrite surjective_pairing.
repeat rewrite std_update_multiple_loc. f_equiv.
apply map_eq'.
intros a v.
split.
+ intros Ha.
destruct (decide (a ∈ elements (dom (gset Addr) m2))).
* rewrite std_sta_update_multiple_lookup_in_i in Ha. inversion Ha.
apply std_sta_update_multiple_lookup_in_i.
apply elem_of_app;right;auto. revert e;rewrite elem_of_elements =>e.
apply elem_of_elements. rewrite dom_union_L. set_solver.
* destruct (decide (a ∈ elements (dom (gset Addr) m1))).
** rewrite std_sta_update_multiple_lookup_in_i in Ha. inversion Ha.
apply std_sta_update_multiple_lookup_in_i.
apply elem_of_app;left;auto. apply elem_of_elements in e.
repeat rewrite dom_union_L. apply elem_of_elements. set_solver.
** rewrite std_sta_update_multiple_lookup_same_i in Ha.
rewrite std_sta_update_multiple_lookup_same_i;auto.
apply not_elem_of_app. split;auto. intros Hcontr%elem_of_elements.
rewrite dom_union_L in Hcontr.
apply elem_of_union in Hcontr as [Hcontr | Hcontr].
{ apply elem_of_elements in Hcontr. done. }
{ apply elem_of_elements in Hcontr. done. }
+ intros Ha.
destruct (decide (a ∈ (elements (dom (gset Addr) m1) ++ elements (dom (gset Addr) m2)))).
* rewrite std_sta_update_multiple_lookup_in_i in Ha;auto. inversion Ha.
apply std_sta_update_multiple_lookup_in_i.
apply elem_of_elements. rewrite dom_union_L.
apply elem_of_app in e as [e | e]; apply elem_of_elements in e;set_solver.
* rewrite std_sta_update_multiple_lookup_same_i in Ha;auto.
rewrite std_sta_update_multiple_lookup_same_i;auto.
rewrite elem_of_elements. apply not_elem_of_app in n.
revert n. repeat rewrite elem_of_elements. intros [n1 n2].
rewrite dom_union_L. set_solver.
Qed.
(* ------------------------------------------ REINSTATE --------------------------------------------------------- *)
(* The following lemma reinstates all relevant static and uninitialized invariants to Temporary. It is in the
format typically applied in proofs: the local stack frame and leftovers are open, the uninitialized part of the
adversary stack is still in region. We need to update both before we close *)
(* open_region_many is monotone wrt public future worlds *)
Lemma open_region_many_monotone l W W':
dom (gset Addr) W.1 = dom (gset Addr) W'.1 →
related_sts_pub_world W W' →
(open_region_many l W -∗ open_region_many l W')%I.
Proof.
iIntros (Hdomeq Hrelated) "HW". rewrite open_region_many_eq /open_region_many_def.
iDestruct "HW" as (M Mρ) "(Hm & % & % & Hmap)". iExists M, Mρ. iFrame.
iSplitR;[iPureIntro;rewrite -Hdomeq;auto|].
iSplitR; auto.
iApply region_map_monotone; eauto.
Qed.
(* The following lemma assumes that m_static contains more than one address *)
Lemma region_close_static_and_uninitialized_to_temporary (m_static: gmap Addr Word)
(m_uninit: gmap Addr Word) W W' :
(W' = (std_update_temp_multiple W (elements (dom (gset Addr) m_static) ++
elements (dom (gset Addr) m_uninit)))) →
size m_static > 1 ->
(∀ a w, m_uninit !! a = Some w -> std W !! a = Some Temporary ∨ std W !! a = Some (Static {[a:=w]})) ->
open_region_many (elements (dom (gset Addr) m_static)) W
∗ sts_full_world W
(* The static resources *)
∗ ([∗ map] a↦v ∈ m_static, ∃ p φ, ⌜forall Wv, Persistent (φ Wv)⌝ ∗
temp_resources W' φ a p ∗ rel a p φ)
∗ sts_state_std_many m_static (Static m_static)
(* Knowledge about the uninitialized resources *)
∗ (□ ([∗ map] a↦w ∈ m_uninit, ∃ φ p, ⌜∀ Wv : WORLD * Word, Persistent (φ Wv)⌝
∗ ⌜p ≠ O⌝
∗ ▷ φ (W',w)
∗ rel a p φ
∗ (if pwl p then future_pub_mono φ w
else future_priv_mono φ w)))
==∗
sts_full_world W'
∗ region W'.
Proof.
iIntros (Heq Hsize Hunint) "(HR & Hsts & Hres & Hst & #Hvalid)".
iDestruct (sts_full_state_std_many with "[Hsts Hst]") as %?. by iFrame.
assert (related_sts_pub_world W W') as Hrelated.
{ rewrite Heq. rewrite /std_update_temp_multiple. rewrite std_update_multiple_app.
eapply related_sts_pub_trans_world;[apply related_sts_pub_world_static_to_temporary with m_static;eauto|].
apply related_sts_pub_world_uninit_to_temporary_region. intros a Hin.
destruct (decide (a ∈ elements (dom (gset Addr) m_static))).
- left. apply std_sta_update_multiple_lookup_in_i. auto.
- rewrite std_sta_update_multiple_lookup_same_i;auto.
apply elem_of_gmap_dom in Hin as [w Hin]. apply Hunint in Hin as [Htemp | Huninit];eauto.
}
assert (elements (dom (gset Addr) m_uninit) ## elements (dom (gset Addr) m_static)) as Hdisj.
{ rewrite elem_of_disjoint. intros x Hxuninit Hxstatic.
apply elem_of_elements,elem_of_gmap_dom in Hxuninit as [w Hw].
apply Hunint in Hw as [Htemp | Huninit].
- revert H;rewrite Forall_forall =>H. apply H in Hxstatic. congruence.
- revert H;rewrite Forall_forall =>H. apply H in Hxstatic.
destruct (decide (m_static = {[x:=w]}));[subst;rewrite map_size_singleton in Hsize;lia|congruence].
}
iDestruct (open_region_many_monotone _ _ W' with "HR") as "HR";auto.
{ rewrite Heq. apply std_update_multiple_dom_equal. intros a Hin%elem_of_app.
revert H;rewrite Forall_forall =>H.
destruct Hin as [Hin | Hin].
- apply elem_of_gmap_dom. eauto.
- apply elem_of_elements,elem_of_gmap_dom in Hin as [w Hw].
apply Hunint in Hw as [Htemp | Huninit]; apply elem_of_gmap_dom;eauto.
}
iMod (region_uninitialized_to_temporary_mid_open with "Hvalid HR Hsts") as "[Hr Hsts]";[auto..|].
iDestruct (region_update_multiple_states _ _ _ Temporary with "[$Hsts $Hst]") as ">[Hsts Hst]".
iModIntro.
(* iDestruct (open_region_world_static_to_temporary with "Hr") as "Hr"; eauto. *)
repeat rewrite -std_update_multiple_app std_update_multiple_app_commute. rewrite Heq.
iDestruct (region_close_temporary_many with "[Hr Hres Hst Hsts]") as "(?&?)"; iFrame.
Qed.
End heap.
|
{"author": "logsem", "repo": "cerise-stack", "sha": "f68111362730aff998798d63c7d6a0a7176eff44", "save_path": "github-repos/coq/logsem-cerise-stack", "path": "github-repos/coq/logsem-cerise-stack/cerise-stack-f68111362730aff998798d63c7d6a0a7176eff44/theories/region_invariants_uninitialized.v"}
|
Require Import A1_Plan A2_Orientation A7_Tactics .
Require Import B7_Tactics .
Require Import C1_Distance C7_Tactics .
Require Import F5_Tactics .
Require Import G1_Angles G3_ParticularAngle .
Require Import H1_Triangles .
Require Import I2_Supplement I3_OpposedAngles .
Require Import K3_Tactics .
Require Import L1_Parallelogramm L2_StrictParallelogramm.
Section PARALLELOGRAMM_ANGLES.
Lemma ParallelogrammDABeqBCD : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B ->
B <> C ->
CongruentAngle D A B B C D.
Proof.
intros.
assert (H4 := ParallelogrammTCongruentBCDDAB A B C D H).
step10 H4.
apply (ParallelogrammDistinctABDistinctCD A B C D H H0).
apply sym_not_eq; apply (ParallelogrammDistinctBCDistinctDA A B C D H H1).
Qed.
Lemma StrictParallelogrammDABeqBCD : forall A B C D : Point,
StrictParallelogramm A B C D ->
CongruentAngle D A B B C D.
Proof.
intros; apply ParallelogrammDABeqBCD.
destruct H; immediate10.
apply (StrictParallelogrammDistinctAB A B C D H).
apply (StrictParallelogrammDistinctBC A B C D H).
Qed.
Lemma ParallelogrammABCeqCDA : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B ->
B <> C ->
CongruentAngle A B C C D A.
Proof.
intros.
assert (H4 := ParallelogrammTCongruentABCCDA A B C D H).
step10 H4.
apply sym_not_eq; apply (ParallelogrammDistinctABDistinctCD A B C D H H0).
apply (ParallelogrammDistinctBCDistinctDA A B C D H H1).
Qed.
Lemma StrictParallelogrammABCeqCDA : forall A B C D : Point,
StrictParallelogramm A B C D ->
CongruentAngle A B C C D A.
Proof.
intros; apply ParallelogrammABCeqCDA.
destruct H; immediate10.
apply (StrictParallelogrammDistinctAB A B C D H).
apply (StrictParallelogrammDistinctBC A B C D H).
Qed.
Lemma ParallelogrammBACeqDCA : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B ->
CongruentAngle B A C D C A.
Proof.
intros; inversion H.
assert (H3 := ParallelogrammTCongruentABCCDA A B C D H).
step10 H3.
apply (ParallelogrammDistinctABDistinctCD A B C D H H0).
Qed.
Lemma StrictParallelogrammBACeqDCA : forall A B C D : Point,
StrictParallelogramm A B C D ->
CongruentAngle B A C D C A.
Proof.
intros; apply ParallelogrammBACeqDCA.
destruct H; immediate10.
apply (StrictParallelogrammDistinctAB A B C D H).
Qed.
Lemma ParallelogrammDACeqBCA : forall A B C D : Point,
Parallelogramm A B C D ->
B <> C ->
CongruentAngle D A C B C A.
Proof.
intros; inversion H.
assert (H3 := ParallelogrammTCongruentABCCDA A B C D H).
step10 H3.
apply sym_not_eq; apply (ParallelogrammDistinctBCDistinctDA A B C D H H0).
Qed.
Lemma StrictParallelogrammDACeqBCA : forall A B C D : Point,
StrictParallelogramm A B C D ->
CongruentAngle D A C B C A.
Proof.
intros; apply ParallelogrammDACeqBCA.
destruct H; immediate10.
apply (StrictParallelogrammDistinctBC A B C D H).
Qed.
Lemma ParallelogrammABDeqCDB : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B ->
CongruentAngle A B D C D B.
Proof.
intros; inversion H.
assert (H3 := ParallelogrammTCongruentBCDDAB A B C D H).
step10 H3.
apply sym_not_eq; apply (ParallelogrammDistinctABDistinctCD A B C D H H0).
Qed.
Lemma StrictParallelogrammABDeqCDB : forall A B C D : Point,
StrictParallelogramm A B C D ->
CongruentAngle A B D C D B.
Proof.
intros; apply ParallelogrammABDeqCDB.
destruct H; immediate10.
apply (StrictParallelogrammDistinctAB A B C D H).
Qed.
Lemma ParallelogrammADBeqCBD : forall A B C D : Point,
Parallelogramm A B C D ->
B <> C ->
CongruentAngle A D B C B D.
Proof.
intros; inversion H.
assert (H3 := ParallelogrammTCongruentBCDDAB A B C D H).
step10 H3.
apply (ParallelogrammDistinctBCDistinctDA A B C D H H0).
Qed.
Lemma StrictParallelogrammADBeqCBD : forall A B C D : Point,
StrictParallelogramm A B C D ->
CongruentAngle A D B C B D.
Proof.
intros; apply ParallelogrammADBeqCBD.
destruct H; immediate10.
apply (StrictParallelogrammDistinctBC A B C D H).
Qed.
Lemma StrictParallelogrammExteriorAngles : forall A B C D E : Point,
StrictParallelogramm A B C D ->
Between A B E ->
CongruentAngle D A B C B E.
Proof.
intros.
since10 (Clockwise C D B).
step10 (StrictParallelogrammClockwiseBCD A B C D H).
pose (G := StrictPVertex4 C D B H1).
pose (H2 := StrictPVertex4Parallelogramm C D B H1); fold G in H2.
since10 (Between G B A).
apply (SumAngles B G C D A).
step10 (StrictParallelogrammClockwiseCDA C D B G H2).
immediate10.
step10 (StrictParallelogrammClockwiseDAB A B C D H).
step10 (StrictParallelogrammBACeqDCA C D B G H2).
step10 (StrictParallelogrammABDeqCDB A B C D H).
since10 (OpenRay B E G).
canonize1.
step10 H6.
step10 H5.
since10 (CongruentAngle C B E C B G).
step10 H5.
step10 (StrictParallelogrammDABeqBCD A B C D H).
step10 (StrictParallelogrammBACeqDCA C D B G H2).
Qed.
Lemma StrictParallelogrammAlternateAngles : forall A B C D E : Point,
StrictParallelogramm A B C D ->
Between C B E ->
CongruentAngle D A B E B A.
Proof.
intros.
setSymmetricPoint5 A B ipattern:(G).
apply (StrictParallelogrammDistinctAB A B C D H).
since10 (OpposedAngles B E A C G).
since10 (CongruentAngle E B A C B G).
step10 H5.
apply CongruentAngleSym; apply (StrictParallelogrammExteriorAngles A B C D G H).
immediate10.
Qed.
Lemma ParallelogrammSegmentElongated : forall A B C D : Point,
Parallelogramm A B C D ->
A <> D ->
Segment A B C ->
ElongatedAngle D A B.
Proof.
intros.
since10 (Segment D C A).
usingChaslesRec2.
rewrite <- (ParallelogrammBCeqDA A B C D H).
rewrite (DistanceSym D C).
rewrite <- (ParallelogrammABeqCD A B C D H).
usingChasles2 A C B.
from10 H2 (Between D A B).
step10 H2.
inversion H; immediate10.
Qed.
Lemma BetweenBetweenElongated : forall A B C E : Point,
Between A B E ->
Between A C B ->
ElongatedAngle C B E.
Proof.
intros.
from10 H (Between C B E).
Qed.
Lemma ParallelogrammSegmentElongated2 : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B ->
Segment B C A ->
ElongatedAngle D A B.
Proof.
intros.
from10 H1 (Between D A B).
since10 (Segment A D C).
usingChaslesRec2.
rewrite (DistanceSym A D).
rewrite <- (ParallelogrammBCeqDA A B C D H).
rewrite <- (ParallelogrammABeqCD A B C D H).
usingChasles2 B A C.
step10 H1.
inversion H; immediate10.
Qed.
Lemma BetweenBetweenElongated2 : forall A B C E : Point,
Between A B E ->
Between C A B ->
ElongatedAngle C B E.
Proof.
intros.
from10 H (Between C B E).
Qed.
Lemma ParallelogrammSegmentNull3 : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B ->
A <> D ->
Segment C A B ->
NullAngle D A B.
Proof.
intros.
since10 (OpenRay A B D).
since10 (OpenRay A B C).
step10 H3.
since10 (Segment A C D).
usingChaslesRec2.
rewrite (DistanceSym A D).
rewrite <- (ParallelogrammBCeqDA A B C D H).
rewrite (DistanceSym D C).
rewrite <- (ParallelogrammABeqCD A B C D H).
usingChasles2 A B C.
Qed.
Lemma BetweenBetweenNull3 : forall A B C E : Point,
Between A B E ->
Between C B A ->
NullAngle C B E.
Proof.
intros.
since10 (OpenRay B C E).
canonize1.
step10 H2.
step10 H3.
Qed.
Lemma ParallelogrammColinearExteriorAngles : forall A B C D E : Point,
Parallelogramm A B C D ->
A <> D ->
Between A B E ->
Collinear A B C ->
CongruentAngle D A B C B E.
Proof.
intros.
by3SegmentCases1 H2.
since10 (ElongatedAngle C B E).
apply (BetweenBetweenElongated A).
immediate10.
step10 H3.
inversion H; immediate10.
assert (H4 := ParallelogrammDistinctDADistinctBC A B C D H).
apply sym_not_eq; apply H4; immediate10.
step10 H4.
apply (ParallelogrammSegmentElongated A B C D); immediate10.
since10 (ElongatedAngle C B E).
apply (BetweenBetweenElongated2 A).
immediate10.
step10 H4.
inversion H; immediate10.
step10 H3.
apply (ParallelogrammSegmentElongated2 A B C D); immediate10.
since10 (NullAngle C B E).
apply (BetweenBetweenNull3 A).
immediate10.
step10 H4.
apply sym_not_eq; apply (ParallelogrammDistinctDADistinctBC A B C D H).
immediate10.
step10 H3.
apply (ParallelogrammSegmentNull3 A B C D); immediate10.
Qed.
Lemma ParallelogrammExteriorAngles : forall A B C D E : Point,
Parallelogramm A B C D ->
A <> D ->
Between A B E ->
CongruentAngle D A B C B E.
Proof.
intros.
by3Cases1 A B C.
pose (H3 := SPDef H H2).
apply (StrictParallelogrammExteriorAngles A B C D E H3).
immediate10.
since10 (Parallelogramm C B A D).
do 2 apply ParallelogrammPerm; apply ParallelogrammRev; immediate10.
since10 (Clockwise C B A).
pose (H5 := SPDef H2 H4).
since10 (CongruentAngle D C B E B C).
apply (StrictParallelogrammAlternateAngles C B A D E H5); immediate10.
step10 H6.
since10 (CongruentAngle D A B B C D).
apply (ParallelogrammDABeqBCD A B C D H); immediate10.
apply ParallelogrammColinearExteriorAngles; immediate10.
Qed.
Lemma ParallelogrammAlternateAngles : forall A B C D E : Point,
Parallelogramm A B C D ->
A <> B ->
Between C B E ->
CongruentAngle D A B E B A.
Proof.
intros.
since10 (CongruentAngle D A B B C D).
apply ParallelogrammDABeqBCD; immediate10.
step10 H2.
since10 (CongruentAngle D C B A B E).
apply ParallelogrammExteriorAngles.
apply ParallelogrammRev.
do 2 apply ParallelogrammPerm; immediate10.
apply (ParallelogrammDistinctABDistinctCD A B C D H H0).
immediate10.
Qed.
Lemma ParallelogrammDABSupplementAngleABC : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B ->
B <> C ->
Supplement D A B A B C.
Proof.
intros.
setSymmetricPoint5 A B ipattern:(G).
since10 (CongruentAngle D A B C B G).
assert (H4 := sym_not_eq (ParallelogrammDistinctBCDistinctDA A B C D H H1)).
apply (ParallelogrammExteriorAngles A B C D G H H4 H3).
step10 H4.
Qed.
Lemma StrictParallelogrammDABSupplementAngleABC : forall A B C D : Point,
StrictParallelogramm A B C D ->
Supplement D A B A B C.
Proof.
intros; apply ParallelogrammDABSupplementAngleABC.
destruct H; immediate10.
apply (StrictParallelogrammDistinctAB A B C D H).
apply (StrictParallelogrammDistinctBC A B C D H).
Qed.
Lemma ParallelogrammABCSupplementAngleBCD : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B ->
B <> C ->
Supplement A B C B C D.
Proof.
intros.
assert (H2 := ParallelogrammDABSupplementAngleABC A B C D H H0 H1).
step10 H2.
apply ParallelogrammDABeqBCD; immediate10.
Qed.
Lemma StrictParallelogrammABCSupplementAngleBCD : forall A B C D : Point,
StrictParallelogramm A B C D ->
Supplement A B C B C D.
Proof.
intros; apply ParallelogrammABCSupplementAngleBCD.
destruct H; immediate10.
apply (StrictParallelogrammDistinctAB A B C D H).
apply (StrictParallelogrammDistinctBC A B C D H).
Qed.
Lemma ParallelogrammBCDSupplementAngleCDA : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B ->
B <> C ->
Supplement B C D C D A.
Proof.
intros.
assert (H2 := ParallelogrammABCSupplementAngleBCD A B C D H H0 H1).
step10 H2.
apply ParallelogrammABCeqCDA; immediate10.
Qed.
Lemma StrictParallelogrammBCDSupplementAngleCDA : forall A B C D : Point,
StrictParallelogramm A B C D ->
Supplement B C D C D A.
Proof.
intros; apply ParallelogrammBCDSupplementAngleCDA.
destruct H; immediate10.
apply (StrictParallelogrammDistinctAB A B C D H).
apply (StrictParallelogrammDistinctBC A B C D H).
Qed.
Lemma ParallelogrammCDASupplementAngleDAB : forall A B C D : Point,
Parallelogramm A B C D ->
A <> B ->
B <> C ->
Supplement C D A D A B.
Proof.
intros.
assert (H2 := ParallelogrammBCDSupplementAngleCDA A B C D H H0 H1).
step10 H2.
apply CongruentAngleSym; apply ParallelogrammDABeqBCD; immediate10.
Qed.
Lemma StrictParallelogrammCDASupplementAngleDAB : forall A B C D : Point,
StrictParallelogramm A B C D ->
Supplement C D A D A B.
Proof.
intros; apply ParallelogrammCDASupplementAngleDAB.
destruct H; immediate10.
apply (StrictParallelogrammDistinctAB A B C D H).
apply (StrictParallelogrammDistinctBC A B C D H).
Qed.
Lemma CongruentAnglesParallelogramm : forall A B C D : Point,
Clockwise A B C ->
Clockwise C B D ->
CongruentAngle A B C B C D ->
Distance A B = Distance C D ->
StrictParallelogramm A B D C.
Proof.
intros.
since10 (TCongruent (Tr A B C) (Tr D C B)).
since10 (StrictParallelogramm C A B D).
apply EquiDistantStrictParallelogramm; immediate10.
apply StrictParallelogrammPerm; immediate10.
Qed.
Lemma SupplementParallelogramm : forall A B C D : Point,
Clockwise A B C ->
Clockwise B C D ->
Supplement A B C B C D ->
Distance A B = Distance C D ->
StrictParallelogramm A B C D.
Proof.
intros.
setSymmetricPoint5 D C ipattern:(E).
since10 (StrictParallelogramm A B E C).
apply CongruentAnglesParallelogramm.
immediate10.
step10 H5.
step10 H1.
immediate10.
since10 (TCongruent (Tr B E C) (Tr A C D)).
step10 3.
destruct H6 as (Hp, H7).
assert (H8 := ParallelogrammBCeqDA A B E C Hp); immediate10.
apply ParallelogrammExteriorAngles.
inversion H6.
do 2 apply ParallelogrammPerm; immediate10.
apply sym_not_eq; apply (StrictParallelogrammDistinctBC A B E C H6).
immediate10.
apply EquiDistantStrictParallelogramm.
immediate10.
step10 H5.
left; apply (StrictParallelogrammClockwiseCDA A B E C H6).
immediate10.
immediate10.
Qed.
End PARALLELOGRAMM_ANGLES.
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|
#
# Copyright (C) 2019 Luca Pasqualini
# University of Siena - Artificial Intelligence Laboratory - SAILab
#
# Inspired by the work of David Johnston (C) 2017: https://github.com/dj-on-github/sp800_22_tests
#
# NistRng is licensed under a BSD 3-Clause.
#
# You should have received a copy of the license along with this
# work. If not, see <https://opensource.org/licenses/BSD-3-Clause>.
# Import packages
import numpy
import scipy.special
# Import required src
from nistrng import Test, Result
class FrequencyWithinBlockTest(Test):
"""
Frequency within block test as described in NIST paper: https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-22r1a.pdf
The focus of the test is the proportion of ones within M-bit blocks. The purpose of this test is to determine whether the frequency of
ones in an M-bit block is approximately M/2, as would be expected under an assumption of randomness.
For block size M=1, this test degenerates to the Frequency (Monobit) test.
The significance value of the test is 0.01.
"""
def __init__(self):
# Define specific test attributes
self._sequence_size_min: int = 100
self._default_block_size: int = 20
self._blocks_number_max: int = 100
# Define cache attributes
self._last_bits_size: int = -1
self._block_size: int = -1
self._blocks_number: int = -1
# Generate base Test class
super(FrequencyWithinBlockTest, self).__init__("Frequency Within Block", 0.01)
def _execute(self,
bits: numpy.ndarray) -> Result:
"""
Overridden method of Test class: check its docstring for further information.
"""
# Reload values is cache is empty or no longer up-to-date
# Otherwise, use cache
if self._last_bits_size == -1 or self._last_bits_size != bits.size:
# Get the number of blocks (N) with the default minimum block size (M)
block_size: int = self._default_block_size
blocks_number: int = int(bits.size // block_size)
# Get the block size (M) if the number of blocks (N) exceed the allowed max
if blocks_number >= self._blocks_number_max:
blocks_number = self._blocks_number_max - 1
block_size = int(bits.size // blocks_number)
# Save in the cache
self._last_bits_size = bits.size
self._block_size = block_size
self._blocks_number = blocks_number
else:
block_size: int = self._block_size
blocks_number: int = self._blocks_number
# Initialize a list of fractions
block_fractions: numpy.ndarray = numpy.zeros(blocks_number, dtype=float)
for i in range(blocks_number):
# Get the bits in the current block
block: numpy.ndarray = bits[i * block_size:((i + 1) * block_size)]
# Compute ones and save the fraction in the array
block_fractions[i] = numpy.count_nonzero(block) / block_size
# Compute Chi-square
chi_square: float = numpy.sum(4.0 * block_size * ((block_fractions[:] - 0.5) ** 2))
# Compute score (P-value) applying the lower incomplete gamma function
score: float = scipy.special.gammaincc((blocks_number / 2.0), chi_square / 2.0)
# Return result
if score >= self.significance_value:
return Result(self.name, True, numpy.array(score))
return Result(self.name, False, numpy.array(score))
def is_eligible(self,
bits: numpy.ndarray) -> bool:
"""
Overridden method of Test class: check its docstring for further information.
"""
# Check for eligibility
if bits.size < self._sequence_size_min:
return False
return True
|
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|
import matplotlib.pyplot as plt
import numpy as np
import qcodes as qc
from qcodes import (
Measurement,
experiments,
initialise_database,
initialise_or_create_database_at,
load_by_guid,
load_by_run_spec,
load_experiment,
load_last_experiment,
load_or_create_experiment,
new_experiment,
ParameterWithSetpoints,
)
from qcodes.dataset.plotting import plot_dataset
from qcodes.instrument_drivers.tektronix.keithley_7510 import GeneratedSetPoints
from qcodes.loops import Loop
from qcodes.logger.logger import start_all_logging
# from qcodes.tests.instrument_mocks import DummyInstrument, DummyInstrumentWithMeasurement
from OPX_driver import *
pulse_len = 1000
config = {
"version": 1,
"controllers": {
"con1": {
"type": "opx1",
"analog_outputs": {
1: {"offset": +0.0},
2: {"offset": +0.0},
},
"analog_inputs": {
1: {"offset": +0.0},
},
}
},
"elements": {
"qe1": {
"mixInputs": {"I": ("con1", 1), "Q": ("con1", 2)},
"outputs": {"output1": ("con1", 1)},
"intermediate_frequency": 5e6,
"operations": {"playOp": "constPulse", "readout": "readoutPulse"},
"time_of_flight": 180,
"smearing": 0,
},
},
"pulses": {
"constPulse": {
"operation": "control",
"length": pulse_len, # in ns
"waveforms": {"I": "const_wf", "Q": "const_wf"},
},
"readoutPulse": {
"operation": "measure",
"length": pulse_len,
"waveforms": {"I": "const_wf", "Q": "const_wf"},
"digital_marker": "ON",
"integration_weights": {"x": "xWeights", "y": "yWeights"},
},
},
"waveforms": {
"const_wf": {"type": "constant", "sample": 0.2},
},
"digital_waveforms": {
"ON": {"samples": [(1, 0)]},
},
"integration_weights": {
"xWeights": {
"cosine": [1.0] * (pulse_len // 4),
"sine": [0.0] * (pulse_len // 4),
},
"yWeights": {
"cosine": [0.0] * (pulse_len // 4),
"sine": [1.0] * (pulse_len // 4),
},
},
}
f_pts = 100
voltage_range = np.linspace(0, 10, 10)
f_range = np.linspace(0, 100, f_pts)
# opx = OPX(config)
opx = OPX_SpectrumScan(config)
opx.f_start(0)
opx.f_stop(100)
opx.sim_time(100000)
opx.n_points(f_pts)
station = qc.Station()
station.add_component(opx)
exp = load_or_create_experiment(
experiment_name="my experiment", sample_name="this sample"
)
meas = Measurement(exp=exp, station=station)
meas.register_parameter(opx.ext_v) # register the independent parameter
meas.register_parameter(
opx.spectrum, setpoints=(opx.ext_v,)
) # now register the dependent one
with meas.run() as datasaver:
for v in voltage_range:
opx.ext_v(v)
# interact with external device here
datasaver.add_result((opx.ext_v, v), (opx.spectrum, opx.spectrum()))
dataset = datasaver.dataset
plot_dataset(dataset)
|
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|
#!/usr/bin/env python
# license removed for brevity
import rospy
import numpy as np
import matplotlib.pyplot as plt
import scipy.io as sio
import math as math
from focus_control.msg import status
from nav_msgs.msg import Odometry
from std_msgs.msg import Float32
def desired_input():
rospy.init_node('desired_data', anonymous=True)
pubv = rospy.Publisher('desired_velocity', Float32, queue_size=10)
puba = rospy.Publisher('desired_angle', Float32, queue_size=10)
rate = rospy.Rate(10) # 10 Hz
#READ GPS DATA FROM FILE
gps_data = sio.loadmat('/home/acostley/Desktop/Paths/desired_data.mat')
desired_velocity = gps_data['veld'];
desired_angle = gps_data['thetad'];
desired_heading = gps_data['psid'];
outvel = Float32()
outang = Float32()
#output = FloatArray()
#out = [desired_velocity, desired_angle, desired_heading]
i = 0
while not rospy.is_shutdown():
#out = [desired_velocity[i], desired_angle[i], desired_heading[i]]
#output.data = out
#rospy.loginfo(desired_velocity[i])
outvel.data = desired_velocity[i]
outang.data = desired_angle[i]
#outvel.data = 15
#outang.data = 2000
pubv.publish(outvel)
puba.publish(outang)
i = i +1
rate.sleep()
if __name__ == '__main__':
try:
desired_input()
except rospy.ROSInterruptException:
pass
|
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|
"""
dot
The dot tool returns the dot product of two arrays.
import numpy
A = numpy.array([ 1, 2 ])
B = numpy.array([ 3, 4 ])
print numpy.dot(A, B) #Output : 11
cross
The cross tool returns the cross product of two arrays.
import numpy
A = numpy.array([ 1, 2 ])
B = numpy.array([ 3, 4 ])
print numpy.cross(A, B) #Output : -2
Task
You are given two arrays and . Both have dimensions of X.
Your task is to compute their matrix product.
Input Format
The first line contains the integer .
The next lines contains space separated integers of array .
The following lines contains space separated integers of array .
Output Format
Print the matrix multiplication of and .
Sample Input
2
1 2
3 4
1 2
3 4
Sample Output
[[ 7 10]
[15 22]]
"""
import numpy as np
np.set_printoptions(legacy="1.13")
N = int(input())
arr1 = np.array([list(map(int, input().split())) for _ in range(N)], int)
arr2 = np.array([list(map(int, input().split())) for _ in range(N)], int)
print(np.dot(arr1, arr2))
|
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|
import torch
import torch.nn as nn
from torchvision import transforms
from tqdm import tqdm
import os
import cv2 as cv
import numpy as np
import models
import models_v16
from config import device
# old_model = models.DIMModel()
# new_model = models_v16.DIMModel()
from config import device
from data_gen import data_transforms
from utils import ensure_folder, compute_mse, compute_sad, draw_str
IMG_FOLDER = 'alphamatting/input_lowres'
ALPHA_FOLDER = 'alphamatting/gt_lowres'
TRIMAP_FOLDERS = ['alphamatting/trimap_lowres/Trimap1', 'alphamatting/trimap_lowres/Trimap2']
OUTPUT_FOLDERS = ['alphamatting/output_lowres_older1/Trimap1', 'alphamatting/output_lowres_older1/Trimap2', 'images/alphamatting/output_lowres_older1/Trimap3', ]
def migrate(new_model):
# print(new_model)
checkpoint = 'BEST_checkpoint_older.tar'
checkpoint = torch.load(checkpoint)
old_model = checkpoint['model'].module
# print(dict(old_model.up1.unpool.named_parameters()))
# print(old_model)
# print("old")
# print(dict(old_model.up1.conv.cbr_unit[0].named_parameters()))
# print("new")
# print(dict(new_model.up1.conv.cbr_unit[0].named_parameters()))
l1s = [
old_model.down1.conv1.cbr_unit[0],
old_model.down1.conv1.cbr_unit[1],
old_model.down1.conv2.cbr_unit[0],
old_model.down1.conv2.cbr_unit[1],
old_model.down2.conv1.cbr_unit[0],
old_model.down2.conv1.cbr_unit[1],
old_model.down2.conv2.cbr_unit[0],
old_model.down2.conv2.cbr_unit[1],
old_model.down3.conv1.cbr_unit[0],
old_model.down3.conv1.cbr_unit[1],
old_model.down3.conv2.cbr_unit[0],
old_model.down3.conv2.cbr_unit[1],
old_model.down3.conv3.cbr_unit[0],
old_model.down3.conv3.cbr_unit[1],
old_model.down4.conv1.cbr_unit[0],
old_model.down4.conv1.cbr_unit[1],
old_model.down4.conv2.cbr_unit[0],
old_model.down4.conv2.cbr_unit[1],
old_model.down4.conv3.cbr_unit[0],
old_model.down4.conv3.cbr_unit[1],
old_model.down5.conv1.cbr_unit[0],
old_model.down5.conv1.cbr_unit[1],
old_model.down5.conv2.cbr_unit[0],
old_model.down5.conv2.cbr_unit[1],
old_model.down5.conv3.cbr_unit[0],
old_model.down5.conv3.cbr_unit[1],
old_model.up5.conv.cbr_unit[0],
old_model.up5.conv.cbr_unit[1],
old_model.up4.conv.cbr_unit[0],
old_model.up4.conv.cbr_unit[1],
old_model.up3.conv.cbr_unit[0],
old_model.up3.conv.cbr_unit[1],
old_model.up2.conv.cbr_unit[0],
old_model.up2.conv.cbr_unit[1],
old_model.up1.conv.cbr_unit[0],
old_model.up1.conv.cbr_unit[1]
]
l2s = [
new_model.down1.conv1.cbr_unit[0],
new_model.down1.conv1.cbr_unit[1],
new_model.down1.conv2.cbr_unit[0],
new_model.down1.conv2.cbr_unit[1],
new_model.down2.conv1.cbr_unit[0],
new_model.down2.conv1.cbr_unit[1],
new_model.down2.conv2.cbr_unit[0],
new_model.down2.conv2.cbr_unit[1],
new_model.down3.conv1.cbr_unit[0],
new_model.down3.conv1.cbr_unit[1],
new_model.down3.conv2.cbr_unit[0],
new_model.down3.conv2.cbr_unit[1],
new_model.down3.conv3.cbr_unit[0],
new_model.down3.conv3.cbr_unit[1],
new_model.down4.conv1.cbr_unit[0],
new_model.down4.conv1.cbr_unit[1],
new_model.down4.conv2.cbr_unit[0],
new_model.down4.conv2.cbr_unit[1],
new_model.down4.conv3.cbr_unit[0],
new_model.down4.conv3.cbr_unit[1],
new_model.down5.conv1.cbr_unit[0],
new_model.down5.conv1.cbr_unit[1],
new_model.down5.conv2.cbr_unit[0],
new_model.down5.conv2.cbr_unit[1],
new_model.down5.conv3.cbr_unit[0],
new_model.down5.conv3.cbr_unit[1],
new_model.up5.conv.cbr_unit[0],
new_model.up5.conv.cbr_unit[1],
new_model.up4.conv.cbr_unit[0],
new_model.up4.conv.cbr_unit[1],
new_model.up3.conv.cbr_unit[0],
new_model.up3.conv.cbr_unit[1],
new_model.up2.conv.cbr_unit[0],
new_model.up2.conv.cbr_unit[1],
new_model.up1.conv.cbr_unit[0],
new_model.up1.conv.cbr_unit[1]
]
for l1, l2 in zip(l1s, l2s):
if isinstance(l1, nn.Conv2d) and isinstance(l2, nn.Conv2d):
if l1.weight.size() == l2.weight.size() and l1.bias.size() == l2.bias.size():
print("success")
# l2.weight.data.copy_(l1.weight.data)
l2.weight.data = l1.weight.data
# l2.bias.data.copy_(l1.bias.data)
l2.bias.data = l1.bias.data
elif isinstance(l1, nn.BatchNorm2d) and isinstance(l2, nn.BatchNorm2d):
if l1.weight.size() == l2.weight.size() and l1.bias.size() == l2.bias.size():
print("success")
# l2.weight.data.copy_(l1.weight.data)
l2.weight.data = l1.weight.data
# l2.bias.data.copy_(l1.bias.data)
l2.bias.data = l1.bias.data
l2.running_mean.data = l1.running_mean.data
l2.running_var.data = l1.running_var.data
del checkpoint
# print("old")
# print(dict(old_model.up1.conv.cbr_unit[0].named_parameters()))
# print("new")
# print(dict(new_model.up1.conv.cbr_unit[0].named_parameters()))
# new_model.load_state_dict(old_model.state_dict())
if __name__ == "__main__":
model = models.DIMModel()
migrate(model)
# print(dict(model.up1.conv.cbr_unit[0].named_parameters()))
model = model.to(device)
model.eval()
# checkpoint = 'BEST_checkpoint_older.tar'
# checkpoint = torch.load(checkpoint)
# old_model = checkpoint['model'].module
# # print(old_model.state_dict())
# print(old_model)
# checkpoint = 'checkpoint_0007_0.0650.tar'
# checkpoint = torch.load(checkpoint)
# model = checkpoint['model']
# model = model.to(device)
# model.eval()
transformer = data_transforms['valid']
ensure_folder('images')
ensure_folder('images/alphamatting')
ensure_folder(OUTPUT_FOLDERS[0])
ensure_folder(OUTPUT_FOLDERS[1])
# ensure_folder(OUTPUT_FOLDERS[2])
files = [f for f in os.listdir(IMG_FOLDER) if f.endswith('.png')]
for file in tqdm(files):
filename = os.path.join(IMG_FOLDER, file)
img = cv.imread(filename)
filename = os.path.join(ALPHA_FOLDER, file)
# print(filename)
alpha = cv.imread(filename, 0)
alpha = alpha / 255
print(img.shape)
h, w = img.shape[:2]
x = torch.zeros((1, 4, h, w), dtype=torch.float)
image = img[..., ::-1] # RGB
image = transforms.ToPILImage()(image)
image = transformer(image)
x[0:, 0:3, :, :] = image
for i in range(2):
filename = os.path.join(TRIMAP_FOLDERS[i], file)
print('reading {}...'.format(filename))
trimap = cv.imread(filename, 0)
x[0:, 3, :, :] = torch.from_numpy(trimap.copy() / 255.)
# print(torch.max(x[0:, 3, :, :]))
# print(torch.min(x[0:, 3, :, :]))
# print(torch.median(x[0:, 3, :, :]))
# Move to GPU, if available
x = x.type(torch.FloatTensor).to(device)
with torch.no_grad():
pred = model(x)
pred = pred.cpu().numpy()
pred = pred.reshape((h, w))
pred[trimap == 0] = 0.0
pred[trimap == 255] = 1.0
# Calculate loss
# loss = criterion(alpha_out, alpha_label)
# print(pred.shape)
# print(alpha.shape)
mse_loss = compute_mse(pred, alpha, trimap)
sad_loss = compute_sad(pred, alpha)
str_msg = 'sad: %.4f, mse: %.4f' % (sad_loss, mse_loss)
print(str_msg)
out = (pred.copy() * 255).astype(np.uint8)
draw_str(out, (10, 20), str_msg)
filename = os.path.join(OUTPUT_FOLDERS[i], file)
cv.imwrite(filename, out)
print('wrote {}.'.format(filename))
|
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|
import numpy as np
import cv2
import torch
import torch.nn.functional as F
def to_homogeneous(points):
return np.concatenate([points, np.ones((points.shape[0], 1), dtype=points.dtype)], axis=-1)
def from_homogeneous(points):
return points[:, :-1] / points[:, -1:]
def compute_homography_error(H, H_gt, h, w):
corners2 = to_homogeneous(np.array([[0, 0], [0, h - 1], [w - 1, h - 1], [w - 1, 0]]))
corners1_gt = np.dot(corners2, np.transpose(H_gt))
corners1_gt = corners1_gt[:, :2] / corners1_gt[:, 2:]
corners2_DM = np.float32([[0, 0], [0, h - 1], [w - 1, h - 1], [w - 1, 0]]).reshape(-1, 1, 2)
dst_DM_GT = cv2.perspectiveTransform(corners2_DM, H_gt).squeeze()
corners1 = np.dot(corners2, np.transpose(H))
corners1 = corners1[:, :2] / corners1[:, 2:]
mean_dist = np.mean(np.linalg.norm(corners1 - corners1_gt, axis=1))
return mean_dist
def desc_similarity(desc1, desc2):
if desc1.shape[0] == 0 or desc2.shape[0] == 0:
return None
descriptors_a = F.normalize(desc1)
descriptors_b = F.normalize(desc2)
sim = torch.sqrt(torch.clamp(2 - 2 * (descriptors_a @ descriptors_b.t()), min=0))
return sim
|
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|
'''
File: HAPT_Dataset.py
Author: Federico Cruciani
Date: 03/10/2019
Version: 1.0
Description:
utility functions to load the
Human Activities and Postural Transitions (HAPT) dataset
'''
import numpy as np
import pandas as pd
from os.path import expanduser
from keras.utils import to_categorical
from multiprocessing import Pool as ThreadPool
import math
import scipy.signal
home = expanduser("~")
'''
Dataset Info - Labels:
1 WALKING
2 W_UPSTAIRS
3 W_DOWNSTAIRS
4 SITTING
5 STANDING
6 LAYING
7 STAND_TO_SIT
8 SIT_TO_STAND
9 SIT_TO_LIE
10 LIE_TO_SIT
11 STAND_TO_LIE
12 LIE_TO_STAND
'''
#Modify this line with the right path.
#Dataset available at: http://archive.ics.uci.edu/ml/machine-learning-databases/00341/
ucihapt_datapath = home+"/HAPT_Dataset/"
def get_test_uuids():
test_uuids = pd.read_csv(ucihapt_datapath+"Test/subject_id_test.txt",names=["UUID"])
all_test_uuids = np.unique(test_uuids.values)
return all_test_uuids
def get_train_uuids():
train_uuids = pd.read_csv(ucihapt_datapath+"Train/subject_id_train.txt",names=["UUID"])
all_train_uuids = np.unique(train_uuids.values)
return all_train_uuids
#Get Data no resampling
def get_all_data_multi_thread_noresampling_3D(uuids, n_threads):
print("Loading data")
print("Initiating pool")
print("resampling 50 -> 40 Hz disabled. Doing 3D ")
uuids_list = [ [x] for x in uuids ]
pool = ThreadPool(n_threads)
print("Pool map")
test_points = pool.map( get_all_data_noresampling_3D,uuids_list)
print("Pool map")
pool.close()
print("Pool join")
pool.join()
#Merging data from treads
print("Merging threads' data")
X_list = []
y_list = []
for res in test_points:
#dataset_size += len(res[1])
X_list.extend(res[0])
y_list.extend(res[1])
X_es = np.zeros((len(y_list),128,8))
X_es[:,:] = [x for x in X_list ]
y_es = np.zeros(len(y_list))
y_es[:] = [y for y in y_list]
y_scaled = to_categorical(y_es, num_classes=7)
return (X_es, y_scaled)
def get_all_data_noresampling_3D(uuids):
gt_df = pd.read_csv(ucihapt_datapath+"RawData/labels.txt",sep="\s",names=['EXP_ID','USER_ID','LABEL','START','END'],engine='python')
#exclude other uuids
#print( gt_df.head() )
filtered_df = pd.DataFrame(columns=['EXP_ID','USER_ID','LABEL','START','END'])
for uuid in uuids:
data_uuid = gt_df[ gt_df['USER_ID'] == uuid ]
filtered_df = pd.concat([filtered_df,data_uuid], ignore_index=True)
X_list = []
y_list = []
for index, row in filtered_df.iterrows():
exp_id = row['EXP_ID']
user_id = row['USER_ID']
start = row['START']
end = row['END']
label = row['LABEL']
str_user_id = str(user_id)
if user_id < 10:
str_user_id = "0"+str(user_id)
str_exp_id = str(exp_id)
if exp_id < 10:
str_exp_id = "0"+str(exp_id)
accfile = ucihapt_datapath+"RawData/acc_exp"+str_exp_id+"_user"+str_user_id+".txt"
gyrfile = ucihapt_datapath+"RawData/gyro_exp"+str_exp_id+"_user"+str_user_id+".txt"
#print(accfile)
acc_data_df = pd.read_csv(accfile,names=['x','y','z'],sep='\s|,', engine='python')
gyr_data_df = pd.read_csv(gyrfile,names=['x','y','z'],sep='\s|,', engine='python')
acc_x = acc_data_df['x'].values
acc_y = acc_data_df['y'].values
acc_z = acc_data_df['z'].values
gyr_x = gyr_data_df['x'].values
gyr_y = gyr_data_df['y'].values
gyr_z = gyr_data_df['z'].values
acc_mag = []
gyr_mag = []
for i in range(len(acc_x)):
acc_mag.append( math.sqrt( (acc_x[i]*acc_x[i]) + (acc_y[i]*acc_y[i]) + (acc_z[i]*acc_z[i]) ) )
gyr_mag.append( math.sqrt( (gyr_x[i]*gyr_x[i]) + (gyr_y[i]*gyr_y[i]) + (gyr_z[i]*gyr_z[i]) ) )
until = start + 128
while until < end:
X_point = np.zeros((128,8))
X_point[:,0] = acc_x[start:until]
X_point[:,1] = acc_y[start:until]
X_point[:,2] = acc_z[start:until]
X_point[:,3] = gyr_x[start:until]
X_point[:,4] = gyr_y[start:until]
X_point[:,5] = gyr_z[start:until]
X_point[:,6] = acc_mag[start:until]
X_point[:,7] = gyr_mag[start:until]
X_list.append(X_point)
#Remapping id from 1-12 to 0-6
if label < 7:
y_list.append(label-1)
else:
y_list.append(6) #considering all trainsitions as NULL class 6
start += 64
until += 64
X_es = np.zeros((len(y_list),128,8))
X_es[:,:] = [x for x in X_list ]
y_es = np.zeros(len(y_list))
y_es[:] = [y for y in y_list]
print("Finished loading: ",uuids)
return (X_es, y_es)
#Loads data resampling from 50 to 40 Hz
def get_all_data_multi_thread_resampling_3D(uuids, n_threads):
print("Loading Test set")
print("Initiating pool")
print("resampling 50 -> 40 Hz Enabled. Doing 3D ")
uuids_list = [ [x] for x in uuids ]
pool = ThreadPool(n_threads)
print("Pool map")
test_points = pool.map( get_all_data_noresampling_3D,uuids_list)
print("Pool map")
pool.close()
print("Pool join")
pool.join()
#Merging data from treads
print("Merging threads' data")
X_list = []
y_list = []
for res in test_points:
#dataset_size += len(res[1])
X_list.extend(res[0])
y_list.extend(res[1])
X_es = np.zeros((len(y_list),128,8))
X_es[:,:] = [x for x in X_list ]
y_es = np.zeros(len(y_list))
y_es[:] = [y for y in y_list]
y_scaled = to_categorical(y_es, num_classes=7)
return (X_es, y_scaled)
def get_all_data_resampling_3D(uuids,resampling=True):
#Load groundtruth
gt_df = pd.read_csv(ucihapt_datapath+"RawData/labels.txt",sep="\s",names=['EXP_ID','USER_ID','LABEL','START','END'],engine='python')
#Filter data: only uuids
#Empty data frame
filtered_df = pd.DataFrame(columns=['EXP_ID','USER_ID','LABEL','START','END'])
for uuid in uuids:
#add data for user ID is in list
data_uuid = gt_df[ gt_df['USER_ID'] == uuid ]
filtered_df = pd.concat([filtered_df,data_uuid], ignore_index=True)
X_list = []
y_list = []
#Iterating filtered groundtruth
for index, row in filtered_df.iterrows():
exp_id = row['EXP_ID'] #Used to retrive raw data file
user_id = row['USER_ID'] #Used to retrieve raw data file
start = row['START'] #Start of data segment with this label
end = row['END'] #End of segment
label = row['LABEL'] #Label of this segment
str_user_id = str(user_id)
if user_id < 10:
str_user_id = "0"+str(user_id)
str_exp_id = str(exp_id)
if exp_id < 10:
str_exp_id = "0"+str(exp_id)
#Load raw data file
accfile = ucihapt_datapath+"RawData/acc_exp"+str_exp_id+"_user"+str_user_id+".txt"
gyrfile = ucihapt_datapath+"RawData/gyro_exp"+str_exp_id+"_user"+str_user_id+".txt"
acc_data_df = pd.read_csv(accfile,names=['x','y','z'],sep='\s|,', engine='python')
gyr_data_df = pd.read_csv(gyrfile,names=['x','y','z'],sep='\s|,', engine='python')
acc_x = acc_data_df['x'].values
acc_y = acc_data_df['y'].values
acc_z = acc_data_df['z'].values
gyr_x = gyr_data_df['x'].values
gyr_y = gyr_data_df['y'].values
gyr_z = gyr_data_df['z'].values
#Isolate relevant data
acc_x = acc_x[ start:end ]
acc_y = acc_z[ start:end ]
acc_z = acc_y[ start:end ]
gyr_x = gyr_x[ start:end ]
gyr_y = gyr_y[ start:end ]
gyr_z = gyr_z[ start:end ]
#Calculate 3D magnitude of the signals
acc_mag = []
gyr_mag = []
for i in range(len(acc_x)):
acc_mag.append( math.sqrt( (acc_x[i]*acc_x[i]) + (acc_y[i]*acc_y[i]) + (acc_z[i]*acc_z[i]) ) )
gyr_mag.append( math.sqrt( (gyr_x[i]*gyr_x[i]) + (gyr_y[i]*gyr_y[i]) + (gyr_z[i]*gyr_z[i]) ) )
#Resampling factor: 50 / 40 = 1.25
#downsampling from 50 to 40 Hz for Extrasensory compatibility
num_samples_50Hz = end - start
num_samples_40Hz = num_samples_50Hz / 1.25
##DOWNSAMPLING from 50 to 40 Hz
acc_x = scipy.signal.resample( acc_x, int(num_samples_40Hz) )
acc_x = scipy.signal.resample( acc_y, int(num_samples_40Hz) )
acc_x = scipy.signal.resample( acc_z, int(num_samples_40Hz) )
gyr_x = scipy.signal.resample( gyr_x, int(num_samples_40Hz) )
gyr_x = scipy.signal.resample( gyr_y, int(num_samples_40Hz) )
gyr_x = scipy.signal.resample( gyr_z, int(num_samples_40Hz) )
acc_mag = scipy.signal.resample( acc_mag, int(num_samples_40Hz) )
gyr_mag = scipy.signal.resample( gyr_mag, int(num_samples_40Hz) )
segment_start = 0
segment_end = num_samples_40Hz
#Performing segmentation: sliding window 50% overlap
until = segment_start + 128
while until < segment_end:
X_point = np.zeros((128,8))
X_point[:,0] = acc_x[segment_start:until]
X_point[:,1] = acc_y[segment_start:until]
X_point[:,2] = acc_z[segment_start:until]
X_point[:,3] = gyr_x[segment_start:until]
X_point[:,4] = gyr_y[segment_start:until]
X_point[:,5] = gyr_z[segment_start:until]
X_point[:,6] = acc_mag[segment_start:until]
X_point[:,7] = gyr_mag[segment_start:until]
X_list.append(X_point)
#All activities + transitions
if label < 7:
#all activities except transitions
y_list.append(label-1)
else:
#putting all transitions in same class
y_list.append(6)
segment_start += 64
until += 64
X_es = np.zeros((len(y_list),128,8))
X_es[:,:] = [x for x in X_list ]
y_es = np.zeros(len(y_list))
y_es[:] = [y for y in y_list]
#y_scaled = to_categorical(y_es, num_classes=7)
print("Finished loading: ",uuids)
return (X_es, y_es)
|
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|
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# File: dataflow.py
# Author: Qian Ge <geqian1001@gmail.com>
import os
import imageio
import numpy as np
from datetime import datetime
import xml.etree.ElementTree as ET
import src.utils.utils as utils
def identity(inputs, *args):
return inputs
def load_image(im_path, read_channel=None, pf=(identity, ())):
""" Load one image from file and apply pre-process function.
Args:
im_path (str): directory of image
read_channel (int): number of image channels. Image will be read
without channel information if ``read_channel`` is None.
pf: pre-process fucntion
Return:
image after pre-processed with size [heigth, width, channel]
"""
if read_channel is None:
im = imageio.imread(im_path)
elif read_channel == 3:
im = imageio.imread(im_path, as_gray=False, pilmode="RGB")
else:
im = imageio.imread(im_path, as_gray=True)
if len(im.shape) < 3:
im = pf[0](im, pf[1])
im = np.reshape(im, [im.shape[0], im.shape[1], 1])
else:
im = pf[0](im, pf[1])
return im
def parse_bbox_xml(xml_path, class_dict=None, pf=(identity,())):
"""
Returns:
[class_name, [xmin, ymin, xmax, ymax]]
"""
tree = ET.parse(xml_path)
root = tree.getroot()
box_list = []
for obj in root.findall('object'):
name = obj.find('name').text
box = obj.find('bndbox')
xmin = float(box.find('xmin').text)
ymin = float(box.find('ymin').text)
xmax = float(box.find('xmax').text)
ymax = float(box.find('ymax').text)
box = [xmin, ymin, xmax, ymax]
box = pf[0](box, pf[1])
# box_list.append(box)
try:
# box_list.append((class_dict[name], box))
box_list.append(np.array([class_dict[name],] + box))
except TypeError:
# box_list.append((name, box))
box_list.append([name,] + box)
try:
return np.array(box_list)
except ValueError:
return box_list
def get_class_dict_from_xml(xml_path):
file_list = get_file_list(xml_path, 'xml')
class_dict = {}
reverse_class_dict = {}
nclass = 0
max_bbox = 0
for xml_file in file_list:
bbox_list = parse_bbox_xml(xml_file)
cnt_bbox = 0
for bbox in bbox_list:
cnt_bbox += 1
cur_name = bbox[0]
if cur_name not in class_dict:
class_dict[cur_name] = nclass
reverse_class_dict[nclass] = cur_name
nclass += 1
max_bbox = max(max_bbox, cnt_bbox)
print('Max number of bbox per image: {}'.format(max_bbox))
return class_dict, reverse_class_dict
def get_voc_bbox(xml_path):
bboxs = []
file_list = get_file_list(xml_path, 'xml')
class_dict = {}
reverse_class_dict = {}
nclass = 0
for xml_file in file_list:
bbox_list = parse_bbox_xml(xml_file)
bbox_list = [bbox[1:] for bbox in bbox_list]
bboxs.extend(bbox_list)
return bboxs
def vec2onehot(vec, n_class):
vec = np.array(vec)
one_hot = np.zeros((len(vec), n_class))
one_hot[np.arange(len(vec)), vec] = 1
return one_hot
def fill_pf_list(pf_list, n_pf, fill_with_fnc=(identity,())):
""" Fill the pre-process function list.
Args:
pf_list (list): input list of pre-process functions
n_pf (int): required number of pre-process functions
fill_with_fnc: function used to fill the list
Returns:
list of pre-process function
"""
if pf_list == None:
return [fill_with_fnc for i in range(n_pf)]
new_list = []
pf_list = utils.make_list(pf_list)
for pf in pf_list:
if not pf:
pf = fill_with_fnc
new_list.append(pf)
pf_list = new_list
if len(pf_list) > n_pf:
raise ValueError('Invalid number of preprocessing functions')
pf_list = pf_list + [fill_with_fnc for i in range(n_pf - len(pf_list))]
return pf_list
def get_file_list(file_dir, file_ext, sub_name=None):
""" Get file list in a directory with sepcific filename and extension
Args:
file_dir (str): directory of files
file_ext (str): filename extension
sub_name (str): Part of filename. Can be None.
Return:
List of filenames under ``file_dir`` as well as subdirectories
"""
re_list = []
if sub_name is None:
return np.array([os.path.join(root, name)
for root, dirs, files in os.walk(file_dir)
for name in sorted(files) if name.lower().endswith(file_ext)])
else:
return np.array([os.path.join(root, name)
for root, dirs, files in os.walk(file_dir)
for name in sorted(files)
if name.lower().endswith(file_ext) and sub_name.lower() in name.lower()])
_RNG_SEED = None
def get_rng(obj=None):
"""
This function is copied from `tensorpack
<https://github.com/ppwwyyxx/tensorpack/blob/master/tensorpack/utils/utils.py>`__.
Get a good RNG seeded with time, pid and the object.
Args:
obj: some object to use to generate random seed.
Returns:
np.random.RandomState: the RNG.
"""
seed = (id(obj) + os.getpid() +
int(datetime.now().strftime("%Y%m%d%H%M%S%f"))) % 4294967295
if _RNG_SEED is not None:
seed = _RNG_SEED
return np.random.RandomState(seed)
|
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|
/*
* This file is a part of HAXX
*
* Copyright (c) 2017 David Williams-Young
* All rights reserved.
*
* See LICENSE.txt
*/
#ifdef BOOST_TEST_MODULE
#undef BOOST_TEST_MODULE
#endif
#define BOOST_NO_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/iterator/counting_iterator.hpp>
#include "haxx.hpp"
#include <random>
#include <iterator>
#include <iostream>
#include <limits>
#include <chrono>
// Length constants
#define HBLAS1_VECLEN 100
#define HBLAS2_MATLEN (HBLAS1_VECLEN) * (HBLAS1_VECLEN)
#define HBLAS1_RAND_MIN -20
#define HBLAS1_RAND_MAX 54
// Setup Random Number generator
static std::random_device rd;
static std::mt19937 gen(rd());
static std::uniform_real_distribution<> dis(HBLAS1_RAND_MIN,HBLAS1_RAND_MAX);
template <typename _F> _F genRandom();
template<> inline double genRandom<double>(){ return double(dis(gen)); }
template<> inline std::complex<double> genRandom<std::complex<double>>(){
return std::complex<double>(dis(gen),dis(gen));
}
template<> inline HAXX::quaternion<double> genRandom<HAXX::quaternion<double>>(){
return HAXX::quaternion<double>(dis(gen),dis(gen),dis(gen),dis(gen));
}
// Index list for HBLAS1 UT conformation
static std::vector<int> indx(boost::counting_iterator<int>(0),
boost::counting_iterator<int>(HBLAS1_VECLEN));
// Strides to be tested
static std::vector<size_t> strides = {1,2,3,5,9};
#define COMPARE_TOL 1e-12
#define CMP_Q(a,b) ( HAXX::norm(((a) * HAXX::inv(b))- 1.) < COMPARE_TOL )
|
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|
# 从整张图中裁剪224*224，能裁多少裁多少
import numpy as np
import os
import cv2
import math
from utility import Method
import torch
import torch.nn as nn
import torch.nn.functional as f
import torchvision.transforms as transforms
from nets.models.unet_model import UNet
class ImageFusion(Method):
block_size = 5
pyramid_level = 4
mean_value = 0.3976813856328417
std_value = 0.05057423681125553
input_size_cnn = 256
center_size = 200
max_input_num = 10
device = "cuda:0"
data_transforms = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize([mean_value], [std_value]),
])
model = UNet(n_channels=1, n_classes=1)
model.to(device)
project_address = os.getcwd()
# sf_ssim_no_aug.pkl sf_ssim.pkl
# parameter_address = os.path.join(os.path.join(os.path.join(project_address, 'nets'), 'parameters'), 'sf_ssim_no_aug_val_256.pkl')
# model.load_state_dict(torch.load(parameter_address))
# parameter_address = os.path.join(os.path.join(os.path.join(project_address, 'nets'), 'parameters'), '7_new_data_load.pth')
# state = torch.load(parameter_address)
# model.load_state_dict(state['model'])
parameter_address = os.path.join(os.path.join(os.path.join(project_address, 'nets'), 'parameters'),
'sf_ssim_aug_val_256.pkl')
model.load_state_dict({k.replace('module.', ''): v for k, v in torch.load(parameter_address).items()})
model.eval()
@staticmethod
def fuse_by_average(images):
"""
均值融合，取两个重合区域逐像素的均值
:param images: 输入两个相同区域的图像
:return:融合后的图像
"""
(last_image, next_image) = images
# 由于相加后数值可能溢出，需要转变类型
fuse_region = np.uint8((last_image.astype(int) + next_image.astype(int)) / 2)
return fuse_region
@staticmethod
def fuse_by_maximum(images):
"""
最大值融合,取两个重合区域逐像素的最大值
:param images: 输入两个相同区域的图像
:return:融合后的图像
"""
(last_image, next_image) = images
fuse_region = np.maximum(last_image, next_image)
return fuse_region
@staticmethod
def fuse_by_minimum(images):
"""
最小值融合,取两个重合区域逐像素的最小值
:param images: 输入两个相同区域的图像
:return: 融合后的图像
"""
(last_image, next_image) = images
fuse_region = np.minimum(last_image, next_image)
return fuse_region
@staticmethod
def _get_weights_matrix(images):
"""
获取权值矩阵
:param images: 带融合两幅图像
:return: last_weight_mat,next_weight_mat
"""
(last_image, next_image) = images
last_weight_mat = np.ones(last_image.shape, dtype=np.float32)
next_weight_mat = np.ones(next_image.shape, dtype=np.float32)
row, col = last_image.shape[:2]
next_weight_mat_1 = next_weight_mat.copy()
next_weight_mat_2 = next_weight_mat.copy()
# 获取四条线的相加和，判断属于哪种模式
compare_list = [np.count_nonzero(last_image[0: row // 2, 0: col // 2] > 0),
np.count_nonzero(last_image[row // 2: row, 0: col // 2] > 0),
np.count_nonzero(last_image[row // 2: row, col // 2: col] > 0),
np.count_nonzero(last_image[0: row // 2, col // 2: col] > 0)]
index = compare_list.index(min(compare_list))
if index == 2:
# 重合区域在imageA的上左部分
# self.printAndWrite("上左")
row_index = 0
col_index = 0
for j in range(1, col):
for i in range(row - 1, -1, -1):
if last_image[i, col - j] != -1:
row_index = i + 1
break
if row_index != 0:
break
for i in range(col - 1, -1, -1):
if last_image[row_index, i] != -1:
col_index = i + 1
break
# 赋值
for i in range(row_index + 1):
if row_index == 0:
row_index = 1
next_weight_mat_1[row_index - i, :] = (row_index - i) * 1 / row_index
for i in range(col_index + 1):
if col_index == 0:
col_index = 1
next_weight_mat_2[:, col_index - i] = (col_index - i) * 1 / col_index
next_weight_mat = next_weight_mat_1 * next_weight_mat_2
last_weight_mat = 1 - next_weight_mat
# elif leftCenter != 0 and bottomCenter != 0 and upCenter == 0 and rightCenter == 0:
elif index == 3:
# 重合区域在imageA的下左部分
# self.printAndWrite("下左")
row_index = 0
col_index = 0
for j in range(1, col):
for i in range(row):
if last_image[i, col - j] != -1:
row_index = i - 1
break
if row_index != 0:
break
for i in range(col - 1, -1, -1):
if last_image[row_index, i] != -1:
col_index = i + 1
break
# 赋值
for i in range(row_index, row):
if row_index == 0:
row_index = 1
next_weight_mat_1[i, :] = (row - i - 1) * 1 / (row - row_index - 1)
for i in range(col_index + 1):
if col_index == 0:
col_index = 1
next_weight_mat_2[:, col_index - i] = (col_index - i) * 1 / col_index
next_weight_mat = next_weight_mat_1 * next_weight_mat_2
last_weight_mat = 1 - next_weight_mat
# elif rightCenter != 0 and bottomCenter != 0 and upCenter == 0 and leftCenter == 0:
elif index == 0:
# 重合区域在imageA的下右部分
row_index = 0
col_index = 0
for j in range(0, col):
for i in range(row):
if last_image[i, j] != -1:
row_index = i - 1
break
if row_index != 0:
break
for i in range(col):
if last_image[row_index, i] != -1:
col_index = i - 1
break
# 赋值
for i in range(row_index, row):
if row_index == 0:
row_index = 1
next_weight_mat_1[i, :] = (row - i - 1) * 1 / (row - row_index - 1)
for i in range(col_index, col):
if col_index == 0:
col_index = 1
next_weight_mat_2[:, i] = (col - i - 1) * 1 / (col - col_index - 1)
next_weight_mat = next_weight_mat_1 * next_weight_mat_2
last_weight_mat = 1 - next_weight_mat
# elif upCenter != 0 and rightCenter != 0 and leftCenter == 0 and bottomCenter == 0:
elif index == 1:
# 重合区域在imageA的上右部分
# self.printAndWrite("上右")
row_index = 0
col_index = 0
for j in range(0, col):
for i in range(row - 1, -1, -1):
if last_image[i, j] != -1:
row_index = i + 1
break
if row_index != 0:
break
for i in range(col):
if last_image[row_index, i] != -1:
col_index = i - 1
break
for i in range(row_index + 1):
if row_index == 0:
row_index = 1
next_weight_mat_1[row_index - i, :] = (row_index - i) * 1 / row_index
for i in range(col_index, col):
if col_index == 0:
col_index = 1
next_weight_mat_2[:, i] = (col - i - 1) * 1 / (col - col_index - 1)
next_weight_mat = next_weight_mat_1 * next_weight_mat_2
last_weight_mat = 1 - next_weight_mat
return last_weight_mat, next_weight_mat
def fuse_by_fade_in_and_fade_out(self, images, offset):
"""
渐入渐出融合
:param images:输入两个相同区域的图像
:param dx: 第二张图像相对于第一张图像原点在x方向上的位移
:param dy: 第二张图像相对于第一张图像原点在y方向上的位移
:return:融合后的图像
"""
(last_image, next_image) = images
(dx, dy) = offset
row, col = last_image.shape[:2]
last_weight_mat = np.ones(last_image.shape, dtype=np.float32)
next_weight_mat = np.ones(next_image.shape, dtype=np.float32)
# self.printAndWrite(" ratio: " + str(np.count_nonzero(imageA > -1) / imageA.size))
if np.count_nonzero(last_image > -1) / last_image.size > 0.65:
# 如果对于imageA中，非0值占比例比较大，则认为是普通融合
# 根据区域的行列大小来判断，如果行数大于列数，是水平方向
if col <= row:
# self.printAndWrite("普通融合-水平方向")
for i in range(0, col):
# print(dy)
if dy >= 0:
last_weight_mat[:, i] = last_weight_mat[:, i] * i * 1.0 / col
next_weight_mat[:, col - i - 1] = next_weight_mat[:, col - i - 1] * i * 1.0 / col
elif dy < 0:
last_weight_mat[:, i] = last_weight_mat[:, i] * (col - i) * 1.0 / col
next_weight_mat[:, col - i - 1] = next_weight_mat[:, col - i - 1] * (col - i) * 1.0 / col
# 根据区域的行列大小来判断，如果列数大于行数，是竖直方向
elif row < col:
# self.printAndWrite("普通融合-竖直方向")
for i in range(0, row):
if dx <= 0:
last_weight_mat[i, :] = last_weight_mat[i, :] * i * 1.0 / row
next_weight_mat[row - i - 1, :] = next_weight_mat[row - i - 1, :] * i * 1.0 / row
elif dx > 0:
last_weight_mat[i, :] = last_weight_mat[i, :] * (row - i) * 1.0 / row
next_weight_mat[row - i - 1, :] = next_weight_mat[row - i - 1, :] * (row - i) * 1.0 / row
else:
# 如果对于imageA中，非0值占比例比较小，则认为是拐角融合
# self.printAndWrite("拐角融合")
last_weight_mat, next_weight_mat = self._get_weights_matrix(images)
last_image[last_image < 0] = next_image[last_image < 0]
next_image[next_image == -1] = 0
result = last_weight_mat * last_image.astype(np.int) + next_weight_mat * next_image.astype(np.int)
result[result < 0] = 0
result[result > 255] = 255
fuse_region = np.uint8(result)
return fuse_region
def fuse_by_trigonometric(self, images, offset):
"""
三角函数融合
引用自《一种三角函数权重的图像拼接算法》知网
:param images:输入两个相同区域的图像
:param dx: 第二张图像相对于第一张图像原点在x方向上的位移
:param dy: 第二张图像相对于第一张图像原点在y方向上的位移
:return:融合后的图像
"""
(last_image, next_image) = images
(dx, dy) = offset
row, col = last_image.shape[:2]
last_weight_mat = np.ones(last_image.shape, dtype=np.float64)
next_weight_mat = np.ones(next_image.shape, dtype=np.float64)
if np.count_nonzero(last_image > -1) / last_image.size > 0.65:
# 如果对于imageA中，非0值占比例比较大，则认为是普通融合
# 根据区域的行列大小来判断，如果行数大于列数，是水平方向
if col <= row:
# self.printAndWrite("普通融合-水平方向")
for i in range(0, col):
if dy >= 0:
last_weight_mat[:, i] = last_weight_mat[:, i] * i * 1.0 / col
next_weight_mat[:, col - i - 1] = next_weight_mat[:, col - i - 1] * i * 1.0 / col
elif dy < 0:
last_weight_mat[:, i] = last_weight_mat[:, i] * (col - i) * 1.0 / col
next_weight_mat[:, col - i - 1] = next_weight_mat[:, col - i - 1] * (col - i) * 1.0 / col
# 根据区域的行列大小来判断，如果列数大于行数，是竖直方向
elif row < col:
# self.printAndWrite("普通融合-竖直方向")
for i in range(0, row):
if dx <= 0:
last_weight_mat[i, :] = last_weight_mat[i, :] * i * 1.0 / row
next_weight_mat[row - i - 1, :] = next_weight_mat[row - i - 1, :] * i * 1.0 / row
elif dx > 0:
last_weight_mat[i, :] = last_weight_mat[i, :] * (row - i) * 1.0 / row
next_weight_mat[row - i - 1, :] = next_weight_mat[row - i - 1, :] * (row - i) * 1.0 / row
else:
# 如果对于imageA中，非0值占比例比较小，则认为是拐角融合
# self.printAndWrite("拐角融合")
last_weight_mat, next_weight_mat = self._get_weights_matrix(images)
last_weight_mat = np.power(np.sin(last_weight_mat * math.pi / 2), 2)
next_weight_mat = 1 - last_weight_mat
last_image[last_image < 0] = next_image[last_image < 0]
next_image[next_image == -1] = 0
result = last_weight_mat * last_image.astype(np.int) + next_weight_mat * next_image.astype(np.int)
result[result < 0] = 0
result[result > 255] = 255
fuse_region = np.uint8(result)
return fuse_region
def fuse_by_possion_image_editing(self, images):
"""
泊松融合
引用自: Rez P, Gangnet M, Blake A. Poisson image editing.[J].
Acm Transactions on Graphics, 2003, 22(3):313-318.
:param images: 输入两个相同区域的图像
:return: 融合后的图像
"""
(last_image, next_image) = images
fuse_region = last_image
return fuse_region
def fuse_by_multi_band_blending(self, images):
"""
多分辨率样条融合,重合区域逐像素各取权重0.5，然后使用拉普拉斯金字塔融合
引用自：《A Multiresolution Spline With Application to Image Mosaics》
:param images: 输入两个相同区域的图像
:return: 融合后的图像
"""
(last_image, next_image) = images
last_lp, last_gp = self._get_laplacian_pyramid(last_image)
next_lp, next_gp = self._get_laplacian_pyramid(next_image)
fuse_lp = []
for i in range(self.pyramid_level):
fuse_lp.append(last_lp[i] * 0.5 + next_lp[i] * 0.5)
fuse_region = np.uint8(self._reconstruct(fuse_lp))
return fuse_region
def fuse_by_spatial_frequency(self, images):
"""
空间频率融合
引用自：《Combination of images with diverse focuses using the spatial frequency》
:param images:输入两个相同区域的图像
:return:融合后的图像
"""
(last_image, next_image) = images
weight_matrix = self._get_spatial_frequency_matrix(images)
fuse_region = last_image * weight_matrix + next_image * (1 - weight_matrix)
# print(np.amin(fuse_region), np.amax(fuse_region))
return fuse_region.astype(np.uint8)
def _get_spatial_frequency_matrix(self, images, block_size=5):
block_num = block_size // 2
(last_image, next_image) = images
weight_matrix = np.ones(last_image.shape)
if torch.cuda.is_available():
# 将图像打入GPU并增加维度
last_cuda = torch.from_numpy(last_image).float().to(self.device).reshape(
(1, 1, last_image.shape[0], last_image.shape[1]))
next_cuda = torch.from_numpy(next_image).float().to(self.device).reshape(
(1, 1, next_image.shape[0], next_image.shape[1]))
# 创建向右/向下平移的卷积核 + 打入GPU + 增加维度
right_shift_kernel = torch.FloatTensor([[0, 0, 0], [1, 0, 0], [0, 0, 0]]).to(self.device).reshape(
(1, 1, 3, 3))
bottom_shift_kernel = torch.FloatTensor([[0, 1, 0], [0, 0, 0], [0, 0, 0]]).to(self.device).reshape(
(1, 1, 3, 3))
last_right_shift = f.conv2d(last_cuda, right_shift_kernel, padding=1)
last_bottom_shift = f.conv2d(last_cuda, bottom_shift_kernel, padding=1)
next_right_shift = f.conv2d(next_cuda, right_shift_kernel, padding=1)
next_bottom_shift = f.conv2d(next_cuda, bottom_shift_kernel, padding=1)
last_sf = torch.pow((last_right_shift - last_cuda), 2) + torch.pow((last_bottom_shift - last_cuda), 2)
next_sf = torch.pow((next_right_shift - next_cuda), 2) + torch.pow((next_bottom_shift - next_cuda), 2)
add_kernel = torch.ones((block_size, block_size)).float().to(self.device).reshape(
(1, 1, block_size, block_size))
last_sf_convolve = f.conv2d(last_sf, add_kernel, padding=block_num)
next_sf_convolve = f.conv2d(next_sf, add_kernel, padding=block_num)
weight_zeros = torch.zeros((last_sf_convolve.shape[2], last_sf_convolve.shape[3])).to(self.device)
weight_ones = torch.ones((last_sf_convolve.shape[2], last_sf_convolve.shape[3])).to(self.device)
sf_compare = torch.where(last_sf_convolve.squeeze(0).squeeze(0) > next_sf_convolve.squeeze(0).squeeze(0),
weight_ones, weight_zeros)
weight_matrix = sf_compare.cpu().numpy()
weight_matrix = cv2.bilateralFilter(src=weight_matrix, d=30, sigmaColor=10, sigmaSpace=7)
return weight_matrix
def fuse_by_sf_and_mbb(self, images):
"""
多分辨率样条和空间频率融合叠加,空间频率生成的权值矩阵，生成高斯金字塔然后与拉普拉斯金字塔结合，
最后将上述金字塔生成图像
:param images: 输入两个相同区域的图像
:return: 融合后的图像
"""
(last_image, next_image) = images
last_lp, last_gp = self._get_laplacian_pyramid(last_image)
next_lp, next_gp = self._get_laplacian_pyramid(next_image)
weight_matrix = self._get_spatial_frequency_matrix(images)
# wm_gp 为weight_matrix的高斯金字塔
wm_gp = self._get_gaussian_pyramid(weight_matrix)
fuse_lp = []
for i in range(self.pyramid_level):
fuse_lp.append(last_lp[i] * wm_gp[self.pyramid_level - i - 1] +
next_lp[i] * (1 - wm_gp[self.pyramid_level - i - 1]))
fuse_region = np.uint8(self._reconstruct(fuse_lp))
return fuse_region
def fuse_by_deep_fuse(self, images):
"""
Deep fuse 融合，引用自：
Prabhakar K R, Srikar V S, Babu R V.DeepFuse: A Deep Unsupervised Approach
for Exposure Fusion with Extreme Exposure Image Pairs[C]//ICCV. 2017: 4724-4732.
:param images: 输入两个相同区域的图像
:return: 融合后的图像
"""
(last_image, next_image) = images
fuse_region = 0
return fuse_region
def fuse_by_our_framework(self, images):
"""
本文算法融合，引用自：
:param images: 输入两个相同区域的图像
:return: 融合后的图像
"""
# 在这里提供接口，包括模型参数引用地址、模型，具体用什么模型在其他py文件封装
(last_image, next_image) = images
fuse_region = np.zeros(last_image.shape)
# 使用overlap-tile策略裁切
last_input_list = []
next_input_list = []
padding_num = int((self.input_size_cnn - self.center_size) // 2)
last_expand = cv2.copyMakeBorder(last_image, padding_num, padding_num, padding_num, padding_num,
cv2.BORDER_REFLECT)
next_expand = cv2.copyMakeBorder(next_image, padding_num, padding_num, padding_num, padding_num,
cv2.BORDER_REFLECT)
row_expand, col_expand = last_expand.shape[0:2]
row_have_remain = True
col_have_remain = True
if (row_expand - padding_num * 2) % self.center_size == 0:
row_have_remain = False
if (col_expand - padding_num * 2) % self.center_size == 0:
col_have_remain = False
row_num = (row_expand - padding_num * 2) // self.center_size
col_num = (col_expand - padding_num * 2) // self.center_size
for i in range(row_num + 1):
for j in range(col_num + 1):
row_start = i * self.center_size
row_end = row_start + self.input_size_cnn
col_start = j * self.center_size
col_end = col_start + self.input_size_cnn
if i == row_num:
if row_have_remain:
row_start = row_expand - self.input_size_cnn
row_end = row_expand
else:
break
if j == col_num:
if col_have_remain:
col_start = col_expand - self.input_size_cnn
col_end = col_expand
else:
continue
last_input_list.append(last_expand[row_start: row_end, col_start:col_end])
next_input_list.append(next_expand[row_start: row_end, col_start:col_end])
input_num = len(last_input_list)
# 将list转化为Tensor
last_input_tensors = self._trans_list_to_tensor(last_input_list, input_num)
next_input_tensors = self._trans_list_to_tensor(next_input_list, input_num)
# 分步送入网络
output_tensors = None
if input_num < self.max_input_num:
output_tensors = self._run_network(last_input_tensors, next_input_tensors).data
else:
output_tensors = torch.zeros([input_num, 1, self.input_size_cnn, self.input_size_cnn])
implement_num = 0
while implement_num < input_num:
remain_num = input_num - implement_num
if remain_num > self.max_input_num:
output_tensors[implement_num:implement_num + self.max_input_num, :] = \
self._run_network(
last_input_tensors[implement_num:implement_num + self.max_input_num, :, :, :],
next_input_tensors[implement_num:implement_num + self.max_input_num, :, :, :],
).data
else:
output_tensors[implement_num:input_num, :] = \
self._run_network(
last_input_tensors[implement_num: input_num, :, :, :],
next_input_tensors[implement_num: input_num, :, :, :],
).data
implement_num += self.max_input_num
# 将Tensor转化为list
output_list = self._trans_tensor_to_list(output_tensors, input_num)
row, col = last_image.shape[0:2]
row_num, col_num = 0, 0
if col_have_remain:
col_num = (col // self.center_size) + 1
else:
col_num = col // self.center_size
if row_have_remain:
row_num = (row // self.center_size) + 1
else:
row_num = row // self.center_size
for index, output in enumerate(output_list):
row_start = (index // col_num) * self.center_size
row_end = ((index // col_num) + 1) * self.center_size
col_start = (index % col_num) * self.center_size
col_end = ((index % col_num) + 1) * self.center_size
if row_have_remain and row_start == (row_num - 1) * self.center_size:
row_start = row - self.center_size
row_end = row
if col_have_remain and col_start == (col_num - 1) * self.center_size:
col_start = col - self.center_size
col_end = col
fuse_region[row_start: row_end, col_start: col_end] = \
output[padding_num: padding_num + self.center_size, padding_num: padding_num + self.center_size]
# cv2.imwrite("fuse_region.png", fuse_region)
# input()
return fuse_region
def _run_network(self, last_input, next_input):
img1, img2 = last_input, next_input
with torch.no_grad():
# Forward
img1, img2 = img1.to(self.device), img2.to(self.device)
img1_lum = img1[:, 0:1]
img2_lum = img2[:, 0:1]
y_f = self.model.forward(img1_lum, img2_lum)
y_f = ((y_f * self.std_value) + self.mean_value) * 255.0
y_f = torch.clamp(y_f, 0, 255, out=None)
return y_f
def _trans_list_to_tensor(self, input_list, input_num):
input_tensors = torch.zeros((input_num, 1, self.input_size_cnn, self.input_size_cnn))
for index, array in enumerate(input_list):
input_tensors[index, :, :, :] = \
self.data_transforms(np.expand_dims(array, axis=2).astype(np.float32) / 255)
return input_tensors
def _trans_tensor_to_list(self, output_tensors, input_num):
output_list = []
for i in range(input_num):
temp = output_tensors[i, 0, :, :].cpu().numpy().astype(np.uint8)
output_list.append(temp)
return output_list
def _get_gaussian_pyramid(self, input_image):
"""
获得图像的高斯金字塔
:param input_image:输入图像
:return: 高斯金字塔，以list形式返回，第一个是原图，以此类推
"""
g = input_image.copy().astype(np.float64)
gp = [g] # 金字塔结构存到list中
for i in range(self.pyramid_level):
g = cv2.pyrDown(g)
gp.append(g)
return gp
def _get_laplacian_pyramid(self, input_image):
"""
求一张图像的拉普拉斯金字塔
:param input_image: 输入图像
:return: 拉普拉斯金字塔(laplacian_pyramid, lp, 从小到大)，高斯金字塔(gaussian_pyramid, gp,从大到小),
均以list形式
"""
gp = self._get_gaussian_pyramid(input_image)
lp = [gp[self.pyramid_level - 1]]
for i in range(self.pyramid_level - 1, -1, -1):
ge = cv2.pyrUp(gp[i])
ge = cv2.resize(ge, (gp[i - 1].shape[1], gp[i - 1].shape[0]), interpolation=cv2.INTER_CUBIC)
lp.append(cv2.subtract(gp[i - 1], ge))
return lp, gp
@staticmethod
def _reconstruct(input_pyramid):
"""
根据拉普拉斯金字塔重构图像，该list第一个是最小的原图，后面是更大的拉普拉斯表示
:param input_pyramid: 输入的金字塔
:return: 返回重构的结果图
"""
construct_result = input_pyramid[0]
for i in range(1, len(input_pyramid)):
construct_result = cv2.pyrUp(construct_result)
construct_result = cv2.resize(construct_result, (input_pyramid[i].shape[1], input_pyramid[i].shape[0]),
interpolation=cv2.INTER_CUBIC)
construct_result = cv2.add(construct_result, input_pyramid[i])
return construct_result
|
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|
import numpy as np
# metodos para calcular porosidade
def PhiVel(vellog, velma, velfl): # calculo da porosidade usando o perfil de velocidade
phiv = (vellog - velma) / (velfl - velma)
phiv = np.clip(phiv, 0.0, 1.0)
return phiv
def PhiDens(denslog, densma, densfl): # calculo da porosidade usando o perfil de densidade
phid = (denslog - densma) / (densfl - densma)
phid = np.clip(phid, 0.0, 1.0)
return phid
def PhiDensNeut(neutlog, denslog, densma, densfl): # calculo da porosidade usando os perfis de densidade e neutron
phid = (denslog - densma) / (densfl - densma)
phidn = np.sqrt((phid ** 2 + neutlog ** 2) / 2)
phidn = np.clip(phidn, 0.0, 1.0)
return phidn
|
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|
"""
FluPop(f::Union{AbstractString,IO}, sequencetype::Symbol, headerfields;
flulineage=missing, segment=missing, strainfilters = [!is_flu_outlier(flulineage), BioTools.hasdate], separator = '|')
Call `readfastastrains` to read `f`. Store the result in a `FluPop` object.
"""
function FluPop(f::Union{AbstractString,IO},
sequencetype,
headerfields;
flulineage=missing,
segment=missing,
strainfilters = flu_usual_filters(flulineage),
separator = '|',
ignore_read_errors=false)
strains = readfastastrains(f, sequencetype, headerfields, separator = separator, strainfilters = strainfilters, ignore_read_errors=ignore_read_errors)
return FluPop(strains = Dict{String, eltype(strains)}(String(x[:strain])=>x for x in strains))
end
"""
AAFluPop(f::Union{AbstractString,IO}, headerfields; [kwargs...])
Call `FluPop(f, :aa, headerfields, [kwargs...])
"""
function AAFluPop(f::Union{AbstractString,IO}, headerfields;
flulineage=missing,
segment=missing,
strainfilters = flu_usual_filters(flulineage),
separator = '|')
return FluPop(f, :aa, headerfields, flulineage=flulineage, segment=segment, strainfilters=strainfilters, separator=separator)
end
"""
read_mutations!(tree::Tree, mutfile::String)
Read mutations from a JSON file outputted by augur. Store them into `tree`.
## Note
This is in the `Flu` module because it is explicitely designed for use of augur on flu. In particular, it uses the `gene_positions` global.
"""
function read_mutations!(tree::Tree, mutfile::String; type=:aa, lineage="h3n2", segment="ha")
if type == :aa
read_mutations_aa!(tree, mutfile, lineage, segment)
else
@warn "Only implemented for `type=:aa`"
end
end
"""
"""
function read_mutations_aa!(tree, mutfile::String, lineage, segment)
muts = JSON.Parser.parsefile(mutfile)["nodes"]
for (label, mut) in muts
if haskey(tree.lnodes, label)
tmp = Array{TreeTools.Mutation}(undef, 0)
for (gene, pos) in gene_offsets[lineage, segment]
if haskey(mut["aa_muts"], gene)
for m in mut["aa_muts"][gene]
push!(tmp, _parse_aa_mut(m))
tmp[end].i = tmp[end].i + pos[1] # Offset for different genes
end
end
end
tree.lnodes[label].data.mutations = tmp
end
end
end
"""
Parse a string of format `XiY` into a `TreeTools.Mutation` object with fields `i`, `X` and `Y`.
"""
function _parse_aa_mut(m::String)
if length(m) < 3
error("Can't parse mutation string of length smaller than 3")
end
i = parse(Int64, m[2:end-1])
old = AminoAcid(m[1])
new = AminoAcid(m[end])
out = TreeTools.Mutation(i, old, new)
return out
end
|
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|
from rdkit import Chem
from mordred import Calculator, descriptors
from Bio.PDB import PDBParser, Dice
from snakemake.shell import shell
import pandas as pd
import numpy as np
import joblib as jl
import warnings
def reset_indices(chain):
for i, residue in enumerate(chain.get_residues(), start=1):
res_id = list(residue.id)
res_id[1] += 1e5 # deal with negative indices
residue.id = tuple(res_id)
for i, residue in enumerate(chain.get_residues(), start=1):
res_id = list(residue.id)
res_id[1] = i
residue.id = tuple(res_id)
return chain
def get_pdb_chunks(full_pdb, window_size, len_residues, token):
len_residues += 1
for chain in full_pdb.get_chains():
chain = reset_indices(chain)
chain_id = chain.get_id()
start_idx, stop_idx = \
list(chain.get_residues())[0].get_id()[1], \
list(chain.get_residues())[-1].get_id()[1]
if len_residues <= window_size:
windows = [[start_idx, stop_idx]]
else:
windows = enumerate(range(window_size, len_residues))
for start, end in windows:
filename = f"data/temp/{token}/{full_pdb.get_id()}_{start}_{end}.pdb"
Dice.extract(full_pdb, chain_id, start, end, filename)
mol_obj = Chem.MolFromPDBFile(filename)
shell(f"rm {filename}")
yield mol_obj
smk_obj = snakemake
name, path, token = \
smk_obj.wildcards.seq_name, smk_obj.input[0], smk_obj.config["token"]
structure = PDBParser().get_structure(name, path)
seqs, class_ = jl.load(smk_obj.input[1])
len_residues = len(list(structure.get_residues()))
pdbs = get_pdb_chunks(structure, 20, len_residues, token)
try:
warnings.filterwarnings("ignore")
calc = Calculator(descriptors)
df = calc.pandas(list(pdbs), quiet=True)
df = df.loc[:, [s.dtype in [np.float, np.int] for n, s in df.items()]]
df.dropna(axis="columns", inplace=True)
df = pd.DataFrame(df.apply(np.mean)).transpose()
df.index = [name]
df["y"] = [class_]
df.to_csv(str(smk_obj.output))
except Exception as e:
print(e)
|
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|
# Simulating Molecules using VQE
In this tutorial, we introduce the Variational Quantum Eigensolver (VQE), motivate its use, explain the necessary theory, and demonstrate its implementation in finding the ground state energy of molecules.
## Contents
1. [Introduction](#introduction)
2. [The Variational Method of Quantum Mechanics](#varmethod)
1. [Mathematical Background](#backgroundmath)
2. [Bounding the Ground State](#groundstate)
3. [The Variational Quantum Eigensolver](#vqe)
1. [Variational Forms](#varforms)
2. [Simple Variational Forms](#simplevarform)
3. [Parameter Optimization](#optimization)
4. [Example with a Single Qubit Variational Form](#example)
5. [Structure of Common Variational Forms](#commonvarforms)
4. [VQE Implementation in Qiskit](#implementation)
1. [Running VQE on a Statevector Simulator](#implementationstatevec)
2. [Running VQE on a Noisy Simulator](#implementationnoisy)
5. [Problems](#problems)
6. [References](#references)
## Introduction<a id='introduction'></a>
In many applications it is important to find the minimum eigenvalue of a matrix. For example, in chemistry, the minimum eigenvalue of a Hermitian matrix characterizing the molecule is the ground state energy of that system. In the future, the quantum phase estimation algorithm may be used to find the minimum eigenvalue. However, its implementation on useful problems requires circuit depths exceeding the limits of hardware available in the NISQ era. Thus, in 2014, Peruzzo *et al.* proposed VQE to estimate the ground state energy of a molecule using much shallower circuits [1].
Formally stated, given a Hermitian matrix $H$ with an unknown minimum eigenvalue $\lambda_{min}$, associated with the eigenstate $|\psi_{min}\rangle$, VQE provides an estimate $\lambda_{\theta}$ bounding $\lambda_{min}$:
\begin{align*}
\lambda_{min} \le \lambda_{\theta} \equiv \langle \psi(\theta) |H|\psi(\theta) \rangle
\end{align*}
where $|\psi(\theta)\rangle$ is the eigenstate associated with $\lambda_{\theta}$. By applying a parameterized circuit, represented by $U(\theta)$, to some arbitrary starting state $|\psi\rangle$, the algorithm obtains an estimate $U(\theta)|\psi\rangle \equiv |\psi(\theta)\rangle$ on $|\psi_{min}\rangle$. The estimate is iteratively optimized by a classical controller changing the parameter $\theta$ minimizing the expectation value of $\langle \psi(\theta) |H|\psi(\theta) \rangle$.
## The Variational Method of Quantum Mechanics<a id='varmethod'></a>
### Mathematical Background<a id='backgroundmath'></a>
VQE is an application of the variational method of quantum mechanics. To better understand the variational method, some preliminary mathematical background is provided. An eigenvector, $|\psi_i\rangle$, of a matrix $A$ is invariant under transformation by $A$ up to a scalar multiplicative constant (the eigenvalue $\lambda_i$). That is,
\begin{align*}
A |\psi_i\rangle = \lambda_i |\psi_i\rangle
\end{align*}
Furthermore, a matrix $H$ is Hermitian when it is equal to its own conjugate transpose.
\begin{align*}
H = H^{\dagger}
\end{align*}
The spectral theorem states that the eigenvalues of a Hermitian matrix must be real. Thus, any eigenvalue of $H$ has the property that $\lambda_i = \lambda_i^*$. As any measurable quantity must be real, Hermitian matrices are suitable for describing the Hamiltonians of quantum systems. Moreover, $H$ may be expressed as
\begin{align*}
H = \sum_{i = 1}^{N} \lambda_i |\psi_i\rangle \langle \psi_i |
\end{align*}
where each $\lambda_i$ is the eigenvalue corresponding to the eigenvector $|\psi_i\rangle$. Furthermore, the expectation value of the observable $H$ on an arbitrary quantum state $|\psi\rangle$ is given by
\begin{align}
\langle H \rangle_{\psi} &\equiv \langle \psi | H | \psi \rangle
\end{align}
Substituting $H$ with its representation as a weighted sum of its eigenvectors,
\begin{align}
\langle H \rangle_{\psi} = \langle \psi | H | \psi \rangle &= \langle \psi | \left(\sum_{i = 1}^{N} \lambda_i |\psi_i\rangle \langle \psi_i |\right) |\psi\rangle\\
&= \sum_{i = 1}^{N} \lambda_i \langle \psi | \psi_i\rangle \langle \psi_i | \psi\rangle \\
&= \sum_{i = 1}^{N} \lambda_i | \langle \psi_i | \psi\rangle |^2
\end{align}
The last equation demonstrates that the expectation value of an observable on any state can be expressed as a linear combination using the eigenvalues associated with $H$ as the weights. Moreover, each of the weights in the linear combination is greater than or equal to 0, as $| \langle \psi_i | \psi\rangle |^2 \ge 0$ and so it is clear that
\begin{align}
\lambda_{min} \le \langle H \rangle_{\psi} = \langle \psi | H | \psi \rangle = \sum_{i = 1}^{N} \lambda_i | \langle \psi_i | \psi\rangle |^2
\end{align}
The above equation is known as the **variational method** (in some texts it is also known as the variational principle) [2]. It is important to note that this implies that the expectation value of any wave function will always be at least the minimum eigenvalue associated with $H$. Moreover, the expectation value of state $|\psi_{min}\rangle$ is given by $\langle \psi_{min}|H|\psi_{min}\rangle = \langle \psi_{min}|\lambda_{min}|\psi_{min}\rangle = \lambda_{min}$. Thus, as expected, $\langle H \rangle_{\psi_{min}}=\lambda_{min}$.
### Bounding the Ground State<a id='groundstate'></a>
When the Hamiltonian of a system is described by the Hermitian matrix $H$ the ground state energy of that system, $E_{gs}$, is the smallest eigenvalue associated with $H$. By arbitrarily selecting a wave function $|\psi \rangle$ (called an *ansatz*) as an initial guess approximating $|\psi_{min}\rangle$, calculating its expectation value, $\langle H \rangle_{\psi}$, and iteratively updating the wave function, arbitrarily tight bounds on the ground state energy of a Hamiltonian may be obtained.
## The Variational Quantum Eigensolver<a id='vqe'></a>
### Variational Forms<a id='varforms'></a>
A systematic approach to varying the ansatz is required to implement the variational method on a quantum computer. VQE does so through the use of a parameterized circuit with a fixed form. Such a circuit is often called a *variational form*, and its action may be represented by the linear transformation $U(\theta)$. A variational form is applied to a starting state $|\psi\rangle$ (such as the vacuum state $|0\rangle$, or the Hartree Fock state) and generates an output state $U(\theta)|\psi\rangle\equiv |\psi(\theta)\rangle$. Iterative optimization over $|\psi(\theta)\rangle$ aims to yield an expectation value $\langle \psi(\theta)|H|\psi(\theta)\rangle \approx E_{gs} \equiv \lambda_{min}$. Ideally, $|\psi(\theta)\rangle$ will be close to $|\psi_{min}\rangle$ (where 'closeness' is characterized by either state fidelity, or Manhattan distance) although in practice, useful bounds on $E_{gs}$ can be obtained even if this is not the case.
Moreover, a fixed variational form with a polynomial number of parameters can only generate transformations to a polynomially sized subspace of all the states in an exponentially sized Hilbert space. Consequently, various variational forms exist. Some, such as Ry and RyRz are heuristically designed, without consideration of the target domain. Others, such as UCCSD, utilize domain specific knowledge to generate close approximations based on the problem's structure. The structure of common variational forms is discussed in greater depth later in this document.
### Simple Variational Forms<a id='simplevarform'></a>
When constructing a variational form we must balance two opposing goals. Ideally, our $n$ qubit variational form would be able to generate any possible state $|\psi\rangle$ where $|\psi\rangle \in \mathbb{C}^N$ and $N=2^n$. However, we would like the variational form to use as few parameters as possible. Here, we aim to give intuition for the construction of variational forms satisfying our first goal, while disregarding the second goal for the sake of simplicity.
Consider the case where $n=1$. The U3 gate takes three parameters, $\theta, \phi$ and $\lambda$, and represents the following transformation:
\begin{align}
U3(\theta, \phi, \lambda) = \begin{pmatrix}\cos(\frac{\theta}{2}) & -e^{i\lambda}\sin(\frac{\theta}{2}) \\ e^{i\phi}\sin(\frac{\theta}{2}) & e^{i\lambda + i\phi}\cos(\frac{\theta}{2}) \end{pmatrix}
\end{align}
Up to a global phase, any possible single qubit transformation may be implemented by appropriately setting these parameters. Consequently, for the single qubit case, a variational form capable of generating any possible state is given by the circuit:
Moreover, this universal 'variational form' only has 3 parameters and thus can be efficiently optimized. It is worth emphasising that the ability to generate an arbitrary state ensures that during the optimization process, the variational form does not limit the set of attainable states over which the expectation value of $H$ can be taken. Ideally, this ensures that the minimum expectation value is limited only by the capabilities of the classical optimizer.
A less trivial universal variational form may be derived for the 2 qubit case, where two body interactions, and thus entanglement, must be considered to achieve universality. Based on the work presented by *Shende et al.* [3] the following is an example of a universal parameterized 2 qubit circuit:
Allow the transformation performed by the above circuit to be represented by $U(\theta)$. When optimized variationally, the expectation value of $H$ is minimized when $U(\theta)|\psi\rangle \equiv |\psi(\theta)\rangle \approx |\psi_{min}\rangle$. By formulation, $U(\theta)$ may produce a transformation to any possible state, and so this variational form may obtain an arbitrarily tight bound on two qubit ground state energies, only limited by the capabilities of the classical optimizer.
### Parameter Optimization<a id='optimization'></a>
Once an efficiently parameterized variational form has been selected, in accordance with the variational method, its parameters must be optimized to minimize the expectation value of the target Hamiltonian. The parameter optimization process has various challenges. For example, quantum hardware has various types of noise and so objective function evaluation (energy calculation) may not necessarily reflect the true objective function. Additionally, some optimizers perform a number of objective function evaluations dependent on cardinality of the parameter set. An appropriate optimizer should be selected by considering the requirements of a application.
A popular optimization strategy is gradient decent where each parameter is updated in the direction yielding the largest local change in energy. Consequently, the number of evaluations performed depends on the number of optimization parameters present. This allows the algorithm to quickly find a local optimum in the search space. However, this optimization strategy often gets stuck at poor local optima, and is relatively expensive in terms of the number of circuit evaluations performed. While an intuitive optimization strategy, it is not recommended for use in VQE.
An appropriate optimizer for optimizing a noisy objective function is the *Simultaneous Perturbation Stochastic Approximation* optimizer (SPSA). SPSA approximates the gradient of the objective function with only two measurements. It does so by concurrently perturbing all of the parameters in a random fashion, in contrast to gradient decent where each parameter is perturbed independently. When utilizing VQE in either a noisy simulator or on real hardware, SPSA is a recommended as the classical optimizer.
When noise is not present in the cost function evaluation (such as when using VQE with a statevector simulator), a wide variety of classical optimizers may be useful. Two such optimizers supported by Qiskit Aqua are the *Sequential Least Squares Programming* optimizer (SLSQP) and the *Constrained Optimization by Linear Approximation* optimizer (COBYLA). It is worth noting that COBYLA only performs one objective function evaluation per optimization iteration (and thus the number of evaluations is independent of the parameter set's cardinality). Therefore, if the objective function is noise-free and minimizing the number of performed evaluations is desirable, it is recommended to try COBYLA.
### Example with a Single Qubit Variational Form<a id='example'></a>
We will now use the simple single qubit variational form to solve a problem similar to ground state energy estimation. Specifically, we are given a random probability vector $\vec{x}$ and wish to determine a possible parameterization for our single qubit variational form such that it outputs a probability distribution that is close to $\vec{x}$ (where closeness is defined in terms of the Manhattan distance between the two probability vectors).
We first create the random probability vector in python:
```python
import numpy as np
np.random.seed(999999)
target_distr = np.random.rand(2)
# We now convert the random vector into a valid probability vector
target_distr /= sum(target_distr)
```
We subsequently create a function that takes the parameters of our single U3 variational form as arguments and returns the corresponding quantum circuit:
```python
from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister
def get_var_form(params):
qr = QuantumRegister(1, name="q")
cr = ClassicalRegister(1, name='c')
qc = QuantumCircuit(qr, cr)
qc.u3(params[0], params[1], params[2], qr[0])
qc.measure(qr, cr[0])
return qc
```
Now we specify the objective function which takes as input a list of the variational form's parameters, and returns the cost associated with those parameters:
```python
from qiskit import Aer, execute
backend = Aer.get_backend("qasm_simulator")
NUM_SHOTS = 10000
def get_probability_distribution(counts):
output_distr = [v / NUM_SHOTS for v in counts.values()]
if len(output_distr) == 1:
output_distr.append(0)
return output_distr
def objective_function(params):
# Obtain a quantum circuit instance from the paramters
qc = get_var_form(params)
# Execute the quantum circuit to obtain the probability distribution associated with the current parameters
result = execute(qc, backend, shots=NUM_SHOTS).result()
# Obtain the counts for each measured state, and convert those counts into a probability vector
output_distr = get_probability_distribution(result.get_counts(qc))
# Calculate the cost as the distance between the output distribution and the target distribution
cost = sum([np.abs(output_distr[i] - target_distr[i]) for i in range(2)])
return cost
```
Finally, we create an instance of the COBYLA optimizer, and run the algorithm. Note that the output varies from run to run. Moreover, while close, the obtained distribution might not be exactly the same as the target distribution, however, increasing the number of shots taken will increase the accuracy of the output.
```python
from qiskit.aqua.components.optimizers import COBYLA
# Initialize the COBYLA optimizer
optimizer = COBYLA(maxiter=500, tol=0.0001)
# Create the initial parameters (noting that our single qubit variational form has 3 parameters)
params = np.random.rand(3)
ret = optimizer.optimize(num_vars=3, objective_function=objective_function, initial_point=params)
# Obtain the output distribution using the final parameters
qc = get_var_form(ret[0])
counts = execute(qc, backend, shots=NUM_SHOTS).result().get_counts(qc)
output_distr = get_probability_distribution(counts)
print("Target Distribution:", target_distr)
print("Obtained Distribution:", output_distr)
print("Output Error (Manhattan Distance):", ret[1])
print("Parameters Found:", ret[0])
```
Target Distribution: [0.51357006 0.48642994]
Obtained Distribution: [0.5182, 0.4818]
Output Error (Manhattan Distance): 0.0001401187388391789
Parameters Found: [1.59966854 0.66273002 0.28432001]
### Structure of Common Variational Forms<a id='commonvarforms'></a>
As already discussed, it is not possible for a polynomially parameterized variational form to generate a transformation to any state. Variational forms can be grouped into two categories, depending on how they deal with this limitation. The first category of variational forms use domain or application specific knowledge to limit the set of possible output states. The second approach uses a heuristic circuit without prior domain or application specific knowledge.
The first category of variational forms exploit characteristics of the problem domain to restrict the set of transformations that may be required. For example, when calculating the ground state energy of a molecule, the number of particles in the system is known *a priori*. Therefore, if a starting state with the correct number of particles is used, by limiting the variational form to only producing particle preserving transformations, the number of parameters required to span the new transformation subspace can be greatly reduced. Indeed, by utilizing similar information from Coupled-Cluster theory, the variational form UCCSD can obtain very accurate results for molecular ground state energy estimation when starting from the Hartree Fock state. Another example illustrating the exploitation of domain-specific knowledge follows from considering the set of circuits realizable on real quantum hardware. Extant quantum computers, such as those based on super conducting qubits, have limited qubit connectivity. That is, it is not possible to implement 2-qubit gates on arbitrary qubit pairs (without inserting swap gates). Thus, variational forms have been constructed for specific quantum computer architectures where the circuits are specifically tuned to maximally exploit the natively available connectivity and gates of a given quantum device. Such a variational form was used in 2017 to successfully implement VQE for the estimation of the ground state energies of molecules as large as BeH$_2$ on an IBM quantum computer [4].
In the second approach, gates are layered such that good approximations on a wide range of states may be obtained. Qiskit Aqua supports three such variational forms: RyRz, Ry and SwapRz (we will only discuss the first two). All of these variational forms accept multiple user-specified configurations. Three essential configurations are the number of qubits in the system, the depth setting, and the entanglement setting. A single layer of a variational form specifies a certain pattern of single qubit rotations and CX gates. The depth setting says how many times the variational form should repeat this pattern. By increasing the depth setting, at the cost of increasing the number of parameters that must be optimized, the set of states the variational form can generate increases. Finally, the entanglement setting selects the configuration, and implicitly the number, of CX gates. For example, when the entanglement setting is linear, CX gates are applied to adjacent qubit pairs in order (and thus $n-1$ CX gates are added per layer). When the entanglement setting is full, a CX gate is applied to each qubit pair in each layer. The circuits for RyRz corresponding to `entanglement="full"` and `entanglement="linear"` can be seen by executing the following code snippet:
```python
from qiskit.aqua.components.variational_forms import RYRZ
entanglements = ["linear", "full"]
for entanglement in entanglements:
form = RYRZ(num_qubits=4, depth=1, entanglement=entanglement)
if entanglement == "linear":
print("=============Linear Entanglement:=============")
else:
print("=============Full Entanglement:=============")
# We initialize all parameters to 0 for this demonstration
print(form.construct_circuit([0] * form.num_parameters).draw(line_length=100))
print()
```
=============Linear Entanglement:=============
┌───────────┐┌───────┐ ┌───────────┐ ┌───────┐ »
q_0: |0>┤ U3(0,0,0) ├┤ U1(0) ├──────────────────■───┤ U3(0,0,0) ├──┤ U1(0) ├────────────────»
├───────────┤├───────┤┌──────────────┐┌─┴─┐┌┴───────────┴─┐└───────┘ ┌───────────┐ »
q_1: |0>┤ U3(0,0,0) ├┤ U1(0) ├┤ U2(0,3.1416) ├┤ X ├┤ U2(0,3.1416) ├────■─────┤ U3(0,0,0) ├──»
├───────────┤├───────┤├──────────────┤└───┘└──────────────┘ ┌─┴─┐ ┌┴───────────┴─┐»
q_2: |0>┤ U3(0,0,0) ├┤ U1(0) ├┤ U2(0,3.1416) ├───────────────────────┤ X ├──┤ U2(0,3.1416) ├»
├───────────┤├───────┤├──────────────┤ └───┘ └──────────────┘»
q_3: |0>┤ U3(0,0,0) ├┤ U1(0) ├┤ U2(0,3.1416) ├──────────────────────────────────────────────»
└───────────┘└───────┘└──────────────┘ »
« ░
«q_0: ────────────────────────────────────────────────░─
« ┌───────┐ ░
«q_1: ┤ U1(0) ├───────────────────────────────────────░─
« └───────┘ ┌───────────┐ ┌───────┐ ░
«q_2: ────■─────┤ U3(0,0,0) ├────┤ U1(0) ├────────────░─
« ┌─┴─┐ ┌┴───────────┴─┐┌─┴───────┴─┐┌───────┐ ░
«q_3: ──┤ X ├──┤ U2(0,3.1416) ├┤ U3(0,0,0) ├┤ U1(0) ├─░─
« └───┘ └──────────────┘└───────────┘└───────┘ ░
=============Full Entanglement:=============
┌───────────┐┌───────┐ »
q_0: |0>┤ U3(0,0,0) ├┤ U1(0) ├──────────────────■────■────────────────────■──────────────────»
├───────────┤├───────┤┌──────────────┐┌─┴─┐ │ ┌──────────────┐ │ »
q_1: |0>┤ U3(0,0,0) ├┤ U1(0) ├┤ U2(0,3.1416) ├┤ X ├──┼──┤ U2(0,3.1416) ├──┼──────────────────»
├───────────┤├───────┤├──────────────┤└───┘┌─┴─┐└──────────────┘ │ ┌──────────────┐»
q_2: |0>┤ U3(0,0,0) ├┤ U1(0) ├┤ U2(0,3.1416) ├─────┤ X ├──────────────────┼──┤ U2(0,3.1416) ├»
├───────────┤├───────┤├──────────────┤ └───┘ ┌─┴─┐└──────────────┘»
q_3: |0>┤ U3(0,0,0) ├┤ U1(0) ├┤ U2(0,3.1416) ├──────────────────────────┤ X ├────────────────»
└───────────┘└───────┘└──────────────┘ └───┘ »
« ┌───────────┐ ┌───────┐ »
«q_0: ─┤ U3(0,0,0) ├─────┤ U1(0) ├──────────────────────────────────────────────────────────────»
« └───────────┘ └───────┘ ┌───────────┐ ┌───────┐ »
«q_1: ───────────────────────■──────────■───────────────────┤ U3(0,0,0) ├─────┤ U1(0) ├─────────»
« ┌──────────────┐ ┌─┴─┐ │ ┌──────────────┐ └───────────┘ └───────┘ »
«q_2: ┤ U2(0,3.1416) ├─────┤ X ├────────┼──┤ U2(0,3.1416) ├──────────────────────────────────■──»
« ├──────────────┤┌────┴───┴─────┐┌─┴─┐└──────────────┘┌──────────────┐┌──────────────┐┌─┴─┐»
«q_3: ┤ U2(0,3.1416) ├┤ U2(0,3.1416) ├┤ X ├────────────────┤ U2(0,3.1416) ├┤ U2(0,3.1416) ├┤ X ├»
« └──────────────┘└──────────────┘└───┘ └──────────────┘└──────────────┘└───┘»
« ░
«q_0: ───────────────────────────────────────░─
« ░
«q_1: ───────────────────────────────────────░─
« ┌───────────┐ ┌───────┐ ░
«q_2: ─┤ U3(0,0,0) ├────┤ U1(0) ├────────────░─
« ┌┴───────────┴─┐┌─┴───────┴─┐┌───────┐ ░
«q_3: ┤ U2(0,3.1416) ├┤ U3(0,0,0) ├┤ U1(0) ├─░─
« └──────────────┘└───────────┘└───────┘ ░
Assume the depth setting is set to $d$. Then, RyRz has $n\times (d+1)\times 2$ parameters, Ry with linear entanglement has $2n\times(d + \frac{1}{2})$ parameters, and Ry with full entanglement has $d\times n\times \frac{(n + 1)}{2} + n$ parameters.
## VQE Implementation in Qiskit<a id='implementation'></a>
This section illustrates an implementation of VQE using the programmatic approach. Qiskit Aqua also enables a declarative implementation, however, it reveals less information about the underlying algorithm. This code, specifically the preparation of qubit operators, is based on the code found in the Qiskit Tutorials repository (and as of July 2019, may be found at: https://github.com/Qiskit/qiskit-tutorials ).
The following libraries must first be imported.
```python
from qiskit.aqua.algorithms import VQE, ExactEigensolver
import matplotlib.pyplot as plt
%matplotlib inline
import numpy as np
from qiskit.chemistry.aqua_extensions.components.variational_forms import UCCSD
from qiskit.aqua.components.variational_forms import RYRZ
from qiskit.chemistry.aqua_extensions.components.initial_states import HartreeFock
from qiskit.aqua.components.optimizers import COBYLA, SPSA, SLSQP
from qiskit import IBMQ, BasicAer, Aer
from qiskit.chemistry.drivers import PySCFDriver, UnitsType
from qiskit.chemistry import FermionicOperator
from qiskit import IBMQ
from qiskit.providers.aer import noise
from qiskit.aqua import QuantumInstance
from qiskit.ignis.mitigation.measurement import CompleteMeasFitter
```
### Running VQE on a Statevector Simulator<a id='implementationstatevec'></a>
We demonstrate the calculation of the ground state energy for LiH at various interatomic distances. A driver for the molecule must be created at each such distance. Note that in this experiment, to reduce the number of qubits used, we freeze the core and remove two unoccupied orbitals. First, we define a function that takes an interatomic distance and returns the appropriate qubit operator, $H$, as well as some other information about the operator.
```python
def get_qubit_op(dist):
driver = PySCFDriver(atom="Li .0 .0 .0; H .0 .0 " + str(dist), unit=UnitsType.ANGSTROM,
charge=0, spin=0, basis='sto3g')
molecule = driver.run()
freeze_list = [0]
remove_list = [-3, -2]
repulsion_energy = molecule.nuclear_repulsion_energy
num_particles = molecule.num_alpha + molecule.num_beta
num_spin_orbitals = molecule.num_orbitals * 2
remove_list = [x % molecule.num_orbitals for x in remove_list]
freeze_list = [x % molecule.num_orbitals for x in freeze_list]
remove_list = [x - len(freeze_list) for x in remove_list]
remove_list += [x + molecule.num_orbitals - len(freeze_list) for x in remove_list]
freeze_list += [x + molecule.num_orbitals for x in freeze_list]
ferOp = FermionicOperator(h1=molecule.one_body_integrals, h2=molecule.two_body_integrals)
ferOp, energy_shift = ferOp.fermion_mode_freezing(freeze_list)
num_spin_orbitals -= len(freeze_list)
num_particles -= len(freeze_list)
ferOp = ferOp.fermion_mode_elimination(remove_list)
num_spin_orbitals -= len(remove_list)
qubitOp = ferOp.mapping(map_type='parity', threshold=0.00000001)
qubitOp = qubitOp.two_qubit_reduced_operator(num_particles)
shift = energy_shift + repulsion_energy
return qubitOp, num_particles, num_spin_orbitals, shift
```
First, the exact ground state energy is calculated using the qubit operator and a classical exact eigensolver. Subsequently, the initial state $|\psi\rangle$ is created, which the VQE instance uses to produce the final ansatz $\min_{\theta}(|\psi(\theta)\rangle)$. The exact result and the VQE result at each interatomic distance is stored. Observe that the result given by `vqe.run(backend)['energy'] + shift` is equivalent the quantity $\min_{\theta}\left(\langle \psi(\theta)|H|\psi(\theta)\rangle\right)$, where the minimum is not necessarily the global minimum.
When initializing the VQE instance with `VQE(qubitOp, var_form, optimizer, 'matrix')` the expectation value of $H$ on $|\psi(\theta)\rangle$ is directly calculated through matrix multiplication. However, when using an actual quantum device, or a true simulator such as the `qasm_simulator` with `VQE(qubitOp, var_form, optimizer, 'paulis')` the calculation of the expectation value is more complicated. A Hamiltonian may be represented as a sum of a Pauli strings, with each Pauli term acting on a qubit as specified by the mapping being used. Each Pauli string has a corresponding circuit appended to the circuit corresponding to $|\psi(\theta)\rangle$. Subsequently, each of these circuits is executed, and all of the results are used to determine the expectation value of $H$ on $|\psi(\theta)\rangle$. In the following example, we initialize the VQE instance with `matrix` mode, and so the expectation value is directly calculated through matrix multiplication.
Note that the following code snippet may take a few minutes to run to completion.
```python
backend = BasicAer.get_backend("statevector_simulator")
distances = np.arange(0.5, 4.0, 0.1)
exact_energies = []
vqe_energies = []
optimizer = SLSQP(maxiter=5)
for dist in distances:
qubitOp, num_particles, num_spin_orbitals, shift = get_qubit_op(dist)
result = ExactEigensolver(qubitOp).run()
exact_energies.append(result['energy'] + shift)
initial_state = HartreeFock(
qubitOp.num_qubits,
num_spin_orbitals,
num_particles,
'parity'
)
var_form = UCCSD(
qubitOp.num_qubits,
depth=1,
num_orbitals=num_spin_orbitals,
num_particles=num_particles,
initial_state=initial_state,
qubit_mapping='parity'
)
vqe = VQE(qubitOp, var_form, optimizer, 'matrix')
results = vqe.run(backend)['energy'] + shift
vqe_energies.append(results)
print("Interatomic Distance:", np.round(dist, 2), "VQE Result:", results, "Exact Energy:", exact_energies[-1])
print("All energies have been calculated")
```
Interatomic Distance: 0.5 VQE Result: -7.039710219020506 Exact Energy: -7.039732521635202
Interatomic Distance: 0.6 VQE Result: -7.313344302334236 Exact Energy: -7.313345828761008
Interatomic Distance: 0.7 VQE Result: -7.500921095743192 Exact Energy: -7.500922090905936
Interatomic Distance: 0.8 VQE Result: -7.630976914468914 Exact Energy: -7.630978249333209
Interatomic Distance: 0.9 VQE Result: -7.7208107952020795 Exact Energy: -7.720812412134773
Interatomic Distance: 1.0 VQE Result: -7.782240655298441 Exact Energy: -7.782242402637011
Interatomic Distance: 1.1 VQE Result: -7.823597493320795 Exact Energy: -7.82359927636281
Interatomic Distance: 1.2 VQE Result: -7.850696622934822 Exact Energy: -7.850698377596024
Interatomic Distance: 1.3 VQE Result: -7.867561602181376 Exact Energy: -7.867563290110052
Interatomic Distance: 1.4 VQE Result: -7.876999876757721 Exact Energy: -7.877001491818373
Interatomic Distance: 1.5 VQE Result: -7.8810141736656405 Exact Energy: -7.881015715646992
Interatomic Distance: 1.6 VQE Result: -7.881070662952161 Exact Energy: -7.88107204403092
Interatomic Distance: 1.7 VQE Result: -7.878267162143656 Exact Energy: -7.878268167584993
Interatomic Distance: 1.8 VQE Result: -7.873440112155302 Exact Energy: -7.873440293132828
Interatomic Distance: 1.9 VQE Result: -7.86723366674701 Exact Energy: -7.8672339648160285
Interatomic Distance: 2.0 VQE Result: -7.860152327529411 Exact Energy: -7.86015320737878
Interatomic Distance: 2.1 VQE Result: -7.852595105536979 Exact Energy: -7.852595827876738
Interatomic Distance: 2.2 VQE Result: -7.844878726366329 Exact Energy: -7.844879093009722
Interatomic Distance: 2.3 VQE Result: -7.837257439448259 Exact Energy: -7.8372579676155025
Interatomic Distance: 2.4 VQE Result: -7.829935045088515 Exact Energy: -7.829937002623394
Interatomic Distance: 2.5 VQE Result: -7.823070191557451 Exact Energy: -7.82307664213409
Interatomic Distance: 2.6 VQE Result: -7.816782591999657 Exact Energy: -7.816795150472929
Interatomic Distance: 2.7 VQE Result: -7.8111534373726 Exact Energy: -7.811168284803366
Interatomic Distance: 2.8 VQE Result: -7.806218299266321 Exact Energy: -7.806229560089845
Interatomic Distance: 2.9 VQE Result: -7.801962397475152 Exact Energy: -7.8019736023325486
Interatomic Distance: 3.0 VQE Result: -7.798352412318197 Exact Energy: -7.7983634309151295
Interatomic Distance: 3.1 VQE Result: -7.795326815750017 Exact Energy: -7.795340451637537
Interatomic Distance: 3.2 VQE Result: -7.792800698225245 Exact Energy: -7.792834806738612
Interatomic Distance: 3.3 VQE Result: -7.790603799019874 Exact Energy: -7.790774009971014
Interatomic Distance: 3.4 VQE Result: -7.788715354695274 Exact Energy: -7.789088897991478
Interatomic Distance: 3.5 VQE Result: -7.787215781080283 Exact Energy: -7.787716973466144
Interatomic Distance: 3.6 VQE Result: -7.786080393658009 Exact Energy: -7.786603763673838
Interatomic Distance: 3.7 VQE Result: -7.785203497342158 Exact Energy: -7.785702912499886
Interatomic Distance: 3.8 VQE Result: -7.7844795319924325 Exact Energy: -7.784975591698873
Interatomic Distance: 3.9 VQE Result: -7.783853361693722 Exact Energy: -7.7843896116723315
All energies have been calculated
```python
plt.plot(distances, exact_energies, label="Exact Energy")
plt.plot(distances, vqe_energies, label="VQE Energy")
plt.xlabel('Atomic distance (Angstrom)')
plt.ylabel('Energy')
plt.legend()
plt.show()
```
Note that the VQE results are very close to the exact results, and so the exact energy curve is hidden by the VQE curve.
### Running VQE on a Noisy Simulator<a id='implementationnoisy'></a>
Here, we calculate the ground state energy for H$_2$ using a noisy simulator and error mitigation.
First, we prepare the qubit operator representing the molecule's Hamiltonian:
```python
driver = PySCFDriver(atom='H .0 .0 -0.3625; H .0 .0 0.3625', unit=UnitsType.ANGSTROM, charge=0, spin=0, basis='sto3g')
molecule = driver.run()
num_particles = molecule.num_alpha + molecule.num_beta
qubitOp = FermionicOperator(h1=molecule.one_body_integrals, h2=molecule.two_body_integrals).mapping(map_type='parity')
qubitOp = qubitOp.two_qubit_reduced_operator(num_particles)
```
Now, we load a device coupling map and noise model from the IBMQ provider and create a quantum instance, enabling error mitigation:
```python
provider = IBMQ.load_account()
backend = Aer.get_backend("qasm_simulator")
device = provider.get_backend("ibmqx4")
coupling_map = device.configuration().coupling_map
noise_model = noise.device.basic_device_noise_model(device.properties())
quantum_instance = QuantumInstance(backend=backend, shots=1000,
noise_model=noise_model,
coupling_map=coupling_map,
measurement_error_mitigation_cls=CompleteMeasFitter,
cals_matrix_refresh_period=30,)
```
Finally, we must configure the optimizer, the variational form, and the VQE instance. As the effects of noise increase as the number of two qubit gates circuit depth increase, we use a heuristic variational form (RYRZ) rather than UCCSD as RYRZ has a much shallower circuit than UCCSD and uses substantially fewer two qubit gates.
The following code may take a few minutes to run to completion.
```python
exact_solution = ExactEigensolver(qubitOp).run()
print("Exact Result:", exact_solution['energy'])
optimizer = SPSA(max_trials=100)
var_form = RYRZ(qubitOp.num_qubits, depth=1, entanglement="linear")
vqe = VQE(qubitOp, var_form, optimizer=optimizer, operator_mode="grouped_paulis")
ret = vqe.run(quantum_instance)
print("VQE Result:", ret['energy'])
```
Exact Result: -1.86712097834127
VQE Result: -1.8220854070067132
When noise mitigation is enabled, even though the result does not fall within chemical accuracy (defined as being within 0.0016 Hartree of the exact result), it is fairly close to the exact solution.
## Problems<a id='problems'></a>
1. You are given a Hamiltonian $H$ with the promise that its ground state is close to a maximally entangled $n$ qubit state. Explain which variational form (or forms) is likely to efficiently and accurately learn the the ground state energy of $H$. You may also answer by creating your own variational form, and explaining why it is appropriate for use with this Hamiltonian.
2. Calculate the number of circuit evaluations performed per optimization iteration, when using the COBYLA optimizer, the `qasm_simulator` with 1000 shots, and a Hamiltonian with 60 Pauli strings.
3. Use VQE to estimate the ground state energy of BeH$_2$ with an interatomic distance of $1.3$Å. You may re-use the function `get_qubit_op(dist)` by replacing `atom="Li .0 .0 .0; H .0 .0 " + str(dist)` with `atom="Be .0 .0 .0; H .0 .0 -" + str(dist) + "; H .0 .0 " + str(dist)` and invoking the function with `get_qubit_op(1.3)`. Note that removing the unoccupied orbitals does not preserve chemical precision for this molecule. However, to get the number of qubits required down to 6 (and thereby allowing efficient simulation on most laptops), the loss of precision is acceptable. While beyond the scope of this exercise, the interested reader may use qubit tapering operations to reduce the number of required qubits to 7, without losing any chemical precision.
## References<a id='references'></a>
1. Peruzzo, Alberto, et al. "A variational eigenvalue solver on a photonic quantum processor." *Nature communications* 5 (2014): 4213.
2. Griffiths, David J., and Darrell F. Schroeter. Introduction to quantum mechanics. *Cambridge University Press*, 2018.
3. Shende, Vivek V., Igor L. Markov, and Stephen S. Bullock. "Minimal universal two-qubit cnot-based circuits." arXiv preprint quant-ph/0308033 (2003).
4. Kandala, Abhinav, et al. "Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets." Nature 549.7671 (2017): 242.
|
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|
"""
@author: Guan'an Wang
@contact: guan.wang0706@gmail.com
"""
import numpy as np
__all__ = ['accuracy']
def accuracy4tensor(output, target, topk=[1]):
maxk = max(topk)
batch_size = target.size(0)
_, pred = output.topk(maxk, 1, True, True)
pred = pred.t()
correct = pred.eq(target.view(1, -1).expand_as(pred))
res = []
for k in topk:
correct_k = correct[:k].view(-1).float().sum(0, keepdim=True)
res.append(correct_k.mul_(100.0 / batch_size))
return np.array(res)
def accuracy4list(output_list, target, topk=[1]):
res = 0
for output in output_list:
res += 1/len(output_list) * accuracy4tensor(output, target, topk)
return res
def accuracy(output, target, topk=[1]):
"""Computes the precision@k for the specified values of k"""
if isinstance(output, list):
return accuracy4list(output, target, topk)
else:
return accuracy4tensor(output, target, topk)
|
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|
Some things Im interested in:
University Airport
Cal Aggie Flying Farmers
Friends of the University Airport
VCOA Volvo Show and Swap Meet VCOAs Annual Davis Volvo Show and Swap Meet
Yolo Masonic Lodge
when is the next Yolo swap meet? Daubert
20130926 18:13:16 nbsp Hey, quick question is the name of the group Friends of University Airport or Friends of the University Airport? Users/JabberWokky Evan JabberWokky Edwards
|
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|
#!/usr/bin/env julia
using Dierckx
using Test
using Random: seed!
# Answers 'ans' are from scipy.interpolate,
# generated with genanswers.py script.
# -----------------------------------------------------------------------------
# Spline1D
x = [1., 2., 3.]
y = [0., 2., 4.]
spl = Spline1D(x, y; k=1, s=length(x))
yi = evaluate(spl, [1.0, 1.5, 2.0])
@test yi ≈ [0.0, 1.0, 2.0]
@test evaluate(spl, 1.5) ≈ 1.0
@test get_knots(spl) ≈ [1., 3.]
@test get_coeffs(spl) ≈ [0., 4.]
@test isapprox(get_residual(spl), 0.0, atol=1.e-30)
@test spl([1.0, 1.5, 2.0]) ≈ [0.0, 1.0, 2.0]
@test spl(1.5) ≈ 1.0
# test that a copy is returned by get_knots()
knots = get_knots(spl)
knots[1] = 1000.
@test get_knots(spl) ≈ [1., 3.]
# test ported from scipy.interpolate testing this bug:
# http://mail.scipy.org/pipermail/scipy-dev/2008-March/008507.html
x = [-1., -0.65016502, -0.58856235, -0.26903553, -0.17370892,
-0.10011001, 0., 0.10011001, 0.17370892, 0.26903553, 0.58856235,
0.65016502, 1.]
y = [1.,0.62928599, 0.5797223, 0.39965815, 0.36322694, 0.3508061,
0.35214793, 0.3508061, 0.36322694, 0.39965815, 0.5797223,
0.62928599, 1.]
w = [1.00000000e+12, 6.88875973e+02, 4.89314737e+02, 4.26864807e+02,
6.07746770e+02, 4.51341444e+02, 3.17480210e+02, 4.51341444e+02,
6.07746770e+02, 4.26864807e+02, 4.89314737e+02, 6.88875973e+02,
1.00000000e+12]
spl = Spline1D(x, y; w=w, s=Float64(length(x)))
desired = [0.35100374, 0.51715855, 0.87789547, 0.98719344]
actual = evaluate(spl, [0.1, 0.5, 0.9, 0.99])
@test isapprox(actual, desired, atol=5e-4)
# test periodic
x = [1., 2., 3., 4., 5.]
y = [4., 1., 4., 1., 4.]
spl = Spline1D(x, y, periodic=true)
@test derivative(spl, 1) ≈ derivative(spl, 5)
@test derivative(spl, 1, nu=2) ≈ derivative(spl, 5, nu=2)
# tests for out-of-range
x = [0.0:4.0;]
y = x.^3
xp = range(-8.0, stop=13.0, length=100)
xp_zeros = Float64[(0. <= xi <= 4.) ? xi : 0.0 for xi in xp]
xp_clip = Float64[(0. <= xi <= 4.) ? xi : (xi < 0.0) ? 0.0 : 4. for xi in xp]
spl = Spline1D(x, y)
t = get_knots(spl)[2: end-1] # knots, excluding those at endpoints
spl2 = Spline1D(x, y, t)
@test evaluate(spl, xp) ≈ xp_clip.^3
@test evaluate(spl2, xp) ≈ xp_clip.^3
# test other bc's
spl = Spline1D(x, y; bc="extrapolate")
@test evaluate(spl, xp) ≈ xp.^3
spl = Spline1D(x, y; bc="zero")
@test evaluate(spl, xp) ≈ xp_zeros.^3
spl = Spline1D(x, y; bc="error")
@test_throws ErrorException evaluate(spl, xp)
# test unknown bc
@test_throws ErrorException Spline1D(x, y; bc="unknown")
# test derivative
x = range(0, stop=1, length = 70)
y = x.^3
spl = Spline1D(x, y)
xt = [0.3, 0.4, 0.5]
@test derivative(spl, xt) ≈ 3xt.^2
# test integral
x = range(0, stop=10, length = 70)
y = x.^2
spl = Spline1D(x, y)
@test integrate(spl, 1.0, 5.0) ≈ 5.0^3/3 - 1/3
# test roots
x = range(0, stop=10, length = 70)
y = (x .- 4).^2 .- 1
spl = Spline1D(x, y)
@test roots(spl) ≈ [3, 5]
# test that show works.
io = IOBuffer()
show(io, spl)
seek(io, 0)
s = read(io, String)
@test s[1:9] == "Spline1D("
# test equality
seed!(0)
x = sort(rand(10))
y = rand(10)
sp1 = Spline1D(x, y)
sp2 = Spline1D(x, y)
sp3 = Spline1D(x.+1, y)
sp4 = Spline1D(x, y.+1)
@test sp1 == sp2
@test allunique([sp1,sp3,sp4])
# -----------------------------------------------------------------------------
# ParametricSpline
u = [1., 2., 3.]
x = [1. 2. 3.; 0. 2. 4.]
spl = ParametricSpline(u, x, k=1, s=size(x, 2))
xi = evaluate(spl, [1.0, 1.5, 2.0])
@test xi ≈ [1.0 1.5 2.0; 0.0 1.0 2.0]
@test evaluate(spl, 1.5) ≈ [1.5, 1.0]
@test get_knots(spl) ≈ [1., 3.]
@test get_coeffs(spl) ≈ [1.0 3.0; 0.0 4.0]
@test isapprox(get_residual(spl), 0.0, atol=1.e-30)
@test spl([1.0, 1.5, 2.0]) ≈ [1.0 1.5 2.0; 0.0 1.0 2.0]
@test spl(1.5) ≈ [1.5, 1.0]
# test that a copy is returned by get_knots()
knots = get_knots(spl)
knots[1] = 1000.
@test get_knots(spl) ≈ [1., 3.]
# test periodic
x = [23. 24. 25. 25. 24. 23.;
13. 12. 12. 13. 13. 13.]
spl = ParametricSpline(x, periodic=true)
@test evaluate(spl, 0) ≈ evaluate(spl, 1)
@test derivative(spl, 0) ≈ derivative(spl, 1)
@test derivative(spl, 0, nu=2) ≈ derivative(spl, 1, nu=2)
# tests for out-of-range
u = 0.0:4.0
x = [u'.^2; u'.^3]
up = range(-8.0, stop=13.0, length = 100)
up_zeros = Float64[(0. <= ui <= 4.) ? ui : 0.0 for ui in up]
up_clip = Float64[(0. <= ui <= 4.) ? ui : (ui < 0.0) ? 0.0 : 4. for ui in up]
spl = ParametricSpline(u, x)
t = get_knots(spl)[2: end-1] # knots, excluding those at endpoints
spl2 = ParametricSpline(u, x, t)
@test evaluate(spl, up) ≈ [up_clip'.^2; up_clip'.^3]
@test evaluate(spl2, up) ≈ [up_clip'.^2; up_clip'.^3]
# test other bc's
spl = ParametricSpline(u, x; bc="extrapolate")
@test evaluate(spl, up) ≈ [up'.^2; up'.^3]
spl = ParametricSpline(u, x; bc="zero")
@test evaluate(spl, up) ≈ [up_zeros'.^2; up_zeros'.^3]
spl = ParametricSpline(u, x; bc="error")
@test_throws ErrorException evaluate(spl, up)
# test unknown bc
@test_throws ErrorException ParametricSpline(u, x; bc="unknown")
# test derivative
u = range(0, stop=1, length = 70)
x = [u'.^2; u'.^3]
spl = ParametricSpline(u, x)
ut = [0.3, 0.4, 0.5]
@test derivative(spl, 0.3) ≈ [2*0.3, 3*0.3^2]
@test derivative(spl, ut) ≈ [2*ut'; 3*ut'.^2]
@test derivative(spl, 0.3, nu=2) ≈ [2.0, 6*0.3]
@test derivative(spl, ut, nu=2) ≈ [2*ones(3)'; 6*ut']
# test integral
u = range(0, stop=10, length = 70)
x = [u'.^2; u'.^3]
spl = ParametricSpline(u, x)
@test integrate(spl, 1.0, 5.0) ≈ [5.0^3/3 - 1/3, 5.0^4/4 - 1/4]
# test that show works.
io = IOBuffer()
show(io, spl)
seek(io, 0)
s = read(io, String)
@test s[1:17] == "ParametricSpline("
# test equality
seed!(0)
x = sort(rand(10))
y = rand(3, 10)
sp1 = ParametricSpline(x, y)
sp2 = ParametricSpline(x, y)
sp3 = ParametricSpline(x.+1, y)
sp4 = ParametricSpline(x, y.+1)
@test sp1 == sp2
@test allunique([sp1,sp3,sp4])
# test too many roots warning
x = (0:100)
y = (-1).^(0:100)
sp = Spline1D(x,y)
@test_logs (:warn,Regex("number of zeros exceeded")) roots(sp)
# -----------------------------------------------------------------------------
# Spline2D
# test linear
x = [1., 1., 1., 2., 2., 2., 3., 3., 3.]
y = [1., 2., 3., 1., 2., 3., 1., 2., 3.]
z = [0., 0., 0., 2., 2., 2., 4., 4., 4.]
spl = Spline2D(x, y, z; kx=1, ky=1, s=length(x))
tx, ty = get_knots(spl)
@test tx ≈ [1., 3.]
@test ty ≈ [1., 3.]
@test isapprox(get_residual(spl), 0.0, atol=1e-16)
@test evaluate(spl, 2.0, 1.5) ≈ 2.0
@test evalgrid(spl, [1.,1.5,2.], [1.,1.5]) ≈ [0. 0.; 1. 1.; 2. 2.]
# test 1-d grid arrays
@test evalgrid(spl, [2.0], [1.5])[1, 1] ≈ 2.0
# In this setting, lwrk2 is too small in the default run.
x = range(-2, stop=2, length = 80)
y = range(-2, stop=2, length = 80)
z = x .+ y
spl = Spline2D(x, y, z; s=length(x))
@test evaluate(spl, 1.0, 1.0) ≈ 2.0
# In this setting lwrk2 is too small multiple times!
# Eventually an error about s being too small is thrown.
seed!(0)
x = rand(100)
y = rand(100)
z = sin.(x) .* sin.(y)
@test_throws ErrorException Spline2D(x, y, z; kx=1, ky=1, s=0.0)
# test grid input creation
x = [0.5, 2., 3., 4., 5.5, 8.]
y = [0.5, 2., 3., 4.]
z = [1. 2. 1. 2.; # shape is (nx, ny)
1. 2. 1. 2.;
1. 2. 3. 2.;
1. 2. 2. 2.;
1. 2. 1. 2.;
1. 2. 3. 1.]
spl = Spline2D(x, y, z)
# element-wise output
xi = [1., 1.5, 2.3, 4.5, 3.3, 3.2, 3.]
yi = [1., 2.3, 5.3, 0.5, 3.3, 1.2, 3.]
ans = [2.94429906542,
1.25537598131,
2.00063588785,
1.0,
2.93952664,
1.06482509358,
3.0]
zi = evaluate(spl, xi, yi)
@test zi ≈ ans
zi = spl(xi, yi)
@test zi ≈ ans
# grid output
xi = [1., 1.5, 2.3, 4.5]
yi = [1., 2.3, 5.3]
ans = [2.94429906542 1.16946130841 1.99831775701;
2.80393858478 1.25537598131 1.99873831776;
1.67143209613 1.94853338542 2.00063588785;
1.89392523364 1.8126946729 2.01042056075]
zi = evalgrid(spl, xi, yi)
@test zi ≈ ans
# Test 2-d integration
test2d_1(x, y) = 1 - x^2 -y^2
test2d_2(x, y) = cos(x) + sin(y)
test2d_3(x, y) = x*exp(x-y)
for (f, domain, exact) in [(test2d_1, (0.0, 1.0, 0.0, 1.0), 1.0/3.0),
(test2d_2, (0.0, pi, 0.0, pi), 2.0*pi),
(test2d_3, (0.0, 1.0, 0.0, 1.0), (ℯ-1.0)/ℯ)]
(x0, x1, y0, y1) = domain
# define grids for x and y dimensions:
npoints = 50
xgrid = range(x0, stop=x1, length = npoints)
ygrid = range(y0, stop=y1, length = npoints)
fxygrid = zeros(npoints, npoints)
for (j, y) in enumerate(ygrid)
local j, y
for (i, x) in enumerate(xgrid)
local i, x
fxygrid[i,j] = f(x, y)
end
end
spl1 = Spline2D(xgrid, ygrid, fxygrid)
@test isapprox(integrate(spl1, x0, x1, y0, y1), exact, atol=1e-6)
end
# test equality
seed!(0)
x = sort(rand(10))
y = sort(rand(10))
z = rand(10,10)
sp1 = Spline2D(x, y, z)
sp2 = Spline2D(x, y, z)
sp3 = Spline2D(x.+1, y, z)
sp4 = Spline2D(x, y.+1, z)
sp5 = Spline2D(x, y, z.+1)
@test sp1 == sp2
@test allunique([sp1, sp3, sp4, sp5])
println("All tests passed.")
|
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#!/usr/bin/env python
# A basic tool that downsamples a radar scan by taking one point for each n
import math
import rospy
import tf
import numpy as np
from sensor_msgs.msg import LaserScan
from geometry_msgs.msg import Point
from visualization_msgs.msg import Marker
from geometry_msgs.msg import Twist
class Coll_avoidance2:
def __init__(self):
rospy.Subscriber('/cmd_vel_coll', Twist, self.vel)
rospy.Subscriber('/down/marker', Marker, self.callback)
self.cmd_vel = rospy.Publisher('cmd_vel', Twist, queue_size=10)
self.vel=None
self.coll_distance=0.5
self.marker=None
def callback(self, mark):
self.marker = mark.points
def vel(self, vel):
self.vel=vel
def peligro(self):
i = 0
enc=False
puntos=self.marker
orient=0
while(i<len(puntos) and not enc):
if(math.fabs(puntos[i].x)<self.coll_distance and math.fabs(puntos[i].y)<0.3):
enc=True
if(puntos[i].y<0):
orient=-1
else:
orient=1
else:
i+=1
return enc,orient
def peligro_lat(self):
i = 0
enc=False
puntos=self.marker
orient=0
while(i<len(puntos) and not enc):
if(math.fabs(puntos[i].x)<self.coll_distance and math.fabs(puntos[i].y)>0.3 and math.fabs(puntos[i].y)<1):
enc=True
rospy.loginfo('X: %f, Y: %f',puntos[i].x, puntos[i].y)
if(puntos[i].y<0):
orient=-1
else:
orient=1
else:
i+=1
return enc,orient #,x,y
def publish(self):
if(self.vel != None and self.marker != None):
move_cmd = Twist()
if(len(self.marker)==0):
lin_vel = self.vel.linear.x
angular = self.vel.angular.z
else:
enc,ori=self.peligro()
enc2,ori2=self.peligro_lat()
if(enc):
rospy.loginfo('PELIGRO!!!!!!!')
#angular=0.4*-ori
angular=0.4*ori
lin_vel=0
elif(enc2):
rospy.loginfo('PELIGRO LATTTT!!!!!!!')
lin_vel=0.2
#angular=0.1*ori2
angular=0
else:
rospy.loginfo('SEGUROO!!!!')
lin_vel = self.vel.linear.x
angular = self.vel.angular.z
# let's go forward at 0.2 m/s
move_cmd.linear.x = lin_vel
# let's turn at 0 radians/s
move_cmd.angular.z = angular
self.cmd_vel.publish(move_cmd)
def shutdown(self):
# stop turtlebot
rospy.loginfo("Stop TurtleBot")
# a default Twist has linear.x of 0 and angular.z of 0. So it'll stop TurtleBot
self.cmd_vel.publish(Twist())
# sleep just makes sure TurtleBot receives the stop command prior to shutting down the script
rospy.sleep(1)
if __name__ == '__main__':
try:
# initiliaze
rospy.init_node('coll_avoidance', anonymous=False)
r = rospy.Rate(10);
# Instantiate downsampler
ca = Coll_avoidance2()
while not rospy.is_shutdown():
ca.publish()
# wait for 0.1 seconds (10 HZ) and publish again
r.sleep()
except:
rospy.loginfo("Error coll_avoidance.")
|
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|
using RealNeuralNetworks
using RealNeuralNetworks.Neurons
using RealNeuralNetworks.Neurons.Segments
using Test
const SWC_BIN_PATH = joinpath(@__DIR__, "../asset/77625.swc.bin")
@testset "test Segments" begin
# construct a segment
neuron = Neurons.load_swc_bin( SWC_BIN_PATH )
# get a random segment
println("indexing from neuron...")
segment = neuron[5]
println("get tortuosity...")
@show Segments.get_tortuosity( segment )
println("get tail head radius ratio ...")
@show Segments.get_tail_head_radius_ratio( segment )
println("merge segments...")
segment2 = neuron[6]
merged_segment = merge(segment, segment2)
@test length(segment) + length(segment2) == length(merged_segment)
println("remove some nodes...")
newSegment = Segments.remove_nodes(segment, 2:4)
@test length(newSegment) == length(segment) - 3
println("remove redundent nodes...")
Segments.remove_redundent_nodes!(segment)
end
|
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|
# This file holds the definition of the functions pertaining to the
# PersonnelDatabase type.
# The functions of the PersonnelDatabase require the HistoryEntry, History, and
# Personnel types.
requiredTypes = [ "personnel", "personnelDatabase" ]
for reqType in requiredTypes
if !isdefined( Symbol( uppercase( string( reqType[ 1 ] ) ) * reqType[ 2:end ] ) )
include( joinpath( typePath, reqType * ".jl" ) )
end # if !isdefined( Symbol( ...
end # for reqType in requiredTypes
# Load in the type aliases.
include( joinpath( typePath, "typeAliases.jl" ) )
# This function tests if the database has the requested attribute.
export hasAttribute
function hasAttribute( dbase::PersonnelDatabase, attr::AttributeType )
return Symbol( attr ) ∈ dbase.attrs
end # hasAttribute( dbase, attr )
# This function adds the given attribute to the database, initializing the
# attribute. If some personnel records have this attribute already, it will be
# overwritten!
export addAttribute!
function addAttribute!( dbase::PersonnelDatabase, attr::AttributeType,
initContent = nothing )
tmpAttr = Symbol( attr )
# Do nothing if the attribute exists in the database.
if hasAttribute( dbase, tmpAttr )
return
end # if hasAttribute( dbase, tmpAttr )
push!( dbase.attrs, tmpAttr )
# Update all personnel records to have this attribute.
map( person -> person[ tmpAttr ] = initContent, dbase.dbase )
end # addAttribute!( dbase, attr, initContent )
# This function adds the given attributes to the database.
export addAttributes!
function addAttributes!( dbase::PersonnelDatabase, attrs::Vector{Symbol} )
map( attr -> addAttribute!( dbase, attr ), attrs )
end # addAttributes!( dbase, attrs )
function addAttributes!( dbase::PersonnelDatabase, attrs::Vector{String} )
map( attr -> addAttribute!( dbase, Symbol( attr ) ), attrs )
end # addAttributes!( dbase, attrs )
# This function removes the given attribute from the database.
export removeAttribute!
function removeAttribute!( dbase::PersonnelDatabase, attr::AttributeType )
tmpAttr = Symbol( attr )
# If the attribute doesn't exist, or it is the ID key, do nothing.
if !hasAttribute( dbase, tmpAttr ) || ( tmpAttr === dbase.idKey )
return
end # if ( attr ∉ dbase.attrs ) || ...
# Otherwise, remove attribute from list.
index = find( x -> x == tmpAttr, dbase.attrs )
deleteat!( dbase.attrs, index[ 1 ] )
# Delete field from personnel records.
map( person -> removeAttribute!( person, tmpAttr ), dbase.dbase )
end # removeAttribute!( dbase, fiattreld )
# This function removes the given attributes from the database.
export removeAttributes!
function removeAttributes!( dbase::PersonnelDatabase, attrs::Vector{Symbol} )
# Find all of the requested attributes that are present in the database, and
# which aren't the ID field.
tmpAttrs = attrs[ unique( find( attr -> ( attr ∈ dbase.attrs ) &&
( attr !== dbase.idKey ), attrs ) ) ]
if isempty( tmpAttrs )
return
end # if isempty( tmpAttrs )
# Find the indices of all the database attributes slated for removal and
# remove them.
attrsIndex = find( attr -> attr ∈ tmpAttrs, dbase.attrs )
deleteat!( dbase.attrs, sort( attrsIndex ) )
# Remove the appropriate attributes from the personnel records.
map( attr -> map( person -> removeAttribute!( person, attr ), dbase.dbase ),
tmpAttrs )
end # removeAttributes!( dbase, attrs )
# This function changes the key field of the database. The old key is kept to
# make sure nothing gets broken.
export changeKey!
function changeKey!( dbase::PersonnelDatabase, key::AttributeType )
tmpKey = Symbol( key )
if !hasAttribute( dbase, tmpKey )
warn( "Proposed ID \"$tmpKey\" is not a database attribute. ",
"Ignoring request." )
return
end # if tmpKey ∉ dbase.attrs
# Stringify the contents of the propsed new ID key.
map( person -> person[ tmpKey ] = string( person[ tmpKey ] ), dbase.dbase )
# Check if the new key is unique.
ids = dbase[ tmpKey ]
if length( ids ) > length( unique( ids ) )
warn( "Proposed ID \"$tmpKey\" does not have unique values." )
return
end # if length( ids ) ...
dbase.idKey = tmpKey
end # changeKey!( dbase, key )
# This function adds an entry to the database.
export addPersonnel!
function addPersonnel!( dbase::PersonnelDatabase, person::Personnel )
# Check if the person has the ID key of the database.
if !hasAttribute( person, dbase.idKey )
warn( "Person does not have the \"$(dbase.idKey)\" attribute. ",
"Ignoring request." )
return
end # if !hasAttribute( person, dbase.idKey )
id = string( person[ dbase.idKey ] )
# Check if the person's ID is not yet in the database.
if exists( dbase, id )
warn( "The database already contains an entry with ID \"$id\". ",
"Ignoring request." )
return
end # if exists( dbase, id )
# Udate the database attribute list.
addAttributes!( dbase, collect( keys( person.persData ) ) )
# We create a new record here to make sure that we don't change the original
# personnel record.
newPerson = person
newPerson[ dbase.idKey ] = id
# Add attributes that are in the database, but which aren't in the perosnnel
# record.
newAttrs = dbase.attrs[ find( attr -> !hasAttribute( person, attr ),
dbase.attrs ) ]
map( attr -> newPerson[ attr ] = nothing, newAttrs )
# Add the enriched copy of the personnel record to the database.
push!( dbase.dbase, newPerson )
dbase.persSize += 1
end # addPersonnel!( dbase, person )
# This function adds a number of personnel records to the database.
function addPersonnel!( dbase::PersonnelDatabase, persons::Vector{Personnel} )
map( person -> addPersonnel!( dbase, person ), persons )
end # addPersonnel!( dbase, persons )
# This function adds a new personnel record with the given ID to the database.
function addPersonnel!( dbase::PersonnelDatabase, personID::String )
# Check if the person's ID is not yet in the database.
if exists( dbase, personID )
warn( "The database already contains an entry with ID \"$personID\". ",
"Ignoring request." )
return
end # if exists( dbase, personID )
# Create a new record with the requested ID.
newPerson = Personnel( dbase.idKey, personID )
# Add attributes that are in the database, but which aren't in the perosnnel
# record.
newAttrs = dbase.attrs[ find( attr -> !hasAttribute( newPerson, attr ),
dbase.attrs ) ]
map( attr -> newPerson[ attr ] = nothing, newAttrs )
# Add the enriched copy of the personnel record to the database.
push!( dbase.dbase, newPerson )
dbase.persSize += 1
end # addPersonnel!( dbase, personID )
# This function adds new personnel records with the given IDs to the database.
function addPersonnel!( dbase::PersonnelDatabase, personIDs::Vector{String} )
map( id -> addPersonnel!( dbase, id ), personIDs )
end # addPersonnel!( dbase, personIDs )
# This function removes the personnel member with the requiested ID from the
# database. If there is no personnel member with this ID, nothing happens.
export removePersonnel!
function removePersonnel!( dbase::PersonnelDatabase, id::String )
index = getPosition( dbase, id )
if index != 0
removePersonnel!( dbase, index, false )
end # if index != 0
end # removePersonnel!( dbase, id )
function removePersonnel!( dbase::PersonnelDatabase, ind::T,
verifyIndex::Bool = true ) where T <: Integer
if verifyIndex && ( ( ind <= 0 ) || ( ind > dbase.persSize ) )
return
end # if verifyIndex && ...
deleteat!( dbase.dbase, ind )
dbase.persSize -= 1
end # removePersonnel!( dbase, ind, verifyIndex )
function removePersonnel!( dbase::PersonnelDatabase, ids::Vector{String} )
indices = Vector{Int}()
for id in ids
index = getPosition( dbase, id )
if index != 0
push!( indices, index )
end # if index != 0
end # for id in ids
removePersonnel!( dbase, indices, false )
end # removePersonnel!( dbase, ids )
function removePersonnel!( dbase::PersonnelDatabase, inds::Vector{Int},
verifyIndices::Bool= true )
indices = Vector{Int}()
# Check which indices are valid.
if verifyIndices
for index in inds
if ( index > 0 ) && ( index <= dbase.persSize )
push!( indices, index )
end # if ( index > 0 ) && ...
end # for index ...
else
indices = inds
end # if verifyIndices
# Delete the records with those indices.
indices = unique( indices )
deleteat!( dbase.dbase, sort( indices ) )
dbase.persSize -= length( indices )
end # removePersonnel!( dbase, inds, verifyIndices )
# This function tests if a personnel member with the requested ID exists in the
# personnel database.
export exists
function exists( dbase::PersonnelDatabase, id::String )
return getPosition( dbase, id ) != 0
end # exists( dbase, id )
# This function returns the position of the person with the given ID in the
# personnel database. If the ID doesn't exist, 0 is returned.
function getPosition( dbase::PersonnelDatabase, id::String )
index = find( x -> x[ dbase.idKey ] == id, dbase.dbase )
return isempty( index ) ? 0 : index[ 1 ]
end # getPosition( dbase, id )
# This function selects all the records in the database with a specific value
# for the given attribute. (necessary?)
export selectRecords
function selectRecords( dbase::PersonnelDatabase, attr::AttributeType, val )
tmpAttr = Symbol( attr )
output = Vector{Personnel}()
if !hasAttribute( dbase, tmpAttr )
return output
end # !hasAttribute( dbase, tmpAttr )
map( person -> if ( person[ tmpAttr ] == val ) push!( output, person ) end,
dbase.dbase )
return output
end # selectRecords( dbase, attr, val )
# This function adds a value to a vector attribute. If the attribute's value is
# nothing, a vector will be created. If the attribute's value is not a vector,
# nothing will happen.
export addValue
# The function using id as a String has to be written like this, because
# otherwise a KeyError is thrown!
function addValue( dbase::PersonnelDatabase, id::String, attr::AttributeType,
value::String )
index = getPosition( dbase, id )
addValue( dbase, index, attr, value )
end # addValue( dbase, id, attr, value )
function addValue( dbase::PersonnelDatabase, ind::Int, attr::AttributeType,
value::String )
if ( ind <= 0 ) || ( ind > dbase.persSize )
return
end # if ( ind <= 0 ) || ...
addValue( dbase[ ind ], attr, value )
end # addValue( dbase, id, key, value )
# This function gets the number of entries in the personnel database.
function Base.length( dbase::PersonnelDatabase )
return dbase.persSize
end # length( dbase )
# This function clears the database, and sets the key to the provided symbol.
export clearPDB!
function clearPDB!( dbase::PersonnelDatabase, key::Symbol = :id )
empty!( dbase.attrs )
empty!( dbase.dbase )
dbase.persSize = 0
addAttribute!( dbase, key )
changeKey!( dbase, key )
end # clearPDB!( dbase, key )
function clearPDB!( dbase::PersonnelDatabase, key::String )
clearPDB!( dbase, Symbol( key ) )
end # clearPDB!( dbase, key )
# This function retrieves the personnel member with the requested ID.
function Base.getindex( dbase::PersonnelDatabase, id::String )
index = getPosition( dbase, id )
# Throw an error if the personnel member with the requested ID doesn't
# exist.
if index == 0
error( "No personnel member with $(string( dbase.idKey )) \"$id\" on ",
"record." )
end # if index == 0
return dbase.dbase[ index ]
end # Base.getIndex( dbase, id )
# This function retrieves the personnel member with the requested index.
function Base.getindex( dbase::PersonnelDatabase, ind::T ) where T <: Integer
if ( ind <= 0 ) || ( ind > dbase.persSize )
error( "Cannot request personnel with index $ind: personnel database ",
"size is only $(dbase.persSize)." )
end # if ind > dbase.persSize
return dbase.dbase[ ind ]
end # Base.getindex( dbase, ind )
# This function retrieves the personnel with the requested IDs.
function Base.getindex( dbase::PersonnelDatabase, indices::DbIndexArrayType )
return map( index -> dbase[ index ], indices )
end # Base.getindex( dbase, indices )
# This function retrieves the requested field from the personnel with the
# requested ID.
function Base.getindex( dbase::PersonnelDatabase, index::DbIndexType,
attr::AttributeType )
return dbase[ index ][ Symbol( attr ) ]
end # Base.getindex( dbase, index, attr )
# This function retrieves the requested attribute from the personnel with the
# requested IDs.
function Base.getindex( dbase::PersonnelDatabase, indices::DbIndexArrayType,
attr::AttributeType )
tmpAttr = Symbol( attr )
output = similar( indices, Any )
map( ii -> output[ ii ] = dbase[ indices[ ii ], tmpAttr ],
eachindex( indices ) )
return output
end # Base.getindex( dbase, indices, attr )
# This function retrieves the requested attribute at the given time from the
# personnel record with the requested index.
function Base.getindex( dbase::PersonnelDatabase, index::DbIndexType,
attr::AttributeType, timestamp::T ) where T <: Real
person = dbase[ index ]
return person[ attr, timestamp ]
end # Base.getindex( dbase, index, attr, timestamp )
# This function retrieves the requested attribute from the entire database.
# XXX There is no overload of this function with a String as second argument
# because such a function has been defined prior to retrieve the personnel
# member with that value as ID.
function Base.getindex( dbase::PersonnelDatabase, field::Symbol )
return dbase[ collect( 1:dbase.persSize ), field ]
end # Base.getindex( dbase, field )
# This function sets the given attribute from the personnel with the requested
# ID to the provided value. If the attribute does not exist, it gets created
# first. If there is no personnel in the database with the provided ID, an
# error gets generated.
function Base.setindex!( dbase::PersonnelDatabase, data, id::String,
attr::AttributeType )
index = getPosition( dbase, id )
# Throw an error if the personnel member with the requested ID doesn't
# exist.
if index == 0
error( "No personnel member with $(string( dbase.idKey )) \"$id\" on ",
"record." )
end # if index == 0
# Make sure the database has the requested field, then fill it in as needed.
tmpAttr = Symbol( attr )
addAttribute!( dbase, tmpAttr )
dbase[ index ][ tmpAttr ] = tmpAttr == dbase.idKey ? String( data ) : data
end # Base.setindex!( dbase, data, id, attr )
function Base.setindex!( dbase::PersonnelDatabase, data, ind::T,
attr::AttributeType ) where T <: Integer
# Check if the index is in bounds.
if ( ind <= 0 ) || ( ind > dbase.persSize )
error( "Cannot request personnel with index $ind: personnel database ",
"size is only $(dbase.persSize)." )
end # if ( ind <= 0 ) || ...
# Make sure the database has the requested attribute, then fill it in as
# needed.
tmpAttr = Symbol( attr )
addAttribute!( dbase, tmpAttr )
dbase[ ind ][ tmpAttr ] = data
end # Base.setindex!( dbase, data, ind, attr )
# This function sets the given attribute at the given time from the personnel
# with the requested ID to the provided value. If the attribute does not
# exist, it gets created first. If there is no personnel in the database with
# the provided ID, an error gets generated.
function Base.setindex!( dbase::PersonnelDatabase, data, index::DbIndexType,
attr::AttributeType, timestamp::T ) where T <: Real
tmpAttr = Symbol( attr )
if !hasAttribute( dbase, tmpAttr )
addAttribute!( dbase, tmpAttr, Dict{Symbol, History}() )
end # if !hasAttribute( dbase, tmpAttr )
person = dbase[ index ]
person[ attr, timestamp ] = data
end # setindex!( dbase, data, index, attr, timestamp )
# This function prints the database.
function Base.show( io::IO, dbase::PersonnelDatabase )
print( io, "ID key: $(dbase.idKey)" )
print( io, "\nAttributes: $(dbase.attrs)" )
if dbase.persSize == 0
print( io, "\nNo persons in database." )
return
end # if dbase.persSize == 0
print( io, "\nPersonnel members" )
map( person -> displayPersonnel( io, person, dbase.idKey ), dbase.dbase )
end # Base.show( io, dbase )
|
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|
#!/usr/bin/python
# -*- coding: utf-8 -*-
from sklearn.metrics import roc_auc_score,roc_curve,auc,classification_report
from sklearn.svm import SVC,SVR,LinearSVR
from sklearn.linear_model import SGDRegressor
from sklearn.neural_network import MLPClassifier
from sklearn.pipeline import Pipeline
from sklearn.feature_extraction import DictVectorizer
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import cross_val_predict
from sklearn.model_selection import GridSearchCV
from sklearn.model_selection import LeaveOneGroupOut
from math import log
import json
import numpy as np
from scipy.stats import spearmanr
clf2=Pipeline([('dv',DictVectorizer(sparse=False)),('scl',StandardScaler()),('clf',SVC(class_weight='balanced',probability=True))])
#inclusive mapping
coarse_map={u'n_nerelevantno': 0., u'x_izvenpodro\u010dni': 1., u'z_znanstveno': 1., 't_termin':1.}
#exclusive mapping
#coarse_map={u'n_nerelevantno': 0., u'x_izvenpodro\u010dni': 0., u'z_znanstveno': 0., 't_termin':1.}
y=[]
group=[]
X=[]
y1_pred={'frequency':[],'tfidf':[]}
for entry in json.load(open('example/kas.term.json')):
if entry['length']==1:
y.append(np.mean([coarse_map[entry['annotator_'+str(i+1)]] for i in range(4)]))
group.append(entry['document_id'])
x={}
x['tfidf']=entry['tfidf']
x['avgtoklen']=len(entry['most_frequent_sequence'])
X.append(x)
y_cat=[1 if e>=0.5 else 0 for e in y]
X=np.array(X)
y_cat=np.array(y_cat)
clf2.fit(X,y_cat)
from sklearn.externals import joblib
joblib.dump(clf2,'model.swt')
|
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|
import dash
import dash_core_components as dcc
import dash_html_components as html
import pandas as pd
import numpy as np
from dash.dependencies import Input, Output
from plotly import graph_objs as go
from plotly.graph_objs import *
from datetime import datetime as dt
app = dash.Dash(
__name__, meta_tags=[{"name": "viewport", "content": "width=device-width"}],
)
app.title = "New York Uber Rides"
server = app.server
# Plotly mapbox public token
mapbox_access_token = "pk.eyJ1IjoicGxvdGx5bWFwYm94IiwiYSI6ImNrOWJqb2F4djBnMjEzbG50amg0dnJieG4ifQ.Zme1-Uzoi75IaFbieBDl3A"
# Dictionary of important locations in New York
list_of_locations = {
"Madison Square Garden": {"lat": 40.7505, "lon": -73.9934},
"Yankee Stadium": {"lat": 40.8296, "lon": -73.9262},
"Empire State Building": {"lat": 40.7484, "lon": -73.9857},
"New York Stock Exchange": {"lat": 40.7069, "lon": -74.0113},
"JFK Airport": {"lat": 40.644987, "lon": -73.785607},
"Grand Central Station": {"lat": 40.7527, "lon": -73.9772},
"Times Square": {"lat": 40.7589, "lon": -73.9851},
"Columbia University": {"lat": 40.8075, "lon": -73.9626},
"United Nations HQ": {"lat": 40.7489, "lon": -73.9680},
}
# Initialize data frame
df1 = pd.read_csv(
"https://raw.githubusercontent.com/plotly/datasets/master/uber-rides-data1.csv",
dtype=object,
)
df2 = pd.read_csv(
"https://raw.githubusercontent.com/plotly/datasets/master/uber-rides-data2.csv",
dtype=object,
)
df3 = pd.read_csv(
"https://raw.githubusercontent.com/plotly/datasets/master/uber-rides-data3.csv",
dtype=object,
)
df = pd.concat([df1, df2, df3], axis=0)
df["Date/Time"] = pd.to_datetime(df["Date/Time"], format="%Y-%m-%d %H:%M")
df.index = df["Date/Time"]
df.drop("Date/Time", 1, inplace=True)
totalList = []
for month in df.groupby(df.index.month):
dailyList = []
for day in month[1].groupby(month[1].index.day):
dailyList.append(day[1])
totalList.append(dailyList)
totalList = np.array(totalList)
# Layout of Dash App
app.layout = html.Div(
children=[
html.Div(
className="row",
children=[
# Column for user controls
html.Div(
className="four columns div-user-controls",
children=[
html.Img(
className="logo", src=app.get_asset_url("dash-logo-new.png")
),
html.H2("DASH - UBER DATA APP"),
html.P(
"""Select different days using the date picker or by selecting
different time frames on the histogram."""
),
html.Div(
className="div-for-dropdown",
children=[
dcc.DatePickerSingle(
id="date-picker",
min_date_allowed=dt(2014, 4, 1),
max_date_allowed=dt(2014, 9, 30),
initial_visible_month=dt(2014, 4, 1),
date=dt(2014, 4, 1).date(),
display_format="MMMM D, YYYY",
style={"border": "0px solid black"},
)
],
),
# Change to side-by-side for mobile layout
html.Div(
className="row",
children=[
html.Div(
className="div-for-dropdown",
children=[
# Dropdown for locations on map
dcc.Dropdown(
id="location-dropdown",
options=[
{"label": i, "value": i}
for i in list_of_locations
],
placeholder="Select a location",
)
],
),
html.Div(
className="div-for-dropdown",
children=[
# Dropdown to select times
dcc.Dropdown(
id="bar-selector",
options=[
{
"label": str(n) + ":00",
"value": str(n),
}
for n in range(24)
],
multi=True,
placeholder="Select certain hours",
)
],
),
],
),
html.P(id="total-rides"),
html.P(id="total-rides-selection"),
html.P(id="date-value"),
dcc.Markdown(
children=[
"Source: [FiveThirtyEight](https://github.com/fivethirtyeight/uber-tlc-foil-response/tree/master/uber-trip-data)"
]
),
],
),
# Column for app graphs and plots
html.Div(
className="eight columns div-for-charts bg-grey",
children=[
dcc.Graph(id="map-graph"),
html.Div(
className="text-padding",
children=[
"Select any of the bars on the histogram to section data by time."
],
),
dcc.Graph(id="histogram"),
],
),
],
)
]
)
# Gets the amount of days in the specified month
# Index represents month (0 is April, 1 is May, ... etc.)
daysInMonth = [30, 31, 30, 31, 31, 30]
# Get index for the specified month in the dataframe
monthIndex = pd.Index(["Apr", "May", "June", "July", "Aug", "Sept"])
# Get the amount of rides per hour based on the time selected
# This also higlights the color of the histogram bars based on
# if the hours are selected
def get_selection(month, day, selection):
xVal = []
yVal = []
xSelected = []
colorVal = [
"#F4EC15",
"#DAF017",
"#BBEC19",
"#9DE81B",
"#80E41D",
"#66E01F",
"#4CDC20",
"#34D822",
"#24D249",
"#25D042",
"#26CC58",
"#28C86D",
"#29C481",
"#2AC093",
"#2BBCA4",
"#2BB5B8",
"#2C99B4",
"#2D7EB0",
"#2D65AC",
"#2E4EA4",
"#2E38A4",
"#3B2FA0",
"#4E2F9C",
"#603099",
]
# Put selected times into a list of numbers xSelected
xSelected.extend([int(x) for x in selection])
for i in range(24):
# If bar is selected then color it white
if i in xSelected and len(xSelected) < 24:
colorVal[i] = "#FFFFFF"
xVal.append(i)
# Get the number of rides at a particular time
yVal.append(len(totalList[month][day][totalList[month][day].index.hour == i]))
return [np.array(xVal), np.array(yVal), np.array(colorVal)]
# Selected Data in the Histogram updates the Values in the Hours selection dropdown menu
@app.callback(
Output("bar-selector", "value"),
[Input("histogram", "selectedData"), Input("histogram", "clickData")],
)
def update_bar_selector(value, clickData):
holder = []
if clickData:
holder.append(str(int(clickData["points"][0]["x"])))
if value:
for x in value["points"]:
holder.append(str(int(x["x"])))
return list(set(holder))
# Clear Selected Data if Click Data is used
@app.callback(Output("histogram", "selectedData"), [Input("histogram", "clickData")])
def update_selected_data(clickData):
if clickData:
return {"points": []}
# Update the total number of rides Tag
@app.callback(Output("total-rides", "children"), [Input("date-picker", "date")])
def update_total_rides(datePicked):
date_picked = dt.strptime(datePicked, "%Y-%m-%d")
return "Total Number of rides: {:,d}".format(
len(totalList[date_picked.month - 4][date_picked.day - 1])
)
# Update the total number of rides in selected times
@app.callback(
[Output("total-rides-selection", "children"), Output("date-value", "children")],
[Input("date-picker", "date"), Input("bar-selector", "value")],
)
def update_total_rides_selection(datePicked, selection):
firstOutput = ""
if selection is not None or len(selection) is not 0:
date_picked = dt.strptime(datePicked, "%Y-%m-%d")
totalInSelection = 0
for x in selection:
totalInSelection += len(
totalList[date_picked.month - 4][date_picked.day - 1][
totalList[date_picked.month - 4][date_picked.day - 1].index.hour
== int(x)
]
)
firstOutput = "Total rides in selection: {:,d}".format(totalInSelection)
if (
datePicked is None
or selection is None
or len(selection) is 24
or len(selection) is 0
):
return firstOutput, (datePicked, " - showing hour(s): All")
holder = sorted([int(x) for x in selection])
if holder == list(range(min(holder), max(holder) + 1)):
return (
firstOutput,
(
datePicked,
" - showing hour(s): ",
holder[0],
"-",
holder[len(holder) - 1],
),
)
holder_to_string = ", ".join(str(x) for x in holder)
return firstOutput, (datePicked, " - showing hour(s): ", holder_to_string)
# Update Histogram Figure based on Month, Day and Times Chosen
@app.callback(
Output("histogram", "figure"),
[Input("date-picker", "date"), Input("bar-selector", "value")],
)
def update_histogram(datePicked, selection):
date_picked = dt.strptime(datePicked, "%Y-%m-%d")
monthPicked = date_picked.month - 4
dayPicked = date_picked.day - 1
[xVal, yVal, colorVal] = get_selection(monthPicked, dayPicked, selection)
layout = go.Layout(
bargap=0.01,
bargroupgap=0,
barmode="group",
margin=go.layout.Margin(l=10, r=0, t=0, b=50),
showlegend=False,
plot_bgcolor="#323130",
paper_bgcolor="#323130",
dragmode="select",
font=dict(color="white"),
xaxis=dict(
range=[-0.5, 23.5],
showgrid=False,
nticks=25,
fixedrange=True,
ticksuffix=":00",
),
yaxis=dict(
range=[0, max(yVal) + max(yVal) / 4],
showticklabels=False,
showgrid=False,
fixedrange=True,
rangemode="nonnegative",
zeroline=False,
),
annotations=[
dict(
x=xi,
y=yi,
text=str(yi),
xanchor="center",
yanchor="bottom",
showarrow=False,
font=dict(color="white"),
)
for xi, yi in zip(xVal, yVal)
],
)
return go.Figure(
data=[
go.Bar(x=xVal, y=yVal, marker=dict(color=colorVal), hoverinfo="x"),
go.Scatter(
opacity=0,
x=xVal,
y=yVal / 2,
hoverinfo="none",
mode="markers",
marker=dict(color="rgb(66, 134, 244, 0)", symbol="square", size=40),
visible=True,
),
],
layout=layout,
)
# Get the Coordinates of the chosen months, dates and times
def getLatLonColor(selectedData, month, day):
listCoords = totalList[month][day]
# No times selected, output all times for chosen month and date
if selectedData is None or len(selectedData) is 0:
return listCoords
listStr = "listCoords["
for time in selectedData:
if selectedData.index(time) is not len(selectedData) - 1:
listStr += "(totalList[month][day].index.hour==" + str(int(time)) + ") | "
else:
listStr += "(totalList[month][day].index.hour==" + str(int(time)) + ")]"
return eval(listStr)
# Update Map Graph based on date-picker, selected data on histogram and location dropdown
@app.callback(
Output("map-graph", "figure"),
[
Input("date-picker", "date"),
Input("bar-selector", "value"),
Input("location-dropdown", "value"),
],
)
def update_graph(datePicked, selectedData, selectedLocation):
zoom = 12.0
latInitial = 40.7272
lonInitial = -73.991251
bearing = 0
if selectedLocation:
zoom = 15.0
latInitial = list_of_locations[selectedLocation]["lat"]
lonInitial = list_of_locations[selectedLocation]["lon"]
date_picked = dt.strptime(datePicked, "%Y-%m-%d")
monthPicked = date_picked.month - 4
dayPicked = date_picked.day - 1
listCoords = getLatLonColor(selectedData, monthPicked, dayPicked)
return go.Figure(
data=[
# Data for all rides based on date and time
Scattermapbox(
lat=listCoords["Lat"],
lon=listCoords["Lon"],
mode="markers",
hoverinfo="lat+lon+text",
text=listCoords.index.hour,
marker=dict(
showscale=True,
color=np.append(np.insert(listCoords.index.hour, 0, 0), 23),
opacity=0.5,
size=5,
colorscale=[
[0, "#F4EC15"],
[0.04167, "#DAF017"],
[0.0833, "#BBEC19"],
[0.125, "#9DE81B"],
[0.1667, "#80E41D"],
[0.2083, "#66E01F"],
[0.25, "#4CDC20"],
[0.292, "#34D822"],
[0.333, "#24D249"],
[0.375, "#25D042"],
[0.4167, "#26CC58"],
[0.4583, "#28C86D"],
[0.50, "#29C481"],
[0.54167, "#2AC093"],
[0.5833, "#2BBCA4"],
[1.0, "#613099"],
],
colorbar=dict(
title="Time of<br>Day",
x=0.93,
xpad=0,
nticks=24,
tickfont=dict(color="#d8d8d8"),
titlefont=dict(color="#d8d8d8"),
thicknessmode="pixels",
),
),
),
# Plot of important locations on the map
Scattermapbox(
lat=[list_of_locations[i]["lat"] for i in list_of_locations],
lon=[list_of_locations[i]["lon"] for i in list_of_locations],
mode="markers",
hoverinfo="text",
text=[i for i in list_of_locations],
marker=dict(size=8, color="#ffa0a0"),
),
],
layout=Layout(
autosize=True,
margin=go.layout.Margin(l=0, r=35, t=0, b=0),
showlegend=False,
mapbox=dict(
accesstoken=mapbox_access_token,
center=dict(lat=latInitial, lon=lonInitial), # 40.7272 # -73.991251
style="dark",
bearing=bearing,
zoom=zoom,
),
updatemenus=[
dict(
buttons=(
[
dict(
args=[
{
"mapbox.zoom": 12,
"mapbox.center.lon": "-73.991251",
"mapbox.center.lat": "40.7272",
"mapbox.bearing": 0,
"mapbox.style": "dark",
}
],
label="Reset Zoom",
method="relayout",
)
]
),
direction="left",
pad={"r": 0, "t": 0, "b": 0, "l": 0},
showactive=False,
type="buttons",
x=0.45,
y=0.02,
xanchor="left",
yanchor="bottom",
bgcolor="#323130",
borderwidth=1,
bordercolor="#6d6d6d",
font=dict(color="#FFFFFF"),
)
],
),
)
if __name__ == "__main__":
app.run_server(debug=True)
|
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|
import numpy as np
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #
# MAIN #
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #
def Larsen_wake(x, r, v_inflow, D_r, C_T, I_a, z_hub):
D_nb = max(1.08 * D_r, 1.08 * D_r + 21.7 * D_r * (I_a - 0.05))
print(D_nb)
D_95 = D_nb + min(z_hub, D_nb)
print(D_95)
x_0 = ((9.5 * D_r) / ((D_95 / D_r)**3)) - 1
print(x_0)
c_1 = ((D_r / 2)**-0.5) * ((C_T * 0.25 * np.pi * D_r**2 * x_0)**(-5/6))
print(c_1)
# 138.48000000000002
# 208.48000000000002
# 41.942799982038316
# 6.968226939885172e-06
D_w = 2 * (((35 * 3 * c_1**2) / (2 * np.pi))**(1/5)) * \
((C_T * 0.25 * np.pi * D_r**2 * x)**(1/3))
print(D_w)
v_deficit = (-1 / 9) * ((C_T * 0.25 * np.pi * D_r**2 * (x + x_0)**-2)**(1/3)) * \
((r**(3/2) * ((3 * (c_1**2) * C_T * 0.25 * np.pi * D_r**2 * (x + x_0)**-2)**(-1/2))) -
(((35 / (2 * np.pi))**(3/10)) * ((3 * c_1**2)**(-1/5))))**2
print(v_deficit)
v_wake = v_inflow * (1 - v_deficit)
return D_w, v_deficit, v_wake
class LarsenWake(object):
def __init__(self, v_inflow, D_r, C_T, I_a, z_hub):
self.v_inflow = v_inflow
self.d_rotor = D_r
self.c_thrust = C_T
self.I_ambient = I_a # assumed to be always greater than 5%
self.z_hub = z_hub
self._D_nb = max(1.08 * self.d_rotor, 1.08 *
self.d_rotor + 21.7 * self.d_rotor * (self.I_ambient - 0.05))
self._D_95 = self._D_nb + min(self.z_hub, self._D_nb)
self._x_0 = ((9.5 * self.d_rotor) / ((self._D_95 / self.d_rotor)**3)) - 1
self._c_1 = ((self.d_rotor / 2)**-0.5) * \
((C_T * 0.25 * np.pi * self.d_rotor**2 * self._x_0)**(-5/6))
self.d_wake = self._wake_width
self.v_deficit = self._velocity_deficit
self.v_wake = self._velocity_wake
def _wake_width(self, x):
return 2 * (((35 * 3 * self._c_1**2) / (2 * np.pi))**(1/5)) * ((self.c_thrust * 0.25 * np.pi * self.d_rotor**2 * x)**(1/3))
def _velocity_deficit(self, x, r):
return (-1 / 9) * ((self.c_thrust * 0.25 * np.pi * self.d_rotor**2 * (x + self._x_0)**-2)**(1/3)) * \
((r**(3/2) * ((3 * (self._c_1**2) * self.c_thrust * 0.25 * np.pi * self.d_rotor**2 * (x + self._x_0)**-2)**(-1/2))) -
(((35 / (2 * np.pi))**(3/10)) * ((3 * self._c_1**2)**(-1/5))))**2
def _velocity_wake(self, x, r):
return self.v_inflow * (1 - self.v_deficit(x, r))
if __name__ == "__main__":
# test = LarsenWake(8, 80, 0.8, 0.08, 70)
# print(test.d_wake(500))
# print(test.v_deficit(500, 150))
# print(test.v_wake(500, 150))
Larsen_wake(500, 150, 8, 80, 0.8, 0.08, 70)
|
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|
using LaTeXTabulars, Test, LaTeXStrings
# for testing
using LaTeXTabulars: latex_cell
"Normalize whitespace, for more convenient testing."
squash_whitespace(string) = strip(replace(string, r"[ \n\t]+" => " "))
@test squash_whitespace(" something \n with line breaks \n and stuff \n") ==
"something with line breaks and stuff"
"Comparison using normalized whitespace. For testing."
≅(a, b) = squash_whitespace(a) == squash_whitespace(b)
@testset "tabular" begin
tb = Tabular("lcl")
tlines = [Rule(:top),
[L"\alpha", L"\beta", "sum"],
Rule(:mid),
[1, 2, 3],
Rule(), # a nice \hline to make it ugly
[4.0 "5" "six"; # a matrix
7 8 9],
(CMidRule(1, 2), CMidRule("lr", 1, 1)), # just to test tuples
[MultiColumn(2, :c, "centered")], # ragged!
Rule(:bottom)]
tlatex = raw"\begin{tabular}{lcl}
\toprule
$\alpha$ & $\beta$ & sum \\
\midrule
1 & 2 & 3 \\
\hline
4.0 & 5 & six \\
7 & 8 & 9 \\ \cmidrule{1-2} \cmidrule(lr){1-1}
\multicolumn{2}{c}{centered} \\
\bottomrule
\end{tabular}"
tlatex = replace(tlatex, "\r\n"=>"\n")
@test latex_tabular(String, tb, tlines) ≅ tlatex
tmp = tempname()
latex_tabular(tmp, tb, tlines)
@test isfile(tmp) && read(tmp, String) ≅ tlatex
@test read(tmp, String) ≅ tlatex
end
@test_throws ArgumentError latex_cell(stdout, MultiColumn(2, :BAD, ""))
@test_throws ArgumentError CMidRule(3, 1) # not ≤
@test_throws MethodError latex_cell(stdout, ("un", "supported"))
@test_throws MethodError CMidRule(1, 1, 1, 2) # invalid types
@testset "longtable" begin
lt = LongTable("rrr", ["alpha", "beta", "gamma"])
tlines = [[1 2 3 ;
4.0 "5" "six"],
Rule(:h)]
tlatex = raw"\begin{longtable}[c]{rrr}
\hline
alpha & beta & gamma \\
\hline
\endfirsthead
\multicolumn{3}{l}
{{\bfseries \tablename\ \thetable{} --- continued from previous page}} \\
\hline
alpha & beta & gamma \\
\hline
\endhead
\hline
\multicolumn{3}{r}{{\bfseries Continued on next page}} \\
\hline
\endfoot
\hline
\endlastfoot
1 & 2 & 3 \\
4.0 & 5 & six \\
\hline
\end{longtable}"
tlatex = replace(tlatex, "\r\n"=>"\n")
@test latex_tabular(String, lt, tlines) ≅ tlatex
tmp = tempname()
latex_tabular(tmp, lt, tlines)
@test isfile(tmp) && read(tmp, String) ≅ tlatex
@test read(tmp, String) ≅ tlatex
end
|
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# -*- coding: utf-8 -*-
import numpy as np
#import numbers
#import re
import numba
from numba.core import types,cgutils # utils, typing, errors, extending, sigutils
from numba import (
njit,
generated_jit
)
from numba.core.errors import TypingError
from numba.extending import (
overload,
overload_attribute,
overload_method,
lower_builtin,
# lower_getattr,
# lower_setattr,
typeof_impl,
type_callable,
models,
register_model,
make_attribute_wrapper,
box,
unbox,
NativeValue
)
from numba.core.imputils import impl_ret_borrowed#, lower_setattr, lower_getattr
# from numba.core.typing.templates import (AttributeTemplate, infer_getattr)
# AbstractTemplate,
# signature, Registry, infer_getattr)
import fractalshades.numpy_utils.xrange as fsx
# import math
import operator
"""
Its purpose is to allow the use of Xrange_arrays, polynomials and SA objects
inside jitted functions by defining mirrored low-level implementations.
By default, Numba will treat all numpy.ndarray subtypes as if they were of the
base numpy.ndarray type. On one side, ndarray subtypes can easily use all of
the support that Numba has for ndarray methods ; on the other side it is not
possible to fully customise the behavior. (This is likely to change in future
release of Numba, see https://github.com/numba/numba/pull/6148)
The workaround followed here is to provide ad-hoc implementation at datatype
level (in numba langage, for our specific numba.types.Record types). User code
in jitted function should fully expand the loops to work on individual array
elements - indeed numba is made for this.
As the extra complexity is not worth it, we drop support for float32, complex64
in numba: only float64, complex128 mantissa are currently supported.
NOte:
https://numba.pydata.org/numba-doc/latest/proposals/extension-points.html
/!\ This submodule has side effects at import time (due to its heavy use of
numba operators overload) it should be imported only once (in fractalshades).
See https://github.com/pygae/clifford
"""
numba_float_types = (numba.float64,)
numba_complex_types = (numba.complex128,)
numba_base_types = numba_float_types + numba_complex_types
def numpy_xr_type(base_type):
return np.dtype([("mantissa", base_type), ("exp", np.int32)], align=False)
def numba_xr_type(base_type):
""" Return the numba "extended" Record type for the 2 implemented base type
float64, complex128 """
return numba.from_dtype(numpy_xr_type(base_type))
numba_xr_types = tuple(numba_xr_type(dt) for dt in (np.float64, np.complex128))
numba_real_xr_types = tuple(numba_xr_type(dt) for dt in (np.float64,))
#numba_xr_dict = {numba_xr_type(v): v for v in (np.float64, np.complex128)}
# Create a datatype for temporary manipulation of Xrange_array items.
# This datatype will only be used in numba jitted functions, so we do not
# expose a full python implementation (e.g, boxing, unboxing)
class Xrange_scalar():
def __init__(self, mantissa, exp):
self.mantissa = mantissa
self.exp = exp
class Xrange_scalar_Type(types.Type):
def __init__(self, base_type):
super().__init__(name="{}_Xrange_scalar".format(base_type))
self.base_type = base_type
self.np_base_type = numba.np.numpy_support.as_dtype(base_type)
# dtype.fields["mantissa"][0])
@type_callable(Xrange_scalar)
def type_extended_item(context):
def typer(mantissa, exp):
if (mantissa in numba_base_types) and (exp == numba.int32):
return Xrange_scalar_Type(mantissa)
return typer
@register_model(Xrange_scalar_Type)
class Xrange_scalar_Model(models.StructModel):
def __init__(self, dmm, fe_type):
members = [
('mantissa', fe_type.base_type),
('exp', numba.int32),
]
models.StructModel.__init__(self, dmm, fe_type, members)
#for attr in ('mantissa', 'exp'):
make_attribute_wrapper(Xrange_scalar_Type, 'mantissa', 'mantissa')
make_attribute_wrapper(Xrange_scalar_Type, 'exp', 'exp')
@lower_builtin(Xrange_scalar, types.Number, types.Integer)
def impl_xrange_scalar(context, builder, sig, args):
typ = sig.return_type
mantissa, exp = args
xrange_scalar = cgutils.create_struct_proxy(typ)(context, builder)
xrange_scalar.mantissa = mantissa
xrange_scalar.exp = exp
return xrange_scalar._getvalue()
#@overload_attribute(Xrange_scalar_Type, "np_base_type")
#def np_base_type(scalar):
# ret = numba.np.numpy_support.as_dtype(
# scalar.fields["mantissa"][0])
# return lambda scalar: ret
#np_base_type = numba.np.numpy_support.as_dtype(
# dtype.fields["mantissa"][0])
# We will support operation between numba_xr_types and Xrange_scalar instances
scalar_xr_types = tuple(Xrange_scalar_Type(dt) for dt in numba_base_types)
xr_types = numba_xr_types + scalar_xr_types
scalar_real_xr_types = tuple(Xrange_scalar_Type(dt) for dt in numba_float_types)
real_xr_types = numba_real_xr_types + scalar_real_xr_types
def is_xr_type(val):
if isinstance(val, Xrange_scalar_Type):
return (val.base_type in numba_base_types)
if isinstance(val, numba.types.Record):
return (
len(val) == 2
and "mantissa" in val.fields
and "exp" in val.fields
and val.fields["mantissa"][0] in numba_base_types)
@overload_attribute(numba.types.Record, "is_xr")
def is_xr(rec):
ret = tuple(rec.fields.keys()) == ("mantissa", "exp")
def impl(rec):
return ret
return impl
# Dedicated typing for Xrange_array adds some overhead with little benefit
# -> not implemented by default (passthrough as types.Array)
xrange_typing = False
xrange_arty = types.Array
class XrangeArray(types.Array):
# Array type source code
# https://github.com/numba/numba/blob/39271156a52c58ca18b15aebcb1c85e4a07e49ed/numba/core/types/npytypes.py#L413
# pd-like use case
# https://github.com/numba/numba/blob/39271156a52c58ca18b15aebcb1c85e4a07e49ed/numba/tests/pdlike_usecase.py
def __init__(self, dtype, ndim, layout, aligned):
layout = 'C'
type_name = "Xrange_array"
name = "%s(%s, %sd, %s)" % (type_name, dtype, ndim, layout)
super().__init__(dtype, ndim, layout, readonly=False, name=name,
aligned=aligned)
if xrange_typing:
numba.extending.register_model(XrangeArray)(
numba.extending.models.ArrayModel)
@numba.extending.typeof_impl.register(fsx.Xrange_array)
def typeof_xrangearray(val, c):
arrty = numba.extending.typeof_impl(np.asarray(val), c)
return XrangeArray(arrty.dtype, arrty.ndim, arrty.layout, arrty.aligned)
xrange_arty = XrangeArray
# The default numba typing for integer addition is int64(int32, int32) (?? ...)
# See https://numba.pydata.org/numba-doc/latest/proposals/integer-typing.html
# 'The typing of Python int values used as function arguments doesn’t change,
# as it works satisfyingly and doesn’t surprise the user.'
# Here we will need proper int32 addition, substraction...
@numba.extending.intrinsic
def add_int32(typingctx, src1, src2):
# check for accepted types
if (src1 == numba.int32) and (src2 == numba.int32):
# create the expected type signature
# result_type = types.int32
sig = types.int32(types.int32, types.int32)
# defines the custom code generation
def codegen(context, builder, signature, args):
# llvm IRBuilder code here
# https://llvmlite.readthedocs.io/en/latest/
(a, b) = args
return builder.add(a, b)
return sig, codegen
@numba.extending.intrinsic
def neg_int32(typingctx, src1):
if (src1 == numba.int32):
sig = types.int32(types.int32)
def codegen(context, builder, signature, args):
(a,) = args
return builder.neg(a)
return sig, codegen
@numba.extending.intrinsic
def sub_int32(typingctx, src1, src2):
if (src1 == numba.int32) and (src2 == numba.int32):
sig = types.int32(types.int32, types.int32)
def codegen(context, builder, signature, args):
(a, b) = args
return builder.sub(a, b)
return sig, codegen
@numba.extending.intrinsic
def sdiv_int32(typingctx, src1, src2):
if (src1 == numba.int32) and (src2 == numba.int32):
sig = types.int32(types.int32, types.int32)
def codegen(context, builder, signature, args):
(a, b) = args
return builder.sdiv(a, b)
return sig, codegen
@numba.extending.intrinsic
def mul_int32(typingctx, src1, src2):
if (src1 == numba.int32) and (src2 == numba.int32):
sig = types.int32(types.int32, types.int32)
def codegen(context, builder, signature, args):
(a, b) = args
return builder.mul(a, b)
return sig, codegen
@overload(operator.setitem)
def extended_setitem_tuple(arr, idx, val):
"""
Usage : if arr is an Xrange_array, then one will be able to do
arr[i] = Xrange_scalar_Type(mantissa, exp)
"""
if isinstance(arr, xrange_arty) and (val in xr_types):
def impl(arr, idx, val):
arr[idx]["mantissa"] = val.mantissa
arr[idx]["exp"] = val.exp
return impl
@overload_attribute(numba.types.Record, "is_complex")
def is_complex(rec):
dtype = rec.fields["mantissa"][0]
is_complex = (dtype in numba_complex_types)
def impl(rec):
return is_complex
return impl
@overload(operator.neg)
def extended_neg(op0):
""" Change sign of a Record field """
if (op0 in xr_types): #is_xr_type(op0)):# in xr_types):
def impl(op0):
return Xrange_scalar(-op0.mantissa, op0.exp)
return impl
else:
# print(op0, op0 in xr_types, xr_types)
raise TypingError("datatype not accepted {}".format(
op0))
@overload(operator.add)#, debug=True)
def extended_add(op0, op1):
""" Add 2 Record fields """
if (op0 in xr_types) and (op1 in xr_types):
def impl(op0, op1):
m0_out, m1_out, exp_out = _coexp_ufunc(
op0.mantissa, op0.exp, op1.mantissa, op1.exp)
return Xrange_scalar(m0_out + m1_out, exp_out)
return impl
elif (op0 in xr_types) and (op1 in numba_base_types):
def impl(op0, op1):
m0_out, m1_out, exp_out = _coexp_ufunc(
op0.mantissa, op0.exp, op1, numba.int32(0))
return Xrange_scalar(m0_out + m1_out, exp_out)
return impl
elif (op0 in numba_base_types) and (op1 in xr_types):
def impl(op0, op1):
m0_out, m1_out, exp_out = _coexp_ufunc(
op0, numba.int32(0), op1.mantissa, op1.exp)
return Xrange_scalar(m0_out + m1_out, exp_out)
return impl
else:
raise TypingError("datatype not accepted xr_add({}, {})".format(
op0, op1))
@overload(operator.sub)
def extended_sub(op0, op1):
""" Substract 2 Record fields """
if (op0 in xr_types) and (op1 in xr_types):
def impl(op0, op1):
m0_out, m1_out, exp_out = _coexp_ufunc(
op0.mantissa, op0.exp, op1.mantissa, op1.exp)
return Xrange_scalar(m0_out - m1_out, exp_out)
return impl
elif (op0 in xr_types) and (op1 in numba_base_types):
def impl(op0, op1):
m0_out, m1_out, exp_out = _coexp_ufunc(
op0.mantissa, op0.exp, op1, numba.int32(0))
return Xrange_scalar(m0_out - m1_out, exp_out)
return impl
elif (op0 in numba_base_types) and (op1 in xr_types):
def impl(op0, op1):
m0_out, m1_out, exp_out = _coexp_ufunc(
op0, numba.int32(0), op1.mantissa, op1.exp)
return Xrange_scalar(m0_out - m1_out, exp_out)
return impl
else:
raise TypingError("datatype not accepted xr_sub({}, {})".format(
op0, op1))
@generated_jit(nopython=True)
def _need_renorm(m):
"""
Returns True if abs(exponent) is above a given threshold
"""
threshold = 100 # as 2.**100 = 1.e30
if (m in numba_float_types):
def impl(m):
bits = numba.cpython.unsafe.numbers.viewer(m, numba.int64)
return abs(((bits >> 52) & 0x7ff) - 1023) > threshold
return impl
elif (m in numba_complex_types):
def impl(m):
bits = numba.cpython.unsafe.numbers.viewer(m.real, numba.int64)
need1 = abs(((bits >> 52) & 0x7ff) - 1023) > threshold
bits = numba.cpython.unsafe.numbers.viewer(m.imag, numba.int64)
need2 = abs(((bits >> 52) & 0x7ff) - 1023) > threshold
return (need1 or need2)
return impl
else:
raise TypingError("datatype not accepted {}".format(m))
@overload(operator.mul)
def extended_mul(op0, op1):
""" Multiply 2 Record fields """
if (op0 in xr_types) and (op1 in xr_types):
def impl(op0, op1):
mul = op0.mantissa * op1.mantissa
# Need to avoid casting to int64... !
exp = add_int32(op0.exp, op1.exp)
if _need_renorm(mul):
return Xrange_scalar(*_normalize(mul, exp))
return Xrange_scalar(mul, exp)
return impl
elif (op0 in xr_types) and (op1 in numba_base_types):
def impl(op0, op1):
mul = op0.mantissa * op1
if _need_renorm(mul):
return Xrange_scalar(*_normalize(mul, op0.exp))
return Xrange_scalar(mul, op0.exp)
return impl
elif (op0 in numba_base_types) and (op1 in xr_types):
def impl(op0, op1):
mul = op0 * op1.mantissa
if _need_renorm(mul):
return Xrange_scalar(*_normalize(mul, op1.exp))
return Xrange_scalar(mul, op1.exp)
return impl
else:
# print(op0 in numba_base_types, op0 in xr_types)
# print(op1 in numba_base_types, op1 in xr_types)
# TypingError: datatype not accepted xr_mul(float64_Xrange_scalar, Record(mantissa[type=float64;offset=0],exp[type=int32;offset=8];12;False))
raise TypingError("datatype not accepted xr_mul({}, {})".format(
op0, op1))
@overload(operator.truediv)
def extended_truediv(op0, op1):
""" Divide 2 Record fields """
if (op0 in xr_types) and (op1 in xr_types):
def impl(op0, op1):
mul = op0.mantissa / op1.mantissa
exp = sub_int32(op0.exp, op1.exp)
if _need_renorm(mul):
return Xrange_scalar(*_normalize(mul, exp))
return Xrange_scalar(mul, exp)
return impl
elif (op0 in xr_types) and (op1 in numba_base_types):
def impl(op0, op1):
mul = op0.mantissa / op1
if _need_renorm(mul):
return Xrange_scalar(*_normalize(mul, op0.exp))
return Xrange_scalar(mul, op0.exp)
return impl
elif (op0 in numba_base_types) and (op1 in xr_types):
def impl(op0, op1):
mul = op0 / op1.mantissa
exp = neg_int32(op1.exp)
if _need_renorm(mul):
return Xrange_scalar(*_normalize(mul, exp))
return Xrange_scalar(mul, exp)
return impl
else:
raise TypingError("datatype not accepted xr_mul({}, {})".format(
op0, op1))
def extended_overload(compare_operator):
@overload(compare_operator)
def extended_compare(op0, op1):
""" Compare 2 Record fields """
if (op0 in xr_types) and (op1 in xr_types):
def impl(op0, op1):
m0_out, m1_out, exp_out = _coexp_ufunc(
op0.mantissa, op0.exp, op1.mantissa, op1.exp)
return compare_operator(m0_out, m1_out)
return impl
elif (op0 in xr_types) and (op1 in numba_base_types):
def impl(op0, op1):
m0_out, m1_out, exp_out = _coexp_ufunc(
op0.mantissa, op0.exp, op1, 0)
return compare_operator(m0_out, m1_out)
return impl
elif (op0 in numba_base_types) and (op1 in xr_types):
def impl(op0, op1):
m0_out, m1_out, exp_out = _coexp_ufunc(
op0, 0, op1.mantissa, op1.exp)
return compare_operator(m0_out, m1_out)
return impl
else:
raise TypingError("datatype not accepted in compare({}, {})".format(
op0, op1))
for compare_operator in (
operator.lt,
operator.le,
operator.eq,
operator.ne,
operator.ge,
operator.gt
):
extended_overload(compare_operator)
@overload(np.sqrt)
def extended_sqrt(op0):
""" sqrt of a Record fields """
if op0 in xr_types:
def impl(op0):
exp = op0.exp
if exp % 2:
exp = sdiv_int32(sub_int32(exp, numba.int32(1)),
numba.int32(2)) # // 2
m = np.sqrt(op0.mantissa * 2.)
else:
exp = sdiv_int32(exp, numba.int32(2)) # // 2
m = np.sqrt(op0.mantissa)
return Xrange_scalar(m, exp)
return impl
else:
raise TypingError("Datatype not accepted xr_sqrt({})".format(
op0))
@generated_jit(nopython=True)
def extended_abs2(op0):
""" square of abs of a Record field """
if op0 in real_xr_types:
def impl(op0):
return Xrange_scalar(np.square(op0.mantissa),
add_int32(op0.exp, op0.exp))
return impl
elif op0 in xr_types:
def impl(op0):
return Xrange_scalar((op0.mantissa * np.conj(op0.mantissa)).real,
add_int32(op0.exp, op0.exp))
return impl
else:
raise TypingError("Datatype not accepted xr_sqrt({})".format(
op0))
@overload(np.abs)
def extended_abs(op0):
""" abs of a Record field """
if op0 in xr_types:
def impl(op0):
return Xrange_scalar(np.abs(op0.mantissa), op0.exp)
return impl
else:
raise TypingError("Datatype not accepted xr_sqrt({})".format(
op0))
@generated_jit(nopython=True)
def _normalize(m, exp):
""" Returns a normalized couple """
# Implementation for float
if (m in numba_float_types):
def impl(m, exp):
return _normalize_real(m, exp)
# Implementation for complex
elif (m in numba_complex_types):
def impl(m, exp):
nm_re, nexp_re = _normalize_real(m.real, exp)
nm_im, nexp_im = _normalize_real(m.imag, exp)
co_nm_real, co_nm_imag, co_nexp = _coexp_ufunc(
nm_re, nexp_re, nm_im, nexp_im)
return (co_nm_real + 1j * co_nm_imag, co_nexp)
else:
raise TypingError("datatype not accepted {}".format(m))
return impl
@njit(types.Tuple((numba.float64, numba.int32))(numba.float64,))
def _frexp(m):
""" Faster unsafe equivalent for math.frexp(m) """
# https://github.com/numba/numba/issues/3763
# https://llvm.org/docs/LangRef.html#bitcast-to-instruction
bits = numba.cpython.unsafe.numbers.viewer(m, numba.int64)
m = numba.cpython.unsafe.numbers.viewer(
(bits & 0x8000000000000000) # signe
+ (0x3ff << 0x34) # exposant (bias) hex(1023) = 0x3ff hex(52) = 0x34
+ (bits & 0xfffffffffffff), numba.float64)
exp = (((bits >> 52)) & 0x7ff) - 0x3ff # numba.int32 ??
return m, exp
@njit(types.Tuple((numba.float64, numba.int32))(numba.float64, numba.int32))
def _normalize_real(m, exp):
""" Returns a normalized couple """
if m == 0.:
return (m, numba.int32(0))
else:
nm, nexp = _frexp(m)
return (nm, exp + nexp)
@njit(numba.float64(numba.float64, numba.int32))
def _exp2_shift(m, shift):
""" Faster unsafe equivalent for math.ldexp(m, shift) """
# https://github.com/numba/numba/issues/3763
# https://llvm.org/docs/LangRef.html#bitcast-to-instruction
bits = numba.cpython.unsafe.numbers.viewer(m, numba.int64)
exp = max(((bits >> 0x34) & 0x7ff) + shift, 0)
return numba.cpython.unsafe.numbers.viewer(
(bits & 0x8000000000000000)
+ (exp << 0x34)
+ (bits & 0xfffffffffffff), numba.float64)
@generated_jit(nopython=True)
def _coexp_ufunc(m0, exp0, m1, exp1):
""" Returns a co-exp couple of couples """
# Implementation for real
if (m0 in numba_float_types) and (m1 in numba_float_types):
def impl(m0, exp0, m1, exp1):
co_m0, co_m1 = m0, m1
d_exp = exp0 - exp1
if m0 == 0.:
exp = exp1
elif m1 == 0.:
exp = exp0
elif (exp1 > exp0):
co_m0 = _exp2_shift(co_m0, d_exp)
exp = exp1
elif (exp0 > exp1):
co_m1 = _exp2_shift(co_m1, -d_exp)
exp = exp0
else: # exp0 == exp1
exp = exp0
return (co_m0, co_m1, exp)
# Implementation for complex
elif (m0 in numba_complex_types) or (m1 in numba_complex_types):
def impl(m0, exp0, m1, exp1):
co_m0, co_m1 = m0, m1
d_exp = exp0 - exp1
if m0 == 0.:
exp = exp1
elif m1 == 0.:
exp = exp0
elif (exp1 > exp0):
co_m0 = (_exp2_shift(co_m0.real, d_exp)
+ 1j * _exp2_shift(co_m0.imag, d_exp))
exp = exp1
elif (exp0 > exp1):
co_m1 = (_exp2_shift(co_m1.real, -d_exp)
+ 1j * _exp2_shift(co_m1.imag, -d_exp))
exp = exp0
else: # exp0 == exp1
exp = exp0
return (co_m0, co_m1, exp)
else:
raise TypingError("datatype not accepted {}{}".format(m0, m1))
return impl
@overload_method(numba.types.Record, "normalize")
def normalize(rec):
""" Normalize in-place a xr Record """
dtype = rec.fields["mantissa"][0]
# Implementation for float
if (dtype in numba_float_types):
def impl(rec):
m = rec.mantissa
if m == 0.:
rec.exp = numba.int32(0)
else:
nm, nexp = _frexp(rec.mantissa)
rec.exp += nexp
rec.mantissa = nm
# Implementation for complex
elif (dtype in numba_complex_types):
def impl(rec):
m = rec.mantissa
if m == 0.:
rec.exp = numba.int32(0)
else:
rec.mantissa, rec.exp = _normalize(m, rec.exp)
else:
raise TypingError("datatype not accepted {}".format(dtype))
return impl
#
# Implementing the Xrange_polynomial class in numba
# https://numba.pydata.org/numba-doc/latest/proposals/extension-points.html
#
class Xrange_polynomial_Type(types.Type):
def __init__(self, dtype, cutdeg):
self.dtype = dtype
self.np_base_type = numba.np.numpy_support.as_dtype(
dtype.fields["mantissa"][0])
# self.cutdeg = cutdeg
self.coeffs = types.Array(dtype, 1, 'C')
# print("numba_xr_dict", numba_xr_dict)
# print("numba_xr_dict", dtype.fields["mantissa"][0])
# The name must be unique if the underlying model is different
super().__init__(name="{}_Xrange_polynomial".format(
dtype.fields["mantissa"][0]))
# @property
# def as_array(self):
# return self.coeffs
#
# def copy(self, dtype=None, ndim=1, layout='C'):
# assert ndim == 1
# assert layout == 'C'
# if dtype is None:
# dtype = self.dtype
# return type(self)(dtype, self.index)
@typeof_impl.register(fsx.Xrange_polynomial)
def typeof_xrange_polynomial(val, c):
coeffs_arrty = typeof_impl(val.coeffs, c)
return Xrange_polynomial_Type(coeffs_arrty.dtype, val.cutdeg)
@type_callable(fsx.Xrange_polynomial)
def type_xrange_polynomial(context):
def typer(coeffs, cutdeg):
if (isinstance(coeffs, types.Array)
and (coeffs.dtype in numba_xr_types)
and isinstance(cutdeg, types.Integer)):
return Xrange_polynomial_Type(coeffs.dtype, cutdeg)
return typer
@register_model(Xrange_polynomial_Type)
class XrangePolynomialModel(models.StructModel):
def __init__(self, dmm, fe_type):
members = [
('coeffs', fe_type.coeffs),
('cutdeg', numba.int64) # Not that we need, but int32 is painful
]
models.StructModel.__init__(self, dmm, fe_type, members)
make_attribute_wrapper(Xrange_polynomial_Type, 'coeffs', 'coeffs')
make_attribute_wrapper(Xrange_polynomial_Type, 'cutdeg', 'cutdeg')
@lower_builtin(fsx.Xrange_polynomial, types.Array, types.Integer)
def impl_xrange_polynomial_constructor(context, builder, sig, args):
typ = sig.return_type
coeffs, cutdeg = args
xrange_polynomial = cgutils.create_struct_proxy(typ)(context, builder)
xrange_polynomial.coeffs = coeffs
# We do not copy !! following implementation in python
xrange_polynomial.cutdeg = cutdeg
return impl_ret_borrowed(context, builder, typ,
xrange_polynomial._getvalue())
@unbox(Xrange_polynomial_Type)
def unbox_xrange_polynomial(typ, obj, c):
"""
Convert a fsx.Xrange_polynomial object to a native xrange_polynomial
structure. """
coeffs_obj = c.pyapi.object_getattr_string(obj, "coeffs")
cutdeg_obj = c.pyapi.object_getattr_string(obj, "cutdeg")
xrange_polynomial = cgutils.create_struct_proxy(typ)(c.context, c.builder)
xrange_polynomial.cutdeg = c.pyapi.long_as_longlong(cutdeg_obj)
xrange_polynomial.coeffs = c.unbox(typ.coeffs, coeffs_obj).value
c.pyapi.decref(coeffs_obj)
c.pyapi.decref(cutdeg_obj)
is_error = cgutils.is_not_null(c.builder, c.pyapi.err_occurred())
return NativeValue(xrange_polynomial._getvalue(), is_error=is_error)
@box(Xrange_polynomial_Type)
def box_xrange_polynomial(typ, val, c):
"""
Convert a native xrange_polynomial structure to a
fsx.Xrange_polynomial object """
xrange_polynomial = cgutils.create_struct_proxy(typ
)(c.context, c.builder, value=val)
classobj = c.pyapi.unserialize(c.pyapi.serialize_object(
fsx.Xrange_polynomial))
coeffs_obj = c.box(typ.coeffs, xrange_polynomial.coeffs)
cutdeg_obj = c.pyapi.long_from_longlong(xrange_polynomial.cutdeg)
xrange_polynomial_obj = c.pyapi.call_function_objargs(
classobj, (coeffs_obj, cutdeg_obj))
c.pyapi.decref(classobj)
c.pyapi.decref(coeffs_obj)
c.pyapi.decref(cutdeg_obj)
return xrange_polynomial_obj
#
# Implementing operations for Xrange_polynomial
#
@overload(operator.neg)
def poly_neg(op0):
""" Copy of a polynomial with sign changed """
if isinstance(op0, Xrange_polynomial_Type):
def impl(op0):
# assert op0.coeffs.size == op0.cutdeg + 1
coeffs = op0.coeffs
new_coeffs = np.empty_like(op0.coeffs)
for i in range(coeffs.size):
new_coeffs[i] = - coeffs[i]
return fsx.Xrange_polynomial(new_coeffs, op0.cutdeg)
return impl
def xr_type_to_base_type(val):
if isinstance(val, Xrange_scalar_Type):
base_type = val.base_type
else:
base_type = val.fields["mantissa"][0]
return numba.np.numpy_support.as_dtype(base_type)
#def get_template()
@overload(operator.add)
def poly_add(op0, op1):
""" Add 2 polynomials or a polynomial and a scalar"""
if (isinstance(op0, Xrange_polynomial_Type)
and isinstance(op1, Xrange_polynomial_Type)
):
# There is no lowering implementation for a structured dtype ; so
# we initiate a template of length 1 for the compilation.
base_dtres = np.result_type(op0.np_base_type,
op1.np_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
def impl(op0, op1):
assert op0.cutdeg == op1.cutdeg
cutdeg = op0.cutdeg
coeffs0 = op0.coeffs
coeffs1 = op1.coeffs
res_len = min(max(coeffs0.size, coeffs1.size), cutdeg + 1)
r01 = min(min(coeffs0.size, coeffs1.size), cutdeg + 1)
r0 = min(coeffs0.size, cutdeg + 1)
r1 = min(coeffs1.size, cutdeg + 1)
new_coeffs = res_template.repeat(res_len)
for i in range(r01):
new_coeffs[i] = coeffs0[i] + coeffs1[i]
for i in range(r01, r0):
new_coeffs[i] = coeffs0[i]
for i in range(r01, r1):
new_coeffs[i] = coeffs1[i]
return fsx.Xrange_polynomial(new_coeffs, cutdeg)
return impl
elif (isinstance(op0, Xrange_polynomial_Type)
and (op1 in xr_types)
):
scalar_base_type = xr_type_to_base_type(op1)
base_dtres = np.result_type(op0.np_base_type,
scalar_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
def impl(op0, op1):
res_len = op0.coeffs.size
new_coeffs = res_template.repeat(res_len)
for i in range(res_len):
new_coeffs[i] = op0.coeffs[i]
new_coeffs[0] = new_coeffs[0] + op1
return fsx.Xrange_polynomial(new_coeffs, op0.cutdeg)
return impl
elif (isinstance(op1, Xrange_polynomial_Type)
and (op0 in xr_types)
):
scalar_base_type = xr_type_to_base_type(op0)
base_dtres = np.result_type(op1.np_base_type,
scalar_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.empty([1], dtype=res_dtype)
def impl(op0, op1):
res_len = op1.coeffs.size
new_coeffs = res_template.repeat(res_len)
for i in range(res_len):
new_coeffs[i] = op1.coeffs[i]
new_coeffs[0] = new_coeffs[0] + op0
return fsx.Xrange_polynomial(new_coeffs, op1.cutdeg)
return impl
@overload_method(Xrange_polynomial_Type, '__call__')
def xrange_polynomial_call(poly, val):
# Implementation for scalars
if (val in xr_types):
# if isinstance(val, Xrange_scalar_Type):
# base_type = val.base_type
# else:
# base_type = val.fields["mantissa"][0]
# base_dtres = numba.np.numpy_support.as_dtype(base_type)
base_dtres = xr_type_to_base_type(val)
base_dtres = np.result_type(base_dtres, poly.np_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.empty([1], dtype=res_dtype)
def call_impl(poly, val):
res = res_template.repeat(1)
coeffs = poly.coeffs
n = coeffs.size
res[0] = coeffs[n - 1]
for i in range(2, coeffs.size + 1):
res[0] = coeffs[n - i] + res[0] * val
return res
return call_impl
# Implementation for arrays
elif isinstance(val , xrange_arty):
base_type = val.dtype.fields["mantissa"][0]
base_dtres = numba.np.numpy_support.as_dtype(base_type)
base_dtres = np.result_type(base_dtres, poly.np_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
def call_impl(poly, val):
res_len = val.size
res = res_template.repeat(res_len)
coeffs = poly.coeffs
n = coeffs.size
for j in range(res_len):
res[j] = coeffs[n - 1]
for i in range(2, coeffs.size + 1):
res[j] = coeffs[n - i] + res[j] * val[j]
return res
return call_impl
@overload_method(Xrange_polynomial_Type, 'deriv')
def xrange_polynomial_deriv(poly):
# Call self as a function.
def call_impl(poly, val, k=1.):
coeffs = poly.coeffs
n = coeffs.size
deriv_coeffs = coeffs[1:] * np.arange(1, n)
if k != 1.:
mul = 1.
for i in range(n - 1):
deriv_coeffs[i] = deriv_coeffs[i] * mul
mul *= k
return fsx.Xrange_polynomial(deriv_coeffs, cutdeg=poly.cutdeg)
return call_impl
@overload(operator.mul)
def poly_mul(op0, op1):
""" Multiply 2 polynomials or a polynomial and a scalar"""
if (isinstance(op0, Xrange_polynomial_Type)
and isinstance(op1, Xrange_polynomial_Type)
):
# There is no lowering implementation for a structured dtype ; so
# we initiate a template of length 1 for the compilation.
base_dtres = np.result_type(op0.np_base_type,
op1.np_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
def impl(op0, op1):
assert op0.cutdeg == op1.cutdeg
cutdeg = op0.cutdeg
coeffs0 = op0.coeffs
coeffs1 = op1.coeffs
l0 = coeffs0.size
l1 = coeffs1.size
res_len = min(l0 + l1 - 1, cutdeg + 1)
new_coeffs = res_template.repeat(res_len)
for i in range(res_len):
window_min = max(0, i - l1 + 1)
window_max = min(l0 - 1, i)
for k in range(window_min, window_max + 1):
new_coeffs[i] = new_coeffs[i] + coeffs0[k] * coeffs1[i - k]
return fsx.Xrange_polynomial(new_coeffs, cutdeg)
return impl
elif (isinstance(op0, Xrange_polynomial_Type)
and (op1 in xr_types)
):
scalar_base_type = xr_type_to_base_type(op1)
base_dtres = np.result_type(op0.np_base_type,
scalar_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
def impl(op0, op1):
res_len = op0.coeffs.size
new_coeffs = res_template.repeat(res_len)
for i in range(res_len):
new_coeffs[i] = op0.coeffs[i] * op1
return fsx.Xrange_polynomial(new_coeffs, op0.cutdeg)
return impl
elif (isinstance(op1, Xrange_polynomial_Type)
and (op0 in xr_types)
):
scalar_base_type = xr_type_to_base_type(op0)
base_dtres = np.result_type(op1.np_base_type,
scalar_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.empty([1], dtype=res_dtype)
def impl(op0, op1):
res_len = op1.coeffs.size
new_coeffs = res_template.repeat(res_len)
for i in range(res_len):
new_coeffs[i] = op0 * op1.coeffs[i]
return fsx.Xrange_polynomial(new_coeffs, op1.cutdeg)
return impl
# Implementing the Xrange_SA class in numba
# https://numba.pydata.org/numba-doc/latest/proposals/extension-points.html
# Caveat : unboxing is too complex and not implemented, so jitted function
# can return xrange_SA instances but not take xrange_SA as argument.
# workarounf is to pass separately xrange_polynomial and err (if not null)
# then use xrange_polynomial_to_SA
class Xrange_SA_Type(types.Type):
def __init__(self, dtype, cutdeg, err):
self.dtype = dtype
numba_base_type = dtype.fields["mantissa"][0]
self.np_base_type = numba.np.numpy_support.as_dtype(numba_base_type)
self.coeffs = types.Array(dtype, 1, 'C')
err_dtype = numba_xr_type(np.float64)
self.err = types.Array(err_dtype, 1, 'C')
#self.err = Xrange_scalar_Type(numba.float64)
prefix = "{}_Xrange_SA"
super().__init__(name=prefix.format(numba_base_type))
@typeof_impl.register(fsx.Xrange_SA)
def typeof_xrange_SA(val, c):
coeffs_arrty = typeof_impl(val.coeffs, c)
return Xrange_SA_Type(coeffs_arrty.dtype, val.cutdeg, val.err)
@type_callable(fsx.Xrange_SA)
def type_xrange_SA(context):
def typer(coeffs, cutdeg, err):
if (isinstance(coeffs, types.Array)
and (coeffs.dtype in numba_xr_types)
and isinstance(cutdeg, types.Integer)
and isinstance(err, types.Array)
):
return Xrange_SA_Type(coeffs.dtype, cutdeg, err.dtype)
return typer
@register_model(Xrange_SA_Type)
class XrangeSAModel(models.StructModel):
def __init__(self, dmm, fe_type):
members = [
('coeffs', fe_type.coeffs),
('cutdeg', numba.int64), # Not that we need, but int32 is painful
('err', fe_type.err)
]
models.StructModel.__init__(self, dmm, fe_type, members)
make_attribute_wrapper(Xrange_SA_Type, 'coeffs', 'coeffs')
make_attribute_wrapper(Xrange_SA_Type, 'cutdeg', 'cutdeg')
make_attribute_wrapper(Xrange_SA_Type, 'err', 'err')
@lower_builtin(fsx.Xrange_SA, types.Array, types.Integer, types.Array)
def impl_xrange_SA_constructor(context, builder, sig, args):
typ = sig.return_type
coeffs, cutdeg, err = args
xrange_SA = cgutils.create_struct_proxy(typ)(context, builder)
# We do not copy !! sticking to implementation in python
xrange_SA.coeffs = coeffs
xrange_SA.cutdeg = cutdeg
xrange_SA.err = err
return impl_ret_borrowed(context, builder, typ, xrange_SA._getvalue())
@unbox(Xrange_SA_Type)
def unbox_xrange_SA(typ, obj, c):
"""
Convert a fsx.Xrange_polynomial object to a native xrange_polynomial
structure. """
coeffs_obj = c.pyapi.object_getattr_string(obj, "coeffs")
cutdeg_obj = c.pyapi.object_getattr_string(obj, "cutdeg")
err_obj = c.pyapi.object_getattr_string(obj, "err")
xrange_sa = cgutils.create_struct_proxy(typ)(c.context, c.builder)
xrange_sa.coeffs = c.unbox(typ.coeffs, coeffs_obj).value
xrange_sa.cutdeg = c.pyapi.long_as_longlong(cutdeg_obj)
xrange_sa.err = c.unbox(typ.err, err_obj).value
c.pyapi.decref(coeffs_obj)
c.pyapi.decref(cutdeg_obj)
c.pyapi.decref(err_obj)
is_error = cgutils.is_not_null(c.builder, c.pyapi.err_occurred())
return NativeValue(xrange_sa._getvalue(), is_error=is_error)
@box(Xrange_SA_Type)
def box_xrange_SA(typ, val, c):
""" Convert a native xrange_SA structure to a
fsx.Xrange_polynomial object """
xrange_SA = cgutils.create_struct_proxy(typ
)(c.context, c.builder, value=val)
classobj = c.pyapi.unserialize(c.pyapi.serialize_object(
fsx.Xrange_SA))
coeffs_obj = c.box(typ.coeffs, xrange_SA.coeffs)
cutdeg_obj = c.pyapi.long_from_longlong(xrange_SA.cutdeg)
err_obj = c.box(typ.err, xrange_SA.err)
xrange_SA_obj = c.pyapi.call_function_objargs(
classobj, (coeffs_obj, cutdeg_obj, err_obj))
c.pyapi.decref(classobj)
c.pyapi.decref(coeffs_obj)
c.pyapi.decref(cutdeg_obj)
c.pyapi.decref(err_obj)
return xrange_SA_obj
@overload_method(Xrange_SA_Type, 'to_polynomial')
def xrange_SA_to_polynomial(sa):
""" Convert a xrange_SA to a xrange_polynomial ; err is disregarded """
def impl(sa):
return fsx.Xrange_polynomial(sa.coeffs, cutdeg=sa.cutdeg)
return impl
@overload_method(Xrange_polynomial_Type, 'to_SA')
def xrange_polynomial_to_SA(poly):
""" Convert a xrange_polynomial to a xrange_SA with err = 0."""
err_template = np.zeros([1], dtype=numpy_xr_type(np.float64))
def impl(poly):
return fsx.Xrange_SA(poly.coeffs, cutdeg=poly.cutdeg,
err=err_template.copy())
return impl
@overload(operator.neg)
def sa_neg(op0):
""" Copy of a polynomial with sign changed """
if isinstance(op0, Xrange_SA_Type):
def impl(op0):
# assert op0.coeffs.size == op0.cutdeg + 1
coeffs = op0.coeffs
new_coeffs = np.empty_like(op0.coeffs)
for i in range(coeffs.size):
new_coeffs[i] = - coeffs[i]
return fsx.Xrange_SA(new_coeffs, op0.cutdeg, op0.err.copy())
return impl
@overload(operator.add)
def sa_add(op0, op1):
""" Add 2 SA or a SA and a scalar"""
if (isinstance(op0, Xrange_SA_Type)
and isinstance(op1, Xrange_SA_Type)
):
# There is no lowering implementation for a structured dtype ; so
# we initiate a template of length 1 for the compilation.
base_dtres = np.result_type(op0.np_base_type, op1.np_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
err_template = np.zeros([1], dtype=numpy_xr_type(np.float64))
def impl(op0, op1):
assert op0.cutdeg == op1.cutdeg
cutdeg = op0.cutdeg
coeffs0 = op0.coeffs
coeffs1 = op1.coeffs
err0 = op0.err
err1 = op1.err
res_len = min(max(coeffs0.size, coeffs1.size), cutdeg + 1)
r01 = min(min(coeffs0.size, coeffs1.size), cutdeg + 1)
r0 = min(coeffs0.size, cutdeg + 1)
r1 = min(coeffs1.size, cutdeg + 1)
new_coeffs = res_template.repeat(res_len)
for i in range(r01):
new_coeffs[i] = coeffs0[i] + coeffs1[i]
for i in range(r01, r0):
new_coeffs[i] = coeffs0[i]
for i in range(r01, r1):
new_coeffs[i] = coeffs1[i]
err = err_template.copy()
err[0] = err0[0] + err1[0]
return fsx.Xrange_SA(new_coeffs, cutdeg, err)
return impl
elif (isinstance(op0, Xrange_SA_Type)
and (op1 in xr_types)
):
scalar_base_type = xr_type_to_base_type(op1)
base_dtres = np.result_type(op0.np_base_type, scalar_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
def impl(op0, op1):
res_len = op0.coeffs.size
new_coeffs = res_template.repeat(res_len)
for i in range(res_len):
new_coeffs[i] = op0.coeffs[i]
new_coeffs[0] = new_coeffs[0] + op1
return fsx.Xrange_SA(new_coeffs, op0.cutdeg, op0.err.copy())
return impl
elif (isinstance(op1, Xrange_SA_Type)
and (op0 in xr_types)
):
scalar_base_type = xr_type_to_base_type(op0)
base_dtres = np.result_type(op1.np_base_type, scalar_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
def impl(op0, op1):
res_len = op1.coeffs.size
new_coeffs = res_template.repeat(res_len)
for i in range(res_len):
new_coeffs[i] = op1.coeffs[i]
new_coeffs[0] = new_coeffs[0] + op0
return fsx.Xrange_SA(new_coeffs, op1.cutdeg, op1.err.copy())
return impl
else:
print("!!!", op0.__class__, op1.__class__)
raise TypingError("sa_add, not a Xrange_SA_Type ({}, {})".format(
op0, op1))
@overload(operator.mul)
def sa_mul(op0, op1):
""" Multiply 2 polynomials or a polynomial and a scalar"""
if (isinstance(op0, Xrange_SA_Type)
and isinstance(op1, Xrange_SA_Type)
):
# There is no lowering implementation for a structured dtype ; so
# we initiate a template of length 1 before compilation.
base_dtres = np.result_type(op0.np_base_type,
op1.np_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
err_template = np.zeros([1], dtype=numpy_xr_type(np.float64))
def impl(op0, op1):
assert op0.cutdeg == op1.cutdeg
cutdeg = op0.cutdeg
coeffs0 = op0.coeffs
coeffs1 = op1.coeffs
l0 = coeffs0.size
l1 = coeffs1.size
res_len = min(l0 + l1 - 1, cutdeg + 1)
new_coeffs = res_template.repeat(res_len)
for i in range(res_len):
window_min = max(0, i - l1 + 1)
window_max = min(l0 - 1, i)
for k in range(window_min, window_max + 1):
new_coeffs[i] = new_coeffs[i] + coeffs0[k] * coeffs1[i - k]
err0 = op0.err[0]
err1 = op1.err[0]
# 4 terms to store: err, op_err0, op_err1, err_trunc
err = err_template.repeat(4)
err_tmp = res_template.copy()
# err[0] = err0 * err1
# We will use L2 norm to control truncature error term.
# Heuristic based on random walk / magnitude of the sum of iud random
# variables
# Exact term is :
# op_err0 = err0 * np.sum(np.abs(op1))
# op_err1 = err1 * np.sum(np.abs(op0))
# Approximated term :
# op_err0 = err0 * np.sqrt(np.sum(op1.abs2()))
# op_err1 = err1 * np.sqrt(np.sum(op0.abs2()))
# > op_err0 term
for i in range(l1):
err[1] = err[1] + extended_abs2(coeffs1[i])
err[1] = np.sqrt(err[1])
err[1] = err0 * err[1]
# > op_err1 term
for i in range(l0):
err[2] = err[2] + extended_abs2(coeffs0[i])
err[2] = np.sqrt(err[2])
err[2] = err1 * err[2]
# Truncature_term
if cutdeg < (l0 + l1 - 2):
# compute the missing terms by deg
for i in range(res_len, l0 + l1 - 1):
window_min = max(0, i - l1 + 1)
window_max = min(l0 - 1, i)
err_tmp[0] = Xrange_scalar(0., numba.int32(0))
for k in range(window_min, window_max + 1):
err_tmp[0] = err_tmp[0] + coeffs0[k] * coeffs1[i - k]
err[3] = err[3] + extended_abs2(err_tmp[0])
err[3] = np.sqrt(err[3])
err[0] = (op0.err[0] * op1.err[0]) + err[1] + err[2] + err[3]
return fsx.Xrange_SA(new_coeffs, cutdeg, err[0:1])
return impl
elif (isinstance(op0, Xrange_SA_Type)
and (op1 in xr_types)
):
scalar_base_type = xr_type_to_base_type(op1)
base_dtres = np.result_type(op0.np_base_type,
scalar_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
err_template = np.zeros([1], dtype=numpy_xr_type(np.float64))
def impl(op0, op1):
res_len = op0.coeffs.size
new_coeffs = res_template.repeat(res_len)
new_err = err_template.copy()
for i in range(res_len):
new_coeffs[i] = op0.coeffs[i] * op1
new_err[0] = new_err[0] * np.abs(op1)
return fsx.Xrange_SA(new_coeffs, op0.cutdeg, new_err)
return impl
elif (isinstance(op1, Xrange_SA_Type)
and (op0 in xr_types)
):
scalar_base_type = xr_type_to_base_type(op0)
base_dtres = np.result_type(op1.np_base_type,
scalar_base_type)
res_dtype = numpy_xr_type(base_dtres)
res_template = np.zeros([1], dtype=res_dtype)
err_template = np.zeros([1], dtype=numpy_xr_type(np.float64))
def impl(op0, op1):
res_len = op1.coeffs.size
new_coeffs = res_template.repeat(res_len)
new_err = err_template.copy()
for i in range(res_len):
new_coeffs[i] = op1.coeffs[i] * op0
new_err[0] = new_err[0] * np.abs(op0)
return fsx.Xrange_SA(new_coeffs, op1.cutdeg, new_err)
return impl
else:
print("!!!", isinstance(op0, Xrange_SA_Type), isinstance(op1, Xrange_SA_Type))
raise TypingError("sa_add, not a Xrange_SA_Type ({}, {})".format(
op0, op1))
# elif (isinstance(op1, Xrange_SA_Type)
# and (op0 in xr_types)
# ):
# scalar_base_type = xr_type_to_base_type(op0)
# base_dtres = np.result_type(op1.np_base_type,
# scalar_base_type)
# res_dtype = numpy_xr_type(base_dtres)
# res_template = np.empty([1], dtype=res_dtype)
#
# def impl(op0, op1):
# res_len = op1.coeffs.size
# new_coeffs = res_template.repeat(res_len)
# for i in range(res_len):
# new_coeffs[i] = op0 * op1.coeffs[i]
# return fsx.Xrange_polynomial(new_coeffs, op1.cutdeg)
# return impl
# @staticmethod
# def _add(ufunc, inputs, cutdeg, out=None):
# """ Add or Subtract 2 Xrange_polynomial """
# op0, op1 = inputs
# res_len = min(max(op0.size, op1.size), cutdeg + 1)
# op0_len = min(op0.size, res_len)
# op1_len = min(op1.size, res_len)
#
# dtype=np.result_type(op0._mantissa, op1._mantissa)
# res = Xrange_array(np.zeros([res_len], dtype=dtype))
#
# res[:op0_len] += op0[:op0_len]
# if ufunc is np.add:
# res[:op1_len] += op1[:op1_len]
# elif ufunc is np.subtract:
# res[:op1_len] -= op1[:op1_len]
# return Xrange_polynomial(res, cutdeg=cutdeg)
print("======================================================================")
print("IMPORTED NUMBA XR ====================================================")
print("======================================================================")
#==============================================================================
# DEV
@numba.njit
def test_poly(pol):
print("in numba")
# print("nb", pol, pol.coeffs.dtype)
# pol.coeffs[1] = Xrange_scalar(45678., numba.int32(0))
coeff2 = pol.coeffs.copy() # * Xrange_scalar(2., numba.int32(0))
# print("nb", coeff2)
for i in range(len(coeff2)):
coeff2[i] = coeff2[i] * coeff2[i]
p2 = - fsx.Xrange_polynomial(coeff2, 2)
# print("init", p2.cutdeg, p2.coeffs)
print("p2 init", p2.cutdeg, p2.coeffs)
return p2
@numba.njit
def test_poly_call(pol):
print("in numba")
# print("nb", pol, pol.coeffs.dtype)
# pol.coeffs[1] = Xrange_scalar(45678., numba.int32(0))
# coeff2 = pol.coeffs.copy() # * Xrange_scalar(2., numba.int32(0))
## print("nb", coeff2)
# for i in range(len(coeff2)):
# coeff2[i] = coeff2[i] * coeff2[i]
# p2 = - fsx.Xrange_polynomial(coeff2, 2)
## print("init", p2.cutdeg, p2.coeffs)
# print("p2 init", p2.cutdeg, p2.coeffs)
return pol.__call__(Xrange_scalar(2., np.int32(0)))
@numba.njit
def test_polyadd(pol1, pol2):
print("in numba")
return pol1 + pol2
#@numba.njit
#def test_iadd(arr, val):
# print("in numba")
# for i in range(len(arr)):
# arr[i] += val[0]
# return arr
@numba.njit
def test_sa(poly):
print("in numba")
sa = poly.to_SA()
# print("nb", pol, pol.coeffs.dtype)
# pol.coeffs[1] = Xrange_scalar(45678., numba.int32(0))
coeff2 = sa.coeffs.copy() # * Xrange_scalar(2., numba.int32(0))
print("coeffs", coeff2)
# print("err", sa.err.mantissa, sa.err.exp)
return sa
@numba.njit
def box_add_sa(poly1, poly2):
print("in numba")
sa1 = poly1.to_SA()
sa2 = poly2.to_SA()
err = Xrange_scalar(1., numba.int32(1))
print("err###", err.mantissa)
sa1.err[0] = err
print("err in SA ###", sa1.err)
# print("nb", pol, pol.coeffs.dtype)
# pol.coeffs[1] = Xrange_scalar(45678., numba.int32(0))
sa_res = sa1 + sa2 # * Xrange_scalar(2., numba.int32(0))
#print("err", sa.err.mantissa, sa.err.exp)
return sa_res
@numba.njit
def test_saadd(sa1, sa2):
print("in numba")
return sa1 + sa2
if __name__ == "__main__":
arr0 = fsx.Xrange_array(["1.e100", "3.14", "2.0"]) #* (1. + 1j)
pol0 = fsx.Xrange_polynomial(arr0, 2)
arr1 = fsx.Xrange_array(["2.e100", "-3.14", "-0.2"]) #* (1. + 1j)
pol1 = fsx.Xrange_polynomial(arr1, 2)
res = test_sa(pol0)
print("res", res)
res = box_add_sa(pol0, pol1)
print("res", res)
sa0 = fsx.Xrange_SA(arr0, 2, fsx.Xrange_array(8.))
sa1 = fsx.Xrange_SA(arr1, 2, fsx.Xrange_array(8.))
res = test_saadd(sa0, sa1)
print("res", res)
# print(pol0.coeffs)
# print(np.asarray(pol0.coeffs).size)
# print(pol0.coeffs.size, pol0.cutdeg + 1)
# p_neg = test_poly(pol0)
# print("p_neg", p_neg)
# arr0 = fsx.Xrange_array(["0.", "1.", "2."]) #* (1. + 1j)
# val = fsx.Xrange_array(["1."]) #* (1. + 1j)
# test = test_iadd(arr0, val)
# print("test", test)
# pol0 = fsx.Xrange_polynomial(arr0, 2)
# res = test_poly_call(pol0)
# print(res.view(fsx.Xrange_array))
# arr1 = fsx.Xrange_array(["1.e100", "3.14", "2.0"]) #* (1. + 1j)
# pol1 = fsx.Xrange_polynomial(arr1, 2)
#
# res = test_polyadd(pol0, pol1)
# print("res", res)
#
# arr0 = fsx.Xrange_array(["1.e100", "3.14", "2.0", "5.0"]) #* (1. + 1j)
# pol0 = fsx.Xrange_polynomial(arr0, 3)
# arr1 = fsx.Xrange_array(["1.e100", "3.14", "2.0", "6.4"]) #* (1. + 1j)
# pol1 = fsx.Xrange_polynomial(arr1, 3)
#
# res = test_polyadd(pol0, pol1)
# print("res", res)
|
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(* (c) Copyright Microsoft Corporation and Inria. All rights reserved. *)
Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice fintype.
Require Import finfun path matrix.
Require Import bigop ssralg poly polydiv ssrnum zmodp div ssrint.
Require Import polyorder polyrcf interval polyXY.
Require Import qe_rcf_th ordered_qelim mxtens.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Import GRing.Theory Num.Theory.
Local Open Scope nat_scope.
Local Open Scope ring_scope.
Import ord.
Section QF.
Variable R : Type.
Inductive term : Type :=
| Var of nat
| Const of R
| NatConst of nat
| Add of term & term
| Opp of term
| NatMul of term & nat
| Mul of term & term
| Exp of term & nat.
Inductive formula : Type :=
| Bool of bool
| Equal of term & term
| Lt of term & term
| Le of term & term
| And of formula & formula
| Or of formula & formula
| Implies of formula & formula
| Not of formula.
Coercion rterm_to_term := fix loop (t : term) : GRing.term R :=
match t with
| Var x => GRing.Var _ x
| Const x => GRing.Const x
| NatConst n => GRing.NatConst _ n
| Add u v => GRing.Add (loop u) (loop v)
| Opp u => GRing.Opp (loop u)
| NatMul u n => GRing.NatMul (loop u) n
| Mul u v => GRing.Mul (loop u) (loop v)
| Exp u n => GRing.Exp (loop u) n
end.
Coercion qfr_to_formula := fix loop (f : formula) : ord.formula R :=
match f with
| Bool b => ord.Bool b
| Equal x y => ord.Equal x y
| Lt x y => ord.Lt x y
| Le x y => ord.Le x y
| And f g => ord.And (loop f) (loop g)
| Or f g => ord.Or (loop f) (loop g)
| Implies f g => ord.Implies (loop f) (loop g)
| Not f => ord.Not (loop f)
end.
Definition to_rterm := fix loop (t : GRing.term R) : term :=
match t with
| GRing.Var x => Var x
| GRing.Const x => Const x
| GRing.NatConst n => NatConst n
| GRing.Add u v => Add (loop u) (loop v)
| GRing.Opp u => Opp (loop u)
| GRing.NatMul u n => NatMul (loop u) n
| GRing.Mul u v => Mul (loop u) (loop v)
| GRing.Exp u n => Exp (loop u) n
| _ => NatConst 0
end.
End QF.
Bind Scope qf_scope with term.
Bind Scope qf_scope with formula.
Arguments Scope Add [_ qf_scope qf_scope].
Arguments Scope Opp [_ qf_scope].
Arguments Scope NatMul [_ qf_scope nat_scope].
Arguments Scope Mul [_ qf_scope qf_scope].
Arguments Scope Mul [_ qf_scope qf_scope].
Arguments Scope Exp [_ qf_scope nat_scope].
Arguments Scope Equal [_ qf_scope qf_scope].
Arguments Scope And [_ qf_scope qf_scope].
Arguments Scope Or [_ qf_scope qf_scope].
Arguments Scope Implies [_ qf_scope qf_scope].
Arguments Scope Not [_ qf_scope].
Implicit Arguments Bool [R].
Prenex Implicits Const Add Opp NatMul Mul Exp Bool Unit And Or Implies Not Lt.
Prenex Implicits to_rterm.
Notation True := (Bool true).
Notation False := (Bool false).
Delimit Scope qf_scope with qfT.
Notation "''X_' i" := (Var _ i) : qf_scope.
Notation "n %:R" := (NatConst _ n) : qf_scope.
Notation "x %:T" := (Const x) : qf_scope.
Notation "0" := 0%:R%qfT : qf_scope.
Notation "1" := 1%:R%qfT : qf_scope.
Infix "+" := Add : qf_scope.
Notation "- t" := (Opp t) : qf_scope.
Notation "t - u" := (Add t (- u)) : qf_scope.
Infix "*" := Mul : qf_scope.
Infix "*+" := NatMul : qf_scope.
Infix "^+" := Exp : qf_scope.
Notation "t ^- n" := (t^-1 ^+ n)%qfT : qf_scope.
Infix "==" := Equal : qf_scope.
Infix "<%" := Lt : qf_scope.
Infix "<=%" := Le : qf_scope.
Infix "/\" := And : qf_scope.
Infix "\/" := Or : qf_scope.
Infix "==>" := Implies : qf_scope.
Notation "~ f" := (Not f) : qf_scope.
Notation "x != y" := (Not (x == y)) : qf_scope.
Section evaluation.
Variable R : realDomainType.
Fixpoint eval (e : seq R) (t : term R) {struct t} : R :=
match t with
| ('X_i)%qfT => e`_i
| (x%:T)%qfT => x
| (n%:R)%qfT => n%:R
| (t1 + t2)%qfT => eval e t1 + eval e t2
| (- t1)%qfT => - eval e t1
| (t1 *+ n)%qfT => eval e t1 *+ n
| (t1 * t2)%qfT => eval e t1 * eval e t2
| (t1 ^+ n)%qfT => eval e t1 ^+ n
end.
Lemma evalE (e : seq R) (t : term R) : eval e t = GRing.eval e t.
Proof. by elim: t=> /=; do ?[move->|move=>?]. Qed.
Definition qf_eval e := fix loop (f : formula R) : bool :=
match f with
| Bool b => b
| t1 == t2 => (eval e t1 == eval e t2)%bool
| t1 <% t2 => (eval e t1 < eval e t2)%bool
| t1 <=% t2 => (eval e t1 <= eval e t2)%bool
| f1 /\ f2 => loop f1 && loop f2
| f1 \/ f2 => loop f1 || loop f2
| f1 ==> f2 => (loop f1 ==> loop f2)%bool
| ~ f1 => ~~ loop f1
end%qfT.
Lemma qf_evalE (e : seq R) (f : formula R) : qf_eval e f = ord.qf_eval e f.
Proof. by elim: f=> /=; do ?[rewrite evalE|move->|move=>?]. Qed.
Lemma to_rtermE (t : GRing.term R) :
GRing.rterm t -> to_rterm t = t :> GRing.term _.
Proof.
elim: t=> //=; do ?
[ by move=> u hu v hv /andP[ru rv]; rewrite hu ?hv
| by move=> u hu *; rewrite hu].
Qed.
End evaluation.
Import Pdiv.Ring.
Definition bind_def T1 T2 T3 (f : (T1 -> T2) -> T3) (k : T1 -> T2) := f k.
Notation "'bind' x <- y ; z" :=
(bind_def y (fun x => z)) (at level 99, x at level 0, y at level 0,
format "'[hv' 'bind' x <- y ; '/' z ']'").
Section ProjDef.
Variable F : realFieldType.
Notation fF := (formula F).
Notation tF := (term F).
Definition polyF := seq tF.
Lemma qf_formF (f : fF) : qf_form f.
Proof. by elim: f=> // *; apply/andP; split. Qed.
Lemma rtermF (t : tF) : GRing.rterm t.
Proof. by elim: t=> //=; do ?[move->|move=>?]. Qed.
Lemma rformulaF (f : fF) : rformula f.
Proof. by elim: f=> /=; do ?[rewrite rtermF|move->|move=>?]. Qed.
Section If.
Implicit Types (pf tf ef : formula F).
Definition If pf tf ef := (pf /\ tf \/ ~ pf /\ ef)%qfT.
End If.
Notation "'If' c1 'Then' c2 'Else' c3" := (If c1 c2 c3)
(at level 200, right associativity, format
"'[hv ' 'If' c1 '/' '[' 'Then' c2 ']' '/' '[' 'Else' c3 ']' ']'").
Notation cps T := ((T -> fF) -> fF).
Section Pick.
Variables (I : finType) (pred_f then_f : I -> fF) (else_f : fF).
Definition Pick :=
\big[Or/False]_(p : {ffun pred I})
((\big[And/True]_i (if p i then pred_f i else ~ pred_f i))
/\ (if pick p is Some i then then_f i else else_f))%qfT.
Lemma eval_Pick e (qev := qf_eval e) :
let P i := qev (pred_f i) in
qev Pick = (if pick P is Some i then qev (then_f i) else qev else_f).
Proof.
move=> P; rewrite ((big_morph qev) false orb) //= big_orE /=.
apply/existsP/idP=> [[p] | true_at_P].
rewrite ((big_morph qev) true andb) //= big_andE /=.
case/andP=> /forallP eq_p_P.
rewrite (@eq_pick _ _ P) => [|i]; first by case: pick.
by move/(_ i): eq_p_P => /=; case: (p i) => //=; move/negbTE.
exists [ffun i => P i] => /=; apply/andP; split.
rewrite ((big_morph qev) true andb) //= big_andE /=.
by apply/forallP=> i; rewrite /= ffunE; case Pi: (P i) => //=; apply: negbT.
rewrite (@eq_pick _ _ P) => [|i]; first by case: pick true_at_P.
by rewrite ffunE.
Qed.
End Pick.
Fixpoint eval_poly (e : seq F) pf :=
if pf is c :: qf then (eval_poly e qf) * 'X + (eval e c)%:P else 0.
Lemma eval_polyP e p : eval_poly e p = Poly (map (eval e) p).
Proof. by elim: p=> // a p /= ->; rewrite cons_poly_def. Qed.
Fixpoint Size (p : polyF) : cps nat := fun k =>
if p is c :: q then
bind n <- Size q;
if n is m.+1 then k m.+2
else If c == 0 Then k 0%N Else k 1%N
else k 0%N.
Definition Isnull (p : polyF) : cps bool := fun k =>
bind n <- Size p; k (n == 0%N).
Definition LtSize (p q : polyF) : cps bool := fun k =>
bind n <- Size p; bind m <- Size q; k (n < m)%N.
Fixpoint LeadCoef p : cps tF := fun k =>
if p is c :: q then
bind l <- LeadCoef q; If l == 0 Then k c Else k l
else k (Const 0).
Fixpoint AmulXn (a : tF) (n : nat) : polyF:=
if n is n'.+1 then (Const 0) :: (AmulXn a n') else [::a].
Fixpoint AddPoly (p q : polyF) :=
if p is a::p' then
if q is b::q' then (a + b)%qfT :: (AddPoly p' q')
else p
else q.
Local Infix "++" := AddPoly : qf_scope.
Definition ScalPoly (c : tF) (p : polyF) : polyF := map (Mul c) p.
Local Infix "*:" := ScalPoly : qf_scope.
Fixpoint MulPoly (p q : polyF) := if p is a :: p'
then (a *: q ++ (0 :: (MulPoly p' q)))%qfT else [::].
Local Infix "**" := MulPoly (at level 40) : qf_scope.
Lemma map_poly0 (R R' : ringType) (f : R -> R') : map_poly f 0 = 0.
Proof. by rewrite map_polyE polyseq0. Qed.
Definition ExpPoly p n := iterop n MulPoly p [::1%qfT].
Local Infix "^^+" := ExpPoly (at level 29) : qf_scope.
Definition OppPoly := ScalPoly (@Const F (-1)).
Local Notation "-- p" := (OppPoly p) (at level 35) : qf_scope.
Local Notation "p -- q" := (p ++ (-- q))%qfT (at level 50) : qf_scope.
Definition NatMulPoly n := ScalPoly (NatConst F n).
Local Infix "+**" := NatMulPoly (at level 40) : qf_scope.
Fixpoint Horner (p : polyF) (x : tF) : tF :=
if p is a :: p then (Horner p x * x + a)%qfT else 0%qfT.
Fixpoint Deriv (p : polyF) : polyF :=
if p is a :: q then (q ++ (0 :: Deriv q))%qfT else [::].
Fixpoint Rediv_rec_loop (q : polyF) sq cq
(c : nat) (qq r : polyF) (n : nat) {struct n} :
cps (nat * polyF * polyF) := fun k =>
bind sr <- Size r;
if (sr < sq)%N then k (c, qq, r) else
bind lr <- LeadCoef r;
let m := AmulXn lr (sr - sq) in
let qq1 := (qq ** [::cq] ++ m)%qfT in
let r1 := (r ** [::cq] -- m ** q)%qfT in
if n is n1.+1 then Rediv_rec_loop q sq cq c.+1 qq1 r1 n1 k
else k (c.+1, qq1, r1).
Definition Rediv (p : polyF) (q : polyF) : cps (nat * polyF * polyF) :=
fun k =>
bind b <- Isnull q;
if b then k (0%N, [::Const 0], p)
else bind sq <- Size q;
bind sp <- Size p;
bind lq <- LeadCoef q;
Rediv_rec_loop q sq lq 0 [::Const 0] p sp k.
Definition Rmod (p : polyF) (q : polyF) (k : polyF -> fF) : fF :=
Rediv p q (fun d => k d.2)%PAIR.
Definition Rdiv (p : polyF) (q : polyF) (k : polyF -> fF) : fF :=
Rediv p q (fun d => k d.1.2)%PAIR.
Definition Rscal (p : polyF) (q : polyF) (k : nat -> fF) : fF :=
Rediv p q (fun d => k d.1.1)%PAIR.
Definition Rdvd (p : polyF) (q : polyF) (k : bool -> fF) : fF :=
bind r <- Rmod p q; bind r_null <- Isnull r; k r_null.
Fixpoint rgcdp_loop n (pp qq : {poly F}) {struct n} :=
if rmodp pp qq == 0 then qq
else if n is n1.+1 then rgcdp_loop n1 qq (rmodp pp qq)
else rmodp pp qq.
Fixpoint Rgcd_loop n pp qq k {struct n} :=
bind r <- Rmod pp qq; bind b <- Isnull r;
if b then (k qq)
else if n is n1.+1 then Rgcd_loop n1 qq r k else k r.
Definition Rgcd (p : polyF) (q : polyF) : cps polyF := fun k =>
let aux p1 q1 k := (bind b <- Isnull p1;
if b then k q1 else bind n <- Size p1; Rgcd_loop n p1 q1 k) in
bind b <- LtSize p q;
if b then aux q p k else aux p q k.
Fixpoint BigRgcd (ps : seq polyF) : cps (seq tF) := fun k =>
if ps is p :: pr then bind r <- BigRgcd pr; Rgcd p r k else k [::Const 0].
Fixpoint Changes (s : seq tF) : cps nat := fun k =>
if s is a :: q then
bind v <- Changes q;
If (Lt (a * head 0 q) 0)%qfT Then k (1 + v)%N Else k v
else k 0%N.
Fixpoint SeqPInfty (ps : seq polyF) : cps (seq tF) := fun k =>
if ps is p :: ps then
bind lp <- LeadCoef p;
bind lps <- SeqPInfty ps;
k (lp :: lps)
else k [::].
Fixpoint SeqMInfty (ps : seq polyF) : cps (seq tF) := fun k =>
if ps is p :: ps then
bind lp <- LeadCoef p;
bind sp <- Size p;
bind lps <- SeqMInfty ps;
k ((-1)%:T ^+ (~~ odd sp) * lp :: lps)%qfT
else k [::].
Definition ChangesPoly ps : cps int := fun k =>
bind mps <- SeqMInfty ps;
bind pps <- SeqPInfty ps;
bind vm <- Changes mps; bind vp <- Changes pps; k (vm%:Z - vp%:Z).
Definition NextMod (p q : polyF) : cps polyF := fun k =>
bind lq <- LeadCoef q;
bind spq <- Rscal p q;
bind rpq <- Rmod p q; k (- lq ^+ spq *: rpq)%qfT.
Fixpoint ModsAux (p q : polyF) n : cps (seq polyF) := fun k =>
if n is m.+1
then
bind p_eq0 <- Isnull p;
if p_eq0 then k [::]
else
bind npq <- NextMod p q;
bind ps <- ModsAux q npq m;
k (p :: ps)
else k [::].
Definition Mods (p q : polyF) : cps (seq polyF) := fun k =>
bind sp <- Size p; bind sq <- Size q;
ModsAux p q (maxn sp sq.+1) k.
Definition PolyComb (sq : seq polyF) (sc : seq int) :=
reducebig [::1%qfT] (iota 0 (size sq))
(fun i => BigBody i MulPoly true (nth [::] sq i ^^+ comb_exp sc`_i)%qfT).
Definition Pcq sq i := (nth [::] (map (PolyComb sq) (sg_tab (size sq))) i).
Definition TaqR (p : polyF) (q : polyF) : cps int := fun k =>
bind r <- Mods p (Deriv p ** q)%qfT; ChangesPoly r k.
Definition TaqsR (p : polyF) (sq : seq polyF) (i : nat) : cps tF :=
fun k => bind n <- TaqR p (Pcq sq i); k ((n%:~R) %:T)%qfT.
Fixpoint ProdPoly T (s : seq T) (f : T -> cps polyF) : cps polyF := fun k =>
if s is a :: s then
bind fa <- f a;
bind fs <- ProdPoly s f;
k (fa ** fs)%qfT
else k [::1%qfT].
Definition BoundingPoly (sq : seq polyF) : polyF :=
Deriv (reducebig [::1%qfT] sq (fun i => BigBody i MulPoly true i)).
Definition Coefs (n i : nat) : tF :=
Const (match n with
| 0 => (i == 0%N)%:R
| 1 => [:: 2%:R^-1; 2%:R^-1; 0]`_i
| n => coefs _ n i
end).
Definition CcountWeak (p : polyF) (sq : seq polyF) : cps tF := fun k =>
let fix aux s (i : nat) k := if i is i'.+1
then bind x <- TaqsR p sq i';
aux (x * (Coefs (size sq) i') + s)%qfT i' k
else k s in
aux 0%qfT (3 ^ size sq)%N k.
Definition CcountGt0 (sp sq : seq polyF) : fF :=
bind p <- BigRgcd sp; bind p0 <- Isnull p;
if ~~ p0 then
bind c <- CcountWeak p sq;
Lt 0%qfT c
else
let bq := BoundingPoly sq in
bind cw <- CcountWeak bq sq;
((reducebig True sq (fun q =>
BigBody q And true (LeadCoef q (fun lq => Lt 0 lq))))
\/ ((reducebig True sq (fun q =>
BigBody q And true
(bind sq <- Size q;
bind lq <- LeadCoef q;
Lt 0 ((Opp 1) ^+ (sq).-1 * lq)
))) \/ Lt 0 cw))%qfT.
Fixpoint abstrX (i : nat) (t : tF) : polyF :=
(match t with
| 'X_n => if n == i then [::0; 1] else [::t]
| - x => -- abstrX i x
| x + y => abstrX i x ++ abstrX i y
| x * y => abstrX i x ** abstrX i y
| x *+ n => n +** abstrX i x
| x ^+ n => abstrX i x ^^+ n
| _ => [::t]
end)%qfT.
Definition wproj (n : nat) (s : seq (GRing.term F) * seq (GRing.term F)) :
formula F :=
let sp := map (abstrX n \o to_rterm) s.1%PAIR in
let sq := map (abstrX n \o to_rterm) s.2%PAIR in
CcountGt0 sp sq.
Definition rcf_sat := proj_sat wproj.
End ProjDef.
Section ProjCorrect.
Variable F : rcfType.
Implicit Types (e : seq F).
Notation fF := (formula F).
Notation tF := (term F).
Notation polyF := (polyF F).
Notation "'If' c1 'Then' c2 'Else' c3" := (If c1 c2 c3)
(at level 200, right associativity, format
"'[hv ' 'If' c1 '/' '[' 'Then' c2 ']' '/' '[' 'Else' c3 ']' ']'").
Notation cps T := ((T -> fF) -> fF).
Local Infix "**" := MulPoly (at level 40) : qf_scope.
Local Infix "+**" := NatMulPoly (at level 40) : qf_scope.
Local Notation "-- p" := (OppPoly p) (at level 35) : qf_scope.
Local Notation "p -- q" := (p ++ (-- q))%qfT (at level 50) : qf_scope.
Local Infix "^^+" := ExpPoly (at level 29) : qf_scope.
Local Infix "**" := MulPoly (at level 40) : qf_scope.
Local Infix "*:" := ScalPoly : qf_scope.
Local Infix "++" := AddPoly : qf_scope.
Lemma eval_If e pf tf ef (ev := qf_eval e) :
ev (If pf Then tf Else ef) = (if ev pf then ev tf else ev ef).
Proof. by unlock (If _ Then _ Else _)=> /=; case: ifP => _; rewrite ?orbF. Qed.
Lemma eval_Size k p e :
qf_eval e (Size p k) = qf_eval e (k (size (eval_poly e p))).
Proof.
elim: p e k=> [|c p ihp] e k; first by rewrite size_poly0.
rewrite ihp /= size_MXaddC -size_poly_eq0; case: size=> //.
by rewrite eval_If /=; case: (_ == _).
Qed.
Lemma eval_Isnull k p e : qf_eval e (Isnull p k)
= qf_eval e (k (eval_poly e p == 0)).
Proof. by rewrite eval_Size size_poly_eq0. Qed.
Lemma eval_LeadCoef e p k k' :
(forall x, qf_eval e (k x) = (k' (eval e x))) ->
qf_eval e (LeadCoef p k) = k' (lead_coef (eval_poly e p)).
Proof.
move=> Pk; elim: p k k' Pk=> [|a p ihp] k k' Pk //=.
by rewrite lead_coef0 Pk.
rewrite (ihp _ (fun l => if l == 0 then qf_eval e (k a) else (k' l))); last first.
by move=> x; rewrite eval_If /= !Pk.
rewrite lead_coef_eq0; have [->|p_neq0] := altP (_ =P 0).
by rewrite mul0r add0r lead_coefC.
rewrite lead_coefDl ?lead_coefMX ?size_mulX // ltnS size_polyC.
by rewrite (leq_trans (leq_b1 _)) // size_poly_gt0.
Qed.
Implicit Arguments eval_LeadCoef [e p k].
Prenex Implicits eval_LeadCoef.
Lemma eval_AmulXn a n e : eval_poly e (AmulXn a n) = (eval e a)%:P * 'X^n.
Proof.
elim: n=> [|n] /=; first by rewrite expr0 mulr1 mul0r add0r.
by move->; rewrite addr0 -mulrA -exprSr.
Qed.
Lemma eval_AddPoly p q e :
eval_poly e (p ++ q)%qfT = (eval_poly e p) + (eval_poly e q).
Proof.
elim: p q => [|a p Hp] q /=; first by rewrite add0r.
case: q => [|b q] /=; first by rewrite addr0.
by rewrite Hp mulrDl rmorphD /= !addrA [X in _ = X + _]addrAC.
Qed.
Lemma eval_ScalPoly e t p :
eval_poly e (ScalPoly t p) = (eval e t) *: (eval_poly e p).
Proof.
elim: p=> [|a p ihp] /=; first by rewrite scaler0.
by rewrite ihp scalerDr scalerAl -!mul_polyC rmorphM.
Qed.
Lemma eval_MulPoly e p q :
eval_poly e (p ** q)%qfT = (eval_poly e p) * (eval_poly e q).
Proof.
elim: p q=> [|a p Hp] q /=; first by rewrite mul0r.
rewrite eval_AddPoly /= eval_ScalPoly Hp.
by rewrite addr0 mulrDl addrC mulrAC mul_polyC.
Qed.
Lemma eval_ExpPoly e p n : eval_poly e (p ^^+ n)%qfT = (eval_poly e p) ^+ n.
Proof.
case: n=> [|n]; first by rewrite /= expr0 mul0r add0r.
rewrite /ExpPoly iteropS exprSr; elim: n=> [|n ihn] //=.
by rewrite expr0 mul1r.
by rewrite eval_MulPoly ihn exprS mulrA.
Qed.
Lemma eval_NatMulPoly p n e :
eval_poly e (n +** p)%qfT = (eval_poly e p) *+ n.
Proof.
elim: p; rewrite //= ?mul0rn // => c p ->.
rewrite mulrnDl mulr_natl polyC_muln; congr (_+_).
by rewrite -mulr_natl mulrAC -mulrA mulr_natl mulrC.
Qed.
Lemma eval_OppPoly p e : eval_poly e (-- p)%qfT = - eval_poly e p.
Proof.
elim: p; rewrite //= ?oppr0 // => t ts ->.
by rewrite !mulNr !opprD polyC_opp mul1r.
Qed.
Lemma eval_Horner e p x : eval e (Horner p x) = (eval_poly e p).[eval e x].
Proof. by elim: p => /= [|a p ihp]; rewrite !(horner0, hornerE) // ihp. Qed.
Lemma eval_ConstPoly e c : eval_poly e [::c] = (eval e c)%:P.
Proof. by rewrite /= mul0r add0r. Qed.
Lemma eval_Deriv e p : eval_poly e (Deriv p) = (eval_poly e p)^`().
Proof.
elim: p=> [|a p ihp] /=; first by rewrite deriv0.
by rewrite eval_AddPoly /= addr0 ihp !derivE.
Qed.
Definition eval_OpPoly :=
(eval_MulPoly, eval_AmulXn, eval_AddPoly, eval_OppPoly, eval_NatMulPoly,
eval_ConstPoly, eval_Horner, eval_ExpPoly, eval_Deriv, eval_ScalPoly).
Lemma eval_Changes e s k : qf_eval e (Changes s k)
= qf_eval e (k (changes (map (eval e) s))).
Proof.
elim: s k=> //= a q ihq k; rewrite ihq eval_If /= -nth0.
by case: q {ihq}=> /= [|b q]; [rewrite /= mulr0 ltrr add0n | case: ltrP].
Qed.
Lemma eval_SeqPInfty e ps k k' :
(forall xs, qf_eval e (k xs) = k' (map (eval e) xs)) ->
qf_eval e (SeqPInfty ps k)
= k' (map lead_coef (map (eval_poly e) ps)).
Proof.
elim: ps k k' => [|p ps ihps] k k' Pk /=; first by rewrite Pk.
rewrite (eval_LeadCoef (fun lp =>
k' (lp :: [seq lead_coef i |i <- [seq eval_poly e i | i <- ps]]))) => // lp.
rewrite (ihps _ (fun ps => k' (eval e lp :: ps))) => //= lps.
by rewrite Pk.
Qed.
Implicit Arguments eval_SeqPInfty [e ps k].
Prenex Implicits eval_SeqPInfty.
Lemma eval_SeqMInfty e ps k k' :
(forall xs, qf_eval e (k xs) = k' (map (eval e) xs)) ->
qf_eval e (SeqMInfty ps k)
= k' (map (fun p : {poly F} => (-1) ^+ (~~ odd (size p)) * lead_coef p)
(map (eval_poly e) ps)).
Proof.
elim: ps k k' => [|p ps ihps] k k' Pk /=; first by rewrite Pk.
rewrite (eval_LeadCoef (fun lp =>
k' ((-1) ^+ (~~ odd (size (eval_poly e p))) * lp
:: [seq (-1) ^+ (~~ odd (size p)) * lead_coef p
| p : {poly _} <- [seq eval_poly e i | i <- ps]]))) => // lp.
rewrite eval_Size /= (ihps _ (fun ps =>
k' (((-1) ^+ (~~ odd (size (eval_poly e p))) * eval e lp) :: ps))) => //= lps.
by rewrite Pk.
Qed.
Implicit Arguments eval_SeqMInfty [e ps k].
Prenex Implicits eval_SeqMInfty.
Lemma eval_ChangesPoly e ps k : qf_eval e (ChangesPoly ps k) =
qf_eval e (k (changes_poly (map (eval_poly e) ps))).
Proof.
rewrite (eval_SeqMInfty (fun mps =>
qf_eval e (k ((changes mps)%:Z -
(changes_pinfty [seq eval_poly e i | i <- ps])%:Z)))) => // mps.
rewrite (eval_SeqPInfty (fun pps =>
qf_eval e (k ((changes (map (eval e) mps))%:Z - (changes pps)%:Z)))) => // pps.
by rewrite !eval_Changes.
Qed.
Fixpoint redivp_rec_loop (q : {poly F}) sq cq
(k : nat) (qq r : {poly F})(n : nat) {struct n} :=
if (size r < sq)%N then (k, qq, r) else
let m := (lead_coef r) *: 'X^(size r - sq) in
let qq1 := qq * cq%:P + m in
let r1 := r * cq%:P - m * q in
if n is n1.+1 then redivp_rec_loop q sq cq k.+1 qq1 r1 n1 else (k.+1, qq1, r1).
Lemma redivp_rec_loopP q c qq r n : redivp_rec q c qq r n
= redivp_rec_loop q (size q) (lead_coef q) c qq r n.
Proof. by elim: n c qq r => [| n Pn] c qq r //=; rewrite Pn. Qed.
Lemma eval_Rediv_rec_loop e q sq cq c qq r n k k'
(d := redivp_rec_loop (eval_poly e q) sq (eval e cq)
c (eval_poly e qq) (eval_poly e r) n) :
(forall c qq r, qf_eval e (k (c, qq, r))
= k' (c, eval_poly e qq, eval_poly e r)) ->
qf_eval e (Rediv_rec_loop q sq cq c qq r n k) = k' d.
Proof.
move=> Pk; elim: n c qq r k Pk @d=> [|n ihn] c qq r k Pk /=.
rewrite eval_Size /=; have [//=|gtq] := ltnP.
rewrite (eval_LeadCoef (fun lr =>
let m := lr *: 'X^(size (eval_poly e r) - sq) in
let qq1 := (eval_poly e qq) * (eval e cq)%:P + m in
let r1 := (eval_poly e r) * (eval e cq)%:P - m * (eval_poly e q) in
k' (c.+1, qq1, r1))) //.
by move=> x /=; rewrite Pk /= !eval_OpPoly /= !mul_polyC.
rewrite eval_Size /=; have [//=|gtq] := ltnP.
rewrite (eval_LeadCoef (fun lr =>
let m := lr *: 'X^(size (eval_poly e r) - sq) in
let qq1 := (eval_poly e qq) * (eval e cq)%:P + m in
let r1 := (eval_poly e r) * (eval e cq)%:P - m * (eval_poly e q) in
k' (redivp_rec_loop (eval_poly e q) sq (eval e cq) c.+1 qq1 r1 n))) //=.
by move=> x; rewrite ihn // !eval_OpPoly /= !mul_polyC.
Qed.
Implicit Arguments eval_Rediv_rec_loop [e q sq cq c qq r n k].
Prenex Implicits eval_Rediv_rec_loop.
Lemma eval_Rediv e p q k k' (d := (redivp (eval_poly e p) (eval_poly e q))) :
(forall c qq r, qf_eval e (k (c, qq, r)) = k' (c, eval_poly e qq, eval_poly e r)) ->
qf_eval e (Rediv p q k) = k' d.
Proof.
move=> Pk; rewrite eval_Isnull /d unlock.
have [_|p_neq0] /= := boolP (_ == _); first by rewrite Pk /= mul0r add0r.
rewrite !eval_Size; set p' := eval_poly e p; set q' := eval_poly e q.
rewrite (eval_LeadCoef (fun lq =>
k' (redivp_rec_loop q' (size q') lq 0 0 p' (size p')))) /=; last first.
by move=> x; rewrite (eval_Rediv_rec_loop k') //= mul0r add0r.
by rewrite redivp_rec_loopP.
Qed.
Implicit Arguments eval_Rediv [e p q k].
Prenex Implicits eval_Rediv.
Lemma eval_NextMod e p q k k' :
(forall p, qf_eval e (k p) = k' (eval_poly e p)) ->
qf_eval e (NextMod p q k) =
k' (next_mod (eval_poly e p) (eval_poly e q)).
Proof.
move=> Pk; set p' := eval_poly e p; set q' := eval_poly e q.
rewrite (eval_LeadCoef (fun lq =>
k' (- lq ^+ rscalp p' q' *: rmodp p' q'))) => // lq.
rewrite (eval_Rediv (fun spq =>
k' (- eval e lq ^+ spq.1.1%PAIR *: rmodp p' q'))) => //= spq _ _.
rewrite (eval_Rediv (fun mpq =>
k' (- eval e lq ^+ spq *: mpq.2%PAIR))) => //= _ _ mpq.
by rewrite Pk !eval_OpPoly.
Qed.
Implicit Arguments eval_NextMod [e p q k].
Prenex Implicits eval_NextMod.
Lemma eval_Rgcd_loop e n p q k k' :
(forall p, qf_eval e (k p) = k' (eval_poly e p))
-> qf_eval e (Rgcd_loop n p q k) =
k' (rgcdp_loop n (eval_poly e p) (eval_poly e q)).
Proof.
elim: n p q k k'=> [|n ihn] p q k k' Pk /=.
rewrite (eval_Rediv (fun r =>
if r.2%PAIR == 0 then k' (eval_poly e q) else k' r.2%PAIR)) /=.
by case: eqP.
by move=> _ _ r; rewrite eval_Isnull; case: eqP.
pose q' := eval_poly e q.
rewrite (eval_Rediv (fun r =>
if r.2%PAIR == 0 then k' q' else k' (rgcdp_loop n q' r.2%PAIR))) /=.
by case: eqP.
move=> _ _ r; rewrite eval_Isnull; case: eqP; first by rewrite Pk.
by rewrite (ihn _ _ _ k').
Qed.
Lemma eval_Rgcd e p q k k' :
(forall p, qf_eval e (k p) = k' (eval_poly e p)) ->
qf_eval e (Rgcd p q k) =
k' (rgcdp (eval_poly e p) (eval_poly e q)).
Proof.
move=> Pk; rewrite /Rgcd /LtSize !eval_Size /rgcdp.
case: ltnP=> _; rewrite !eval_Isnull; case: eqP=> // _;
by rewrite eval_Size; apply: eval_Rgcd_loop.
Qed.
Lemma eval_BigRgcd e ps k k' :
(forall p, qf_eval e (k p) = k' (eval_poly e p)) ->
qf_eval e (BigRgcd ps k) =
k' (\big[@rgcdp _/0%:P]_(i <- ps) (eval_poly e i)).
Proof.
elim: ps k k'=> [|p sp ihsp] k k' Pk /=.
by rewrite big_nil Pk /= mul0r add0r.
rewrite big_cons (ihsp _ (fun r => k' (rgcdp (eval_poly e p) r))) //.
by move=> r; apply: eval_Rgcd.
Qed.
Implicit Arguments eval_Rgcd [e p q k].
Prenex Implicits eval_Rgcd.
Fixpoint mods_aux (p q : {poly F}) (n : nat) : seq {poly F} :=
if n is m.+1
then if p == 0 then [::]
else p :: (mods_aux q (next_mod p q) m)
else [::].
Lemma eval_ModsAux e p q n k k' :
(forall sp, qf_eval e (k sp) = k' (map (eval_poly e) sp)) ->
qf_eval e (ModsAux p q n k) =
k' (mods_aux (eval_poly e p) (eval_poly e q) n).
Proof.
elim: n p q k k'=> [|n ihn] p q k k' Pk; first by rewrite /= Pk.
rewrite /= eval_Isnull; have [|ep_neq0] := altP (_ =P _); first by rewrite Pk.
set q' := eval_poly e q; set p' := eval_poly e p.
rewrite (eval_NextMod (fun npq => k' (p' :: mods_aux q' npq n))) => // npq.
by rewrite (ihn _ _ _ (fun ps => k' (p' :: ps))) => // ps; rewrite Pk.
Qed.
Implicit Arguments eval_ModsAux [e p q n k].
Prenex Implicits eval_ModsAux.
Lemma eval_Mods e p q k k' :
(forall sp, qf_eval e (k sp) = k' (map (eval_poly e) sp)) ->
qf_eval e (Mods p q k) = k' (mods (eval_poly e p) (eval_poly e q)).
Proof. by move=> Pk; rewrite !eval_Size; apply: eval_ModsAux. Qed.
Implicit Arguments eval_Mods [e p q k].
Prenex Implicits eval_Mods.
Lemma eval_TaqR e p q k :
qf_eval e (TaqR p q k) =
qf_eval e (k (taqR (eval_poly e p) (eval_poly e q))).
Proof.
rewrite (eval_Mods (fun r => qf_eval e (k (changes_poly r)))).
by rewrite !eval_OpPoly.
by move=> sp; rewrite !eval_ChangesPoly.
Qed.
Lemma eval_PolyComb e sq sc :
eval_poly e (PolyComb sq sc) = poly_comb (map (eval_poly e) sq) sc.
Proof.
rewrite /PolyComb /poly_comb size_map.
rewrite -BigOp.bigopE -val_enum_ord -filter_index_enum !big_map.
apply: (big_ind2 (fun u v => eval_poly e u = v)).
+ by rewrite /= mul0r add0r.
+ by move=> x x' y y'; rewrite eval_MulPoly=> -> ->.
by move=> i _; rewrite eval_ExpPoly /= (nth_map [::]).
Qed.
Definition pcq (sq : seq {poly F}) i :=
(map (poly_comb sq) (sg_tab (size sq)))`_i.
Lemma eval_Pcq e sq i :
eval_poly e (Pcq sq i) = pcq (map (eval_poly e) sq) i.
Proof.
rewrite /Pcq /pcq size_map; move: (sg_tab _)=> s.
have [ge_is|lt_is] := leqP (size s) i.
by rewrite !nth_default ?size_map // /=.
rewrite -(nth_map _ 0) ?size_map //; congr _`_i; rewrite -map_comp.
by apply: eq_map=> x /=; rewrite eval_PolyComb.
Qed.
Lemma eval_TaqsR e p sq i k k' :
(forall x, qf_eval e (k x) = k' (eval e x)) ->
qf_eval e (TaqsR p sq i k) =
k' (taqsR (eval_poly e p) (map (eval_poly e) sq) i).
Proof. by move=> Pk; rewrite /TaqsR /taqsR eval_TaqR Pk /= eval_Pcq. Qed.
Implicit Arguments eval_TaqsR [e p sq i k].
Prenex Implicits eval_TaqsR.
Fact invmx_ctmat1 : invmx (map_mx (intr : int -> F) ctmat1) =
\matrix_(i, j)
(nth [::] [:: [:: 2%:R^-1; - 2%:R^-1; 0];
[:: 2%:R^-1; 2%:R^-1; -1];
[:: 0; 0; 1]] i)`_j :> 'M[F]_3.
Proof.
rewrite -[lhs in lhs = _]mul1r; apply: (canLR (mulrK _)).
exact: ctmat1_unit.
symmetry; rewrite /ctmat1.
apply/matrixP => i j; rewrite !(big_ord_recl, big_ord0, mxE) /=.
have halfP (K : numFieldType) : 2%:R^-1 + 2%:R^-1 = 1 :> K.
by rewrite -mulr2n -[_ *+ 2]mulr_natl mulfV // pnatr_eq0.
move: i; do ?[case => //=]; move: j; do ?[case => //=] => _ _;
rewrite !(mulr1, mul1r, mulrN1, mulN1r, mulr0, mul0r, opprK);
by rewrite !(addr0, add0r, oppr0, subrr, addrA, halfP).
Qed.
Lemma eval_Coefs e n i : eval e (Coefs F n i) = coefs F n i.
Proof.
case: n => [|[|n]] //=; rewrite /coefs /=.
case: i => [|i]; last first.
by rewrite nth_default // size_map size_enum_ord expn0.
rewrite (nth_map 0) ?size_enum_ord //.
set O := _`_0; rewrite (_ : O = ord0).
by rewrite ?castmxE ?cast_ord_id map_mx1 invmx1 mxE.
by apply: val_inj => /=; rewrite nth_enum_ord.
have [lt_i3|le_3i] := ltnP i 3; last first.
by rewrite !nth_default // size_map size_enum_ord.
rewrite /ctmat /= ?ntensmx1 invmx_ctmat1 /=.
rewrite (nth_map 0) ?size_enum_ord // castmxE /=.
rewrite !mxE !cast_ord_id //= nth_enum_ord //=.
by move: i lt_i3; do 3?case.
Qed.
Lemma eval_CcountWeak e p sq k k' :
(forall x, qf_eval e (k x) = k' (eval e x)) ->
qf_eval e (CcountWeak p sq k) =
k' (ccount_weak (eval_poly e p) (map (eval_poly e) sq)).
Proof.
move=> Pk; rewrite /CcountWeak /ccount_weak.
set Aux := (fix Aux s i k := match i with 0 => _ | _ => _ end).
set aux := (fix aux s i := match i with 0 => _ | _ => _ end).
rewrite size_map -[0]/(eval e 0%qfT); move: 0%qfT=> x.
elim: (_ ^ _)%N k k' Pk x=> /= [|n ihn] k k' Pk x.
by rewrite Pk.
rewrite (eval_TaqsR
(fun y => k' (aux (y * (coefs F (size sq) n) + eval e x) n))).
by rewrite size_map.
by move=> y; rewrite (ihn _ k') // -(eval_Coefs e).
Qed.
Implicit Arguments eval_CcountWeak [e p sq k].
Prenex Implicits eval_CcountWeak.
Lemma eval_ProdPoly e T s f k f' k' :
(forall x k k', (forall p, (qf_eval e (k p) = k' (eval_poly e p))) ->
qf_eval e (f x k) = k' (f' x)) ->
(forall p, qf_eval e (k p) = k' (eval_poly e p)) ->
qf_eval e (@ProdPoly _ T s f k) = k' (\prod_(x <- s) f' x).
Proof.
move=> Pf; elim: s k k'=> [|a s ihs] k k' Pk /=.
by rewrite big_nil Pk /= !(mul0r, add0r).
rewrite (Pf _ _ (fun fa => k' (fa * \prod_(x <- s) f' x))).
by rewrite big_cons.
move=> fa; rewrite (ihs _ (fun fs => k' (eval_poly e fa * fs))) //.
by move=> fs; rewrite Pk eval_OpPoly.
Qed.
Implicit Arguments eval_ProdPoly [e T s f k].
Prenex Implicits eval_ProdPoly.
Lemma eval_BoundingPoly e sq :
eval_poly e (BoundingPoly sq) = bounding_poly (map (eval_poly e) sq).
Proof.
rewrite eval_Deriv -BigOp.bigopE; congr _^`(); rewrite big_map.
by apply: big_morph => [p q | ]/=; rewrite ?eval_MulPoly // mul0r add0r.
Qed.
Lemma eval_CcountGt0 e sp sq : qf_eval e (CcountGt0 sp sq) =
ccount_gt0 (map (eval_poly e) sp) (map (eval_poly e) sq).
Proof.
pose sq' := map (eval_poly e) sq; rewrite /ccount_gt0.
rewrite (@eval_BigRgcd _ _ _ (fun p => if p != 0
then 0 < ccount_weak p sq'
else let bq := bounding_poly sq' in
[|| \big[andb/true]_(q <- sq') (0 < lead_coef q),
\big[andb/true]_(q <- sq') (0 < (-1) ^+ (size q).-1 * lead_coef q)
| 0 < ccount_weak bq sq'])).
by rewrite !big_map.
move=> p; rewrite eval_Isnull; case: eqP=> _ /=; last first.
by rewrite (eval_CcountWeak (> 0)).
rewrite (eval_CcountWeak (fun n =>
[|| \big[andb/true]_(q <- sq') (0 < lead_coef q),
\big[andb/true]_(q <- sq') (0 < (-1) ^+ (size q).-1 * lead_coef q)
| 0 < n ])).
by rewrite eval_BoundingPoly.
move=> n /=; rewrite -!BigOp.bigopE !big_map; congr [|| _, _| _].
apply: (big_ind2 (fun u v => qf_eval e u = v))=> //=.
by move=> u v u' v' -> ->.
by move=> i _; rewrite (eval_LeadCoef (> 0)).
apply: (big_ind2 (fun u v => qf_eval e u = v))=> //=.
by move=> u v u' v' -> ->.
by move=> i _; rewrite eval_Size (eval_LeadCoef (fun lq =>
(0 < (-1) ^+ (size (eval_poly e i)).-1 * lq))).
Qed.
Lemma abstrXP e i t x :
(eval_poly e (abstrX i t)).[x] = eval (set_nth 0 e i x) t.
Proof.
elim: t.
- move=> n /=; case ni: (_ == _);
rewrite //= ?(mul0r,add0r,addr0,polyC1,mul1r,hornerX,hornerC);
by rewrite // nth_set_nth /= ni.
- by move=> r; rewrite /= mul0r add0r hornerC.
- by move=> r; rewrite /= mul0r add0r hornerC.
- by move=> t tP s sP; rewrite /= eval_AddPoly hornerD tP ?sP.
- by move=> t tP; rewrite /= eval_OppPoly hornerN tP.
- by move=> t tP n; rewrite /= eval_NatMulPoly hornerMn tP.
- by move=> t tP s sP; rewrite /= eval_MulPoly hornerM tP ?sP.
- by move=> t tP n; rewrite /= eval_ExpPoly horner_exp tP.
Qed.
Lemma wf_QE_wproj i bc (bc_i := @wproj F i bc) :
dnf_rterm (w_to_oclause bc) -> qf_form bc_i && rformula bc_i.
Proof.
case: bc @bc_i=> sp sq /=; rewrite /dnf_rterm /= /wproj andbT=> /andP[rsp rsq].
by rewrite qf_formF rformulaF.
Qed.
Lemma valid_QE_wproj i bc (bc' := w_to_oclause bc)
(ex_i_bc := ('exists 'X_i, odnf_to_oform [:: bc'])%oT) e :
dnf_rterm bc' -> reflect (holds e ex_i_bc) (ord.qf_eval e (wproj i bc)).
Proof.
case: bc @bc' @ex_i_bc=> sp sq /=; rewrite /dnf_rterm /wproj /= andbT.
move=> /andP[rsp rsq]; rewrite -qf_evalE.
rewrite eval_CcountGt0 /=; apply: (equivP (ccount_gt0P _ _)).
set P1 := (fun x => _); set P2 := (fun x => _).
suff: forall x, P1 x <-> P2 x.
by move=> hP; split=> [] [x Px]; exists x; rewrite (hP, =^~ hP).
move=> x; rewrite /P1 /P2 {P1 P2} !big_map !(big_seq_cond xpredT) /=.
rewrite (eq_bigr (fun t => GRing.eval (set_nth 0 e i x) t == 0)); last first.
by move=> t /andP[t_in_sp _]; rewrite abstrXP evalE to_rtermE ?(allP rsp).
rewrite [X in _ && X](eq_bigr (fun t => 0 < GRing.eval (set_nth 0 e i x) t));
last by move=> t /andP[tsq _]; rewrite abstrXP evalE to_rtermE ?(allP rsq).
rewrite -!big_seq_cond !(rwP (qf_evalP _ _)); first last.
+ elim: sp rsp => //= p sp ihsp /andP[rp rsp]; first by rewrite ihsp.
+ elim: sq rsq => //= q sq ihsq /andP[rq rsq]; first by rewrite ihsq.
rewrite !(rwP andP) (rwP orP) orbF !andbT /=.
have unfoldr P s : foldr (fun t => ord.And (P t)) ord.True s =
\big[ord.And/ord.True]_(t <- s) P t by rewrite unlock /reducebig.
rewrite !unfoldr; set e' := set_nth _ _ _ _.
by rewrite !(@big_morph _ _ (ord.qf_eval _) true andb).
Qed.
Lemma rcf_satP e f : reflect (holds e f) (rcf_sat e f).
Proof. exact: (proj_satP wf_QE_wproj valid_QE_wproj). Qed.
End ProjCorrect.
(* Section Example. *)
(* no chances it computes *)
(* Require Import rat. *)
(* Eval vm_compute in (54%:R / 289%:R + 2%:R^-1 :rat). *)
(* Local Open Scope qf_scope. *)
(* Notation polyF := (polyF [realFieldType of rat]). *)
(* Definition p : polyF := [::'X_2; 'X_1; 'X_0]. *)
(* Definition q : polyF := [:: 0; 1]. *)
(* Definition sq := [::q]. *)
(* Eval vm_compute in MulPoly p q. *)
(* Eval vm_compute in Rediv ([:: 1] : polyF) [::1]. *)
(* Definition fpq := Eval vm_compute in (CcountWeak p [::q]). *)
(* End Example. *)
|
{"author": "math-comp", "repo": "mathcomp-history-before-github", "sha": "19ef9415e2b509a2327f9ef704268ce8570b607c", "save_path": "github-repos/coq/math-comp-mathcomp-history-before-github", "path": "github-repos/coq/math-comp-mathcomp-history-before-github/mathcomp-history-before-github-19ef9415e2b509a2327f9ef704268ce8570b607c/attic/theories/qe_rcf.v"}
|
import cv2
import os
import numpy as np
import faceRecognition as fr
import xlrd
#This module takes images stored in diskand performs face recognition
test_img=cv2.imread('TestImages/a.jpg')#test_img path
faces_detected,gray_img=fr.faceDetection(test_img)
print("faces_detected:",faces_detected)
#Comment belows lines when running this program second time.Since it saves training.yml file in directory
#faces,faceID=fr.labels_for_training_data('/home/rahul/FaceRecognition-master/trainingImages')
#face_recognizer=fr.train_classifier(faces,faceID)
#face_recognizer.save('trainingData.yml')
#face_recognizer=cv2.face.LBPHFaceRecognizer_create()
face_recognizer = cv2.face_LBPHFaceRecognizer().create()
#face_recognizer = cv2.createLBPHFaceRecognizer()
#Uncomment below line for subsequent runs
face_recognizer.read('trainingData.yml')#use this to load training data for subsequent runs
wb = xlrd.open_workbook("db.xls")
xl_sheet = wb.sheet_by_index(0)
name = dict()
for i in range(xl_sheet.nrows):
name[int(xl_sheet.cell(i, 0).value)] = xl_sheet.cell(i, 1).value
#name={0:"a",1:"b",2:"c",3:"d",4:"e",5:"f",6:"g",7:"h"}#creating dictionary containing names for each label
for face in faces_detected:
(x,y,w,h)=face
roi_gray=gray_img[y:y+h,x:x+h]
label,confidence=face_recognizer.predict(roi_gray)#predicting the label of given image
print("confidence:",confidence)
print("label:",label)
fr.draw_rect(test_img,face)
predicted_name=name[label]
fr.put_text(test_img,predicted_name,x,y)
resized_img=cv2.resize(test_img,(300,700))
cv2.imshow("face dtecetion tutorial",resized_img)
cv2.waitKey(0)#Waits indefinitely until a key is pressed
cv2.destroyAllWindows()
|
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|
import tensorflow as tf
import numpy as np
import deepirl.utils.vizualization as v
import time
w = 512
h = 512
batch_size = 1024
noise_dim = 32
layers = 10
num_hidden = 64
stddev = 1.0
use_color = False
position_scale = 1.2
activation = tf.nn.tanh
def get_pos(x: int, y: int, w: int, h: int):
x = position_scale * (float(x) - w // 2) / w
y = position_scale * (float(y) - h // 2) / h
return [x, y, np.sqrt(np.square(x) + np.square(y))]
inputs = tf.placeholder(tf.float32, (None, noise_dim + 3, ))
x = inputs
for i in range(layers):
x = tf.layers.dense(x, num_hidden, activation=activation, kernel_initializer=tf.initializers.random_normal(stddev=stddev))
x = tf.exp(x)
if use_color:
x = tf.layers.dense(x, 3, activation=tf.nn.sigmoid)
else:
x = tf.reshape(tf.layers.dense(x, 1, activation=tf.nn.sigmoid), [-1])
out = x
if use_color:
image = np.zeros((h, w, 3), dtype=np.float32)
else:
image = np.zeros((h, w), dtype=np.float32)
wnd = v.Window(w, h)
image_drawer = v.ImageDrawer(v.Rect(0, 0, wnd.width, wnd.height))
wnd.add_drawer(image_drawer)
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
while True:
z = np.random.standard_normal((noise_dim,)) * 10.0
z_batch = np.zeros((batch_size, noise_dim), np.float32)
z_batch[:] = z
pos_batch = np.zeros((batch_size, 3), np.float32)
x_batch = np.zeros((batch_size,), np.uint16)
y_batch = np.zeros((batch_size,), np.uint16)
idx = 0
for i in range(h):
for j in range(w):
pos_batch[idx] = get_pos(j, i, w, h)
x_batch[idx] = i
y_batch[idx] = j
idx += 1
if idx >= batch_size:
values = sess.run(out, feed_dict={inputs: np.concatenate((z_batch, pos_batch), axis=1)})
for ii, jj, val in zip(x_batch, y_batch, values):
image[ii, jj] = val
image_drawer.img = image
wnd.draw()
idx = 0
wnd.draw()
time.sleep(2.0)
|
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|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Mar 18 14:27:27 2019
@author: avelinojaver
"""
import math
import random
from pathlib import Path
import numpy as np
import cv2
from torch.utils.data import Dataset
#%%
class MergeFlow(Dataset):
def __init__(self,
ch1_dir = None,
ch2_dir = None,
img_ext = '.tif',
samples_per_epoch = 2000,
roi_size = 96,
zoom_range = (0.75, 1.5),
int_factor_range = (0.2, 1.2),
int_base_range = (0., 0.1),
patch_scale = True,
min_mix_frac = 0.3,
scale_int = (0, 255),
loc_sigma = 1.5,
is_scaled_output = False,
is_clipped_output = False,
is_preloaded = False,
add_inverse = False,
shuffle_ch2_color = False
):
self.ch1_dir = Path(ch1_dir)
self.ch2_dir = Path(ch2_dir)
self.samples_per_epoch = samples_per_epoch
self.roi_size = roi_size
self.roi_padding = math.ceil(roi_size*(math.sqrt(2)-1)/2)
self.padded_roi_size = self.roi_size + 2*self.roi_padding
self.zoom_range = zoom_range
self.int_factor_range = int_factor_range
self.int_base_range = int_base_range
self.patch_scale = patch_scale
self.scale_int = scale_int
self.loc_sigma = loc_sigma
assert min_mix_frac is None or min_mix_frac <= 0.5
self.min_mix_frac = min_mix_frac
self.is_scaled_output = is_scaled_output
self.is_clipped_output = is_clipped_output
self.add_inverse = add_inverse
self.shuffle_ch2_color = shuffle_ch2_color
self.is_preloaded = is_preloaded
#print(self.ch1_dir)
#print(self.ch2_dir)
self.ch1_files = [x for x in self.ch1_dir.rglob('*' + img_ext) if not x.name.startswith('.')]
self.ch2_files = [x for x in self.ch2_dir.rglob('*' + img_ext) if not x.name.startswith('.')]
if self.is_preloaded:
self.ch1_files = [cv2.imread(str(x), -1).astype(np.float32) for x in self.ch1_files]
self.ch2_files = [cv2.imread(str(x), -1).astype(np.float32) for x in self.ch2_files]
def __len__(self):
return self.samples_per_epoch
def __getitem__(self, ind):
ch1_img = self._read_sample(self.ch1_files)
ch2_img = self._read_sample(self.ch2_files)
if self.shuffle_ch2_color:
rand_factor = 0.3*np.random.random_sample(3) + 0.7
rand_factor = rand_factor.astype(np.float32)
ch_l = [0,1,2]
random.shuffle(ch_l)
ch2_img = ch2_img[ch_l, ...]*rand_factor[:, None, None]
int_factor = random.uniform(*self.int_factor_range)
int_base = random.uniform(*self.int_base_range)
ch1_img *= int_factor
ch1_img += int_base
ch2_img *= int_factor
ch2_img += int_base
if self.min_mix_frac is not None:
mix_factor = random.uniform(self.min_mix_frac, 1 - self.min_mix_frac)
A, B = mix_factor*ch1_img, (1 - mix_factor)*ch2_img
else:
A, B = ch1_img, ch2_img
if self.add_inverse:
# 1 - ((1-A) + (1-B))
Xin = A + B - 1
else:
Xin = A + B
if self.is_scaled_output:
Xout = np.concatenate((ch1_img, ch2_img), axis=0)
else:
Xout = np.concatenate((A, B), axis=0)
if self.is_clipped_output:
Xout = np.clip(Xout, 0, 1)
Xin = np.clip(Xin, 0, 1)
return Xin, Xout
def _read_sample(self, _files):
if not self.is_preloaded:
_file = random.choice(_files)
img = cv2.imread(str(_file), -1)
img = img.astype(np.float32)
else:
img = random.choice(_files)
img = self._crop_augment(img)
if img.ndim == 3:
img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)
if self.patch_scale:
bot, top = img.min(), img.max()
if bot < top:
img_n = (img.astype(np.float32) - bot)/(top - bot)
else:
#image everything equal, nothing to do here...min_mix_frac
img_n = np.zeros(img.shape, np.float32)
else:
img_n = (img.astype(np.float32) - self.scale_int[0])/(self.scale_int[1] - self.scale_int[0])
if img_n.ndim == 2:
img_n = img_n[None]
else:
img_n = np.rollaxis(img_n, 2, 0)
return img_n
def _crop_augment(self, img):
#### select the limits allowed for a random crop
xlims = (self.roi_padding, img.shape[1] - self.roi_size - self.roi_padding - 1)
ylims = (self.roi_padding, img.shape[0] - self.roi_size - self.roi_padding - 1)
#### crop with padding in order to keep a valid rotation
xl = random.randint(*xlims) - self.roi_padding
yl = random.randint(*ylims) - self.roi_padding
yr = yl + self.padded_roi_size
xr = xl + self.padded_roi_size
crop_padded = img[yl:yr, xl:xr]
if crop_padded.shape[:2] != (self.padded_roi_size, self.padded_roi_size):
#import pdb
#pdb.set_trace()
raise ValueError(f'Incorrect crop size {crop_padded.shape[:2]}. This needs to be debugged.')
##### rotate
theta = np.random.uniform(-180, 180)
scaling = 1/np.random.uniform(*self.zoom_range)
cols, rows = crop_padded.shape[0], crop_padded.shape[1]
M = cv2.getRotationMatrix2D((rows/2,cols/2), theta, scaling)
translation_matrix = np.array([[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
M = np.dot(M, translation_matrix)
crop_rotated = cv2.warpAffine(crop_padded, M, (rows, cols), borderMode = cv2.BORDER_REFLECT_101)
##### remove padding
crop_out = crop_rotated[self.roi_padding:-self.roi_padding, self.roi_padding:-self.roi_padding]
##### flips
if random.random() > 0.5:
crop_out = crop_out[::-1]
if random.random() > 0.5:
crop_out = crop_out[:, ::-1]
return crop_out
#%%
if __name__ == '__main__':
import matplotlib.pylab as plt
root_dir = '/Users/avelinojaver/OneDrive - Nexus365/heba/WoundHealing/manually_filtered/'
root_dir = Path(root_dir)
flow_args = dict(
ch1_dir = root_dir / 'nuclei',
ch2_dir = root_dir / 'membrane',
img_ext = '.tif',
patch_scale = True
)
root_dir = Path.home() / 'workspace/denoising/data/inked_slides'
flow_args = dict(
ch1_dir = root_dir / 'clean',
ch2_dir = root_dir / 'ink',
img_ext = '.jpg',
roi_size = 512,
int_factor_range = (0.8, 1.2),
int_base_range = (0., 0.05),
min_mix_frac = None,
patch_scale = False,
is_scaled_output = True,
is_clipped_output = True,
shuffle_ch2_color = False,
add_inverse = True
)
gen = MergeFlow(**flow_args, is_preloaded = False)
# for _ in range(1000):
# X, target = gen[0]
# assert not np.isnan(X).any()
# assert not np.isnan(target).any()
#
for ii, (X,Y) in enumerate(gen):
fig, axs = plt.subplots(1, 3, sharex=True, sharey=True)
if Y.shape[0] == 6:
y = np.rollaxis(Y, 0, 3)
x = np.rollaxis(X, 0, 3)
axs[0].imshow(x, vmin = 0., vmax = 1.)
axs[1].imshow(y[..., :3], vmin = 0., vmax = 1.)
axs[2].imshow(y[..., 3:], vmin = 0., vmax = 1.)
else:
axs[0].imshow(X[0], vmin = 0., vmax = 1.)
axs[1].imshow(Y[0], vmin = 0., vmax = 1.)
axs[2].imshow(Y[1], vmin = 0., vmax = 1.)
axs[0].set_title('Ch1 + Ch2')
axs[1].set_title('Ch1')
axs[2].set_title('Ch2')
if ii > 3:
break
|
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|
"""Define the types of Game of Life (GoL) initial conditions"""
import numpy as np
def loaf():
"""Create the canvas with the initial values of the loaf"""
canvas = np.zeros(shape=(6, 6), dtype=int, order='F')
# make the loaf
canvas[1][2] = 1
canvas[1][3] = 1
canvas[2][4] = 1
canvas[3][4] = 1
canvas[2][1] = 1
canvas[3][2] = 1
canvas[4][3] = 1
return canvas
def beacon():
"""Create the canvas with the initial values of the beacon"""
canvas = np.zeros(shape=(6, 6), dtype=int, order='F')
# make the beacon
canvas[1][1] = 1
canvas[1][2] = 1
canvas[2][1] = 1
canvas[4][4] = 1
canvas[3][4] = 1
canvas[4][3] = 1
return canvas
def glider():
"""Create the canvas with the initial values of the glider"""
canvas = np.zeros(shape=(10, 10), dtype=int, order='F')
# make the glider
canvas[2][3] = 1
canvas[3][3] = 1
canvas[4][3] = 1
canvas[4][2] = 1
canvas[3][1] = 1
return canvas
def eater_glider():
"""Create the canvas with the initial values of eater and glider"""
canvas = np.zeros(shape=(10, 10), dtype=int, order='F')
# make the glider
canvas[1][6] = 1
canvas[2][5] = 1
canvas[3][5] = 1
canvas[3][6] = 1
canvas[3][7] = 1
# now the eater...
canvas[5][3] = 1
canvas[5][4] = 1
canvas[6][4] = 1
canvas[7][1] = 1
canvas[7][2] = 1
canvas[7][3] = 1
canvas[8][1] = 1
return canvas
|
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|
"""Dynamic Object Models
AgentDoubleInt2D : Double Integrator Model in 2D
state: x,y,xdot,ydot
AgentSE2 : SE2 Model
state x,y,theta
Agent2DFixedPath : Model with a pre-defined path
Agent_InfoPlanner : Model from the InfoPlanner repository
SE2Dynamics : update dynamics function with a control input -- linear, angular velocities
SEDynamicsVel : update dynamics function for contant linear and angular velocities
"""
import numpy as np
from envs.target_tracking.metadata import *
import envs.env_utils as util
# import pyInfoGathering as IGL
class Agent(object):
def __init__(self, dim, sampling_period, limit, collision_func, margin=MARGIN):
self.dim = dim
self.sampling_period = sampling_period
self.limit = limit
self.collision_func = collision_func
self.margin = margin
def range_check(self):
self.state = np.clip(self.state, self.limit[0], self.limit[1])
def collision_check(self, pos):
return self.collision_func(pos[:2])
def margin_check(self, pos, target_pos):
return np.sqrt(np.sum((pos - target_pos)**2)) < self.margin # no update
def reset(self, init_state):
self.state = init_state
class AgentDoubleInt2D(Agent):
def __init__(self, dim, sampling_period, limit, collision_func,
margin=MARGIN, A=None, W=None):
Agent.__init__(self, dim, sampling_period, limit, collision_func, margin=margin)
self.A = np.eye(self.dim) if A is None else A
self.W = W
def update(self, margin_pos=None):
new_state = np.matmul(self.A, self.state)
if self.W is not None:
noise_sample = np.random.multivariate_normal(np.zeros(self.dim,), self.W)
new_state += noise_sample
if self.collision_check(new_state[:2]):
new_state = self.collision_control(new_state)
self.state = new_state
def collision_control(self, new_state):
new_state[0] = self.state[0]
new_state[1] = self.state[1]
if self.dim > 2:
new_state[2] = -2 * .2 * new_state[2] + np.random.normal(0.0, 0.2)#-0.001*np.sign(new_state[2])
new_state[3] = -2 * .2 * new_state[3] + np.random.normal(0.0, 0.2)#-0.001*np.sign(new_state[3])
return new_state
class AgentSE2(Agent):
def __init__(self, dim, sampling_period, limit, collision_func, margin=MARGIN, policy=None):
Agent.__init__(self, dim, sampling_period, limit, collision_func, margin=margin)
self.policy = policy
def update(self, control_input=None, margin_pos=None, col=False):
"""
control_input : [linear_velocity, angular_velocity]
margin_pos : a minimum distance to a target
"""
if control_input is None:
control_input = self.policy.get_control(self.state)
new_state = SE2Dynamics(self.state, self.sampling_period, control_input)
is_col = 0
if self.collision_check(new_state[:2]):
is_col = 1
new_state[:2] = self.state[:2]
if self.policy is not None:
self.policy.collision(new_state)
elif margin_pos is not None:
if type(margin_pos) != list:
margin_pos = [margin_pos]
for mp in margin_pos:
if self.margin_check(new_state[:2], margin_pos):
new_state[:2] = self.state[:2]
break
self.state = new_state
self.range_check()
return is_col
def SE2Dynamics(x, dt, u):
assert(len(x)==3)
tw = dt * u[1]
# Update the agent state
if abs(tw) < 0.001:
diff = np.array([dt*u[0]*np.cos(x[2]+tw/2),
dt*u[0]*np.sin(x[2]+tw/2),
tw])
else:
diff = np.array([u[0]/u[1]*(np.sin(x[2]+tw) - np.sin(x[2])),
u[0]/u[1]*(np.cos(x[2]) - np.cos(x[2]+tw)),
tw])
new_x = x + diff
new_x[2] = util.wrap_around(new_x[2])
return new_x
def SE2DynamicsVel(x, dt, u=None):
assert(len(x)==5) # x = [x,y,theta,v,w]
odom = SE2Dynamics(x[:3], dt, x[-2:])
return np.concatenate((odom, x[-2:]))
class Agent2DFixedPath(Agent):
def __init__(self, dim, sampling_period, limit, collision_func, path, margin=MARGIN):
Agent.__init__(self, dim, sampling_period, limit, collision_func, margin=margin)
self.path = path
def update(self, margin_pos=None):
# fixed policy for now
self.t += 1
self.state = np.concatenate((self.path[self.t][:2], self.path[self.t][-2:]))
def reset(self, init_state):
self.t = 0
self.state = np.concatenate((self.path[self.t][:2], self.path[self.t][-2:]))
class Agent_InfoPlanner(Agent):
def __init__(self, dim, sampling_period, limit, collision_func,
se2_env, sensor_obj, margin=MARGIN):
Agent.__init__(self, dim, sampling_period, limit, collision_func, margin=margin)
self.se2_env = se2_env
self.sensor = sensor_obj
self.sampling_period = sampling_period
self.action_map = {}
for (i,v) in enumerate([3,2,1,0]):
for (j,w) in enumerate([np.pi/2, 0, -np.pi/2]):
self.action_map[3*i+j] = (v,w)
def reset(self, init_state, belief_target):
self.agent = IGL.Robot(init_state, self.se2_env, belief_target, self.sensor)
self.state = self.get_state()
return self.state
def update(self, action, target_state):
action = self.update_filter(action, target_state)
self.agent.applyControl([int(action)], 1)
self.state = self.get_state()
def get_state(self):
return np.concatenate((self.agent.getState().position[:2], [self.agent.getState().getYaw()]))
def get_state_object(self):
return self.agent.getState()
def observation(self, target_obj):
return self.agent.sensor.senseMultiple(self.get_state_object(), target_obj)
def get_belief_state(self):
return self.agent.tmm.getTargetState()
def get_belief_cov(self):
return self.agent.tmm.getCovarianceMatrix()
def update_belief(self, GaussianBelief):
self.agent.tmm.updateBelief(GaussianBelief.mean, GaussianBelief.cov)
def update_filter(self, action, target_state):
state = self.get_state()
control_input = self.action_map[action]
tw = self.sampling_period*control_input[1]
# Update the agent state
if abs(tw) < 0.001:
diff = np.array([self.sampling_period*control_input[0]*np.cos(state[2]+tw/2),
self.sampling_period*control_input[0]*np.sin(state[2]+tw/2),
tw])
else:
diff = np.array([control_input[0]/control_input[1]*(np.sin(state[2]+tw) - np.sin(state[2])),
control_input[0]/control_input[1]*(np.cos(state[2]) - np.cos(state[2]+tw)),
tw])
new_state = state + diff
if len(target_state.shape)==1:
target_state = [target_state]
target_col = False
for n in range(target_state.shape[0]): # For each target
target_col = np.sqrt(np.sum((new_state[:2] - target_state[n][:2])**2)) < MARGIN
if target_col:
break
if self.collision_check(new_state) or target_col: # no update
new_action = 9 + action%3
else:
new_action = action
return new_action
|
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|
import sys
sys.path.append('..')
import numpy as np
from truefalsepython import fast_sample
random_arr = np.random.random(100)
random_probs = random_arr/random_arr.sum()
%timeit np.random.choice(random_arr, 1, p = random_probs)
# 72.9 µs ± 7.18 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)
%timeit fast_sample(random_arr, probs = random_probs)
# 31.4 µs ± 404 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
|
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|
from flask import Flask, request, render_template, Markup, url_for
import cPickle as pickle
import json
import socket
import requests
import pandas as pd
import numpy as np
import pymongo as mdb
import operator
app = Flask(__name__)
# helper function
@app.context_processor
def add_vars_to_context():
return dict(site_title="Amazon Feature Extractor")
# home page
@app.route('/')
def index():
return render_template('index.html',
page_title="Home")
# search results page
@app.route('/search', methods=['GET', 'POST'])
def search():
# create index
coll.create_index([("title", "text")])
# setup query
query=request.form['queryText']
# get search results
search_results = coll.find({'$text':{'$search':query}},
{'score': {'$meta': 'textScore'}})
# sort results
search_results.sort([('score', {'$meta': 'textScore'})]).limit(15)
# collect results
results = [result for result in search_results]
# extract output
results_html = ""
for result in results:
title = result["title"]
asin = result["asin"]
# get avg rating
sum_ratings = sum([result["ratings"][key]*int(key) for key in result["ratings"]])
count_ratings = sum([result["ratings"][key] for key in result["ratings"]])
avg_rating = sum_ratings * 1.0 / count_ratings
# get star image path
rating_rounded = int(round(avg_rating * 2) * 5)
fname = 'images/stars_{}.svg'.format(rating_rounded)
star_path = url_for('static', filename=fname)
#create html
url = url_for("product", asin=asin)
html = '<div class="search-result">'
html += '<span class="result-title"><a href={}>{}</a></span>'.format(url, title)
html += '<img class="stars" src="{}" />'.format(star_path)
html += '<span class="avg-rating">{}</span></div>'.format(round(avg_rating, 2))
results_html += html
return render_template('search.html',
page_title="Search Results",
results=Markup(results_html)
)
# product page
@app.route('/product/<string:asin>')
def product(asin):
# setup vars
product = coll.find_one({'asin':asin})
title = product["title"]
# get avg rating
sum_ratings = sum([product["ratings"][key]*int(key) for key in product["ratings"]])
count_ratings = sum([product["ratings"][key] for key in product["ratings"]])
avg_rating = round(sum_ratings * 1.0 / count_ratings, 2)
# get star image path
rating_rounded = int(round(avg_rating * 2) * 5)
fname = 'images/stars_{}.svg'.format(rating_rounded)
star_path = url_for('static', filename=fname)
# build html for avg_ratings
avg_rating_html = '<img class="stars" src="{}" /><div class="avg-rating">{}</div>'.format(star_path, avg_rating)
# build html for ratings distribution
dist_bars_html = ""
dist_bar_html = '<div class="bar-row"><span class="rating">{}</span>' \
+ '<span class="bar"><span class="fill" style="width:{}%;"></span></span>' \
+ '<span class="count">{}%</span></div>'
"""
# 5 star dist
for rating in reversed(range(1,6)):
count = product["ratings"].get(str(rating), 0)
bar_width = round(count * 100.0 / count_ratings, 1)
dist_bars_html += dist_bar_html.format(rating,
bar_width,
bar_width)
"""
# pos neg dist
rating_types = {"+": (5,4), "-": (2,1)}
for rating_type in rating_types:
ratings = rating_types[rating_type]
count = product["ratings"].get(str(ratings[0]), 0)
count += product["ratings"].get(str(ratings[1]), 0)
bar_width = round(count * 100.0 / count_ratings, 1)
dist_bars_html += dist_bar_html.format(rating_type,
bar_width,
bar_width)
# add dist bars html
ratings_dist_html = '<div class="dist-ratings">{}</div>'.format(dist_bars_html)
# build html for posFeatures
feature_html = '<div class="feature-row"><div class="feature">{}</div>' \
+ '<div class="bar-row"><span class="rating"></span>' \
+ '<span class="bar"><span class="fill" style="width:{}%;"></span></span>' \
+ '<span class="value">{}%</span></div></div>'
posFeatures_html = "None"
if "posFeatures" in product.keys():
posFeatures = sorted(product["posFeatures"], key=lambda x: float(x[1]))
temp = ""
total_importance = sum([float(feature[1]) for feature in posFeatures])
for feature in posFeatures:
rel_importance = round(total_importance / float(feature[1]), 1)
temp += feature_html.format(feature[0], rel_importance, rel_importance)
posFeatures_html = '<div class="posFeatures">{}</div>'.format(temp.strip(', '))
# build html for negFeatures
negFeatures_html = "None"
if "negFeatures" in product.keys():
negFeatures = sorted(product["negFeatures"], key=lambda x: float(x[1]))
temp = ""
total_importance = sum([float(feature[1]) for feature in negFeatures])
for feature in negFeatures:
rel_importance = round(total_importance / float(feature[1]), 1)
temp += feature_html.format(feature[0], rel_importance, rel_importance)
negFeatures_html = '<div class="negFeatures">{}</div>'.format(temp.strip(", "))
return render_template('product.html',
page_title=title,
product_title=title,
avg_rating=Markup(avg_rating_html),
ratings_dist=Markup(ratings_dist_html),
pos_features=Markup(posFeatures_html),
neg_features=Markup(negFeatures_html)
)
if __name__ == '__main__':
# setup global vars
conn = mdb.MongoClient()
db = conn.reviews
coll = db.products
my_port = 8080
my_ip = socket.gethostbyname(socket.gethostname())
app.run(host='0.0.0.0', port=my_port, debug=True)
|
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|
#!/usr/bin/env python
# coding: utf-8
import os
import csv
import time
import random
import cPickle
import pandas as pd
os.environ["CUDA_VISIBLE_DEVICES"]="0"
import pylab
import matplotlib.pyplot as plt
#from IPython.display import Image as IPImage
from sklearn import preprocessing
#normalized_data, norm = sklearn.preprocessing.normalize(data, norm='l2', axis=0, copy=False, return_norm=True) #version update needed
import numpy as np
import tensorflow as tf
#from tensorflow.models.rnn import rnn, rnn_cell
import utils
import models
def rmse(predictions, targets):
return np.sqrt(((predictions - targets) ** 2).mean())
def test(model, save_path, path, model_name, epoch, data_columns, target_features, target_delay, test_data, time_point, time_step,
scaler, xrange=5000, file_name='test_output', load_model=False):
if load_model :
model.load(os.path.join(save_path, path, model_name, str(epoch+1)+'.ckpt'))
test_file = os.path.join(save_path, path, model_name, str(epoch+1)+'epoch-'+file_name+'.npz')
if os.path.exists(test_file):
test_output = np.load(test_file)['arr_0']
test_output = test_output.reshape([-1,len(target_delay)])
print 'test output {} loaded.'.format(test_output.shape)
else:
test_output = []
for batch in utils.iterate_3d_2(inputs=np.delete(test_data, [data.columns.tolist().index(i) for i in unused_features], axis=2),
targets=test_data[:,:,[data.columns.tolist().index(i) for i in target_features]],
target_delay=np.array(target_delay), batch_size=batch_size, length = max(test_data.shape),
time_point=time_point, time_step=time_step, time_int=1):
test_in, test_target = batch
test_output.append(model.reconstruct(test_in))
test_output = np.asarray(test_output)
print test_output.shape
test_output = test_output.reshape([-1,(len(target_features)*len(target_delay))])
print test_output.shape
np.savez(os.path.join(save_path,path,model_name, str(epoch+1)+'epoch-'+file_name+'.npz'), [test_output])
print 'test output saved.'
for i in range(len(target_delay)):
#xrange=10000
if xrange is None:
xrange = np.max(test_output.shape)
target_data = test_data[0,
(time_point*time_step-1 + target_delay[i]):(time_point*time_step-1 + target_delay[i]+test_output.shape[0]),
np.where(data.columns==target_features[0])[0][0]]
cp = np.append([False],np.diff(target_data)!=0)
cp_rmse = rmse(target_data[cp]*scaler.scale_[np.where(data_columns==target_features[0])[0][0]],
test_output[cp,i]*scaler.scale_[np.where(data_columns==target_features[0])[0][0]])
all_rmse = rmse(test_output[:, i]*scaler.scale_[np.where(data_columns==target_features[0])[0][0]],
test_data[0,
(time_point*time_step-1 + target_delay[i]):\
(time_point*time_step-1 + target_delay[i]+test_output.shape[0]),
np.where(data_columns==target_features[0])[0][0]] * scaler.scale_[np.where(data.columns==target_features[0])[0][0]] )
test_output_roll = pd.rolling_mean(test_output, batch_size)
#
print test_output.shape
plt.figure(figsize=(15,6))
plt.plot(range(time_point*time_step-1 + target_delay[i], time_point*time_step-1 + target_delay[i]+xrange),
test_output[0:xrange,i]*\
scaler.scale_[np.where(data_columns==target_features[0])[0][0]]+\
scaler.mean_[np.where(data_columns==target_features[0])[0][0]],
label=target_features[0]+" " +str(target_delay[i])+'min pred', color='red')
plt.plot(test_data[0, 0:xrange,
np.where(data_columns==target_features[0])[0][0]]*\
scaler.scale_[np.where(data_columns==target_features[0])[0][0]]+\
scaler.mean_[np.where(data_columns==target_features[0])[0][0]],
label=target_features[0], color='blue')
plt.legend()#fontsize=11)
#plt.ylim([1440, 1560])
plt.xlim([0, time_point*time_step-1 + target_delay[i]+xrange])
plt.figtext(0.1, 0.01, 'all_rmse: ' +str(all_rmse))
plt.figtext(0.7, 0.01, 'cp_rmse: ' +str(cp_rmse))
#plt.savefig(os.path.join(save_path, path, model_name, str(xrange)+'-'+str(epoch)+'epoch-'+str(target_delay[i])+'m_test_output.png'))
plt.savefig(os.path.join('./', path, model_name, str(xrange)+'-'+str(epoch+1)+'epoch-'+str(target_delay[i])+'m_'+file_name+'.png'))
plt.close()
class GRCNN(object):
def __init__(self, batch_size=128, time_point=1024, in_channels = 126, out_channels=256, ch_multiplier=None,
cluster=None, rrcl_iter=[2,2,2,2], rrcl_num=4, forward_layers=[200,3], pool=['n','p','p','p','c'],
use_batchnorm=True, scale=1, offset=0.01, epsilon=0.01, nonlinearity=None, keep_probs=None,
std=0.01, w_filter_size=9, p_filter_size=4, l_rate=0.01, l_decay=0.95, l_step=1000,
optimizer='RMSProp', opt_epsilon=0.1, decay=0.9, momentum=0.9, tpa_coeff=0.0001):
print 'start initializing...'
self.batch_size = batch_size
self.time_point = time_point
self.in_channels = in_channels
#self.out_channels= ch_multiplier
self.out_channels = out_channels
if ch_multiplier!=None:
print'\'ch_multiplier\' is depreciated. Use \'out_channels\''
self.out_channels = ch_multiplier
self.cluster = cluster
self.rrcl_iter = rrcl_iter
self.rrcl_num = rrcl_num
self.use_batchnorm = use_batchnorm
self.offset = offset
self.scale = scale
self.epsilon = epsilon
self.nonlinearity = nonlinearity
#self.keep_probs = keep_probs
self.use_dropout = not (keep_probs == None or keep_probs == [1.0 for i in range(len(keep_probs))])
#if keep_probs == None:
# self.keep_probs = [1.0 for i in range(1+rrcl_num+len(forward_layers)-1)]
if self.use_dropout and len(keep_probs) != (1 + rrcl_num + len(forward_layers)-1):
raise ValueError('\'keep_probs\' length is wrong')
self.std = std
self.w_filter_size = w_filter_size
self.p_filter_size = p_filter_size
t=0
for i in range(len(np.unique(self.cluster)) ):
t = t+ self.out_channels*np.sum(self.cluster==i)/self.in_channels
self.ch_sum = t
self.forward_layers = [t] + forward_layers ################
self.pool = pool
if len(self.pool) != rrcl_num+1:
raise ValueError('Parameter \'pool\' length does not match with the model shape.')
global_step = tf.Variable(0, trainable=False)
self.l_rate = tf.train.exponential_decay(l_rate, global_step, l_step, l_decay, staircase=True)
self.decay = decay
self.momentum = momentum
self.y = tf.placeholder(tf.float32, [None, self.forward_layers[-1]], name='y');
self.x = [tf.placeholder(tf.float32, [None, 1, time_point, np.sum(cluster==i)], name='x'+str(i)) for i
in range(len(np.unique(cluster))) ]
self.keep_probs = tf.placeholder(tf.float32, [1+rrcl_num+len(forward_layers)-1], name='keep_probs')
self.keep_probs_values = keep_probs
print ' start building...'
self.build_model( )
print ' done.'
# Define loss and optimizer, minimize the squared error
#self.cost = tf.reduce_mean(tf.pow(self.y - self.output, 2))
#self.cost = tf.reduce_mean(-tf.reduce_sum(self.y*tf.log(self.output), reduction_indices=[1]))
self.cost = tf.reduce_mean(tf.pow(self.y - self.output_layer, 2))
if optimizer=='Adam':
self.optimizer = tf.train.AdamOptimizer(self.l_rate, epsilon=opt_epsilon).minimize(self.cost, global_step=global_step)
else :#optimizer=='RMSProp':
self.optimizer = tf.train.RMSPropOptimizer(self.l_rate,
decay=self.decay,
momentum=self.momentum).minimize(self.cost, global_step = global_step)
# Initializing the tensor flow variables
#init = tf.initialize_all_variables()
# Launch the session
self.session_conf = tf.ConfigProto()
self.session_conf.gpu_options.allow_growth = True
self.sess = tf.InteractiveSession(config=self.session_conf)
#self.sess = tf.InteractiveSession()
self.sess.run(tf.global_variables_initializer())
self.saver = tf.train.Saver(max_to_keep=10000)
print'done.'
def build_model(self):
#self.weights, self.biases = self.init_weights()
length = self.time_point ##length
filter_size = self.w_filter_size
while filter_size> length:
filter_size = filter_size/2
self.conv1=[]
networks=[]
for i in range( len(np.unique(self.cluster))):
"""
conv2d(input, filter, strides=[1,1,1,1], padding='SAME', nonlinearity=None, use_dropout=True, keep_prob=1.0,
use_batchnorm=True, std=0.01, offset=1e-10, scale=1, epsilon=1e-10, name='conv2d_default'):
"""
#print i
#print self.x[i],
#print [1, self.w_filter_size, np.sum(self.cluster==i), self.out_channels*np.sum(self.cluster==i)/self.in_channels]
conv1 = models.conv2d(self.x[i],
weight_size=[1, filter_size, np.sum(self.cluster==i), self.out_channels*np.sum(self.cluster==i)/self.in_channels],
nonlinearity=self.nonlinearity,
pool = self.pool[0],
pool_size = self.p_filter_size,
use_dropout=self.use_dropout,
keep_prob=self.keep_probs[0],
use_batchnorm=self.use_batchnorm,
std=self.std,
offset=self.offset,
scale=self.scale,
epsilon=self.epsilon,
name='conv2d_cluster'+str(i))
self.conv1.append(conv1)
networks.append(conv1)
#print conv1.get_layer()
#(batch, time, in_ch, ch_mult)
print ' conv done. {}'.format(conv1.get_layer())
"""
self.conv1p = tf.nn.max_pool(value=self.conv1,
ksize=[1,1,4,1],
strides=[1,1,4,1],
padding='SAME')
"""
#output: (batch_size, 1, in_width, out_channels*in_channels)
"""
RCL(input, filter, strides=[1,1,1,1], padding='SAME', num_iter=3, nonlinearity=None, use_dropout=True, keep_prob=1.0,
use_batchnorm=True, std=0.01, offset=1e-10, scale=1, epsilon=1e-10, name='RCL_default'):
"""
#networks = self.conv1.get_layer()
self.rrcls = []
for r in range(self.rrcl_num):
rrcl = []
while filter_size> length:
filter_size = filter_size/2
for i in range( len(np.unique(self.cluster))):
#print ' cluster{} start'.format(i),
tmp = models.RCL(input = networks[i].get_layer(),
weight_size = [1, filter_size, self.out_channels*np.sum(self.cluster==i)/self.in_channels,
self.out_channels*np.sum(self.cluster==i)/self.in_channels],
num_iter = self.rrcl_iter[r],
nonlinearity = self.nonlinearity,
use_dropout = self.use_dropout,
keep_prob = self.keep_probs[1+r],
use_batchnorm = self.use_batchnorm,
std=self.std,
offset=self.offset,
scale=self.scale,
epsilon=self.epsilon,
pool=self.pool[r+1],
pool_size=self.p_filter_size,
name='RCL'+str(r)+'_cluster'+str(i))
rrcl.append(tmp)
#print 'done'
networks = rrcl
self.rrcls.append(rrcl)
length = length/self.p_filter_size
print' rrcl{} done'.format(r),
print' {}'.format(rrcl[-1].get_layer())
#
networks=[]
for i in range(len(rrcl)):
networks.append( rrcl[i].get_layer())
#print networks[i]
self.concat = tf.concat(3, networks)
print ' concatenated to {}'.format(self.concat)
network = tf.reshape(self.concat, shape=[-1, self.ch_sum])# * self.keep_probs[1]]) ###
self.flatten = network
print ' flatten to {}'.format(self.flatten)
"""
(input, weight, nonlinearity=None, use_dropout=False, keep_prob=1.0,
use_batchnorm=False, std=0.01, offset=1e-10, scale=1, epsilon=1e-10, name='feedforward_default')
"""
if len(self.forward_layers) == 2:
network = models.feedforward(input = network,
weight_size=[self.forward_layers[0], self.forward_layers[1]],
nonlinearity=None,
use_dropout = False,
use_batchnorm = False,
std=self.std,
offset=self.offset,
scale=self.scale,
epsilon=self.epsilon,
name='output')
self.output = network#.get_layer()
self.output_layer = network.get_layer()
print' feedforward {} done, {}'.format(i+1, self.output_layer)
print' model built'
else:
self.forwards=[]
for i in range(len(self.forward_layers)-1 -1):
network = models.feedforward(input = network,
weight_size=[self.forward_layers[i], self.forward_layers[i+1]],
nonlinearity=self.nonlinearity,
use_dropout = self.use_dropout,
keep_prob = self.keep_probs[1+r],
use_batchnorm = self.use_batchnorm,
std=self.std,
offset=self.offset,
scale=self.scale,
epsilon=self.epsilon,
name='forward'+str(i))
self.forwards.append(network)
network = network.get_layer()
print' feedforward {} done, {}'.format(i, network)
network = models.feedforward(input = network,
weight_size=[self.forward_layers[-2], self.forward_layers[-1]],
nonlinearity=None,
use_dropout = False,
use_batchnorm = False,
std=self.std,
offset=self.offset,
scale=self.scale,
epsilon=self.epsilon,
name='output')
self.output = network#.get_layer()
self.output_layer = network.get_layer()
print' feedforward {} done, {}'.format(i+1, self.output_layer)
print' model built'
def train(self, data, target, keep_probs=None):
## data: [batch, time_idx]
## x: [batch, in_height, in_width, in_channels]
train_feed_dict = {self.x[i]:data[:,:,:,np.where(self.cluster==i)[0]] for i in range(len(np.unique(self.cluster))) }
train_feed_dict.update({self.y:target})
if keep_probs is None:
train_feed_dict.update({self.keep_probs:self.keep_probs_values})
else:
self.keep_probs_values = keep_probs
train_feed_dict.update({self.keep_probs:keep_probs})
opt, cost = self.sess.run((self.optimizer, self.cost),
feed_dict=train_feed_dict
)
return cost
def test(self, data, target, keep_probs=None):
test_feed_dict = {self.x[i]:data[:,:,:,np.where(self.cluster==i)[0]] for i in range(len(np.unique(self.cluster))) }
test_feed_dict.update({self.y:target})
if keep_probs is None:
test_feed_dict.update({self.keep_probs:self.keep_probs_values})
else:
self.keep_probs_values = keep_probs
test_feed_dict.update({self.keep_probs:keep_probs})
cost = self.sess.run(self.cost,
feed_dict=test_feed_dict
)
return cost
def reconstruct(self, data, keep_probs=None):
recon_feed_dict = {self.x[i]:data[:,:,:,np.where(self.cluster==i)[0]] for i in range(len(np.unique(self.cluster))) }
if keep_probs is None:
recon_feed_dict.update({self.keep_probs:self.keep_probs_values})
else:
self.keep_probs_values = keep_probs
recon_feed_dict.update({self.keep_probs:keep_probs})
return self.sess.run(self.output_layer,
feed_dict=recon_feed_dict
)
def save(self, save_path='./model.ckpt'):
saved_path = self.saver.save(self.sess, save_path)
print("Model saved in file: %s"%saved_path)
def load(self, load_path = './model.ckpt'):
self.saver.restore(self.sess, load_path)
print("Model restored")
def terminate(self):
self.sess.close()
tf.reset_default_graph()
# Main
"""
Load Data
"""
# os.getcwd() #current path
#data_path = os.path.join('/data2/data','data3')
#data = pd.read_csv( os.path.join(data_path,'toy_data.csv'))
data_path = '/data1/data-v0/'
data = pd.read_csv(os.path.join(data_path,'data.csv'))
#dataColumns = data.columns.tolist()
print("data shape: "+data.shape)
# data: (time_index, features)
cluster = pd.read_csv(os.path.join(data_path, 'data_SpectralClustering10', 'cluster.csv'))
print("cluster shape: "+cluster.shape)
if data.shape[-1] != cluster.shape[-1]:
raise ValueError('wrong cluster file 1')
if sum(data.columns == cluster.columns) != data.shape[-1]:
raise ValueError('wrong cluster file 2. Possibly not in order.')
# standardization
scaler = preprocessing.StandardScaler(with_mean=True, with_std=True).fit(data)
# scaler.mean_.shape, scaler.scale_.shape #mean, std
train_data = data[:int(data.shape[0]*0.8)]
valid_data = data[int(data.shape[0]*0.8):int(data.shape[0]*0.9)]
test_data = data[int(data.shape[0]*0.9):]
print("train data: {} \nvalid data:{} \ntest data:{}".format(train_data.shape, valid_data.shape, test_data.shape))
train_data = scaler.transform(train_data)
valid_data = scaler.transform(valid_data)
test_data = scaler.transform(test_data)
train_data = train_data[np.newaxis,:]
valid_data = valid_data[np.newaxis,:]
test_data = test_data[np.newaxis,:]
print("train data: {} \nvalid data:{} \ntest data:{}".format(train_data.shape, valid_data.shape, test_data.shape))
"""
Set Parameters
"""
unused_features = ['feature_1', 'feature_2']
used_features = [col for col in cluster.columns if col not in unused_features]
target_features = ['feature_0']
print(len(used_features), len(target_features))
batch_size = 64
time_step = 1 # length between each timepoint
time_int = 1 # interval between each starting point
target_delay = np.array([30, 60])
out_channels = 1024
rrcl_num = 4
rrcl_iter = [3,3,3,3]
w_filter_size = 9
p_filter_size = 4
time_point = p_filter_size**rrcl_num
forward_layers = [200, len(target_delay)]
use_batchnorm = False
split_train = False
nonlinearity = tf.nn.elu
keep_probs = [0.5,0.5, 0.5, 0.5, 0.5, 0.5] # None or an array of 1.0 values will turn off the dropout
pool=['n','p','p','p','p']
std = 0.01
l_rate = 0.0000001
l_decay = 0.1
l_step = 200*(np.max(train_data.shape)-time_point*time_step-batch_size*time_int-np.max(target_delay))/(batch_size*time_int) # 200 epochs
# optimizer = 'RMSProp'
decay = 0.8
momentum = 0
tpa_coeff = 10
## optimizer='Adam'
##opt_epsilon = 1
"""
Set Path
"""
save_path = os.path.join('/data2/data-v0/')
path = os.path.join('data-v0')
if not os.path.exists(os.path.join('./', path)):
os.mkdir(os.path.join('./',path))
if not os.path.exists(os.path.join(save_path,path)):
os.mkdir(os.path.join(save_path,path))
path = os.path.join(path, 'data0')
if not os.path.exists(os.path.join('./',path)):
os.mkdir(os.path.join('./',path))
if not os.path.exists(os.path.join(save_path,path)):
os.mkdir(os.path.join(save_path,path))
path = os.path.join(path, 'target-'+ str(target_features)[1:-1].replace("'","").replace(", ","_"))
if not os.path.exists(os.path.join('./',path)):
os.mkdir(os.path.join('./',path))
if not os.path.exists(os.path.join(save_path,path)):
os.mkdir(os.path.join(save_path,path))
path = os.path.join(path, 'use_batch_norm') if use_batchnorm else os.path.join(path, 'no_batch_norm')
if not os.path.exists(os.path.join('./',path)):
print 'creating difectory {}'.format(path)
os.mkdir(os.path.join('./',path))
if not os.path.exists(os.path.join(save_path,path)):
os.mkdir(os.path.join(save_path,path))
path = os.path.join(path, 'no_dropout') if (keep_probs == None or keep_probs == [1.0 for i in range(len(keep_probs))]) else os.path.join(path, 'dropout')
if not os.path.exists(os.path.join('./',path)):
print 'creating difectory {}'.format(path)
os.mkdir(os.path.join('./',path))
if not os.path.exists(os.path.join(save_path,path)):
os.mkdir(os.path.join(save_path,path))
path = os.path.join(path, 'None') if nonlinearity==None else os.path.join(path, str(nonlinearity).split(" ")[1])
if not os.path.exists(os.path.join('./',path)):
print 'creating difectory {}'.format(path)
os.mkdir(os.path.join('./',path))
if not os.path.exists(os.path.join(save_path,path)):
os.mkdir(os.path.join(save_path,path))
model_name = 'cl6-1-'+str(target_delay)[1:-1].replace(' ','_')+'m-RRCL4_iter'+str(rrcl_iter)[1:-1].replace(', ','_')+'-'+\
str([out_channels] + forward_layers)[1:-1].replace(', ','_')+\
'-keep'+str(keep_probs)[1:-1].replace(', ','_').replace('0.','')+\
'-batch128-tstep1-tint'+str(time_int)+'-std0_01-lrate'+str(l_rate)+\
'-lstep200-l_decay0_1-decay'+str(decay).replace('.','_')+'-mom'+str(momentum).replace('.','_')
print(os.path.join(path, model_name))
if not os.path.exists(os.path.join('./', path, model_name)):
os.mkdir(os.path.join('./', path, model_name))
print('path created: {}'.format(os.path.join('./',path, model_name)))
if not os.path.exists(os.path.join(save_path,path, model_name)):
os.mkdir(os.path.join(save_path, path, model_name))
print('path created: {}'.format(os.path.join(save_path, path, model_name)))
"""
Train
"""
# train parameters
num_epochs = 200
t_loss=[]
v_loss=[]
val_freq = 1
test_freq = 20
save_freq = 50
train_history = pd.DataFrame(index=np.arange(0, num_epochs),
columns=['epoch', 'loss', 'timestamp'])
valid_history = pd.DataFrame(index=np.arange(0, num_epochs/val_freq),
columns=['epoch', 'loss', 'timestamp'])
#val_epoch = range(1,10,1) + range(10,50,5) + range(50,100,10) + range(100, num_epochs+1, 20)
#valid_history = pd.DataFrame(index=val_epoch,
# columns=['epoch', 'loss', 'timestamp'])
if 'model' in globals():
model.terminate()
model = GRCNN(batch_size = batch_size,
time_point = time_point, # length.
in_channels = len(used_features), #number of channels of input data.
out_channels = out_channels,
cluster = np.asarray(cluster[used_features].loc['cluster'].tolist()), #cluster index list.
rrcl_iter = rrcl_iter, # number of iterations in each RRCL.
rrcl_num = rrcl_num, # number of RRCLs.
forward_layers = forward_layers, # [(concatenated layer node omitted) forward_1, ..., forward_fin, output]
use_batchnorm = use_batchnorm,
scale=1, offset=1e-10, epsilon=1e-10, # parameters for batch_normalization.
nonlinearity = nonlinearity, # nonlinearity function
keep_probs = keep_probs, # dropout keep_probs.
# Must be in form [conv_layer, RRCL_1, ..., RRCL_fin, forward_1, ..., forward_fin],
# length should be rrcl_num + len(forward_layers)-2
# Use None if you don't want to use dropout.
pool=pool,
std = std,
w_filter_size=w_filter_size, # filter size for conv layer and RRCLs. cut into half if too long.
p_filter_size=p_filter_size, # max pooling filter size. p_filter_size**rrcl_num must be same as time_point.
l_rate=l_rate, l_decay=l_decay, l_step=l_step,
decay=decay, momentum=momentum,
tpa_coeff=tpa_coeff
#optimizer='Adam',
)
for epoch in range(num_epochs):
loss = 0 ;
train_batches = 0
start_time = time.time()
flag=False
for batch in utils.iterate_3d_2(inputs=np.delete(train_data, [data.columns.tolist().index(i) for i in unused_features], axis=2),
targets=train_data[:,:,[data.columns.tolist().index(i) for i in target_features]],
target_delay=np.array(target_delay), batch_size=batch_size, length = max(train_data.shape),
time_point=time_point, time_step=time_step, time_int=time_int):
train_in, train_target = batch
train_target = train_target.reshape([batch_size,-1])
train_batches += 1
loss += model.train(data=train_in, target=train_target)
if np.isnan(loss):
print 'ERROR!'
flag=True
break
if flag:
train_history.to_csv(os.path.join('./', path, model_name, "history_train.csv"))
valid_history.to_csv(os.path.join('./', path, model_name, "history_valid.csv"))
break
t_loss.append(loss/train_batches)
train_history.loc[epoch] = [epoch+1, t_loss[epoch], time.strftime("%Y-%m-%d-%H:%M", time.localtime())]
if(epoch+1)%val_freq ==0:
loss = 0 ;
val_batches=0
for batch in utils.iterate_3d_2(inputs=np.delete(valid_data, [data.columns.tolist().index(i) for i in unused_features], axis=2),
targets=valid_data[:,:,[data.columns.tolist().index(i) for i in target_features]],
target_delay=np.array(target_delay), batch_size=batch_size, length = max(valid_data.shape),
time_point=time_point, time_step=time_step, time_int=time_int):
val_in, val_target = batch
val_target = val_target.reshape([batch_size,-1])
val_batches = val_batches+1
loss += model.test(data= val_in, target=val_target)
v_loss.append(loss/val_batches)
valid_history.loc[epoch/val_freq] = [epoch+1, v_loss[epoch/val_freq], time.strftime("%Y-%m-%d-%H:%M", time.localtime())]
if not os.path.exists(os.path.join('./', path, model_name)):
os.mkdir( os.path.join('./', path,model_name) )
if(epoch+1)%test_freq==0:
test(model, save_path, path, model_name, epoch, data_columns=data.columns, target_features=target_features,
target_delay=target_delay, test_data=train_data, time_point=time_point, time_step=time_step, scaler=scaler,
xrange=10000, file_name='train_output')
print("Epoch {} of {} took {:.3f}s".format(epoch + 1, num_epochs, time.time() - start_time))
print(" training loss:\t{:.6f}".format(t_loss[epoch]))
if (epoch+1)%val_freq==0:
print(" validation loss:\t{:.6f}".format(loss/val_batches))
if (epoch+1)%save_freq==0:
#model.save( os.path.join('./', path, model_name, str(epoch+1)+'.ckpt') )
model.save( os.path.join(save_path, path, model_name, str(epoch+1)+'.ckpt') )
train_history.to_csv(os.path.join('./', path, model_name, "history_train.csv"))
valid_history.to_csv(os.path.join('./', path, model_name, "history_valid.csv"))
plt.figure(figsize=(15,5))
plt.subplot(121)
plt.plot(train_history['loss'].tolist(), label='train loss')
plt.plot( range(val_freq, len(train_history)+val_freq, val_freq), valid_history['loss'], label='valid loss', color='Red')#, marker='o'
plt.axis([0, len(train_history), 0, 2])
plt.legend(fontsize=12, bbox_to_anchor=(1.05,1),loc=2)
#plt.legend(['train loss'])#,'test loss'])#,'accuracy'])
plt.title('Loss graph', fontsize=15)
plt.xlabel('epoch', fontsize=13)
plt.ylabel('loss', fontsize=13)
plt.savefig(os.path.join('./', path, model_name, str(len(train_history))+'epochs_tvloss.png'))
print os.path.join('./', path, model_name, str(len(train_history))+'epochs_tvloss.png')
#plt.savefig(os.path.join(save_path, path, model_name, str(len(train_history))+'epochs_tvloss.png'))
#print os.path.join(save_path, path, model_name, str(len(train_history))+'epochs_tvloss.png')
|
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|
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
from astropy.io import ascii
from uncertainties import ufloat
import uncertainties.unumpy as unp
Z=[29,29,29,30,32,35,37,38,40,41,79,79]
Z=np.asarray(Z)
E=[8.048,8.028,8.905,9.65,11.1031,13.4737,15.1997,16.1046,17.9976,18.9856,13.7336,11.9187]
E=np.asarray(E)
E=E*1000
enull=1.6021766208*10**(-19)
R=13.6
r=10973731.568508
c=299792458
d=201.4*10**(-12)
h=ufloat(6.626070040*10**(-34),0.000000081*10**(-34))
Rzwo=r*h.nominal_value*c
R=Rzwo
E=E*enull
a=1/137
theta=(360/(2*np.pi))*(np.arcsin(((c*h.nominal_value)/(2*d*E))))
sigma=Z-np.sqrt(E/R-(a**2*Z**4)/4)
print(sigma)
print(theta)
ascii.write([Z,E/enull,np.round(theta,2),np.round(sigma,2)],'Tabelle_literatur.tex',format='latex')
grenz=5*(2*np.pi/360)
lambdi=2*d*np.sin(grenz)
print("lambda min= ",lambdi)
power=(h*c)/lambdi
power=power/enull
print("Emax= ",power)
Etheo=35*1000
Etheo=Etheo*enull
ltheo=(h*c)/Etheo
print("lamnda theo= ",ltheo )
xalpha1=[44.8,45.2]
yalpha1=[5.0,28.0]
xalpha2=[45.5,46.0]
yalpha2=[15.0,5.0]
xbeta1=[40,40.4]
ybeta1=[8.0,18.0]
xbeta2=[41.2,41.5]
ybeta2=[14.0,7.0]
def ausgabe(x,y,peak):
m=np.sqrt(((y[0]-y[1])/(x[0]-x[1]))**2)
b=y[0]-m*x[0]
yval=peak/2
value=(yval-b)/m
value=value/2
vtheta=value*(2*np.pi/360)
Ehalb=(h*c)/(2*d*np.sin(vtheta))
Ehalb=Ehalb/enull
print(Ehalb)
#print(m)
#print(b)
print("Wert= ",value)
betatheta=20.4*(2*np.pi/360)
alphatheta=22.6*(2*np.pi/360)
Ealpha=(h.nominal_value*c)/(2*d*np.sin(alphatheta))
Ebeta=(h.nominal_value*c)/(2*d*np.sin(betatheta))
sigmaone=29-np.sqrt(Ebeta/R-(a**2*29**4)/4)
sigmazwo=29-np.sqrt((Ebeta-Ealpha)/R-(a**2*29**4)/4)
print(sigmaone)
print(sigmazwo)
ausgabe(xalpha1,yalpha1,28)
ausgabe(xalpha2,yalpha2,28)
ausgabe(xbeta1,ybeta1,19)
ausgabe(xbeta2,ybeta2,19)
###########################################################################################
# Absorptionsspektren
Ry = ufloat(13.605693009, 0.000000084)
#Zink
E_zi = h*c/(2*d*np.sin(18.8*2*np.pi/360)*enull)
print('E_ZI = ', E_zi)
sigma_zn = 30-unp.sqrt(E_zi/Ry - (30**4)/(4*137**2))
print('sigma_zn= ', sigma_zn)
#Germanium
E_ge = h*c/(2*d*np.sin(16.3*2*np.pi/360)*enull)
print('E_GE = ', E_ge)
sigma_ge = 32-unp.sqrt(E_ge/Ry - (32**4)/(4*137**2))
print('sigma_ge= ', sigma_ge)
#Brom
E_br = h*c/(2*d*np.sin(13.35*2*np.pi/360)*enull)
print('E_BR = ', E_br)
sigma_br = 35-unp.sqrt(E_br/Ry - (35**4)/(4*137**2))
print('sigma_br= ', sigma_br)
#Zirkonium
E_zr = h*c/(2*d*np.sin(10*2*np.pi/360)*enull)
print('E_ZR = ', E_zr)
sigma_zr = 40-unp.sqrt(E_zr/Ry - (40**4)/(4*137**2))
print('sigma_zr= ', sigma_zr)
#Gold
E_au_beta = h*c/(2*d*np.sin(13.0*2*np.pi/360)*enull)
E_au_gamma = h*c/(2*d*np.sin(15.2*2*np.pi/360)*enull)
print('Gold', E_au_beta/enull, 'zweite:', E_au_gamma)
sigma_au = 79-unp.sqrt(4*137*unp.sqrt((E_au_beta-E_au_gamma)/Ry)-5*(E_au_beta-E_au_gamma)/Ry) * (1+19/(32*137**2)*(E_au_gamma-E_au_beta)/Ry)**(1/2)
print('SIGMAGOLD= ', sigma_au)
#########################################################################################
Ek=[9.55,10.97,13.33,17.73]
Ek=np.asarray(Ek)*1000
Z=[30,32,35,40]
Zls=np.linspace(29,41)
def theorie(x,m,b):
return m*x+b
ascii.write([np.sqrt(Ek),Z],'tab_007.tex',format='latex',names=["wurzel e","Z"])
plt.plot(Z,np.sqrt(Ek), 'rx', label="Messwerte")
params, covariance = curve_fit(theorie,Z,np.sqrt(Ek))
errors = np.sqrt(np.diag(covariance))
ryd=ufloat(params[0],errors[0])
ryd=ryd**2
print('m= Rydbeck=',ryd)
print('b=',params[1],errors[1])
plt.plot(Zls, params[0]*Zls+params[1], 'b-', label="Lineare Regression")
plt.ylabel(r"$\sqrt{E_\mathrm{K}}$/$\sqrt{\si{\electronvolt}}$")
plt.xlabel(r"Kernladungszahl $Z$")
plt.xlim(29,41)
plt.legend(loc='best')
plt.tight_layout()
plt.savefig('R.pdf')
|
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|
# Copyright 2019 GreenWaves Technologies, SAS
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from collections.abc import Iterable
import numpy as np
from graph.dim import Dim
from quantization.quantization_record import (FilterQuantizationRecord,
QuantizationRecord)
def shape_dict(ord_, dims):
return [dims[i] for i in ord_]
def srange(dim, **kwargs):
slice_ = []
for k in dim.order:
if k in kwargs:
v = kwargs[k]
if isinstance(v, Iterable):
slice_.append(slice(*v))
elif isinstance(v, int):
slice_.append(slice(v, v+1, 1))
else:
slice_.append(slice(None))
return tuple(slice_)
def zeros(shape, qrec: QuantizationRecord, elem: str):
dtype = getattr(qrec, elem).dtype if qrec else None
return np.zeros(shape, dtype=dtype)
def pad(array: np.array, in_dim: Dim, padding: Dim, pad_type: str):
if pad_type == "zero":
return np.pad(array, padding.numpy_pad_shape(in_dim),\
'constant', constant_values=0)
raise NotImplementedError()
def prepare_acc(biases: np.array, out_dims: Dim, qrec: FilterQuantizationRecord):
if biases is None:
acc_tensor = zeros(out_dims.shape, qrec, 'acc_q')
else:
acc_tensor = zeros((out_dims.c, out_dims.h, out_dims.w), qrec, 'acc_q')
if qrec and qrec.acc_q != qrec.biases_q:
biases = qrec.acc_q.expand_from(biases, qrec.biases_q)
for i in range(out_dims.c):
acc_tensor[i, :] = biases[i]
acc_tensor = acc_tensor.transpose(out_dims.transpose_from_order(('c', 'h', 'w')))
return acc_tensor
|
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