def nufft_interpolation1d(x_out, in_hat, transformer=None):
"""
Interpolate fourier data given by in_hat to x_out locations
x_out should either live in the range [0,2*pi] or an AffineTransformer
should be specified that transforms it to that range
"""
if transformer is not None:
x_out = transformer(x_out)
out = np.zeros(x_out.shape[0], dtype=complex)
if old_nufft:
finufftpy.nufft1d2(x_out, out, 1, 1e-15, in_hat, modeord=1)
else:
finufft.nufft1d2(x_out, in_hat, out, isign=1, eps=1e-15, modeord=1)
adj = 1.0 / in_hat.shape[0]
return out.real * adj
def __call__(self, x_out):
if old_nufft:
finufftpy.nufft1d2(x_out,
self.out,
1,
1e-15,
self.in_hat,
modeord=1)
else:
finufft.nufft1d2(x_out,
self.in_hat,
self.out,
isign=1,
eps=1e-15,
modeord=1)
if self.realit:
return self.out.real * self.adj
else:
return self.out * self.adj
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=finufftpy.nufft1d1(xj,cj,iflag,eps,ms,fk)
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=finufftpy.nufft1d2(xj,cj,iflag,eps,fk)
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=finufftpy.nufft1d3(x,c,iflag,eps,s,f)
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,order='F')
timer=time.time()
ret=finufftpy.nufft2d1(xj,yj,cj,iflag,eps,ms,mt,fk)
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 = 5 # how many vectors to do
cj=np.array(np.random.rand(nj,ndata)+1j*np.random.rand(nj,ndata),order='F')
fk=np.zeros([ms,mt,ndata],dtype=np.complex128,order='F')
timer=time.time()
ret=finufftpy.nufft2d1many(xj,yj,cj,iflag,eps,ms,mt,fk)
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(order='F')[ii]*xj+Kt.ravel(order='F')[ii]*yj))) # note fortran-ravel-order needed throughout - mess.
Xtrue[ii]=fk.ravel(order='F')[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=finufftpy.nufft2d2(xj,yj,cj,iflag,eps,fk)
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([nj,ndata],order='F',dtype=np.complex128);
fk=np.array(np.random.rand(ms,mt,ndata)+1j*np.random.rand(ms,mt,ndata),order='F')
timer=time.time()
ret=finufftpy.nufft2d2many(xj,yj,cj,iflag,eps,fk)
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[ii,dtest]
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=finufftpy.nufft2d3(x,y,c,iflag,eps,s,t,f)
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,order='F')
timer=time.time()
ret=finufftpy.nufft3d1(xj,yj,zj,cj,iflag,eps,ms,mt,mu,fk)
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=finufftpy.nufft3d2(xj,yj,zj,cj,iflag,eps,fk)
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=finufftpy.nufft3d3(x,y,z,c,iflag,eps,s,t,u,f)
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)
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(20, num_uniform_points * 0.5 +
1)) #for estimating accuracy
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
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 = finufftpy.nufft1d1(xj, cj, iflag, eps, ms, fk)
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 = finufftpy.nufft1d2(xj, cj, iflag, eps, fk)
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 = finufftpy.nufft1d3(x, c, iflag, eps, s, f)
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
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, order='F')
timer = time.time()
ret = finufftpy.nufft2d1(xj, yj, cj, iflag, eps, ms, mt, fk)
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)
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 = finufftpy.nufft2d2(xj, yj, cj, iflag, eps, fk)
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)
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 = finufftpy.nufft2d3(x, y, c, iflag, eps, s, t, f)
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
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, order='F')
timer = time.time()
ret = finufftpy.nufft3d1(xj, yj, zj, cj, iflag, eps, ms, mt, mu, fk)
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 = finufftpy.nufft3d2(xj, yj, zj, cj, iflag, eps, fk)
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 = finufftpy.nufft3d3(x, y, z, c, iflag, eps, s, t, u, f)
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)