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"""Tests for spline filtering.""" |
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import pytest |
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import numpy as np |
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from scipy._lib._array_api import assert_almost_equal |
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from scipy import ndimage |
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from scipy.conftest import array_api_compatible |
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skip_xp_backends = pytest.mark.skip_xp_backends |
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pytestmark = [array_api_compatible, pytest.mark.usefixtures("skip_xp_backends"), |
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skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'],)] |
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def get_spline_knot_values(order): |
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"""Knot values to the right of a B-spline's center.""" |
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knot_values = {0: [1], |
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1: [1], |
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2: [6, 1], |
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3: [4, 1], |
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4: [230, 76, 1], |
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5: [66, 26, 1]} |
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return knot_values[order] |
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def make_spline_knot_matrix(xp, n, order, mode='mirror'): |
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"""Matrix to invert to find the spline coefficients.""" |
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knot_values = get_spline_knot_values(order) |
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matrix = np.zeros((n, n)) |
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for diag, knot_value in enumerate(knot_values): |
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indices = np.arange(diag, n) |
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if diag == 0: |
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matrix[indices, indices] = knot_value |
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else: |
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matrix[indices, indices - diag] = knot_value |
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matrix[indices - diag, indices] = knot_value |
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knot_values_sum = knot_values[0] + 2 * sum(knot_values[1:]) |
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if mode == 'mirror': |
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start, step = 1, 1 |
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elif mode == 'reflect': |
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start, step = 0, 1 |
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elif mode == 'grid-wrap': |
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start, step = -1, -1 |
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else: |
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raise ValueError(f'unsupported mode {mode}') |
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for row in range(len(knot_values) - 1): |
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for idx, knot_value in enumerate(knot_values[row + 1:]): |
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matrix[row, start + step*idx] += knot_value |
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matrix[-row - 1, -start - 1 - step*idx] += knot_value |
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return xp.asarray(matrix / knot_values_sum) |
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@pytest.mark.parametrize('order', [0, 1, 2, 3, 4, 5]) |
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@pytest.mark.parametrize('mode', ['mirror', 'grid-wrap', 'reflect']) |
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def test_spline_filter_vs_matrix_solution(order, mode, xp): |
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n = 100 |
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eye = xp.eye(n, dtype=xp.float64) |
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spline_filter_axis_0 = ndimage.spline_filter1d(eye, axis=0, order=order, |
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mode=mode) |
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spline_filter_axis_1 = ndimage.spline_filter1d(eye, axis=1, order=order, |
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mode=mode) |
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matrix = make_spline_knot_matrix(xp, n, order, mode=mode) |
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assert_almost_equal(eye, spline_filter_axis_0 @ matrix) |
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assert_almost_equal(eye, spline_filter_axis_1 @ matrix.T) |
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