def test_random_real(self):
for size in [1, 51, 111, 100, 200, 64, 128, 256, 1024]:
x = random([size]).astype(self.rdt)
y1 = ifft(fft(x))
y2 = fft(ifft(x))
assert_equal(y1.dtype, self.cdt)
assert_equal(y2.dtype, self.cdt)
assert_array_almost_equal(y1, x)
assert_array_almost_equal(y2, x)
def test_definition(self):
x = np.array([1, 2, 3, 4 + 1j, 1, 2, 3, 4 + 2j], self.cdt)
y = ifft(x)
y1 = direct_idft(x)
assert_equal(y.dtype, self.cdt)
assert_array_almost_equal(y, y1)
x = np.array([1, 2, 3, 4 + 0j, 5], self.cdt)
assert_array_almost_equal(ifft(x), direct_idft(x))
def test_definition_real(self):
x = np.array([1, 2, 3, 4, 1, 2, 3, 4], self.rdt)
y = ifft(x)
assert_equal(y.dtype, self.cdt)
y1 = direct_idft(x)
assert_array_almost_equal(y, y1)
x = np.array([1, 2, 3, 4, 5], dtype=self.rdt)
assert_equal(y.dtype, self.cdt)
assert_array_almost_equal(ifft(x), direct_idft(x))
def direct_shift(x, a, period=None):
n = len(x)
if period is None:
k = fftfreq(n) * 1j * n
else:
k = fftfreq(n) * 2j * pi / period * n
return ifft(fft(x) * exp(k * a)).real
def direct_itilbert(x, h=1, period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2 * pi
w = fftfreq(n) * h * 2 * pi / period * n
w = -1j * tanh(w)
return ifft(w * fx)
def direct_tilbert(x, h=1, period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2 * pi
w = fftfreq(n) * h * 2 * pi / period * n
w[0] = 1
w = 1j / tanh(w)
w[0] = 0j
return ifft(w * fx)
def test_size_accuracy(self):
# Sanity check for the accuracy for prime and non-prime sized inputs
if self.rdt == np.float32:
rtol = 1e-5
elif self.rdt == np.float64:
rtol = 1e-10
for size in LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES:
np.random.seed(1234)
x = np.random.rand(size).astype(self.rdt)
y = ifft(fft(x))
_assert_close_in_norm(x, y, rtol, size, self.rdt)
y = fft(ifft(x))
_assert_close_in_norm(x, y, rtol, size, self.rdt)
x = (x + 1j * np.random.rand(size)).astype(self.cdt)
y = ifft(fft(x))
_assert_close_in_norm(x, y, rtol, size, self.rdt)
y = fft(ifft(x))
_assert_close_in_norm(x, y, rtol, size, self.rdt)
def direct_diff(x, k=1, period=None):
fx = fft(x)
n = len(fx)
if period is None:
period = 2 * pi
w = fftfreq(n) * 2j * pi / period * n
if k < 0:
w = 1 / w**k
w[0] = 0.0
else:
w = w**k
if n > 2000:
w[250:n - 250] = 0.0
return ifft(w * fx).real
def direct_idftn(x):
x = asarray(x)
for axis in range(len(x.shape)):
x = ifft(x, axis=axis)
return x
def _test(x, xr):
y = irfft(np.array(x, dtype=self.rdt))
y1 = direct_irdft(x)
assert_equal(y.dtype, self.rdt)
assert_array_almost_equal(y, y1, decimal=self.ndec)
assert_array_almost_equal(y, ifft(xr), decimal=self.ndec)
def direct_hilbert(x):
fx = fft(x)
n = len(fx)
w = fftfreq(n) * n
w = 1j * sign(w)
return ifft(w * fx)