65 lines
2 KiB
Python
65 lines
2 KiB
Python
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"""Tests for spline filtering."""
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from __future__ import division, print_function, absolute_import
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import numpy as np
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import pytest
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from numpy.testing import assert_almost_equal
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from scipy import ndimage
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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(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 == 'wrap':
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start, step = -1, -1
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else:
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raise ValueError('unsupported mode {}'.format(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 matrix / knot_values_sum
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@pytest.mark.parametrize('order', [0, 1, 2, 3, 4, 5])
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def test_spline_filter_vs_matrix_solution(order):
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n = 100
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eye = np.eye(n, dtype=float)
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spline_filter_axis_0 = ndimage.spline_filter1d(eye, axis=0, order=order)
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spline_filter_axis_1 = ndimage.spline_filter1d(eye, axis=1, order=order)
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matrix = make_spline_knot_matrix(n, order)
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assert_almost_equal(eye, np.dot(spline_filter_axis_0, matrix))
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assert_almost_equal(eye, np.dot(spline_filter_axis_1, matrix.T))
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