from __future__ import division, print_function, absolute_import import sys from decimal import Decimal from itertools import product from nose import SkipTest from numpy.testing import ( TestCase, run_module_suite, assert_equal, assert_almost_equal, assert_array_equal, assert_array_almost_equal, assert_raises, assert_allclose, assert_, dec) from numpy import array, arange import numpy as np from scipy.optimize import fmin from scipy import signal from scipy.signal import ( correlate, convolve, convolve2d, fftconvolve, hann, hilbert, hilbert2, lfilter, lfilter_zi, filtfilt, butter, zpk2tf, zpk2sos, invres, invresz, vectorstrength, lfiltic, tf2sos, sosfilt, sosfiltfilt, sosfilt_zi, tf2zpk) from scipy.signal.signaltools import _filtfilt_gust if sys.version_info.major >= 3 and sys.version_info.minor >= 5: from math import gcd else: from fractions import gcd class _TestConvolve(TestCase): def test_basic(self): a = [3, 4, 5, 6, 5, 4] b = [1, 2, 3] c = convolve(a, b) assert_array_equal(c, array([3, 10, 22, 28, 32, 32, 23, 12])) def test_same(self): a = [3, 4, 5] b = [1, 2, 3, 4] c = convolve(a, b, mode="same") assert_array_equal(c, array([10, 22, 34])) def test_same_eq(self): a = [3, 4, 5] b = [1, 2, 3] c = convolve(a, b, mode="same") assert_array_equal(c, array([10, 22, 22])) def test_complex(self): x = array([1 + 1j, 2 + 1j, 3 + 1j]) y = array([1 + 1j, 2 + 1j]) z = convolve(x, y) assert_array_equal(z, array([2j, 2 + 6j, 5 + 8j, 5 + 5j])) def test_zero_rank(self): a = 1289 b = 4567 c = convolve(a, b) assert_equal(c, a * b) def test_single_element(self): a = array([4967]) b = array([3920]) c = convolve(a, b) assert_equal(c, a * b) def test_2d_arrays(self): a = [[1, 2, 3], [3, 4, 5]] b = [[2, 3, 4], [4, 5, 6]] c = convolve(a, b) d = array([[2, 7, 16, 17, 12], [10, 30, 62, 58, 38], [12, 31, 58, 49, 30]]) assert_array_equal(c, d) def test_input_swapping(self): small = arange(8).reshape(2, 2, 2) big = 1j * arange(27).reshape(3, 3, 3) big += arange(27)[::-1].reshape(3, 3, 3) out_array = array( [[[0 + 0j, 26 + 0j, 25 + 1j, 24 + 2j], [52 + 0j, 151 + 5j, 145 + 11j, 93 + 11j], [46 + 6j, 133 + 23j, 127 + 29j, 81 + 23j], [40 + 12j, 98 + 32j, 93 + 37j, 54 + 24j]], [[104 + 0j, 247 + 13j, 237 + 23j, 135 + 21j], [282 + 30j, 632 + 96j, 604 + 124j, 330 + 86j], [246 + 66j, 548 + 180j, 520 + 208j, 282 + 134j], [142 + 66j, 307 + 161j, 289 + 179j, 153 + 107j]], [[68 + 36j, 157 + 103j, 147 + 113j, 81 + 75j], [174 + 138j, 380 + 348j, 352 + 376j, 186 + 230j], [138 + 174j, 296 + 432j, 268 + 460j, 138 + 278j], [70 + 138j, 145 + 323j, 127 + 341j, 63 + 197j]], [[32 + 72j, 68 + 166j, 59 + 175j, 30 + 100j], [68 + 192j, 139 + 433j, 117 + 455j, 57 + 255j], [38 + 222j, 73 + 499j, 51 + 521j, 21 + 291j], [12 + 144j, 20 + 318j, 7 + 331j, 0 + 182j]]]) assert_array_equal(convolve(small, big, 'full'), out_array) assert_array_equal(convolve(big, small, 'full'), out_array) assert_array_equal(convolve(small, big, 'same'), out_array[1:3, 1:3, 1:3]) assert_array_equal(convolve(big, small, 'same'), out_array[0:3, 0:3, 0:3]) assert_array_equal(convolve(small, big, 'valid'), out_array[1:3, 1:3, 1:3]) assert_array_equal(convolve(big, small, 'valid'), out_array[1:3, 1:3, 1:3]) class TestConvolve(_TestConvolve): def test_valid_mode2(self): # See gh-5897 a = [1, 2, 3, 6, 5, 3] b = [2, 3, 4, 5, 3, 4, 2, 2, 1] expected = [70, 78, 73, 65] out = convolve(a, b, 'valid') assert_array_equal(out, expected) out = convolve(b, a, 'valid') assert_array_equal(out, expected) a = [1 + 5j, 2 - 1j, 3 + 0j] b = [2 - 3j, 1 + 0j] expected = [2 - 3j, 8 - 10j] out = convolve(a, b, 'valid') assert_array_equal(out, expected) out = convolve(b, a, 'valid') assert_array_equal(out, expected) def test_same_mode(self): a = [1, 2, 3, 3, 1, 2] b = [1, 4, 3, 4, 5, 6, 7, 4, 3, 2, 1, 1, 3] c = convolve(a, b, 'same') d = array([57, 61, 63, 57, 45, 36]) assert_array_equal(c, d) 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)) self.assertRaises(ValueError, convolve, *(a, b), **{'mode': 'valid'}) self.assertRaises(ValueError, convolve, *(b, a), **{'mode': 'valid'}) class _TestConvolve2d(TestCase): def test_2d_arrays(self): a = [[1, 2, 3], [3, 4, 5]] b = [[2, 3, 4], [4, 5, 6]] d = array([[2, 7, 16, 17, 12], [10, 30, 62, 58, 38], [12, 31, 58, 49, 30]]) e = convolve2d(a, b) assert_array_equal(e, d) def test_valid_mode(self): e = [[2, 3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9, 10]] f = [[1, 2, 3], [3, 4, 5]] h = array([[62, 80, 98, 116, 134]]) g = convolve2d(e, f, 'valid') assert_array_equal(g, h) # See gh-5897 g = convolve2d(f, e, 'valid') assert_array_equal(g, h) def test_valid_mode_complx(self): e = [[2, 3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9, 10]] f = np.array([[1, 2, 3], [3, 4, 5]], dtype=complex) + 1j h = array([[62.+24.j, 80.+30.j, 98.+36.j, 116.+42.j, 134.+48.j]]) g = convolve2d(e, f, 'valid') assert_array_almost_equal(g, h) # See gh-5897 g = convolve2d(f, e, 'valid') assert_array_equal(g, h) def test_fillvalue(self): a = [[1, 2, 3], [3, 4, 5]] b = [[2, 3, 4], [4, 5, 6]] fillval = 1 c = convolve2d(a, b, 'full', 'fill', fillval) d = array([[24, 26, 31, 34, 32], [28, 40, 62, 64, 52], [32, 46, 67, 62, 48]]) assert_array_equal(c, d) def test_wrap_boundary(self): a = [[1, 2, 3], [3, 4, 5]] b = [[2, 3, 4], [4, 5, 6]] c = convolve2d(a, b, 'full', 'wrap') d = array([[80, 80, 74, 80, 80], [68, 68, 62, 68, 68], [80, 80, 74, 80, 80]]) assert_array_equal(c, d) def test_sym_boundary(self): a = [[1, 2, 3], [3, 4, 5]] b = [[2, 3, 4], [4, 5, 6]] c = convolve2d(a, b, 'full', 'symm') d = array([[34, 30, 44, 62, 66], [52, 48, 62, 80, 84], [82, 78, 92, 110, 114]]) assert_array_equal(c, d) 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)) self.assertRaises(ValueError, convolve2d, *(a, b), **{'mode': 'valid'}) self.assertRaises(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)) class TestFFTConvolve(TestCase): def test_real(self): x = array([1, 2, 3]) assert_array_almost_equal(signal.fftconvolve(x, x), [1, 4, 10, 12, 9.]) def test_complex(self): x = array([1 + 1j, 2 + 2j, 3 + 3j]) assert_array_almost_equal(signal.fftconvolve(x, x), [0 + 2j, 0 + 8j, 0 + 20j, 0 + 24j, 0 + 18j]) def test_2d_real_same(self): a = array([[1, 2, 3], [4, 5, 6]]) assert_array_almost_equal(signal.fftconvolve(a, a), array([[1, 4, 10, 12, 9], [8, 26, 56, 54, 36], [16, 40, 73, 60, 36]])) def test_2d_complex_same(self): a = array([[1 + 2j, 3 + 4j, 5 + 6j], [2 + 1j, 4 + 3j, 6 + 5j]]) c = fftconvolve(a, a) d = 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]]) assert_array_almost_equal(c, d) def test_real_same_mode(self): a = array([1, 2, 3]) b = array([3, 3, 5, 6, 8, 7, 9, 0, 1]) c = fftconvolve(a, b, 'same') d = array([35., 41., 47.]) assert_array_almost_equal(c, d) def test_real_same_mode2(self): a = array([3, 3, 5, 6, 8, 7, 9, 0, 1]) b = array([1, 2, 3]) c = fftconvolve(a, b, 'same') d = array([9., 20., 25., 35., 41., 47., 39., 28., 2.]) assert_array_almost_equal(c, d) def test_valid_mode(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.]) out = fftconvolve(a, b, 'valid') assert_array_almost_equal(out, expected) out = fftconvolve(b, a, 'valid') assert_array_almost_equal(out, expected) 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]) out = fftconvolve(a, b, 'valid') assert_array_almost_equal(out, expected) out = fftconvolve(b, a, 'valid') assert_array_almost_equal(out, expected) def test_real_valid_mode(self): a = array([3, 3, 5, 6, 8, 7, 9, 0, 1]) b = array([3, 2, 1]) d = array([24., 31., 41., 43., 49., 25., 12.]) c = fftconvolve(a, b, 'valid') assert_array_almost_equal(c, d) # See gh-5897 c = fftconvolve(b, a, 'valid') assert_array_almost_equal(c, d) 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) c = fftconvolve(a, b) assert_equal(c, a * b) def test_single_element(self): a = array([4967]) b = array([3920]) c = fftconvolve(a, b) assert_equal(c, a * b) def test_random_data(self): np.random.seed(1234) a = np.random.rand(1233) + 1j * np.random.rand(1233) b = np.random.rand(1321) + 1j * np.random.rand(1321) c = fftconvolve(a, b, 'full') d = np.convolve(a, b, 'full') assert_(np.allclose(c, d, rtol=1e-10)) @dec.slow def test_many_sizes(self): np.random.seed(1234) def ns(): for j in range(1, 100): yield j for j in range(1000, 1500): yield j for k in range(50): yield np.random.randint(1001, 10000) for n in ns(): msg = 'n=%d' % (n,) a = np.random.rand(n) + 1j * np.random.rand(n) b = np.random.rand(n) + 1j * np.random.rand(n) c = fftconvolve(a, b, 'full') d = np.convolve(a, b, 'full') assert_allclose(c, d, atol=1e-10, err_msg=msg) 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)) self.assertRaises(ValueError, fftconvolve, *(a, b), **{'mode': 'valid'}) self.assertRaises(ValueError, fftconvolve, *(b, a), **{'mode': 'valid'}) class TestMedFilt(TestCase): def test_basic(self): f = [[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]] d = signal.medfilt(f, [7, 3]) e = signal.medfilt2d(np.array(f, float), [7, 3]) assert_array_equal(d, [[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]]) assert_array_equal(d, e) def test_none(self): # Ticket #1124. Ensure this does not segfault. try: signal.medfilt(None) except: pass # 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.) class TestWiener(TestCase): 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) class TestResample(TestCase): 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) def test_fft(self): # Test FFT-based resampling self._test_data(method='fft') def test_polyphase(self): # Test polyphase resampling self._test_data(method='polyphase') def test_polyphase_extfilter(self): # Test external specification of downsampling filter self._test_data(method='polyphase', ext=True) def _test_data(self, method, ext=False): # 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} else: polyargs = {} 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 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) assert_array_equal(y_to.shape, y_resamp.shape) corr = np.corrcoef(y_to, y_resamp)[0, 1] assert_(corr > 0.99, msg=corr) 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, wheras 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) class TestCSpline1DEval(TestCase): 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) class TestOrderFilt(TestCase): def test_basic(self): assert_array_equal(signal.order_filter([1, 2, 3], [1, 0, 1], 1), [2, 3, 2]) class _TestLinearFilter(TestCase): 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]) class _TestCorrelateReal(TestCase): dt = None def _setup_rank1(self): a = np.linspace(0, 3, 4).astype(self.dt) b = np.linspace(1, 2, 2).astype(self.dt) y_r = np.array([0, 2, 5, 8, 3]).astype(self.dt) return a, b, y_r def test_rank1_valid(self): a, b, y_r = self._setup_rank1() y = correlate(a, b, 'valid') assert_array_almost_equal(y, y_r[1:4]) assert_equal(y.dtype, self.dt) # See gh-5897 y = correlate(b, a, 'valid') assert_array_almost_equal(y, y_r[1:4][::-1]) assert_equal(y.dtype, self.dt) def test_rank1_same(self): a, b, y_r = self._setup_rank1() y = correlate(a, b, 'same') assert_array_almost_equal(y, y_r[:-1]) assert_equal(y.dtype, self.dt) def test_rank1_full(self): a, b, y_r = self._setup_rank1() y = correlate(a, b, 'full') assert_array_almost_equal(y, y_r) assert_equal(y.dtype, self.dt) def _setup_rank3(self): a = np.linspace(0, 39, 40).reshape((2, 4, 5), order='F').astype( self.dt) b = np.linspace(0, 23, 24).reshape((2, 3, 4), order='F').astype( self.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=self.dt) return a, b, y_r def test_rank3_valid(self): a, b, y_r = self._setup_rank3() y = correlate(a, b, "valid") assert_array_almost_equal(y, y_r[1:2, 2:4, 3:5]) assert_equal(y.dtype, self.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, self.dt) def test_rank3_same(self): a, b, y_r = self._setup_rank3() y = correlate(a, b, "same") assert_array_almost_equal(y, y_r[0:-1, 1:-1, 1:-2]) assert_equal(y.dtype, self.dt) def test_rank3_all(self): a, b, y_r = self._setup_rank3() y = correlate(a, b) assert_array_almost_equal(y, y_r) assert_equal(y.dtype, self.dt) 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)) self.assertRaises(ValueError, correlate, *(a, b), **{'mode': 'valid'}) self.assertRaises(ValueError, correlate, *(b, a), **{'mode': 'valid'}) def _get_testcorrelate_class(datatype, base): class TestCorrelateX(base): dt = datatype TestCorrelateX.__name__ = "TestCorrelate%s" % datatype.__name__.title() return TestCorrelateX for datatype in [np.ubyte, np.byte, np.ushort, np.short, np.uint, int, np.ulonglong, np.ulonglong, np.float32, np.float64, np.longdouble, Decimal]: cls = _get_testcorrelate_class(datatype, _TestCorrelateReal) globals()[cls.__name__] = cls class _TestCorrelateComplex(TestCase): # The numpy data type to use. dt = None # The decimal precision to be used for comparing results. # This value will be passed as the 'decimal' keyword argument of # assert_array_almost_equal(). decimal = None def _setup_rank1(self, mode): np.random.seed(9) a = np.random.randn(10).astype(self.dt) a += 1j * np.random.randn(10).astype(self.dt) b = np.random.randn(8).astype(self.dt) b += 1j * np.random.randn(8).astype(self.dt) y_r = (correlate(a.real, b.real, mode=mode) + correlate(a.imag, b.imag, mode=mode)).astype(self.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): a, b, y_r = self._setup_rank1('valid') y = correlate(a, b, 'valid') assert_array_almost_equal(y, y_r, decimal=self.decimal) assert_equal(y.dtype, self.dt) # See gh-5897 y = correlate(b, a, 'valid') assert_array_almost_equal(y, y_r[::-1].conj(), decimal=self.decimal) assert_equal(y.dtype, self.dt) def test_rank1_same(self): a, b, y_r = self._setup_rank1('same') y = correlate(a, b, 'same') assert_array_almost_equal(y, y_r, decimal=self.decimal) assert_equal(y.dtype, self.dt) def test_rank1_full(self): a, b, y_r = self._setup_rank1('full') y = correlate(a, b, 'full') assert_array_almost_equal(y, y_r, decimal=self.decimal) assert_equal(y.dtype, self.dt) def test_swap_full(self): d = np.array([0.+0.j, 1.+1.j, 2.+2.j], dtype=self.dt) k = np.array([1.+3.j, 2.+4.j, 3.+5.j, 4.+6.j], dtype=self.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): 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): a = np.random.randn(10, 8, 6).astype(self.dt) a += 1j * np.random.randn(10, 8, 6).astype(self.dt) b = np.random.randn(8, 6, 4).astype(self.dt) b += 1j * np.random.randn(8, 6, 4).astype(self.dt) y_r = (correlate(a.real, b.real) + correlate(a.imag, b.imag)).astype(self.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 - 1) assert_equal(y.dtype, self.dt) class TestCorrelate2d(TestCase): 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)) self.assertRaises(ValueError, signal.correlate2d, *(a, b), **{'mode': 'valid'}) self.assertRaises(ValueError, signal.correlate2d, *(b, a), **{'mode': 'valid'}) # Create three classes, one for each complex data type. The actual class # name will be TestCorrelateComplex###, where ### is the number of bits. for datatype in [np.csingle, np.cdouble, np.clongdouble]: cls = _get_testcorrelate_class(datatype, _TestCorrelateComplex) # will either return a too large value for longdouble # or nonconvergence RuntimeError see #702169 try: cls.decimal = int(2 * np.finfo(datatype).precision / 3) if cls.decimal > 25: cls.decimal = 14 except RuntimeError: cls.decimal = 14 globals()[cls.__name__] = cls class TestLFilterZI(TestCase): 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) class TestFiltFilt(TestCase): 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=1e-14) 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': raise SkipTest('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': raise SkipTest('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-9, atol=1e-10) assert_allclose(yg, yo, rtol=1e-9, atol=1e-10) assert_allclose(zg1, zo1, rtol=1e-9, atol=1e-10) assert_allclose(zg2, zo2, rtol=1e-9, atol=1e-10) 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 yield 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 yield 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 yield check_filtfilt_gust, b, a, (length,), 0, approx_impulse_len class TestDecimate(TestCase): 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): self._test_phaseshift(method='fir', zero_phase=False) def test_zero_phase_FIR(self): 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.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.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) class TestHilbert(object): 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) yield assert_equal, hilbert(a.T, axis=0), aa.T # test 1d yield assert_equal, hilbert(a[0]), aa[0] # test N aan = hilbert(a, N=20, axis=-1) yield assert_equal, aan.shape, [3, 20] yield 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]) yield assert_almost_equal, aan[0], a0hilb, 14, 'N regression' class TestHilbert2(object): 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,)) class TestPartialFractionExpansion(TestCase): def test_invresz_one_coefficient_bug(self): # Regression test for issue in gh-4646. r = [1] p = [2] k = [0] a_expected = [1.0, 0.0] b_expected = [1.0, -2.0] a_observed, b_observed = invresz(r, p, k) assert_allclose(a_observed, a_expected) assert_allclose(b_observed, b_expected) def test_invres_distinct_roots(self): # This test was inspired by github issue 2496. r = [3 / 10, -1 / 6, -2 / 15] p = [0, -2, -5] k = [] a_expected = [1, 3] b_expected = [1, 7, 10, 0] a_observed, b_observed = invres(r, p, k) assert_allclose(a_observed, a_expected) assert_allclose(b_observed, b_expected) rtypes = ('avg', 'mean', 'min', 'minimum', 'max', 'maximum') # With the default tolerance, the rtype does not matter # for this example. for rtype in rtypes: a_observed, b_observed = invres(r, p, k, rtype=rtype) assert_allclose(a_observed, a_expected) assert_allclose(b_observed, b_expected) # With unrealistically large tolerances, repeated roots may be inferred # and the rtype comes into play. ridiculous_tolerance = 1e10 for rtype in rtypes: a, b = invres(r, p, k, tol=ridiculous_tolerance, rtype=rtype) def test_invres_repeated_roots(self): r = [3 / 20, -7 / 36, -1 / 6, 2 / 45] p = [0, -2, -2, -5] k = [] a_expected = [1, 3] b_expected = [1, 9, 24, 20, 0] rtypes = ('avg', 'mean', 'min', 'minimum', 'max', 'maximum') for rtype in rtypes: a_observed, b_observed = invres(r, p, k, rtype=rtype) assert_allclose(a_observed, a_expected) assert_allclose(b_observed, b_expected) def test_invres_bad_rtype(self): r = [3 / 20, -7 / 36, -1 / 6, 2 / 45] p = [0, -2, -2, -5] k = [] assert_raises(ValueError, invres, r, p, k, rtype='median') class TestVectorstrength(TestCase): 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) class TestSOSFilt(TestCase): # For sosfilt we only test a single datatype. Since sosfilt wraps # to lfilter under the hood, it's hopefully good enough to ensure # lfilter is extensively tested. dt = np.float64 # The test_rank* tests are pulled from _TestLinearFilter def test_rank1(self): x = np.linspace(0, 5, 6).astype(self.dt) b = np.array([1, -1]).astype(self.dt) a = np.array([0.5, -0.5]).astype(self.dt) # Test simple IIR y_r = np.array([0, 2, 4, 6, 8, 10.]).astype(self.dt) assert_array_almost_equal(sosfilt(tf2sos(b, a), x), y_r) # Test simple FIR b = np.array([1, 1]).astype(self.dt) # NOTE: This was changed (rel. to TestLinear...) to add a pole @zero: a = np.array([1, 0]).astype(self.dt) y_r = np.array([0, 1, 3, 5, 7, 9.]).astype(self.dt) assert_array_almost_equal(sosfilt(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): shape = (4, 3) x = np.linspace(0, np.prod(shape) - 1, np.prod(shape)).reshape(shape) x = x.astype(self.dt) b = np.array([1, -1]).astype(self.dt) a = np.array([0.5, 0.5]).astype(self.dt) y_r2_a0 = np.array([[0, 2, 4], [6, 4, 2], [0, 2, 4], [6, 4, 2]], dtype=self.dt) y_r2_a1 = np.array([[0, 2, 0], [6, -4, 6], [12, -10, 12], [18, -16, 18]], dtype=self.dt) y = sosfilt(tf2sos(b, a), x, axis=0) assert_array_almost_equal(y_r2_a0, y) y = sosfilt(tf2sos(b, a), x, axis=1) assert_array_almost_equal(y_r2_a1, y) def test_rank3(self): shape = (4, 3, 2) x = np.linspace(0, np.prod(shape) - 1, np.prod(shape)).reshape(shape) b = np.array([1, -1]).astype(self.dt) a = np.array([0.5, 0.5]).astype(self.dt) # Test last axis y = sosfilt(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): 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) # 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(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(y_true, y_sos) # Use a step function zi = sosfilt_zi(sos) x = np.ones(8) y, zf = sosfilt(sos, x, zi=zi) assert_allclose(y, np.ones(8)) assert_allclose(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(y[0, 0], np.ones(8)) assert_allclose(zf[:, 0, 0, :], zi) def test_initial_conditions_3d_axis1(self): # 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)) # 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(y, yf, rtol=1e-10, atol=1e-13) assert_allclose(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(y, y_tf, rtol=1e-10, atol=1e-13) def test_bad_zi_shape(self): # 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)) sos = np.empty((4, 6)) zi = np.empty((4, 3, 3, 2)) # Correct shape is (4, 3, 2, 3) assert_raises(ValueError, sosfilt, sos, x, zi=zi, axis=1) def test_sosfilt_zi(self): sos = signal.butter(6, 0.2, output='sos') zi = sosfilt_zi(sos) y, zf = sosfilt(sos, np.ones(40), zi=zi) assert_allclose(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(y, ss, rtol=1e-13) if __name__ == "__main__": run_module_suite()