Spaces:
Sleeping
Sleeping
File size: 13,135 Bytes
dc2106c |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 |
import numpy as np
import pytest
from numpy.random import random
from numpy.testing import (
assert_array_equal, assert_raises, assert_allclose
)
import threading
import queue
def fft1(x):
L = len(x)
phase = -2j*np.pi*(np.arange(L)/float(L))
phase = np.arange(L).reshape(-1, 1) * phase
return np.sum(x*np.exp(phase), axis=1)
class TestFFTShift:
def test_fft_n(self):
assert_raises(ValueError, np.fft.fft, [1, 2, 3], 0)
class TestFFT1D:
def test_identity(self):
maxlen = 512
x = random(maxlen) + 1j*random(maxlen)
xr = random(maxlen)
for i in range(1, maxlen):
assert_allclose(np.fft.ifft(np.fft.fft(x[0:i])), x[0:i],
atol=1e-12)
assert_allclose(np.fft.irfft(np.fft.rfft(xr[0:i]), i),
xr[0:i], atol=1e-12)
def test_fft(self):
x = random(30) + 1j*random(30)
assert_allclose(fft1(x), np.fft.fft(x), atol=1e-6)
assert_allclose(fft1(x), np.fft.fft(x, norm="backward"), atol=1e-6)
assert_allclose(fft1(x) / np.sqrt(30),
np.fft.fft(x, norm="ortho"), atol=1e-6)
assert_allclose(fft1(x) / 30.,
np.fft.fft(x, norm="forward"), atol=1e-6)
@pytest.mark.parametrize('norm', (None, 'backward', 'ortho', 'forward'))
def test_ifft(self, norm):
x = random(30) + 1j*random(30)
assert_allclose(
x, np.fft.ifft(np.fft.fft(x, norm=norm), norm=norm),
atol=1e-6)
# Ensure we get the correct error message
with pytest.raises(ValueError,
match='Invalid number of FFT data points'):
np.fft.ifft([], norm=norm)
def test_fft2(self):
x = random((30, 20)) + 1j*random((30, 20))
assert_allclose(np.fft.fft(np.fft.fft(x, axis=1), axis=0),
np.fft.fft2(x), atol=1e-6)
assert_allclose(np.fft.fft2(x),
np.fft.fft2(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.fft2(x) / np.sqrt(30 * 20),
np.fft.fft2(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.fft2(x) / (30. * 20.),
np.fft.fft2(x, norm="forward"), atol=1e-6)
def test_ifft2(self):
x = random((30, 20)) + 1j*random((30, 20))
assert_allclose(np.fft.ifft(np.fft.ifft(x, axis=1), axis=0),
np.fft.ifft2(x), atol=1e-6)
assert_allclose(np.fft.ifft2(x),
np.fft.ifft2(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.ifft2(x) * np.sqrt(30 * 20),
np.fft.ifft2(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.ifft2(x) * (30. * 20.),
np.fft.ifft2(x, norm="forward"), atol=1e-6)
def test_fftn(self):
x = random((30, 20, 10)) + 1j*random((30, 20, 10))
assert_allclose(
np.fft.fft(np.fft.fft(np.fft.fft(x, axis=2), axis=1), axis=0),
np.fft.fftn(x), atol=1e-6)
assert_allclose(np.fft.fftn(x),
np.fft.fftn(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.fftn(x) / np.sqrt(30 * 20 * 10),
np.fft.fftn(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.fftn(x) / (30. * 20. * 10.),
np.fft.fftn(x, norm="forward"), atol=1e-6)
def test_ifftn(self):
x = random((30, 20, 10)) + 1j*random((30, 20, 10))
assert_allclose(
np.fft.ifft(np.fft.ifft(np.fft.ifft(x, axis=2), axis=1), axis=0),
np.fft.ifftn(x), atol=1e-6)
assert_allclose(np.fft.ifftn(x),
np.fft.ifftn(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.ifftn(x) * np.sqrt(30 * 20 * 10),
np.fft.ifftn(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.ifftn(x) * (30. * 20. * 10.),
np.fft.ifftn(x, norm="forward"), atol=1e-6)
def test_rfft(self):
x = random(30)
for n in [x.size, 2*x.size]:
for norm in [None, 'backward', 'ortho', 'forward']:
assert_allclose(
np.fft.fft(x, n=n, norm=norm)[:(n//2 + 1)],
np.fft.rfft(x, n=n, norm=norm), atol=1e-6)
assert_allclose(
np.fft.rfft(x, n=n),
np.fft.rfft(x, n=n, norm="backward"), atol=1e-6)
assert_allclose(
np.fft.rfft(x, n=n) / np.sqrt(n),
np.fft.rfft(x, n=n, norm="ortho"), atol=1e-6)
assert_allclose(
np.fft.rfft(x, n=n) / n,
np.fft.rfft(x, n=n, norm="forward"), atol=1e-6)
def test_irfft(self):
x = random(30)
assert_allclose(x, np.fft.irfft(np.fft.rfft(x)), atol=1e-6)
assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="backward"),
norm="backward"), atol=1e-6)
assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="ortho"),
norm="ortho"), atol=1e-6)
assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="forward"),
norm="forward"), atol=1e-6)
def test_rfft2(self):
x = random((30, 20))
assert_allclose(np.fft.fft2(x)[:, :11], np.fft.rfft2(x), atol=1e-6)
assert_allclose(np.fft.rfft2(x),
np.fft.rfft2(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.rfft2(x) / np.sqrt(30 * 20),
np.fft.rfft2(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.rfft2(x) / (30. * 20.),
np.fft.rfft2(x, norm="forward"), atol=1e-6)
def test_irfft2(self):
x = random((30, 20))
assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x)), atol=1e-6)
assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="backward"),
norm="backward"), atol=1e-6)
assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="ortho"),
norm="ortho"), atol=1e-6)
assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="forward"),
norm="forward"), atol=1e-6)
def test_rfftn(self):
x = random((30, 20, 10))
assert_allclose(np.fft.fftn(x)[:, :, :6], np.fft.rfftn(x), atol=1e-6)
assert_allclose(np.fft.rfftn(x),
np.fft.rfftn(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.rfftn(x) / np.sqrt(30 * 20 * 10),
np.fft.rfftn(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.rfftn(x) / (30. * 20. * 10.),
np.fft.rfftn(x, norm="forward"), atol=1e-6)
def test_irfftn(self):
x = random((30, 20, 10))
assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x)), atol=1e-6)
assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="backward"),
norm="backward"), atol=1e-6)
assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="ortho"),
norm="ortho"), atol=1e-6)
assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="forward"),
norm="forward"), atol=1e-6)
def test_hfft(self):
x = random(14) + 1j*random(14)
x_herm = np.concatenate((random(1), x, random(1)))
x = np.concatenate((x_herm, x[::-1].conj()))
assert_allclose(np.fft.fft(x), np.fft.hfft(x_herm), atol=1e-6)
assert_allclose(np.fft.hfft(x_herm),
np.fft.hfft(x_herm, norm="backward"), atol=1e-6)
assert_allclose(np.fft.hfft(x_herm) / np.sqrt(30),
np.fft.hfft(x_herm, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.hfft(x_herm) / 30.,
np.fft.hfft(x_herm, norm="forward"), atol=1e-6)
def test_ihfft(self):
x = random(14) + 1j*random(14)
x_herm = np.concatenate((random(1), x, random(1)))
x = np.concatenate((x_herm, x[::-1].conj()))
assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm)), atol=1e-6)
assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
norm="backward"), norm="backward"), atol=1e-6)
assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
norm="ortho"), norm="ortho"), atol=1e-6)
assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
norm="forward"), norm="forward"), atol=1e-6)
@pytest.mark.parametrize("op", [np.fft.fftn, np.fft.ifftn,
np.fft.rfftn, np.fft.irfftn])
def test_axes(self, op):
x = random((30, 20, 10))
axes = [(0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0)]
for a in axes:
op_tr = op(np.transpose(x, a))
tr_op = np.transpose(op(x, axes=a), a)
assert_allclose(op_tr, tr_op, atol=1e-6)
def test_all_1d_norm_preserving(self):
# verify that round-trip transforms are norm-preserving
x = random(30)
x_norm = np.linalg.norm(x)
n = x.size * 2
func_pairs = [(np.fft.fft, np.fft.ifft),
(np.fft.rfft, np.fft.irfft),
# hfft: order so the first function takes x.size samples
# (necessary for comparison to x_norm above)
(np.fft.ihfft, np.fft.hfft),
]
for forw, back in func_pairs:
for n in [x.size, 2*x.size]:
for norm in [None, 'backward', 'ortho', 'forward']:
tmp = forw(x, n=n, norm=norm)
tmp = back(tmp, n=n, norm=norm)
assert_allclose(x_norm,
np.linalg.norm(tmp), atol=1e-6)
@pytest.mark.parametrize("dtype", [np.half, np.single, np.double,
np.longdouble])
def test_dtypes(self, dtype):
# make sure that all input precisions are accepted and internally
# converted to 64bit
x = random(30).astype(dtype)
assert_allclose(np.fft.ifft(np.fft.fft(x)), x, atol=1e-6)
assert_allclose(np.fft.irfft(np.fft.rfft(x)), x, atol=1e-6)
@pytest.mark.parametrize(
"dtype",
[np.float32, np.float64, np.complex64, np.complex128])
@pytest.mark.parametrize("order", ["F", 'non-contiguous'])
@pytest.mark.parametrize(
"fft",
[np.fft.fft, np.fft.fft2, np.fft.fftn,
np.fft.ifft, np.fft.ifft2, np.fft.ifftn])
def test_fft_with_order(dtype, order, fft):
# Check that FFT/IFFT produces identical results for C, Fortran and
# non contiguous arrays
rng = np.random.RandomState(42)
X = rng.rand(8, 7, 13).astype(dtype, copy=False)
# See discussion in pull/14178
_tol = 8.0 * np.sqrt(np.log2(X.size)) * np.finfo(X.dtype).eps
if order == 'F':
Y = np.asfortranarray(X)
else:
# Make a non contiguous array
Y = X[::-1]
X = np.ascontiguousarray(X[::-1])
if fft.__name__.endswith('fft'):
for axis in range(3):
X_res = fft(X, axis=axis)
Y_res = fft(Y, axis=axis)
assert_allclose(X_res, Y_res, atol=_tol, rtol=_tol)
elif fft.__name__.endswith(('fft2', 'fftn')):
axes = [(0, 1), (1, 2), (0, 2)]
if fft.__name__.endswith('fftn'):
axes.extend([(0,), (1,), (2,), None])
for ax in axes:
X_res = fft(X, axes=ax)
Y_res = fft(Y, axes=ax)
assert_allclose(X_res, Y_res, atol=_tol, rtol=_tol)
else:
raise ValueError()
class TestFFTThreadSafe:
threads = 16
input_shape = (800, 200)
def _test_mtsame(self, func, *args):
def worker(args, q):
q.put(func(*args))
q = queue.Queue()
expected = func(*args)
# Spin off a bunch of threads to call the same function simultaneously
t = [threading.Thread(target=worker, args=(args, q))
for i in range(self.threads)]
[x.start() for x in t]
[x.join() for x in t]
# Make sure all threads returned the correct value
for i in range(self.threads):
assert_array_equal(q.get(timeout=5), expected,
'Function returned wrong value in multithreaded context')
def test_fft(self):
a = np.ones(self.input_shape) * 1+0j
self._test_mtsame(np.fft.fft, a)
def test_ifft(self):
a = np.ones(self.input_shape) * 1+0j
self._test_mtsame(np.fft.ifft, a)
def test_rfft(self):
a = np.ones(self.input_shape)
self._test_mtsame(np.fft.rfft, a)
def test_irfft(self):
a = np.ones(self.input_shape) * 1+0j
self._test_mtsame(np.fft.irfft, a)
|