3576 lines
134 KiB
Python
3576 lines
134 KiB
Python
![]() |
# -*- coding: utf-8 -*-
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import sys
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from concurrent.futures import ThreadPoolExecutor, as_completed
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from decimal import Decimal
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from itertools import product
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from math import gcd
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import pytest
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from pytest import raises as assert_raises
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from numpy.testing import (
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assert_equal,
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assert_almost_equal, assert_array_equal, assert_array_almost_equal,
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assert_allclose, assert_, assert_array_less,
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suppress_warnings)
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from numpy import array, arange
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import numpy as np
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from scipy.fft import fft
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from scipy.ndimage import correlate1d
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from scipy.optimize import fmin, linear_sum_assignment
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from scipy import signal
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from scipy.signal import (
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correlate, correlate2d, correlation_lags, convolve, convolve2d,
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fftconvolve, oaconvolve, choose_conv_method,
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hilbert, hilbert2, lfilter, lfilter_zi, filtfilt, butter, zpk2tf, zpk2sos,
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invres, invresz, vectorstrength, lfiltic, tf2sos, sosfilt, sosfiltfilt,
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sosfilt_zi, tf2zpk, BadCoefficients, detrend, unique_roots, residue,
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residuez)
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from scipy.signal.windows import hann
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from scipy.signal._signaltools import (_filtfilt_gust, _compute_factors,
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_group_poles)
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from scipy.signal._upfirdn import _upfirdn_modes
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from scipy._lib import _testutils
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class _TestConvolve:
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def test_basic(self):
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a = [3, 4, 5, 6, 5, 4]
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b = [1, 2, 3]
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c = convolve(a, b)
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assert_array_equal(c, array([3, 10, 22, 28, 32, 32, 23, 12]))
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def test_same(self):
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a = [3, 4, 5]
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b = [1, 2, 3, 4]
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c = convolve(a, b, mode="same")
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assert_array_equal(c, array([10, 22, 34]))
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def test_same_eq(self):
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a = [3, 4, 5]
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b = [1, 2, 3]
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c = convolve(a, b, mode="same")
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assert_array_equal(c, array([10, 22, 22]))
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def test_complex(self):
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x = array([1 + 1j, 2 + 1j, 3 + 1j])
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y = array([1 + 1j, 2 + 1j])
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z = convolve(x, y)
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assert_array_equal(z, array([2j, 2 + 6j, 5 + 8j, 5 + 5j]))
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def test_zero_rank(self):
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a = 1289
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b = 4567
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c = convolve(a, b)
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assert_equal(c, a * b)
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def test_broadcastable(self):
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a = np.arange(27).reshape(3, 3, 3)
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b = np.arange(3)
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for i in range(3):
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b_shape = [1]*3
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b_shape[i] = 3
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x = convolve(a, b.reshape(b_shape), method='direct')
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y = convolve(a, b.reshape(b_shape), method='fft')
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assert_allclose(x, y)
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def test_single_element(self):
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a = array([4967])
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b = array([3920])
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c = convolve(a, b)
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assert_equal(c, a * b)
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def test_2d_arrays(self):
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a = [[1, 2, 3], [3, 4, 5]]
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b = [[2, 3, 4], [4, 5, 6]]
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c = convolve(a, b)
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d = array([[2, 7, 16, 17, 12],
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[10, 30, 62, 58, 38],
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[12, 31, 58, 49, 30]])
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assert_array_equal(c, d)
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def test_input_swapping(self):
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small = arange(8).reshape(2, 2, 2)
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big = 1j * arange(27).reshape(3, 3, 3)
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big += arange(27)[::-1].reshape(3, 3, 3)
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out_array = array(
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[[[0 + 0j, 26 + 0j, 25 + 1j, 24 + 2j],
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[52 + 0j, 151 + 5j, 145 + 11j, 93 + 11j],
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[46 + 6j, 133 + 23j, 127 + 29j, 81 + 23j],
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[40 + 12j, 98 + 32j, 93 + 37j, 54 + 24j]],
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[[104 + 0j, 247 + 13j, 237 + 23j, 135 + 21j],
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[282 + 30j, 632 + 96j, 604 + 124j, 330 + 86j],
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[246 + 66j, 548 + 180j, 520 + 208j, 282 + 134j],
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[142 + 66j, 307 + 161j, 289 + 179j, 153 + 107j]],
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[[68 + 36j, 157 + 103j, 147 + 113j, 81 + 75j],
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[174 + 138j, 380 + 348j, 352 + 376j, 186 + 230j],
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[138 + 174j, 296 + 432j, 268 + 460j, 138 + 278j],
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[70 + 138j, 145 + 323j, 127 + 341j, 63 + 197j]],
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[[32 + 72j, 68 + 166j, 59 + 175j, 30 + 100j],
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[68 + 192j, 139 + 433j, 117 + 455j, 57 + 255j],
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[38 + 222j, 73 + 499j, 51 + 521j, 21 + 291j],
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[12 + 144j, 20 + 318j, 7 + 331j, 0 + 182j]]])
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assert_array_equal(convolve(small, big, 'full'), out_array)
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assert_array_equal(convolve(big, small, 'full'), out_array)
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assert_array_equal(convolve(small, big, 'same'),
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out_array[1:3, 1:3, 1:3])
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assert_array_equal(convolve(big, small, 'same'),
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out_array[0:3, 0:3, 0:3])
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assert_array_equal(convolve(small, big, 'valid'),
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out_array[1:3, 1:3, 1:3])
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assert_array_equal(convolve(big, small, 'valid'),
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out_array[1:3, 1:3, 1:3])
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def test_invalid_params(self):
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a = [3, 4, 5]
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b = [1, 2, 3]
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assert_raises(ValueError, convolve, a, b, mode='spam')
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assert_raises(ValueError, convolve, a, b, mode='eggs', method='fft')
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assert_raises(ValueError, convolve, a, b, mode='ham', method='direct')
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assert_raises(ValueError, convolve, a, b, mode='full', method='bacon')
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assert_raises(ValueError, convolve, a, b, mode='same', method='bacon')
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class TestConvolve(_TestConvolve):
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def test_valid_mode2(self):
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# See gh-5897
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a = [1, 2, 3, 6, 5, 3]
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b = [2, 3, 4, 5, 3, 4, 2, 2, 1]
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expected = [70, 78, 73, 65]
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out = convolve(a, b, 'valid')
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assert_array_equal(out, expected)
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out = convolve(b, a, 'valid')
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assert_array_equal(out, expected)
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a = [1 + 5j, 2 - 1j, 3 + 0j]
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b = [2 - 3j, 1 + 0j]
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expected = [2 - 3j, 8 - 10j]
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out = convolve(a, b, 'valid')
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assert_array_equal(out, expected)
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out = convolve(b, a, 'valid')
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assert_array_equal(out, expected)
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def test_same_mode(self):
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a = [1, 2, 3, 3, 1, 2]
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b = [1, 4, 3, 4, 5, 6, 7, 4, 3, 2, 1, 1, 3]
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c = convolve(a, b, 'same')
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d = array([57, 61, 63, 57, 45, 36])
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assert_array_equal(c, d)
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def test_invalid_shapes(self):
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# By "invalid," we mean that no one
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# array has dimensions that are all at
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# least as large as the corresponding
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# dimensions of the other array. This
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# setup should throw a ValueError.
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a = np.arange(1, 7).reshape((2, 3))
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b = np.arange(-6, 0).reshape((3, 2))
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assert_raises(ValueError, convolve, *(a, b), **{'mode': 'valid'})
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assert_raises(ValueError, convolve, *(b, a), **{'mode': 'valid'})
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def test_convolve_method(self, n=100):
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types = sum([t for _, t in np.sctypes.items()], [])
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types = {np.dtype(t).name for t in types}
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# These types include 'bool' and all precisions (int8, float32, etc)
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# The removed types throw errors in correlate or fftconvolve
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for dtype in ['complex256', 'complex192', 'float128', 'float96',
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'str', 'void', 'bytes', 'object', 'unicode', 'string']:
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if dtype in types:
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types.remove(dtype)
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args = [(t1, t2, mode) for t1 in types for t2 in types
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for mode in ['valid', 'full', 'same']]
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# These are random arrays, which means test is much stronger than
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# convolving testing by convolving two np.ones arrays
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np.random.seed(42)
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array_types = {'i': np.random.choice([0, 1], size=n),
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'f': np.random.randn(n)}
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array_types['b'] = array_types['u'] = array_types['i']
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array_types['c'] = array_types['f'] + 0.5j*array_types['f']
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for t1, t2, mode in args:
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x1 = array_types[np.dtype(t1).kind].astype(t1)
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x2 = array_types[np.dtype(t2).kind].astype(t2)
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results = {key: convolve(x1, x2, method=key, mode=mode)
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for key in ['fft', 'direct']}
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assert_equal(results['fft'].dtype, results['direct'].dtype)
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if 'bool' in t1 and 'bool' in t2:
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assert_equal(choose_conv_method(x1, x2), 'direct')
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continue
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# Found by experiment. Found approx smallest value for (rtol, atol)
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# threshold to have tests pass.
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if any([t in {'complex64', 'float32'} for t in [t1, t2]]):
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kwargs = {'rtol': 1.0e-4, 'atol': 1e-6}
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elif 'float16' in [t1, t2]:
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# atol is default for np.allclose
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kwargs = {'rtol': 1e-3, 'atol': 1e-3}
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else:
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# defaults for np.allclose (different from assert_allclose)
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kwargs = {'rtol': 1e-5, 'atol': 1e-8}
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assert_allclose(results['fft'], results['direct'], **kwargs)
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def test_convolve_method_large_input(self):
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# This is really a test that convolving two large integers goes to the
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# direct method even if they're in the fft method.
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for n in [10, 20, 50, 51, 52, 53, 54, 60, 62]:
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z = np.array([2**n], dtype=np.int64)
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fft = convolve(z, z, method='fft')
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direct = convolve(z, z, method='direct')
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# this is the case when integer precision gets to us
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# issue #6076 has more detail, hopefully more tests after resolved
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if n < 50:
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assert_equal(fft, direct)
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assert_equal(fft, 2**(2*n))
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assert_equal(direct, 2**(2*n))
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def test_mismatched_dims(self):
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# Input arrays should have the same number of dimensions
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assert_raises(ValueError, convolve, [1], 2, method='direct')
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assert_raises(ValueError, convolve, 1, [2], method='direct')
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assert_raises(ValueError, convolve, [1], 2, method='fft')
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assert_raises(ValueError, convolve, 1, [2], method='fft')
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assert_raises(ValueError, convolve, [1], [[2]])
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assert_raises(ValueError, convolve, [3], 2)
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class _TestConvolve2d:
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def test_2d_arrays(self):
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a = [[1, 2, 3], [3, 4, 5]]
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b = [[2, 3, 4], [4, 5, 6]]
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d = array([[2, 7, 16, 17, 12],
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[10, 30, 62, 58, 38],
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[12, 31, 58, 49, 30]])
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e = convolve2d(a, b)
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assert_array_equal(e, d)
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def test_valid_mode(self):
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e = [[2, 3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9, 10]]
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f = [[1, 2, 3], [3, 4, 5]]
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h = array([[62, 80, 98, 116, 134]])
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g = convolve2d(e, f, 'valid')
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assert_array_equal(g, h)
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# See gh-5897
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g = convolve2d(f, e, 'valid')
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assert_array_equal(g, h)
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def test_valid_mode_complx(self):
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e = [[2, 3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9, 10]]
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f = np.array([[1, 2, 3], [3, 4, 5]], dtype=complex) + 1j
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h = array([[62.+24.j, 80.+30.j, 98.+36.j, 116.+42.j, 134.+48.j]])
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g = convolve2d(e, f, 'valid')
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assert_array_almost_equal(g, h)
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# See gh-5897
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g = convolve2d(f, e, 'valid')
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assert_array_equal(g, h)
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def test_fillvalue(self):
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a = [[1, 2, 3], [3, 4, 5]]
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b = [[2, 3, 4], [4, 5, 6]]
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fillval = 1
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c = convolve2d(a, b, 'full', 'fill', fillval)
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d = array([[24, 26, 31, 34, 32],
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[28, 40, 62, 64, 52],
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[32, 46, 67, 62, 48]])
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assert_array_equal(c, d)
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def test_fillvalue_errors(self):
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msg = "could not cast `fillvalue` directly to the output "
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with np.testing.suppress_warnings() as sup:
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sup.filter(np.ComplexWarning, "Casting complex values")
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with assert_raises(ValueError, match=msg):
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convolve2d([[1]], [[1, 2]], fillvalue=1j)
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msg = "`fillvalue` must be scalar or an array with "
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with assert_raises(ValueError, match=msg):
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convolve2d([[1]], [[1, 2]], fillvalue=[1, 2])
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def test_fillvalue_empty(self):
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# Check that fillvalue being empty raises an error:
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assert_raises(ValueError, convolve2d, [[1]], [[1, 2]],
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fillvalue=[])
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def test_wrap_boundary(self):
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a = [[1, 2, 3], [3, 4, 5]]
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b = [[2, 3, 4], [4, 5, 6]]
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c = convolve2d(a, b, 'full', 'wrap')
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d = array([[80, 80, 74, 80, 80],
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[68, 68, 62, 68, 68],
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[80, 80, 74, 80, 80]])
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assert_array_equal(c, d)
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def test_sym_boundary(self):
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a = [[1, 2, 3], [3, 4, 5]]
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b = [[2, 3, 4], [4, 5, 6]]
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c = convolve2d(a, b, 'full', 'symm')
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d = array([[34, 30, 44, 62, 66],
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[52, 48, 62, 80, 84],
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[82, 78, 92, 110, 114]])
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assert_array_equal(c, d)
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@pytest.mark.parametrize('func', [convolve2d, correlate2d])
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@pytest.mark.parametrize('boundary, expected',
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[('symm', [[37.0, 42.0, 44.0, 45.0]]),
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('wrap', [[43.0, 44.0, 42.0, 39.0]])])
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def test_same_with_boundary(self, func, boundary, expected):
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# Test boundary='symm' and boundary='wrap' with a "long" kernel.
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# The size of the kernel requires that the values in the "image"
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# be extended more than once to handle the requested boundary method.
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# This is a regression test for gh-8684 and gh-8814.
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image = np.array([[2.0, -1.0, 3.0, 4.0]])
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kernel = np.ones((1, 21))
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result = func(image, kernel, mode='same', boundary=boundary)
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# The expected results were calculated "by hand". Because the
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# kernel is all ones, the same result is expected for convolve2d
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# and correlate2d.
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assert_array_equal(result, expected)
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def test_boundary_extension_same(self):
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# Regression test for gh-12686.
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# Use ndimage.convolve with appropriate arguments to create the
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# expected result.
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import scipy.ndimage as ndi
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a = np.arange(1, 10*3+1, dtype=float).reshape(10, 3)
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b = np.arange(1, 10*10+1, dtype=float).reshape(10, 10)
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c = convolve2d(a, b, mode='same', boundary='wrap')
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assert_array_equal(c, ndi.convolve(a, b, mode='wrap', origin=(-1, -1)))
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def test_boundary_extension_full(self):
|
||
|
# Regression test for gh-12686.
|
||
|
# Use ndimage.convolve with appropriate arguments to create the
|
||
|
# expected result.
|
||
|
import scipy.ndimage as ndi
|
||
|
a = np.arange(1, 3*3+1, dtype=float).reshape(3, 3)
|
||
|
b = np.arange(1, 6*6+1, dtype=float).reshape(6, 6)
|
||
|
c = convolve2d(a, b, mode='full', boundary='wrap')
|
||
|
apad = np.pad(a, ((3, 3), (3, 3)), 'wrap')
|
||
|
assert_array_equal(c, ndi.convolve(apad, b, mode='wrap')[:-1, :-1])
|
||
|
|
||
|
def test_invalid_shapes(self):
|
||
|
# By "invalid," we mean that no one
|
||
|
# array has dimensions that are all at
|
||
|
# least as large as the corresponding
|
||
|
# dimensions of the other array. This
|
||
|
# setup should throw a ValueError.
|
||
|
a = np.arange(1, 7).reshape((2, 3))
|
||
|
b = np.arange(-6, 0).reshape((3, 2))
|
||
|
|
||
|
assert_raises(ValueError, convolve2d, *(a, b), **{'mode': 'valid'})
|
||
|
assert_raises(ValueError, convolve2d, *(b, a), **{'mode': 'valid'})
|
||
|
|
||
|
|
||
|
class TestConvolve2d(_TestConvolve2d):
|
||
|
|
||
|
def test_same_mode(self):
|
||
|
e = [[1, 2, 3], [3, 4, 5]]
|
||
|
f = [[2, 3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9, 10]]
|
||
|
g = convolve2d(e, f, 'same')
|
||
|
h = array([[22, 28, 34],
|
||
|
[80, 98, 116]])
|
||
|
assert_array_equal(g, h)
|
||
|
|
||
|
def test_valid_mode2(self):
|
||
|
# See gh-5897
|
||
|
e = [[1, 2, 3], [3, 4, 5]]
|
||
|
f = [[2, 3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9, 10]]
|
||
|
expected = [[62, 80, 98, 116, 134]]
|
||
|
|
||
|
out = convolve2d(e, f, 'valid')
|
||
|
assert_array_equal(out, expected)
|
||
|
|
||
|
out = convolve2d(f, e, 'valid')
|
||
|
assert_array_equal(out, expected)
|
||
|
|
||
|
e = [[1 + 1j, 2 - 3j], [3 + 1j, 4 + 0j]]
|
||
|
f = [[2 - 1j, 3 + 2j, 4 + 0j], [4 - 0j, 5 + 1j, 6 - 3j]]
|
||
|
expected = [[27 - 1j, 46. + 2j]]
|
||
|
|
||
|
out = convolve2d(e, f, 'valid')
|
||
|
assert_array_equal(out, expected)
|
||
|
|
||
|
# See gh-5897
|
||
|
out = convolve2d(f, e, 'valid')
|
||
|
assert_array_equal(out, expected)
|
||
|
|
||
|
def test_consistency_convolve_funcs(self):
|
||
|
# Compare np.convolve, signal.convolve, signal.convolve2d
|
||
|
a = np.arange(5)
|
||
|
b = np.array([3.2, 1.4, 3])
|
||
|
for mode in ['full', 'valid', 'same']:
|
||
|
assert_almost_equal(np.convolve(a, b, mode=mode),
|
||
|
signal.convolve(a, b, mode=mode))
|
||
|
assert_almost_equal(np.squeeze(
|
||
|
signal.convolve2d([a], [b], mode=mode)),
|
||
|
signal.convolve(a, b, mode=mode))
|
||
|
|
||
|
def test_invalid_dims(self):
|
||
|
assert_raises(ValueError, convolve2d, 3, 4)
|
||
|
assert_raises(ValueError, convolve2d, [3], [4])
|
||
|
assert_raises(ValueError, convolve2d, [[[3]]], [[[4]]])
|
||
|
|
||
|
@pytest.mark.slow
|
||
|
@pytest.mark.xfail_on_32bit("Can't create large array for test")
|
||
|
def test_large_array(self):
|
||
|
# Test indexing doesn't overflow an int (gh-10761)
|
||
|
n = 2**31 // (1000 * np.int64().itemsize)
|
||
|
_testutils.check_free_memory(2 * n * 1001 * np.int64().itemsize / 1e6)
|
||
|
|
||
|
# Create a chequered pattern of 1s and 0s
|
||
|
a = np.zeros(1001 * n, dtype=np.int64)
|
||
|
a[::2] = 1
|
||
|
a = np.lib.stride_tricks.as_strided(a, shape=(n, 1000), strides=(8008, 8))
|
||
|
|
||
|
count = signal.convolve2d(a, [[1, 1]])
|
||
|
fails = np.where(count > 1)
|
||
|
assert fails[0].size == 0
|
||
|
|
||
|
|
||
|
class TestFFTConvolve:
|
||
|
|
||
|
@pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
|
||
|
def test_real(self, axes):
|
||
|
a = array([1, 2, 3])
|
||
|
expected = array([1, 4, 10, 12, 9.])
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(a, a)
|
||
|
else:
|
||
|
out = fftconvolve(a, a, axes=axes)
|
||
|
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [1, [1], -1, [-1]])
|
||
|
def test_real_axes(self, axes):
|
||
|
a = array([1, 2, 3])
|
||
|
expected = array([1, 4, 10, 12, 9.])
|
||
|
|
||
|
a = np.tile(a, [2, 1])
|
||
|
expected = np.tile(expected, [2, 1])
|
||
|
|
||
|
out = fftconvolve(a, a, axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
|
||
|
def test_complex(self, axes):
|
||
|
a = array([1 + 1j, 2 + 2j, 3 + 3j])
|
||
|
expected = array([0 + 2j, 0 + 8j, 0 + 20j, 0 + 24j, 0 + 18j])
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(a, a)
|
||
|
else:
|
||
|
out = fftconvolve(a, a, axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [1, [1], -1, [-1]])
|
||
|
def test_complex_axes(self, axes):
|
||
|
a = array([1 + 1j, 2 + 2j, 3 + 3j])
|
||
|
expected = array([0 + 2j, 0 + 8j, 0 + 20j, 0 + 24j, 0 + 18j])
|
||
|
|
||
|
a = np.tile(a, [2, 1])
|
||
|
expected = np.tile(expected, [2, 1])
|
||
|
|
||
|
out = fftconvolve(a, a, axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', ['',
|
||
|
None,
|
||
|
[0, 1],
|
||
|
[1, 0],
|
||
|
[0, -1],
|
||
|
[-1, 0],
|
||
|
[-2, 1],
|
||
|
[1, -2],
|
||
|
[-2, -1],
|
||
|
[-1, -2]])
|
||
|
def test_2d_real_same(self, axes):
|
||
|
a = array([[1, 2, 3],
|
||
|
[4, 5, 6]])
|
||
|
expected = array([[1, 4, 10, 12, 9],
|
||
|
[8, 26, 56, 54, 36],
|
||
|
[16, 40, 73, 60, 36]])
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(a, a)
|
||
|
else:
|
||
|
out = fftconvolve(a, a, axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [[1, 2],
|
||
|
[2, 1],
|
||
|
[1, -1],
|
||
|
[-1, 1],
|
||
|
[-2, 2],
|
||
|
[2, -2],
|
||
|
[-2, -1],
|
||
|
[-1, -2]])
|
||
|
def test_2d_real_same_axes(self, axes):
|
||
|
a = array([[1, 2, 3],
|
||
|
[4, 5, 6]])
|
||
|
expected = array([[1, 4, 10, 12, 9],
|
||
|
[8, 26, 56, 54, 36],
|
||
|
[16, 40, 73, 60, 36]])
|
||
|
|
||
|
a = np.tile(a, [2, 1, 1])
|
||
|
expected = np.tile(expected, [2, 1, 1])
|
||
|
|
||
|
out = fftconvolve(a, a, axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', ['',
|
||
|
None,
|
||
|
[0, 1],
|
||
|
[1, 0],
|
||
|
[0, -1],
|
||
|
[-1, 0],
|
||
|
[-2, 1],
|
||
|
[1, -2],
|
||
|
[-2, -1],
|
||
|
[-1, -2]])
|
||
|
def test_2d_complex_same(self, axes):
|
||
|
a = array([[1 + 2j, 3 + 4j, 5 + 6j],
|
||
|
[2 + 1j, 4 + 3j, 6 + 5j]])
|
||
|
expected = array([
|
||
|
[-3 + 4j, -10 + 20j, -21 + 56j, -18 + 76j, -11 + 60j],
|
||
|
[10j, 44j, 118j, 156j, 122j],
|
||
|
[3 + 4j, 10 + 20j, 21 + 56j, 18 + 76j, 11 + 60j]
|
||
|
])
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(a, a)
|
||
|
else:
|
||
|
out = fftconvolve(a, a, axes=axes)
|
||
|
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [[1, 2],
|
||
|
[2, 1],
|
||
|
[1, -1],
|
||
|
[-1, 1],
|
||
|
[-2, 2],
|
||
|
[2, -2],
|
||
|
[-2, -1],
|
||
|
[-1, -2]])
|
||
|
def test_2d_complex_same_axes(self, axes):
|
||
|
a = array([[1 + 2j, 3 + 4j, 5 + 6j],
|
||
|
[2 + 1j, 4 + 3j, 6 + 5j]])
|
||
|
expected = array([
|
||
|
[-3 + 4j, -10 + 20j, -21 + 56j, -18 + 76j, -11 + 60j],
|
||
|
[10j, 44j, 118j, 156j, 122j],
|
||
|
[3 + 4j, 10 + 20j, 21 + 56j, 18 + 76j, 11 + 60j]
|
||
|
])
|
||
|
|
||
|
a = np.tile(a, [2, 1, 1])
|
||
|
expected = np.tile(expected, [2, 1, 1])
|
||
|
|
||
|
out = fftconvolve(a, a, axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
|
||
|
def test_real_same_mode(self, axes):
|
||
|
a = array([1, 2, 3])
|
||
|
b = array([3, 3, 5, 6, 8, 7, 9, 0, 1])
|
||
|
expected_1 = array([35., 41., 47.])
|
||
|
expected_2 = array([9., 20., 25., 35., 41., 47., 39., 28., 2.])
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(a, b, 'same')
|
||
|
else:
|
||
|
out = fftconvolve(a, b, 'same', axes=axes)
|
||
|
assert_array_almost_equal(out, expected_1)
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(b, a, 'same')
|
||
|
else:
|
||
|
out = fftconvolve(b, a, 'same', axes=axes)
|
||
|
assert_array_almost_equal(out, expected_2)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [1, -1, [1], [-1]])
|
||
|
def test_real_same_mode_axes(self, axes):
|
||
|
a = array([1, 2, 3])
|
||
|
b = array([3, 3, 5, 6, 8, 7, 9, 0, 1])
|
||
|
expected_1 = array([35., 41., 47.])
|
||
|
expected_2 = array([9., 20., 25., 35., 41., 47., 39., 28., 2.])
|
||
|
|
||
|
a = np.tile(a, [2, 1])
|
||
|
b = np.tile(b, [2, 1])
|
||
|
expected_1 = np.tile(expected_1, [2, 1])
|
||
|
expected_2 = np.tile(expected_2, [2, 1])
|
||
|
|
||
|
out = fftconvolve(a, b, 'same', axes=axes)
|
||
|
assert_array_almost_equal(out, expected_1)
|
||
|
|
||
|
out = fftconvolve(b, a, 'same', axes=axes)
|
||
|
assert_array_almost_equal(out, expected_2)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
|
||
|
def test_valid_mode_real(self, axes):
|
||
|
# See gh-5897
|
||
|
a = array([3, 2, 1])
|
||
|
b = array([3, 3, 5, 6, 8, 7, 9, 0, 1])
|
||
|
expected = array([24., 31., 41., 43., 49., 25., 12.])
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(a, b, 'valid')
|
||
|
else:
|
||
|
out = fftconvolve(a, b, 'valid', axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(b, a, 'valid')
|
||
|
else:
|
||
|
out = fftconvolve(b, a, 'valid', axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [1, [1]])
|
||
|
def test_valid_mode_real_axes(self, axes):
|
||
|
# See gh-5897
|
||
|
a = array([3, 2, 1])
|
||
|
b = array([3, 3, 5, 6, 8, 7, 9, 0, 1])
|
||
|
expected = array([24., 31., 41., 43., 49., 25., 12.])
|
||
|
|
||
|
a = np.tile(a, [2, 1])
|
||
|
b = np.tile(b, [2, 1])
|
||
|
expected = np.tile(expected, [2, 1])
|
||
|
|
||
|
out = fftconvolve(a, b, 'valid', axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
|
||
|
def test_valid_mode_complex(self, axes):
|
||
|
a = array([3 - 1j, 2 + 7j, 1 + 0j])
|
||
|
b = array([3 + 2j, 3 - 3j, 5 + 0j, 6 - 1j, 8 + 0j])
|
||
|
expected = array([45. + 12.j, 30. + 23.j, 48 + 32.j])
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(a, b, 'valid')
|
||
|
else:
|
||
|
out = fftconvolve(a, b, 'valid', axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(b, a, 'valid')
|
||
|
else:
|
||
|
out = fftconvolve(b, a, 'valid', axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [1, [1], -1, [-1]])
|
||
|
def test_valid_mode_complex_axes(self, axes):
|
||
|
a = array([3 - 1j, 2 + 7j, 1 + 0j])
|
||
|
b = array([3 + 2j, 3 - 3j, 5 + 0j, 6 - 1j, 8 + 0j])
|
||
|
expected = array([45. + 12.j, 30. + 23.j, 48 + 32.j])
|
||
|
|
||
|
a = np.tile(a, [2, 1])
|
||
|
b = np.tile(b, [2, 1])
|
||
|
expected = np.tile(expected, [2, 1])
|
||
|
|
||
|
out = fftconvolve(a, b, 'valid', axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
out = fftconvolve(b, a, 'valid', axes=axes)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
def test_valid_mode_ignore_nonaxes(self):
|
||
|
# See gh-5897
|
||
|
a = array([3, 2, 1])
|
||
|
b = array([3, 3, 5, 6, 8, 7, 9, 0, 1])
|
||
|
expected = array([24., 31., 41., 43., 49., 25., 12.])
|
||
|
|
||
|
a = np.tile(a, [2, 1])
|
||
|
b = np.tile(b, [1, 1])
|
||
|
expected = np.tile(expected, [2, 1])
|
||
|
|
||
|
out = fftconvolve(a, b, 'valid', axes=1)
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
def test_empty(self):
|
||
|
# Regression test for #1745: crashes with 0-length input.
|
||
|
assert_(fftconvolve([], []).size == 0)
|
||
|
assert_(fftconvolve([5, 6], []).size == 0)
|
||
|
assert_(fftconvolve([], [7]).size == 0)
|
||
|
|
||
|
def test_zero_rank(self):
|
||
|
a = array(4967)
|
||
|
b = array(3920)
|
||
|
out = fftconvolve(a, b)
|
||
|
assert_equal(out, a * b)
|
||
|
|
||
|
def test_single_element(self):
|
||
|
a = array([4967])
|
||
|
b = array([3920])
|
||
|
out = fftconvolve(a, b)
|
||
|
assert_equal(out, a * b)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', ['', None, 0, [0], -1, [-1]])
|
||
|
def test_random_data(self, axes):
|
||
|
np.random.seed(1234)
|
||
|
a = np.random.rand(1233) + 1j * np.random.rand(1233)
|
||
|
b = np.random.rand(1321) + 1j * np.random.rand(1321)
|
||
|
expected = np.convolve(a, b, 'full')
|
||
|
|
||
|
if axes == '':
|
||
|
out = fftconvolve(a, b, 'full')
|
||
|
else:
|
||
|
out = fftconvolve(a, b, 'full', axes=axes)
|
||
|
assert_(np.allclose(out, expected, rtol=1e-10))
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [1, [1], -1, [-1]])
|
||
|
def test_random_data_axes(self, axes):
|
||
|
np.random.seed(1234)
|
||
|
a = np.random.rand(1233) + 1j * np.random.rand(1233)
|
||
|
b = np.random.rand(1321) + 1j * np.random.rand(1321)
|
||
|
expected = np.convolve(a, b, 'full')
|
||
|
|
||
|
a = np.tile(a, [2, 1])
|
||
|
b = np.tile(b, [2, 1])
|
||
|
expected = np.tile(expected, [2, 1])
|
||
|
|
||
|
out = fftconvolve(a, b, 'full', axes=axes)
|
||
|
assert_(np.allclose(out, expected, rtol=1e-10))
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [[1, 4],
|
||
|
[4, 1],
|
||
|
[1, -1],
|
||
|
[-1, 1],
|
||
|
[-4, 4],
|
||
|
[4, -4],
|
||
|
[-4, -1],
|
||
|
[-1, -4]])
|
||
|
def test_random_data_multidim_axes(self, axes):
|
||
|
a_shape, b_shape = (123, 22), (132, 11)
|
||
|
np.random.seed(1234)
|
||
|
a = np.random.rand(*a_shape) + 1j * np.random.rand(*a_shape)
|
||
|
b = np.random.rand(*b_shape) + 1j * np.random.rand(*b_shape)
|
||
|
expected = convolve2d(a, b, 'full')
|
||
|
|
||
|
a = a[:, :, None, None, None]
|
||
|
b = b[:, :, None, None, None]
|
||
|
expected = expected[:, :, None, None, None]
|
||
|
|
||
|
a = np.moveaxis(a.swapaxes(0, 2), 1, 4)
|
||
|
b = np.moveaxis(b.swapaxes(0, 2), 1, 4)
|
||
|
expected = np.moveaxis(expected.swapaxes(0, 2), 1, 4)
|
||
|
|
||
|
# use 1 for dimension 2 in a and 3 in b to test broadcasting
|
||
|
a = np.tile(a, [2, 1, 3, 1, 1])
|
||
|
b = np.tile(b, [2, 1, 1, 4, 1])
|
||
|
expected = np.tile(expected, [2, 1, 3, 4, 1])
|
||
|
|
||
|
out = fftconvolve(a, b, 'full', axes=axes)
|
||
|
assert_allclose(out, expected, rtol=1e-10, atol=1e-10)
|
||
|
|
||
|
@pytest.mark.slow
|
||
|
@pytest.mark.parametrize(
|
||
|
'n',
|
||
|
list(range(1, 100)) +
|
||
|
list(range(1000, 1500)) +
|
||
|
np.random.RandomState(1234).randint(1001, 10000, 5).tolist())
|
||
|
def test_many_sizes(self, n):
|
||
|
a = np.random.rand(n) + 1j * np.random.rand(n)
|
||
|
b = np.random.rand(n) + 1j * np.random.rand(n)
|
||
|
expected = np.convolve(a, b, 'full')
|
||
|
|
||
|
out = fftconvolve(a, b, 'full')
|
||
|
assert_allclose(out, expected, atol=1e-10)
|
||
|
|
||
|
out = fftconvolve(a, b, 'full', axes=[0])
|
||
|
assert_allclose(out, expected, atol=1e-10)
|
||
|
|
||
|
def test_fft_nan(self):
|
||
|
n = 1000
|
||
|
rng = np.random.default_rng(43876432987)
|
||
|
sig_nan = rng.standard_normal(n)
|
||
|
|
||
|
for val in [np.nan, np.inf]:
|
||
|
sig_nan[100] = val
|
||
|
coeffs = signal.firwin(200, 0.2)
|
||
|
|
||
|
with pytest.warns(RuntimeWarning, match="Use of fft convolution"):
|
||
|
signal.convolve(sig_nan, coeffs, mode='same', method='fft')
|
||
|
|
||
|
def fftconvolve_err(*args, **kwargs):
|
||
|
raise RuntimeError('Fell back to fftconvolve')
|
||
|
|
||
|
|
||
|
def gen_oa_shapes(sizes):
|
||
|
return [(a, b) for a, b in product(sizes, repeat=2)
|
||
|
if abs(a - b) > 3]
|
||
|
|
||
|
|
||
|
def gen_oa_shapes_2d(sizes):
|
||
|
shapes0 = gen_oa_shapes(sizes)
|
||
|
shapes1 = gen_oa_shapes(sizes)
|
||
|
shapes = [ishapes0+ishapes1 for ishapes0, ishapes1 in
|
||
|
zip(shapes0, shapes1)]
|
||
|
|
||
|
modes = ['full', 'valid', 'same']
|
||
|
return [ishapes+(imode,) for ishapes, imode in product(shapes, modes)
|
||
|
if imode != 'valid' or
|
||
|
(ishapes[0] > ishapes[1] and ishapes[2] > ishapes[3]) or
|
||
|
(ishapes[0] < ishapes[1] and ishapes[2] < ishapes[3])]
|
||
|
|
||
|
|
||
|
def gen_oa_shapes_eq(sizes):
|
||
|
return [(a, b) for a, b in product(sizes, repeat=2)
|
||
|
if a >= b]
|
||
|
|
||
|
|
||
|
class TestOAConvolve:
|
||
|
@pytest.mark.slow()
|
||
|
@pytest.mark.parametrize('shape_a_0, shape_b_0',
|
||
|
gen_oa_shapes_eq(list(range(100)) +
|
||
|
list(range(100, 1000, 23)))
|
||
|
)
|
||
|
def test_real_manylens(self, shape_a_0, shape_b_0):
|
||
|
a = np.random.rand(shape_a_0)
|
||
|
b = np.random.rand(shape_b_0)
|
||
|
|
||
|
expected = fftconvolve(a, b)
|
||
|
out = oaconvolve(a, b)
|
||
|
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('shape_a_0, shape_b_0',
|
||
|
gen_oa_shapes([50, 47, 6, 4, 1]))
|
||
|
@pytest.mark.parametrize('is_complex', [True, False])
|
||
|
@pytest.mark.parametrize('mode', ['full', 'valid', 'same'])
|
||
|
def test_1d_noaxes(self, shape_a_0, shape_b_0,
|
||
|
is_complex, mode, monkeypatch):
|
||
|
a = np.random.rand(shape_a_0)
|
||
|
b = np.random.rand(shape_b_0)
|
||
|
if is_complex:
|
||
|
a = a + 1j*np.random.rand(shape_a_0)
|
||
|
b = b + 1j*np.random.rand(shape_b_0)
|
||
|
|
||
|
expected = fftconvolve(a, b, mode=mode)
|
||
|
|
||
|
monkeypatch.setattr(signal._signaltools, 'fftconvolve',
|
||
|
fftconvolve_err)
|
||
|
out = oaconvolve(a, b, mode=mode)
|
||
|
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [0, 1])
|
||
|
@pytest.mark.parametrize('shape_a_0, shape_b_0',
|
||
|
gen_oa_shapes([50, 47, 6, 4]))
|
||
|
@pytest.mark.parametrize('shape_a_extra', [1, 3])
|
||
|
@pytest.mark.parametrize('shape_b_extra', [1, 3])
|
||
|
@pytest.mark.parametrize('is_complex', [True, False])
|
||
|
@pytest.mark.parametrize('mode', ['full', 'valid', 'same'])
|
||
|
def test_1d_axes(self, axes, shape_a_0, shape_b_0,
|
||
|
shape_a_extra, shape_b_extra,
|
||
|
is_complex, mode, monkeypatch):
|
||
|
ax_a = [shape_a_extra]*2
|
||
|
ax_b = [shape_b_extra]*2
|
||
|
ax_a[axes] = shape_a_0
|
||
|
ax_b[axes] = shape_b_0
|
||
|
|
||
|
a = np.random.rand(*ax_a)
|
||
|
b = np.random.rand(*ax_b)
|
||
|
if is_complex:
|
||
|
a = a + 1j*np.random.rand(*ax_a)
|
||
|
b = b + 1j*np.random.rand(*ax_b)
|
||
|
|
||
|
expected = fftconvolve(a, b, mode=mode, axes=axes)
|
||
|
|
||
|
monkeypatch.setattr(signal._signaltools, 'fftconvolve',
|
||
|
fftconvolve_err)
|
||
|
out = oaconvolve(a, b, mode=mode, axes=axes)
|
||
|
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('shape_a_0, shape_b_0, '
|
||
|
'shape_a_1, shape_b_1, mode',
|
||
|
gen_oa_shapes_2d([50, 47, 6, 4]))
|
||
|
@pytest.mark.parametrize('is_complex', [True, False])
|
||
|
def test_2d_noaxes(self, shape_a_0, shape_b_0,
|
||
|
shape_a_1, shape_b_1, mode,
|
||
|
is_complex, monkeypatch):
|
||
|
a = np.random.rand(shape_a_0, shape_a_1)
|
||
|
b = np.random.rand(shape_b_0, shape_b_1)
|
||
|
if is_complex:
|
||
|
a = a + 1j*np.random.rand(shape_a_0, shape_a_1)
|
||
|
b = b + 1j*np.random.rand(shape_b_0, shape_b_1)
|
||
|
|
||
|
expected = fftconvolve(a, b, mode=mode)
|
||
|
|
||
|
monkeypatch.setattr(signal._signaltools, 'fftconvolve',
|
||
|
fftconvolve_err)
|
||
|
out = oaconvolve(a, b, mode=mode)
|
||
|
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
@pytest.mark.parametrize('axes', [[0, 1], [0, 2], [1, 2]])
|
||
|
@pytest.mark.parametrize('shape_a_0, shape_b_0, '
|
||
|
'shape_a_1, shape_b_1, mode',
|
||
|
gen_oa_shapes_2d([50, 47, 6, 4]))
|
||
|
@pytest.mark.parametrize('shape_a_extra', [1, 3])
|
||
|
@pytest.mark.parametrize('shape_b_extra', [1, 3])
|
||
|
@pytest.mark.parametrize('is_complex', [True, False])
|
||
|
def test_2d_axes(self, axes, shape_a_0, shape_b_0,
|
||
|
shape_a_1, shape_b_1, mode,
|
||
|
shape_a_extra, shape_b_extra,
|
||
|
is_complex, monkeypatch):
|
||
|
ax_a = [shape_a_extra]*3
|
||
|
ax_b = [shape_b_extra]*3
|
||
|
ax_a[axes[0]] = shape_a_0
|
||
|
ax_b[axes[0]] = shape_b_0
|
||
|
ax_a[axes[1]] = shape_a_1
|
||
|
ax_b[axes[1]] = shape_b_1
|
||
|
|
||
|
a = np.random.rand(*ax_a)
|
||
|
b = np.random.rand(*ax_b)
|
||
|
if is_complex:
|
||
|
a = a + 1j*np.random.rand(*ax_a)
|
||
|
b = b + 1j*np.random.rand(*ax_b)
|
||
|
|
||
|
expected = fftconvolve(a, b, mode=mode, axes=axes)
|
||
|
|
||
|
monkeypatch.setattr(signal._signaltools, 'fftconvolve',
|
||
|
fftconvolve_err)
|
||
|
out = oaconvolve(a, b, mode=mode, axes=axes)
|
||
|
|
||
|
assert_array_almost_equal(out, expected)
|
||
|
|
||
|
def test_empty(self):
|
||
|
# Regression test for #1745: crashes with 0-length input.
|
||
|
assert_(oaconvolve([], []).size == 0)
|
||
|
assert_(oaconvolve([5, 6], []).size == 0)
|
||
|
assert_(oaconvolve([], [7]).size == 0)
|
||
|
|
||
|
def test_zero_rank(self):
|
||
|
a = array(4967)
|
||
|
b = array(3920)
|
||
|
out = oaconvolve(a, b)
|
||
|
assert_equal(out, a * b)
|
||
|
|
||
|
def test_single_element(self):
|
||
|
a = array([4967])
|
||
|
b = array([3920])
|
||
|
out = oaconvolve(a, b)
|
||
|
assert_equal(out, a * b)
|
||
|
|
||
|
|
||
|
class TestAllFreqConvolves:
|
||
|
|
||
|
@pytest.mark.parametrize('convapproach',
|
||
|
[fftconvolve, oaconvolve])
|
||
|
def test_invalid_shapes(self, convapproach):
|
||
|
a = np.arange(1, 7).reshape((2, 3))
|
||
|
b = np.arange(-6, 0).reshape((3, 2))
|
||
|
with assert_raises(ValueError,
|
||
|
match="For 'valid' mode, one must be at least "
|
||
|
"as large as the other in every dimension"):
|
||
|
convapproach(a, b, mode='valid')
|
||
|
|
||
|
@pytest.mark.parametrize('convapproach',
|
||
|
[fftconvolve, oaconvolve])
|
||
|
def test_invalid_shapes_axes(self, convapproach):
|
||
|
a = np.zeros([5, 6, 2, 1])
|
||
|
b = np.zeros([5, 6, 3, 1])
|
||
|
with assert_raises(ValueError,
|
||
|
match=r"incompatible shapes for in1 and in2:"
|
||
|
r" \(5L?, 6L?, 2L?, 1L?\) and"
|
||
|
r" \(5L?, 6L?, 3L?, 1L?\)"):
|
||
|
convapproach(a, b, axes=[0, 1])
|
||
|
|
||
|
@pytest.mark.parametrize('a,b',
|
||
|
[([1], 2),
|
||
|
(1, [2]),
|
||
|
([3], [[2]])])
|
||
|
@pytest.mark.parametrize('convapproach',
|
||
|
[fftconvolve, oaconvolve])
|
||
|
def test_mismatched_dims(self, a, b, convapproach):
|
||
|
with assert_raises(ValueError,
|
||
|
match="in1 and in2 should have the same"
|
||
|
" dimensionality"):
|
||
|
convapproach(a, b)
|
||
|
|
||
|
@pytest.mark.parametrize('convapproach',
|
||
|
[fftconvolve, oaconvolve])
|
||
|
def test_invalid_flags(self, convapproach):
|
||
|
with assert_raises(ValueError,
|
||
|
match="acceptable mode flags are 'valid',"
|
||
|
" 'same', or 'full'"):
|
||
|
convapproach([1], [2], mode='chips')
|
||
|
|
||
|
with assert_raises(ValueError,
|
||
|
match="when provided, axes cannot be empty"):
|
||
|
convapproach([1], [2], axes=[])
|
||
|
|
||
|
with assert_raises(ValueError, match="axes must be a scalar or "
|
||
|
"iterable of integers"):
|
||
|
convapproach([1], [2], axes=[[1, 2], [3, 4]])
|
||
|
|
||
|
with assert_raises(ValueError, match="axes must be a scalar or "
|
||
|
"iterable of integers"):
|
||
|
convapproach([1], [2], axes=[1., 2., 3., 4.])
|
||
|
|
||
|
with assert_raises(ValueError,
|
||
|
match="axes exceeds dimensionality of input"):
|
||
|
convapproach([1], [2], axes=[1])
|
||
|
|
||
|
with assert_raises(ValueError,
|
||
|
match="axes exceeds dimensionality of input"):
|
||
|
convapproach([1], [2], axes=[-2])
|
||
|
|
||
|
with assert_raises(ValueError,
|
||
|
match="all axes must be unique"):
|
||
|
convapproach([1], [2], axes=[0, 0])
|
||
|
|
||
|
@pytest.mark.parametrize('dtype', [np.longfloat, np.longcomplex])
|
||
|
def test_longdtype_input(self, dtype):
|
||
|
x = np.random.random((27, 27)).astype(dtype)
|
||
|
y = np.random.random((4, 4)).astype(dtype)
|
||
|
if np.iscomplexobj(dtype()):
|
||
|
x += .1j
|
||
|
y -= .1j
|
||
|
|
||
|
res = fftconvolve(x, y)
|
||
|
assert_allclose(res, convolve(x, y, method='direct'))
|
||
|
assert res.dtype == dtype
|
||
|
|
||
|
|
||
|
class TestMedFilt:
|
||
|
|
||
|
IN = [[50, 50, 50, 50, 50, 92, 18, 27, 65, 46],
|
||
|
[50, 50, 50, 50, 50, 0, 72, 77, 68, 66],
|
||
|
[50, 50, 50, 50, 50, 46, 47, 19, 64, 77],
|
||
|
[50, 50, 50, 50, 50, 42, 15, 29, 95, 35],
|
||
|
[50, 50, 50, 50, 50, 46, 34, 9, 21, 66],
|
||
|
[70, 97, 28, 68, 78, 77, 61, 58, 71, 42],
|
||
|
[64, 53, 44, 29, 68, 32, 19, 68, 24, 84],
|
||
|
[3, 33, 53, 67, 1, 78, 74, 55, 12, 83],
|
||
|
[7, 11, 46, 70, 60, 47, 24, 43, 61, 26],
|
||
|
[32, 61, 88, 7, 39, 4, 92, 64, 45, 61]]
|
||
|
|
||
|
OUT = [[0, 50, 50, 50, 42, 15, 15, 18, 27, 0],
|
||
|
[0, 50, 50, 50, 50, 42, 19, 21, 29, 0],
|
||
|
[50, 50, 50, 50, 50, 47, 34, 34, 46, 35],
|
||
|
[50, 50, 50, 50, 50, 50, 42, 47, 64, 42],
|
||
|
[50, 50, 50, 50, 50, 50, 46, 55, 64, 35],
|
||
|
[33, 50, 50, 50, 50, 47, 46, 43, 55, 26],
|
||
|
[32, 50, 50, 50, 50, 47, 46, 45, 55, 26],
|
||
|
[7, 46, 50, 50, 47, 46, 46, 43, 45, 21],
|
||
|
[0, 32, 33, 39, 32, 32, 43, 43, 43, 0],
|
||
|
[0, 7, 11, 7, 4, 4, 19, 19, 24, 0]]
|
||
|
|
||
|
KERNEL_SIZE = [7,3]
|
||
|
|
||
|
def test_basic(self):
|
||
|
d = signal.medfilt(self.IN, self.KERNEL_SIZE)
|
||
|
e = signal.medfilt2d(np.array(self.IN, float), self.KERNEL_SIZE)
|
||
|
assert_array_equal(d, self.OUT)
|
||
|
assert_array_equal(d, e)
|
||
|
|
||
|
@pytest.mark.parametrize('dtype', [np.ubyte, np.byte, np.ushort, np.short,
|
||
|
np.uint, int, np.ulonglong, np.ulonglong,
|
||
|
np.float32, np.float64, np.longdouble])
|
||
|
def test_types(self, dtype):
|
||
|
# volume input and output types match
|
||
|
in_typed = np.array(self.IN, dtype=dtype)
|
||
|
assert_equal(signal.medfilt(in_typed).dtype, dtype)
|
||
|
assert_equal(signal.medfilt2d(in_typed).dtype, dtype)
|
||
|
|
||
|
@pytest.mark.parametrize('dtype', [np.bool_, np.cfloat, np.cdouble,
|
||
|
np.clongdouble, np.float16,])
|
||
|
def test_invalid_dtypes(self, dtype):
|
||
|
in_typed = np.array(self.IN, dtype=dtype)
|
||
|
with pytest.raises(ValueError, match="order_filterND"):
|
||
|
signal.medfilt(in_typed)
|
||
|
|
||
|
with pytest.raises(ValueError, match="order_filterND"):
|
||
|
signal.medfilt2d(in_typed)
|
||
|
|
||
|
def test_none(self):
|
||
|
# gh-1651, trac #1124. Ensure this does not segfault.
|
||
|
with pytest.warns(UserWarning):
|
||
|
assert_raises(TypeError, signal.medfilt, None)
|
||
|
# Expand on this test to avoid a regression with possible contiguous
|
||
|
# numpy arrays that have odd strides. The stride value below gets
|
||
|
# us into wrong memory if used (but it does not need to be used)
|
||
|
dummy = np.arange(10, dtype=np.float64)
|
||
|
a = dummy[5:6]
|
||
|
a.strides = 16
|
||
|
assert_(signal.medfilt(a, 1) == 5.)
|
||
|
|
||
|
def test_refcounting(self):
|
||
|
# Check a refcounting-related crash
|
||
|
a = Decimal(123)
|
||
|
x = np.array([a, a], dtype=object)
|
||
|
if hasattr(sys, 'getrefcount'):
|
||
|
n = 2 * sys.getrefcount(a)
|
||
|
else:
|
||
|
n = 10
|
||
|
# Shouldn't segfault:
|
||
|
with pytest.warns(UserWarning):
|
||
|
for j in range(n):
|
||
|
signal.medfilt(x)
|
||
|
if hasattr(sys, 'getrefcount'):
|
||
|
assert_(sys.getrefcount(a) < n)
|
||
|
assert_equal(x, [a, a])
|
||
|
|
||
|
def test_object(self,):
|
||
|
in_object = np.array(self.IN, dtype=object)
|
||
|
out_object = np.array(self.OUT, dtype=object)
|
||
|
assert_array_equal(signal.medfilt(in_object, self.KERNEL_SIZE),
|
||
|
out_object)
|
||
|
|
||
|
@pytest.mark.parametrize("dtype", [np.ubyte, np.float32, np.float64])
|
||
|
def test_medfilt2d_parallel(self, dtype):
|
||
|
in_typed = np.array(self.IN, dtype=dtype)
|
||
|
expected = np.array(self.OUT, dtype=dtype)
|
||
|
|
||
|
# This is used to simplify the indexing calculations.
|
||
|
assert in_typed.shape == expected.shape
|
||
|
|
||
|
# We'll do the calculation in four chunks. M1 and N1 are the dimensions
|
||
|
# of the first output chunk. We have to extend the input by half the
|
||
|
# kernel size to be able to calculate the full output chunk.
|
||
|
M1 = expected.shape[0] // 2
|
||
|
N1 = expected.shape[1] // 2
|
||
|
offM = self.KERNEL_SIZE[0] // 2 + 1
|
||
|
offN = self.KERNEL_SIZE[1] // 2 + 1
|
||
|
|
||
|
def apply(chunk):
|
||
|
# in = slice of in_typed to use.
|
||
|
# sel = slice of output to crop it to the correct region.
|
||
|
# out = slice of output array to store in.
|
||
|
M, N = chunk
|
||
|
if M == 0:
|
||
|
Min = slice(0, M1 + offM)
|
||
|
Msel = slice(0, -offM)
|
||
|
Mout = slice(0, M1)
|
||
|
else:
|
||
|
Min = slice(M1 - offM, None)
|
||
|
Msel = slice(offM, None)
|
||
|
Mout = slice(M1, None)
|
||
|
if N == 0:
|
||
|
Nin = slice(0, N1 + offN)
|
||
|
Nsel = slice(0, -offN)
|
||
|
Nout = slice(0, N1)
|
||
|
else:
|
||
|
Nin = slice(N1 - offN, None)
|
||
|
Nsel = slice(offN, None)
|
||
|
Nout = slice(N1, None)
|
||
|
|
||
|
# Do the calculation, but do not write to the output in the threads.
|
||
|
chunk_data = in_typed[Min, Nin]
|
||
|
med = signal.medfilt2d(chunk_data, self.KERNEL_SIZE)
|
||
|
return med[Msel, Nsel], Mout, Nout
|
||
|
|
||
|
# Give each chunk to a different thread.
|
||
|
output = np.zeros_like(expected)
|
||
|
with ThreadPoolExecutor(max_workers=4) as pool:
|
||
|
chunks = {(0, 0), (0, 1), (1, 0), (1, 1)}
|
||
|
futures = {pool.submit(apply, chunk) for chunk in chunks}
|
||
|
|
||
|
# Store each result in the output as it arrives.
|
||
|
for future in as_completed(futures):
|
||
|
data, Mslice, Nslice = future.result()
|
||
|
output[Mslice, Nslice] = data
|
||
|
|
||
|
assert_array_equal(output, expected)
|
||
|
|
||
|
|
||
|
class TestWiener:
|
||
|
|
||
|
def test_basic(self):
|
||
|
g = array([[5, 6, 4, 3],
|
||
|
[3, 5, 6, 2],
|
||
|
[2, 3, 5, 6],
|
||
|
[1, 6, 9, 7]], 'd')
|
||
|
h = array([[2.16374269, 3.2222222222, 2.8888888889, 1.6666666667],
|
||
|
[2.666666667, 4.33333333333, 4.44444444444, 2.8888888888],
|
||
|
[2.222222222, 4.4444444444, 5.4444444444, 4.801066874837],
|
||
|
[1.33333333333, 3.92735042735, 6.0712560386, 5.0404040404]])
|
||
|
assert_array_almost_equal(signal.wiener(g), h, decimal=6)
|
||
|
assert_array_almost_equal(signal.wiener(g, mysize=3), h, decimal=6)
|
||
|
|
||
|
|
||
|
padtype_options = ["mean", "median", "minimum", "maximum", "line"]
|
||
|
padtype_options += _upfirdn_modes
|
||
|
|
||
|
|
||
|
class TestResample:
|
||
|
def test_basic(self):
|
||
|
# Some basic tests
|
||
|
|
||
|
# Regression test for issue #3603.
|
||
|
# window.shape must equal to sig.shape[0]
|
||
|
sig = np.arange(128)
|
||
|
num = 256
|
||
|
win = signal.get_window(('kaiser', 8.0), 160)
|
||
|
assert_raises(ValueError, signal.resample, sig, num, window=win)
|
||
|
|
||
|
# Other degenerate conditions
|
||
|
assert_raises(ValueError, signal.resample_poly, sig, 'yo', 1)
|
||
|
assert_raises(ValueError, signal.resample_poly, sig, 1, 0)
|
||
|
assert_raises(ValueError, signal.resample_poly, sig, 2, 1, padtype='')
|
||
|
assert_raises(ValueError, signal.resample_poly, sig, 2, 1,
|
||
|
padtype='mean', cval=10)
|
||
|
|
||
|
# test for issue #6505 - should not modify window.shape when axis ≠ 0
|
||
|
sig2 = np.tile(np.arange(160), (2, 1))
|
||
|
signal.resample(sig2, num, axis=-1, window=win)
|
||
|
assert_(win.shape == (160,))
|
||
|
|
||
|
@pytest.mark.parametrize('window', (None, 'hamming'))
|
||
|
@pytest.mark.parametrize('N', (20, 19))
|
||
|
@pytest.mark.parametrize('num', (100, 101, 10, 11))
|
||
|
def test_rfft(self, N, num, window):
|
||
|
# Make sure the speed up using rfft gives the same result as the normal
|
||
|
# way using fft
|
||
|
x = np.linspace(0, 10, N, endpoint=False)
|
||
|
y = np.cos(-x**2/6.0)
|
||
|
assert_allclose(signal.resample(y, num, window=window),
|
||
|
signal.resample(y + 0j, num, window=window).real)
|
||
|
|
||
|
y = np.array([np.cos(-x**2/6.0), np.sin(-x**2/6.0)])
|
||
|
y_complex = y + 0j
|
||
|
assert_allclose(
|
||
|
signal.resample(y, num, axis=1, window=window),
|
||
|
signal.resample(y_complex, num, axis=1, window=window).real,
|
||
|
atol=1e-9)
|
||
|
|
||
|
def test_input_domain(self):
|
||
|
# Test if both input domain modes produce the same results.
|
||
|
tsig = np.arange(256) + 0j
|
||
|
fsig = fft(tsig)
|
||
|
num = 256
|
||
|
assert_allclose(
|
||
|
signal.resample(fsig, num, domain='freq'),
|
||
|
signal.resample(tsig, num, domain='time'),
|
||
|
atol=1e-9)
|
||
|
|
||
|
@pytest.mark.parametrize('nx', (1, 2, 3, 5, 8))
|
||
|
@pytest.mark.parametrize('ny', (1, 2, 3, 5, 8))
|
||
|
@pytest.mark.parametrize('dtype', ('float', 'complex'))
|
||
|
def test_dc(self, nx, ny, dtype):
|
||
|
x = np.array([1] * nx, dtype)
|
||
|
y = signal.resample(x, ny)
|
||
|
assert_allclose(y, [1] * ny)
|
||
|
|
||
|
@pytest.mark.parametrize('padtype', padtype_options)
|
||
|
def test_mutable_window(self, padtype):
|
||
|
# Test that a mutable window is not modified
|
||
|
impulse = np.zeros(3)
|
||
|
window = np.random.RandomState(0).randn(2)
|
||
|
window_orig = window.copy()
|
||
|
signal.resample_poly(impulse, 5, 1, window=window, padtype=padtype)
|
||
|
assert_array_equal(window, window_orig)
|
||
|
|
||
|
@pytest.mark.parametrize('padtype', padtype_options)
|
||
|
def test_output_float32(self, padtype):
|
||
|
# Test that float32 inputs yield a float32 output
|
||
|
x = np.arange(10, dtype=np.float32)
|
||
|
h = np.array([1, 1, 1], dtype=np.float32)
|
||
|
y = signal.resample_poly(x, 1, 2, window=h, padtype=padtype)
|
||
|
assert y.dtype == np.float32
|
||
|
|
||
|
@pytest.mark.parametrize('padtype', padtype_options)
|
||
|
@pytest.mark.parametrize('dtype', [np.float32, np.float64])
|
||
|
def test_output_match_dtype(self, padtype, dtype):
|
||
|
# Test that the dtype of x is preserved per issue #14733
|
||
|
x = np.arange(10, dtype=dtype)
|
||
|
y = signal.resample_poly(x, 1, 2, padtype=padtype)
|
||
|
assert y.dtype == x.dtype
|
||
|
|
||
|
@pytest.mark.parametrize(
|
||
|
"method, ext, padtype",
|
||
|
[("fft", False, None)]
|
||
|
+ list(
|
||
|
product(
|
||
|
["polyphase"], [False, True], padtype_options,
|
||
|
)
|
||
|
),
|
||
|
)
|
||
|
def test_resample_methods(self, method, ext, padtype):
|
||
|
# Test resampling of sinusoids and random noise (1-sec)
|
||
|
rate = 100
|
||
|
rates_to = [49, 50, 51, 99, 100, 101, 199, 200, 201]
|
||
|
|
||
|
# Sinusoids, windowed to avoid edge artifacts
|
||
|
t = np.arange(rate) / float(rate)
|
||
|
freqs = np.array((1., 10., 40.))[:, np.newaxis]
|
||
|
x = np.sin(2 * np.pi * freqs * t) * hann(rate)
|
||
|
|
||
|
for rate_to in rates_to:
|
||
|
t_to = np.arange(rate_to) / float(rate_to)
|
||
|
y_tos = np.sin(2 * np.pi * freqs * t_to) * hann(rate_to)
|
||
|
if method == 'fft':
|
||
|
y_resamps = signal.resample(x, rate_to, axis=-1)
|
||
|
else:
|
||
|
if ext and rate_to != rate:
|
||
|
# Match default window design
|
||
|
g = gcd(rate_to, rate)
|
||
|
up = rate_to // g
|
||
|
down = rate // g
|
||
|
max_rate = max(up, down)
|
||
|
f_c = 1. / max_rate
|
||
|
half_len = 10 * max_rate
|
||
|
window = signal.firwin(2 * half_len + 1, f_c,
|
||
|
window=('kaiser', 5.0))
|
||
|
polyargs = {'window': window, 'padtype': padtype}
|
||
|
else:
|
||
|
polyargs = {'padtype': padtype}
|
||
|
|
||
|
y_resamps = signal.resample_poly(x, rate_to, rate, axis=-1,
|
||
|
**polyargs)
|
||
|
|
||
|
for y_to, y_resamp, freq in zip(y_tos, y_resamps, freqs):
|
||
|
if freq >= 0.5 * rate_to:
|
||
|
y_to.fill(0.) # mostly low-passed away
|
||
|
if padtype in ['minimum', 'maximum']:
|
||
|
assert_allclose(y_resamp, y_to, atol=3e-1)
|
||
|
else:
|
||
|
assert_allclose(y_resamp, y_to, atol=1e-3)
|
||
|
else:
|
||
|
assert_array_equal(y_to.shape, y_resamp.shape)
|
||
|
corr = np.corrcoef(y_to, y_resamp)[0, 1]
|
||
|
assert_(corr > 0.99, msg=(corr, rate, rate_to))
|
||
|
|
||
|
# Random data
|
||
|
rng = np.random.RandomState(0)
|
||
|
x = hann(rate) * np.cumsum(rng.randn(rate)) # low-pass, wind
|
||
|
for rate_to in rates_to:
|
||
|
# random data
|
||
|
t_to = np.arange(rate_to) / float(rate_to)
|
||
|
y_to = np.interp(t_to, t, x)
|
||
|
if method == 'fft':
|
||
|
y_resamp = signal.resample(x, rate_to)
|
||
|
else:
|
||
|
y_resamp = signal.resample_poly(x, rate_to, rate,
|
||
|
padtype=padtype)
|
||
|
assert_array_equal(y_to.shape, y_resamp.shape)
|
||
|
corr = np.corrcoef(y_to, y_resamp)[0, 1]
|
||
|
assert_(corr > 0.99, msg=corr)
|
||
|
|
||
|
# More tests of fft method (Master 0.18.1 fails these)
|
||
|
if method == 'fft':
|
||
|
x1 = np.array([1.+0.j, 0.+0.j])
|
||
|
y1_test = signal.resample(x1, 4)
|
||
|
# upsampling a complex array
|
||
|
y1_true = np.array([1.+0.j, 0.5+0.j, 0.+0.j, 0.5+0.j])
|
||
|
assert_allclose(y1_test, y1_true, atol=1e-12)
|
||
|
x2 = np.array([1., 0.5, 0., 0.5])
|
||
|
y2_test = signal.resample(x2, 2) # downsampling a real array
|
||
|
y2_true = np.array([1., 0.])
|
||
|
assert_allclose(y2_test, y2_true, atol=1e-12)
|
||
|
|
||
|
def test_poly_vs_filtfilt(self):
|
||
|
# Check that up=1.0 gives same answer as filtfilt + slicing
|
||
|
random_state = np.random.RandomState(17)
|
||
|
try_types = (int, np.float32, np.complex64, float, complex)
|
||
|
size = 10000
|
||
|
down_factors = [2, 11, 79]
|
||
|
|
||
|
for dtype in try_types:
|
||
|
x = random_state.randn(size).astype(dtype)
|
||
|
if dtype in (np.complex64, np.complex128):
|
||
|
x += 1j * random_state.randn(size)
|
||
|
|
||
|
# resample_poly assumes zeros outside of signl, whereas filtfilt
|
||
|
# can only constant-pad. Make them equivalent:
|
||
|
x[0] = 0
|
||
|
x[-1] = 0
|
||
|
|
||
|
for down in down_factors:
|
||
|
h = signal.firwin(31, 1. / down, window='hamming')
|
||
|
yf = filtfilt(h, 1.0, x, padtype='constant')[::down]
|
||
|
|
||
|
# Need to pass convolved version of filter to resample_poly,
|
||
|
# since filtfilt does forward and backward, but resample_poly
|
||
|
# only goes forward
|
||
|
hc = convolve(h, h[::-1])
|
||
|
y = signal.resample_poly(x, 1, down, window=hc)
|
||
|
assert_allclose(yf, y, atol=1e-7, rtol=1e-7)
|
||
|
|
||
|
def test_correlate1d(self):
|
||
|
for down in [2, 4]:
|
||
|
for nx in range(1, 40, down):
|
||
|
for nweights in (32, 33):
|
||
|
x = np.random.random((nx,))
|
||
|
weights = np.random.random((nweights,))
|
||
|
y_g = correlate1d(x, weights[::-1], mode='constant')
|
||
|
y_s = signal.resample_poly(
|
||
|
x, up=1, down=down, window=weights)
|
||
|
assert_allclose(y_g[::down], y_s)
|
||
|
|
||
|
|
||
|
class TestCSpline1DEval:
|
||
|
|
||
|
def test_basic(self):
|
||
|
y = array([1, 2, 3, 4, 3, 2, 1, 2, 3.0])
|
||
|
x = arange(len(y))
|
||
|
dx = x[1] - x[0]
|
||
|
cj = signal.cspline1d(y)
|
||
|
|
||
|
x2 = arange(len(y) * 10.0) / 10.0
|
||
|
y2 = signal.cspline1d_eval(cj, x2, dx=dx, x0=x[0])
|
||
|
|
||
|
# make sure interpolated values are on knot points
|
||
|
assert_array_almost_equal(y2[::10], y, decimal=5)
|
||
|
|
||
|
def test_complex(self):
|
||
|
# create some smoothly varying complex signal to interpolate
|
||
|
x = np.arange(2)
|
||
|
y = np.zeros(x.shape, dtype=np.complex64)
|
||
|
T = 10.0
|
||
|
f = 1.0 / T
|
||
|
y = np.exp(2.0J * np.pi * f * x)
|
||
|
|
||
|
# get the cspline transform
|
||
|
cy = signal.cspline1d(y)
|
||
|
|
||
|
# determine new test x value and interpolate
|
||
|
xnew = np.array([0.5])
|
||
|
ynew = signal.cspline1d_eval(cy, xnew)
|
||
|
|
||
|
assert_equal(ynew.dtype, y.dtype)
|
||
|
|
||
|
class TestOrderFilt:
|
||
|
|
||
|
def test_basic(self):
|
||
|
assert_array_equal(signal.order_filter([1, 2, 3], [1, 0, 1], 1),
|
||
|
[2, 3, 2])
|
||
|
|
||
|
|
||
|
class _TestLinearFilter:
|
||
|
|
||
|
def generate(self, shape):
|
||
|
x = np.linspace(0, np.prod(shape) - 1, np.prod(shape)).reshape(shape)
|
||
|
return self.convert_dtype(x)
|
||
|
|
||
|
def convert_dtype(self, arr):
|
||
|
if self.dtype == np.dtype('O'):
|
||
|
arr = np.asarray(arr)
|
||
|
out = np.empty(arr.shape, self.dtype)
|
||
|
iter = np.nditer([arr, out], ['refs_ok','zerosize_ok'],
|
||
|
[['readonly'],['writeonly']])
|
||
|
for x, y in iter:
|
||
|
y[...] = self.type(x[()])
|
||
|
return out
|
||
|
else:
|
||
|
return np.array(arr, self.dtype, copy=False)
|
||
|
|
||
|
def test_rank_1_IIR(self):
|
||
|
x = self.generate((6,))
|
||
|
b = self.convert_dtype([1, -1])
|
||
|
a = self.convert_dtype([0.5, -0.5])
|
||
|
y_r = self.convert_dtype([0, 2, 4, 6, 8, 10.])
|
||
|
assert_array_almost_equal(lfilter(b, a, x), y_r)
|
||
|
|
||
|
def test_rank_1_FIR(self):
|
||
|
x = self.generate((6,))
|
||
|
b = self.convert_dtype([1, 1])
|
||
|
a = self.convert_dtype([1])
|
||
|
y_r = self.convert_dtype([0, 1, 3, 5, 7, 9.])
|
||
|
assert_array_almost_equal(lfilter(b, a, x), y_r)
|
||
|
|
||
|
def test_rank_1_IIR_init_cond(self):
|
||
|
x = self.generate((6,))
|
||
|
b = self.convert_dtype([1, 0, -1])
|
||
|
a = self.convert_dtype([0.5, -0.5])
|
||
|
zi = self.convert_dtype([1, 2])
|
||
|
y_r = self.convert_dtype([1, 5, 9, 13, 17, 21])
|
||
|
zf_r = self.convert_dtype([13, -10])
|
||
|
y, zf = lfilter(b, a, x, zi=zi)
|
||
|
assert_array_almost_equal(y, y_r)
|
||
|
assert_array_almost_equal(zf, zf_r)
|
||
|
|
||
|
def test_rank_1_FIR_init_cond(self):
|
||
|
x = self.generate((6,))
|
||
|
b = self.convert_dtype([1, 1, 1])
|
||
|
a = self.convert_dtype([1])
|
||
|
zi = self.convert_dtype([1, 1])
|
||
|
y_r = self.convert_dtype([1, 2, 3, 6, 9, 12.])
|
||
|
zf_r = self.convert_dtype([9, 5])
|
||
|
y, zf = lfilter(b, a, x, zi=zi)
|
||
|
assert_array_almost_equal(y, y_r)
|
||
|
assert_array_almost_equal(zf, zf_r)
|
||
|
|
||
|
def test_rank_2_IIR_axis_0(self):
|
||
|
x = self.generate((4, 3))
|
||
|
b = self.convert_dtype([1, -1])
|
||
|
a = self.convert_dtype([0.5, 0.5])
|
||
|
y_r2_a0 = self.convert_dtype([[0, 2, 4], [6, 4, 2], [0, 2, 4],
|
||
|
[6, 4, 2]])
|
||
|
y = lfilter(b, a, x, axis=0)
|
||
|
assert_array_almost_equal(y_r2_a0, y)
|
||
|
|
||
|
def test_rank_2_IIR_axis_1(self):
|
||
|
x = self.generate((4, 3))
|
||
|
b = self.convert_dtype([1, -1])
|
||
|
a = self.convert_dtype([0.5, 0.5])
|
||
|
y_r2_a1 = self.convert_dtype([[0, 2, 0], [6, -4, 6], [12, -10, 12],
|
||
|
[18, -16, 18]])
|
||
|
y = lfilter(b, a, x, axis=1)
|
||
|
assert_array_almost_equal(y_r2_a1, y)
|
||
|
|
||
|
def test_rank_2_IIR_axis_0_init_cond(self):
|
||
|
x = self.generate((4, 3))
|
||
|
b = self.convert_dtype([1, -1])
|
||
|
a = self.convert_dtype([0.5, 0.5])
|
||
|
zi = self.convert_dtype(np.ones((4,1)))
|
||
|
|
||
|
y_r2_a0_1 = self.convert_dtype([[1, 1, 1], [7, -5, 7], [13, -11, 13],
|
||
|
[19, -17, 19]])
|
||
|
zf_r = self.convert_dtype([-5, -17, -29, -41])[:, np.newaxis]
|
||
|
y, zf = lfilter(b, a, x, axis=1, zi=zi)
|
||
|
assert_array_almost_equal(y_r2_a0_1, y)
|
||
|
assert_array_almost_equal(zf, zf_r)
|
||
|
|
||
|
def test_rank_2_IIR_axis_1_init_cond(self):
|
||
|
x = self.generate((4,3))
|
||
|
b = self.convert_dtype([1, -1])
|
||
|
a = self.convert_dtype([0.5, 0.5])
|
||
|
zi = self.convert_dtype(np.ones((1,3)))
|
||
|
|
||
|
y_r2_a0_0 = self.convert_dtype([[1, 3, 5], [5, 3, 1],
|
||
|
[1, 3, 5], [5, 3, 1]])
|
||
|
zf_r = self.convert_dtype([[-23, -23, -23]])
|
||
|
y, zf = lfilter(b, a, x, axis=0, zi=zi)
|
||
|
assert_array_almost_equal(y_r2_a0_0, y)
|
||
|
assert_array_almost_equal(zf, zf_r)
|
||
|
|
||
|
def test_rank_3_IIR(self):
|
||
|
x = self.generate((4, 3, 2))
|
||
|
b = self.convert_dtype([1, -1])
|
||
|
a = self.convert_dtype([0.5, 0.5])
|
||
|
|
||
|
for axis in range(x.ndim):
|
||
|
y = lfilter(b, a, x, axis)
|
||
|
y_r = np.apply_along_axis(lambda w: lfilter(b, a, w), axis, x)
|
||
|
assert_array_almost_equal(y, y_r)
|
||
|
|
||
|
def test_rank_3_IIR_init_cond(self):
|
||
|
x = self.generate((4, 3, 2))
|
||
|
b = self.convert_dtype([1, -1])
|
||
|
a = self.convert_dtype([0.5, 0.5])
|
||
|
|
||
|
for axis in range(x.ndim):
|
||
|
zi_shape = list(x.shape)
|
||
|
zi_shape[axis] = 1
|
||
|
zi = self.convert_dtype(np.ones(zi_shape))
|
||
|
zi1 = self.convert_dtype([1])
|
||
|
y, zf = lfilter(b, a, x, axis, zi)
|
||
|
lf0 = lambda w: lfilter(b, a, w, zi=zi1)[0]
|
||
|
lf1 = lambda w: lfilter(b, a, w, zi=zi1)[1]
|
||
|
y_r = np.apply_along_axis(lf0, axis, x)
|
||
|
zf_r = np.apply_along_axis(lf1, axis, x)
|
||
|
assert_array_almost_equal(y, y_r)
|
||
|
assert_array_almost_equal(zf, zf_r)
|
||
|
|
||
|
def test_rank_3_FIR(self):
|
||
|
x = self.generate((4, 3, 2))
|
||
|
b = self.convert_dtype([1, 0, -1])
|
||
|
a = self.convert_dtype([1])
|
||
|
|
||
|
for axis in range(x.ndim):
|
||
|
y = lfilter(b, a, x, axis)
|
||
|
y_r = np.apply_along_axis(lambda w: lfilter(b, a, w), axis, x)
|
||
|
assert_array_almost_equal(y, y_r)
|
||
|
|
||
|
def test_rank_3_FIR_init_cond(self):
|
||
|
x = self.generate((4, 3, 2))
|
||
|
b = self.convert_dtype([1, 0, -1])
|
||
|
a = self.convert_dtype([1])
|
||
|
|
||
|
for axis in range(x.ndim):
|
||
|
zi_shape = list(x.shape)
|
||
|
zi_shape[axis] = 2
|
||
|
zi = self.convert_dtype(np.ones(zi_shape))
|
||
|
zi1 = self.convert_dtype([1, 1])
|
||
|
y, zf = lfilter(b, a, x, axis, zi)
|
||
|
lf0 = lambda w: lfilter(b, a, w, zi=zi1)[0]
|
||
|
lf1 = lambda w: lfilter(b, a, w, zi=zi1)[1]
|
||
|
y_r = np.apply_along_axis(lf0, axis, x)
|
||
|
zf_r = np.apply_along_axis(lf1, axis, x)
|
||
|
assert_array_almost_equal(y, y_r)
|
||
|
assert_array_almost_equal(zf, zf_r)
|
||
|
|
||
|
def test_zi_pseudobroadcast(self):
|
||
|
x = self.generate((4, 5, 20))
|
||
|
b,a = signal.butter(8, 0.2, output='ba')
|
||
|
b = self.convert_dtype(b)
|
||
|
a = self.convert_dtype(a)
|
||
|
zi_size = b.shape[0] - 1
|
||
|
|
||
|
# lfilter requires x.ndim == zi.ndim exactly. However, zi can have
|
||
|
# length 1 dimensions.
|
||
|
zi_full = self.convert_dtype(np.ones((4, 5, zi_size)))
|
||
|
zi_sing = self.convert_dtype(np.ones((1, 1, zi_size)))
|
||
|
|
||
|
y_full, zf_full = lfilter(b, a, x, zi=zi_full)
|
||
|
y_sing, zf_sing = lfilter(b, a, x, zi=zi_sing)
|
||
|
|
||
|
assert_array_almost_equal(y_sing, y_full)
|
||
|
assert_array_almost_equal(zf_full, zf_sing)
|
||
|
|
||
|
# lfilter does not prepend ones
|
||
|
assert_raises(ValueError, lfilter, b, a, x, -1, np.ones(zi_size))
|
||
|
|
||
|
def test_scalar_a(self):
|
||
|
# a can be a scalar.
|
||
|
x = self.generate(6)
|
||
|
b = self.convert_dtype([1, 0, -1])
|
||
|
a = self.convert_dtype([1])
|
||
|
y_r = self.convert_dtype([0, 1, 2, 2, 2, 2])
|
||
|
|
||
|
y = lfilter(b, a[0], x)
|
||
|
assert_array_almost_equal(y, y_r)
|
||
|
|
||
|
def test_zi_some_singleton_dims(self):
|
||
|
# lfilter doesn't really broadcast (no prepending of 1's). But does
|
||
|
# do singleton expansion if x and zi have the same ndim. This was
|
||
|
# broken only if a subset of the axes were singletons (gh-4681).
|
||
|
x = self.convert_dtype(np.zeros((3,2,5), 'l'))
|
||
|
b = self.convert_dtype(np.ones(5, 'l'))
|
||
|
a = self.convert_dtype(np.array([1,0,0]))
|
||
|
zi = np.ones((3,1,4), 'l')
|
||
|
zi[1,:,:] *= 2
|
||
|
zi[2,:,:] *= 3
|
||
|
zi = self.convert_dtype(zi)
|
||
|
|
||
|
zf_expected = self.convert_dtype(np.zeros((3,2,4), 'l'))
|
||
|
y_expected = np.zeros((3,2,5), 'l')
|
||
|
y_expected[:,:,:4] = [[[1]], [[2]], [[3]]]
|
||
|
y_expected = self.convert_dtype(y_expected)
|
||
|
|
||
|
# IIR
|
||
|
y_iir, zf_iir = lfilter(b, a, x, -1, zi)
|
||
|
assert_array_almost_equal(y_iir, y_expected)
|
||
|
assert_array_almost_equal(zf_iir, zf_expected)
|
||
|
|
||
|
# FIR
|
||
|
y_fir, zf_fir = lfilter(b, a[0], x, -1, zi)
|
||
|
assert_array_almost_equal(y_fir, y_expected)
|
||
|
assert_array_almost_equal(zf_fir, zf_expected)
|
||
|
|
||
|
def base_bad_size_zi(self, b, a, x, axis, zi):
|
||
|
b = self.convert_dtype(b)
|
||
|
a = self.convert_dtype(a)
|
||
|
x = self.convert_dtype(x)
|
||
|
zi = self.convert_dtype(zi)
|
||
|
assert_raises(ValueError, lfilter, b, a, x, axis, zi)
|
||
|
|
||
|
def test_bad_size_zi(self):
|
||
|
# rank 1
|
||
|
x1 = np.arange(6)
|
||
|
self.base_bad_size_zi([1], [1], x1, -1, [1])
|
||
|
self.base_bad_size_zi([1, 1], [1], x1, -1, [0, 1])
|
||
|
self.base_bad_size_zi([1, 1], [1], x1, -1, [[0]])
|
||
|
self.base_bad_size_zi([1, 1], [1], x1, -1, [0, 1, 2])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x1, -1, [[0]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x1, -1, [0, 1, 2])
|
||
|
self.base_bad_size_zi([1], [1, 1], x1, -1, [0, 1])
|
||
|
self.base_bad_size_zi([1], [1, 1], x1, -1, [[0]])
|
||
|
self.base_bad_size_zi([1], [1, 1], x1, -1, [0, 1, 2])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x1, -1, [0])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x1, -1, [[0], [1]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x1, -1, [0, 1, 2])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x1, -1, [0, 1, 2, 3])
|
||
|
self.base_bad_size_zi([1, 1], [1, 1, 1], x1, -1, [0])
|
||
|
self.base_bad_size_zi([1, 1], [1, 1, 1], x1, -1, [[0], [1]])
|
||
|
self.base_bad_size_zi([1, 1], [1, 1, 1], x1, -1, [0, 1, 2])
|
||
|
self.base_bad_size_zi([1, 1], [1, 1, 1], x1, -1, [0, 1, 2, 3])
|
||
|
|
||
|
# rank 2
|
||
|
x2 = np.arange(12).reshape((4,3))
|
||
|
# for axis=0 zi.shape should == (max(len(a),len(b))-1, 3)
|
||
|
self.base_bad_size_zi([1], [1], x2, 0, [0])
|
||
|
|
||
|
# for each of these there are 5 cases tested (in this order):
|
||
|
# 1. not deep enough, right # elements
|
||
|
# 2. too deep, right # elements
|
||
|
# 3. right depth, right # elements, transposed
|
||
|
# 4. right depth, too few elements
|
||
|
# 5. right depth, too many elements
|
||
|
|
||
|
self.base_bad_size_zi([1, 1], [1], x2, 0, [0,1,2])
|
||
|
self.base_bad_size_zi([1, 1], [1], x2, 0, [[[0,1,2]]])
|
||
|
self.base_bad_size_zi([1, 1], [1], x2, 0, [[0], [1], [2]])
|
||
|
self.base_bad_size_zi([1, 1], [1], x2, 0, [[0,1]])
|
||
|
self.base_bad_size_zi([1, 1], [1], x2, 0, [[0,1,2,3]])
|
||
|
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x2, 0, [0,1,2,3,4,5])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x2, 0, [[[0,1,2],[3,4,5]]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x2, 0, [[0,1],[2,3],[4,5]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x2, 0, [[0,1],[2,3]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x2, 0, [[0,1,2,3],[4,5,6,7]])
|
||
|
|
||
|
self.base_bad_size_zi([1], [1, 1], x2, 0, [0,1,2])
|
||
|
self.base_bad_size_zi([1], [1, 1], x2, 0, [[[0,1,2]]])
|
||
|
self.base_bad_size_zi([1], [1, 1], x2, 0, [[0], [1], [2]])
|
||
|
self.base_bad_size_zi([1], [1, 1], x2, 0, [[0,1]])
|
||
|
self.base_bad_size_zi([1], [1, 1], x2, 0, [[0,1,2,3]])
|
||
|
|
||
|
self.base_bad_size_zi([1], [1, 1, 1], x2, 0, [0,1,2,3,4,5])
|
||
|
self.base_bad_size_zi([1], [1, 1, 1], x2, 0, [[[0,1,2],[3,4,5]]])
|
||
|
self.base_bad_size_zi([1], [1, 1, 1], x2, 0, [[0,1],[2,3],[4,5]])
|
||
|
self.base_bad_size_zi([1], [1, 1, 1], x2, 0, [[0,1],[2,3]])
|
||
|
self.base_bad_size_zi([1], [1, 1, 1], x2, 0, [[0,1,2,3],[4,5,6,7]])
|
||
|
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 0, [0,1,2,3,4,5])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 0, [[[0,1,2],[3,4,5]]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 0, [[0,1],[2,3],[4,5]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 0, [[0,1],[2,3]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 0, [[0,1,2,3],[4,5,6,7]])
|
||
|
|
||
|
# for axis=1 zi.shape should == (4, max(len(a),len(b))-1)
|
||
|
self.base_bad_size_zi([1], [1], x2, 1, [0])
|
||
|
|
||
|
self.base_bad_size_zi([1, 1], [1], x2, 1, [0,1,2,3])
|
||
|
self.base_bad_size_zi([1, 1], [1], x2, 1, [[[0],[1],[2],[3]]])
|
||
|
self.base_bad_size_zi([1, 1], [1], x2, 1, [[0, 1, 2, 3]])
|
||
|
self.base_bad_size_zi([1, 1], [1], x2, 1, [[0],[1],[2]])
|
||
|
self.base_bad_size_zi([1, 1], [1], x2, 1, [[0],[1],[2],[3],[4]])
|
||
|
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x2, 1, [0,1,2,3,4,5,6,7])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x2, 1, [[[0,1],[2,3],[4,5],[6,7]]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x2, 1, [[0,1,2,3],[4,5,6,7]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x2, 1, [[0,1],[2,3],[4,5]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1], x2, 1, [[0,1],[2,3],[4,5],[6,7],[8,9]])
|
||
|
|
||
|
self.base_bad_size_zi([1], [1, 1], x2, 1, [0,1,2,3])
|
||
|
self.base_bad_size_zi([1], [1, 1], x2, 1, [[[0],[1],[2],[3]]])
|
||
|
self.base_bad_size_zi([1], [1, 1], x2, 1, [[0, 1, 2, 3]])
|
||
|
self.base_bad_size_zi([1], [1, 1], x2, 1, [[0],[1],[2]])
|
||
|
self.base_bad_size_zi([1], [1, 1], x2, 1, [[0],[1],[2],[3],[4]])
|
||
|
|
||
|
self.base_bad_size_zi([1], [1, 1, 1], x2, 1, [0,1,2,3,4,5,6,7])
|
||
|
self.base_bad_size_zi([1], [1, 1, 1], x2, 1, [[[0,1],[2,3],[4,5],[6,7]]])
|
||
|
self.base_bad_size_zi([1], [1, 1, 1], x2, 1, [[0,1,2,3],[4,5,6,7]])
|
||
|
self.base_bad_size_zi([1], [1, 1, 1], x2, 1, [[0,1],[2,3],[4,5]])
|
||
|
self.base_bad_size_zi([1], [1, 1, 1], x2, 1, [[0,1],[2,3],[4,5],[6,7],[8,9]])
|
||
|
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 1, [0,1,2,3,4,5,6,7])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 1, [[[0,1],[2,3],[4,5],[6,7]]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 1, [[0,1,2,3],[4,5,6,7]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 1, [[0,1],[2,3],[4,5]])
|
||
|
self.base_bad_size_zi([1, 1, 1], [1, 1], x2, 1, [[0,1],[2,3],[4,5],[6,7],[8,9]])
|
||
|
|
||
|
def test_empty_zi(self):
|
||
|
# Regression test for #880: empty array for zi crashes.
|
||
|
x = self.generate((5,))
|
||
|
a = self.convert_dtype([1])
|
||
|
b = self.convert_dtype([1])
|
||
|
zi = self.convert_dtype([])
|
||
|
y, zf = lfilter(b, a, x, zi=zi)
|
||
|
assert_array_almost_equal(y, x)
|
||
|
assert_equal(zf.dtype, self.dtype)
|
||
|
assert_equal(zf.size, 0)
|
||
|
|
||
|
def test_lfiltic_bad_zi(self):
|
||
|
# Regression test for #3699: bad initial conditions
|
||
|
a = self.convert_dtype([1])
|
||
|
b = self.convert_dtype([1])
|
||
|
# "y" sets the datatype of zi, so it truncates if int
|
||
|
zi = lfiltic(b, a, [1., 0])
|
||
|
zi_1 = lfiltic(b, a, [1, 0])
|
||
|
zi_2 = lfiltic(b, a, [True, False])
|
||
|
assert_array_equal(zi, zi_1)
|
||
|
assert_array_equal(zi, zi_2)
|
||
|
|
||
|
def test_short_x_FIR(self):
|
||
|
# regression test for #5116
|
||
|
# x shorter than b, with non None zi fails
|
||
|
a = self.convert_dtype([1])
|
||
|
b = self.convert_dtype([1, 0, -1])
|
||
|
zi = self.convert_dtype([2, 7])
|
||
|
x = self.convert_dtype([72])
|
||
|
ye = self.convert_dtype([74])
|
||
|
zfe = self.convert_dtype([7, -72])
|
||
|
y, zf = lfilter(b, a, x, zi=zi)
|
||
|
assert_array_almost_equal(y, ye)
|
||
|
assert_array_almost_equal(zf, zfe)
|
||
|
|
||
|
def test_short_x_IIR(self):
|
||
|
# regression test for #5116
|
||
|
# x shorter than b, with non None zi fails
|
||
|
a = self.convert_dtype([1, 1])
|
||
|
b = self.convert_dtype([1, 0, -1])
|
||
|
zi = self.convert_dtype([2, 7])
|
||
|
x = self.convert_dtype([72])
|
||
|
ye = self.convert_dtype([74])
|
||
|
zfe = self.convert_dtype([-67, -72])
|
||
|
y, zf = lfilter(b, a, x, zi=zi)
|
||
|
assert_array_almost_equal(y, ye)
|
||
|
assert_array_almost_equal(zf, zfe)
|
||
|
|
||
|
def test_do_not_modify_a_b_IIR(self):
|
||
|
x = self.generate((6,))
|
||
|
b = self.convert_dtype([1, -1])
|
||
|
b0 = b.copy()
|
||
|
a = self.convert_dtype([0.5, -0.5])
|
||
|
a0 = a.copy()
|
||
|
y_r = self.convert_dtype([0, 2, 4, 6, 8, 10.])
|
||
|
y_f = lfilter(b, a, x)
|
||
|
assert_array_almost_equal(y_f, y_r)
|
||
|
assert_equal(b, b0)
|
||
|
assert_equal(a, a0)
|
||
|
|
||
|
def test_do_not_modify_a_b_FIR(self):
|
||
|
x = self.generate((6,))
|
||
|
b = self.convert_dtype([1, 0, 1])
|
||
|
b0 = b.copy()
|
||
|
a = self.convert_dtype([2])
|
||
|
a0 = a.copy()
|
||
|
y_r = self.convert_dtype([0, 0.5, 1, 2, 3, 4.])
|
||
|
y_f = lfilter(b, a, x)
|
||
|
assert_array_almost_equal(y_f, y_r)
|
||
|
assert_equal(b, b0)
|
||
|
assert_equal(a, a0)
|
||
|
|
||
|
|
||
|
class TestLinearFilterFloat32(_TestLinearFilter):
|
||
|
dtype = np.dtype('f')
|
||
|
|
||
|
|
||
|
class TestLinearFilterFloat64(_TestLinearFilter):
|
||
|
dtype = np.dtype('d')
|
||
|
|
||
|
|
||
|
class TestLinearFilterFloatExtended(_TestLinearFilter):
|
||
|
dtype = np.dtype('g')
|
||
|
|
||
|
|
||
|
class TestLinearFilterComplex64(_TestLinearFilter):
|
||
|
dtype = np.dtype('F')
|
||
|
|
||
|
|
||
|
class TestLinearFilterComplex128(_TestLinearFilter):
|
||
|
dtype = np.dtype('D')
|
||
|
|
||
|
|
||
|
class TestLinearFilterComplexExtended(_TestLinearFilter):
|
||
|
dtype = np.dtype('G')
|
||
|
|
||
|
class TestLinearFilterDecimal(_TestLinearFilter):
|
||
|
dtype = np.dtype('O')
|
||
|
|
||
|
def type(self, x):
|
||
|
return Decimal(str(x))
|
||
|
|
||
|
|
||
|
class TestLinearFilterObject(_TestLinearFilter):
|
||
|
dtype = np.dtype('O')
|
||
|
type = float
|
||
|
|
||
|
|
||
|
def test_lfilter_bad_object():
|
||
|
# lfilter: object arrays with non-numeric objects raise TypeError.
|
||
|
# Regression test for ticket #1452.
|
||
|
assert_raises(TypeError, lfilter, [1.0], [1.0], [1.0, None, 2.0])
|
||
|
assert_raises(TypeError, lfilter, [1.0], [None], [1.0, 2.0, 3.0])
|
||
|
assert_raises(TypeError, lfilter, [None], [1.0], [1.0, 2.0, 3.0])
|
||
|
|
||
|
|
||
|
def test_lfilter_notimplemented_input():
|
||
|
# Should not crash, gh-7991
|
||
|
assert_raises(NotImplementedError, lfilter, [2,3], [4,5], [1,2,3,4,5])
|
||
|
|
||
|
|
||
|
@pytest.mark.parametrize('dt', [np.ubyte, np.byte, np.ushort, np.short,
|
||
|
np.uint, int, np.ulonglong, np.ulonglong,
|
||
|
np.float32, np.float64, np.longdouble,
|
||
|
Decimal])
|
||
|
class TestCorrelateReal:
|
||
|
def _setup_rank1(self, dt):
|
||
|
a = np.linspace(0, 3, 4).astype(dt)
|
||
|
b = np.linspace(1, 2, 2).astype(dt)
|
||
|
|
||
|
y_r = np.array([0, 2, 5, 8, 3]).astype(dt)
|
||
|
return a, b, y_r
|
||
|
|
||
|
def equal_tolerance(self, res_dt):
|
||
|
# default value of keyword
|
||
|
decimal = 6
|
||
|
try:
|
||
|
dt_info = np.finfo(res_dt)
|
||
|
if hasattr(dt_info, 'resolution'):
|
||
|
decimal = int(-0.5*np.log10(dt_info.resolution))
|
||
|
except Exception:
|
||
|
pass
|
||
|
return decimal
|
||
|
|
||
|
def equal_tolerance_fft(self, res_dt):
|
||
|
# FFT implementations convert longdouble arguments down to
|
||
|
# double so don't expect better precision, see gh-9520
|
||
|
if res_dt == np.longdouble:
|
||
|
return self.equal_tolerance(np.double)
|
||
|
else:
|
||
|
return self.equal_tolerance(res_dt)
|
||
|
|
||
|
def test_method(self, dt):
|
||
|
if dt == Decimal:
|
||
|
method = choose_conv_method([Decimal(4)], [Decimal(3)])
|
||
|
assert_equal(method, 'direct')
|
||
|
else:
|
||
|
a, b, y_r = self._setup_rank3(dt)
|
||
|
y_fft = correlate(a, b, method='fft')
|
||
|
y_direct = correlate(a, b, method='direct')
|
||
|
|
||
|
assert_array_almost_equal(y_r, y_fft, decimal=self.equal_tolerance_fft(y_fft.dtype))
|
||
|
assert_array_almost_equal(y_r, y_direct, decimal=self.equal_tolerance(y_direct.dtype))
|
||
|
assert_equal(y_fft.dtype, dt)
|
||
|
assert_equal(y_direct.dtype, dt)
|
||
|
|
||
|
def test_rank1_valid(self, dt):
|
||
|
a, b, y_r = self._setup_rank1(dt)
|
||
|
y = correlate(a, b, 'valid')
|
||
|
assert_array_almost_equal(y, y_r[1:4])
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
# See gh-5897
|
||
|
y = correlate(b, a, 'valid')
|
||
|
assert_array_almost_equal(y, y_r[1:4][::-1])
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
def test_rank1_same(self, dt):
|
||
|
a, b, y_r = self._setup_rank1(dt)
|
||
|
y = correlate(a, b, 'same')
|
||
|
assert_array_almost_equal(y, y_r[:-1])
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
def test_rank1_full(self, dt):
|
||
|
a, b, y_r = self._setup_rank1(dt)
|
||
|
y = correlate(a, b, 'full')
|
||
|
assert_array_almost_equal(y, y_r)
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
def _setup_rank3(self, dt):
|
||
|
a = np.linspace(0, 39, 40).reshape((2, 4, 5), order='F').astype(
|
||
|
dt)
|
||
|
b = np.linspace(0, 23, 24).reshape((2, 3, 4), order='F').astype(
|
||
|
dt)
|
||
|
|
||
|
y_r = array([[[0., 184., 504., 912., 1360., 888., 472., 160.],
|
||
|
[46., 432., 1062., 1840., 2672., 1698., 864., 266.],
|
||
|
[134., 736., 1662., 2768., 3920., 2418., 1168., 314.],
|
||
|
[260., 952., 1932., 3056., 4208., 2580., 1240., 332.],
|
||
|
[202., 664., 1290., 1984., 2688., 1590., 712., 150.],
|
||
|
[114., 344., 642., 960., 1280., 726., 296., 38.]],
|
||
|
|
||
|
[[23., 400., 1035., 1832., 2696., 1737., 904., 293.],
|
||
|
[134., 920., 2166., 3680., 5280., 3306., 1640., 474.],
|
||
|
[325., 1544., 3369., 5512., 7720., 4683., 2192., 535.],
|
||
|
[571., 1964., 3891., 6064., 8272., 4989., 2324., 565.],
|
||
|
[434., 1360., 2586., 3920., 5264., 3054., 1312., 230.],
|
||
|
[241., 700., 1281., 1888., 2496., 1383., 532., 39.]],
|
||
|
|
||
|
[[22., 214., 528., 916., 1332., 846., 430., 132.],
|
||
|
[86., 484., 1098., 1832., 2600., 1602., 772., 206.],
|
||
|
[188., 802., 1698., 2732., 3788., 2256., 1018., 218.],
|
||
|
[308., 1006., 1950., 2996., 4052., 2400., 1078., 230.],
|
||
|
[230., 692., 1290., 1928., 2568., 1458., 596., 78.],
|
||
|
[126., 354., 636., 924., 1212., 654., 234., 0.]]],
|
||
|
dtype=dt)
|
||
|
|
||
|
return a, b, y_r
|
||
|
|
||
|
def test_rank3_valid(self, dt):
|
||
|
a, b, y_r = self._setup_rank3(dt)
|
||
|
y = correlate(a, b, "valid")
|
||
|
assert_array_almost_equal(y, y_r[1:2, 2:4, 3:5])
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
# See gh-5897
|
||
|
y = correlate(b, a, "valid")
|
||
|
assert_array_almost_equal(y, y_r[1:2, 2:4, 3:5][::-1, ::-1, ::-1])
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
def test_rank3_same(self, dt):
|
||
|
a, b, y_r = self._setup_rank3(dt)
|
||
|
y = correlate(a, b, "same")
|
||
|
assert_array_almost_equal(y, y_r[0:-1, 1:-1, 1:-2])
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
def test_rank3_all(self, dt):
|
||
|
a, b, y_r = self._setup_rank3(dt)
|
||
|
y = correlate(a, b)
|
||
|
assert_array_almost_equal(y, y_r)
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
|
||
|
class TestCorrelate:
|
||
|
# Tests that don't depend on dtype
|
||
|
|
||
|
def test_invalid_shapes(self):
|
||
|
# By "invalid," we mean that no one
|
||
|
# array has dimensions that are all at
|
||
|
# least as large as the corresponding
|
||
|
# dimensions of the other array. This
|
||
|
# setup should throw a ValueError.
|
||
|
a = np.arange(1, 7).reshape((2, 3))
|
||
|
b = np.arange(-6, 0).reshape((3, 2))
|
||
|
|
||
|
assert_raises(ValueError, correlate, *(a, b), **{'mode': 'valid'})
|
||
|
assert_raises(ValueError, correlate, *(b, a), **{'mode': 'valid'})
|
||
|
|
||
|
def test_invalid_params(self):
|
||
|
a = [3, 4, 5]
|
||
|
b = [1, 2, 3]
|
||
|
assert_raises(ValueError, correlate, a, b, mode='spam')
|
||
|
assert_raises(ValueError, correlate, a, b, mode='eggs', method='fft')
|
||
|
assert_raises(ValueError, correlate, a, b, mode='ham', method='direct')
|
||
|
assert_raises(ValueError, correlate, a, b, mode='full', method='bacon')
|
||
|
assert_raises(ValueError, correlate, a, b, mode='same', method='bacon')
|
||
|
|
||
|
def test_mismatched_dims(self):
|
||
|
# Input arrays should have the same number of dimensions
|
||
|
assert_raises(ValueError, correlate, [1], 2, method='direct')
|
||
|
assert_raises(ValueError, correlate, 1, [2], method='direct')
|
||
|
assert_raises(ValueError, correlate, [1], 2, method='fft')
|
||
|
assert_raises(ValueError, correlate, 1, [2], method='fft')
|
||
|
assert_raises(ValueError, correlate, [1], [[2]])
|
||
|
assert_raises(ValueError, correlate, [3], 2)
|
||
|
|
||
|
def test_numpy_fastpath(self):
|
||
|
a = [1, 2, 3]
|
||
|
b = [4, 5]
|
||
|
assert_allclose(correlate(a, b, mode='same'), [5, 14, 23])
|
||
|
|
||
|
a = [1, 2, 3]
|
||
|
b = [4, 5, 6]
|
||
|
assert_allclose(correlate(a, b, mode='same'), [17, 32, 23])
|
||
|
assert_allclose(correlate(a, b, mode='full'), [6, 17, 32, 23, 12])
|
||
|
assert_allclose(correlate(a, b, mode='valid'), [32])
|
||
|
|
||
|
|
||
|
@pytest.mark.parametrize("mode", ["valid", "same", "full"])
|
||
|
@pytest.mark.parametrize("behind", [True, False])
|
||
|
@pytest.mark.parametrize("input_size", [100, 101, 1000, 1001, 10000, 10001])
|
||
|
def test_correlation_lags(mode, behind, input_size):
|
||
|
# generate random data
|
||
|
rng = np.random.RandomState(0)
|
||
|
in1 = rng.standard_normal(input_size)
|
||
|
offset = int(input_size/10)
|
||
|
# generate offset version of array to correlate with
|
||
|
if behind:
|
||
|
# y is behind x
|
||
|
in2 = np.concatenate([rng.standard_normal(offset), in1])
|
||
|
expected = -offset
|
||
|
else:
|
||
|
# y is ahead of x
|
||
|
in2 = in1[offset:]
|
||
|
expected = offset
|
||
|
# cross correlate, returning lag information
|
||
|
correlation = correlate(in1, in2, mode=mode)
|
||
|
lags = correlation_lags(in1.size, in2.size, mode=mode)
|
||
|
# identify the peak
|
||
|
lag_index = np.argmax(correlation)
|
||
|
# Check as expected
|
||
|
assert_equal(lags[lag_index], expected)
|
||
|
# Correlation and lags shape should match
|
||
|
assert_equal(lags.shape, correlation.shape)
|
||
|
|
||
|
|
||
|
@pytest.mark.parametrize('dt', [np.csingle, np.cdouble, np.clongdouble])
|
||
|
class TestCorrelateComplex:
|
||
|
# The decimal precision to be used for comparing results.
|
||
|
# This value will be passed as the 'decimal' keyword argument of
|
||
|
# assert_array_almost_equal().
|
||
|
# Since correlate may chose to use FFT method which converts
|
||
|
# longdoubles to doubles internally don't expect better precision
|
||
|
# for longdouble than for double (see gh-9520).
|
||
|
|
||
|
def decimal(self, dt):
|
||
|
if dt == np.clongdouble:
|
||
|
dt = np.cdouble
|
||
|
return int(2 * np.finfo(dt).precision / 3)
|
||
|
|
||
|
def _setup_rank1(self, dt, mode):
|
||
|
np.random.seed(9)
|
||
|
a = np.random.randn(10).astype(dt)
|
||
|
a += 1j * np.random.randn(10).astype(dt)
|
||
|
b = np.random.randn(8).astype(dt)
|
||
|
b += 1j * np.random.randn(8).astype(dt)
|
||
|
|
||
|
y_r = (correlate(a.real, b.real, mode=mode) +
|
||
|
correlate(a.imag, b.imag, mode=mode)).astype(dt)
|
||
|
y_r += 1j * (-correlate(a.real, b.imag, mode=mode) +
|
||
|
correlate(a.imag, b.real, mode=mode))
|
||
|
return a, b, y_r
|
||
|
|
||
|
def test_rank1_valid(self, dt):
|
||
|
a, b, y_r = self._setup_rank1(dt, 'valid')
|
||
|
y = correlate(a, b, 'valid')
|
||
|
assert_array_almost_equal(y, y_r, decimal=self.decimal(dt))
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
# See gh-5897
|
||
|
y = correlate(b, a, 'valid')
|
||
|
assert_array_almost_equal(y, y_r[::-1].conj(), decimal=self.decimal(dt))
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
def test_rank1_same(self, dt):
|
||
|
a, b, y_r = self._setup_rank1(dt, 'same')
|
||
|
y = correlate(a, b, 'same')
|
||
|
assert_array_almost_equal(y, y_r, decimal=self.decimal(dt))
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
def test_rank1_full(self, dt):
|
||
|
a, b, y_r = self._setup_rank1(dt, 'full')
|
||
|
y = correlate(a, b, 'full')
|
||
|
assert_array_almost_equal(y, y_r, decimal=self.decimal(dt))
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
def test_swap_full(self, dt):
|
||
|
d = np.array([0.+0.j, 1.+1.j, 2.+2.j], dtype=dt)
|
||
|
k = np.array([1.+3.j, 2.+4.j, 3.+5.j, 4.+6.j], dtype=dt)
|
||
|
y = correlate(d, k)
|
||
|
assert_equal(y, [0.+0.j, 10.-2.j, 28.-6.j, 22.-6.j, 16.-6.j, 8.-4.j])
|
||
|
|
||
|
def test_swap_same(self, dt):
|
||
|
d = [0.+0.j, 1.+1.j, 2.+2.j]
|
||
|
k = [1.+3.j, 2.+4.j, 3.+5.j, 4.+6.j]
|
||
|
y = correlate(d, k, mode="same")
|
||
|
assert_equal(y, [10.-2.j, 28.-6.j, 22.-6.j])
|
||
|
|
||
|
def test_rank3(self, dt):
|
||
|
a = np.random.randn(10, 8, 6).astype(dt)
|
||
|
a += 1j * np.random.randn(10, 8, 6).astype(dt)
|
||
|
b = np.random.randn(8, 6, 4).astype(dt)
|
||
|
b += 1j * np.random.randn(8, 6, 4).astype(dt)
|
||
|
|
||
|
y_r = (correlate(a.real, b.real)
|
||
|
+ correlate(a.imag, b.imag)).astype(dt)
|
||
|
y_r += 1j * (-correlate(a.real, b.imag) + correlate(a.imag, b.real))
|
||
|
|
||
|
y = correlate(a, b, 'full')
|
||
|
assert_array_almost_equal(y, y_r, decimal=self.decimal(dt) - 1)
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
def test_rank0(self, dt):
|
||
|
a = np.array(np.random.randn()).astype(dt)
|
||
|
a += 1j * np.array(np.random.randn()).astype(dt)
|
||
|
b = np.array(np.random.randn()).astype(dt)
|
||
|
b += 1j * np.array(np.random.randn()).astype(dt)
|
||
|
|
||
|
y_r = (correlate(a.real, b.real)
|
||
|
+ correlate(a.imag, b.imag)).astype(dt)
|
||
|
y_r += 1j * np.array(-correlate(a.real, b.imag) +
|
||
|
correlate(a.imag, b.real))
|
||
|
|
||
|
y = correlate(a, b, 'full')
|
||
|
assert_array_almost_equal(y, y_r, decimal=self.decimal(dt) - 1)
|
||
|
assert_equal(y.dtype, dt)
|
||
|
|
||
|
assert_equal(correlate([1], [2j]), correlate(1, 2j))
|
||
|
assert_equal(correlate([2j], [3j]), correlate(2j, 3j))
|
||
|
assert_equal(correlate([3j], [4]), correlate(3j, 4))
|
||
|
|
||
|
|
||
|
class TestCorrelate2d:
|
||
|
|
||
|
def test_consistency_correlate_funcs(self):
|
||
|
# Compare np.correlate, signal.correlate, signal.correlate2d
|
||
|
a = np.arange(5)
|
||
|
b = np.array([3.2, 1.4, 3])
|
||
|
for mode in ['full', 'valid', 'same']:
|
||
|
assert_almost_equal(np.correlate(a, b, mode=mode),
|
||
|
signal.correlate(a, b, mode=mode))
|
||
|
assert_almost_equal(np.squeeze(signal.correlate2d([a], [b],
|
||
|
mode=mode)),
|
||
|
signal.correlate(a, b, mode=mode))
|
||
|
|
||
|
# See gh-5897
|
||
|
if mode == 'valid':
|
||
|
assert_almost_equal(np.correlate(b, a, mode=mode),
|
||
|
signal.correlate(b, a, mode=mode))
|
||
|
assert_almost_equal(np.squeeze(signal.correlate2d([b], [a],
|
||
|
mode=mode)),
|
||
|
signal.correlate(b, a, mode=mode))
|
||
|
|
||
|
def test_invalid_shapes(self):
|
||
|
# By "invalid," we mean that no one
|
||
|
# array has dimensions that are all at
|
||
|
# least as large as the corresponding
|
||
|
# dimensions of the other array. This
|
||
|
# setup should throw a ValueError.
|
||
|
a = np.arange(1, 7).reshape((2, 3))
|
||
|
b = np.arange(-6, 0).reshape((3, 2))
|
||
|
|
||
|
assert_raises(ValueError, signal.correlate2d, *(a, b), **{'mode': 'valid'})
|
||
|
assert_raises(ValueError, signal.correlate2d, *(b, a), **{'mode': 'valid'})
|
||
|
|
||
|
def test_complex_input(self):
|
||
|
assert_equal(signal.correlate2d([[1]], [[2j]]), -2j)
|
||
|
assert_equal(signal.correlate2d([[2j]], [[3j]]), 6)
|
||
|
assert_equal(signal.correlate2d([[3j]], [[4]]), 12j)
|
||
|
|
||
|
|
||
|
class TestLFilterZI:
|
||
|
|
||
|
def test_basic(self):
|
||
|
a = np.array([1.0, -1.0, 0.5])
|
||
|
b = np.array([1.0, 0.0, 2.0])
|
||
|
zi_expected = np.array([5.0, -1.0])
|
||
|
zi = lfilter_zi(b, a)
|
||
|
assert_array_almost_equal(zi, zi_expected)
|
||
|
|
||
|
def test_scale_invariance(self):
|
||
|
# Regression test. There was a bug in which b was not correctly
|
||
|
# rescaled when a[0] was nonzero.
|
||
|
b = np.array([2, 8, 5])
|
||
|
a = np.array([1, 1, 8])
|
||
|
zi1 = lfilter_zi(b, a)
|
||
|
zi2 = lfilter_zi(2*b, 2*a)
|
||
|
assert_allclose(zi2, zi1, rtol=1e-12)
|
||
|
|
||
|
@pytest.mark.parametrize('dtype', [np.float32, np.float64])
|
||
|
def test_types(self, dtype):
|
||
|
b = np.zeros((8), dtype=dtype)
|
||
|
a = np.array([1], dtype=dtype)
|
||
|
assert_equal(np.real(signal.lfilter_zi(b, a)).dtype, dtype)
|
||
|
|
||
|
|
||
|
class TestFiltFilt:
|
||
|
filtfilt_kind = 'tf'
|
||
|
|
||
|
def filtfilt(self, zpk, x, axis=-1, padtype='odd', padlen=None,
|
||
|
method='pad', irlen=None):
|
||
|
if self.filtfilt_kind == 'tf':
|
||
|
b, a = zpk2tf(*zpk)
|
||
|
return filtfilt(b, a, x, axis, padtype, padlen, method, irlen)
|
||
|
elif self.filtfilt_kind == 'sos':
|
||
|
sos = zpk2sos(*zpk)
|
||
|
return sosfiltfilt(sos, x, axis, padtype, padlen)
|
||
|
|
||
|
def test_basic(self):
|
||
|
zpk = tf2zpk([1, 2, 3], [1, 2, 3])
|
||
|
out = self.filtfilt(zpk, np.arange(12))
|
||
|
assert_allclose(out, arange(12), atol=5.28e-11)
|
||
|
|
||
|
def test_sine(self):
|
||
|
rate = 2000
|
||
|
t = np.linspace(0, 1.0, rate + 1)
|
||
|
# A signal with low frequency and a high frequency.
|
||
|
xlow = np.sin(5 * 2 * np.pi * t)
|
||
|
xhigh = np.sin(250 * 2 * np.pi * t)
|
||
|
x = xlow + xhigh
|
||
|
|
||
|
zpk = butter(8, 0.125, output='zpk')
|
||
|
# r is the magnitude of the largest pole.
|
||
|
r = np.abs(zpk[1]).max()
|
||
|
eps = 1e-5
|
||
|
# n estimates the number of steps for the
|
||
|
# transient to decay by a factor of eps.
|
||
|
n = int(np.ceil(np.log(eps) / np.log(r)))
|
||
|
|
||
|
# High order lowpass filter...
|
||
|
y = self.filtfilt(zpk, x, padlen=n)
|
||
|
# Result should be just xlow.
|
||
|
err = np.abs(y - xlow).max()
|
||
|
assert_(err < 1e-4)
|
||
|
|
||
|
# A 2D case.
|
||
|
x2d = np.vstack([xlow, xlow + xhigh])
|
||
|
y2d = self.filtfilt(zpk, x2d, padlen=n, axis=1)
|
||
|
assert_equal(y2d.shape, x2d.shape)
|
||
|
err = np.abs(y2d - xlow).max()
|
||
|
assert_(err < 1e-4)
|
||
|
|
||
|
# Use the previous result to check the use of the axis keyword.
|
||
|
# (Regression test for ticket #1620)
|
||
|
y2dt = self.filtfilt(zpk, x2d.T, padlen=n, axis=0)
|
||
|
assert_equal(y2d, y2dt.T)
|
||
|
|
||
|
def test_axis(self):
|
||
|
# Test the 'axis' keyword on a 3D array.
|
||
|
x = np.arange(10.0 * 11.0 * 12.0).reshape(10, 11, 12)
|
||
|
zpk = butter(3, 0.125, output='zpk')
|
||
|
y0 = self.filtfilt(zpk, x, padlen=0, axis=0)
|
||
|
y1 = self.filtfilt(zpk, np.swapaxes(x, 0, 1), padlen=0, axis=1)
|
||
|
assert_array_equal(y0, np.swapaxes(y1, 0, 1))
|
||
|
y2 = self.filtfilt(zpk, np.swapaxes(x, 0, 2), padlen=0, axis=2)
|
||
|
assert_array_equal(y0, np.swapaxes(y2, 0, 2))
|
||
|
|
||
|
def test_acoeff(self):
|
||
|
if self.filtfilt_kind != 'tf':
|
||
|
return # only necessary for TF
|
||
|
# test for 'a' coefficient as single number
|
||
|
out = signal.filtfilt([.5, .5], 1, np.arange(10))
|
||
|
assert_allclose(out, np.arange(10), rtol=1e-14, atol=1e-14)
|
||
|
|
||
|
def test_gust_simple(self):
|
||
|
if self.filtfilt_kind != 'tf':
|
||
|
pytest.skip('gust only implemented for TF systems')
|
||
|
# The input array has length 2. The exact solution for this case
|
||
|
# was computed "by hand".
|
||
|
x = np.array([1.0, 2.0])
|
||
|
b = np.array([0.5])
|
||
|
a = np.array([1.0, -0.5])
|
||
|
y, z1, z2 = _filtfilt_gust(b, a, x)
|
||
|
assert_allclose([z1[0], z2[0]],
|
||
|
[0.3*x[0] + 0.2*x[1], 0.2*x[0] + 0.3*x[1]])
|
||
|
assert_allclose(y, [z1[0] + 0.25*z2[0] + 0.25*x[0] + 0.125*x[1],
|
||
|
0.25*z1[0] + z2[0] + 0.125*x[0] + 0.25*x[1]])
|
||
|
|
||
|
def test_gust_scalars(self):
|
||
|
if self.filtfilt_kind != 'tf':
|
||
|
pytest.skip('gust only implemented for TF systems')
|
||
|
# The filter coefficients are both scalars, so the filter simply
|
||
|
# multiplies its input by b/a. When it is used in filtfilt, the
|
||
|
# factor is (b/a)**2.
|
||
|
x = np.arange(12)
|
||
|
b = 3.0
|
||
|
a = 2.0
|
||
|
y = filtfilt(b, a, x, method="gust")
|
||
|
expected = (b/a)**2 * x
|
||
|
assert_allclose(y, expected)
|
||
|
|
||
|
|
||
|
class TestSOSFiltFilt(TestFiltFilt):
|
||
|
filtfilt_kind = 'sos'
|
||
|
|
||
|
def test_equivalence(self):
|
||
|
"""Test equivalence between sosfiltfilt and filtfilt"""
|
||
|
x = np.random.RandomState(0).randn(1000)
|
||
|
for order in range(1, 6):
|
||
|
zpk = signal.butter(order, 0.35, output='zpk')
|
||
|
b, a = zpk2tf(*zpk)
|
||
|
sos = zpk2sos(*zpk)
|
||
|
y = filtfilt(b, a, x)
|
||
|
y_sos = sosfiltfilt(sos, x)
|
||
|
assert_allclose(y, y_sos, atol=1e-12, err_msg='order=%s' % order)
|
||
|
|
||
|
|
||
|
def filtfilt_gust_opt(b, a, x):
|
||
|
"""
|
||
|
An alternative implementation of filtfilt with Gustafsson edges.
|
||
|
|
||
|
This function computes the same result as
|
||
|
`scipy.signal._signaltools._filtfilt_gust`, but only 1-d arrays
|
||
|
are accepted. The problem is solved using `fmin` from `scipy.optimize`.
|
||
|
`_filtfilt_gust` is significanly faster than this implementation.
|
||
|
"""
|
||
|
def filtfilt_gust_opt_func(ics, b, a, x):
|
||
|
"""Objective function used in filtfilt_gust_opt."""
|
||
|
m = max(len(a), len(b)) - 1
|
||
|
z0f = ics[:m]
|
||
|
z0b = ics[m:]
|
||
|
y_f = lfilter(b, a, x, zi=z0f)[0]
|
||
|
y_fb = lfilter(b, a, y_f[::-1], zi=z0b)[0][::-1]
|
||
|
|
||
|
y_b = lfilter(b, a, x[::-1], zi=z0b)[0][::-1]
|
||
|
y_bf = lfilter(b, a, y_b, zi=z0f)[0]
|
||
|
value = np.sum((y_fb - y_bf)**2)
|
||
|
return value
|
||
|
|
||
|
m = max(len(a), len(b)) - 1
|
||
|
zi = lfilter_zi(b, a)
|
||
|
ics = np.concatenate((x[:m].mean()*zi, x[-m:].mean()*zi))
|
||
|
result = fmin(filtfilt_gust_opt_func, ics, args=(b, a, x),
|
||
|
xtol=1e-10, ftol=1e-12,
|
||
|
maxfun=10000, maxiter=10000,
|
||
|
full_output=True, disp=False)
|
||
|
opt, fopt, niter, funcalls, warnflag = result
|
||
|
if warnflag > 0:
|
||
|
raise RuntimeError("minimization failed in filtfilt_gust_opt: "
|
||
|
"warnflag=%d" % warnflag)
|
||
|
z0f = opt[:m]
|
||
|
z0b = opt[m:]
|
||
|
|
||
|
# Apply the forward-backward filter using the computed initial
|
||
|
# conditions.
|
||
|
y_b = lfilter(b, a, x[::-1], zi=z0b)[0][::-1]
|
||
|
y = lfilter(b, a, y_b, zi=z0f)[0]
|
||
|
|
||
|
return y, z0f, z0b
|
||
|
|
||
|
|
||
|
def check_filtfilt_gust(b, a, shape, axis, irlen=None):
|
||
|
# Generate x, the data to be filtered.
|
||
|
np.random.seed(123)
|
||
|
x = np.random.randn(*shape)
|
||
|
|
||
|
# Apply filtfilt to x. This is the main calculation to be checked.
|
||
|
y = filtfilt(b, a, x, axis=axis, method="gust", irlen=irlen)
|
||
|
|
||
|
# Also call the private function so we can test the ICs.
|
||
|
yg, zg1, zg2 = _filtfilt_gust(b, a, x, axis=axis, irlen=irlen)
|
||
|
|
||
|
# filtfilt_gust_opt is an independent implementation that gives the
|
||
|
# expected result, but it only handles 1-D arrays, so use some looping
|
||
|
# and reshaping shenanigans to create the expected output arrays.
|
||
|
xx = np.swapaxes(x, axis, -1)
|
||
|
out_shape = xx.shape[:-1]
|
||
|
yo = np.empty_like(xx)
|
||
|
m = max(len(a), len(b)) - 1
|
||
|
zo1 = np.empty(out_shape + (m,))
|
||
|
zo2 = np.empty(out_shape + (m,))
|
||
|
for indx in product(*[range(d) for d in out_shape]):
|
||
|
yo[indx], zo1[indx], zo2[indx] = filtfilt_gust_opt(b, a, xx[indx])
|
||
|
yo = np.swapaxes(yo, -1, axis)
|
||
|
zo1 = np.swapaxes(zo1, -1, axis)
|
||
|
zo2 = np.swapaxes(zo2, -1, axis)
|
||
|
|
||
|
assert_allclose(y, yo, rtol=1e-8, atol=1e-9)
|
||
|
assert_allclose(yg, yo, rtol=1e-8, atol=1e-9)
|
||
|
assert_allclose(zg1, zo1, rtol=1e-8, atol=1e-9)
|
||
|
assert_allclose(zg2, zo2, rtol=1e-8, atol=1e-9)
|
||
|
|
||
|
|
||
|
def test_choose_conv_method():
|
||
|
for mode in ['valid', 'same', 'full']:
|
||
|
for ndim in [1, 2]:
|
||
|
n, k, true_method = 8, 6, 'direct'
|
||
|
x = np.random.randn(*((n,) * ndim))
|
||
|
h = np.random.randn(*((k,) * ndim))
|
||
|
|
||
|
method = choose_conv_method(x, h, mode=mode)
|
||
|
assert_equal(method, true_method)
|
||
|
|
||
|
method_try, times = choose_conv_method(x, h, mode=mode, measure=True)
|
||
|
assert_(method_try in {'fft', 'direct'})
|
||
|
assert_(type(times) is dict)
|
||
|
assert_('fft' in times.keys() and 'direct' in times.keys())
|
||
|
|
||
|
n = 10
|
||
|
for not_fft_conv_supp in ["complex256", "complex192"]:
|
||
|
if hasattr(np, not_fft_conv_supp):
|
||
|
x = np.ones(n, dtype=not_fft_conv_supp)
|
||
|
h = x.copy()
|
||
|
assert_equal(choose_conv_method(x, h, mode=mode), 'direct')
|
||
|
|
||
|
x = np.array([2**51], dtype=np.int64)
|
||
|
h = x.copy()
|
||
|
assert_equal(choose_conv_method(x, h, mode=mode), 'direct')
|
||
|
|
||
|
x = [Decimal(3), Decimal(2)]
|
||
|
h = [Decimal(1), Decimal(4)]
|
||
|
assert_equal(choose_conv_method(x, h, mode=mode), 'direct')
|
||
|
|
||
|
|
||
|
def test_filtfilt_gust():
|
||
|
# Design a filter.
|
||
|
z, p, k = signal.ellip(3, 0.01, 120, 0.0875, output='zpk')
|
||
|
|
||
|
# Find the approximate impulse response length of the filter.
|
||
|
eps = 1e-10
|
||
|
r = np.max(np.abs(p))
|
||
|
approx_impulse_len = int(np.ceil(np.log(eps) / np.log(r)))
|
||
|
|
||
|
np.random.seed(123)
|
||
|
|
||
|
b, a = zpk2tf(z, p, k)
|
||
|
for irlen in [None, approx_impulse_len]:
|
||
|
signal_len = 5 * approx_impulse_len
|
||
|
|
||
|
# 1-d test case
|
||
|
check_filtfilt_gust(b, a, (signal_len,), 0, irlen)
|
||
|
|
||
|
# 3-d test case; test each axis.
|
||
|
for axis in range(3):
|
||
|
shape = [2, 2, 2]
|
||
|
shape[axis] = signal_len
|
||
|
check_filtfilt_gust(b, a, shape, axis, irlen)
|
||
|
|
||
|
# Test case with length less than 2*approx_impulse_len.
|
||
|
# In this case, `filtfilt_gust` should behave the same as if
|
||
|
# `irlen=None` was given.
|
||
|
length = 2*approx_impulse_len - 50
|
||
|
check_filtfilt_gust(b, a, (length,), 0, approx_impulse_len)
|
||
|
|
||
|
|
||
|
class TestDecimate:
|
||
|
def test_bad_args(self):
|
||
|
x = np.arange(12)
|
||
|
assert_raises(TypeError, signal.decimate, x, q=0.5, n=1)
|
||
|
assert_raises(TypeError, signal.decimate, x, q=2, n=0.5)
|
||
|
|
||
|
def test_basic_IIR(self):
|
||
|
x = np.arange(12)
|
||
|
y = signal.decimate(x, 2, n=1, ftype='iir', zero_phase=False).round()
|
||
|
assert_array_equal(y, x[::2])
|
||
|
|
||
|
def test_basic_FIR(self):
|
||
|
x = np.arange(12)
|
||
|
y = signal.decimate(x, 2, n=1, ftype='fir', zero_phase=False).round()
|
||
|
assert_array_equal(y, x[::2])
|
||
|
|
||
|
def test_shape(self):
|
||
|
# Regression test for ticket #1480.
|
||
|
z = np.zeros((30, 30))
|
||
|
d0 = signal.decimate(z, 2, axis=0, zero_phase=False)
|
||
|
assert_equal(d0.shape, (15, 30))
|
||
|
d1 = signal.decimate(z, 2, axis=1, zero_phase=False)
|
||
|
assert_equal(d1.shape, (30, 15))
|
||
|
|
||
|
def test_phaseshift_FIR(self):
|
||
|
with suppress_warnings() as sup:
|
||
|
sup.filter(BadCoefficients, "Badly conditioned filter")
|
||
|
self._test_phaseshift(method='fir', zero_phase=False)
|
||
|
|
||
|
def test_zero_phase_FIR(self):
|
||
|
with suppress_warnings() as sup:
|
||
|
sup.filter(BadCoefficients, "Badly conditioned filter")
|
||
|
self._test_phaseshift(method='fir', zero_phase=True)
|
||
|
|
||
|
def test_phaseshift_IIR(self):
|
||
|
self._test_phaseshift(method='iir', zero_phase=False)
|
||
|
|
||
|
def test_zero_phase_IIR(self):
|
||
|
self._test_phaseshift(method='iir', zero_phase=True)
|
||
|
|
||
|
def _test_phaseshift(self, method, zero_phase):
|
||
|
rate = 120
|
||
|
rates_to = [15, 20, 30, 40] # q = 8, 6, 4, 3
|
||
|
|
||
|
t_tot = int(100) # Need to let antialiasing filters settle
|
||
|
t = np.arange(rate*t_tot+1) / float(rate)
|
||
|
|
||
|
# Sinusoids at 0.8*nyquist, windowed to avoid edge artifacts
|
||
|
freqs = np.array(rates_to) * 0.8 / 2
|
||
|
d = (np.exp(1j * 2 * np.pi * freqs[:, np.newaxis] * t)
|
||
|
* signal.windows.tukey(t.size, 0.1))
|
||
|
|
||
|
for rate_to in rates_to:
|
||
|
q = rate // rate_to
|
||
|
t_to = np.arange(rate_to*t_tot+1) / float(rate_to)
|
||
|
d_tos = (np.exp(1j * 2 * np.pi * freqs[:, np.newaxis] * t_to)
|
||
|
* signal.windows.tukey(t_to.size, 0.1))
|
||
|
|
||
|
# Set up downsampling filters, match v0.17 defaults
|
||
|
if method == 'fir':
|
||
|
n = 30
|
||
|
system = signal.dlti(signal.firwin(n + 1, 1. / q,
|
||
|
window='hamming'), 1.)
|
||
|
elif method == 'iir':
|
||
|
n = 8
|
||
|
wc = 0.8*np.pi/q
|
||
|
system = signal.dlti(*signal.cheby1(n, 0.05, wc/np.pi))
|
||
|
|
||
|
# Calculate expected phase response, as unit complex vector
|
||
|
if zero_phase is False:
|
||
|
_, h_resps = signal.freqz(system.num, system.den,
|
||
|
freqs/rate*2*np.pi)
|
||
|
h_resps /= np.abs(h_resps)
|
||
|
else:
|
||
|
h_resps = np.ones_like(freqs)
|
||
|
|
||
|
y_resamps = signal.decimate(d.real, q, n, ftype=system,
|
||
|
zero_phase=zero_phase)
|
||
|
|
||
|
# Get phase from complex inner product, like CSD
|
||
|
h_resamps = np.sum(d_tos.conj() * y_resamps, axis=-1)
|
||
|
h_resamps /= np.abs(h_resamps)
|
||
|
subnyq = freqs < 0.5*rate_to
|
||
|
|
||
|
# Complex vectors should be aligned, only compare below nyquist
|
||
|
assert_allclose(np.angle(h_resps.conj()*h_resamps)[subnyq], 0,
|
||
|
atol=1e-3, rtol=1e-3)
|
||
|
|
||
|
def test_auto_n(self):
|
||
|
# Test that our value of n is a reasonable choice (depends on
|
||
|
# the downsampling factor)
|
||
|
sfreq = 100.
|
||
|
n = 1000
|
||
|
t = np.arange(n) / sfreq
|
||
|
# will alias for decimations (>= 15)
|
||
|
x = np.sqrt(2. / n) * np.sin(2 * np.pi * (sfreq / 30.) * t)
|
||
|
assert_allclose(np.linalg.norm(x), 1., rtol=1e-3)
|
||
|
x_out = signal.decimate(x, 30, ftype='fir')
|
||
|
assert_array_less(np.linalg.norm(x_out), 0.01)
|
||
|
|
||
|
def test_long_float32(self):
|
||
|
# regression: gh-15072. With 32-bit float and either lfilter
|
||
|
# or filtfilt, this is numerically unstable
|
||
|
x = signal.decimate(np.ones(10_000, dtype=np.float32), 10)
|
||
|
assert not any(np.isnan(x))
|
||
|
|
||
|
def test_float16_upcast(self):
|
||
|
# float16 must be upcast to float64
|
||
|
x = signal.decimate(np.ones(100, dtype=np.float16), 10)
|
||
|
assert x.dtype.type == np.float64
|
||
|
|
||
|
|
||
|
class TestHilbert:
|
||
|
|
||
|
def test_bad_args(self):
|
||
|
x = np.array([1.0 + 0.0j])
|
||
|
assert_raises(ValueError, hilbert, x)
|
||
|
x = np.arange(8.0)
|
||
|
assert_raises(ValueError, hilbert, x, N=0)
|
||
|
|
||
|
def test_hilbert_theoretical(self):
|
||
|
# test cases by Ariel Rokem
|
||
|
decimal = 14
|
||
|
|
||
|
pi = np.pi
|
||
|
t = np.arange(0, 2 * pi, pi / 256)
|
||
|
a0 = np.sin(t)
|
||
|
a1 = np.cos(t)
|
||
|
a2 = np.sin(2 * t)
|
||
|
a3 = np.cos(2 * t)
|
||
|
a = np.vstack([a0, a1, a2, a3])
|
||
|
|
||
|
h = hilbert(a)
|
||
|
h_abs = np.abs(h)
|
||
|
h_angle = np.angle(h)
|
||
|
h_real = np.real(h)
|
||
|
|
||
|
# The real part should be equal to the original signals:
|
||
|
assert_almost_equal(h_real, a, decimal)
|
||
|
# The absolute value should be one everywhere, for this input:
|
||
|
assert_almost_equal(h_abs, np.ones(a.shape), decimal)
|
||
|
# For the 'slow' sine - the phase should go from -pi/2 to pi/2 in
|
||
|
# the first 256 bins:
|
||
|
assert_almost_equal(h_angle[0, :256],
|
||
|
np.arange(-pi / 2, pi / 2, pi / 256),
|
||
|
decimal)
|
||
|
# For the 'slow' cosine - the phase should go from 0 to pi in the
|
||
|
# same interval:
|
||
|
assert_almost_equal(
|
||
|
h_angle[1, :256], np.arange(0, pi, pi / 256), decimal)
|
||
|
# The 'fast' sine should make this phase transition in half the time:
|
||
|
assert_almost_equal(h_angle[2, :128],
|
||
|
np.arange(-pi / 2, pi / 2, pi / 128),
|
||
|
decimal)
|
||
|
# Ditto for the 'fast' cosine:
|
||
|
assert_almost_equal(
|
||
|
h_angle[3, :128], np.arange(0, pi, pi / 128), decimal)
|
||
|
|
||
|
# The imaginary part of hilbert(cos(t)) = sin(t) Wikipedia
|
||
|
assert_almost_equal(h[1].imag, a0, decimal)
|
||
|
|
||
|
def test_hilbert_axisN(self):
|
||
|
# tests for axis and N arguments
|
||
|
a = np.arange(18).reshape(3, 6)
|
||
|
# test axis
|
||
|
aa = hilbert(a, axis=-1)
|
||
|
assert_equal(hilbert(a.T, axis=0), aa.T)
|
||
|
# test 1d
|
||
|
assert_almost_equal(hilbert(a[0]), aa[0], 14)
|
||
|
|
||
|
# test N
|
||
|
aan = hilbert(a, N=20, axis=-1)
|
||
|
assert_equal(aan.shape, [3, 20])
|
||
|
assert_equal(hilbert(a.T, N=20, axis=0).shape, [20, 3])
|
||
|
# the next test is just a regression test,
|
||
|
# no idea whether numbers make sense
|
||
|
a0hilb = np.array([0.000000000000000e+00 - 1.72015830311905j,
|
||
|
1.000000000000000e+00 - 2.047794505137069j,
|
||
|
1.999999999999999e+00 - 2.244055555687583j,
|
||
|
3.000000000000000e+00 - 1.262750302935009j,
|
||
|
4.000000000000000e+00 - 1.066489252384493j,
|
||
|
5.000000000000000e+00 + 2.918022706971047j,
|
||
|
8.881784197001253e-17 + 3.845658908989067j,
|
||
|
-9.444121133484362e-17 + 0.985044202202061j,
|
||
|
-1.776356839400251e-16 + 1.332257797702019j,
|
||
|
-3.996802888650564e-16 + 0.501905089898885j,
|
||
|
1.332267629550188e-16 + 0.668696078880782j,
|
||
|
-1.192678053963799e-16 + 0.235487067862679j,
|
||
|
-1.776356839400251e-16 + 0.286439612812121j,
|
||
|
3.108624468950438e-16 + 0.031676888064907j,
|
||
|
1.332267629550188e-16 - 0.019275656884536j,
|
||
|
-2.360035624836702e-16 - 0.1652588660287j,
|
||
|
0.000000000000000e+00 - 0.332049855010597j,
|
||
|
3.552713678800501e-16 - 0.403810179797771j,
|
||
|
8.881784197001253e-17 - 0.751023775297729j,
|
||
|
9.444121133484362e-17 - 0.79252210110103j])
|
||
|
assert_almost_equal(aan[0], a0hilb, 14, 'N regression')
|
||
|
|
||
|
@pytest.mark.parametrize('dtype', [np.float32, np.float64])
|
||
|
def test_hilbert_types(self, dtype):
|
||
|
in_typed = np.zeros(8, dtype=dtype)
|
||
|
assert_equal(np.real(signal.hilbert(in_typed)).dtype, dtype)
|
||
|
|
||
|
|
||
|
class TestHilbert2:
|
||
|
|
||
|
def test_bad_args(self):
|
||
|
# x must be real.
|
||
|
x = np.array([[1.0 + 0.0j]])
|
||
|
assert_raises(ValueError, hilbert2, x)
|
||
|
|
||
|
# x must be rank 2.
|
||
|
x = np.arange(24).reshape(2, 3, 4)
|
||
|
assert_raises(ValueError, hilbert2, x)
|
||
|
|
||
|
# Bad value for N.
|
||
|
x = np.arange(16).reshape(4, 4)
|
||
|
assert_raises(ValueError, hilbert2, x, N=0)
|
||
|
assert_raises(ValueError, hilbert2, x, N=(2, 0))
|
||
|
assert_raises(ValueError, hilbert2, x, N=(2,))
|
||
|
|
||
|
@pytest.mark.parametrize('dtype', [np.float32, np.float64])
|
||
|
def test_hilbert2_types(self, dtype):
|
||
|
in_typed = np.zeros((2, 32), dtype=dtype)
|
||
|
assert_equal(np.real(signal.hilbert2(in_typed)).dtype, dtype)
|
||
|
|
||
|
|
||
|
class TestPartialFractionExpansion:
|
||
|
@staticmethod
|
||
|
def assert_rp_almost_equal(r, p, r_true, p_true, decimal=7):
|
||
|
r_true = np.asarray(r_true)
|
||
|
p_true = np.asarray(p_true)
|
||
|
|
||
|
distance = np.hypot(abs(p[:, None] - p_true),
|
||
|
abs(r[:, None] - r_true))
|
||
|
|
||
|
rows, cols = linear_sum_assignment(distance)
|
||
|
assert_almost_equal(p[rows], p_true[cols], decimal=decimal)
|
||
|
assert_almost_equal(r[rows], r_true[cols], decimal=decimal)
|
||
|
|
||
|
def test_compute_factors(self):
|
||
|
factors, poly = _compute_factors([1, 2, 3], [3, 2, 1])
|
||
|
assert_equal(len(factors), 3)
|
||
|
assert_almost_equal(factors[0], np.poly([2, 2, 3]))
|
||
|
assert_almost_equal(factors[1], np.poly([1, 1, 1, 3]))
|
||
|
assert_almost_equal(factors[2], np.poly([1, 1, 1, 2, 2]))
|
||
|
assert_almost_equal(poly, np.poly([1, 1, 1, 2, 2, 3]))
|
||
|
|
||
|
factors, poly = _compute_factors([1, 2, 3], [3, 2, 1],
|
||
|
include_powers=True)
|
||
|
assert_equal(len(factors), 6)
|
||
|
assert_almost_equal(factors[0], np.poly([1, 1, 2, 2, 3]))
|
||
|
assert_almost_equal(factors[1], np.poly([1, 2, 2, 3]))
|
||
|
assert_almost_equal(factors[2], np.poly([2, 2, 3]))
|
||
|
assert_almost_equal(factors[3], np.poly([1, 1, 1, 2, 3]))
|
||
|
assert_almost_equal(factors[4], np.poly([1, 1, 1, 3]))
|
||
|
assert_almost_equal(factors[5], np.poly([1, 1, 1, 2, 2]))
|
||
|
assert_almost_equal(poly, np.poly([1, 1, 1, 2, 2, 3]))
|
||
|
|
||
|
def test_group_poles(self):
|
||
|
unique, multiplicity = _group_poles(
|
||
|
[1.0, 1.001, 1.003, 2.0, 2.003, 3.0], 0.1, 'min')
|
||
|
assert_equal(unique, [1.0, 2.0, 3.0])
|
||
|
assert_equal(multiplicity, [3, 2, 1])
|
||
|
|
||
|
def test_residue_general(self):
|
||
|
# Test are taken from issue #4464, note that poles in scipy are
|
||
|
# in increasing by absolute value order, opposite to MATLAB.
|
||
|
r, p, k = residue([5, 3, -2, 7], [-4, 0, 8, 3])
|
||
|
assert_almost_equal(r, [1.3320, -0.6653, -1.4167], decimal=4)
|
||
|
assert_almost_equal(p, [-0.4093, -1.1644, 1.5737], decimal=4)
|
||
|
assert_almost_equal(k, [-1.2500], decimal=4)
|
||
|
|
||
|
r, p, k = residue([-4, 8], [1, 6, 8])
|
||
|
assert_almost_equal(r, [8, -12])
|
||
|
assert_almost_equal(p, [-2, -4])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residue([4, 1], [1, -1, -2])
|
||
|
assert_almost_equal(r, [1, 3])
|
||
|
assert_almost_equal(p, [-1, 2])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residue([4, 3], [2, -3.4, 1.98, -0.406])
|
||
|
self.assert_rp_almost_equal(
|
||
|
r, p, [-18.125 - 13.125j, -18.125 + 13.125j, 36.25],
|
||
|
[0.5 - 0.2j, 0.5 + 0.2j, 0.7])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residue([2, 1], [1, 5, 8, 4])
|
||
|
self.assert_rp_almost_equal(r, p, [-1, 1, 3], [-1, -2, -2])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residue([3, -1.1, 0.88, -2.396, 1.348],
|
||
|
[1, -0.7, -0.14, 0.048])
|
||
|
assert_almost_equal(r, [-3, 4, 1])
|
||
|
assert_almost_equal(p, [0.2, -0.3, 0.8])
|
||
|
assert_almost_equal(k, [3, 1])
|
||
|
|
||
|
r, p, k = residue([1], [1, 2, -3])
|
||
|
assert_almost_equal(r, [0.25, -0.25])
|
||
|
assert_almost_equal(p, [1, -3])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residue([1, 0, -5], [1, 0, 0, 0, -1])
|
||
|
self.assert_rp_almost_equal(r, p,
|
||
|
[1, 1.5j, -1.5j, -1], [-1, -1j, 1j, 1])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residue([3, 8, 6], [1, 3, 3, 1])
|
||
|
self.assert_rp_almost_equal(r, p, [1, 2, 3], [-1, -1, -1])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residue([3, -1], [1, -3, 2])
|
||
|
assert_almost_equal(r, [-2, 5])
|
||
|
assert_almost_equal(p, [1, 2])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residue([2, 3, -1], [1, -3, 2])
|
||
|
assert_almost_equal(r, [-4, 13])
|
||
|
assert_almost_equal(p, [1, 2])
|
||
|
assert_almost_equal(k, [2])
|
||
|
|
||
|
r, p, k = residue([7, 2, 3, -1], [1, -3, 2])
|
||
|
assert_almost_equal(r, [-11, 69])
|
||
|
assert_almost_equal(p, [1, 2])
|
||
|
assert_almost_equal(k, [7, 23])
|
||
|
|
||
|
r, p, k = residue([2, 3, -1], [1, -3, 4, -2])
|
||
|
self.assert_rp_almost_equal(r, p, [4, -1 + 3.5j, -1 - 3.5j],
|
||
|
[1, 1 - 1j, 1 + 1j])
|
||
|
assert_almost_equal(k.size, 0)
|
||
|
|
||
|
def test_residue_leading_zeros(self):
|
||
|
# Leading zeros in numerator or denominator must not affect the answer.
|
||
|
r0, p0, k0 = residue([5, 3, -2, 7], [-4, 0, 8, 3])
|
||
|
r1, p1, k1 = residue([0, 5, 3, -2, 7], [-4, 0, 8, 3])
|
||
|
r2, p2, k2 = residue([5, 3, -2, 7], [0, -4, 0, 8, 3])
|
||
|
r3, p3, k3 = residue([0, 0, 5, 3, -2, 7], [0, 0, 0, -4, 0, 8, 3])
|
||
|
assert_almost_equal(r0, r1)
|
||
|
assert_almost_equal(r0, r2)
|
||
|
assert_almost_equal(r0, r3)
|
||
|
assert_almost_equal(p0, p1)
|
||
|
assert_almost_equal(p0, p2)
|
||
|
assert_almost_equal(p0, p3)
|
||
|
assert_almost_equal(k0, k1)
|
||
|
assert_almost_equal(k0, k2)
|
||
|
assert_almost_equal(k0, k3)
|
||
|
|
||
|
def test_resiude_degenerate(self):
|
||
|
# Several tests for zero numerator and denominator.
|
||
|
r, p, k = residue([0, 0], [1, 6, 8])
|
||
|
assert_almost_equal(r, [0, 0])
|
||
|
assert_almost_equal(p, [-2, -4])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residue(0, 1)
|
||
|
assert_equal(r.size, 0)
|
||
|
assert_equal(p.size, 0)
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
with pytest.raises(ValueError, match="Denominator `a` is zero."):
|
||
|
residue(1, 0)
|
||
|
|
||
|
def test_residuez_general(self):
|
||
|
r, p, k = residuez([1, 6, 6, 2], [1, -(2 + 1j), (1 + 2j), -1j])
|
||
|
self.assert_rp_almost_equal(r, p, [-2+2.5j, 7.5+7.5j, -4.5-12j],
|
||
|
[1j, 1, 1])
|
||
|
assert_almost_equal(k, [2j])
|
||
|
|
||
|
r, p, k = residuez([1, 2, 1], [1, -1, 0.3561])
|
||
|
self.assert_rp_almost_equal(r, p,
|
||
|
[-0.9041 - 5.9928j, -0.9041 + 5.9928j],
|
||
|
[0.5 + 0.3257j, 0.5 - 0.3257j],
|
||
|
decimal=4)
|
||
|
assert_almost_equal(k, [2.8082], decimal=4)
|
||
|
|
||
|
r, p, k = residuez([1, -1], [1, -5, 6])
|
||
|
assert_almost_equal(r, [-1, 2])
|
||
|
assert_almost_equal(p, [2, 3])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residuez([2, 3, 4], [1, 3, 3, 1])
|
||
|
self.assert_rp_almost_equal(r, p, [4, -5, 3], [-1, -1, -1])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residuez([1, -10, -4, 4], [2, -2, -4])
|
||
|
assert_almost_equal(r, [0.5, -1.5])
|
||
|
assert_almost_equal(p, [-1, 2])
|
||
|
assert_almost_equal(k, [1.5, -1])
|
||
|
|
||
|
r, p, k = residuez([18], [18, 3, -4, -1])
|
||
|
self.assert_rp_almost_equal(r, p,
|
||
|
[0.36, 0.24, 0.4], [0.5, -1/3, -1/3])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residuez([2, 3], np.polymul([1, -1/2], [1, 1/4]))
|
||
|
assert_almost_equal(r, [-10/3, 16/3])
|
||
|
assert_almost_equal(p, [-0.25, 0.5])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residuez([1, -2, 1], [1, -1])
|
||
|
assert_almost_equal(r, [0])
|
||
|
assert_almost_equal(p, [1])
|
||
|
assert_almost_equal(k, [1, -1])
|
||
|
|
||
|
r, p, k = residuez(1, [1, -1j])
|
||
|
assert_almost_equal(r, [1])
|
||
|
assert_almost_equal(p, [1j])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residuez(1, [1, -1, 0.25])
|
||
|
assert_almost_equal(r, [0, 1])
|
||
|
assert_almost_equal(p, [0.5, 0.5])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residuez(1, [1, -0.75, .125])
|
||
|
assert_almost_equal(r, [-1, 2])
|
||
|
assert_almost_equal(p, [0.25, 0.5])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residuez([1, 6, 2], [1, -2, 1])
|
||
|
assert_almost_equal(r, [-10, 9])
|
||
|
assert_almost_equal(p, [1, 1])
|
||
|
assert_almost_equal(k, [2])
|
||
|
|
||
|
r, p, k = residuez([6, 2], [1, -2, 1])
|
||
|
assert_almost_equal(r, [-2, 8])
|
||
|
assert_almost_equal(p, [1, 1])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residuez([1, 6, 6, 2], [1, -2, 1])
|
||
|
assert_almost_equal(r, [-24, 15])
|
||
|
assert_almost_equal(p, [1, 1])
|
||
|
assert_almost_equal(k, [10, 2])
|
||
|
|
||
|
r, p, k = residuez([1, 0, 1], [1, 0, 0, 0, 0, -1])
|
||
|
self.assert_rp_almost_equal(r, p,
|
||
|
[0.2618 + 0.1902j, 0.2618 - 0.1902j,
|
||
|
0.4, 0.0382 - 0.1176j, 0.0382 + 0.1176j],
|
||
|
[-0.8090 + 0.5878j, -0.8090 - 0.5878j,
|
||
|
1.0, 0.3090 + 0.9511j, 0.3090 - 0.9511j],
|
||
|
decimal=4)
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
def test_residuez_trailing_zeros(self):
|
||
|
# Trailing zeros in numerator or denominator must not affect the
|
||
|
# answer.
|
||
|
r0, p0, k0 = residuez([5, 3, -2, 7], [-4, 0, 8, 3])
|
||
|
r1, p1, k1 = residuez([5, 3, -2, 7, 0], [-4, 0, 8, 3])
|
||
|
r2, p2, k2 = residuez([5, 3, -2, 7], [-4, 0, 8, 3, 0])
|
||
|
r3, p3, k3 = residuez([5, 3, -2, 7, 0, 0], [-4, 0, 8, 3, 0, 0, 0])
|
||
|
assert_almost_equal(r0, r1)
|
||
|
assert_almost_equal(r0, r2)
|
||
|
assert_almost_equal(r0, r3)
|
||
|
assert_almost_equal(p0, p1)
|
||
|
assert_almost_equal(p0, p2)
|
||
|
assert_almost_equal(p0, p3)
|
||
|
assert_almost_equal(k0, k1)
|
||
|
assert_almost_equal(k0, k2)
|
||
|
assert_almost_equal(k0, k3)
|
||
|
|
||
|
def test_residuez_degenerate(self):
|
||
|
r, p, k = residuez([0, 0], [1, 6, 8])
|
||
|
assert_almost_equal(r, [0, 0])
|
||
|
assert_almost_equal(p, [-2, -4])
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
r, p, k = residuez(0, 1)
|
||
|
assert_equal(r.size, 0)
|
||
|
assert_equal(p.size, 0)
|
||
|
assert_equal(k.size, 0)
|
||
|
|
||
|
with pytest.raises(ValueError, match="Denominator `a` is zero."):
|
||
|
residuez(1, 0)
|
||
|
|
||
|
with pytest.raises(ValueError,
|
||
|
match="First coefficient of determinant `a` must "
|
||
|
"be non-zero."):
|
||
|
residuez(1, [0, 1, 2, 3])
|
||
|
|
||
|
def test_inverse_unique_roots_different_rtypes(self):
|
||
|
# This test was inspired by github issue 2496.
|
||
|
r = [3 / 10, -1 / 6, -2 / 15]
|
||
|
p = [0, -2, -5]
|
||
|
k = []
|
||
|
b_expected = [0, 1, 3]
|
||
|
a_expected = [1, 7, 10, 0]
|
||
|
|
||
|
# With the default tolerance, the rtype does not matter
|
||
|
# for this example.
|
||
|
for rtype in ('avg', 'mean', 'min', 'minimum', 'max', 'maximum'):
|
||
|
b, a = invres(r, p, k, rtype=rtype)
|
||
|
assert_allclose(b, b_expected)
|
||
|
assert_allclose(a, a_expected)
|
||
|
|
||
|
b, a = invresz(r, p, k, rtype=rtype)
|
||
|
assert_allclose(b, b_expected)
|
||
|
assert_allclose(a, a_expected)
|
||
|
|
||
|
def test_inverse_repeated_roots_different_rtypes(self):
|
||
|
r = [3 / 20, -7 / 36, -1 / 6, 2 / 45]
|
||
|
p = [0, -2, -2, -5]
|
||
|
k = []
|
||
|
b_expected = [0, 0, 1, 3]
|
||
|
b_expected_z = [-1/6, -2/3, 11/6, 3]
|
||
|
a_expected = [1, 9, 24, 20, 0]
|
||
|
|
||
|
for rtype in ('avg', 'mean', 'min', 'minimum', 'max', 'maximum'):
|
||
|
b, a = invres(r, p, k, rtype=rtype)
|
||
|
assert_allclose(b, b_expected, atol=1e-14)
|
||
|
assert_allclose(a, a_expected)
|
||
|
|
||
|
b, a = invresz(r, p, k, rtype=rtype)
|
||
|
assert_allclose(b, b_expected_z, atol=1e-14)
|
||
|
assert_allclose(a, a_expected)
|
||
|
|
||
|
def test_inverse_bad_rtype(self):
|
||
|
r = [3 / 20, -7 / 36, -1 / 6, 2 / 45]
|
||
|
p = [0, -2, -2, -5]
|
||
|
k = []
|
||
|
with pytest.raises(ValueError, match="`rtype` must be one of"):
|
||
|
invres(r, p, k, rtype='median')
|
||
|
with pytest.raises(ValueError, match="`rtype` must be one of"):
|
||
|
invresz(r, p, k, rtype='median')
|
||
|
|
||
|
def test_invresz_one_coefficient_bug(self):
|
||
|
# Regression test for issue in gh-4646.
|
||
|
r = [1]
|
||
|
p = [2]
|
||
|
k = [0]
|
||
|
b, a = invresz(r, p, k)
|
||
|
assert_allclose(b, [1.0])
|
||
|
assert_allclose(a, [1.0, -2.0])
|
||
|
|
||
|
def test_invres(self):
|
||
|
b, a = invres([1], [1], [])
|
||
|
assert_almost_equal(b, [1])
|
||
|
assert_almost_equal(a, [1, -1])
|
||
|
|
||
|
b, a = invres([1 - 1j, 2, 0.5 - 3j], [1, 0.5j, 1 + 1j], [])
|
||
|
assert_almost_equal(b, [3.5 - 4j, -8.5 + 0.25j, 3.5 + 3.25j])
|
||
|
assert_almost_equal(a, [1, -2 - 1.5j, 0.5 + 2j, 0.5 - 0.5j])
|
||
|
|
||
|
b, a = invres([0.5, 1], [1 - 1j, 2 + 2j], [1, 2, 3])
|
||
|
assert_almost_equal(b, [1, -1 - 1j, 1 - 2j, 0.5 - 3j, 10])
|
||
|
assert_almost_equal(a, [1, -3 - 1j, 4])
|
||
|
|
||
|
b, a = invres([-1, 2, 1j, 3 - 1j, 4, -2],
|
||
|
[-1, 2 - 1j, 2 - 1j, 3, 3, 3], [])
|
||
|
assert_almost_equal(b, [4 - 1j, -28 + 16j, 40 - 62j, 100 + 24j,
|
||
|
-292 + 219j, 192 - 268j])
|
||
|
assert_almost_equal(a, [1, -12 + 2j, 53 - 20j, -96 + 68j, 27 - 72j,
|
||
|
108 - 54j, -81 + 108j])
|
||
|
|
||
|
b, a = invres([-1, 1j], [1, 1], [1, 2])
|
||
|
assert_almost_equal(b, [1, 0, -4, 3 + 1j])
|
||
|
assert_almost_equal(a, [1, -2, 1])
|
||
|
|
||
|
def test_invresz(self):
|
||
|
b, a = invresz([1], [1], [])
|
||
|
assert_almost_equal(b, [1])
|
||
|
assert_almost_equal(a, [1, -1])
|
||
|
|
||
|
b, a = invresz([1 - 1j, 2, 0.5 - 3j], [1, 0.5j, 1 + 1j], [])
|
||
|
assert_almost_equal(b, [3.5 - 4j, -8.5 + 0.25j, 3.5 + 3.25j])
|
||
|
assert_almost_equal(a, [1, -2 - 1.5j, 0.5 + 2j, 0.5 - 0.5j])
|
||
|
|
||
|
b, a = invresz([0.5, 1], [1 - 1j, 2 + 2j], [1, 2, 3])
|
||
|
assert_almost_equal(b, [2.5, -3 - 1j, 1 - 2j, -1 - 3j, 12])
|
||
|
assert_almost_equal(a, [1, -3 - 1j, 4])
|
||
|
|
||
|
b, a = invresz([-1, 2, 1j, 3 - 1j, 4, -2],
|
||
|
[-1, 2 - 1j, 2 - 1j, 3, 3, 3], [])
|
||
|
assert_almost_equal(b, [6, -50 + 11j, 100 - 72j, 80 + 58j,
|
||
|
-354 + 228j, 234 - 297j])
|
||
|
assert_almost_equal(a, [1, -12 + 2j, 53 - 20j, -96 + 68j, 27 - 72j,
|
||
|
108 - 54j, -81 + 108j])
|
||
|
|
||
|
b, a = invresz([-1, 1j], [1, 1], [1, 2])
|
||
|
assert_almost_equal(b, [1j, 1, -3, 2])
|
||
|
assert_almost_equal(a, [1, -2, 1])
|
||
|
|
||
|
def test_inverse_scalar_arguments(self):
|
||
|
b, a = invres(1, 1, 1)
|
||
|
assert_almost_equal(b, [1, 0])
|
||
|
assert_almost_equal(a, [1, -1])
|
||
|
|
||
|
b, a = invresz(1, 1, 1)
|
||
|
assert_almost_equal(b, [2, -1])
|
||
|
assert_almost_equal(a, [1, -1])
|
||
|
|
||
|
|
||
|
class TestVectorstrength:
|
||
|
|
||
|
def test_single_1dperiod(self):
|
||
|
events = np.array([.5])
|
||
|
period = 5.
|
||
|
targ_strength = 1.
|
||
|
targ_phase = .1
|
||
|
|
||
|
strength, phase = vectorstrength(events, period)
|
||
|
|
||
|
assert_equal(strength.ndim, 0)
|
||
|
assert_equal(phase.ndim, 0)
|
||
|
assert_almost_equal(strength, targ_strength)
|
||
|
assert_almost_equal(phase, 2 * np.pi * targ_phase)
|
||
|
|
||
|
def test_single_2dperiod(self):
|
||
|
events = np.array([.5])
|
||
|
period = [1, 2, 5.]
|
||
|
targ_strength = [1.] * 3
|
||
|
targ_phase = np.array([.5, .25, .1])
|
||
|
|
||
|
strength, phase = vectorstrength(events, period)
|
||
|
|
||
|
assert_equal(strength.ndim, 1)
|
||
|
assert_equal(phase.ndim, 1)
|
||
|
assert_array_almost_equal(strength, targ_strength)
|
||
|
assert_almost_equal(phase, 2 * np.pi * targ_phase)
|
||
|
|
||
|
def test_equal_1dperiod(self):
|
||
|
events = np.array([.25, .25, .25, .25, .25, .25])
|
||
|
period = 2
|
||
|
targ_strength = 1.
|
||
|
targ_phase = .125
|
||
|
|
||
|
strength, phase = vectorstrength(events, period)
|
||
|
|
||
|
assert_equal(strength.ndim, 0)
|
||
|
assert_equal(phase.ndim, 0)
|
||
|
assert_almost_equal(strength, targ_strength)
|
||
|
assert_almost_equal(phase, 2 * np.pi * targ_phase)
|
||
|
|
||
|
def test_equal_2dperiod(self):
|
||
|
events = np.array([.25, .25, .25, .25, .25, .25])
|
||
|
period = [1, 2, ]
|
||
|
targ_strength = [1.] * 2
|
||
|
targ_phase = np.array([.25, .125])
|
||
|
|
||
|
strength, phase = vectorstrength(events, period)
|
||
|
|
||
|
assert_equal(strength.ndim, 1)
|
||
|
assert_equal(phase.ndim, 1)
|
||
|
assert_almost_equal(strength, targ_strength)
|
||
|
assert_almost_equal(phase, 2 * np.pi * targ_phase)
|
||
|
|
||
|
def test_spaced_1dperiod(self):
|
||
|
events = np.array([.1, 1.1, 2.1, 4.1, 10.1])
|
||
|
period = 1
|
||
|
targ_strength = 1.
|
||
|
targ_phase = .1
|
||
|
|
||
|
strength, phase = vectorstrength(events, period)
|
||
|
|
||
|
assert_equal(strength.ndim, 0)
|
||
|
assert_equal(phase.ndim, 0)
|
||
|
assert_almost_equal(strength, targ_strength)
|
||
|
assert_almost_equal(phase, 2 * np.pi * targ_phase)
|
||
|
|
||
|
def test_spaced_2dperiod(self):
|
||
|
events = np.array([.1, 1.1, 2.1, 4.1, 10.1])
|
||
|
period = [1, .5]
|
||
|
targ_strength = [1.] * 2
|
||
|
targ_phase = np.array([.1, .2])
|
||
|
|
||
|
strength, phase = vectorstrength(events, period)
|
||
|
|
||
|
assert_equal(strength.ndim, 1)
|
||
|
assert_equal(phase.ndim, 1)
|
||
|
assert_almost_equal(strength, targ_strength)
|
||
|
assert_almost_equal(phase, 2 * np.pi * targ_phase)
|
||
|
|
||
|
def test_partial_1dperiod(self):
|
||
|
events = np.array([.25, .5, .75])
|
||
|
period = 1
|
||
|
targ_strength = 1. / 3.
|
||
|
targ_phase = .5
|
||
|
|
||
|
strength, phase = vectorstrength(events, period)
|
||
|
|
||
|
assert_equal(strength.ndim, 0)
|
||
|
assert_equal(phase.ndim, 0)
|
||
|
assert_almost_equal(strength, targ_strength)
|
||
|
assert_almost_equal(phase, 2 * np.pi * targ_phase)
|
||
|
|
||
|
def test_partial_2dperiod(self):
|
||
|
events = np.array([.25, .5, .75])
|
||
|
period = [1., 1., 1., 1.]
|
||
|
targ_strength = [1. / 3.] * 4
|
||
|
targ_phase = np.array([.5, .5, .5, .5])
|
||
|
|
||
|
strength, phase = vectorstrength(events, period)
|
||
|
|
||
|
assert_equal(strength.ndim, 1)
|
||
|
assert_equal(phase.ndim, 1)
|
||
|
assert_almost_equal(strength, targ_strength)
|
||
|
assert_almost_equal(phase, 2 * np.pi * targ_phase)
|
||
|
|
||
|
def test_opposite_1dperiod(self):
|
||
|
events = np.array([0, .25, .5, .75])
|
||
|
period = 1.
|
||
|
targ_strength = 0
|
||
|
|
||
|
strength, phase = vectorstrength(events, period)
|
||
|
|
||
|
assert_equal(strength.ndim, 0)
|
||
|
assert_equal(phase.ndim, 0)
|
||
|
assert_almost_equal(strength, targ_strength)
|
||
|
|
||
|
def test_opposite_2dperiod(self):
|
||
|
events = np.array([0, .25, .5, .75])
|
||
|
period = [1.] * 10
|
||
|
targ_strength = [0.] * 10
|
||
|
|
||
|
strength, phase = vectorstrength(events, period)
|
||
|
|
||
|
assert_equal(strength.ndim, 1)
|
||
|
assert_equal(phase.ndim, 1)
|
||
|
assert_almost_equal(strength, targ_strength)
|
||
|
|
||
|
def test_2d_events_ValueError(self):
|
||
|
events = np.array([[1, 2]])
|
||
|
period = 1.
|
||
|
assert_raises(ValueError, vectorstrength, events, period)
|
||
|
|
||
|
def test_2d_period_ValueError(self):
|
||
|
events = 1.
|
||
|
period = np.array([[1]])
|
||
|
assert_raises(ValueError, vectorstrength, events, period)
|
||
|
|
||
|
def test_zero_period_ValueError(self):
|
||
|
events = 1.
|
||
|
period = 0
|
||
|
assert_raises(ValueError, vectorstrength, events, period)
|
||
|
|
||
|
def test_negative_period_ValueError(self):
|
||
|
events = 1.
|
||
|
period = -1
|
||
|
assert_raises(ValueError, vectorstrength, events, period)
|
||
|
|
||
|
|
||
|
def cast_tf2sos(b, a):
|
||
|
"""Convert TF2SOS, casting to complex128 and back to the original dtype."""
|
||
|
# tf2sos does not support all of the dtypes that we want to check, e.g.:
|
||
|
#
|
||
|
# TypeError: array type complex256 is unsupported in linalg
|
||
|
#
|
||
|
# so let's cast, convert, and cast back -- should be fine for the
|
||
|
# systems and precisions we are testing.
|
||
|
dtype = np.asarray(b).dtype
|
||
|
b = np.array(b, np.complex128)
|
||
|
a = np.array(a, np.complex128)
|
||
|
return tf2sos(b, a).astype(dtype)
|
||
|
|
||
|
|
||
|
def assert_allclose_cast(actual, desired, rtol=1e-7, atol=0):
|
||
|
"""Wrap assert_allclose while casting object arrays."""
|
||
|
if actual.dtype.kind == 'O':
|
||
|
dtype = np.array(actual.flat[0]).dtype
|
||
|
actual, desired = actual.astype(dtype), desired.astype(dtype)
|
||
|
assert_allclose(actual, desired, rtol, atol)
|
||
|
|
||
|
|
||
|
@pytest.mark.parametrize('func', (sosfilt, lfilter))
|
||
|
def test_nonnumeric_dtypes(func):
|
||
|
x = [Decimal(1), Decimal(2), Decimal(3)]
|
||
|
b = [Decimal(1), Decimal(2), Decimal(3)]
|
||
|
a = [Decimal(1), Decimal(2), Decimal(3)]
|
||
|
x = np.array(x)
|
||
|
assert x.dtype.kind == 'O'
|
||
|
desired = lfilter(np.array(b, float), np.array(a, float), x.astype(float))
|
||
|
if func is sosfilt:
|
||
|
actual = sosfilt([b + a], x)
|
||
|
else:
|
||
|
actual = lfilter(b, a, x)
|
||
|
assert all(isinstance(x, Decimal) for x in actual)
|
||
|
assert_allclose(actual.astype(float), desired.astype(float))
|
||
|
# Degenerate cases
|
||
|
if func is lfilter:
|
||
|
args = [1., 1.]
|
||
|
else:
|
||
|
args = [tf2sos(1., 1.)]
|
||
|
|
||
|
with pytest.raises(ValueError, match='must be at least 1-D'):
|
||
|
func(*args, x=1.)
|
||
|
|
||
|
|
||
|
@pytest.mark.parametrize('dt', 'fdgFDGO')
|
||
|
class TestSOSFilt:
|
||
|
|
||
|
# The test_rank* tests are pulled from _TestLinearFilter
|
||
|
def test_rank1(self, dt):
|
||
|
x = np.linspace(0, 5, 6).astype(dt)
|
||
|
b = np.array([1, -1]).astype(dt)
|
||
|
a = np.array([0.5, -0.5]).astype(dt)
|
||
|
|
||
|
# Test simple IIR
|
||
|
y_r = np.array([0, 2, 4, 6, 8, 10.]).astype(dt)
|
||
|
sos = cast_tf2sos(b, a)
|
||
|
assert sos.dtype.char == dt
|
||
|
assert_array_almost_equal(sosfilt(cast_tf2sos(b, a), x), y_r)
|
||
|
|
||
|
# Test simple FIR
|
||
|
b = np.array([1, 1]).astype(dt)
|
||
|
# NOTE: This was changed (rel. to TestLinear...) to add a pole @zero:
|
||
|
a = np.array([1, 0]).astype(dt)
|
||
|
y_r = np.array([0, 1, 3, 5, 7, 9.]).astype(dt)
|
||
|
assert_array_almost_equal(sosfilt(cast_tf2sos(b, a), x), y_r)
|
||
|
|
||
|
b = [1, 1, 0]
|
||
|
a = [1, 0, 0]
|
||
|
x = np.ones(8)
|
||
|
sos = np.concatenate((b, a))
|
||
|
sos.shape = (1, 6)
|
||
|
y = sosfilt(sos, x)
|
||
|
assert_allclose(y, [1, 2, 2, 2, 2, 2, 2, 2])
|
||
|
|
||
|
def test_rank2(self, dt):
|
||
|
shape = (4, 3)
|
||
|
x = np.linspace(0, np.prod(shape) - 1, np.prod(shape)).reshape(shape)
|
||
|
x = x.astype(dt)
|
||
|
|
||
|
b = np.array([1, -1]).astype(dt)
|
||
|
a = np.array([0.5, 0.5]).astype(dt)
|
||
|
|
||
|
y_r2_a0 = np.array([[0, 2, 4], [6, 4, 2], [0, 2, 4], [6, 4, 2]],
|
||
|
dtype=dt)
|
||
|
|
||
|
y_r2_a1 = np.array([[0, 2, 0], [6, -4, 6], [12, -10, 12],
|
||
|
[18, -16, 18]], dtype=dt)
|
||
|
|
||
|
y = sosfilt(cast_tf2sos(b, a), x, axis=0)
|
||
|
assert_array_almost_equal(y_r2_a0, y)
|
||
|
|
||
|
y = sosfilt(cast_tf2sos(b, a), x, axis=1)
|
||
|
assert_array_almost_equal(y_r2_a1, y)
|
||
|
|
||
|
def test_rank3(self, dt):
|
||
|
shape = (4, 3, 2)
|
||
|
x = np.linspace(0, np.prod(shape) - 1, np.prod(shape)).reshape(shape)
|
||
|
|
||
|
b = np.array([1, -1]).astype(dt)
|
||
|
a = np.array([0.5, 0.5]).astype(dt)
|
||
|
|
||
|
# Test last axis
|
||
|
y = sosfilt(cast_tf2sos(b, a), x)
|
||
|
for i in range(x.shape[0]):
|
||
|
for j in range(x.shape[1]):
|
||
|
assert_array_almost_equal(y[i, j], lfilter(b, a, x[i, j]))
|
||
|
|
||
|
def test_initial_conditions(self, dt):
|
||
|
b1, a1 = signal.butter(2, 0.25, 'low')
|
||
|
b2, a2 = signal.butter(2, 0.75, 'low')
|
||
|
b3, a3 = signal.butter(2, 0.75, 'low')
|
||
|
b = np.convolve(np.convolve(b1, b2), b3)
|
||
|
a = np.convolve(np.convolve(a1, a2), a3)
|
||
|
sos = np.array((np.r_[b1, a1], np.r_[b2, a2], np.r_[b3, a3]))
|
||
|
|
||
|
x = np.random.rand(50).astype(dt)
|
||
|
|
||
|
# Stopping filtering and continuing
|
||
|
y_true, zi = lfilter(b, a, x[:20], zi=np.zeros(6))
|
||
|
y_true = np.r_[y_true, lfilter(b, a, x[20:], zi=zi)[0]]
|
||
|
assert_allclose_cast(y_true, lfilter(b, a, x))
|
||
|
|
||
|
y_sos, zi = sosfilt(sos, x[:20], zi=np.zeros((3, 2)))
|
||
|
y_sos = np.r_[y_sos, sosfilt(sos, x[20:], zi=zi)[0]]
|
||
|
assert_allclose_cast(y_true, y_sos)
|
||
|
|
||
|
# Use a step function
|
||
|
zi = sosfilt_zi(sos)
|
||
|
x = np.ones(8, dt)
|
||
|
y, zf = sosfilt(sos, x, zi=zi)
|
||
|
|
||
|
assert_allclose_cast(y, np.ones(8))
|
||
|
assert_allclose_cast(zf, zi)
|
||
|
|
||
|
# Initial condition shape matching
|
||
|
x.shape = (1, 1) + x.shape # 3D
|
||
|
assert_raises(ValueError, sosfilt, sos, x, zi=zi)
|
||
|
zi_nd = zi.copy()
|
||
|
zi_nd.shape = (zi.shape[0], 1, 1, zi.shape[-1])
|
||
|
assert_raises(ValueError, sosfilt, sos, x,
|
||
|
zi=zi_nd[:, :, :, [0, 1, 1]])
|
||
|
y, zf = sosfilt(sos, x, zi=zi_nd)
|
||
|
assert_allclose_cast(y[0, 0], np.ones(8))
|
||
|
assert_allclose_cast(zf[:, 0, 0, :], zi)
|
||
|
|
||
|
def test_initial_conditions_3d_axis1(self, dt):
|
||
|
# Test the use of zi when sosfilt is applied to axis 1 of a 3-d input.
|
||
|
|
||
|
# Input array is x.
|
||
|
x = np.random.RandomState(159).randint(0, 5, size=(2, 15, 3))
|
||
|
x = x.astype(dt)
|
||
|
|
||
|
# Design a filter in ZPK format and convert to SOS
|
||
|
zpk = signal.butter(6, 0.35, output='zpk')
|
||
|
sos = zpk2sos(*zpk)
|
||
|
nsections = sos.shape[0]
|
||
|
|
||
|
# Filter along this axis.
|
||
|
axis = 1
|
||
|
|
||
|
# Initial conditions, all zeros.
|
||
|
shp = list(x.shape)
|
||
|
shp[axis] = 2
|
||
|
shp = [nsections] + shp
|
||
|
z0 = np.zeros(shp)
|
||
|
|
||
|
# Apply the filter to x.
|
||
|
yf, zf = sosfilt(sos, x, axis=axis, zi=z0)
|
||
|
|
||
|
# Apply the filter to x in two stages.
|
||
|
y1, z1 = sosfilt(sos, x[:, :5, :], axis=axis, zi=z0)
|
||
|
y2, z2 = sosfilt(sos, x[:, 5:, :], axis=axis, zi=z1)
|
||
|
|
||
|
# y should equal yf, and z2 should equal zf.
|
||
|
y = np.concatenate((y1, y2), axis=axis)
|
||
|
assert_allclose_cast(y, yf, rtol=1e-10, atol=1e-13)
|
||
|
assert_allclose_cast(z2, zf, rtol=1e-10, atol=1e-13)
|
||
|
|
||
|
# let's try the "step" initial condition
|
||
|
zi = sosfilt_zi(sos)
|
||
|
zi.shape = [nsections, 1, 2, 1]
|
||
|
zi = zi * x[:, 0:1, :]
|
||
|
y = sosfilt(sos, x, axis=axis, zi=zi)[0]
|
||
|
# check it against the TF form
|
||
|
b, a = zpk2tf(*zpk)
|
||
|
zi = lfilter_zi(b, a)
|
||
|
zi.shape = [1, zi.size, 1]
|
||
|
zi = zi * x[:, 0:1, :]
|
||
|
y_tf = lfilter(b, a, x, axis=axis, zi=zi)[0]
|
||
|
assert_allclose_cast(y, y_tf, rtol=1e-10, atol=1e-13)
|
||
|
|
||
|
def test_bad_zi_shape(self, dt):
|
||
|
# The shape of zi is checked before using any values in the
|
||
|
# arguments, so np.empty is fine for creating the arguments.
|
||
|
x = np.empty((3, 15, 3), dt)
|
||
|
sos = np.zeros((4, 6))
|
||
|
zi = np.empty((4, 3, 3, 2)) # Correct shape is (4, 3, 2, 3)
|
||
|
with pytest.raises(ValueError, match='should be all ones'):
|
||
|
sosfilt(sos, x, zi=zi, axis=1)
|
||
|
sos[:, 3] = 1.
|
||
|
with pytest.raises(ValueError, match='Invalid zi shape'):
|
||
|
sosfilt(sos, x, zi=zi, axis=1)
|
||
|
|
||
|
def test_sosfilt_zi(self, dt):
|
||
|
sos = signal.butter(6, 0.2, output='sos')
|
||
|
zi = sosfilt_zi(sos)
|
||
|
|
||
|
y, zf = sosfilt(sos, np.ones(40, dt), zi=zi)
|
||
|
assert_allclose_cast(zf, zi, rtol=1e-13)
|
||
|
|
||
|
# Expected steady state value of the step response of this filter:
|
||
|
ss = np.prod(sos[:, :3].sum(axis=-1) / sos[:, 3:].sum(axis=-1))
|
||
|
assert_allclose_cast(y, ss, rtol=1e-13)
|
||
|
|
||
|
# zi as array-like
|
||
|
_, zf = sosfilt(sos, np.ones(40, dt), zi=zi.tolist())
|
||
|
assert_allclose_cast(zf, zi, rtol=1e-13)
|
||
|
|
||
|
|
||
|
class TestDeconvolve:
|
||
|
|
||
|
def test_basic(self):
|
||
|
# From docstring example
|
||
|
original = [0, 1, 0, 0, 1, 1, 0, 0]
|
||
|
impulse_response = [2, 1]
|
||
|
recorded = [0, 2, 1, 0, 2, 3, 1, 0, 0]
|
||
|
recovered, remainder = signal.deconvolve(recorded, impulse_response)
|
||
|
assert_allclose(recovered, original)
|
||
|
|
||
|
def test_n_dimensional_signal(self):
|
||
|
recorded = [[0, 0], [0, 0]]
|
||
|
impulse_response = [0, 0]
|
||
|
with pytest.raises(ValueError, match="signal must be 1-D."):
|
||
|
quotient, remainder = signal.deconvolve(recorded, impulse_response)
|
||
|
|
||
|
def test_n_dimensional_divisor(self):
|
||
|
recorded = [0, 0]
|
||
|
impulse_response = [[0, 0], [0, 0]]
|
||
|
with pytest.raises(ValueError, match="divisor must be 1-D."):
|
||
|
quotient, remainder = signal.deconvolve(recorded, impulse_response)
|
||
|
|
||
|
|
||
|
class TestDetrend:
|
||
|
|
||
|
def test_basic(self):
|
||
|
detrended = detrend(array([1, 2, 3]))
|
||
|
detrended_exact = array([0, 0, 0])
|
||
|
assert_array_almost_equal(detrended, detrended_exact)
|
||
|
|
||
|
def test_copy(self):
|
||
|
x = array([1, 1.2, 1.5, 1.6, 2.4])
|
||
|
copy_array = detrend(x, overwrite_data=False)
|
||
|
inplace = detrend(x, overwrite_data=True)
|
||
|
assert_array_almost_equal(copy_array, inplace)
|
||
|
|
||
|
|
||
|
class TestUniqueRoots:
|
||
|
def test_real_no_repeat(self):
|
||
|
p = [-1.0, -0.5, 0.3, 1.2, 10.0]
|
||
|
unique, multiplicity = unique_roots(p)
|
||
|
assert_almost_equal(unique, p, decimal=15)
|
||
|
assert_equal(multiplicity, np.ones(len(p)))
|
||
|
|
||
|
def test_real_repeat(self):
|
||
|
p = [-1.0, -0.95, -0.89, -0.8, 0.5, 1.0, 1.05]
|
||
|
|
||
|
unique, multiplicity = unique_roots(p, tol=1e-1, rtype='min')
|
||
|
assert_almost_equal(unique, [-1.0, -0.89, 0.5, 1.0], decimal=15)
|
||
|
assert_equal(multiplicity, [2, 2, 1, 2])
|
||
|
|
||
|
unique, multiplicity = unique_roots(p, tol=1e-1, rtype='max')
|
||
|
assert_almost_equal(unique, [-0.95, -0.8, 0.5, 1.05], decimal=15)
|
||
|
assert_equal(multiplicity, [2, 2, 1, 2])
|
||
|
|
||
|
unique, multiplicity = unique_roots(p, tol=1e-1, rtype='avg')
|
||
|
assert_almost_equal(unique, [-0.975, -0.845, 0.5, 1.025], decimal=15)
|
||
|
assert_equal(multiplicity, [2, 2, 1, 2])
|
||
|
|
||
|
def test_complex_no_repeat(self):
|
||
|
p = [-1.0, 1.0j, 0.5 + 0.5j, -1.0 - 1.0j, 3.0 + 2.0j]
|
||
|
unique, multiplicity = unique_roots(p)
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||
|
assert_almost_equal(unique, p, decimal=15)
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|
assert_equal(multiplicity, np.ones(len(p)))
|
||
|
|
||
|
def test_complex_repeat(self):
|
||
|
p = [-1.0, -1.0 + 0.05j, -0.95 + 0.15j, -0.90 + 0.15j, 0.0,
|
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|
0.5 + 0.5j, 0.45 + 0.55j]
|
||
|
|
||
|
unique, multiplicity = unique_roots(p, tol=1e-1, rtype='min')
|
||
|
assert_almost_equal(unique, [-1.0, -0.95 + 0.15j, 0.0, 0.45 + 0.55j],
|
||
|
decimal=15)
|
||
|
assert_equal(multiplicity, [2, 2, 1, 2])
|
||
|
|
||
|
unique, multiplicity = unique_roots(p, tol=1e-1, rtype='max')
|
||
|
assert_almost_equal(unique,
|
||
|
[-1.0 + 0.05j, -0.90 + 0.15j, 0.0, 0.5 + 0.5j],
|
||
|
decimal=15)
|
||
|
assert_equal(multiplicity, [2, 2, 1, 2])
|
||
|
|
||
|
unique, multiplicity = unique_roots(p, tol=1e-1, rtype='avg')
|
||
|
assert_almost_equal(
|
||
|
unique, [-1.0 + 0.025j, -0.925 + 0.15j, 0.0, 0.475 + 0.525j],
|
||
|
decimal=15)
|
||
|
assert_equal(multiplicity, [2, 2, 1, 2])
|
||
|
|
||
|
def test_gh_4915(self):
|
||
|
p = np.roots(np.convolve(np.ones(5), np.ones(5)))
|
||
|
true_roots = [-(-1)**(1/5), (-1)**(4/5), -(-1)**(3/5), (-1)**(2/5)]
|
||
|
|
||
|
unique, multiplicity = unique_roots(p)
|
||
|
unique = np.sort(unique)
|
||
|
|
||
|
assert_almost_equal(np.sort(unique), true_roots, decimal=7)
|
||
|
assert_equal(multiplicity, [2, 2, 2, 2])
|
||
|
|
||
|
def test_complex_roots_extra(self):
|
||
|
unique, multiplicity = unique_roots([1.0, 1.0j, 1.0])
|
||
|
assert_almost_equal(unique, [1.0, 1.0j], decimal=15)
|
||
|
assert_equal(multiplicity, [2, 1])
|
||
|
|
||
|
unique, multiplicity = unique_roots([1, 1 + 2e-9, 1e-9 + 1j], tol=0.1)
|
||
|
assert_almost_equal(unique, [1.0, 1e-9 + 1.0j], decimal=15)
|
||
|
assert_equal(multiplicity, [2, 1])
|
||
|
|
||
|
def test_single_unique_root(self):
|
||
|
p = np.random.rand(100) + 1j * np.random.rand(100)
|
||
|
unique, multiplicity = unique_roots(p, 2)
|
||
|
assert_almost_equal(unique, [np.min(p)], decimal=15)
|
||
|
assert_equal(multiplicity, [100])
|