init

2026-02-12 23:22:11 +08:00
parent 7b09eb3d89
commit 89660bba4e
5988 changed files with 2517516 additions and 0 deletions
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+"""Tests for spline filtering."""
+import pytest
+
+import numpy as np
+from scipy._lib._array_api import assert_almost_equal
+
+from scipy import ndimage
+
+skip_xp_backends = pytest.mark.skip_xp_backends
+pytestmark = [skip_xp_backends(cpu_only=True, exceptions=['cupy', 'jax.numpy'])]
+
+
+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(xp, n, order, mode='mirror'):
+    """Matrix to invert to find the spline coefficients."""
+    knot_values = get_spline_knot_values(order)
+
+    # NB: do computations with numpy, convert to xp as the last step only
+
+    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 xp.asarray(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, xp):
+    n = 100
+    eye = xp.eye(n, dtype=xp.float64)
+    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(xp, n, order, mode=mode)
+    assert_almost_equal(eye, spline_filter_axis_0 @ matrix)
+    assert_almost_equal(eye, spline_filter_axis_1 @ matrix.T)