/usr/lib/python3/dist-packages/mdp/test/test_ISFANode.py is in python3-mdp 3.5-1ubuntu1.
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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 | from __future__ import division
from builtins import range
from past.utils import old_div
from ._tools import *
def _std(x):
return x.std(axis=0)
# standard deviation without bias
mx = mean(x, axis=0)
mx2 = mean(x*x, axis=0)
return numx.sqrt(old_div((mx2-mx),(x.shape[0]-1)))
def _cov(x,y=None):
#return covariance matrix for x and y
if y is None:
y = x.copy()
x = x - mean(x,0)
x = old_div(x, _std(x))
y = y - mean(y,0)
y = old_div(y, _std(y))
#return mult(numx.transpose(x),y)/(x.shape[0]-1)
return old_div(mult(numx.transpose(x),y),(x.shape[0]))
def testISFANodeGivensRotations():
ncovs = 5
dim = 7
ratio = uniform(2).tolist()
covs = [uniform((dim,dim)) for j in range(ncovs)]
covs= mdp.utils.MultipleCovarianceMatrices(covs)
covs.symmetrize()
i = mdp.nodes.ISFANode(list(range(1, ncovs+1)),sfa_ica_coeff=ratio,
icaweights=uniform(ncovs),
sfaweights=uniform(ncovs),
output_dim = dim-1, dtype="d")
i._adjust_ica_sfa_coeff()
ratio = i._bica_bsfa
# case 2: only one axis within output space
# get contrast using internal function
phi, cont1, min_, dummy =\
i._givens_angle_case2(dim-2,dim-1,covs,ratio,complete=1)
# get contrast using explicit rotations
cont2 = []
for angle in phi:
cp = covs.copy()
cp.rotate(angle,[dim-2,dim-1])
cont2.append(numx.sum(i._get_contrast(cp,ratio)))
assert_array_almost_equal(cont1,cont2,decimal)
# case 1: both axes within output space
# get contrast using internal function
phi,cont1, min_ , dummy =\
i._givens_angle_case1(0,1,covs,ratio,complete = 1)
# get contrast using explicit rotations
cont2 = []
for angle in phi:
cp = covs.copy()
cp.rotate(angle,[0,1])
cont2.append(numx.sum(i._get_contrast(cp,ratio)))
assert abs(min_) < old_div(numx.pi,4), 'Estimated Minimum out of bounds'
assert_array_almost_equal(cont1,cont2,decimal)
def testISFANode_SFAPart():
# create independent sources
mat = uniform((100000,3))*2-1
fmat = numx_fft.rfft(mat,axis=0)
# enforce different speeds
for i in range(3):
fmat[(i+1)*5000:,i] = 0.
mat = numx_fft.irfft(fmat,axis=0)
_sfanode = mdp.nodes.SFANode()
_sfanode.train(mat)
src = _sfanode.execute(mat)
# test with unmixed signals (i.e. the node should make nothing at all)
out = mdp.nodes.ISFANode(lags=1,
whitened=True,
sfa_ica_coeff=[1.,0.])(src)
max_cv = numx.diag(abs(_cov(out,src)))
assert_array_almost_equal(max_cv, numx.ones((3,)),5)
# mix linearly the signals
mix = mult(src,uniform((3,3))*2-1)
out = mdp.nodes.ISFANode(lags=1,
whitened=False,
sfa_ica_coeff=[1.,0.])(mix)
max_cv = numx.diag(abs(_cov(out,src)))
assert_array_almost_equal(max_cv, numx.ones((3,)),5)
def testISFANode_ICAPart():
# create independent sources
src = uniform((100000,3))*2-1
fsrc = numx_fft.rfft(src,axis=0)
# enforce different speeds
for i in range(3):
fsrc[(i+1)*5000:,i] = 0.
src = numx_fft.irfft(fsrc,axis=0)
# enforce time-lag-1-independence
src = mdp.nodes.ISFANode(lags=1, sfa_ica_coeff=[1.,0.])(src)
out = mdp.nodes.ISFANode(lags=1,
whitened=True,
sfa_ica_coeff=[0.,1.])(src)
max_cv = numx.diag(abs(_cov(out,src)))
assert_array_almost_equal(max_cv, numx.ones((3,)),5)
# mix linearly the signals
mix = mult(src,uniform((3,3))*2-1)
out = mdp.nodes.ISFANode(lags=1,
whitened=False,
sfa_ica_coeff=[0.,1.])(mix)
max_cv = numx.diag(abs(_cov(out,src)))
assert_array_almost_equal(max_cv, numx.ones((3,)),5)
def testISFANode_3Complete():
# test transition from ica to sfa behavior of isfa
# use ad hoc sources
lag = 25
src = numx.zeros((1001,3),"d")
idx = [(2,4),(80,1),(2+lag,6)]
for i in range(len(idx)):
i0, il = idx[i]
src[i0:i0+il,i] = 1.
src[i0+il:i0+2*il,i] = -1.
src[:,i] -= mean(src[:,i])
src[:,i] /= std(src[:,i])
# test extreme cases
# case 1: ICA
out = mdp.nodes.ISFANode(lags=[1,lag],
icaweights=[1.,1.],
sfaweights=[1.,0.],
output_dim=2,
whitened=True,
sfa_ica_coeff=[1E-4,1.])(src)
cv = abs(_cov(src,out))
idx_cv = numx.argmax(cv,axis=0)
assert_array_equal(idx_cv,[2,1])
max_cv = numx.amax(cv,axis=0)
assert_array_almost_equal(max_cv, numx.ones((2,)),5)
# case 2: SFA
out = mdp.nodes.ISFANode(lags=[1,lag],
icaweights=[1.,1.],
sfaweights=[1.,0.],
output_dim=2,
whitened=True,
sfa_ica_coeff=[1.,0.])(src)
cv = abs(_cov(src,out))
idx_cv = numx.argmax(cv,axis=0)
assert_array_equal(idx_cv,[2,0])
max_cv = numx.amax(cv,axis=0)
assert_array_almost_equal(max_cv, numx.ones((2,)),5)
def _ISFA_analytical_solution( nsources, nmat, dim, ica_ambiguity):
# build a sequence of random diagonal matrices
matrices = [numx.eye(dim, dtype='d')]*nmat
# build first matrix:
# - create random diagonal with elements
# in [0, 1]
diag = uniform(dim)
# - sort it in descending order (in absolute value)
# [large first]
diag = numx.take(diag, numx.argsort(abs(diag)))[::-1]
# - save larger elements [sfa solution]
sfa_solution = diag[:nsources].copy()
# - modify diagonal elements order to allow for a
# different solution for isfa:
# create index array
idx = list(range(0,dim))
# take the second slowest element and put it at the end
idx = [idx[0]]+idx[2:]+[idx[1]]
diag = numx.take(diag, idx)
# - save isfa solution
isfa_solution = diag[:nsources]
# - set the first matrix
matrices[0] = matrices[0]*diag
# build other matrices
diag_dim = nsources+ica_ambiguity
for i in range(1,nmat):
# get a random symmetric matrix
matrices[i] = mdp.utils.symrand(dim)
# diagonalize the subspace diag_dim
tmp_diag = (uniform(diag_dim)-0.5)*2
matrices[i][:diag_dim,:diag_dim] = numx.diag(tmp_diag)
# put everything in MultCovMat
matrices = mdp.utils.MultipleCovarianceMatrices(matrices)
return matrices, sfa_solution, isfa_solution
def _ISFA_unmixing_error( nsources, goal, estimate):
check = mult(goal[:nsources,:], estimate[:,:nsources])
error = (abs(numx.sum(numx.sum(abs(check),axis=1)-1))+
abs(numx.sum(numx.sum(abs(check),axis=0)-1)))
error /= nsources*nsources
return error
def testISFANode_AnalyticalSolution():
nsources = 2
# number of time lags
nmat = 20
# degree of polynomial expansion
deg = 3
# sfa_ica coefficient
sfa_ica_coeff = [1., 1.]
# how many independent subspaces in addition to the sources
ica_ambiguity = 2
# dimensions of expanded space
dim = mdp.nodes._expanded_dim(deg, nsources)
assert (nsources+ica_ambiguity) < dim, 'Too much ica ambiguity.'
trials = 20
for trial in range(trials):
# get analytical solution:
# prepared matrices, solution for sfa, solution for isf
covs,sfa_solution,isfa_solution=_ISFA_analytical_solution(
nsources,nmat,dim,ica_ambiguity)
# get contrast of analytical solution
# sfasrc, icasrc = _get_matrices_contrast(covs, nsources, dim,
# sfa_ica_coeff)
# set rotation matrix
R = mdp.utils.random_rot(dim)
covs_rot = covs.copy()
# rotate the analytical solution
covs_rot.transform(R)
# find the SFA solution to initialize ISFA
eigval, SFARP = mdp.utils.symeig(covs_rot.covs[:,:,0])
# order SFA solution by slowness
SFARP = SFARP[:,-1::-1]
# run ISFA
isfa = mdp.nodes.ISFANode(lags = covs_rot.ncovs, whitened=True,
sfa_ica_coeff = sfa_ica_coeff,
eps_contrast = 1e-7,
output_dim = nsources,
max_iter = 500,
verbose = False,
RP = SFARP)
isfa.train(uniform((100,dim)))
isfa.stop_training(covs = covs_rot.copy())
# check that the rotation matrix found by ISFA is R
# up to a permutation matrix.
# Unmixing error as in Tobias paper
error = _ISFA_unmixing_error(nsources, R, isfa.RPC)
if error < 1E-4:
break
assert error < 1E-4, 'None out of the %d trials succeded.' % trials
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