def test_reflection(self, rep=10):
for i in range(rep):
from mvpa2.testing.datasets import get_random_rotation
d = np.random.random((100, 2))
T = get_random_rotation(d.shape[1])
d2 = np.dot(d, T)
# scale it up a bit
d2 *= 1.2
# add a reflection by flipping the first dimension
d2[:, 0] *= -1
ds = dataset_wizard(samples=d, targets=d2)
norm0 = np.linalg.norm(d - d2)
mapper = ProcrusteanMapper(scaling=False, reflection=False)
mapper.train(ds)
norm1 = np.linalg.norm(d2 - mapper.forward(ds).samples)
eps = 1e-7
self.assertLess(norm1,
norm0 + eps,
msg='Procrustes should reduce difference, '
'but %f > %f' % (norm1, norm0))
mapper = ProcrusteanMapper(scaling=True, reflection=False)
mapper.train(ds)
norm2 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(norm2,
norm1 + eps,
msg='Procrustes with scaling should work better, '
'but %f > %f' % (norm2, norm1))
mapper = ProcrusteanMapper(scaling=False, reflection=True)
mapper.train(ds)
norm3 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(
norm3,
norm1 + eps,
msg='Procrustes with reflection should work better, '
'but %f > %f' % (norm3, norm1))
mapper = ProcrusteanMapper(scaling=True, reflection=True)
mapper.train(ds)
norm4 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(norm4,
norm3 + eps,
msg='Procrustes with scaling should work better, '
'but %f > %f' % (norm4, norm3))
self.assertLess(
norm4,
norm2 + eps,
msg='Procrustes with reflection should work better, '
'but %f > %f' % (norm4, norm2))
def test_reflection(self, rep=10):
for i in range(rep):
from mvpa2.testing.datasets import get_random_rotation
d = np.random.random((100, 2))
T = get_random_rotation(d.shape[1])
d2 = np.dot(d, T)
# scale it up a bit
d2 *= 1.2
# add a reflection by flipping the first dimension
d2[:, 0] *= -1
ds = dataset_wizard(samples=d, targets=d2)
norm0 = np.linalg.norm(d - d2)
mapper = ProcrusteanMapper(scaling=False, reflection=False)
mapper.train(ds)
norm1 = np.linalg.norm(d2 - mapper.forward(ds).samples)
eps = 1e-7
self.assertLess(norm1, norm0 + eps,
msg='Procrustes should reduce difference, '
'but %f > %f' % (norm1, norm0))
mapper = ProcrusteanMapper(scaling=True, reflection=False)
mapper.train(ds)
norm2 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(norm2, norm1 + eps,
msg='Procrustes with scaling should work better, '
'but %f > %f' % (norm2, norm1))
mapper = ProcrusteanMapper(scaling=False, reflection=True)
mapper.train(ds)
norm3 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(norm3, norm1 + eps,
msg='Procrustes with reflection should work better, '
'but %f > %f' % (norm3, norm1))
mapper = ProcrusteanMapper(scaling=True, reflection=True)
mapper.train(ds)
norm4 = np.linalg.norm(d2 - mapper.forward(ds).samples)
self.assertLess(norm4, norm3 + eps,
msg='Procrustes with scaling should work better, '
'but %f > %f' % (norm4, norm3))
self.assertLess(norm4, norm2 + eps,
msg='Procrustes with reflection should work better, '
'but %f > %f' % (norm4, norm2))
def mds_withprocrust(a, t, **kwargs):
# data should already be in the needed scale -- we just care about
# rotation, shift, reflection
pm = ProcrusteanMapper(reflection=True,
scaling=False,
reduction=False,
oblique=False)
a_ = mdsf(a, **kwargs)
ds = dataset_wizard(a_, targets=t)
pm.train(ds)
return pm.forward(a_)
def test_simple(self, oblique):
d_orig = datasets['uni2large'].samples
d_orig2 = datasets['uni4large'].samples
for sdim, nf_s, nf_t, full_test \
in (('Same 2D', 2, 2, True),
('Same 10D', 10, 10, True),
('2D -> 3D', 2, 3, True),
('3D -> 2D', 3, 2, False)):
# figure out some "random" rotation
d = max(nf_s, nf_t)
R = get_random_rotation(nf_s, nf_t, d_orig)
if nf_s == nf_t:
adR = np.abs(1.0 - np.linalg.det(R))
self.failUnless(adR < 1e-10,
"Determinant of rotation matrix should "
"be 1. Got it 1+%g" % adR)
self.failUnless(norm(np.dot(R, R.T)
- np.eye(R.shape[0])) < 1e-10)
for s, scaling in ((0.3, True), (1.0, False)):
pm = ProcrusteanMapper(scaling=scaling, oblique=oblique)
pm2 = ProcrusteanMapper(scaling=scaling, oblique=oblique)
t1, t2 = d_orig[23, 1], d_orig[22, 1]
# Create source/target data
d = d_orig[:, :nf_s]
d_s = d + t1
d_t = np.dot(s * d, R) + t2
# train bloody mapper(s)
ds = dataset_wizard(samples=d_s, targets=d_t)
pm.train(ds)
## not possible with new interface
#pm2.train(d_s, d_t)
## verify that both created the same transformation
#npm2proj = norm(pm.proj - pm2.proj)
#self.failUnless(npm2proj <= 1e-10,
# msg="Got transformation different by norm %g."
# " Had to be less than 1e-10" % npm2proj)
#self.failUnless(norm(pm._offset_in - pm2._offset_in) <= 1e-10)
#self.failUnless(norm(pm._offset_out - pm2._offset_out) <= 1e-10)
# do forward transformation on the same source data
d_s_f = pm.forward(d_s)
self.failUnlessEqual(d_s_f.shape, d_t.shape,
msg="Mapped shape should be identical to the d_t")
dsf = d_s_f - d_t
ndsf = norm(dsf)/norm(d_t)
if full_test:
dsR = norm(s*R - pm.proj)
if not oblique:
self.failUnless(dsR <= 1e-12,
msg="We should have got reconstructed rotation+scaling "
"perfectly. Now got d scale*R=%g" % dsR)
self.failUnless(np.abs(s - pm._scale) < 1e-12,
msg="We should have got reconstructed scale "
"perfectly. Now got %g for %g" % (pm._scale, s))
self.failUnless(ndsf <= 1e-12,
msg="%s: Failed to get to the target space correctly."
" normed error=%g" % (sdim, ndsf))
# Test if we get back
d_s_f_r = pm.reverse(d_s_f)
dsfr = d_s_f_r - d_s
ndsfr = norm(dsfr)/norm(d_s)
if full_test:
self.failUnless(ndsfr <= 1e-12,
msg="%s: Failed to reconstruct into source space correctly."
" normed error=%g" % (sdim, ndsfr))
def test_simple(self, svd, oblique):
d_orig = datasets['uni2large'].samples
d_orig2 = datasets['uni4large'].samples
for sdim, nf_s, nf_t, full_test \
in (('Same 2D', 2, 2, True),
('Same 10D', 10, 10, True),
('2D -> 3D', 2, 3, True),
('3D -> 2D', 3, 2, False)):
# figure out some "random" rotation
d = max(nf_s, nf_t)
R = get_random_rotation(nf_s, nf_t, d_orig)
if nf_s == nf_t:
adR = np.abs(1.0 - np.linalg.det(R))
self.assertTrue(
adR < 1e-10, "Determinant of rotation matrix should "
"be 1. Got it 1+%g" % adR)
self.assertTrue(
norm(np.dot(R, R.T) - np.eye(R.shape[0])) < 1e-10)
for s, scaling in ((0.3, True), (1.0, False)):
pm = ProcrusteanMapper(scaling=scaling,
oblique=oblique,
svd=svd)
# pm2 = ProcrusteanMapper(scaling=scaling, oblique=oblique)
t1, t2 = d_orig[23, 1], d_orig[22, 1]
# Create source/target data
d = d_orig[:, :nf_s]
d_s = d + t1
d_t = np.dot(s * d, R) + t2
# train bloody mapper(s)
ds = dataset_wizard(samples=d_s, targets=d_t)
pm.train(ds)
## not possible with new interface
#pm2.train(d_s, d_t)
## verify that both created the same transformation
#npm2proj = norm(pm.proj - pm2.proj)
#self.assertTrue(npm2proj <= 1e-10,
# msg="Got transformation different by norm %g."
# " Had to be less than 1e-10" % npm2proj)
#self.assertTrue(norm(pm._offset_in - pm2._offset_in) <= 1e-10)
#self.assertTrue(norm(pm._offset_out - pm2._offset_out) <= 1e-10)
# do forward transformation on the same source data
d_s_f = pm.forward(d_s)
self.assertEqual(
d_s_f.shape,
d_t.shape,
msg="Mapped shape should be identical to the d_t")
dsf = d_s_f - d_t
ndsf = norm(dsf) / norm(d_t)
if full_test:
dsR = norm(s * R - pm.proj)
if not oblique:
self.assertTrue(
dsR <= 1e-12,
msg=
"We should have got reconstructed rotation+scaling "
"perfectly. Now got d scale*R=%g" % dsR)
self.assertTrue(
np.abs(s - pm._scale) < 1e-12,
msg="We should have got reconstructed scale "
"perfectly. Now got %g for %g" % (pm._scale, s))
self.assertTrue(
ndsf <= 1e-12,
msg="%s: Failed to get to the target space correctly."
" normed error=%g" % (sdim, ndsf))
# Test if we get back
d_s_f_r = pm.reverse(d_s_f)
dsfr = d_s_f_r - d_s
ndsfr = norm(dsfr) / norm(d_s)
if full_test:
self.assertTrue(
ndsfr <= 1e-12,
msg=
"%s: Failed to reconstruct into source space correctly."
" normed error=%g" % (sdim, ndsfr))