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ENH: use real FFTs for real-valued CWT convolution #864

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ENH: use real FFTs for real-valued CWT convolution #864

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16 changes: 13 additions & 3 deletions pywt/_cwt.py
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Original file line number Diff line number Diff line change
Expand Up @@ -139,6 +139,7 @@ def cwt(data, scales, wavelet, sampling_period=1., method='conv', axis=-1,
if method == 'fft':
size_scale0 = -1
fft_data = None
use_real_fft = data.dtype.kind != 'c' and int_psi.dtype.kind != 'c'
elif method != "conv":
raise ValueError("method must be 'conv' or 'fft'")

Expand Down Expand Up @@ -179,10 +180,19 @@ def cwt(data, scales, wavelet, sampling_period=1., method='conv', axis=-1,
)
if size_scale != size_scale0:
# Must recompute fft_data when the padding size changes.
fft_data = np.fft.fft(data, size_scale, axis=-1)
if use_real_fft:
fft_data = np.fft.rfft(data, size_scale, axis=-1)
else:
fft_data = np.fft.fft(data, size_scale, axis=-1)
size_scale0 = size_scale
fft_wav = np.fft.fft(int_psi_scale, size_scale, axis=-1)
conv = np.fft.ifft(fft_wav * fft_data, axis=-1)
if use_real_fft:
fft_wav = np.fft.rfft(int_psi_scale, size_scale, axis=-1)
conv = np.fft.irfft(
fft_wav * fft_data, n=size_scale, axis=-1
)
else:
fft_wav = np.fft.fft(int_psi_scale, size_scale, axis=-1)
conv = np.fft.ifft(fft_wav * fft_data, axis=-1)
conv = conv[..., :data.shape[-1] + int_psi_scale.size - 1]

coef = - np.sqrt(scale) * np.diff(conv, axis=-1)
Expand Down
35 changes: 35 additions & 0 deletions pywt/tests/test_cwt_wavelets.py
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Original file line number Diff line number Diff line change
Expand Up @@ -471,6 +471,41 @@ def test_cwt_method_fft():
assert_allclose(cfs_conv, cfs_fft, rtol=0, atol=1e-13)


@pytest.mark.parametrize('dtype, tol', [(np.float32, 1e-5),
(np.float64, 1e-13)])
@pytest.mark.parametrize('shape, axis', [((49,), -1),
((3, 50), 1),
((49, 3), 0)])
def test_cwt_method_fft_real(dtype, tol, shape, axis):
rstate = np.random.RandomState(1)
data = rstate.randn(*shape).astype(dtype)
scales = np.r_[1.0625, np.arange(1, 64)]

cfs_conv, _ = pywt.cwt(
data, scales, 'morl', method='conv', axis=axis
)
cfs_fft, _ = pywt.cwt(
data, scales, 'morl', method='fft', axis=axis
)

assert_equal(cfs_fft.dtype, dtype)
assert_allclose(cfs_conv, cfs_fft, rtol=tol, atol=tol)


@pytest.mark.parametrize('dtype, tol', [(np.complex64, 1e-5),
(np.complex128, 1e-13)])
def test_cwt_method_fft_complex_data_real_wavelet(dtype, tol):
rstate = np.random.RandomState(1)
data = (rstate.randn(49) + 1j * rstate.randn(49)).astype(dtype)
scales = np.r_[1.0625, np.arange(1, 16)]

cfs_conv, _ = pywt.cwt(data, scales, 'morl', method='conv')
cfs_fft, _ = pywt.cwt(data, scales, 'morl', method='fft')

assert_equal(cfs_fft.dtype, dtype)
assert_allclose(cfs_conv, cfs_fft, rtol=tol, atol=tol)


def test_continuous_wavelet_pickle(tmpdir):
wavelet = pywt.ContinuousWavelet('cmor1.5-1.0')
filename = os.path.join(tmpdir, 'cwav.pickle')
Expand Down