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Vehicle-Anti-Theft-Face-Rec.../venv/Lib/site-packages/scipy/signal/tests/test_signaltools.py

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# -*- coding: utf-8 -*-
import sys
from decimal import Decimal
from itertools import product
from math import gcd
import warnings
import pytest
from pytest import raises as assert_raises
from numpy.testing import (
assert_equal,
assert_almost_equal, assert_array_equal, assert_array_almost_equal,
assert_allclose, assert_, assert_warns, assert_array_less,
suppress_warnings)
from numpy import array, arange
import numpy as np
from scipy.fft import fft
from scipy.ndimage.filters import correlate1d
from scipy.optimize import fmin, linear_sum_assignment
from scipy import signal
from scipy.signal import (
correlate, convolve, convolve2d,
fftconvolve, oaconvolve, choose_conv_method,
hilbert, hilbert2, lfilter, lfilter_zi, filtfilt, butter, zpk2tf, zpk2sos,
invres, invresz, vectorstrength, lfiltic, tf2sos, sosfilt, sosfiltfilt,
sosfilt_zi, tf2zpk, BadCoefficients, detrend, unique_roots, residue,
residuez)
from scipy.signal.windows import hann
from scipy.signal.signaltools import (_filtfilt_gust, _compute_factors,
_group_poles)
from scipy.signal._upfirdn import _upfirdn_modes
class _TestConvolve(object):
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_broadcastable(self):
a = np.arange(27).reshape(3, 3, 3)
b = np.arange(3)
for i in range(3):
b_shape = [1]*3
b_shape[i] = 3
x = convolve(a, b.reshape(b_shape), method='direct')
y = convolve(a, b.reshape(b_shape), method='fft')
assert_allclose(x, y)
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])
def test_invalid_params(self):
a = [3, 4, 5]
b = [1, 2, 3]
assert_raises(ValueError, convolve, a, b, mode='spam')
assert_raises(ValueError, convolve, a, b, mode='eggs', method='fft')
assert_raises(ValueError, convolve, a, b, mode='ham', method='direct')
assert_raises(ValueError, convolve, a, b, mode='full', method='bacon')
assert_raises(ValueError, convolve, a, b, mode='same', method='bacon')
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))
assert_raises(ValueError, convolve, *(a, b), **{'mode': 'valid'})
assert_raises(ValueError, convolve, *(b, a), **{'mode': 'valid'})
def test_convolve_method(self, n=100):
types = sum([t for _, t in np.sctypes.items()], [])
types = {np.dtype(t).name for t in types}
# These types include 'bool' and all precisions (int8, float32, etc)
# The removed types throw errors in correlate or fftconvolve
for dtype in ['complex256', 'complex192', 'float128', 'float96',
'str', 'void', 'bytes', 'object', 'unicode', 'string']:
if dtype in types:
types.remove(dtype)
args = [(t1, t2, mode) for t1 in types for t2 in types
for mode in ['valid', 'full', 'same']]
# These are random arrays, which means test is much stronger than
# convolving testing by convolving two np.ones arrays
np.random.seed(42)
array_types = {'i': np.random.choice([0, 1], size=n),
'f': np.random.randn(n)}
array_types['b'] = array_types['u'] = array_types['i']
array_types['c'] = array_types['f'] + 0.5j*array_types['f']
for t1, t2, mode in args:
x1 = array_types[np.dtype(t1).kind].astype(t1)
x2 = array_types[np.dtype(t2).kind].astype(t2)
results = {key: convolve(x1, x2, method=key, mode=mode)
for key in ['fft', 'direct']}
assert_equal(results['fft'].dtype, results['direct'].dtype)
if 'bool' in t1 and 'bool' in t2:
assert_equal(choose_conv_method(x1, x2), 'direct')
continue
# Found by experiment. Found approx smallest value for (rtol, atol)
# threshold to have tests pass.
if any([t in {'complex64', 'float32'} for t in [t1, t2]]):
kwargs = {'rtol': 1.0e-4, 'atol': 1e-6}
elif 'float16' in [t1, t2]:
# atol is default for np.allclose
kwargs = {'rtol': 1e-3, 'atol': 1e-3}
else:
# defaults for np.allclose (different from assert_allclose)
kwargs = {'rtol': 1e-5, 'atol': 1e-8}
assert_allclose(results['fft'], results['direct'], **kwargs)
def test_convolve_method_large_input(self):
# This is really a test that convolving two large integers goes to the
# direct method even if they're in the fft method.
for n in [10, 20, 50, 51, 52, 53, 54, 60, 62]:
z = np.array([2**n], dtype=np.int64)
fft = convolve(z, z, method='fft')
direct = convolve(z, z, method='direct')
# this is the case when integer precision gets to us
# issue #6076 has more detail, hopefully more tests after resolved
if n < 50:
assert_equal(fft, direct)
assert_equal(fft, 2**(2*n))
assert_equal(direct, 2**(2*n))
def test_mismatched_dims(self):
# Input arrays should have the same number of dimensions
assert_raises(ValueError, convolve, [1], 2, method='direct')
assert_raises(ValueError, convolve, 1, [2], method='direct')
assert_raises(ValueError, convolve, [1], 2, method='fft')
assert_raises(ValueError, convolve, 1, [2], method='fft')
assert_raises(ValueError, convolve, [1], [[2]])
assert_raises(ValueError, convolve, [3], 2)
class _TestConvolve2d(object):
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_fillvalue_deprecations(self):
# Deprecated 2017-07, scipy version 1.0.0
with suppress_warnings() as sup:
sup.filter(np.ComplexWarning, "Casting complex values to real")
r = sup.record(DeprecationWarning, "could not cast `fillvalue`")
convolve2d([[1]], [[1, 2]], fillvalue=1j)
assert_(len(r) == 1)
warnings.filterwarnings(
"error", message="could not cast `fillvalue`",
category=DeprecationWarning)
assert_raises(DeprecationWarning, convolve2d, [[1]], [[1, 2]],
fillvalue=1j)
with suppress_warnings():
warnings.filterwarnings(
"always", message="`fillvalue` must be scalar or an array ",
category=DeprecationWarning)
assert_warns(DeprecationWarning, convolve2d, [[1]], [[1, 2]],
fillvalue=[1, 2])
warnings.filterwarnings(
"error", message="`fillvalue` must be scalar or an array ",
category=DeprecationWarning)
assert_raises(DeprecationWarning, convolve2d, [[1]], [[1, 2]],
fillvalue=[1, 2])
def test_fillvalue_empty(self):
# Check that fillvalue being empty raises an error:
assert_raises(ValueError, convolve2d, [[1]], [[1, 2]],
fillvalue=[])
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))
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)
# 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(object):
@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.rollaxis(a.swapaxes(0, 2), 1, 5)
b = np.rollaxis(b.swapaxes(0, 2), 1, 5)
expected = np.rollaxis(expected.swapaxes(0, 2), 1, 5)
# 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 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(object):
@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(object):
@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(object):
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.
with pytest.warns(UserWarning):
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])
class TestWiener(object):
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(object):
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(
"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(object):
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(object):
def test_basic(self):
assert_array_equal(signal.order_filter([1, 2, 3], [1, 0, 1], 1),
[2, 3, 2])
class _TestLinearFilter(object):
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])
with assert_raises(ValueError, match='common type'):
lfilter([1.], [1., 1.], ['a', 'b', 'c'])
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(object):
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(object):
# 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('dt', [np.csingle, np.cdouble, np.clongdouble])
class TestCorrelateComplex(object):
# 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 * (-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(object):
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(object):
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(object):
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-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_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(object):
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)
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)
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')
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(object):
@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(object):
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(NotImplementedError,
match='input type .* not supported'):
func(*args, x=['foo'])
with pytest.raises(ValueError, match='must be at least 1-D'):
func(*args, x=1.)
@pytest.mark.parametrize('dt', 'fdgFDGO')
class TestSOSFilt(object):
# 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_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(object):
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)
class TestDetrend(object):
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(object):
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)
assert_almost_equal(unique, p, decimal=15)
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,
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])
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