def testPCAToolsPCA(self):
from PyMca5.PyMcaMath.mva.PCATools import numpyPCA
x = numpy.array([[0.0, 2.0, 3.0],
[3.0, 0.0, -1.0],
[4.0, -4.0, 4.0],
[4.0, 4.0, 4.0]])
# that corresponds to 4 spectra of 3 channels
nSpectra = x.shape[0]
# calculate eigenvalues and eigenvectors with numpy
tmpArray = numpy.dot(x.T, x)/(nSpectra - 1)
numpyEigenvalues, numpyEigenvectors = numpy.linalg.eigh(tmpArray)
# sort from higher to lower
idx = list(range(numpyEigenvalues.shape[0]-1, -1 , -1))
numpyEigenvalues = numpy.take(numpyEigenvalues, idx)
numpyEigenvectors = numpyEigenvectors[:, ::-1].T
# now use PyMca
# centering has to be false to obtain the same results
ncomp = x.shape[1]
for force in [True, False]:
images, eigenvalues, eigenvectors = numpyPCA(x,
ncomponents=ncomp,
force=force,
center=False,
scale=False)
self.assertTrue(numpy.allclose(eigenvalues, numpyEigenvalues))
for i in range(ncomp):
if (eigenvectors[i,0] >= 0 and numpyEigenvectors[i,0] >=0) or\
(eigenvectors[i,0] <= 0 and numpyEigenvectors[i,0] <=0):
# both same sign
self.assertTrue(numpy.allclose(eigenvectors[i],
numpyEigenvectors[i]))
else:
self.assertTrue(numpy.allclose(-eigenvectors[i],
numpyEigenvectors[i]))
# test with a different shape
x.shape = 2, 2, -1
ncomp = 3
for force in [True, False]:
images, eigenvalues, eigenvectors = numpyPCA(x,
ncomponents=ncomp,
force=force,
center=False,
scale=False)
self.assertTrue(numpy.allclose(eigenvalues, numpyEigenvalues))
for i in range(ncomp):
if (eigenvectors[i,0] >= 0 and numpyEigenvectors[i,0] >=0) or\
(eigenvectors[i,0] <= 0 and numpyEigenvectors[i,0] <=0):
# both same sign
self.assertTrue(numpy.allclose(eigenvectors[i],
numpyEigenvectors[i]))
else:
self.assertTrue(numpy.allclose(-eigenvectors[i],
numpyEigenvectors[i]))
def testPCAToolsMDP(self):
from PyMca5.PyMcaMath.mva.PCATools import getCovarianceMatrix, numpyPCA
x = numpy.array([[0.0, 2.0, 3.0],
[3.0, 0.0, -1.0],
[4.0, -4.0, 4.0],
[4.0, 4.0, 4.0]])
# use mdp
pcaNode = mdp.nodes.PCANode()
pcaNode.train(x)
pcaNode.stop_training()
pcaEigenvectors = pcaNode.v.T
# and compare with PyMca
ncomp = x.shape[1]
for force in [True, False]:
images, eigenvalues, eigenvectors = numpyPCA(x,
ncomponents=ncomp,
force=force,
center=True,
scale=False)
# the eigenvalues must be the same
self.assertTrue(numpy.allclose(eigenvalues, pcaNode.d))
# the eigenvectors can be multiplied by -1
for i in range(ncomp):
if (eigenvectors[i,0] >= 0 and pcaEigenvectors[i,0] >=0) or\
(eigenvectors[i,0] <= 0 and pcaEigenvectors[i,0] <=0):
# both same sign
self.assertTrue(numpy.allclose(eigenvectors[i],
pcaEigenvectors[i]))
else:
self.assertTrue(numpy.allclose(-eigenvectors[i],
pcaEigenvectors[i]))
def testPCAToolsMDP(self):
from PyMca5.PyMcaMath.mva.PCATools import getCovarianceMatrix, numpyPCA
x = numpy.array([[0.0, 2.0, 3.0],
[3.0, 0.0, -1.0],
[4.0, -4.0, 4.0],
[4.0, 4.0, 4.0]])
# use mdp
pcaNode = mdp.nodes.PCANode()
pcaNode.train(x)
pcaNode.stop_training()
pcaEigenvectors = pcaNode.v.T
# and compare with PyMca
for force in [True, False]:
images, eigenvalues, eigenvectors = numpyPCA(x,
ncomponents=x.shape[1],
force=force,
center=True,
scale=False)
# the eigenvalues must be the same
self.assertTrue(numpy.allclose(eigenvalues, pcaNode.d))
# the eigenvectors can be multiplied by -1
for i in range(x.shape[1]):
if (eigenvectors[i,0] >= 0 and pcaEigenvectors[i,0] >=0) or\
(eigenvectors[i,0] <= 0 and pcaEigenvectors[i,0] <=0):
# both same sign
self.assertTrue(numpy.allclose(eigenvectors[i],
pcaEigenvectors[i]))
else:
self.assertTrue(numpy.allclose(-eigenvectors[i],
pcaEigenvectors[i]))
def testPCAToolsPCA(self):
from PyMca5.PyMcaMath.mva.PCATools import numpyPCA
x = numpy.array([[0.0, 2.0, 3.0],
[3.0, 0.0, -1.0],
[4.0, -4.0, 4.0],
[4.0, 4.0, 4.0]])
# that corresponds to 4 spectra of 3 channels
nSpectra = x.shape[0]
# calculate eigenvalues and eigenvectors with numpy
tmpArray = numpy.dot(x.T, x)/(nSpectra - 1)
numpyEigenvalues, numpyEigenvectors = numpy.linalg.eigh(tmpArray)
# sort from higher to lower
idx = list(range(numpyEigenvalues.shape[0]-1, -1 , -1))
numpyEigenvalues = numpy.take(numpyEigenvalues, idx)
numpyEigenvectors = numpyEigenvectors[:, ::-1].T
# now use PyMca
# centering has to be false to obtain the same results
for force in [True, False]:
images, eigenvalues, eigenvectors = numpyPCA(x,
ncomponents=x.shape[1],
force=force,
center=False,
scale=False)
self.assertTrue(numpy.allclose(eigenvalues, numpyEigenvalues))
self.assertTrue(numpy.allclose(eigenvectors, numpyEigenvectors))
# test with a different shape
x.shape = 2, 2, -1
for force in [True, False]:
images, eigenvalues, eigenvectors = numpyPCA(x,
ncomponents=3,
force=force,
center=False,
scale=False)
self.assertTrue(numpy.allclose(eigenvalues, numpyEigenvalues))
self.assertTrue(numpy.allclose(eigenvectors, numpyEigenvectors))
