/usr/lib/python3/dist-packages/mdp/test/test_ISFANode.py is in python3-mdp 3.5-1.
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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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