def testPCA(self):
# " test the PCA calculation "
eVals, eVects = Stats.PrincipalComponents(self.d)
tVals = numpy.array([1.76877414, 0.92707592, 0.30414995])
tVect = numpy.array([[-0.64200458, -0.66321742, 0.38467229],
[0.34166917, 0.20166619, 0.91792861],
[-0.68636164, 0.72074503, 0.09713033]])
assert max((abs(eVals - tVals)).ravel()) < FLOAT_TOL, 'bad variances from PCA'
for i in range(eVects.shape[0]):
assert (max((abs(eVects[i] - tVect[i])).ravel()) < FLOAT_TOL or
max((abs(eVects[i] + tVect[i])).ravel()) < FLOAT_TOL), 'bad vectors from PCA'
def testTransform2(self):
""" testing that rotation of points into PCA frame
doesn't change dot products
"""
self.d = numpy.array(
[[1, 2.068703704, 2.040555556, 2.068703704, 2.141782407, 7.46],
[2, 1.48537037, -0.186756425, 1.48537037, 1.803819444, 8.16],
[3, 1.917469136, 0.785465797, 1.917469136, 2.046875, 8.68],
[4, 2.068703704, 1.125743575, 2.068703704, 2.131944444, 8.89],
[5, 2.138703704, 1.283243575, 2.138703704, 2.171319444, 9.25],
[6, 2.152037037, 1.313243575, 2.152037037, 2.178819444, 9.3],
[7, 1.730740741, 1.457222222, -0.179901738, 1.558449074, 7.52],
[8, 1.973796296, 1.889320988, 0.792320484, 1.99054784, 8.16],
[9, 2.058865741, 2.040555556, 1.132598262, 2.141782407, 8.3],
[10, 2.098240741, 2.110555556, 1.290098262, 2.211782407, 8.4],
[11, 2.105740741, 2.123888889, 1.320098262, 2.225115741, 8.46],
[12, 1.390462963, -0.37502803, 0.171950113, 1.652584877, 8.19],
[13, 1.475532407, -0.223793462, 0.512227891, 1.803819444, 8.57],
[14, 1.522407407, -0.140460128, 0.699727891, 1.887152778, 8.82],
[15, 1.822561728, 0.597194192, 0.604048879, 1.895640432, 8.89],
[16, 1.907631173, 0.74842876, 0.944326657, 2.046875, 8.92],
[17, 1.954506173, 0.831762094, 1.131826657, 2.130208333, 8.96],
[18, 1.973796296, 0.93747197, 0.755283447, 1.980709877, 9],
[19, 2.058865741, 1.088706538, 1.095561224, 2.131944444, 9.35],
[20, 2.105740741, 1.172039872, 1.283061224, 2.215277778, 9.22],
[21, 2.189074074, 1.359539872, 1.366394558, 2.262152778, 9.3],
[22, 2.142199074, 1.276206538, 1.178894558, 2.178819444, 9.52]],
'd')
self.d = self.d[:, 1:-2]
eVals, eVects = Stats.PrincipalComponents(self.d)
pts = Stats.TransformPoints(eVects, self.d)
avg = sum(self.d) / len(self.d)
self.d -= avg
for i in range(len(pts)):
for j in range(len(pts)):
vi = self.d[i]
vi /= numpy.sqrt(numpy.dot(vi, vi))
vj = self.d[j]
vj /= numpy.sqrt(numpy.dot(vj, vj))
pvi = pts[i]
pvi /= numpy.sqrt(numpy.dot(pvi, pvi))
pvj = pts[j]
pvj /= numpy.sqrt(numpy.dot(pvj, pvj))
assert feq(numpy.dot(vi, vj), numpy.dot(
pvi, pvj)), 'bad dot: %4.4f %4.4f' % (numpy.dot(
vi, vj), numpy.dot(pvi, pvj))
def testTransform(self):
" test transformation to PCA frame "
eVals, eVects = Stats.PrincipalComponents(self.d)
pts = Stats.TransformPoints(eVects, self.d)
p0 = numpy.array([-1.12488653, -1.84061768, -0.1294482])
p3 = numpy.array([-3.82295273, -3.09754194, 0.24549203])
p5 = numpy.array([2.29785176, 3.4726933, -0.36094115])
assert max(abs(pts[0] -
p0)) < FLOAT_TOL, 'p0 comparison failed %s!=%s' % (str(
pts[0]), str(p0))
assert max(abs(pts[3] -
p3)) < FLOAT_TOL, 'p3 comparison failed %s!=%s' % (str(
pts[3]), str(p3))
assert max(abs(pts[5] -
p5)) < FLOAT_TOL, 'p5 comparison failed %s!=%s' % (str(
pts[5]), str(p5))
def testTransform(self):
# " test transformation to PCA frame "
_, eVects = Stats.PrincipalComponents(self.d)
pts = Stats.TransformPoints(eVects, self.d)
refPs = [numpy.array([-1.20362098, -1.79265006, 0.08776266]),
numpy.array([4.63540648, 1.1669869, 0.47026415]),
numpy.array([0.8709456, -0.50012821, 0.24763993]),
numpy.array([-3.94140499, -2.88350573, 0.64863041]),
numpy.array([-0.97015382, 2.42239972, 0.51066736]),
numpy.array([2.43084762, 3.3115892, -0.77094542]),
numpy.array([0.74360559, -2.67765459, 0.73974091]),
numpy.array([-1.2274861, 3.6819975, -0.07856395]),
numpy.array([-0.4342764, 0.04320715, 0.28202332]),
numpy.array([-0.903863, -2.77224188, -2.13721937])]
p0 = refPs[0]
p3 = refPs[3]
p5 = refPs[5]
assert max(abs(pts[0] - p0)) < FLOAT_TOL, 'p0 comparison failed %s!=%s' % (str(pts[0]), str(p0))
assert max(abs(pts[3] - p3)) < FLOAT_TOL, 'p3 comparison failed %s!=%s' % (str(pts[3]), str(p3))
assert max(abs(pts[5] - p5)) < FLOAT_TOL, 'p5 comparison failed %s!=%s' % (str(pts[5]), str(p5))