def test_nufft_ndft(self):
n = 5
w = np.exp(-1j * 2 * np.pi / n)
coord = np.array([[-2], [0], [0.1]])
w2 = w**-2
w1 = w**0.1
A = np.array([[w2**-2, w2**-1, 1, w2, w2**2], [1, 1, 1, 1, 1],
[w1**-2, w1**-1, 1, w1, w1**2]]) / n**0.5
for i in range(n):
input = np.zeros(n, np.complex)
input[i] = 1
npt.assert_allclose(A[:, i],
fourier.nufft(input, coord),
atol=0.01,
rtol=0.01)
n = 6
w = np.exp(-1j * 2 * np.pi / n)
coord = np.array([[-2], [0], [0.1]])
w2 = w**-2
w1 = w**0.1
A = np.array([[w2**-3, w2**-2, w2**-1, 1, w2, w2**2], [
1, 1, 1, 1, 1, 1
], [w1**-3, w1**-2, w1**-1, 1, w1, w1**2]]) / n**0.5
for i in range(n):
input = np.zeros(n, np.complex)
input[i] = 1
npt.assert_allclose(A[:, i],
fourier.nufft(input, coord),
atol=0.01,
rtol=0.01)
def test_nufft(self):
# Check deltas
ishape = [3]
input = np.array([0, 1, 0], np.complex) # delta
coord = np.array([[-1], [0], [1]], np.float)
npt.assert_allclose(fourier.nufft(input, coord),
np.array([1.0, 1.0, 1.0]) / (3**0.5),
atol=0.01,
rtol=0.01)
ishape = [4]
input = np.array([0, 0, 1, 0], np.complex) # delta
coord = np.array([[-2], [-1], [0], [1]], np.float)
npt.assert_allclose(fourier.nufft(input, coord),
np.array([1.0, 1.0, 1.0, 1.0]) / (4**0.5),
atol=0.01,
rtol=0.01)
ishape = [5]
input = np.array([0, 0, 1, 0, 0], np.complex) # delta
coord = np.array([[-2], [-1], [0], [1], [2]], np.float)
npt.assert_allclose(fourier.nufft(input, coord),
np.ones(5) / (5**0.5),
atol=0.01,
rtol=0.01)
# Check shifted delta
ishape = [3]
input = np.array([0, 0, 1], np.complex) # shifted delta
coord = np.array([[-1], [0], [1]], np.float)
w = np.exp(-1j * 2.0 * np.pi / 3.0)
npt.assert_allclose(fourier.nufft(input, coord),
np.array([w.conjugate(), 1.0, w]) / (3**0.5),
atol=0.01,
rtol=0.01)
ishape = [4]
input = np.array([0, 0, 0, 1], np.complex) # delta
coord = np.array([[-2], [-1], [0], [1]], np.float)
w = np.exp(-1j * 2.0 * np.pi / 4.0)
npt.assert_allclose(fourier.nufft(input, coord),
np.array([w.conjugate()**2,
w.conjugate(), 1.0, w]) / (4**0.5),
atol=0.01,
rtol=0.01)
def _apply(self, input):
return fourier.nufft(input,
self.coord,
oversamp=self.oversamp,
width=self.width,
n=self.n)
def _apply(self, input):
device = backend.get_device(input)
with device:
coord = backend.to_device(self.coord, device)
return fourier.nufft(
input, coord,
oversamp=self.oversamp, width=self.width)
def test_nufft_nd(self):
for ndim in range(3):
input = np.array([[0], [1], [0]], np.complex)
coord = np.array([[-1, 0], [0, 0], [1, 0]], np.float)
npt.assert_allclose(fourier.nufft(input, coord),
np.array([1.0, 1.0, 1.0]) / 3**0.5,
atol=0.01,
rtol=0.01)
def test_nufft_normal(self):
# Check delta
oshape = [3]
input = np.array([0.0, 1.0, 0.0], dtype=np.complex)
coord = np.array([[-1], [0], [1]], np.float)
npt.assert_allclose(fourier.nufft_adjoint(fourier.nufft(input, coord),
coord, oshape),
np.array([0, 1, 0]),
atol=0.01,
rtol=0.01)
# Check delta scale
oshape = [3]
input = np.array([0.0, 1.0, 0.0], dtype=np.complex)
coord = np.array([[-1], [-0.5], [0], [0.5], [1]], np.float)
npt.assert_allclose(fourier.nufft_adjoint(fourier.nufft(input,
coord), coord,
oshape)[len(input) // 2],
5 / 3,
atol=0.01,
rtol=0.01)
