def test_fft_complex_1d():
""" Compare the result from the spectrum.fft function to numpy.fft.fft
"""
a = np.exp(2j * np.pi * np.arange(8) / 8)
dummy_array = xr.DataArray(a, dims=['x'])
chunked_array = dummy_array.chunk(chunks={'x': 2})
spectrum_array, spectrum_coords, spectrum_dims = \
xfft._fft(chunked_array, nfft={'x': 16}, dim=['x'], dx={'x': 0.5})
assert np.array_equal(np.asarray(spectrum_array), np.fft.fft(a))
assert np.array_equal(spectrum_coords['f_x'], np.fft.fftfreq(16, d=0.5))
assert 'f_x' in spectrum_dims
def test_fft_real_1d():
""" Compare the result from the spectrum._fft function to numpy.fft.rfft
"""
a = [0, 1, 0, 0]
dummy_array = xr.DataArray(a, dims=['x'])
chunked_array = dummy_array.chunk(chunks={'x': 2})
spectrum_array, spectrum_coords, spectrum_dims = \
xfft._fft(chunked_array, nfft={'x': 4}, dim=['x'], dx={'x': 0.01},
sym=False)
assert np.array_equal(np.asarray(spectrum_array), np.fft.rfft(a))
assert np.array_equal(spectrum_coords['f_x'], np.fft.rfftfreq(4, d=0.01))
assert 'f_x' in spectrum_dims
def test_fft_real_2d():
""" Compare the result from the spectrum.fft function to numpy.fft.rfftn
"""
a = np.mgrid[:5, :5, :5][0]
dummy_array = xr.DataArray(a, dims=['x', 'y', 'z'])
chunked_array = dummy_array.chunk(chunks={'x': 2, 'y': 2, 'z': 2})
spectrum_array, spectrum_coords, spectrum_dims = \
xfft._fft(chunked_array, nfft={'y': 14, 'z': 18}, dim=['y', 'z'],
dx={'y': 0.01, 'z': 0.02}, sym=False)
assert np.array_equal(np.asarray(spectrum_array),
np.fft.rfftn(a, axes=(2, 1)))
assert np.array_equal(spectrum_coords['f_y'], np.fft.rfftfreq(14, d=0.01))
assert np.array_equal(spectrum_coords['f_z'], np.fft.fftfreq(18, d=0.02))
assert ('x', 'f_y', 'f_z') == spectrum_dims
def test_fft_complex_3d():
""" Compare the result from the spectrum.fft function to numpy.fft.fftn
"""
a, b, c = np.meshgrid([0, 1, 0, 0], [0, 1j, 1j], [0, 1, 1, 1])
dummy_array = xr.DataArray(a * b * c, dims=['x', 'y', 'z'])
chunked_array = dummy_array.chunk(chunks={'x': 2, 'y': 2, 'z': 2})
spectrum_array, spectrum_coords, spectrum_dims = \
xfft._fft(chunked_array, nfft={'x': 11, 'y': 14, 'z': 18},
dim=['x', 'y', 'z'], dx={'x':12, 'y': 0.01, 'z': 0.02})
assert np.array_equal(np.asarray(spectrum_array), np.fft.fftn(a * b * c))
assert np.array_equal(spectrum_coords['f_x'], np.fft.fftfreq(11, d=12))
assert np.array_equal(spectrum_coords['f_y'], np.fft.fftfreq(14, d=0.01))
assert np.array_equal(spectrum_coords['f_z'], np.fft.fftfreq(18, d=0.02))
assert ('f_x', 'f_y', 'f_z') == spectrum_dims
def test_fft_complex_2d():
""" Compare the result from the spectrum.fft function to
numpy.fft.fftn
"""
a, b, c = np.meshgrid([0, 1, 0, 0], [0, 1j, 1j], [0, 1, 1, 1])
dummy_array = xr.DataArray(a * b * c, dims=['x', 'y', 'z'])
chunked_array = dummy_array.chunk(chunks={'x': 2, 'y': 2, 'z': 2})
spectrum_array, spectrum_coords, spectrum_dims = \
xfft._fft(chunked_array, nfft={'y': 6, 'z': 8}, dim=['y', 'z'],
dx={'y': 0.01, 'z': 0.02})
assert np.allclose(spectrum_array.compute(),
np.fft.fftn(a * b * c, s=(8, 6), axes=(2, 1)))
assert np.array_equal(spectrum_coords['f_y'], np.fft.fftfreq(6, d=0.01))
assert np.array_equal(spectrum_coords['f_z'], np.fft.fftfreq(8, d=0.02))
assert ('x', 'f_y', 'f_z') == spectrum_dims
def test_fft_real_3d():
""" Compare the result from the spectrum.fft function to numpy.fft.rfftn
"""
a = np.mgrid[:7, :5, :5][0]
dummy_array = xr.DataArray(a, dims=['x', 'y', 'z'])
chunked_array = dummy_array.chunk(chunks={'x': 7, 'y': 5, 'z': 5})
spectrum_array, spectrum_coords, spectrum_dims = \
xfft._fft(chunked_array, nfft={'x': 11, 'y': 14, 'z': 18},
dim=['x', 'y', 'z'], dx={'x':12, 'y': 0.01, 'z': 0.02},
sym=False)
assert np.allclose(spectrum_array.compute(),
np.fft.rfftn(a.T, s=(18, 14, 11)).T)
assert np.array_equal(spectrum_coords['f_x'], np.fft.rfftfreq(11, d=12))
assert np.array_equal(spectrum_coords['f_y'], np.fft.fftfreq(14, d=0.01))
assert np.array_equal(spectrum_coords['f_z'], np.fft.fftfreq(18, d=0.02))
assert ('f_x', 'f_y', 'f_z') == spectrum_dims
