markdown stringlengths 0 1.02M | code stringlengths 0 832k | output stringlengths 0 1.02M | license stringlengths 3 36 | path stringlengths 6 265 | repo_name stringlengths 6 127 |
|---|---|---|---|---|---|
Using a utility we provide, we will create a sparse matrix representation of the documents. This is the same utility function you used during the previous assignment on k-means with text data. | wiki = wiki.add_row_number()
tf_idf, map_word_to_index = sframe_to_scipy(wiki, 'tf_idf')
map_index_to_word = dict([[map_word_to_index[i], i] for i in map_word_to_index.keys()]) | _____no_output_____ | MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
As in the previous assignment, we will normalize each document's TF-IDF vector to be a unit vector. | %%time
tf_idf = normalize(tf_idf) | CPU times: user 4.56 ms, sys: 733 µs, total: 5.29 ms
Wall time: 5.8 ms
| MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
We can check that the length (Euclidean norm) of each row is now 1.0, as expected. | for i in range(5):
doc = tf_idf[i]
print(np.linalg.norm(doc.todense())) | 1.0
1.0
0.9999999999999997
1.0000000000000007
1.0
| MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
EM in high dimensionsEM for high-dimensional data requires some special treatment: * E step and M step must be vectorized as much as possible, as explicit loops are dreadfully slow in Python. * All operations must be cast in terms of sparse matrix operations, to take advantage of computational savings enabled by spars... | %%time
from sklearn.cluster import KMeans
np.random.seed(5)
num_clusters = 25
# Use scikit-learn's k-means to simplify workflow
#kmeans_model = KMeans(n_clusters=num_clusters, n_init=5, max_iter=400, random_state=1, n_jobs=-1) # uncomment to use parallelism -- may break on your installation
kmeans_model = KMeans(n_... | /home/offbeat/Environments/turicreate/lib/python3.7/site-packages/sklearn/cluster/_kmeans.py:974: FutureWarning: 'n_jobs' was deprecated in version 0.23 and will be removed in 0.25.
" removed in 0.25.", FutureWarning)
| MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
**Initializing cluster weights**We will initialize each cluster weight to be the proportion of documents assigned to that cluster by k-means above. | %%time
num_docs = tf_idf.shape[0]
weights = []
for i in range(num_clusters):
# Compute the number of data points assigned to cluster i:
num_assigned = np.sum(cluster_assignment == i) # YOUR CODE HERE
w = float(num_assigned) / num_docs
weights.append(w)
np.sum(cluster_assignment == 1) | _____no_output_____ | MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
**Initializing covariances**To initialize our covariance parameters, we compute $\hat{\sigma}_{k, j}^2 = \sum_{i=1}^{N}(x_{i,j} - \hat{\mu}_{k, j})^2$ for each feature $j$. For features with really tiny variances, we assign 1e-8 instead to prevent numerical instability. We do this computation in a vectorized fashion i... | covs = []
for i in range(num_clusters):
member_rows = tf_idf[cluster_assignment==i]
cov = (member_rows.multiply(member_rows) - 2*member_rows.dot(diag(means[i]))).sum(axis=0).A1 / member_rows.shape[0] \
+ means[i]**2
cov[cov < 1e-8] = 1e-8
covs.append(cov) | _____no_output_____ | MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
**Running EM**Now that we have initialized all of our parameters, run EM. | out = EM_for_high_dimension(tf_idf, means, covs, weights, cov_smoothing=1e-10)
out['loglik'] | _____no_output_____ | MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
Interpret clustering results In contrast to k-means, EM is able to explicitly model clusters of varying sizes and proportions. The relative magnitude of variances in the word dimensions tell us much about the nature of the clusters.Write yourself a cluster visualizer as follows. Examining each cluster's mean vector, ... | # Fill in the blanks
def visualize_EM_clusters(tf_idf, means, covs, map_index_to_word):
print('')
print('==========================================================')
num_clusters = len(means)
for c in range(num_clusters):
print('Cluster {0:d}: Largest mean parameters in cluster '.format(c))... |
==========================================================
Cluster 0: Largest mean parameters in cluster
Word Mean Variance
minister 7.57e-02 7.42e-03
election 5.89e-02 3.21e-03
party 5.89e-02 2.61e-03
liberal 2.93e-02 4.55e-03
elected 2.91e-02 8.95e-04
=========... | MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
**Quiz Question**. Select all the topics that have a cluster in the model created above. [multiple choice]- Baseball- Basketball- Soccer/Football- Music- Politics- Law- Finance Comparing to random initialization Create variables for randomly initializing the EM algorithm. Complete the following code block. | np.random.seed(5) # See the note below to see why we set seed=5.
num_clusters = len(means)
num_docs, num_words = tf_idf.shape
random_means = []
random_covs = []
random_weights = []
for k in range(num_clusters):
# Create a numpy array of length num_words with random normally distributed values.
# Use the ... | _____no_output_____ | MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
**Quiz Question**: Try fitting EM with the random initial parameters you created above. (Use `cov_smoothing=1e-5`.) Store the result to `out_random_init`. What is the final loglikelihood that the algorithm converges to? | out_random_init = EM_for_high_dimension(tf_idf, random_means, random_covs, random_weights, cov_smoothing=1e-5)
print("{:e}".format(out_random_init['loglik'][-1])) | 2.362457e+09
| MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
**Quiz Question:** Is the final loglikelihood larger or smaller than the final loglikelihood we obtained above when initializing EM with the results from running k-means? | out['loglik'] | _____no_output_____ | MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
**Quiz Question**: For the above model, `out_random_init`, use the `visualize_EM_clusters` method you created above. Are the clusters more or less interpretable than the ones found after initializing using k-means? | # YOUR CODE HERE. Use visualize_EM_clusters, which will require you to pass in tf_idf and map_index_to_word.
visualize_EM_clusters(tf_idf, out_random_init['means'], out_random_init['covs'], map_index_to_word) |
==========================================================
Cluster 0: Largest mean parameters in cluster
Word Mean Variance
she 2.24e-02 3.54e-03
award 1.53e-02 1.18e-03
music 1.45e-02 1.29e-03
university 1.43e-02 6.32e-04
law 1.27e-02 2.59e-03
=========... | MIT | 4-ml-clustering-and-retrieval/Week_4-assignment-2.ipynb | anilk991/Coursera-Machine-Learning-Specialization-UW |
Example notebook for the functions contained in cry_file_readwrite.py Crystal_input class | from crystal_functions.file_readwrite import Crystal_input | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
Create a crystal input object from blocks | geom_block = ['MGO BULK - GEOMETRY TEST\n',
'CRYSTAL\n',
'0 0 0\n',
'225\n',
'4.217\n',
'2\n',
'12 0. 0. 0.\n',
'8 0.5 0.5 0.5\n',
'END\n']
bs_block = ['BASISSET\n','POB-DZVP\n']
func_block = ['DFT\n', 'B... | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
Create a crystal input object from an existing input file | mgo_input = Crystal_input().from_file('data/mgo.d12')
mgo_input.geom_block | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
Crystal_output class | from crystal_functions.file_readwrite import Crystal_output | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
3D system | mgo_output = Crystal_output().read_cry_output('data/mgo_optgeom.out')
mgo_output | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
Functions and properties | #Final energy
print("Final energy = %s eV \n" % mgo_output.get_final_energy())
#Fermi energy
print("Fermi energy = %s eV \n" % mgo_output.get_fermi_energy())
#Primitive lattice
print("Primitive lattice \n %s \n" % mgo_output.get_primitive_lattice())
#Reciprocal lattice
print("Reciprocal lattice \n %s \n" % mgo_outpu... | Final energy = -7495.341792877063 eV
Fermi energy = -4.13671240282 eV
Primitive lattice
[[0. 2.1085 2.1085]
[2.1085 0. 2.1085]
[2.1085 2.1085 0. ]]
Reciprocal lattice
[[-1.48996571 1.48996571 1.48996571]
[ 1.48996571 -1.48996571 1.48996571]
[ 1.48996571 1.48996571 -1.48996571]]
Band gap =... | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
0D system | co_output = Crystal_output().read_cry_output('data/co.out')
#Final energy
print("Final energy = %s eV \n" % co_output.get_final_energy())
#Fermi energy
print("Fermi energy = %s eV \n" % co_output.get_fermi_energy())
#Primitive lattice
print("Primitive lattice \n %s \n" % co_output.get_primitive_lattice())
#Reciproca... | Final energy = -3037.8807073392627 eV
Fermi energy = -7.247937617924001 eV
WARNING: no lattice vectors found in the output file. lattice = []
Primitive lattice
None
Reciprocal lattice
None
Band gap = 10.9012 eV
Last geometry =
[[[12.0, 0.0, 0.0], [0.0, 12.0, 0.0], [0.0, 0.0, 12.0]], [6, 8], [[-0.0637262... | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
Properties_output class | from crystal_functions.file_readwrite import Properties_output | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
Bands | mgo_bands = Properties_output()
mgo_bands.read_cry_bands('../examples/data/mgo_BAND_dat.BAND')
mgo_bands | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
Doss | mgo_doss = Properties_output()
mgo_doss = mgo_doss.read_cry_doss('data/mgo_DOSS_dat.DOSS')
mgo_doss | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
write_cry_input function | from crystal_functions.file_readwrite import Crystal_input
from crystal_functions.file_readwrite import write_crystal_input | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
Use existing input file | #Read the original input
mgo_original_input = Crystal_input().from_file('data/mgo.d12')
#Write the input
new_input_name = 'data/mgo_from_file.d12'
write_crystal_input(new_input_name,crystal_input=mgo_original_input) | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
Build from blocks | #Define the blocks
geom_block = ['MGO BULK - GEOMETRY TEST\n',
'CRYSTAL\n',
'0 0 0\n',
'225\n',
'4.217\n',
'2\n',
'12 0. 0. 0.\n',
'8 0.5 0.5 0.5\n',
'END\n']
bs_block = ['12 4\n',
'0 0 8 2.0 1.0\n',
' 68370.0 0.0002226\n',
' 9661.0 0.001901\n',
' 2041.0 0.011042\n',
' 529.6 0.05005\n',
' 159.17... | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
write_cry_properties function bands from k points coordinates | from crystal_functions.file_readwrite import Properties_input
from crystal_functions.file_readwrite import write_properties_input
#Create the bands input object
bands_input = Properties_input()
#Add the newk block to the input object
bands_input.make_newk_block(12,24)
#Prepare the band_block
k_path = [[0,0,0],[0.5,0,... | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
bands from pymatgen HighSymmKpath object | from pymatgen.symmetry.bandstructure import HighSymmKpath
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from crystal_functions.file_readwrite import write_properties_input
from crystal_functions.file_readwrite import Crystal_output
from crystal_functions.file_readwrite import Properties_input
from crystal_... | _____no_output_____ | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
doss | from crystal_functions.file_readwrite import write_properties_input
from crystal_functions.file_readwrite import Properties_input
#Create the doss input object
doss_input = Properties_input()
#Add the newk block to the input object
doss_input.make_newk_block(12,24)
#Prepare the doss_block
doss_input.make_doss_block(... | NEWK
12 24
1 0
DOSS
0 200 -1 -1 2 12 1
-0.18374651800348382 0.5512395540104514
END
| MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
pdoss (atoms) | from crystal_functions.file_readwrite import write_properties_input
from crystal_functions.file_readwrite import Properties_input
#Create the doss input object
pdoss_input = Properties_input()
#Add the newk block to the input object
pdoss_input.make_newk_block(12,24)
#Prepare the pdoss_block
projections = [[1],[2]]
p... | NEWK
12 24
1 0
PDOS
2 200 1 26 2 12 1
-1 1
-1 2
END
| MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
pdoss (ao) | from crystal_functions.file_readwrite import write_properties_input
from crystal_functions.file_readwrite import Properties_input
#Create the doss input object
pdoss_input = Properties_input()
#Add the newk block to the input object
pdoss_input.make_newk_block(12,24)
#Prepare the pdoss_block
projections = [[1, 2, 3, ... | NEWK
12 24
1 0
PDOS
2 200 1 26 2 12 1
13 1 2 3 4 5 6 7 8 9 10 11 12 13
13 14 15 16 17 18 19 20 21 22 23 24 25 26
END
| MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
write_cry_gui function from pymatgen structure bulk (3D) | from crystal_functions.file_readwrite import Crystal_gui, write_crystal_gui
from crystal_functions.convert import cry_pmg2gui
from pymatgen.core import Structure, Lattice
#Generate bulk structure
substrate = Structure.from_spacegroup("Fm-3m", Lattice.cubic(4.217), ["Mg",'O'], [[0, 0, 0],[0.5,0.5,0.5]])
#The dimensio... | 2 1 1
4.217 0.0 0.0
0.0 4.217 0.0
0.0 0.0 500.0
32
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
0.0 0.0 0.0
0.0 -1.0 0.0
1.0 0.0 0.0
0.0 0.0 1.0
0.0 0.0 0.0
-1.0 0.0 0.0
0.0 -1.0 0.0
0.0 0.0 1.0
0.0 0.0 0.0
0.0 1.0 0.0
-1.0 0.0 0.0
0.0 0.0 1.0
0.0 0.0 0.0
-1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
0.0 0.0 ... | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
slab (2D) | import sys
sys.path.insert(1,'../crystal_functions/')
from file_readwrite import *
from convert import *
#from crystal_functions.file_readwrite import write_crystal_gui
from pymatgen.core import Structure, Lattice
from pymatgen.core.surface import SlabGenerator
#Generate bulk structure
substrate = Structure.from_spac... | 2 1 1
2.9818692962636706 0.0 1.8258683445725374e-16
-1.8258683445725374e-16 2.9818692962636706 1.8258683445725374e-16
0.0 0.0 500.0
8
1.0 -0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
0.0 0.0 0.0
-0.0 -1.0 0.0
1.0 0.0 0.0
0.0 -0.0 1.0
0.0 0.0 0.0
-1.0 0.0 0.0
0.0 -1.0 0.0
-0.0 -0.0 1.0
0.0 0.0 0.0
0.0 1.0 0.0
... | MIT | examples/file_readwrite.ipynb | acossard/crystal_functions |
Text Data Explanation Benchmarking: Emotion Multiclass Classification This notebook demonstrates how to use the benchmark utility to benchmark the performance of an explainer for text data. In this demo, we showcase explanation performance for partition explainer on an Emotion Multiclass Classification model. The metr... | import copy
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from transformers import AutoTokenizer, AutoModelForSequenceClassification
import shap.benchmark as benchmark
import shap
import scipy as sp
import nlp
import torch
pd.set_option('display.max_columns', None)
pd.set_option('display.max_r... | _____no_output_____ | MIT | notebooks/benchmark/text/Text Emotion Multiclass Classification Benchmark Demo.ipynb | afzalmushtaque/shap |
Load Data and Model | train, test = nlp.load_dataset("emotion", split = ["train", "test"])
data={'text':train['text'],
'emotion':train['label']}
data = pd.DataFrame(data)
tokenizer = AutoTokenizer.from_pretrained("nateraw/bert-base-uncased-emotion",use_fast=True)
model = AutoModelForSequenceClassification.from_pretrained("nat... | _____no_output_____ | MIT | notebooks/benchmark/text/Text Emotion Multiclass Classification Benchmark Demo.ipynb | afzalmushtaque/shap |
Class Label Mapping | # set mapping between label and id
id2label = model.config.id2label
label2id = model.config.label2id
labels = sorted(label2id, key=label2id.get) | _____no_output_____ | MIT | notebooks/benchmark/text/Text Emotion Multiclass Classification Benchmark Demo.ipynb | afzalmushtaque/shap |
Define Score Function | def f(x):
tv = torch.tensor([tokenizer.encode(v, padding='max_length', max_length=128,truncation=True) for v in x])
attention_mask = (tv!=0).type(torch.int64)
outputs = model(tv,attention_mask=attention_mask)[0].detach().numpy()
scores = (np.exp(outputs).T / np.exp(outputs).sum(-1)).T
val = sp.speci... | _____no_output_____ | MIT | notebooks/benchmark/text/Text Emotion Multiclass Classification Benchmark Demo.ipynb | afzalmushtaque/shap |
Create Explainer Object | explainer = shap.Explainer(f,tokenizer,output_names=labels) | explainers.Partition is still in an alpha state, so use with caution...
| MIT | notebooks/benchmark/text/Text Emotion Multiclass Classification Benchmark Demo.ipynb | afzalmushtaque/shap |
Run SHAP Explanation | shap_values = explainer(data['text'][0:20]) | _____no_output_____ | MIT | notebooks/benchmark/text/Text Emotion Multiclass Classification Benchmark Demo.ipynb | afzalmushtaque/shap |
Define Metrics (Sort Order & Perturbation Method) | sort_order = 'positive'
perturbation = 'keep' | _____no_output_____ | MIT | notebooks/benchmark/text/Text Emotion Multiclass Classification Benchmark Demo.ipynb | afzalmushtaque/shap |
Benchmark Explainer | sequential_perturbation = benchmark.perturbation.SequentialPerturbation(explainer.model, explainer.masker, sort_order, perturbation)
xs, ys, auc = sequential_perturbation.model_score(shap_values, data['text'][0:20])
sequential_perturbation.plot(xs, ys, auc)
sort_order = 'negative'
perturbation = 'keep'
sequential_pertu... | _____no_output_____ | MIT | notebooks/benchmark/text/Text Emotion Multiclass Classification Benchmark Demo.ipynb | afzalmushtaque/shap |
**Download** (right-click, save target as ...) this page as a jupyterlab notebook [Lab 30](http://54.243.252.9/engr-1330-webroot/8-Labs/Lab30/Lab30.ipynb)___ Laboratory 30: Logarithmic and Power-Law Models LAST NAME, FIRST NAMER00000000ENGR 1330 Laboratory 30 - In Lab___ BackgroundThe last couple lessons contain the ... | # Load the necessary packages
# build the data lists
# build a dataframe
# Initialise and fit regression model using `statsmodels`
# Predict values
# Plot regression against actual data
# Is the model "good" if not try a different data model (linear,exponential,power law,logarithmic,polynomial)
# with your "good" mode... | _____no_output_____ | CC0-1.0 | 8-Labs/Lab30/Lab30.ipynb | dustykat/engr-1330-psuedo-course |
Unsupervised outliers detection (event detection) | import drama as drm
import numpy as np
import matplotlib.pylab as plt
from matplotlib import gridspec
from drama.outlier_finder import grid_run_drama
from keras.datasets import mnist
%matplotlib inline
n_try = 5
# MNIST dataset
(x_train, y_train), (x_test, y_test) = mnist.load_data()
image_size = x_train.shape[1]
... | _____no_output_____ | BSD-3-Clause | notebooks/trial/MNIST.ipynb | vafaei-ar/pymce |
Outlier detection | metrics = ['cityblock', 'L2', 'L4', 'braycurtis', 'canberra', 'chebyshev',
'correlation', 'mahalanobis', 'wL2', 'wL4']
drt_list = ['DAE1D', 'DVAE1D']
result = []
for i in range(n_try):
# auc,mcc,rws,conf = grid_run_drama(X,y)
auc,mcc,rws,conf = grid_run_drama(X,y,
... | Unsupervised outlier detection mode.
| BSD-3-Clause | notebooks/trial/MNIST.ipynb | vafaei-ar/pymce |
Ensemble Learning Advantages of CARTs- simple to understand, interpret, and use- flexibility: ability to describe non-linear dependencies- preprocessing: no need to standardize or normalize features Limitations of CARTS- classification: can only produce orthogonal decision boundaries- sensitive to small variations in ... | # import the packages
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.linear_model import LogisticRegression
from sklearn.tree import DecisionTreeClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.ensemble import VotingClassifier
from s... | Accuracy score of the Voting Classifier: 0.942
| MIT | datacamp_ml/ml_trees/ensemble_learning.ipynb | issagaliyeva/machine_learning |
Further information What are the differences between recursion and iteration?When giving instructions to a computer it is possible to use recursion todirectly implement a common mathematical definition. For example consider thefollowing sequence:$$ \left\{\begin{array}{l} a_1 = 1\\ a_{n + 1}= 3a_n, n > 1 \... | def generate_sequence(n):
"""
Generate the sequence defined by:
a_1 = 1
a_n = 3 a_{n - 1}
This is done using recursion.
"""
if n == 1:
return 1
return 3 * generate_sequence(n - 1) | _____no_output_____ | MIT | book/tools-for-mathematics/07-sequences/why/.main.md.bcp.ipynb | daffidwilde/pfm |
The first 6 terms: | [generate_sequence(n) for n in range(1, 7)] | _____no_output_____ | MIT | book/tools-for-mathematics/07-sequences/why/.main.md.bcp.ipynb | daffidwilde/pfm |
We note that in this case this corresponds to powers of $3$, and indeed we canprove that: $a_n = 3 ^ {n - 1}$. We will not carry out the proof here but oneapproach to doing it would be to use proof by induction which is closely relatedto recursive functions.We can write a different python function that uses this formul... | def calculate_sequence(n):
"""
Calculate the nth term of the sequence defined by:
a_1 = 1
a_n = 3 a_{n - 1}
This is done using iteration using the direct formula:
a_n = 3 ^ n
"""
return 3 ** (n - 1)
[calculate_sequence(n) for n in range(1, 7)] | _____no_output_____ | MIT | book/tools-for-mathematics/07-sequences/why/.main.md.bcp.ipynb | daffidwilde/pfm |
We can in fact use a Jupyter [magiccommand](https://ipython.readthedocs.io/en/stable/interactive/magics.html) totime the run time of a command. It is clear that recursion is slower. | %timeit [generate_sequence(n) for n in range(1, 25)]
%timeit [calculate_sequence(n) for n in range(1, 25)] | 7.63 µs ± 89.5 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
| MIT | book/tools-for-mathematics/07-sequences/why/.main.md.bcp.ipynb | daffidwilde/pfm |
In practice:- Using recursion is powerful as it can be used to directly implement recursive definitions.- Using iteration is more computationally efficient but it is not always straightforward to obtain an iterative formula.(what_is_caching)= What is cachingOne of the reasons that recursion is computationally ineffic... | import functools
def generate_sequence(n):
"""
Generate the sequence defined by:
a_1 = 1
a_n = 3 a_{n - 1}
This is done using recursion.
"""
if n == 1:
return 1
return 3 * generate_sequence(n - 1)
@functools.lru_cache()
def cached_generate_sequence(n):
"""
Generate ... | _____no_output_____ | MIT | book/tools-for-mathematics/07-sequences/why/.main.md.bcp.ipynb | daffidwilde/pfm |
Timing both these approaches confirms a substantial increase in time for thecached version. | %timeit [generate_sequence(n) for n in range(1, 25)]
%timeit [cached_generate_sequence(n) for n in range(1, 25)] | 1.53 µs ± 7.47 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)
| MIT | book/tools-for-mathematics/07-sequences/why/.main.md.bcp.ipynb | daffidwilde/pfm |
Limits, Legends, and LayoutsIn this section, we'll focus on what happens around the edges of the axes: Ticks, ticklabels, limits, layouts, and legends. Limits and autoscalingBy default, Matplotlib will attempt to determine limits for you that encompasses all the data you have plotted. This is the "autoscale" featur... | fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=plt.figaspect(0.5))
ax1.plot([-10, -5, 0, 5, 10, 15], [-1.2, 2, 3.5, -0.3, -4, 1])
ax2.scatter([-10, -5, 0, 5, 10, 15], [-1.2, 2, 3.5, -0.3, -4, 1])
plt.show() | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
`ax.margins(...)`If you'd like to add a bit of "padding" to a plot, `ax.margins()` is a very handy way to do so. Instead of choosing "even-ish" numbers as min/max ranges for each axis, `margins` will make Matplotlib calculate the min/max of each axis by taking the range of the data and adding on a fractional amount o... | fig, (ax1, ax2) = plt.subplots(1, 2, figsize=plt.figaspect(0.5))
ax1.plot([-10, -5, 0, 5, 10, 15], [-1.2, 2, 3.5, -0.3, -4, 1])
ax2.scatter([-10, -5, 0, 5, 10, 15], [-1.2, 2, 3.5, -0.3, -4, 1])
ax1.margins(x=0.0, y=0.1) # 10% padding in the y-direction only
ax2.margins(0.05) # 5% padding in all directions
plt.show() | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
`ax.axis(...)`The `ax.axis(...)` method is a convienent way of controlling the axes limits and enabling/disabling autoscaling.If you ever need to get all of the current plot limits, calling `ax.axis()` with no arguments will return the xmin/max/etc: xmin, xmax, ymin, ymax = ax.axis() If you'd like to manually se... | fig, axes = plt.subplots(nrows=3)
for ax in axes:
ax.plot([-10, -5, 0, 5, 10, 15], [-1.2, 2, 3.5, -0.3, -4, 1])
axes[0].set_title('Normal Autoscaling', y=0.7, x=0.8)
axes[1].set_title('ax.axis("tight")', y=0.7, x=0.8)
axes[1].axis('tight')
axes[2].set_title('ax.axis("equal")', y=0.7, x=0.8)
axes[2].axis('equal'... | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
Manually setting only one limitAnother trick with limits is to specify only half of a limit. When done **after** a plot is made, this has the effect of allowing the user to anchor a limit while letting Matplotlib autoscale the rest of it. | # Good -- setting limits after plotting is done
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=plt.figaspect(0.5))
ax1.plot([-10, -5, 0, 5, 10, 15], [-1.2, 2, 3.5, -0.3, -4, 1])
ax2.scatter([-10, -5, 0, 5, 10, 15], [-1.2, 2, 3.5, -0.3, -4, 1])
ax1.set_ylim(bottom=-10)
ax2.set_xlim(right=25)
plt.show()
# Bad -- Setting li... | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
LegendsAs you've seen in some of the examples so far, the X and Y axis can also be labeled, as well as the subplot itself via the title. However, another thing you can label is the line/point/bar/etc that you plot. You can provide a label to your plot, which allows your legend to automatically build itself. | fig, ax = plt.subplots()
ax.plot([1, 2, 3, 4], [10, 20, 25, 30], label='Philadelphia')
ax.plot([1, 2, 3, 4], [30, 23, 13, 4], label='Boston')
ax.set(ylabel='Temperature (deg C)', xlabel='Time', title='A tale of two cities')
ax.legend()
plt.show() | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
In `classic` mode, legends will go in the upper right corner by default (you can control this with the `loc` kwarg). As of v2.0, by default Matplotlib will choose a location to avoid overlapping plot elements as much as possible. To force this option, you can pass in: ax.legend(loc="best") Also, if you happen to ... | fig, ax = plt.subplots(1, 1)
ax.bar([1, 2, 3, 4], [10, 20, 25, 30], label="Foobar", align='center', color='lightblue')
ax.plot([1, 2, 3, 4], [10, 20, 25, 30], label="_nolegend_", marker='o', color='darkred')
ax.legend(loc='best')
plt.show() | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
Exercise 4.1Once again, let's use a bit of what we've learned. Try to reproduce the following figure:Hint: You'll need to combine `ax.axis(...)` and `ax.margins(...)`. Here's the data and some code to get you started: | import numpy as np
import matplotlib.pyplot as plt
t = np.linspace(0, 2 * np.pi, 150)
x1, y1 = np.cos(t), np.sin(t)
x2, y2 = 2 * x1, 2 * y1
colors = ['darkred', 'darkgreen']
# Try to plot the two circles, scale the axes as shown and add a legend
# Hint: it's easiest to combine `ax.axis(...)` and `ax.margins(...)` to... | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
Dealing with the boundaries: Layout, ticks, spines, etcOne key thing we haven't talked about yet is all of the annotation on the outside of the axes, the borders of the axes, and how to adjust the amount of space around the axes. We won't go over every detail, but this next section should give you a reasonable workin... | fig, ax = plt.subplots()
ax.plot([1, 2, 3, 4], [10, 20, 25, 30])
# Manually set ticks and tick labels *on the x-axis* (note ax.xaxis.set, not ax.set!)
ax.xaxis.set(ticks=range(1, 5), ticklabels=[3, 100, -12, "foo"])
# Make the y-ticks a bit longer and go both in and out...
ax.tick_params(axis='y', direction='inout',... | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
A commonly-asked question is "How do I plot categories?"Starting in version 2.0 of mpl, just like any other data.For example: | data = [('apples', 2), ('oranges', 3), ('peaches', 1)]
fruit, value = zip(*data)
fig, ax = plt.subplots()
ax.bar(fruit, value, align='center', color='gray')
plt.show() | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
Subplot SpacingThe spacing between the subplots can be adjusted using [`fig.subplots_adjust()`](http://matplotlib.org/api/pyplot_api.html?matplotlib.pyplot.subplots_adjust). Play around with the example below to see how the different arguments affect the spacing. | fig, axes = plt.subplots(2, 2, figsize=(9, 9))
fig.subplots_adjust(wspace=0.5, hspace=0.3,
left=0.125, right=0.9,
top=0.9, bottom=0.1)
plt.show() | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
A common "gotcha" is that the labels are not automatically adjusted to avoid overlapping those of another subplot. Matplotlib does not currently have any sort of robust layout engine, as it is a design decision to minimize the amount of "magical plotting". We intend to let users have complete, 100% control over their p... | def example_plot(ax):
ax.plot([1, 2])
ax.set_xlabel('x-label', fontsize=16)
ax.set_ylabel('y-label', fontsize=8)
ax.set_title('Title', fontsize=24)
fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2)
example_plot(ax1)
example_plot(ax2)
example_plot(ax3)
example_plot(ax4)
# Enable fig.tight_... | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
GridSpecUnder the hood, Matplotlib utilizes [`GridSpec`](http://matplotlib.org/api/gridspec_api.html) to lay out the subplots. While `plt.subplots()` is fine for simple cases, sometimes you will need more advanced subplot layouts. In such cases, you should use GridSpec directly. GridSpec is outside the scope of this t... | fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, sharey=True)
ax1.plot([1, 2, 3, 4], [1, 2, 3, 4])
ax2.plot([3, 4, 5, 6], [6, 5, 4, 3])
plt.show() | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
"Twinning" axesSometimes one may want to overlay two plots on the same axes, but the scales may be entirely different. You can simply treat them as separate plots, but then twin them. | fig, ax1 = plt.subplots(1, 1)
ax1.plot([1, 2, 3, 4], [1, 2, 3, 4])
ax2 = ax1.twinx()
ax2.scatter([1, 2, 3, 4], [60, 50, 40, 30])
ax1.set(xlabel='X', ylabel='First scale')
ax2.set(ylabel='Other scale')
plt.show() | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
Axis SpinesSpines are the axis lines for a plot. Each plot can have four spines: "top", "bottom", "left" and "right". By default, they are set so that they frame the plot, but they can be individually positioned and configured via the [`set_position()`](http://matplotlib.org/api/spines_api.htmlmatplotlib.spines.Spine.... | fig, ax = plt.subplots()
ax.plot([-2, 2, 3, 4], [-10, 20, 25, 5])
ax.spines['top'].set_visible(False)
ax.xaxis.set_ticks_position('bottom') # no ticklines at the top
ax.spines['right'].set_visible(False)
ax.yaxis.set_ticks_position('left') # no ticklines on the right
# "outward"
# Move the two remaining spines "out"... | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
Exercise 4.2This one is a bit trickier. Once again, try to reproduce the figure below:A few key hints: The two subplots have no vertical space between them (this means that the `hspace` is `0`). Note that the bottom spine is at 0 in data coordinates and the tick lines are missing from the right and top sides.Because ... | import matplotlib.pyplot as plt
import numpy as np
# Try to reproduce the figure shown in images/exercise_4.2.png
# This one is a bit trickier!
# Here's the data...
data = [('dogs', 4, 4), ('frogs', -3, 1), ('cats', 1, 5), ('goldfish', -2, 2)]
animals, friendliness, popularity = zip(*data)
%load solutions/4.2-spines_... | _____no_output_____ | CC-BY-4.0 | anatomy-of-matplotlib-scipyconf-2018/04-limits-legends-and-layouts.ipynb | dlimpid/np-mpl-pd-nims-moderator-2019-04 |
Matplot normal usage and example | import matplotlib.pyplot as plt
%matplotlib inline
import numpy as np
x = np.linspace(0,5, 11)
y = x ** 2
x
y
plt.plot(x,y,"black")
plt.xlabel("x label")
plt.ylabel("y label")
plt.title("title")
plt.show()
plt.subplot(1, 2, 1)
plt.plot(x,y, "b")
plt.subplot(2, 2, 2)
plt.plot(y, x, "r")
fig = plt.figure()
axes = fig.... | _____no_output_____ | MIT | Data Visualization/Matplot/matplot_usage.ipynb | PS3132/pyDS_ML_bootcamp |
Figure Size and DPI | fig, axes = plt.subplots(figsize=(8,2))
ax = fig.add_axes([0,0,1,1])
ax.plot(x,y)
fig, axes = plt.subplots(figsize=(8,2), dpi=100)
ax = fig.add_axes([0,0,1,1])
ax.plot(x,y)
fig, axes = plt.subplots(nrows=2, ncols =1, figsize=(8,2))
axes[0].plot(x,y)
axes[1].plot(y,x)
plt.tight_layout()
fig
fig.savefig("axis plot", dpi... | _____no_output_____ | MIT | Data Visualization/Matplot/matplot_usage.ipynb | PS3132/pyDS_ML_bootcamp |
Plot Color and decoration | fig = plt.figure()
ax = fig.add_axes([0,0,1,1])
ax.plot(x, y, "#000000", lw=3, linestyle="--", marker="o", markersize=20,
markerfacecolor="yellow", markeredgewidth=3, markeredgecolor="green") # rgb, hex #linewidth is lw
fig = plt.figure()
ax = fig.add_axes([0,0,1,1])
ax.plot(x,y, "r--")
ax.set_xlim([0,1])
a... | _____no_output_____ | MIT | Data Visualization/Matplot/matplot_usage.ipynb | PS3132/pyDS_ML_bootcamp |
Imports | import numpy as np
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from IPython import display
plt.style.use('seaborn-white') | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Read and process data. Download the file from this URL: https://drive.google.com/file/d/1UWWIi-sz9g0x3LFvkIZjvK1r2ZaCqgGS/view?usp=sharing | data = open('text.txt', 'r').read() | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Process data and calculate indices | chars = list(set(data))
data_size, X_size = len(data), len(chars)
print("Corona Virus article has %d characters, %d unique characters" %(data_size, X_size))
char_to_idx = {ch:i for i,ch in enumerate(chars)}
idx_to_char = {i:ch for i,ch in enumerate(chars)} | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Constants and Hyperparameters | Hidden_Layer_size = 10 #size of the hidden layer
Time_steps = 10 # Number of time steps (length of the sequence) used for training
learning_rate = 1e-1 # Learning Rate
weight_sd = 0.1 #Standard deviation of weights for initialization
z_size = Hidden_Layer_size + X_size #Size of concatenation(H, X) vector | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Activation Functions and Derivatives | def sigmoid(x): # sigmoid function
return # write your code here
def dsigmoid(y): # derivative of sigmoid function
return # write your code here
def tanh(x): # tanh function
return # write your code here
def dtanh(y): # derivative of tanh
return # write your code here | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Quiz Question 1What is the value of sigmoid(0) calculated from your code? (Answer up to 1 decimal point, e.g. 4.2 and NOT 4.29999999, no rounding off). Quiz Question 2What is the value of dsigmoid(sigmoid(0)) calculated from your code?? (Answer up to 2 decimal point, e.g. 4.29 and NOT 4.29999999, no rounding off). Q... | class Param:
def __init__(self, name, value):
self.name = name
self.v = value # parameter value
self.d = np.zeros_like(value) # derivative
self.m = np.zeros_like(value) # momentum for Adagrad | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
We use random weights with normal distribution (0, weight_sd) for tanh activation function and (0.5, weight_sd) for `sigmoid` activation function.Biases are initialized to zeros. LSTM You are making this network, please note f, i, c and o (also "v") in the image below::
self.W_f = Param('W_f', np.random.randn(size_a, size_b) * weight_sd + 0.5)
self.b_f = Param('b_f', np.zeros((size_a, 1)))
self.W_i = Param('W_i', np.random.... | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Look at these operations which we'll be writing:**Concatenation of h and x:**$z\:=\:\left[h_{t-1},\:x\right]$$f_t=\sigma\left(W_f\cdot z\:+\:b_f\:\right)$$i_i=\sigma\left(W_i\cdot z\:+\:b_i\right)$$\overline{C_t}=\tanh\left(W_C\cdot z\:+\:b_C\right)$$C_t=f_t\ast C_{t-1}+i_t\ast \overline{C}_t$$o_t=\sigma\left(W_o\cdot ... | def forward(x, h_prev, C_prev, p = parameters):
assert x.shape == (X_size, 1)
assert h_prev.shape == (Hidden_Layer_size, 1)
assert C_prev.shape == (Hidden_Layer_size, 1)
z = np.row_stack((h_prev, x))
f = # write your code here
i = # write your code here
C_bar = # write your code here
... | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
You must finish the function above before you can attempt the questions below. Quiz Question 5What is the output of 'print(len(forward(np.zeros((X_size, 1)), np.zeros((Hidden_Layer_size, 1)), np.zeros((Hidden_Layer_size, 1)), parameters)))'? Quiz Question 6. Assuming you have fixed the forward function, run this comm... | z, f, i, C_bar, C, o, h, v, y = forward(np.zeros((X_size, 1)), np.zeros((Hidden_Layer_size, 1)), np.zeros((Hidden_Layer_size, 1))) | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
BackpropagationHere we are defining the backpropagation. It's too complicated, here is the whole code. (Please note that this would work only if your earlier code is perfect). | def backward(target, dh_next, dC_next, C_prev,
z, f, i, C_bar, C, o, h, v, y,
p = parameters):
assert z.shape == (X_size + Hidden_Layer_size, 1)
assert v.shape == (X_size, 1)
assert y.shape == (X_size, 1)
for param in [dh_next, dC_next, C_prev, f, i, C_bar, C, o, h]:
... | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Forward and Backward Combined PassLet's first clear the gradients before each backward pass | def clear_gradients(params = parameters):
for p in params.all():
p.d.fill(0) | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Clip gradients to mitigate exploding gradients | def clip_gradients(params = parameters):
for p in params.all():
np.clip(p.d, -1, 1, out=p.d) | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Calculate and store the values in forward pass. Accumulate gradients in backward pass and clip gradients to avoid exploding gradients.input, target are list of integers, with character indexes.h_prev is the array of initial h at h−1 (size H x 1)C_prev is the array of initial C at C−1 (size H x 1)Returns loss, final... | def forward_backward(inputs, targets, h_prev, C_prev):
global paramters
# To store the values for each time step
x_s, z_s, f_s, i_s, = {}, {}, {}, {}
C_bar_s, C_s, o_s, h_s = {}, {}, {}, {}
v_s, y_s = {}, {}
# Values at t - 1
h_s[-1] = np.copy(h_prev)
C_s[-1] = np.copy(C_prev... | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Sample the next character | def sample(h_prev, C_prev, first_char_idx, sentence_length):
x = np.zeros((X_size, 1))
x[first_char_idx] = 1
h = h_prev
C = C_prev
indexes = []
for t in range(sentence_length):
_, _, _, _, C, _, h, _, p = forward(x, h, C)
idx = np.random.choice(range(X_size), p=p.ravel())
... | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Training (Adagrad)Update the graph and display a sample output | def update_status(inputs, h_prev, C_prev):
#initialized later
global plot_iter, plot_loss
global smooth_loss
# Get predictions for 200 letters with current model
sample_idx = sample(h_prev, C_prev, inputs[0], 200)
txt = ''.join(idx_to_char[idx] for idx in sample_idx)
# Clear and plot
... | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Update Parameters\begin{align}\theta_i &= \theta_i - \eta\frac{d\theta_i}{\sum dw_{\tau}^2} \\d\theta_i &= \frac{\partial L}{\partial \theta_i}\end{align} | def update_paramters(params = parameters):
for p in params.all():
p.m += p.d * p.d # Calculate sum of gradients
#print(learning_rate * dparam)
p.v += -(learning_rate * p.d / np.sqrt(p.m + 1e-8)) | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
To delay the keyboard interrupt to prevent the training from stopping in the middle of an iteration | # Exponential average of loss
# Initialize to a error of a random model
smooth_loss = -np.log(1.0 / X_size) * Time_steps
iteration, pointer = 0, 0
# For the graph
plot_iter = np.zeros((0))
plot_loss = np.zeros((0)) | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
Training Loop | iter = 1000
while iter > 0:
# Reset
if pointer + Time_steps >= len(data) or iteration == 0:
g_h_prev = np.zeros((Hidden_Layer_size, 1))
g_C_prev = np.zeros((Hidden_Layer_size, 1))
pointer = 0
inputs = ([char_to_idx[ch]
for ch in data[pointer: pointer + Time_steps]])
targets = ... | _____no_output_____ | MIT | NLP/Resources/EVA_P2S3.ipynb | piyushjain220/TSAI |
QE methods and QE_utilsIn this tutorial, we will explore various methods needed to handle Quantum Espresso (QE) calculations - to run them, prepare input, and extract output. All that will be done with the help of the **QE_methods** and **QE_utils** modules, which contains the following functions:**QE_methods*** cryst... | import os
import sys
import math
import copy
if sys.platform=="cygwin":
from cyglibra_core import *
elif sys.platform=="linux" or sys.platform=="linux2":
from liblibra_core import *
#from libra_py import *
from libra_py import units
from libra_py import QE_methods
from libra_py import QE_utils
from libra_py im... | /projects/academic/cyberwksp21/Software/Conda/Miniconda3/envs/libra/lib/python3.6/importlib/_bootstrap.py:219: RuntimeWarning: to-Python converter for std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > > already registered; second conversion method ignored.
ret... | CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
First, lets prepare the working directories and run simple SCF calculations to generate the output files | PWSCF = os.environ['PWSCF62']
# Setup the calculations
params = {}
# I run the calculations on laptop, so no BATCH system
params["BATCH_SYSTEM"] = None
# The number of processors to use
params["NP"] = 1
# The QE executable
params["EXE"] = F"{PWSCF}/pw.x"
# The executable to generate the wavefunction files
params["E... | _____no_output_____ | CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
1. run_qe(params, t, dirname0, dirname1)Use it to actually run the calculationsComment this out if you have already done the calculations | help(QE_methods.run_qe)
!pwd
os.chdir("wd")
QE_methods.run_qe(params, 0, "res", "res2")
os.chdir("../") | The time to run the QE calculations = 0.01
| CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
2. read_qe_schema(filename, verbose=0)Can be used to read the information about the completed run | pwd
info = QE_methods.read_qe_schema("wd/res/x0.save/data-file-schema.xml", verbose=0)
print(info)
nat = info["nat"]
R, F = info["coords"], info["forces"]
for at in range(nat):
print(F"Atom {at} \t {info['atom_labels'][at]} \t\
x={R.get(3*at+0):.5f}, y={R.get(3*at+1):.5f}, z={R.get(3*at+2):.5f}\
... | Atom 0 Li x=0.00000, y=0.00000, z=0.00000 fx=0.00000, fy=0.00000, fz=0.00000
Atom 1 H x=2.83459, y=0.00000, z=0.00000 fx=0.00000, fy=0.00000, fz=0.00000
| CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
3. read_qe_index(filename, orb_list, verbose=0)Is analogous to **read_qe_schema** in many regards, it just extracts a bit different info, including orbital energies.One would also need to specify which energy levels we want to extract, so one would need that info beforehands.In this example, we have just 4 electrons, ... | info2, all_e = QE_methods.read_qe_index("wd/res/x0.export/index.xml", [1,2,3,4], verbose=1)
print( info2)
print(all_e)
e_alp = all_e[0]
e_bet = all_e[1]
for i in range(4):
print(F"E_{i}^alpha = {e_alp.get(i,i).real:12.8f} \t E_{i}^beta = {e_bet.get(i,i).real:12.8f}") | E_0^alpha = -1.86244053 E_0^beta = -1.86219594
E_1^alpha = -0.16462949 E_1^beta = -0.16475681
E_2^alpha = -0.08691250 E_2^beta = -0.08650036
E_3^alpha = -0.04025010 E_3^beta = -0.04013592
| CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
4. read_qe_wfc_info(filename, verbose=0)Can be used to extract some descriptors of the wavefunctions produced | wfc_info1 = QE_methods.read_qe_wfc_info("wd/res/x0.export/wfc.1", verbose=1)
wfc_info2 = QE_methods.read_qe_wfc_info("wd/res/x0.export/wfc.2", verbose=1)
print(wfc_info1)
print(wfc_info2) | {'ngw': 36889, 'igwx': 36889, 'nbnd': 10, 'nspin': 2, 'gamma_only': 'F', 'ik': 1, 'nk': 2}
{'ngw': 36889, 'igwx': 36889, 'nbnd': 10, 'nspin': 2, 'gamma_only': 'F', 'ik': 2, 'nk': 2}
| CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
5. read_qe_wfc(filename, orb_list, verbose=0)Can be used to read in the actual wavefunctions produced | alpha = QE_methods.read_qe_wfc("wd/res/x0.export/wfc.1", [1,2,3,4], verbose=0)
beta = QE_methods.read_qe_wfc("wd/res/x0.export/wfc.2", [1,2,3,4], verbose=0)
print(alpha)
print(alpha.num_of_rows, alpha.num_of_cols)
print(beta)
print(beta.num_of_rows, beta.num_of_cols) | <liblibra_core.CMATRIX object at 0x7fae6817b340>
36889 4
<liblibra_core.CMATRIX object at 0x7fae3ffb3730>
36889 4
| CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
Orthogonality and normalizationBelow we can see that MO overlaps are almost orthonormal - the diagonal elements are coorectly 1.0But the off-diagonal elements are not quite 0.0Same is true for However, there is no any expectation about the orthogonality or normalization across the two sets | S_aa = alpha.H() * alpha
S_bb = beta.H() * beta
S_ab = alpha.H() * beta
def print_mat(X):
nr, nc = X.num_of_rows, X.num_of_cols
for i in range(nr):
line = ""
for j in range(nc):
line = line + "%8.5f " % (X.get(i,j).real)
print(line)
print("S_aa")
print_mat(S_a... | S_aa
1.00000 -0.08150 -0.04761 0.03307
-0.08150 1.00000 0.03712 -0.02467
-0.04761 0.03712 1.00000 -0.01177
0.03307 -0.02467 -0.01177 1.00000
S_bb
1.00000 -0.08093 -0.04785 0.03336
-0.08093 1.00000 0.03755 -0.02485
-0.04785 0.03755 1.00000 -0.01246
0.03336 -0.02485 -0.... | CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
6. QE_utils.orthogonalize_orbitals(C)Can be used to orthogonalize orbitals if they are not.So lets transform alpha and beta orbitals such they are now orthonormal within each set.The resulting orbitals are not orthonormal across the two sets still | alp = QE_utils.orthogonalize_orbitals(alpha)
bet = QE_utils.orthogonalize_orbitals(beta)
S_aa = alp.H() * alp
S_bb = bet.H() * bet
S_ab = alp.H() * bet
print("S_aa")
print_mat(S_aa)
print("S_bb")
print_mat(S_bb)
print("S_ab")
print_mat(S_ab) |
Testing if S is invertabile
[4, 1]
Det = (0.9881907434095535-8.072456740942809e-20j)
Testing if S is invertabile
[4, 1]
Det = (0.9883023952546621+8.762301957458487e-20j)
S_aa
1.00000 0.00000 0.00000 -0.00000
0.00000 1.00000 -0.00000 0.00000
0.00000 -0.00000 1.00000 0.00000
-0.00000 0.000... | CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
7. QE_utils.merge_orbitals(Ca, Cb)Sometimes (usually in the non-collinear case), we want to have a single set of orbitals (many are nearly doubly degenerate), not just alpha and beta components. We can prepare the single set from the spinor components using this function. In this example, we just gonna mimic non-colli... | C = QE_utils.merge_orbitals(alpha, beta)
S = C.H() * C
print_mat(S) | 1.00000 -0.08150 -0.04761 0.03307 0.17301 -0.01049 -0.00412 0.00214
-0.08150 1.00000 0.03712 -0.02467 -0.01635 0.15735 0.00452 -0.00236
-0.04761 0.03712 1.00000 -0.01177 -0.00102 -0.00083 -0.06732 0.00139
0.03307 -0.02467 -0.01177 1.00000 0.01173 -0.00747 -0.00248 0.2442... | CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
8. QE_utils.orthogonalize_orbitals2(Ca, Cb)This is a special orthogonalization procedure - the one for 2-component spinors. The inputs are assumed to be the components for each orbital. The orthogonalization works such that it is S_aa + S_bb = I | alpha = QE_methods.read_qe_wfc("wd/res/x0.export/wfc.1", [1,2,3,4], verbose=0)
beta = QE_methods.read_qe_wfc("wd/res/x0.export/wfc.2", [1,2,3,4], verbose=0)
alp, bet = QE_utils.orthogonalize_orbitals2(alpha, beta)
S_aa = alp.H() * alp
S_bb = bet.H() * bet
print("S_aa")
print_mat(S_aa)
print("S_bb")
print_mat(S_bb)
p... | S_aa
0.49999 -0.00014 0.00006 -0.00007
-0.00014 0.49999 -0.00010 0.00004
0.00006 -0.00010 0.50000 0.00016
-0.00007 0.00004 0.00016 0.50000
S_bb
0.50001 0.00014 -0.00006 0.00007
0.00014 0.50001 0.00010 -0.00004
-0.00006 0.00010 0.50000 -0.00016
0.00007 -0.00004 -0.... | CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
9. read_qe_wfc_grid(filename, verbose=0)Can be used to read the grid points for the given PW representation. | G1 = QE_methods.read_qe_wfc_grid("wd/res/x0.export/grid.1", verbose=0)
print(len(G1))
for i in range(10):
print(F"{i} \t {G1[i].x} \t {G1[i].y} \t {G1[i].z}") | 0 0.0 0.0 0.0
1 -1.0 0.0 0.0
2 1.0 0.0 0.0
3 -2.0 0.0 0.0
4 2.0 0.0 0.0
5 0.0 -1.0 0.0
6 0.0 0.0 -1.0
7 0.0 0.0 1.0
8 0.0 1.0 0.0
9 -1.0 -1.0 0.0
| CC0-1.0 | 5_interactive_qe/1_LiH/test_QE_methods.ipynb | compchem-cybertraining/Tutorials_QE_and_eQE |
`BondGraphTools` Modelling Network Bioenergetics.https://github.com/peter-cudmore/seminars/ANZIAM-2019 Dr. Peter Cudmore. Systems Biology Labratory, The School of Chemical and Biomedical Engineering, The University of Melbourne. In this talk i discuss* Problems in compartmental modelling of ... | # Reaction Network from BondGraphTools
reaction = Reaction_Network(
"S + B = P", name="One Step Reaction"
)
model = reaction.as_network_model()
# Basic Visualisation.
from BondGraphTools import draw
figure = draw(model, size=(8,6)) | _____no_output_____ | CC-BY-4.0 | ANZIAM-2019/ANZIAM Slides.ipynb | peter-cudmore/seminars |
Kinetic parameters from Network Thermodynamics. Partitions $S + B = P$ into _components_.1. Energy Storage Compartments: $S$, $B$ and $P$.2. Dissipative Processes: (The chemical reaction itself).3. Conservation Laws: (The flow from A is the flow from B and is equal to the flow into reaction). Gibbs Energy:$$\mathrm{d... | import BondGraphTools
help(BondGraphTools) | Help on package BondGraphTools:
NAME
BondGraphTools
DESCRIPTION
BondGraphTools
==============
BondGraphTools is a python library for symbolic modelling and control of multi-physics
systems using bond graphs. Bond graph modelling is a network base framework concerned
with the distribution of en... | CC-BY-4.0 | ANZIAM-2019/ANZIAM Slides.ipynb | peter-cudmore/seminars |
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