You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
68 lines
2.2 KiB
Python
68 lines
2.2 KiB
Python
"""Tests for spline filtering."""
|
|
from __future__ import division, print_function, absolute_import
|
|
|
|
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))
|