def get_sigma2_map(self,nu,model,rotavg=True):
N = self.cryodata.N
N_D = float(self.cryodata.N_D_Train)
num_batches = float(self.cryodata.num_batches)
base_sigma2 = self.cryodata.get_noise_std()**2
mean_sigma2 = self.error_history.get_mean().reshape((N,N))
mean_mask = self.mask_history.get_mean().reshape((N,N))
mask_w = self.mask_history.get_wsum() * (N_D / num_batches)
if rotavg:
mean_sigma2 = cryoem.rotational_average(mean_sigma2,normalize=True,doexpand=True)
mean_mask = cryoem.rotational_average(mean_mask,normalize=False,doexpand=True)
obsw = mask_w * mean_mask
map_sigma2 = (mean_sigma2 * obsw + nu * base_sigma2) / (obsw + nu)
assert np.all(np.isfinite(map_sigma2))
if model == 'coloured':
map_sigma2 = map_sigma2
elif model == 'white':
map_sigma2 = np.mean(map_sigma2)
else:
assert False, 'model must be one of white or coloured'
return map_sigma2
def get_envelope_map(self,
sigma2,
rho,
env_lb=None,
env_ub=None,
minFreq=None,
bfactor=None,
rotavg=True):
N = self.cryodata.N
N_D = float(self.cryodata.N_D_Train)
num_batches = float(self.cryodata.num_batches)
psize = self.params['pixel_size']
mean_corr = self.correlation_history.get_mean().reshape((N, N))
mean_power = self.power_history.get_mean().reshape((N, N))
mean_mask = self.mask_history.get_mean().reshape((N, N))
mask_w = self.mask_history.get_wsum() * (N_D / num_batches)
if rotavg:
mean_corr = cryoem.rotational_average(mean_corr,
normalize=True,
doexpand=True)
mean_power = cryoem.rotational_average(mean_power,
normalize=True,
doexpand=True)
mean_mask = cryoem.rotational_average(mean_mask,
normalize=False,
doexpand=True)
if isinstance(sigma2, n.ndarray):
sigma2 = sigma2.reshape((N, N))
if bfactor is not None:
coords = gencoords(N, 2).reshape((N**2, 2))
freqs = n.sqrt(n.sum(coords**2, axis=1)) / (psize * N)
prior_envelope = ctf.envelope_function(freqs, bfactor).reshape(
(N, N))
else:
prior_envelope = 1.0
obsw = (mask_w * mean_mask / sigma2)
exp_env = (mean_corr * obsw +
prior_envelope * rho) / (mean_power * obsw + rho)
if minFreq is not None:
# Only consider envelope parameters for frequencies above a threshold
minRad = minFreq * 2.0 * psize
_, _, minRadMask = gencoords(N, 2, minRad, True)
exp_env[minRadMask.reshape((N, N))] = 1.0
if env_lb is not None or env_ub is not None:
n.clip(exp_env, env_lb, env_ub, out=exp_env)
return exp_env
def get_envelope_mle(self,rotavg=False):
N = self.cryodata.N
mean_corr = self.correlation_history.get_mean()
mean_power = self.power_history.get_mean()
mean_mask = self.mask_history.get_mean()
if rotavg:
mean_corr = cryoem.rotational_average(mean_corr.reshape((N,N)),doexpand=True)
mean_power = cryoem.rotational_average(mean_power.reshape((N,N)),doexpand=True)
mean_mask = cryoem.rotational_average(mean_mask.reshape((N,N)),doexpand=True)
obs_mask = mean_mask > 0
exp_env = np.ones_like(mean_corr)
exp_env[obs_mask] = (mean_corr[obs_mask] / mean_power[obs_mask])
return exp_env.reshape((N,N))
def rot_power_spectra(fM,powerLen = None,resolution = None):
if resolution == None:
resolution = 1
powerfM = fM.real**2 + fM.imag**2
raps = cryoem.rotational_average(powerfM,powerLen)
radius = np.linspace(0,len(raps)-1,len(raps))
return (radius,raps)
def rot_power_spectra(fM,powerLen = None,resolution = None):
if resolution == None:
resolution = 1
powerfM = fM.real**2 + fM.imag**2
raps = c.rotational_average(powerfM,powerLen)
radius = n.linspace(0,len(raps)-1,len(raps))
return (radius,raps)
def get_envelope_map(self,sigma2,rho,env_lb=None,env_ub=None,minFreq=None,bfactor=None,rotavg=True):
N = self.cryodata.N
N_D = float(self.cryodata.N_D_Train)
num_batches = float(self.cryodata.num_batches)
psize = self.params['pixel_size']
mean_corr = self.correlation_history.get_mean().reshape((N,N))
mean_power = self.power_history.get_mean().reshape((N,N))
mean_mask = self.mask_history.get_mean().reshape((N,N))
mask_w = self.mask_history.get_wsum() * (N_D / num_batches)
if rotavg:
mean_corr = cryoem.rotational_average(mean_corr,normalize=True,doexpand=True)
mean_power = cryoem.rotational_average(mean_power,normalize=True,doexpand=True)
mean_mask = cryoem.rotational_average(mean_mask,normalize=False,doexpand=True)
if isinstance(sigma2,np.ndarray):
sigma2 = sigma2.reshape((N,N))
if bfactor is not None:
coords = gencoords(N,2).reshape((N**2,2))
freqs = np.sqrt(np.sum(coords**2,axis=1))/(psize*N)
prior_envelope = ctf.envelope_function(freqs,bfactor).reshape((N,N))
else:
prior_envelope = 1.0
obsw = (mask_w * mean_mask / sigma2)
exp_env = (mean_corr * obsw + prior_envelope*rho) / (mean_power * obsw + rho)
if minFreq is not None:
# Only consider envelope parameters for frequencies above a threshold
minRad = minFreq*2.0*psize
_, _, minRadMask = gencoords(N, 2, minRad, True)
exp_env[minRadMask.reshape((N,N))] = 1.0
if env_lb is not None or env_ub is not None:
np.clip(exp_env,env_lb,env_ub,out=exp_env)
return exp_env
def show_noise_plot(self,cfig):
cdiag = self.diag
cparams = cdiag['params']
vox_size = cparams['voxel_size']
name = cparams['name']
maxfreq = cparams['max_frequency']
N = self.M.shape[0]
rad_cutoff = cparams.get('rad_cutoff', 1.0)
rad = min(rad_cutoff,maxfreq*2.0*vox_size)
startI = int((1-rad)*N/2)+1
endI = N/2 + int(rad*N/2)+1
imextent = [startI-(N+1.0)/2,endI-(N+1.0)/2,startI-(N+1.0)/2,endI-(N+1.0)/2]
imextent = [e/(2.0*vox_size)/(N/2) for e in imextent]
sigma_est = cparams['sigma']
sigma_mle = np.sqrt(cdiag['sigma2_mle'])
train_sigma_est = np.sqrt(cdiag['train_sigma2_est']).reshape((N,N))
test_sigma_est = np.sqrt(cdiag['test_sigma2_est']).reshape((N,N))
showsigma = isinstance(sigma_est,np.ndarray)
vmin = min([np.min(sigma_est),sigma_mle[startI:endI,startI:endI].min()])
vmax = max([np.max(sigma_est),sigma_mle[startI:endI,startI:endI].max()])
imshow_kws = { 'interpolation':'nearest', \
'vmin':vmin, 'vmax':vmax, 'extent':imextent, \
'norm':LogNorm(vmin=vmin, vmax=vmax) }
cbaxs = []
plt.figure(cfig.number)
plt.clf()
plt.subplot(2,1,1)
raps = np.sqrt(cryoem.rotational_average(train_sigma_est**2))
fs = np.linspace(0,(len(raps)-1)/(N/2.0)/(2.0*vox_size),len(raps))
plt.plot(fs,raps,label='Training RMSE')
raps = np.sqrt(cryoem.rotational_average(test_sigma_est**2))
fs = np.linspace(0,(len(raps)-1)/(N/2.0)/(2.0*vox_size),len(raps))
plt.plot(fs,raps,label='Testing RMSE')
plt.legend()
plt.grid()
if showsigma:
cbaxs.append(plt.subplot(2,2,3))
else:
cbaxs.append(plt.subplot(2,1,2))
im = plt.imshow(sigma_mle[startI:endI,startI:endI], **imshow_kws)
plt.title('Freq RMSE (MLE)')
if showsigma:
sigma_est = sigma_est.reshape((N,N))
cbaxs.append(plt.subplot(2,2,4))
im = plt.imshow(sigma_est[startI:endI,startI:endI], **imshow_kws)
plt.title('Coloured Noise Std Dev')
plt.subplot(2,1,1)
if showsigma:
raps = np.sqrt(cryoem.rotational_average(sigma_est**2))
fs = np.linspace(0,(len(raps)-1)/(N/2.0)/(2.0*vox_size),len(raps))
else:
raps = [sigma_est,sigma_est]
fs = [fs[0],fs[-1]]
plt.plot(fs,raps,label='Noise Std Dev')
plt.xlim((0,rad/(2.0*vox_size)))
plt.yscale('log',basey=2)
plt.legend()
plt.title(name + ' Noise Levels')
plt.colorbar(im, ax=cbaxs, ticks=LogLocator(base=2), format=LogFormatterMathtext(base=2))
def show_envelope_plot(self,cfig):
cdiag = self.diag
cparams = cdiag['params']
resolution = cparams['pixel_size']
name = cparams['name']
maxfreq = cparams['max_frequency']
N = self.M.shape[0]
rad_cutoff = cparams.get('rad_cutoff', 1.0)
rad = min(rad_cutoff,maxfreq*2.0*resolution)
envelope_mle = cdiag['envelope_mle']
vmin = envelope_mle.min()
vmax = envelope_mle.max()
exp_envelope = cparams.get('exp_envelope',None)
have_exp = exp_envelope is not None
if have_exp:
vmin = exp_envelope.min()
vmax = exp_envelope.max()
startI = int((1-rad)*N/2)+1
endI = N/2 + int(rad*N/2)+1
imextent = [startI-(N+1.0)/2,endI-(N+1.0)/2,startI-(N+1.0)/2,endI-(N+1.0)/2]
imextent = [e/(2.0*resolution)/(N/2) for e in imextent]
cbaxs = []
plt.figure(cfig.number)
plt.clf()
cbaxs.append(plt.subplot(2,1+have_exp,1))
im = plt.imshow(envelope_mle[startI:endI,startI:endI], interpolation='nearest',
vmin=vmin, vmax=vmax, extent=imextent)
plt.title('ML')
if have_exp:
cbaxs.append(plt.subplot(2,2,2))
plt.imshow(exp_envelope[startI:endI,startI:endI], interpolation='nearest',
vmin=vmin, vmax=vmax, extent=imextent)
plt.title('MAP')
plt.colorbar(im,ax=cbaxs)
env_max = 1.0
env_min = 0.0
bfactor = cparams.get('learn_like_envelope_bfactor',500.0)
have_bfactor = bfactor is not None
if have_bfactor:
plt.subplot(2,1,2)
(fs,bfactor_env) = get_env_func(N, resolution=resolution,
bfactor=bfactor)
plt.plot(fs,bfactor_env,label='Prior (bfactor {0})'.format(bfactor),linewidth=2)
env_max = max(env_max,bfactor_env.max())
env_min = min(env_min,bfactor_env.min())
else:
fs = np.linspace(0,1.0/(2.0*resolution),N/2)
bfactor_env = 1.0
ra_mle_envelope = cryoem.rotational_average(envelope_mle,maxRadius=N/2)
plt.plot(fs[0:int(rad*N/2)],ra_mle_envelope[0:int(rad*N/2)],label='ML')
env_max = max(env_max,ra_mle_envelope.max())
env_min = min(env_min,ra_mle_envelope.min())
if have_exp:
ra_exp_envelope = cryoem.rotational_average(exp_envelope,maxRadius=N/2)
plt.plot(fs[0:N/2],ra_exp_envelope[0:N/2],label='MAP',linewidth=2)
env_max = max(env_max,ra_exp_envelope.max())
env_min = min(env_min,ra_exp_envelope.min())
plt.legend()
plt.grid()
plt.plot((rad/(2.0*resolution))*np.ones((2,)), np.array([env_min,env_max]))
plt.suptitle(name + ' Envelope')
def show_noise_plot(self,cfig):
cdiag = self.diag
cparams = cdiag['params']
vox_size = cparams['voxel_size']
name = cparams['name']
maxfreq = cparams['max_frequency']
N = self.M.shape[0]
rad_cutoff = cparams.get('rad_cutoff', 1.0)
rad = min(rad_cutoff,maxfreq*2.0*vox_size)
startI = int((1-rad)*N/2)+1
endI = N/2 + int(rad*N/2)+1
imextent = [startI-(N+1.0)/2,endI-(N+1.0)/2,startI-(N+1.0)/2,endI-(N+1.0)/2]
imextent = [e/(2.0*vox_size)/(N/2) for e in imextent]
sigma_est = cparams['sigma']
sigma_mle = n.sqrt(cdiag['sigma2_mle'])
train_sigma_est = n.sqrt(cdiag['train_sigma2_est']).reshape((N,N))
test_sigma_est = n.sqrt(cdiag['test_sigma2_est']).reshape((N,N))
showsigma = isinstance(sigma_est,n.ndarray)
vmin = min([n.min(sigma_est),sigma_mle[startI:endI,startI:endI].min()])
vmax = max([n.max(sigma_est),sigma_mle[startI:endI,startI:endI].max()])
imshow_kws = { 'interpolation':'nearest', \
'vmin':vmin, 'vmax':vmax, 'extent':imextent, \
'norm':LogNorm(vmin=vmin, vmax=vmax) }
cbaxs = []
plt.figure(cfig.number)
plt.clf()
plt.subplot(2,1,1)
raps = n.sqrt(c.rotational_average(train_sigma_est**2))
fs = n.linspace(0,(len(raps)-1)/(N/2.0)/(2.0*vox_size),len(raps))
plt.plot(fs,raps,label='Training RMSE')
raps = n.sqrt(c.rotational_average(test_sigma_est**2))
fs = n.linspace(0,(len(raps)-1)/(N/2.0)/(2.0*vox_size),len(raps))
plt.plot(fs,raps,label='Testing RMSE')
plt.legend()
plt.grid()
if showsigma:
cbaxs.append(plt.subplot(2,2,3))
else:
cbaxs.append(plt.subplot(2,1,2))
im = plt.imshow(sigma_mle[startI:endI,startI:endI], **imshow_kws)
plt.title('Freq RMSE (MLE)')
if showsigma:
sigma_est = sigma_est.reshape((N,N))
cbaxs.append(plt.subplot(2,2,4))
im = plt.imshow(sigma_est[startI:endI,startI:endI], **imshow_kws)
plt.title('Coloured Noise Std Dev')
plt.subplot(2,1,1)
if showsigma:
raps = n.sqrt(c.rotational_average(sigma_est**2))
fs = n.linspace(0,(len(raps)-1)/(N/2.0)/(2.0*vox_size),len(raps))
else:
raps = [sigma_est,sigma_est]
fs = [fs[0],fs[-1]]
plt.plot(fs,raps,label='Noise Std Dev')
plt.xlim((0,rad/(2.0*vox_size)))
plt.yscale('log',basey=2)
plt.legend()
plt.title(name + ' Noise Levels')
plt.colorbar(im, ax=cbaxs, ticks=LogLocator(base=2), format=LogFormatterMathtext(base=2))
def show_envelope_plot(self,cfig):
cdiag = self.diag
cparams = cdiag['params']
resolution = cparams['pixel_size']
name = cparams['name']
maxfreq = cparams['max_frequency']
N = self.M.shape[0]
rad_cutoff = cparams.get('rad_cutoff', 1.0)
rad = min(rad_cutoff,maxfreq*2.0*resolution)
envelope_mle = cdiag['envelope_mle']
vmin = envelope_mle.min()
vmax = envelope_mle.max()
exp_envelope = cparams.get('exp_envelope',None)
have_exp = exp_envelope is not None
if have_exp:
vmin = exp_envelope.min()
vmax = exp_envelope.max()
startI = int((1-rad)*N/2)+1
endI = N/2 + int(rad*N/2)+1
imextent = [startI-(N+1.0)/2,endI-(N+1.0)/2,startI-(N+1.0)/2,endI-(N+1.0)/2]
imextent = [e/(2.0*resolution)/(N/2) for e in imextent]
cbaxs = []
plt.figure(cfig.number)
plt.clf()
cbaxs.append(plt.subplot(2,1+have_exp,1))
im = plt.imshow(envelope_mle[startI:endI,startI:endI], interpolation='nearest',
vmin=vmin, vmax=vmax, extent=imextent)
plt.title('ML')
if have_exp:
cbaxs.append(plt.subplot(2,2,2))
plt.imshow(exp_envelope[startI:endI,startI:endI], interpolation='nearest',
vmin=vmin, vmax=vmax, extent=imextent)
plt.title('MAP')
plt.colorbar(im,ax=cbaxs)
env_max = 1.0
env_min = 0.0
bfactor = cparams.get('learn_like_envelope_bfactor',500.0)
have_bfactor = bfactor is not None
if have_bfactor:
plt.subplot(2,1,2)
(fs,bfactor_env) = get_env_func(N, resolution=resolution,
bfactor=bfactor)
plt.plot(fs,bfactor_env,label='Prior (bfactor {0})'.format(bfactor),linewidth=2)
env_max = max(env_max,bfactor_env.max())
env_min = min(env_min,bfactor_env.min())
else:
fs = n.linspace(0,1.0/(2.0*resolution),N/2)
bfactor_env = 1.0
ra_mle_envelope = c.rotational_average(envelope_mle,maxRadius=N/2)
plt.plot(fs[0:int(rad*N/2)],ra_mle_envelope[0:int(rad*N/2)],label='ML')
env_max = max(env_max,ra_mle_envelope.max())
env_min = min(env_min,ra_mle_envelope.min())
if have_exp:
ra_exp_envelope = c.rotational_average(exp_envelope,maxRadius=N/2)
plt.plot(fs[0:N/2],ra_exp_envelope[0:N/2],label='MAP',linewidth=2)
env_max = max(env_max,ra_exp_envelope.max())
env_min = min(env_min,ra_exp_envelope.min())
plt.legend()
plt.grid()
plt.plot((rad/(2.0*resolution))*n.ones((2,)), n.array([env_min,env_max]))
plt.suptitle(name + ' Envelope')
