def check_definition(self):
x = [1, 2, 3, 4 + 1j, 1, 2, 3, 4 + 2j]
y = fft(x)
y1 = direct_dft(x)
assert_array_almost_equal(y, y1)
x = [1, 2, 3, 4 + 0j, 5]
assert_array_almost_equal(fft(x), direct_dft(x))
def check_shape_axes_argument(self):
small_x = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
large_x1 = array([[1, 2, 3, 0], [4, 5, 6, 0], [7, 8, 9, 0], [0, 0, 0, 0]])
y = fftn(small_x, shape=(4, 4), axes=(-1,))
for i in range(4):
assert_array_almost_equal(y[i], fft(large_x1[i]))
y = fftn(small_x, shape=(4, 4), axes=(-2,))
for i in range(4):
assert_array_almost_equal(y[:, i], fft(large_x1[:, i]))
y = fftn(small_x, shape=(4, 4), axes=(-2, -1))
assert_array_almost_equal(y, fftn(large_x1))
y = fftn(small_x, shape=(4, 4), axes=(-1, -2))
assert_array_almost_equal(y, swapaxes(fftn(swapaxes(large_x1, -1, -2)), -1, -2))
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 _check_n_argument_complex(self):
x1 = [1, 2, 3, 4 + 1j]
x2 = [1, 2, 3, 4 + 1j]
y = fft([x1, x2], n=4)
assert_equal(y.shape, (2, 4))
assert_array_almost_equal(y[0], direct_dft(x1))
assert_array_almost_equal(y[1], direct_dft(x2))
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 bench_random(self, level=5):
from numpy.fft import fft as numpy_fft
print
print " Fast Fourier Transform"
print "================================================="
print " | real input | complex input "
print "-------------------------------------------------"
print " size | scipy | numpy | scipy | numpy "
print "-------------------------------------------------"
for size, repeat in [
(100, 7000),
(1000, 2000),
(256, 10000),
(512, 10000),
(1024, 1000),
(2048, 1000),
(2048 * 2, 500),
(2048 * 4, 500),
]:
print "%5s" % size,
sys.stdout.flush()
for x in [
random([size]).astype(double),
random([size]).astype(cdouble) + random([size]).astype(cdouble) * 1j,
]:
if size > 500:
y = fft(x)
else:
y = direct_dft(x)
assert_array_almost_equal(fft(x), y)
print "|%8.2f" % self.measure("fft(x)", repeat),
sys.stdout.flush()
assert_array_almost_equal(numpy_fft(x), y)
print "|%8.2f" % self.measure("numpy_fft(x)", repeat),
sys.stdout.flush()
print " (secs for %s calls)" % (repeat)
sys.stdout.flush()
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_hilbert(x):
fx = fft(x)
n = len (fx)
w = fftfreq(n)*n
w = 1j*sign(w)
return ifft(w*fx)
def direct_dftn(x):
x = asarray(x)
for axis in range(len(x.shape)):
x = fft(x, axis=axis)
return x
def check_axes_argument(self):
# plane == ji_plane, x== kji_space
plane1 = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
plane2 = [[10, 11, 12], [13, 14, 15], [16, 17, 18]]
plane3 = [[19, 20, 21], [22, 23, 24], [25, 26, 27]]
ki_plane1 = [[1, 2, 3], [10, 11, 12], [19, 20, 21]]
ki_plane2 = [[4, 5, 6], [13, 14, 15], [22, 23, 24]]
ki_plane3 = [[7, 8, 9], [16, 17, 18], [25, 26, 27]]
jk_plane1 = [[1, 10, 19], [4, 13, 22], [7, 16, 25]]
jk_plane2 = [[2, 11, 20], [5, 14, 23], [8, 17, 26]]
jk_plane3 = [[3, 12, 21], [6, 15, 24], [9, 18, 27]]
kj_plane1 = [[1, 4, 7], [10, 13, 16], [19, 22, 25]]
kj_plane2 = [[2, 5, 8], [11, 14, 17], [20, 23, 26]]
kj_plane3 = [[3, 6, 9], [12, 15, 18], [21, 24, 27]]
ij_plane1 = [[1, 4, 7], [2, 5, 8], [3, 6, 9]]
ij_plane2 = [[10, 13, 16], [11, 14, 17], [12, 15, 18]]
ij_plane3 = [[19, 22, 25], [20, 23, 26], [21, 24, 27]]
ik_plane1 = [[1, 10, 19], [2, 11, 20], [3, 12, 21]]
ik_plane2 = [[4, 13, 22], [5, 14, 23], [6, 15, 24]]
ik_plane3 = [[7, 16, 25], [8, 17, 26], [9, 18, 27]]
ijk_space = [jk_plane1, jk_plane2, jk_plane3]
ikj_space = [kj_plane1, kj_plane2, kj_plane3]
jik_space = [ik_plane1, ik_plane2, ik_plane3]
jki_space = [ki_plane1, ki_plane2, ki_plane3]
kij_space = [ij_plane1, ij_plane2, ij_plane3]
x = array([plane1, plane2, plane3])
assert_array_almost_equal(fftn(x), fftn(x, axes=(-3, -2, -1))) # kji_space
assert_array_almost_equal(fftn(x), fftn(x, axes=(0, 1, 2)))
y = fftn(x, axes=(2, 1, 0)) # ijk_space
assert_array_almost_equal(swapaxes(y, -1, -3), fftn(ijk_space))
y = fftn(x, axes=(2, 0, 1)) # ikj_space
assert_array_almost_equal(swapaxes(swapaxes(y, -1, -3), -1, -2), fftn(ikj_space))
y = fftn(x, axes=(1, 2, 0)) # jik_space
assert_array_almost_equal(swapaxes(swapaxes(y, -1, -3), -3, -2), fftn(jik_space))
y = fftn(x, axes=(1, 0, 2)) # jki_space
assert_array_almost_equal(swapaxes(y, -2, -3), fftn(jki_space))
y = fftn(x, axes=(0, 2, 1)) # kij_space
assert_array_almost_equal(swapaxes(y, -2, -1), fftn(kij_space))
y = fftn(x, axes=(-2, -1)) # ji_plane
assert_array_almost_equal(fftn(plane1), y[0])
assert_array_almost_equal(fftn(plane2), y[1])
assert_array_almost_equal(fftn(plane3), y[2])
y = fftn(x, axes=(1, 2)) # ji_plane
assert_array_almost_equal(fftn(plane1), y[0])
assert_array_almost_equal(fftn(plane2), y[1])
assert_array_almost_equal(fftn(plane3), y[2])
y = fftn(x, axes=(-3, -2)) # kj_plane
assert_array_almost_equal(fftn(x[:, :, 0]), y[:, :, 0])
assert_array_almost_equal(fftn(x[:, :, 1]), y[:, :, 1])
assert_array_almost_equal(fftn(x[:, :, 2]), y[:, :, 2])
y = fftn(x, axes=(-3, -1)) # ki_plane
assert_array_almost_equal(fftn(x[:, 0, :]), y[:, 0, :])
assert_array_almost_equal(fftn(x[:, 1, :]), y[:, 1, :])
assert_array_almost_equal(fftn(x[:, 2, :]), y[:, 2, :])
y = fftn(x, axes=(-1, -2)) # ij_plane
assert_array_almost_equal(fftn(ij_plane1), swapaxes(y[0], -2, -1))
assert_array_almost_equal(fftn(ij_plane2), swapaxes(y[1], -2, -1))
assert_array_almost_equal(fftn(ij_plane3), swapaxes(y[2], -2, -1))
y = fftn(x, axes=(-1, -3)) # ik_plane
assert_array_almost_equal(fftn(ik_plane1), swapaxes(y[:, 0, :], -1, -2))
assert_array_almost_equal(fftn(ik_plane2), swapaxes(y[:, 1, :], -1, -2))
assert_array_almost_equal(fftn(ik_plane3), swapaxes(y[:, 2, :], -1, -2))
y = fftn(x, axes=(-2, -3)) # jk_plane
assert_array_almost_equal(fftn(jk_plane1), swapaxes(y[:, :, 0], -1, -2))
assert_array_almost_equal(fftn(jk_plane2), swapaxes(y[:, :, 1], -1, -2))
assert_array_almost_equal(fftn(jk_plane3), swapaxes(y[:, :, 2], -1, -2))
y = fftn(x, axes=(-1,)) # i_line
for i in range(3):
for j in range(3):
assert_array_almost_equal(fft(x[i, j, :]), y[i, j, :])
y = fftn(x, axes=(-2,)) # j_line
for i in range(3):
for j in range(3):
assert_array_almost_equal(fft(x[i, :, j]), y[i, :, j])
y = fftn(x, axes=(0,)) # k_line
for i in range(3):
for j in range(3):
assert_array_almost_equal(fft(x[:, i, j]), y[:, i, j])
y = fftn(x, axes=()) # point
assert_array_almost_equal(y, x)
def check_random_real(self):
for size in [1, 51, 111, 100, 200, 64, 128, 256, 1024]:
x = random([size]).astype(double)
assert_array_almost_equal(ifft(fft(x)), x)
assert_array_almost_equal(fft(ifft(x)), x)