def _nufft(self, freq_domain_data, iflag=1, eps=1E-7):
"""
rotate coordinates and perform nufft
:param freq_domain_data:
:param iflag/eps: see finufftpy doc
:param eps: precision of nufft
:return: nufft of freq_domain_data after applying self.rotations
"""
if not finufft:
raise ImportError('finufftpy not available')
new_grid_coords = self._rotate_coordinates()[0]
# initialize array for nufft output
f = np.zeros([len(new_grid_coords[0])], dtype=np.complex128, order='F')
freq_domain_data_flat = np.asfortranarray(
freq_domain_data.flatten(order='F'))
finufftpy.nufft3d1(
new_grid_coords[0],
new_grid_coords[1],
new_grid_coords[2],
freq_domain_data_flat,
iflag,
eps,
self.im_shape[0],
self.im_shape[1],
self.im_shape[2],
f,
debug=0,
spread_debug=0,
spread_sort=2,
fftw=0,
modeord=0,
chkbnds=0,
upsampfac=1.25) # upsampling at 1.25 saves time at low precisions
im_out = f.reshape(self.im_shape, order='F')
return im_out
def anufft3(vol_f, fourier_pts, sz):
if len(sz) != 3:
raise ValueError('sz must be 3')
if len(fourier_pts.shape) != 2:
raise ValueError('fourier_pts must be 2D with shape 3x_')
if fourier_pts.shape[0] != 3:
raise ValueError('fourier_pts must be 2D with shape 3x_')
if not fourier_pts.flags.c_contiguous:
fourier_pts = fourier_pts.copy()
if not vol_f.flags.c_contiguous:
vol_f = vol_f.copy()
x = fourier_pts[0]
y = fourier_pts[1]
z = fourier_pts[2]
isign = 1
eps = 1e-15
ms, mt, mu = sz
f = np.empty(sz, dtype='complex128', order='F')
finufftpy.nufft3d1(x, y, z, vol_f, isign, eps, ms, mt, mu, f)
return f.copy()
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)
def EwaldFarVel(self, ptsxyz, forces, nThr):
"""
This function computes the far field Ewald velocity.
Inputs: ptsxyz = the list of points
in undeformed, Cartesian coordinates, forces = forces at those points.
This function relies entirely on calls to FINUFFT. See the documentation
there for more information.
"""
# Compute the coordinates in the transformed basis
pts = self._currentDomain.primecoords(ptsxyz)
# Rescale to [-pi,pi] (for FINUFFT)
Lens = self._currentDomain.getPeriodicLens()
pts = 2 * pi * np.mod(pts, Lens) / Lens - pi
# Forcing on the grid (FINUFFT type 1)
fi.nufft3d1(pts[:,0],pts[:,1],pts[:,2],forces[:,0],-1,fartol,\
self._nx,self._ny,self._nz,self._fxhat,modeord=1,nThreads=nThr)
fi.nufft3d1(pts[:,0],pts[:,1],pts[:,2],forces[:,1],-1,fartol,\
self._nx,self._ny,self._nz,self._fyhat,modeord=1,nThreads=nThr)
fi.nufft3d1(pts[:,0],pts[:,1],pts[:,2],forces[:,2],-1,fartol,\
self._nx,self._ny,self._nz,self._fzhat,modeord=1,nThreads=nThr)
# Manipulation in Fourier space
kxP, kyP, kzP = self._currentDomain.primeWaveNumbersFromUnprimed(
self._kx, self._ky, self._kz)
k = np.sqrt(kxP * kxP + kyP * kyP + kzP * kzP)
# Multiplication factor for the RPY tensor
factor = 1.0 / (self._mu * k * k) * np.sinc(k * self._a / pi)**2
factor *= (1 + k * k / (4 * self._xi * self._xi)) * np.exp(
-k * k / (4 * self._xi * self._xi))
# splitting function
factor[0, 0, 0] = 0
# zero out 0 mode
uxhat = factor * self._fxhat
uyhat = factor * self._fyhat
uzhat = factor * self._fzhat
# Project off so we get divergence free
uprojx = uxhat - (kxP * uxhat + kyP * uyhat + kzP * uzhat) * kxP / (k *
k)
uprojx[0, 0, 0] = 0
uprojy = uyhat - (kxP * uxhat + kyP * uyhat + kzP * uzhat) * kyP / (k *
k)
uprojy[0, 0, 0] = 0
uprojz = uzhat - (kxP * uxhat + kyP * uyhat + kzP * uzhat) * kzP / (k *
k)
uprojz[0, 0, 0] = 0
# Velocities at the points (FINUFFT type 2)
fi.nufft3d2(pts[:, 0],
pts[:, 1],
pts[:, 2],
self._ufarx,
1,
fartol,
uprojx,
modeord=1,
nThreads=nThr)
fi.nufft3d2(pts[:, 0],
pts[:, 1],
pts[:, 2],
self._ufary,
1,
fartol,
uprojy,
modeord=1,
nThreads=nThr)
fi.nufft3d2(pts[:, 0],
pts[:, 1],
pts[:, 2],
self._ufarz,
1,
fartol,
uprojz,
modeord=1,
nThreads=nThr)
vol = self._currentDomain.getVol()
return np.concatenate(
([np.real(self._ufarx) / vol], [np.real(self._ufary) / vol],
[np.real(self._ufarz) / vol])).T
def apply_affine_transform(
self,
tensor: torch.Tensor,
scaling_params: List[float],
rotation_params: List[float],
padding_values: List[float]
) -> torch.Tensor:
assert tensor.ndim == 4
assert len(tensor) == 1
from torchio.transforms.augmentation.intensity.random_motion_from_time_course import create_rotation_matrix_3d
import math
import finufftpy
image = tensor[0]
#noise_mean, nois_std = estimate_borders_mean_std(np.abs(image.numpy())) #random_noise gives negativ values ...
noise_mean, nois_std = estimate_borders_mean_std(image.numpy())
original_image_shape = image.shape
if self.oversampling_pct > 0.0:
if len(padding_values) == 2: #mean std
padd_mode = 'random.normal'
else:
padd_mode = 'constant'
image = self._oversample(image, self.oversampling_pct, padding_mode=padd_mode,
padding_normal=padding_values)
#im_freq_domain = (np.fft.fftshift(np.fft.fftn(np.fft.ifftshift(image)))).astype(np.complex128)
im_freq_domain = self._fft_im(image)
#if self.oversampling_pct > 0.0:
# im_freq_domain = self._oversample(im_freq_domain, self.oversampling_pct,
# padding_mode='random.normal', padding_normal=(noise_mean, nois_std))
rrrot = -np.radians(rotation_params); rrrot[1] = - rrrot[1] #to get the same as sitk ... hmmm
rotation_matrices = create_rotation_matrix_3d(rrrot)
scaling_matrices = np.eye(3) / np.array(scaling_params) #/ to have same convention as
rotation_matrices = np.matmul(rotation_matrices, scaling_matrices)
im_shape = im_freq_domain.shape
center = [math.ceil((x - 1) / 2) for x in im_shape]
[i1, i2, i3] = np.meshgrid(2*(np.arange(im_shape[0]) - center[0])/im_shape[0],
2*(np.arange(im_shape[1]) - center[1])/im_shape[1],
2*(np.arange(im_shape[2]) - center[2])/im_shape[2], indexing='ij')
grid_coordinates = np.array([i1.flatten('F'), i2.flatten('F'), i3.flatten('F')])
method='one_matrix'
if method=='one_matrix':
new_grid_coords = np.matmul(rotation_matrices, grid_coordinates)
else: #grrr marche pas ! (inspirer de random_motion_from_time_course
rotation_matrices = np.expand_dims(rotation_matrices, [2, 3, 4])
rotation_matrices = np.tile(rotation_matrices, [1, 1] + list(im_shape)) # 3 x 3 x img_shape
rotation_matrices = rotation_matrices.reshape([-1, 3, 3], order='F')
# tile grid coordinates for vectorizing computation
grid_coordinates_tiled = np.tile(grid_coordinates, [3, 1])
grid_coordinates_tiled = grid_coordinates_tiled.reshape([3, -1], order='F').T
rotation_matrices = rotation_matrices.reshape([-1, 3]) #reshape for matrix multiplication, so no order F
new_grid_coords = (rotation_matrices * grid_coordinates_tiled).sum(axis=1)
# reshape new grid coords back to 3 x nvoxels
new_grid_coords = new_grid_coords.reshape([3, -1], order='F')
# scale data between -pi and pi
max_vals = [1, 1, 1]
new_grid_coordinates_scaled = [(new_grid_coords[i, :] / max_vals[i]) * math.pi for i in [0, 1, 2]]
# initialize array for nufft output
f = np.zeros([len(new_grid_coordinates_scaled[0])], dtype=np.complex128, order='F')
freq_domain_data_flat = np.asfortranarray(im_freq_domain.flatten(order='F'))
iflag, eps = 1, 1E-7
finufftpy.nufft3d1(new_grid_coordinates_scaled[0], new_grid_coordinates_scaled[1],
new_grid_coordinates_scaled[2], freq_domain_data_flat,
iflag, eps, im_shape[0], im_shape[1], im_shape[2],
f, debug=0, spread_debug=0, spread_sort=2, fftw=0, modeord=0,
chkbnds=0, upsampfac=1.25) # upsampling at 1.25 saves time at low precisions
im_out = f.reshape(im_shape, order='F')
im_out = abs(im_out / im_out.size)
if im_shape[0] - original_image_shape[0]:
im_out = self.crop_volume(im_out, original_image_shape)
#ov(im_out)
tensor[0] = torch.from_numpy(im_out)
return tensor
