def test_type1_rdft(self):
"""Is the NUFFT type 1 RDFT correct?"""
f_dir1 = np.roll(np.roll(nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0],
self.N[1],
iflag=-1,
direct=True),
-int(self.N[0] / 2),
0),
-int(self.N[1] / 2),
1)[:, :int(self.N[1] / 2) + 1] * self.N.prod()
f_nufft1 = np.roll(np.roll(nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0],
self.N[1],
iflag=-1,
direct=False),
-int(self.N[0] / 2),
0),
-int(self.N[1] / 2),
1)[:, :int(self.N[1] / 2) + 1] * self.N.prod()
self.assertTrue(_error(self.fr_numpy.reshape(-1),
f_dir1.reshape(-1)) < self.eps,
"NUFFT direct RDFT (1) vs. NumPy RFFT: error too large")
self.assertTrue(_error(self.fr_numpy.reshape(-1),
f_nufft1.reshape(-1)) < self.eps,
"NUFFT RFFT (1) vs. NumPy RFFT: error too large")
def test_type1_rdft(self):
"""Is the NUFFT type 1 RDFT correct?"""
f_dir1 = np.roll(
np.roll(
nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0],
self.N[1],
iflag=-1,
direct=True), -int(self.N[0] / 2),
0), -int(self.N[1] / 2),
1)[:, :int(self.N[1] / 2) + 1] * self.N.prod()
f_nufft1 = np.roll(
np.roll(
nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0],
self.N[1],
iflag=-1,
direct=False), -int(self.N[0] / 2),
0), -int(self.N[1] / 2),
1)[:, :int(self.N[1] / 2) + 1] * self.N.prod()
self.assertTrue(
_error(self.fr_numpy.reshape(-1), f_dir1.reshape(-1)) < self.eps,
"NUFFT direct RDFT (1) vs. NumPy RFFT: error too large")
self.assertTrue(
_error(self.fr_numpy.reshape(-1), f_nufft1.reshape(-1)) < self.eps,
"NUFFT RFFT (1) vs. NumPy RFFT: error too large")
def test_type1_idft(self):
"""Is the NUFFT type 1 IDFT correct?"""
c_dir = np.roll(np.roll(nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.f_numpy.reshape(-1),
self.N[0],
self.N[1],
iflag=1,
direct=True),
-int(self.N[0] / 2),
0),
-int(self.N[1] / 2),
1)
c_nufft = np.roll(np.roll(nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.f_numpy.reshape(-1),
self.N[0],
self.N[1],
iflag=1,
direct=False),
-int(self.N[0] / 2),
0),
-int(self.N[1] / 2),
1)
self.assertTrue(_error(self.c_numpy.reshape(-1),
c_dir.reshape(-1)) < self.eps,
"NUFFT direct IDFT (1) vs. NumPy IFFT: error too large")
self.assertTrue(_error(self.c_numpy.reshape(-1),
c_nufft.reshape(-1)) < self.eps,
"NUFFT IFFT (1) vs. NumPy IFFT: error too large")
def test_type1_idft(self):
"""Is the NUFFT type 1 IDFT correct?"""
c_dir = np.roll(
np.roll(
nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.f_numpy.reshape(-1),
self.N[0],
self.N[1],
iflag=1,
direct=True), -int(self.N[0] / 2), 0),
-int(self.N[1] / 2), 1)
c_nufft = np.roll(
np.roll(
nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.f_numpy.reshape(-1),
self.N[0],
self.N[1],
iflag=1,
direct=False), -int(self.N[0] / 2), 0),
-int(self.N[1] / 2), 1)
self.assertTrue(
_error(self.c_numpy.reshape(-1), c_dir.reshape(-1)) < self.eps,
"NUFFT direct IDFT (1) vs. NumPy IFFT: error too large")
self.assertTrue(
_error(self.c_numpy.reshape(-1), c_nufft.reshape(-1)) < self.eps,
"NUFFT IFFT (1) vs. NumPy IFFT: error too large")
def _type_1_odd(self, eps=1e-10):
p2 = nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0] + 1,
self.N[1] + 1,
direct=True)
p1 = nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0] + 1,
self.N[1] + 1,
eps=eps)
self.assertTrue(_error(p1, p2) < eps,
"Type 1: Discrepancy between direct and fft function")
def _type_1_odd(self, eps=1e-10):
p2 = nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0] + 1,
self.N[1] + 1,
direct=True)
p1 = nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0] + 1,
self.N[1] + 1,
eps=eps)
self.assertTrue(
_error(p1, p2) < eps,
"Type 1: Discrepancy between direct and fft function")
def test_type1_irdft(self):
"""Is the NUFFT type 1 IRDFT correct?"""
# Trick to make it think it is seeing a full FFT
K = np.meshgrid(-self.kx,
-self.ky[int(self.N[1] / 2) + 1:],
indexing='ij')
f = np.concatenate((self.fr_numpy,
np.conj(self.fr_numpy[K[0], K[1]])),
axis=1)
c_dir = np.roll(np.roll(nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
f.reshape(-1),
self.N[0],
self.N[1],
iflag=1,
direct=True),
-int(self.N[0] / 2),
0),
-int(self.N[1] / 2),
1)
c_nufft = np.roll(np.roll(nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
f.reshape(-1),
self.N[0],
self.N[1],
iflag=1,
direct=False),
-int(self.N[0] / 2),
0),
-int(self.N[1] / 2),
1)
self.assertTrue(_error(self.cr_numpy.reshape(-1),
c_dir.reshape(-1)) < self.eps,
"NUFFT direct IRDFT (1) vs. NumPy IRFFT: error too large")
self.assertTrue(_error(self.cr_numpy.reshape(-1),
c_nufft.reshape(-1)) < self.eps,
"NUFFT IRFFT (1) vs. NumPy IRFFT: error too large")
def test_type1_irdft(self):
"""Is the NUFFT type 1 IRDFT correct?"""
# Trick to make it think it is seeing a full FFT
K = np.meshgrid(-self.kx,
-self.ky[int(self.N[1] / 2) + 1:],
indexing='ij')
f = np.concatenate((self.fr_numpy, np.conj(self.fr_numpy[K[0], K[1]])),
axis=1)
c_dir = np.roll(
np.roll(
nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
f.reshape(-1),
self.N[0],
self.N[1],
iflag=1,
direct=True), -int(self.N[0] / 2), 0),
-int(self.N[1] / 2), 1)
c_nufft = np.roll(
np.roll(
nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
f.reshape(-1),
self.N[0],
self.N[1],
iflag=1,
direct=False), -int(self.N[0] / 2), 0),
-int(self.N[1] / 2), 1)
self.assertTrue(
_error(self.cr_numpy.reshape(-1), c_dir.reshape(-1)) < self.eps,
"NUFFT direct IRDFT (1) vs. NumPy IRFFT: error too large")
self.assertTrue(
_error(self.cr_numpy.reshape(-1), c_nufft.reshape(-1)) < self.eps,
"NUFFT IRFFT (1) vs. NumPy IRFFT: error too large")
def _type_1_2_roundtrip(self, eps=1e-10):
p = nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0],
self.N[1],
iflag=-1,
eps=eps)
c2 = nufft2d2(self.X[0].reshape(-1),
self.X[1].reshape(-1),
p,
iflag=1,
direct=True)
self.assertTrue(_error(self.c.reshape(-1), c2) < eps,
"Type 1 and 2: roundtrip error.")
def _type_1_2_roundtrip(self, eps=1e-10):
p = nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0],
self.N[1],
iflag=-1,
eps=eps)
c2 = nufft2d2(self.X[0].reshape(-1),
self.X[1].reshape(-1),
p,
iflag=1,
direct=True)
self.assertTrue(
_error(self.c.reshape(-1), c2) < eps,
"Type 1 and 2: roundtrip error.")
def _type_1_and_3(self, eps=1e-10):
p2 = nufft2d3(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.st_grid[0].reshape(-1),
self.st_grid[1].reshape(-1),
eps=eps)
p1 = np.roll(
np.roll(
nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0],
self.N[1],
eps=eps), -int(self.N[0] / 2), 0),
-int(self.N[1] / 2), 1)
self.assertTrue(
_error(p1.reshape(-1), p2) < eps, "Type 1 and 3 and not close")
def _type_1_and_3(self, eps=1e-10):
p2 = nufft2d3(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.st_grid[0].reshape(-1),
self.st_grid[1].reshape(-1),
eps=eps)
p1 = np.roll(np.roll(nufft2d1(self.X[0].reshape(-1),
self.X[1].reshape(-1),
self.c.reshape(-1),
self.N[0],
self.N[1],
eps=eps),
-int(self.N[0] / 2),
0),
-int(self.N[1] / 2),
1)
self.assertTrue(_error(p1.reshape(-1), p2) < eps,
"Type 1 and 3 and not close")