test__procrustes.py
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import numpy as np
from numpy.testing import assert_allclose, assert_equal, assert_almost_equal
from pytest import raises as assert_raises
from scipy.spatial import procrustes
class TestProcrustes(object):
def setup_method(self):
"""creates inputs"""
# an L
self.data1 = np.array([[1, 3], [1, 2], [1, 1], [2, 1]], 'd')
# a larger, shifted, mirrored L
self.data2 = np.array([[4, -2], [4, -4], [4, -6], [2, -6]], 'd')
# an L shifted up 1, right 1, and with point 4 shifted an extra .5
# to the right
# pointwise distance disparity with data1: 3*(2) + (1 + 1.5^2)
self.data3 = np.array([[2, 4], [2, 3], [2, 2], [3, 2.5]], 'd')
# data4, data5 are standardized (trace(A*A') = 1).
# procrustes should return an identical copy if they are used
# as the first matrix argument.
shiftangle = np.pi / 8
self.data4 = np.array([[1, 0], [0, 1], [-1, 0],
[0, -1]], 'd') / np.sqrt(4)
self.data5 = np.array([[np.cos(shiftangle), np.sin(shiftangle)],
[np.cos(np.pi / 2 - shiftangle),
np.sin(np.pi / 2 - shiftangle)],
[-np.cos(shiftangle),
-np.sin(shiftangle)],
[-np.cos(np.pi / 2 - shiftangle),
-np.sin(np.pi / 2 - shiftangle)]],
'd') / np.sqrt(4)
def test_procrustes(self):
# tests procrustes' ability to match two matrices.
#
# the second matrix is a rotated, shifted, scaled, and mirrored version
# of the first, in two dimensions only
#
# can shift, mirror, and scale an 'L'?
a, b, disparity = procrustes(self.data1, self.data2)
assert_allclose(b, a)
assert_almost_equal(disparity, 0.)
# if first mtx is standardized, leaves first mtx unchanged?
m4, m5, disp45 = procrustes(self.data4, self.data5)
assert_equal(m4, self.data4)
# at worst, data3 is an 'L' with one point off by .5
m1, m3, disp13 = procrustes(self.data1, self.data3)
#assert_(disp13 < 0.5 ** 2)
def test_procrustes2(self):
# procrustes disparity should not depend on order of matrices
m1, m3, disp13 = procrustes(self.data1, self.data3)
m3_2, m1_2, disp31 = procrustes(self.data3, self.data1)
assert_almost_equal(disp13, disp31)
# try with 3d, 8 pts per
rand1 = np.array([[2.61955202, 0.30522265, 0.55515826],
[0.41124708, -0.03966978, -0.31854548],
[0.91910318, 1.39451809, -0.15295084],
[2.00452023, 0.50150048, 0.29485268],
[0.09453595, 0.67528885, 0.03283872],
[0.07015232, 2.18892599, -1.67266852],
[0.65029688, 1.60551637, 0.80013549],
[-0.6607528, 0.53644208, 0.17033891]])
rand3 = np.array([[0.0809969, 0.09731461, -0.173442],
[-1.84888465, -0.92589646, -1.29335743],
[0.67031855, -1.35957463, 0.41938621],
[0.73967209, -0.20230757, 0.52418027],
[0.17752796, 0.09065607, 0.29827466],
[0.47999368, -0.88455717, -0.57547934],
[-0.11486344, -0.12608506, -0.3395779],
[-0.86106154, -0.28687488, 0.9644429]])
res1, res3, disp13 = procrustes(rand1, rand3)
res3_2, res1_2, disp31 = procrustes(rand3, rand1)
assert_almost_equal(disp13, disp31)
def test_procrustes_shape_mismatch(self):
assert_raises(ValueError, procrustes,
np.array([[1, 2], [3, 4]]),
np.array([[5, 6, 7], [8, 9, 10]]))
def test_procrustes_empty_rows_or_cols(self):
empty = np.array([[]])
assert_raises(ValueError, procrustes, empty, empty)
def test_procrustes_no_variation(self):
assert_raises(ValueError, procrustes,
np.array([[42, 42], [42, 42]]),
np.array([[45, 45], [45, 45]]))
def test_procrustes_bad_number_of_dimensions(self):
# fewer dimensions in one dataset
assert_raises(ValueError, procrustes,
np.array([1, 1, 2, 3, 5, 8]),
np.array([[1, 2], [3, 4]]))
# fewer dimensions in both datasets
assert_raises(ValueError, procrustes,
np.array([1, 1, 2, 3, 5, 8]),
np.array([1, 1, 2, 3, 5, 8]))
# zero dimensions
assert_raises(ValueError, procrustes, np.array(7), np.array(11))
# extra dimensions
assert_raises(ValueError, procrustes,
np.array([[[11], [7]]]),
np.array([[[5, 13]]]))