def nufft2(field, fx, fy, size=None, sign=1, eps=10**(-12)):
"""
"""
if np.__name__ == 'cupy':
fx = np.asnumpy(fx).astype(np.float64)
fy = np.asnumpy(fy).astype(np.float64)
image = np.asnumpy(np.copy(field)).astype(np.complex128)
else:
image = np.copy(field).astype(np.complex128)
if type(size) == type(None):
result = finufft.nufft2d1(fx.flatten(),
fy.flatten(),
image.flatten(),
image.shape,
eps=eps,
isign=sign)
else:
result = finufft.nufft2d1(fx.flatten(),
fy.flatten(),
image.flatten(), (size[0], size[1]),
eps=eps,
isign=sign)
if np.__name__ == 'cupy':
result = np.asarray(result)
return result
def nuifft2(field, fx, fy, size=None, sign=1, eps=10**(-12)):
"""
A definition to take 2D Adjoint Non-Uniform Fast Fourier Transform (NUFFT).
Parameters
----------
field : ndarray
Input field.
fx : ndarray
Frequencies along x axis.
fy : ndarray
Frequencies along y axis.
size : list or ndarray
Shape of the NUFFT calculated for an input field.
sign : float
Sign of the exponential used in NUFFT kernel.
eps : float
Accuracy of NUFFT.
Returns
----------
result : ndarray
NUFFT of the input field.
"""
if np.__name__ == 'cupy':
fx = np.asnumpy(fx).astype(np.float64)
fy = np.asnumpy(fy).astype(np.float64)
image = np.asnumpy(np.copy(field)).astype(np.complex128)
else:
image = np.copy(field).astype(np.complex128)
if type(size) == type(None):
result = finufft.nufft2d1(fx.flatten(),
fy.flatten(),
image.flatten(),
image.shape,
eps=eps,
isign=sign)
else:
result = finufft.nufft2d1(fx.flatten(),
fy.flatten(),
image.flatten(), (size[0], size[1]),
eps=eps,
isign=sign)
if np.__name__ == 'cupy':
result = np.asarray(result)
return result
def test_nufft2d1(seed=42, iflag=1):
np.random.seed(seed)
ms = 100
mt = 89
n = int(1e3)
tol = 1.0e-9
x = np.random.uniform(-np.pi, np.pi, n)
y = np.random.uniform(-np.pi, np.pi, n)
c = np.random.uniform(-1.0, 1.0,
n) + 1.0j * np.random.uniform(-1.0, 1.0, n)
f = finufft.nufft2d1(x, y, c, ms, mt, eps=tol, iflag=iflag)
f0 = interface.dirft2d1(x, y, c, ms, mt, iflag=iflag)
assert np.all(np.abs((f - f0) / f0) < 1e-6)
def with_finufft(uvw, freq, ms, wgt, nxdirty, nydirty, xpixsize, ypixsize,
mask, epsilon):
u = np.outer(uvw[:, 0], freq) * (xpixsize / SPEEDOFLIGHT) * 2 * np.pi
v = np.outer(uvw[:, 1], freq) * (ypixsize / SPEEDOFLIGHT) * 2 * np.pi
if wgt is not None:
ms = ms * wgt
if mask is not None:
ms = ms * mask
eps = epsilon / 10 # Apparently finufft measures epsilon differently
# Plan on the fly
res0 = finufft.nufft2d1(u.ravel(),
v.ravel(),
ms.ravel(), (nxdirty, nydirty),
eps=eps).real
# Plan beforehand
plan = finufft.Plan(1, (nxdirty, nydirty), eps=eps)
plan.setpts(u.ravel(), v.ravel())
res1 = plan.execute(ms.ravel()).real
np.testing.assert_allclose(res0, res1)
return res0
# ahb updated for v2.0 interface, and complex c. Bug seems to have been fixed :)
import numpy as np
from finufft import nufft2d1
c = np.complex128(np.random.rand(2))
omega = np.arange(4).reshape((2, 2)) / 3 * np.pi
x0 = omega[:, 0]
y0 = omega[:, 1]
f0 = np.zeros((4, 4), order='F', dtype=np.complex128)
nufft2d1(x0, y0, c, f0.shape, out=f0, eps=1e-14)
x1 = x0.copy()
y1 = y0.copy()
f1 = np.zeros((4, 4), order='F', dtype=np.complex128)
nufft2d1(x1, y1, c, f1.shape, out=f1, eps=1e-14)
print('difference: %e' % np.linalg.norm(f0 - f1))
def accuracy_speed_tests(num_nonuniform_points, num_uniform_points, eps):
nj, nk = int(num_nonuniform_points), int(num_nonuniform_points)
iflag = 1
num_samples = int(
np.minimum(5, num_uniform_points * 0.5 + 1)
) # number of outputs used for estimating accuracy; is small for speed
print(
'Accuracy and speed tests for %d nonuniform points and eps=%g (error estimates use %d samples per run)'
% (num_nonuniform_points, eps, num_samples))
# for doing the error estimates
Xest = np.zeros(num_samples, dtype=np.complex128)
Xtrue = np.zeros(num_samples, dtype=np.complex128)
###### 1-d cases ........................................................
ms = int(num_uniform_points)
xj = np.random.rand(nj) * 2 * math.pi - math.pi
cj = np.random.rand(nj) + 1j * np.random.rand(nj)
fk = np.zeros([ms], dtype=np.complex128)
timer = time.time()
ret = finufft.nufft1d1(xj, cj, ms, fk, eps, iflag)
elapsed = time.time() - timer
k = np.arange(-np.floor(ms / 2), np.floor((ms - 1) / 2 + 1))
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(cj * np.exp(1j * k[ii] * xj))
Xtrue[ii] = fk[ii]
print_report('finufft1d1', elapsed, Xest, Xtrue, nj)
xj = np.random.rand(nj) * 2 * math.pi - math.pi
cj = np.zeros([nj], dtype=np.complex128)
fk = np.random.rand(ms) + 1j * np.random.rand(ms)
timer = time.time()
ret = finufft.nufft1d2(xj, fk, cj, eps, iflag)
elapsed = time.time() - timer
k = np.arange(-np.floor(ms / 2), np.floor((ms - 1) / 2 + 1))
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(fk * np.exp(1j * k * xj[ii]))
Xtrue[ii] = cj[ii]
print_report('finufft1d2', elapsed, Xest, Xtrue, nj)
x = np.random.rand(nj) * 2 * math.pi - math.pi
c = np.random.rand(nj) + 1j * np.random.rand(nj)
s = np.random.rand(nk) * 2 * math.pi - math.pi
f = np.zeros([nk], dtype=np.complex128)
timer = time.time()
ret = finufft.nufft1d3(x, c, s, f, eps, iflag)
elapsed = time.time() - timer
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(c * np.exp(1j * s[ii] * x))
Xtrue[ii] = f[ii]
print_report('finufft1d3', elapsed, Xest, Xtrue, nj + nk)
###### 2-d cases ....................................................
ms = int(np.ceil(np.sqrt(num_uniform_points)))
mt = ms
xj = np.random.rand(nj) * 2 * math.pi - math.pi
yj = np.random.rand(nj) * 2 * math.pi - math.pi
cj = np.random.rand(nj) + 1j * np.random.rand(nj)
fk = np.zeros([ms, mt], dtype=np.complex128)
timer = time.time()
ret = finufft.nufft2d1(xj, yj, cj, (ms, mt), fk, eps, iflag)
elapsed = time.time() - timer
Ks, Kt = np.mgrid[-np.floor(ms / 2):np.floor((ms - 1) / 2 + 1),
-np.floor(mt / 2):np.floor((mt - 1) / 2 + 1)]
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(
cj * np.exp(1j * (Ks.ravel()[ii] * xj + Kt.ravel()[ii] * yj)))
Xtrue[ii] = fk.ravel()[ii]
print_report('finufft2d1', elapsed, Xest, Xtrue, nj)
## 2d1many:
ndata = 8 # how many vectors to do
cj = np.array(np.random.rand(ndata, nj) + 1j * np.random.rand(ndata, nj))
fk = np.zeros([ndata, ms, mt], dtype=np.complex128)
timer = time.time()
ret = finufft.nufft2d1(xj, yj, cj, ms, fk, eps, iflag)
elapsed = time.time() - timer
dtest = ndata - 1 # which of the ndata to test (in 0,..,ndata-1)
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(
cj[dtest, :] * np.exp(1j *
(Ks.ravel()[ii] * xj + Kt.ravel()[ii] * yj))
) # note fortran-ravel-order needed throughout - mess.
Xtrue[ii] = fk.ravel()[
ii + dtest * ms *
mt] # hack the offset in fk array - has to be better way
print_report('finufft2d1many', elapsed, Xest, Xtrue, ndata * nj)
# 2d2
xj = np.random.rand(nj) * 2 * math.pi - math.pi
yj = np.random.rand(nj) * 2 * math.pi - math.pi
cj = np.zeros([nj], dtype=np.complex128)
fk = np.random.rand(ms, mt) + 1j * np.random.rand(ms, mt)
timer = time.time()
ret = finufft.nufft2d2(xj, yj, fk, cj, eps, iflag)
elapsed = time.time() - timer
Ks, Kt = np.mgrid[-np.floor(ms / 2):np.floor((ms - 1) / 2 + 1),
-np.floor(mt / 2):np.floor((mt - 1) / 2 + 1)]
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(fk * np.exp(1j * (Ks * xj[ii] + Kt * yj[ii])))
Xtrue[ii] = cj[ii]
print_report('finufft2d2', elapsed, Xest, Xtrue, nj)
# 2d2many (using same ndata and dtest as 2d1many; see above)
cj = np.zeros([ndata, nj], dtype=np.complex128)
fk = np.array(
np.random.rand(ndata, ms, mt) + 1j * np.random.rand(ndata, ms, mt))
timer = time.time()
ret = finufft.nufft2d2(xj, yj, fk, cj, eps, iflag)
elapsed = time.time() - timer
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(fk[dtest, :, :] *
np.exp(1j * (Ks * xj[ii] + Kt * yj[ii])))
Xtrue[ii] = cj[dtest, ii]
print_report('finufft2d2many', elapsed, Xest, Xtrue, ndata * nj)
# 2d3
x = np.random.rand(nj) * 2 * math.pi - math.pi
y = np.random.rand(nj) * 2 * math.pi - math.pi
c = np.random.rand(nj) + 1j * np.random.rand(nj)
s = np.random.rand(nk) * 2 * math.pi - math.pi
t = np.random.rand(nk) * 2 * math.pi - math.pi
f = np.zeros([nk], dtype=np.complex128)
timer = time.time()
ret = finufft.nufft2d3(x, y, c, s, t, f, eps, iflag)
elapsed = time.time() - timer
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(c * np.exp(1j * (s[ii] * x + t[ii] * y)))
Xtrue[ii] = f[ii]
print_report('finufft2d3', elapsed, Xest, Xtrue, nj + nk)
###### 3-d cases ............................................................
ms = int(np.ceil(num_uniform_points**(1.0 / 3)))
mt = ms
mu = ms
xj = np.random.rand(nj) * 2 * math.pi - math.pi
yj = np.random.rand(nj) * 2 * math.pi - math.pi
zj = np.random.rand(nj) * 2 * math.pi - math.pi
cj = np.random.rand(nj) + 1j * np.random.rand(nj)
fk = np.zeros([ms, mt, mu], dtype=np.complex128)
timer = time.time()
ret = finufft.nufft3d1(xj, yj, zj, cj, fk.shape, fk, eps, iflag)
elapsed = time.time() - timer
Ks, Kt, Ku = np.mgrid[-np.floor(ms / 2):np.floor((ms - 1) / 2 + 1),
-np.floor(mt / 2):np.floor((mt - 1) / 2 + 1),
-np.floor(mu / 2):np.floor((mu - 1) / 2 + 1)]
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(cj * np.exp(
1j *
(Ks.ravel()[ii] * xj + Kt.ravel()[ii] * yj + Ku.ravel()[ii] * zj)))
Xtrue[ii] = fk.ravel()[ii]
print_report('finufft3d1', elapsed, Xest, Xtrue, nj)
xj = np.random.rand(nj) * 2 * math.pi - math.pi
yj = np.random.rand(nj) * 2 * math.pi - math.pi
zj = np.random.rand(nj) * 2 * math.pi - math.pi
cj = np.zeros([nj], dtype=np.complex128)
fk = np.random.rand(ms, mt, mu) + 1j * np.random.rand(ms, mt, mu)
timer = time.time()
ret = finufft.nufft3d2(xj, yj, zj, fk, cj, eps, iflag)
elapsed = time.time() - timer
Ks, Kt, Ku = np.mgrid[-np.floor(ms / 2):np.floor((ms - 1) / 2 + 1),
-np.floor(mt / 2):np.floor((mt - 1) / 2 + 1),
-np.floor(mu / 2):np.floor((mu - 1) / 2 + 1)]
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(
fk * np.exp(1j * (Ks * xj[ii] + Kt * yj[ii] + Ku * zj[ii])))
Xtrue[ii] = cj[ii]
print_report('finufft3d2', elapsed, Xest, Xtrue, nj)
x = np.random.rand(nj) * 2 * math.pi - math.pi
y = np.random.rand(nj) * 2 * math.pi - math.pi
z = np.random.rand(nj) * 2 * math.pi - math.pi
c = np.random.rand(nj) + 1j * np.random.rand(nj)
s = np.random.rand(nk) * 2 * math.pi - math.pi
t = np.random.rand(nk) * 2 * math.pi - math.pi
u = np.random.rand(nk) * 2 * math.pi - math.pi
f = np.zeros([nk], dtype=np.complex128)
timer = time.time()
ret = finufft.nufft3d3(x, y, z, c, s, t, u, f, eps, iflag)
elapsed = time.time() - timer
for ii in np.arange(0, num_samples):
Xest[ii] = np.sum(c * np.exp(1j * (s[ii] * x + t[ii] * y + u[ii] * z)))
Xtrue[ii] = f[ii]
print_report('finufft3d3', elapsed, Xest, Xtrue, nj + nk)
import time
np.random.seed(42)
# number of nonuniform points
M = 100000
# the nonuniform points in the square [0,2pi)^2
x = 2 * np.pi * np.random.uniform(size=M)
y = 2 * np.pi * np.random.uniform(size=M)
# their complex strengths
c = (np.random.standard_normal(size=M) +
1J * np.random.standard_normal(size=M))
# desired number of Fourier modes (in x,y directions respectively)
N1 = 1000
N2 = 2000
# calculate the transform
t0 = time.time()
f = finufft.nufft2d1(x, y, c, (N1, N2), eps=1e-9)
print("finufft2d1 done in {0:.2g} s.".format(time.time() - t0))
k1 = 376 # do a math check, for a single output mode index (k1,k2)
k2 = -1000
assert ((k1 >= -N1 / 2.) & (k1 < N1 / 2.)) # float division easier here
assert ((k2 >= -N2 / 2.) & (k2 < N2 / 2.))
ftest = sum(c * np.exp(1.j * (k1 * x + k2 * y)))
err = np.abs(f[k1 + N1 // 2, k2 + N2 // 2] - ftest) / np.max(np.abs(f))
print("Error relative to max: {0:.2e}".format(err))
import numpy as np
from finufft import nufft2d1
c = np.arange(2)
omega = np.arange(4).reshape((2, 2)) / 3 * np.pi
x0 = omega[:, 0]
y0 = omega[:, 1]
f0 = np.zeros((4, 4), order='F', dtype=np.complex128)
nufft2d1(x0, y0, c, 1, 1e-15, f0.shape[0], f0.shape[1], f0)
x1 = x0.copy()
y1 = y0.copy()
f1 = np.zeros((4, 4), order='F', dtype=np.complex128)
nufft2d1(x1, y1, c, 1, 1e-15, f1.shape[0], f1.shape[1], f1)
print('difference: %e' % np.linalg.norm(f0 - f1))