File size: 5,680 Bytes
095b0c2 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 |
#!/usr/bin/env python
# encoding: utf-8
"""
Author(s): Matthew Loper
See LICENCE.txt for licensing and contact information.
"""
import time
from numpy import *
import unittest
from . import ch
from .optimization import minimize
from .ch import Ch
import numpy as np
from scipy.optimize import rosen, rosen_der
from .utils import row, col
visualize = False
def Rosen():
args = {
'x1': Ch(-120.),
'x2': Ch(-100.)
}
r1 = Ch(lambda x1, x2 : (x2 - x1**2.) * 10., args)
r2 = Ch(lambda x1 : x1 * -1. + 1, args)
func = [r1, r2]
return func, [args['x1'], args['x2']]
class Madsen(Ch):
dterms = ('x',)
def compute_r(self):
x1 = self.x.r[0]
x2 = self.x.r[1]
result = np.array((
x1**2 + x2**2 + x1 * x2,
np.sin(x1),
np.cos(x2)
))
return result
def compute_dr_wrt(self, wrt):
if wrt is not self.x:
return None
jac = np.zeros((3,2))
x1 = self.x.r[0]
x2 = self.x.r[1]
jac[0,0] = 2. * x1 + x2
jac[0,1] = 2. * x2 + x1
jac[1,0] = np.cos(x1)
jac[1,1] = 0
jac[2,0] = 0
jac[2,1] = -np.sin(x2)
return jac
def set_and_get_r(self, x_in):
self.x = Ch(x_in)
return col(self.r)
def set_and_get_dr(self, x_in):
self.x = Ch(x_in)
return self.dr_wrt(self.x)
class RosenCh(Ch):
dterms = ('x',)
def compute_r(self):
result = np.array((rosen(self.x.r) ))
return result
def set_and_get_r(self, x_in):
self.x = Ch(x_in)
return col(self.r)
def set_and_get_dr(self, x_in):
self.x = Ch(x_in)
return self.dr_wrt(self.x).flatten()
def compute_dr_wrt(self, wrt):
if wrt is self.x:
if visualize:
import matplotlib.pyplot as plt
residuals = np.sum(self.r**2)
print('------> RESIDUALS %.2e' % (residuals,))
print('------> CURRENT GUESS %s' % (str(self.x.r),))
plt.figure(123)
if not hasattr(self, 'vs'):
self.vs = []
self.xs = []
self.ys = []
self.vs.append(residuals)
self.xs.append(self.x.r[0])
self.ys.append(self.x.r[1])
plt.clf();
plt.subplot(1,2,1)
plt.plot(self.vs)
plt.subplot(1,2,2)
plt.plot(self.xs, self.ys)
plt.draw()
return row(rosen_der(self.x.r))
class TestOptimization(unittest.TestCase):
def test_dogleg_rosen(self):
obj, freevars = Rosen()
minimize(fun=obj, x0=freevars, method='dogleg', options={'maxiter': 337, 'disp': False})
self.assertTrue(freevars[0].r[0]==1.)
self.assertTrue(freevars[1].r[0]==1.)
def test_dogleg_madsen(self):
obj = Madsen(x = Ch(np.array((3.,1.))))
minimize(fun=obj, x0=[obj.x], method='dogleg', options={'maxiter': 34, 'disp': False})
self.assertTrue(np.sum(obj.r**2)/2 < 0.386599528247)
@unittest.skip('negative sign in exponent screws with reverse mode')
def test_bfgs_rosen(self):
from .optimization import minimize_bfgs_lsq
obj, freevars = Rosen()
minimize_bfgs_lsq(obj=obj, niters=421, verbose=False, free_variables=freevars)
self.assertTrue(freevars[0].r[0]==1.)
self.assertTrue(freevars[1].r[0]==1.)
def test_bfgs_madsen(self):
from .ch import SumOfSquares
import scipy.optimize
obj = Ch(lambda x : SumOfSquares(Madsen(x = x)) )
def errfunc(x):
obj.x = Ch(x)
return obj.r
def gradfunc(x):
obj.x = Ch(x)
return obj.dr_wrt(obj.x).ravel()
x0 = np.array((3., 1.))
# Optimize with built-in bfgs.
# Note: with 8 iters, this actually requires 14 gradient evaluations.
# This can be verified by setting "disp" to 1.
#tm = time.time()
x1 = scipy.optimize.fmin_bfgs(errfunc, x0, fprime=gradfunc, maxiter=8, disp=0)
#print 'forward: took %.es' % (time.time() - tm,)
self.assertLess(obj.r/2., 0.4)
# Optimize with chumpy's minimize (which uses scipy's bfgs).
obj.x = x0
minimize(fun=obj, x0=[obj.x], method='bfgs', options={'maxiter': 8, 'disp': False})
self.assertLess(obj.r/2., 0.4)
def test_nested_select(self):
def beales(x, y):
e1 = 1.5 - x + x*y
e2 = 2.25 - x + x*(y**2)
e3 = 2.625 - x + x*(y**3)
return {'e1': e1, 'e2': e2, 'e3': e3}
x1 = ch.zeros(10)
y1 = ch.zeros(10)
# With a single select this worked
minimize(beales(x1, y1), x0=[x1[1:4], y1], method='dogleg', options={'disp': False})
x2 = ch.zeros(10)
y2 = ch.zeros(10)
# But this used to raise `AttributeError: 'Select' object has no attribute 'x'`
minimize(beales(x2, y2), x0=[x2[1:8][:3], y2], method='dogleg', options={'disp': False})
np.testing.assert_array_equal(x1, x2)
np.testing.assert_array_equal(y1, y2)
suite = unittest.TestLoader().loadTestsFromTestCase(TestOptimization)
if __name__ == '__main__':
if False: # show rosen
import matplotlib.pyplot as plt
visualize = True
plt.ion()
unittest.main()
import pdb; pdb.set_trace()
else:
unittest.main()
|