"""Tests for spline filtering.""" import numpy as np import pytest from numpy.testing import assert_almost_equal from scipy import ndimage def get_spline_knot_values(order): """Knot values to the right of a B-spline's center.""" knot_values = {0: [1], 1: [1], 2: [6, 1], 3: [4, 1], 4: [230, 76, 1], 5: [66, 26, 1]} return knot_values[order] def make_spline_knot_matrix(n, order, mode='mirror'): """Matrix to invert to find the spline coefficients.""" knot_values = get_spline_knot_values(order) matrix = np.zeros((n, n)) for diag, knot_value in enumerate(knot_values): indices = np.arange(diag, n) if diag == 0: matrix[indices, indices] = knot_value else: matrix[indices, indices - diag] = knot_value matrix[indices - diag, indices] = knot_value knot_values_sum = knot_values[0] + 2 * sum(knot_values[1:]) if mode == 'mirror': start, step = 1, 1 elif mode == 'reflect': start, step = 0, 1 elif mode == 'wrap': start, step = -1, -1 else: raise ValueError('unsupported mode {}'.format(mode)) for row in range(len(knot_values) - 1): for idx, knot_value in enumerate(knot_values[row + 1:]): matrix[row, start + step*idx] += knot_value matrix[-row - 1, -start - 1 - step*idx] += knot_value return matrix / knot_values_sum @pytest.mark.parametrize('order', [0, 1, 2, 3, 4, 5]) @pytest.mark.parametrize('mode', ['mirror', 'wrap', 'reflect']) def test_spline_filter_vs_matrix_solution(order, mode): n = 100 eye = np.eye(n, dtype=float) spline_filter_axis_0 = ndimage.spline_filter1d(eye, axis=0, order=order, mode=mode) spline_filter_axis_1 = ndimage.spline_filter1d(eye, axis=1, order=order, mode=mode) matrix = make_spline_knot_matrix(n, order, mode=mode) assert_almost_equal(eye, np.dot(spline_filter_axis_0, matrix)) assert_almost_equal(eye, np.dot(spline_filter_axis_1, matrix.T))