name : test_pocketfft.py import numpy as np import pytest from numpy.random import random from numpy.testing import ( assert_array_equal, assert_raises, assert_allclose, IS_WASM ) import threading import queue def fft1(x): L = len(x) phase = -2j * np.pi * (np.arange(L) / 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() @pytest.mark.skipif(IS_WASM, reason="Cannot start thread") 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)