def test_params(self):
inputs_val = np.random.random((1, N)).astype(aesara.config.floatX)
inputs = aesara.shared(inputs_val)
with pytest.raises(ValueError):
fft.rfft(inputs, norm=123)
inputs_val = np.random.random((1, N // 2 + 1, 2)).astype(aesara.config.floatX)
inputs = aesara.shared(inputs_val)
with pytest.raises(ValueError):
fft.irfft(inputs, norm=123)
with pytest.raises(ValueError):
fft.irfft(inputs, is_odd=123)
def test_norm_rfft(self):
inputs_val = np.random.random((1, N, N)).astype(aesara.config.floatX)
inputs = aesara.shared(inputs_val)
# Unitary normalization
rfft = fft.rfft(inputs, norm="ortho")
f_rfft = aesara.function([], rfft)
res_rfft = f_rfft()
res_rfft_comp = np.asarray(res_rfft[:, :, :, 0]) + 1j * np.asarray(
res_rfft[:, :, :, 1]
)
rfft_ref = np.fft.rfftn(inputs_val, axes=(1, 2))
utt.assert_allclose(rfft_ref / N, res_rfft_comp, atol=1e-4, rtol=1e-4)
# No normalization
rfft = fft.rfft(inputs, norm="no_norm")
f_rfft = aesara.function([], rfft)
res_rfft = f_rfft()
res_rfft_comp = np.asarray(res_rfft[:, :, :, 0]) + 1j * np.asarray(
res_rfft[:, :, :, 1]
)
utt.assert_allclose(rfft_ref, res_rfft_comp, atol=1e-4, rtol=1e-4)
# Inverse FFT inputs
inputs_val = np.random.random((1, N, N // 2 + 1, 2)).astype(
aesara.config.floatX
)
inputs = aesara.shared(inputs_val)
inputs_ref = inputs_val[..., 0] + 1j * inputs_val[..., 1]
# Unitary normalization inverse FFT
irfft = fft.irfft(inputs, norm="ortho")
f_irfft = aesara.function([], irfft)
res_irfft = f_irfft()
irfft_ref = np.fft.irfftn(inputs_ref, axes=(1, 2))
utt.assert_allclose(irfft_ref * N, res_irfft, atol=1e-4, rtol=1e-4)
# No normalization inverse FFT
irfft = fft.irfft(inputs, norm="no_norm")
f_irfft = aesara.function([], irfft)
res_irfft = f_irfft()
utt.assert_allclose(irfft_ref * N ** 2, res_irfft, atol=1e-4, rtol=1e-4)
def test_irfft(self):
inputs_val = np.random.random((1, N, N)).astype(aesara.config.floatX)
inputs = aesara.shared(inputs_val)
rfft = fft.rfft(inputs)
f_rfft = aesara.function([], rfft)
res_fft = f_rfft()
m = rfft.type()
irfft = fft.irfft(m)
f_irfft = aesara.function([m], irfft)
res_irfft = f_irfft(res_fft)
utt.assert_allclose(inputs_val, np.asarray(res_irfft))
inputs_val = np.random.random((1, N, N, 2)).astype(aesara.config.floatX)
inputs = aesara.shared(inputs_val)
irfft = fft.irfft(inputs)
f_irfft = aesara.function([], irfft)
res_irfft = f_irfft()
inputs_ref = inputs_val[..., 0] + inputs_val[..., 1] * 1j
irfft_ref = np.fft.irfftn(inputs_ref, axes=(1, 2))
utt.assert_allclose(irfft_ref, res_irfft, atol=1e-4, rtol=1e-4)
def test_rfft(self):
inputs_val = np.random.random((1, N, N)).astype(aesara.config.floatX)
inputs = aesara.shared(inputs_val)
rfft = fft.rfft(inputs)
f_rfft = aesara.function([], rfft)
res_rfft = f_rfft()
res_rfft_comp = np.asarray(res_rfft[:, :, :, 0]) + 1j * np.asarray(
res_rfft[:, :, :, 1]
)
rfft_ref = np.fft.rfftn(inputs_val, axes=(1, 2))
utt.assert_allclose(rfft_ref, res_rfft_comp, atol=1e-4, rtol=1e-4)
def test_1Drfft(self):
inputs_val = np.random.random((1, N)).astype(aesara.config.floatX)
x = tt.matrix("x")
rfft = fft.rfft(x)
f_rfft = aesara.function([x], rfft)
res_rfft = f_rfft(inputs_val)
res_rfft_comp = np.asarray(res_rfft[:, :, 0]) + 1j * np.asarray(
res_rfft[:, :, 1]
)
rfft_ref = np.fft.rfft(inputs_val, axis=1)
utt.assert_allclose(rfft_ref, res_rfft_comp)
m = rfft.type()
print(m.ndim)
irfft = fft.irfft(m)
f_irfft = aesara.function([m], irfft)
res_irfft = f_irfft(res_rfft)
utt.assert_allclose(inputs_val, np.asarray(res_irfft))
# The numerical gradient of the FFT is sensitive, must set large
# enough epsilon to get good accuracy.
eps = 1e-1
def f_rfft(inp):
return fft.rfft(inp)
inputs_val = np.random.random((1, N)).astype(aesara.config.floatX)
utt.verify_grad(f_rfft, [inputs_val], eps=eps)
def f_irfft(inp):
return fft.irfft(inp)
inputs_val = np.random.random((1, N // 2 + 1, 2)).astype(aesara.config.floatX)
utt.verify_grad(f_irfft, [inputs_val], eps=eps)
def f_rfft(inp):
return fft.rfft(inp)
def f_rfft(inp):
return fft.rfft(inp, norm="ortho")
