venv/lib/python3.10/site-packages/scipy/ndimage/tests/test_splines.py

"""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 == 'grid-wrap':
        start, step = -1, -1
    else:
        raise ValueError(f'unsupported mode {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', 'grid-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))