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]]]))

