def bench_random(self, level=5):
from numpy.fft import fftn as numpy_fftn
print
print " Multi-dimensional Fast Fourier Transform"
print "==================================================="
print " | real input | complex input "
print "---------------------------------------------------"
print " size | scipy | numpy | scipy | numpy "
print "---------------------------------------------------"
for size, repeat in [((100, 100), 100), ((1000, 100), 7), ((256, 256), 10), ((512, 512), 3)]:
print "%9s" % ("%sx%s" % size),
sys.stdout.flush()
for x in [random(size).astype(double), random(size).astype(cdouble) + random(size).astype(cdouble) * 1j]:
y = fftn(x)
# if size > 500: y = fftn(x)
# else: y = direct_dft(x)
assert_array_almost_equal(fftn(x), y)
print "|%8.2f" % self.measure("fftn(x)", repeat),
sys.stdout.flush()
assert_array_almost_equal(numpy_fftn(x), y)
print "|%8.2f" % self.measure("numpy_fftn(x)", repeat),
sys.stdout.flush()
print " (secs for %s calls)" % (repeat)
sys.stdout.flush()
def check_shape_argument(self):
small_x = [[1, 2, 3], [4, 5, 6]]
large_x1 = [[1, 2, 3, 0], [4, 5, 6, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
y = fftn(small_x, shape=(4, 4))
assert_array_almost_equal(y, fftn(large_x1))
y = fftn(small_x, shape=(3, 4))
assert_array_almost_equal(y, fftn(large_x1[:-1]))
def check_definition(self):
x = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
y = fftn(x)
assert_array_almost_equal(y, direct_dftn(x))
x = random((20, 26))
assert_array_almost_equal(fftn(x), direct_dftn(x))
x = random((5, 4, 3, 20))
assert_array_almost_equal(fftn(x), direct_dftn(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 check_random_complex(self):
for size in [1, 2, 51, 32, 64, 92]:
x = random([size, size]) + 1j * random([size, size])
assert_array_almost_equal(ifftn(fftn(x)), x)
assert_array_almost_equal(fftn(ifftn(x)), 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)