def realspace_benchmark_new_algorithm_comparison(model, ea=None, num_inplane_angles=360, rad=0.6,
save_animation=False, animation_name=None):
N = model.shape[0]
ea, euler_angles = gen_EAs_randomly(ea, num_inplane_angles)
sl = projector.project(model, ea, rad=rad, truncate=True)
rot_slice = projector.project(M, euler_angles, rad=rad, truncate=True)
full_slice = projector.trunc_to_full(sl, N, rad)
full_rot_slices = projector.trunc_to_full(rot_slice, N, rad)
proj = density.fspace_to_real(full_slice)
full_rot_projs = np.zeros_like(full_rot_slices, dtype=density.real_t)
for i, fs in enumerate(full_rot_slices):
full_rot_projs[i] = density.fspace_to_real(fs)
trunc_proj = projector.full_to_trunc(proj, rad)
trunc_rot_projs = projector.full_to_trunc(full_rot_projs, rad)
corr_trunc_proj = correlation.calc_angular_correlation(trunc_proj, N, rad)
corr_trunc_rot_projs = correlation.calc_angular_correlation(trunc_rot_projs, N, rad)
diff = calc_difference(trunc_proj, trunc_rot_projs, only_real=True)
corr_diff = calc_difference(corr_trunc_proj, corr_trunc_rot_projs, only_real=True)
vis_real_space_comparison(
full_rot_projs,
projector.trunc_to_full(corr_trunc_rot_projs, N, rad),
diff, corr_diff,
original_img=proj,
original_corr_img=projector.trunc_to_full(corr_trunc_proj, N, rad),
save_animation=save_animation, animation_name=animation_name)
def shift_vis(model):
N = model.shape[0]
rad = 0.8
kernel = 'lanczos'
kernsize = 4
xy, trunc_xy, truncmask = geometry.gencoords(N, 2, rad, True)
N_T = trunc_xy.shape[0]
premult = cryoops.compute_premultiplier(N,
kernel=kernel,
kernsize=kernsize)
TtoF = sincint.gentrunctofull(N=N, rad=rad)
fM = density.real_to_fspace(model)
prefM = density.real_to_fspace(
premult.reshape((1, 1, -1)) * premult.reshape(
(1, -1, 1)) * premult.reshape((-1, 1, 1)) * model)
pt = np.random.randn(3)
pt /= np.linalg.norm(pt)
psi = 2 * np.pi * np.random.rand()
ea = geometry.genEA(pt)[0]
ea[2] = psi
print('project model for Euler angel: ({:.2f}, {:.2f}, {:.2f}) degree'.
format(*np.rad2deg(ea)))
rot_matrix = geometry.rotmat3D_EA(*ea)[:, 0:2]
slop = cryoops.compute_projection_matrix([rot_matrix], N, kernel, kernsize,
rad, 'rots')
# trunc_slice = slop.dot(prefM.reshape((-1,)))
trunc_slice = cryoem.getslices(prefM, slop)
fourier_slice = TtoF.dot(trunc_slice).reshape(N, N)
real_proj = density.fspace_to_real(fourier_slice)
fig, axes = plt.subplots(4, 4, figsize=(12.8, 8))
im_real = axes[0, 0].imshow(real_proj)
im_fourier = axes[1, 0].imshow(np.log(np.abs(fourier_slice)))
for i, ax in enumerate(axes[:, 1:].T):
shift = np.random.randn(2) * (N / 4.0)
S = cryoops.compute_shift_phases(shift.reshape(1, 2), N, rad)[0]
shift_trunc_slice = S * trunc_slice
shift_fourier_slice = TtoF.dot(shift_trunc_slice).reshape(N, N)
shift_real_proj = density.fspace_to_real(shift_fourier_slice)
ax[0].imshow(shift_real_proj)
ax[1].imshow(np.log(np.abs(shift_fourier_slice)))
ax[2].imshow(np.log(shift_fourier_slice.real))
ax[3].imshow(np.log(shift_fourier_slice.imag))
fig.tight_layout()
plt.show()
def premult_test(model, kernel='lanczos', kernsize=6):
if isinstance(model, str):
M = mrc.readMRC(model)
elif isinstance(model, np.ndarray):
M = model
shape = np.asarray(M.shape)
assert (shape - shape.mean()).sum() == 0
N = M.shape[0]
rad = 0.6
premult = cryoops.compute_premultiplier(N, kernel, kernsize)
TtoF = sincint.gentrunctofull(N=N, rad=rad)
premulter = premult.reshape((1, 1, -1)) \
* premult.reshape((1, -1, 1)) \
* premult.reshape((-1, 1, 1))
fM = density.real_to_fspace(M)
prefM = density.real_to_fspace(premulter * M)
pt = np.random.randn(3)
pt /= np.linalg.norm(pt)
psi = 2 * np.pi * np.random.rand()
ea = geometry.genEA(pt)[0]
ea[2] = psi
print('project model for Euler angel: ({:.2f}, {:.2f}, {:.2f}) degree'.
format(*np.rad2deg(ea)))
rot_matrix = geometry.rotmat3D_EA(*ea)[:, 0:2]
slop = cryoops.compute_projection_matrix([rot_matrix], N, kernel, kernsize,
rad, 'rots')
trunc_slice = slop.dot(fM.reshape((-1, )))
premult_trunc_slice = slop.dot(prefM.reshape((-1, )))
proj = density.fspace_to_real(TtoF.dot(trunc_slice).reshape(N, N))
premult_proj = density.fspace_to_real(
TtoF.dot(premult_trunc_slice).reshape(N, N))
fig, ax = plt.subplots(1, 3, figsize=(14.4, 4.8))
im_proj = ax[0].imshow(proj, origin='lower')
fig.colorbar(im_proj, ax=ax[0])
ax[0].set_title('no premulter')
im_pre = ax[1].imshow(premult_proj, origin='lower')
fig.colorbar(im_pre, ax=ax[1])
ax[1].set_title('with premulter')
im_diff = ax[2].imshow(proj - premult_proj, origin='lower')
fig.colorbar(im_diff, ax=ax[2])
ax[2].set_title('difference of two image')
fig.tight_layout()
plt.show()
def apply(self,M,normalize=True,kernel='sinc',kernelsize=3,rad=2):
if self.symclass == '':
return M
if n.iscomplexobj(M):
symRs = n.array(self.get_rotations(exclude_dsym=True), dtype=n.float32)
N = M.shape[0]
if rad*self.get_order()*N < 500: # VERY heuristic
symM = sincint.symmetrize_fspace_volume(M,rad,kernel,kernelsize,symRs=symRs)
if self.symclass == 'd':
symR = n.array([ [ [ -1.0, 0, 0 ],
[ 0, 1.0, 0 ],
[ 0, 0, -1.0 ] ] ], dtype=n.float32)
symM = sincint.symmetrize_fspace_volume(symM,rad,kernel,kernelsize,symRs=symR)
else:
return density.real_to_fspace(self.apply(density.fspace_to_real(M),normalize=normalize))
else:
symRs = n.array(self.get_rotations(), dtype=n.float32)
symM = sincint.symmetrize_volume(n.require(M,dtype=n.float32),symRs)
# symRs = n.array(self.get_rotations(exclude_dsym=True), dtype=n.float32)
#
# symM = sincint.symmetrize_volume_z(M,symRs)
#
# if self.symclass == 'd':
# symR = n.array([ [ [ -1.0, 0, 0 ],
# [ 0, -1.0, 0 ],
# [ 0, 0, 1.0 ] ] ], dtype=n.float32)
# symM = n.swapaxes(sincint.symmetrize_volume_z(n.swapaxes(symM,1,2),symR),1,2)
if normalize:
symM /= self.get_order()
return symM
def eval(self, M=None, compute_gradient=True, fM=None, **kwargs):
tic_start = time.time()
if self.kernel.slice_premult is not None:
pfM = density.real_to_fspace(self.kernel.slice_premult * M)
else:
pfM = density.real_to_fspace(M)
pmtime = time.time() - tic_start
ret = self.kernel.eval(fM=pfM,
M=None,
compute_gradient=compute_gradient)
if not self.minibatch['test_batch'] and not kwargs.get(
'intermediate', False):
tic_record = time.time()
curr_var = ret[-1]['sigma2_est']
assert n.all(n.isfinite(curr_var))
if self.error_history.N_sum != self.cryodata.N_batches:
self.error_history.setup(curr_var,
self.cryodata.N_batches,
allow_decay=False)
self.error_history.set_value(self.minibatch['id'], curr_var)
curr_corr = ret[-1]['correlation']
assert n.all(n.isfinite(curr_corr))
if self.correlation_history.N_sum != self.cryodata.N_batches:
self.correlation_history.setup(curr_corr,
self.cryodata.N_batches,
allow_decay=False)
self.correlation_history.set_value(self.minibatch['id'], curr_corr)
curr_power = ret[-1]['power']
assert n.all(n.isfinite(curr_power))
if self.power_history.N_sum != self.cryodata.N_batches:
self.power_history.setup(curr_power,
self.cryodata.N_batches,
allow_decay=False)
self.power_history.set_value(self.minibatch['id'], curr_power)
curr_mask = self.kernel.truncmask
if self.mask_history.N_sum != self.cryodata.N_batches:
self.mask_history.setup(n.require(curr_mask, dtype=n.float32),
self.cryodata.N_batches,
allow_decay=False)
self.mask_history.set_value(self.minibatch['id'], curr_mask)
ret[-1]['like_timing']['record'] = time.time() - tic_record
if compute_gradient and self.kernel.slice_premult is not None:
tic_record = time.time()
ret = (ret[0],
self.kernel.slice_premult * density.fspace_to_real(ret[1]),
ret[2])
ret[-1]['like_timing']['premult'] = pmtime + time.time(
) - tic_record
ret[-1]['like_timing']['total'] = time.time() - tic_start
return ret
def convert_parameter(self,x,comp_real=False,comp_fspace=False):
is_x0 = x is self.x0
if is_x0:
M, fM = self.M0, self.fM0
else:
M, fM = param2density(x, self.xtype, self.M0.shape, \
precond=self.precond)
if comp_real and M is None:
M = density.fspace_to_real(fM)
if comp_fspace and fM is None:
fM = density.real_to_fspace(M)
return M, fM
def eval(self, M=None, compute_gradient=True, fM=None, **kwargs):
tic_start = time.time()
if self.kernel.slice_premult is not None:
pfM = density.real_to_fspace(self.kernel.slice_premult * M)
else:
pfM = density.real_to_fspace(M)
pmtime = time.time() - tic_start
ret = self.kernel.eval(fM=pfM, M=None, compute_gradient=compute_gradient)
if not self.minibatch['test_batch'] and not kwargs.get('intermediate', False):
tic_record = time.time()
curr_var = ret[-1]['sigma2_est']
assert n.all(n.isfinite(curr_var))
if self.error_history.N_sum != self.cryodata.N_batches:
self.error_history.setup(curr_var, self.cryodata.N_batches, allow_decay=False)
self.error_history.set_value(self.minibatch['id'], curr_var)
curr_corr = ret[-1]['correlation']
assert n.all(n.isfinite(curr_corr))
if self.correlation_history.N_sum != self.cryodata.N_batches:
self.correlation_history.setup(curr_corr, self.cryodata.N_batches, allow_decay=False)
self.correlation_history.set_value(self.minibatch['id'], curr_corr)
curr_power = ret[-1]['power']
assert n.all(n.isfinite(curr_power))
if self.power_history.N_sum != self.cryodata.N_batches:
self.power_history.setup(curr_power, self.cryodata.N_batches, allow_decay=False)
self.power_history.set_value(self.minibatch['id'], curr_power)
curr_mask = self.kernel.truncmask
if self.mask_history.N_sum != self.cryodata.N_batches:
self.mask_history.setup(n.require(curr_mask, dtype=n.float32), self.cryodata.N_batches,
allow_decay=False)
self.mask_history.set_value(self.minibatch['id'], curr_mask)
ret[-1]['like_timing']['record'] = time.time() - tic_record
if compute_gradient and self.kernel.slice_premult is not None:
tic_record = time.time()
ret = (ret[0], self.kernel.slice_premult * density.fspace_to_real(ret[1]), ret[2])
ret[-1]['like_timing']['premult'] = pmtime + time.time() - tic_record
ret[-1]['like_timing']['total'] = time.time() - tic_start
return ret
def apply(self, M, normalize=True, kernel='sinc', kernelsize=3, rad=2):
if self.symclass == '':
return M
if np.iscomplexobj(M):
symRs = np.array(self.get_rotations(exclude_dsym=True),
dtype=np.float32)
N = M.shape[0]
if rad * self.get_order() * N < 500: # VERY heuristic
symM = sincint.symmetrize_fspace_volume(M,
rad,
kernel,
kernelsize,
symRs=symRs)
if self.symclass == 'd':
symR = np.array(
[[[-1.0, 0, 0], [0, 1.0, 0], [0, 0, -1.0]]],
dtype=np.float32)
symM = sincint.symmetrize_fspace_volume(symM,
rad,
kernel,
kernelsize,
symRs=symR)
else:
return density.real_to_fspace(
self.apply(density.fspace_to_real(M), normalize=normalize))
else:
symRs = np.array(self.get_rotations(), dtype=np.float32)
symM = sincint.symmetrize_volume(np.require(M, dtype=np.float32),
symRs)
# symRs = n.array(self.get_rotations(exclude_dsym=True), dtype=n.float32)
# symM = sincint.symmetrize_volume_z(M,symRs)
# if self.symclass == 'd':
# symR = n.array([ [ [ -1.0, 0, 0 ],
# [ 0, -1.0, 0 ],
# [ 0, 0, 1.0 ] ] ], dtype=n.float32)
# symM = n.swapaxes(sincint.symmetrize_volume_z(n.swapaxes(symM,1,2),symR),1,2)
if normalize:
symM /= self.get_order()
return symM
def project(model, euler_angles, rad=0.95, truncate=False):
if isinstance(model, str):
M = mrc.readMRC(model)
elif isinstance(model, np.ndarray):
M = model
N = M.shape[0]
kernel = 'lanczos'
ksize = 6
premult = cryoops.compute_premultiplier(N, kernel, ksize)
TtoF = sincint.gentrunctofull(N=N, rad=rad)
premulter = premult.reshape((1, 1, -1)) \
* premult.reshape((1, -1, 1)) \
* premult.reshape((-1, 1, 1))
# premulter = 1
fM = density.real_to_fspace(premulter * M)
euler_angles = euler_angles.reshape((-1, 3))
num_projs = euler_angles.shape[0]
if truncate:
projs = np.zeros((num_projs, TtoF.shape[1]), dtype=fM.dtype)
else:
projs = np.zeros((num_projs, N, N), dtype=M.dtype)
for i, ea in enumerate(euler_angles):
rot_matrix = geometry.rotmat3D_EA(*ea)[:, 0:2]
slop = cryoops.compute_projection_matrix([rot_matrix], N, kernel, ksize, rad, 'rots')
trunc_slice = slop.dot(fM.reshape((-1,)))
if truncate:
projs[i, :] = trunc_slice
else:
projs[i, :, :] = density.fspace_to_real(TtoF.dot(trunc_slice).reshape(N, N))
if num_projs == 1 and not truncate:
projs = projs.reshape((N, N))
return projs
def learn_params(self, params, cparams, M=None, fM=None):
anyfspace = any([obj.fspace for obj in self.objs])
anyrspace = any([not obj.fspace for obj in self.objs])
N = None
if fM is None and anyfspace:
assert M is not None, 'M or fM must be set!'
N = M.shape[0]
fM = density.real_to_fspace(M)
elif fM is not None:
N = fM.shape[0]
if M is None and anyrspace:
assert fM is not None, 'M or fM must be set!'
N = fM.shape[0]
M = density.fspace_to_real(fM)
elif M is not None:
assert N is None or N == M.shape[0]
N = M.shape[0]
assert N is not None
for obj in self.objs:
obj.learn_params(params, cparams, M=M, fM=fM)
def learn_params(self, params, cparams, M=None, fM=None):
anyfspace = any([obj.fspace for obj in self.objs])
anyrspace = any([not obj.fspace for obj in self.objs])
N = None
if fM is None and anyfspace:
assert M is not None, 'M or fM must be set!'
N = M.shape[0]
fM = density.real_to_fspace(M)
elif fM is not None:
N = fM.shape[0]
if M is None and anyrspace:
assert fM is not None, 'M or fM must be set!'
N = fM.shape[0]
M = density.fspace_to_real(fM)
elif M is not None:
assert N is None or N == M.shape[0]
N = M.shape[0]
assert N is not None
for obj in self.objs:
obj.learn_params(params,cparams,M=M,fM=fM)
def genphantomdata(N_D, phantompath, ctfparfile):
mscope_params = {
'akv': 200,
'wgh': 0.07,
'cs': 2.0,
'psize': 2.8,
'bfactor': 500.0
}
N = 128
rad = 0.95
shift_sigma = 3.0
sigma_noise = 25.0
M_totalmass = 80000
kernel = 'lanczos'
ksize = 6
premult = cryoops.compute_premultiplier(N, kernel, ksize)
tic = time.time()
N_D = int(N_D)
N = int(N)
rad = float(rad)
psize = mscope_params['psize']
bfactor = mscope_params['bfactor']
shift_sigma = float(shift_sigma)
sigma_noise = float(sigma_noise)
M_totalmass = float(M_totalmass)
srcctf_stack = CTFStack(ctfparfile, mscope_params)
genctf_stack = GeneratedCTFStack(
mscope_params, parfields=['PHI', 'THETA', 'PSI', 'SHX', 'SHY'])
TtoF = sincint.gentrunctofull(N=N, rad=rad)
Cmap = n.sort(
n.random.random_integers(0,
srcctf_stack.get_num_ctfs() - 1, N_D))
M = mrc.readMRC(phantompath)
cryoem.window(M, 'circle')
M[M < 0] = 0
if M_totalmass is not None:
M *= M_totalmass / M.sum()
V = density.real_to_fspace(
premult.reshape((1, 1, -1)) * premult.reshape(
(1, -1, 1)) * premult.reshape((-1, 1, 1)) * M)
print "Generating data..."
sys.stdout.flush()
imgdata = n.empty((N_D, N, N), dtype=density.real_t)
pardata = {'R': [], 't': []}
prevctfI = None
for i, srcctfI in enumerate(Cmap):
ellapse_time = time.time() - tic
remain_time = float(N_D - i) * ellapse_time / max(i, 1)
print "\r%.2f Percent.. (Elapsed: %s, Remaining: %s) " % (
i / float(N_D) * 100.0, format_timedelta(ellapse_time),
format_timedelta(remain_time)),
sys.stdout.flush()
# Get the CTF for this image
cCTF = srcctf_stack.get_ctf(srcctfI)
if prevctfI != srcctfI:
genctfI = genctf_stack.add_ctf(cCTF)
C = cCTF.dense_ctf(N, psize, bfactor).reshape((N**2, ))
prevctfI = srcctfI
# Randomly generate the viewing direction/shift
pt = n.random.randn(3)
pt /= n.linalg.norm(pt)
psi = 2 * n.pi * n.random.rand()
EA = geom.genEA(pt)[0]
EA[2] = psi
shift = n.random.randn(2) * shift_sigma
R = geom.rotmat3D_EA(*EA)[:, 0:2]
slop = cryoops.compute_projection_matrix([R], N, kernel, ksize, rad,
'rots')
S = cryoops.compute_shift_phases(shift.reshape((1, 2)), N, rad)[0]
D = slop.dot(V.reshape((-1, )))
D *= S
imgdata[i] = density.fspace_to_real((C * TtoF.dot(D)).reshape(
(N, N))) + n.require(n.random.randn(N, N) * sigma_noise,
dtype=density.real_t)
genctf_stack.add_img(genctfI,
PHI=EA[0] * 180.0 / n.pi,
THETA=EA[1] * 180.0 / n.pi,
PSI=EA[2] * 180.0 / n.pi,
SHX=shift[0],
SHY=shift[1])
pardata['R'].append(R)
pardata['t'].append(shift)
print "\rDone in ", time.time() - tic, " seconds."
return imgdata, genctf_stack, pardata, mscope_params
def eval(self,
M=None,
fM=None,
compute_gradient=True,
all_grads=False,
**kwargs):
anyfspace = any([obj.fspace for obj in self.objs])
anyrspace = any([not obj.fspace for obj in self.objs])
N = None
if fM is None and anyfspace:
assert M is not None, 'M or fM must be set!'
N = M.shape[0]
fM = density.real_to_fspace(M)
elif fM is not None:
N = fM.shape[0]
if M is None and anyrspace:
assert fM is not None, 'M or fM must be set!'
N = fM.shape[0]
M = density.fspace_to_real(fM)
elif M is not None:
assert N is None or N == M.shape[0]
N = M.shape[0]
assert N is not None
logP = 0
logPs = []
if compute_gradient:
if all_grads:
dlogP = density.zeros_like(
fM) if self.fspace else density.zeros_like(M)
dlogPs = []
else:
if (not self.fspace) or anyrspace:
dlogPdM = density.zeros_like(M)
if self.fspace or anyfspace:
dlogPdfM = density.zeros_like(fM)
outputs = {}
for w, obj in zip(self.ws, self.objs):
if compute_gradient:
clogP, cdlogP, coutputs = obj.eval(
M=M, fM=fM, compute_gradient=compute_gradient, **kwargs)
if w is not None and w != 1:
clogP *= w
cdlogP *= w
if all_grads:
if obj.fspace == self.fspace:
dlogPs.append(cdlogP)
elif self.fspace:
dlogPs.append(density.real_to_fspace(cdlogP))
else:
dlogPs.append(density.fspace_to_real(cdlogP))
dlogP += dlogPs[-1]
else:
if obj.fspace:
dlogPdfM += cdlogP
else:
dlogPdM += cdlogP
else:
clogP, coutputs = obj.eval(M=M,
fM=fM,
compute_gradient=compute_gradient,
**kwargs)
if w is not None and w != 1:
clogP *= w
logP += clogP
logPs.append(clogP)
outputs.update(coutputs)
if compute_gradient and not all_grads:
if self.fspace:
dlogP = dlogPdfM
if anyrspace:
dlogP += density.real_to_fspace(dlogPdM)
else:
dlogP = dlogPdM
if anyfspace:
dlogP += density.fspace_to_real(dlogPdfM)
outputs['all_logPs'] = logPs
if compute_gradient and all_grads:
outputs['all_dlogPs'] = dlogPs
if compute_gradient:
return logP, dlogP, outputs
else:
return logP, outputs
def calc_angular_correlation(
trunc_slices,
N,
rad,
beamstop_rad=None,
pixel_size=1.0,
interpolation='nearest',
sort_theta=True,
clip=True,
outside=False,
):
"""compute angular correlation for input array
outside: True or False (default: False)
calculate angular correlation in radius or outside of radius
sort_theta: True or False (default: True)
sort theta when slicing the same rho in trunc array
"""
# 1. get a input (single: N_T or multi: N_R x N_T) with normal sequence.
# 2. sort truncation array by rho value of polar coordinates
# 3. apply angular correlation function to sorted slice for both real part and imaginary part
# 4. deal with outlier beyond 3 sigma (no enough points to do sampling via fft)
# (oversampling is unavailable, hence dropout points beyond 3 sigma)
# 5. return angluar correlation slice with normal sequence.
# 1.
iscomplex = np.iscomplexobj(trunc_slices)
if outside:
trunc_xy = gencoords_outside(N, 2, rad)
else:
if beamstop_rad is None:
trunc_xy = geometry.gencoords(N, 2, rad)
else:
trunc_xy = geometry.gencoords_centermask(N, 2, rad, beamstop_rad)
if trunc_slices.ndim < 2:
assert trunc_xy.shape[0] == trunc_slices.shape[
0], "wrong length of trunc slice or wrong radius"
else:
assert trunc_xy.shape[0] == trunc_slices.shape[
1], "wrong length of trunc slice or wrong radius"
# 2.
pol_trunc_xy = cart2pol(trunc_xy)
if sort_theta:
# lexsort; first, sort rho; second, sort theta
sorted_idx = np.lexsort((pol_trunc_xy[:, 1], pol_trunc_xy[:, 0]))
else:
sorted_idx = np.argsort(pol_trunc_xy[:, 0])
axis = trunc_slices.ndim - 1
sorted_rho = np.take(pol_trunc_xy[:, 0], sorted_idx)
sorted_slice = np.take(trunc_slices, sorted_idx, axis=axis)
# 3.
if 'none' in interpolation:
pass
elif 'nearest' in interpolation:
sorted_rho = np.round(sorted_rho)
elif 'linear' in interpolation:
raise NotImplementedError()
else:
raise ValueError('unsupported method for interpolation')
# sorted_rho_freqs = sorted_rho / (N * pixel_size)
resolution = 1.0 / (N * pixel_size)
_, unique_idx, unique_counts = np.unique(sorted_rho,
return_index=True,
return_counts=True)
indices = [slice(None)] * trunc_slices.ndim
angular_correlation = np.zeros_like(trunc_slices, dtype=trunc_slices.dtype)
for i, count in enumerate(unique_counts):
indices[axis] = slice(unique_idx[i], unique_idx[i] + count)
# minimum points to do fft (2 or 4 times than Nyquist frequency)
# minimum_sample_points = (4 / count) / resolution
minimum_sample_points = 2000
same_rho = np.copy(sorted_slice[indices])
if count < minimum_sample_points:
for shift in range(count):
curr_delta_phi = same_rho * np.roll(same_rho, shift, axis=axis)
indices[axis] = unique_idx[i] + shift
angular_correlation[indices] = np.mean(curr_delta_phi,
axis=axis)
else:
# use view (slicing) or copy (fancy indexing, np.take(), np.put())?
fpcimg_real = density.real_to_fspace(
same_rho.real, axes=(axis, )) # polar image in fourier sapce
angular_correlation[indices].real = density.fspace_to_real(
fpcimg_real * fpcimg_real.conjugate(), axes=(axis, )).real
if iscomplex: # FIXME: stupid way. optimize this
fpcimg_fourier = density.real_to_fspace(
same_rho.imag,
axes=(axis, )) # polar image in fourier sapce
angular_correlation[indices].imag = density.fspace_to_real(
fpcimg_fourier * fpcimg_fourier.conjugate(),
axes=(axis, )).real
# check inf and nan
if np.any(np.isinf(angular_correlation)):
warnings.warn(
"Some values in angular correlation occur inf. These values have been set to zeros."
)
angular_correlation.real[np.isinf(angular_correlation.real)] = 0
if iscomplex:
angular_correlation.imag[np.isinf(angular_correlation.imag)] = 0
if np.any(np.isnan(angular_correlation)):
warnings.warn(
"Some values in angular correlation occur inf. These values have been set to zeros."
)
angular_correlation.real[np.isnan(angular_correlation.real)] = 0
if iscomplex:
angular_correlation.imag[np.isnan(angular_correlation.imag)] = 0
# 4.
if clip:
factor = 3.0
for i, count in enumerate(unique_counts):
# minimum_sample_points = (4 / count) / resolution
indices[axis] = slice(unique_idx[i], unique_idx[i] + count)
mean = np.tile(angular_correlation[indices].mean(axis),
(count, 1)).T
std = np.tile(angular_correlation[indices].std(axis), (count, 1)).T
# print(mean)
# print(std)
vmin = mean.mean(axis) - factor * std.mean(axis)
vmax = mean.mean(axis) + factor * std.mean(axis)
# if np.all(std < 1e-16):
# # why ???
# warnings.warn("Standard deviation all equal to zero")
# vmin = mean.mean(axis) - factor * std.mean(axis)
# vmax = mean.mean(axis) + factor * std.mean(axis)
# else:
# # Normalize to N(0, 1)
# angular_correlation[indices] = (angular_correlation[indices] - mean) / std
# vmin = -factor
# vmax = +factor
angular_correlation[indices] = np.clip(
angular_correlation[indices].T, vmin,
vmax).T # set outlier to nearby boundary
# 5.
corr_trunc_slices = np.take(angular_correlation,
sorted_idx.argsort(),
axis=axis)
return corr_trunc_slices
def genphantomdata(N_D, phantompath, ctfparfile):
# mscope_params = {'akv': 200, 'wgh': 0.07,
# 'cs': 2.0, 'psize': 2.8, 'bfactor': 500.0}
mscope_params = {'akv': 200, 'wgh': 0.07,
'cs': 2.0, 'psize': 3.0, 'bfactor': 500.0}
M = mrc.readMRC(phantompath)
N = M.shape[0]
rad = 0.95
shift_sigma = 3.0
sigma_noise = 25.0
M_totalmass = 80000
kernel = 'lanczos'
ksize = 6
premult = cryoops.compute_premultiplier(N, kernel, ksize)
tic = time.time()
N_D = int(N_D)
N = int(N)
rad = float(rad)
psize = mscope_params['psize']
bfactor = mscope_params['bfactor']
shift_sigma = float(shift_sigma)
sigma_noise = float(sigma_noise)
M_totalmass = float(M_totalmass)
srcctf_stack = CTFStack(ctfparfile, mscope_params)
genctf_stack = GeneratedCTFStack(mscope_params, parfields=[
'PHI', 'THETA', 'PSI', 'SHX', 'SHY'])
TtoF = sincint.gentrunctofull(N=N, rad=rad)
Cmap = np.sort(np.random.random_integers(
0, srcctf_stack.get_num_ctfs() - 1, N_D))
cryoem.window(M, 'circle')
M[M < 0] = 0
if M_totalmass is not None:
M *= M_totalmass / M.sum()
V = density.real_to_fspace(
premult.reshape((1, 1, -1)) * premult.reshape((1, -1, 1)) * premult.reshape((-1, 1, 1)) * M)
print("Generating data...")
sys.stdout.flush()
imgdata = np.empty((N_D, N, N), dtype=density.real_t)
pardata = {'R': [], 't': []}
prevctfI = None
for i, srcctfI in enumerate(Cmap):
ellapse_time = time.time() - tic
remain_time = float(N_D - i) * ellapse_time / max(i, 1)
print("\r%.2f Percent.. (Elapsed: %s, Remaining: %s)" % (i / float(N_D)
* 100.0, format_timedelta(ellapse_time), format_timedelta(remain_time)))
sys.stdout.flush()
# Get the CTF for this image
cCTF = srcctf_stack.get_ctf(srcctfI)
if prevctfI != srcctfI:
genctfI = genctf_stack.add_ctf(cCTF)
C = cCTF.dense_ctf(N, psize, bfactor).reshape((N**2,))
prevctfI = srcctfI
# Randomly generate the viewing direction/shift
pt = np.random.randn(3)
pt /= np.linalg.norm(pt)
psi = 2 * np.pi * np.random.rand()
EA = geometry.genEA(pt)[0]
EA[2] = psi
shift = np.random.randn(2) * shift_sigma
R = geometry.rotmat3D_EA(*EA)[:, 0:2]
slop = cryoops.compute_projection_matrix(
[R], N, kernel, ksize, rad, 'rots')
S = cryoops.compute_shift_phases(shift.reshape((1, 2)), N, rad)[0]
D = slop.dot(V.reshape((-1,)))
D *= S
imgdata[i] = density.fspace_to_real((C * TtoF.dot(D)).reshape((N, N))) + np.require(
np.random.randn(N, N) * sigma_noise, dtype=density.real_t)
genctf_stack.add_img(genctfI,
PHI=EA[0] * 180.0 / np.pi, THETA=EA[1] * 180.0 / np.pi, PSI=EA[2] * 180.0 / np.pi,
SHX=shift[0], SHY=shift[1])
pardata['R'].append(R)
pardata['t'].append(shift)
print("\rDone in ", time.time() - tic, " seconds.")
return imgdata, genctf_stack, pardata, mscope_params
slices_sampled = cryoem.getslices(fM, slice_ops).reshape(
(EAs_grid.shape[0], trunc_xy.shape[0]))
premult_slices_sampled = cryoem.getslices(prefM, slice_ops).reshape(
(EAs_grid.shape[0], trunc_xy.shape[0]))
S = cryoops.compute_shift_phases(
np.asarray([100, -20]).reshape((1, 2)), N, rad)[0]
trunc_slice = slices_sampled[0]
premult_trunc_slice = premult_slices_sampled[0]
premult_trunc_slice_shift = S * premult_slices_sampled[0]
fourier_slice = TtoF.dot(trunc_slice).reshape((N, N))
real_proj = density.fspace_to_real(fourier_slice)
premult_fourier_slice = TtoF.dot(premult_trunc_slice).reshape((N, N))
premult_fourier_slice_shift = TtoF.dot(premult_trunc_slice_shift).reshape(
(N, N))
premult_real_proj = density.fspace_to_real(premult_fourier_slice)
premult_real_proj_shift = density.fspace_to_real(premult_fourier_slice_shift)
fig, axes = plt.subplots(2, 2)
ax = axes.flatten()
ax[0].imshow(real_proj)
ax[1].imshow(np.log(np.abs(fourier_slice)))
ax[2].imshow(premult_real_proj)
ax[3].imshow(np.log(np.abs(premult_fourier_slice)))
fig, axes = plt.subplots(2, 2)
ax = axes.flatten()
EAs_grid = healpix.gen_EAs_grid(nside=2, psi_step=360) Rs = [geometry.rotmat3D_EA(*EA)[:, 0:2] for EA in EAs_grid] slice_ops = cryoops.compute_projection_matrix(Rs, N, kern='lanczos', kernsize=ksize, rad=rad, projdirtype='rots') slices_sampled = cryoem.getslices(fM, slice_ops).reshape((EAs_grid.shape[0], trunc_xy.shape[0])) premult_slices_sampled = cryoem.getslices(prefM, slice_ops).reshape((EAs_grid.shape[0], trunc_xy.shape[0])) S = cryoops.compute_shift_phases(np.asarray([100, -20]).reshape((1,2)), N, rad)[0] trunc_slice = slices_sampled[0] premult_trunc_slice = premult_slices_sampled[0] premult_trunc_slice_shift = S * premult_slices_sampled[0] fourier_slice = TtoF.dot(trunc_slice).reshape((N, N)) real_proj = density.fspace_to_real(fourier_slice) premult_fourier_slice = TtoF.dot(premult_trunc_slice).reshape((N, N)) premult_fourier_slice_shift = TtoF.dot(premult_trunc_slice_shift).reshape((N, N)) premult_real_proj = density.fspace_to_real(premult_fourier_slice) premult_real_proj_shift = density.fspace_to_real(premult_fourier_slice_shift) fig, axes = plt.subplots(2, 2) ax = axes.flatten() ax[0].imshow(real_proj) ax[1].imshow(np.log(np.abs(fourier_slice))) ax[2].imshow(premult_real_proj) ax[3].imshow(np.log(np.abs(premult_fourier_slice))) fig, axes = plt.subplots(2, 2) ax = axes.flatten() ax[0].imshow(premult_real_proj)
def eval(self, M=None, fM=None, compute_gradient=True, all_grads=False,**kwargs):
anyfspace = any([obj.fspace for obj in self.objs])
anyrspace = any([not obj.fspace for obj in self.objs])
N = None
if fM is None and anyfspace:
assert M is not None, 'M or fM must be set!'
N = M.shape[0]
fM = density.real_to_fspace(M)
elif fM is not None:
N = fM.shape[0]
if M is None and anyrspace:
assert fM is not None, 'M or fM must be set!'
N = fM.shape[0]
M = density.fspace_to_real(fM)
elif M is not None:
assert N is None or N == M.shape[0]
N = M.shape[0]
assert N is not None
logP = 0
logPs = []
if compute_gradient:
if all_grads:
dlogP = density.zeros_like(fM) if self.fspace else density.zeros_like(M)
dlogPs = []
else:
if (not self.fspace) or anyrspace:
dlogPdM = density.zeros_like(M)
if self.fspace or anyfspace:
dlogPdfM = density.zeros_like(fM)
outputs = {}
for w,obj in zip(self.ws,self.objs):
if compute_gradient:
clogP, cdlogP, coutputs = obj.eval(M = M, fM = fM,
compute_gradient = compute_gradient,
**kwargs)
if w is not None and w != 1:
clogP *= w
cdlogP *= w
if all_grads:
if obj.fspace == self.fspace:
dlogPs.append(cdlogP)
elif self.fspace:
dlogPs.append(density.real_to_fspace(cdlogP))
else:
dlogPs.append(density.fspace_to_real(cdlogP))
dlogP += dlogPs[-1]
else:
if obj.fspace:
dlogPdfM += cdlogP
else:
dlogPdM += cdlogP
else:
clogP, coutputs = obj.eval(M = M, fM = fM,
compute_gradient = compute_gradient,
**kwargs)
if w is not None and w != 1:
clogP *= w
logP += clogP
logPs.append(clogP)
outputs.update(coutputs)
if compute_gradient and not all_grads:
if self.fspace:
dlogP = dlogPdfM
if anyrspace:
dlogP += density.real_to_fspace(dlogPdM)
else:
dlogP = dlogPdM
if anyfspace:
dlogP += density.fspace_to_real(dlogPdfM)
outputs['all_logPs'] = logPs
if compute_gradient and all_grads:
outputs['all_dlogPs'] = dlogPs
if compute_gradient:
return logP, dlogP, outputs
else:
return logP, outputs
