if '_'+algs[i]+'_' in f_i:
try:
f=df.HDF5File(bip.pde.mpi_comm,os.path.join(folder,f_i),"r")
samp_mean.zero(); samp_std.zero(); num_read=0
for s in range(num_samp):
if s+1 in prog:
print('{0:.0f}% has been completed.'.format(np.float(s+1)/num_samp*100))
f.read(samp_f,'sample_{0}'.format(s))
u=samp_f.vector()
if '_whitened_latent' in f_i: u=bip.prior.v2u(u)
if 'DREAM' in algs[i]:
if 'c' in AE:
u_latin=fun2img(vec2fun(u, elliptic_latent.pde.V))
width=tuple(np.mod(i,2) for i in u_latin.shape)
u_latin=chop(u_latin,width)[None,:,:,None] if autoencoder.activations['latent'] is None else u_latin.flatten()[None,:]
u=img2fun(pad(np.squeeze(autoencoder.decode(u_latin)),width),elliptic.pde.V).vector()
else:
u_latin=u.get_local()[None,:]
u=elliptic.prior.gen_vector(autoencoder.decode(u_latin).flatten())
# else:
# u=u_
if '_whitened_emulated' in f_i: u=elliptic.prior.v2u(u)
samp_mean.axpy(wts[s],u)
samp_std.axpy(wts[s],u*u)
# num_read+=1
f.close()
print(f_i+' has been read!')
f_read=f_i
found=True
except:
pass
# plot
import matplotlib.pyplot as plt
import matplotlib as mp
plt.rcParams['image.cmap'] = 'jet'
fig, axes = plt.subplots(nrows=1,
ncols=3,
sharex=True,
sharey=True,
figsize=(15, 5))
sub_figs = [None] * 3
# plot
plt.axes(axes.flat[0])
u_f.vector().set_local(dll_xact)
sub_figs[0] = df.plot(u_f)
plt.title('Calculated Gradient')
plt.axes(axes.flat[1])
u_f = img2fun(dll_cnn, elliptic.pde.V)
sub_figs[1] = df.plot(u_f)
plt.title('Emulated Gradient (CNN)')
plt.axes(axes.flat[2])
u_f = vec2fun(dll_dnn, elliptic.pde.V)
sub_figs[2] = df.plot(u_f)
plt.title('Emulated Gradient (DNN)')
# add common colorbar
from util.common_colorbar import common_colorbar
fig = common_colorbar(fig, axes, sub_figs)
# save plots
# fig.tight_layout(h_pad=1)
plt.savefig(os.path.join(folder, 'extrctgrad.png'), bbox_inches='tight')
# plt.show()
def geom(unknown_lat,
V_lat,
V,
autoencoder,
geom_ord=[0],
whitened=False,
**kwargs):
loglik = None
gradlik = None
metact = None
rtmetact = None
eigs = None
# un-whiten if necessary
if whitened == 'latent':
bip_lat = kwargs.get('bip_lat')
unknown_lat = bip_lat.prior.v2u(unknown_lat)
# u_latin={'AutoEncoder':unknown_lat.get_local()[None,:],'ConvAutoEncoder':chop(fun2img(vec2fun(unknown_lat, V_lat)))[None,:,:,None]}[type(autoencoder).__name__]
if 'Conv' in type(autoencoder).__name__:
u_latin = fun2img(vec2fun(unknown_lat, V_lat))
width = tuple(np.mod(i, 2) for i in u_latin.shape)
u_latin = chop(u_latin,
width)[None, :, :, None] if autoencoder.activations[
'latent'] is None else u_latin.flatten()[None, :]
unknown = img2fun(pad(np.squeeze(autoencoder.decode(u_latin)), width),
V).vector()
else:
u_latin = unknown_lat.get_local()[None, :]
unknown = df.Function(V).vector()
unknown.set_local(autoencoder.decode(u_latin).flatten())
emul_geom = kwargs.pop('emul_geom', None)
full_geom = kwargs.pop('full_geom', None)
bip_lat = kwargs.pop('bip_lat', None)
bip = kwargs.pop('bip', None)
try:
if len(kwargs) == 0:
loglik, gradlik, metact_, rtmetact_ = emul_geom(
unknown, geom_ord, whitened == 'emulated')
else:
loglik, gradlik, metact_, eigs_ = emul_geom(
unknown, geom_ord, whitened == 'emulated', **kwargs)
except:
try:
if len(kwargs) == 0:
loglik, gradlik, metact_, rtmetact_ = full_geom(
unknown, geom_ord, whitened == 'original')
else:
loglik, gradlik, metact_, eigs_ = full_geom(
unknown, geom_ord, whitened == 'original', **kwargs)
except:
raise RuntimeError('No geometry in the original space available!')
if any(s >= 1 for s in geom_ord):
if whitened == 'latent':
gradlik = bip.prior.C_act(gradlik, .5, op='C', transp=True)
# jac_=autoencoder.jacobian(u_latin,'decode')
if 'Conv' in type(autoencoder).__name__:
# if autoencoder.activations['latent'] is None:
# # jac__=np.zeros(jac_.shape[:2]+tuple(i+1 for i in jac_.shape[2:]))
# # jac__[:,:,:-1,:-1]=jac_; jac_=jac__
# jac_=pad(jac_,(0,)*2+width)
# jac_=jac_.reshape(jac_.shape[:2]+(-1,))
# d2v = df.dof_to_vertex_map(V_lat)
# jac_=jac_[:,:,d2v]
# jac=MultiVector(unknown,V_lat.dim())
# # [jac[i].set_local(img2fun(pad(jac_[:,:,i]), V).vector() if 'Conv' in type(autoencoder).__name__ else jac_[:,i]) for i in range(V_lat.dim())] # not working: too many indices?
# if 'Conv' in type(autoencoder).__name__:
# [jac[i].set_local(img2fun(pad(jac_[:,:,i],width), V).vector()) for i in range(V_lat.dim())] # for loop is too slow
# else:
# [jac[i].set_local(jac_[:,i]) for i in range(V_lat.dim()) for i in range(V_lat.dim())] # for loop is too slow
# gradlik_=jac.dot(gradlik)
jac_ = autoencoder.jacobian(u_latin, 'decode')
jac_ = pad(
jac_, width *
2 if autoencoder.activations['latent'] is None else width +
(0, ))
jac_ = jac_.reshape(
(np.prod(jac_.shape[:2]), np.prod(jac_.shape[2:])))
jac_ = jac_[np.ix_(df.dof_to_vertex_map(V),
df.dof_to_vertex_map(V_lat))]
# try:
# import timeit
# t_start=timeit.default_timer()
# jac=create_PETScMatrix(jac_.shape,V.mesh().mpi_comm(),range(jac_.shape[0]),range(jac_.shape[1]),jac_)
# gradlik_=df.as_backend_type(gradlik).vec()
# gradlik1=df.Vector(unknown_lat)
# jac.multTranspose(gradlik_,df.as_backend_type(gradlik1).vec())
# print('time consumed:{}'.format(timeit.default_timer()-t_start))
# except:
# t_start=timeit.default_timer()
gradlik_ = jac_.T.dot(gradlik.get_local())
gradlik_ = autoencoder.jacvec(u_latin, gradlik.get_local()[None, :])
gradlik = df.Vector(unknown_lat)
gradlik.set_local(gradlik_)
# print('time consumed:{}'.format(timeit.default_timer()-t_start))
if any(s >= 1.5 for s in geom_ord):
def _get_metact_misfit(u_actedon):
if type(u_actedon) is df.Vector:
u_actedon = u_actedon.get_local()
tmp = df.Vector(unknown)
tmp.zero()
jac.reduce(tmp, u_actedon)
v = df.Vector(unknown_lat)
v.set_local(jac.dot(metact_(tmp)))
return v
def _get_rtmetact_misfit(u_actedon):
if type(u_actedon) is not df.Vector:
u_ = df.Vector(unknown)
u_.set_local(u_actedon)
u_actedon = u_
v = df.Vector(unknown_lat)
v.set_local(jac.dot(rtmetact_(u_actedon)))
return v
metact = _get_metact_misfit
rtmetact = _get_rtmetact_misfit
if any(s > 1 for s in geom_ord) and len(kwargs) != 0:
if bip_lat is None:
raise ValueError('No latent inverse problem defined!')
# compute eigen-decomposition using randomized algorithms
if whitened == 'latent':
# generalized eigen-decomposition (_C^(1/2) F _C^(1/2), M), i.e. _C^(1/2) F _C^(1/2) = M V D V', V' M V = I
def invM(a):
a = bip_lat.prior.gen_vector(a)
invMa = bip_lat.prior.gen_vector()
bip_lat.prior.Msolver.solve(invMa, a)
return invMa
eigs = geigen_RA(metact,
lambda u: bip_lat.prior.M * u,
invM,
dim=bip_lat.pde.V.dim(),
**kwargs)
else:
# generalized eigen-decomposition (F, _C^(-1)), i.e. F = _C^(-1) U D U^(-1), U' _C^(-1) U = I, V = _C^(-1/2) U
eigs = geigen_RA(metact,
lambda u: bip_lat.prior.C_act(u, -1, op='K'),
lambda u: bip_lat.prior.C_act(u, op='K'),
dim=bip_lat.pde.V.dim(),
**kwargs)
if any(s > 1.5 for s in geom_ord):
# adjust the gradient
# update low-rank approximate Gaussian posterior
bip_lat.post_Ga = Gaussian_apx_posterior(bip_lat.prior, eigs=eigs)
# Hu = bip_lat.prior.gen_vector()
# bip_lat.post_Ga.Hlr.mult(unknown, Hu)
# gradlik.axpy(1.0,Hu)
if len(kwargs) == 0:
return loglik, gradlik, metact, rtmetact
else:
return loglik, gradlik, metact, eigs
# u_decoded=cae.model.predict(chop(fun2img(u_f))[None,:,:,None])
# compute the log-volumes
# logvol_enc=cae.logvol(chop(fun2img(u_f))[None,:,:,None],'encode')
# print('Log-volume of encoder: {}'.format(logvol_enc))
# logvol_dec=cae.logvol(u_encoded,'decode')
# print('Log-volume of decoder: {}'.format(logvol_dec))
# plot
plt.subplot(131)
u_f.vector().set_local(u)
df.plot(u_f)
plt.title('Original Sample')
plt.subplot(132)
if activations['latent'] is None:
u_f_lat = img2fun(pad(np.squeeze(u_encoded)), elliptic_latent.pde.V)
else:
u_f_lat.vector().set_local(u_encoded.flatten())
# u_f_lat=img2fun(u_encoded.reshape((nx+1,ny+1)),elliptic_latent.pde.V)
df.plot(u_f_lat)
plt.title('Latent Sample')
plt.subplot(133)
u_decoded = np.squeeze(u_decoded)
# u_decoded*=X_max; u_decoded+=X_min
u_f = img2fun(pad(u_decoded), elliptic.pde.V)
df.plot(u_f)
plt.title('Reconstructed Sample')
plt.draw()
plt.pause(1.0 / 10.0)
# read data and construct plot functions
dif_fun = np.abs(ll_xact - ll_emul)
dif_grad = dll_xact.get_local() - dll_emul
fun_errors[0, s, t, n] = dif_fun
grad_errors[0, s, t,
n] = np.linalg.norm(dif_grad) / dll_xact.norm('l2')
# emulation by CNN
t_start = timeit.default_timer()
u_img = fun2img(vec2fun(u, elliptic.pde.V))
ll_emul = logLik_c(u_img[None, :, :, None]).numpy()
dll_emul = cnn.gradient(u_img[None, :, :, None],
logLik_c) #* grad_scalfctr
t_used[2] += timeit.default_timer() - t_start
# record difference
dif_fun = np.abs(ll_xact - ll_emul)
dif_grad = dll_xact - img2fun(dll_emul,
elliptic.pde.V).vector()
fun_errors[1, s, t, n] = dif_fun
grad_errors[1, s, t,
n] = dif_grad.norm('l2') / dll_xact.norm('l2')
print(
'Time used for calculation: {} vs GP-emulation: {} vs CNN-emulation: {}'
.format(*t_used.tolist()))
pred_times[0, s, t] = t_used[1]
pred_times[1, s, t] = t_used[2]
pred_times[2, s, t] = t_used[0]
# save results
with open(os.path.join(folder, 'compare_gp_cnn.pckl'), 'wb') as f:
pickle.dump([fun_errors, grad_errors, train_times, pred_times], f)
# plt.show(block=True)
u_f = df.Function(elliptic.pde.V)
for n in range(20):
u = elliptic.prior.sample()
# calculate gradient
t_start = timeit.default_timer()
dll_xact = elliptic.get_geom(u, [0, 1])[1]
t_used[0] += timeit.default_timer() - t_start
# emulate gradient
t_start = timeit.default_timer()
u_img = fun2img(vec2fun(u, elliptic.pde.V))
dll_emul = cnn.gradient(u_img[None, :, :, None], logLik)
t_used[1] += timeit.default_timer() - t_start
# test difference
dif = dll_xact - img2fun(dll_emul, elliptic.pde.V).vector()
print(
'Difference between the calculated and emulated gradients: min ({}), med ({}), max ({})'
.format(dif.min(), np.median(dif.get_local()), dif.max()))
# check the gradient extracted from emulation with finite difference
v = elliptic.prior.sample()
v_img = fun2img(vec2fun(v, elliptic.pde.V))
h = 1e-4
dll_emul_fd_v = (
logLik(u_img[None, :, :, None] + h * v_img[None, :, :, None]) -
logLik(u_img[None, :, :, None])) / h
reldif = abs(dll_emul_fd_v -
dll_emul.flatten().dot(v_img.flatten())) / v.norm('l2')
print(
'Relative difference between finite difference and extracted results: {}'
def geom(unknown, bip, emulator, geom_ord=[0], whitened=False, **kwargs):
loglik = None
gradlik = None
metact = None
rtmetact = None
eigs = None
# un-whiten if necessary
if whitened:
unknown = bip.prior.v2u(unknown)
u_input = {
'DNN': unknown.get_local()[None, :],
'CNN': fun2img(vec2fun(unknown, bip.pde.V))[None, :, :, None]
}[type(emulator).__name__]
ll_f = lambda x: -0.5 * bip.misfit.prec * tf.math.reduce_sum(
(emulator.model(x) - bip.misfit.obs)**2, axis=1)
if any(s >= 0 for s in geom_ord):
loglik = ll_f(u_input).numpy()
if any(s >= 1 for s in geom_ord):
gradlik_ = emulator.gradient(u_input, ll_f)
# gradlik = {'DNN':bip.prior.gen_vector(gradlik_), 'CNN':img2fun(gradlik_, bip.pde.V).vector()}[type(emulator).__name__] # not working
if type(emulator).__name__ == 'DNN':
gradlik = bip.prior.gen_vector(gradlik_)
elif type(emulator).__name__ == 'CNN':
gradlik = img2fun(gradlik_, bip.pde.V).vector()
if whitened:
gradlik = bip.prior.C_act(gradlik, .5, op='C', transp=True)
if any(s >= 1.5 for s in geom_ord):
jac_ = emulator.jacobian(u_input)
n_obs = len(bip.misfit.idx)
jac = MultiVector(unknown, n_obs)
[
jac[i].set_local({
'DNN': jac_[i],
'CNN': img2fun(jac_[i], bip.pde.V).vector()
}[type(emulator).__name__]) for i in range(n_obs)
]
def _get_metact_misfit(u_actedon): # GNH
if type(u_actedon) is not df.Vector:
u_actedon = bip.prior.gen_vector(u_actedon)
v = bip.prior.gen_vector()
jac.reduce(v, bip.misfit.prec * jac.dot(u_actedon))
return bip.prior.M * v
def _get_rtmetact_misfit(u_actedon):
if type(u_actedon) is df.Vector:
u_actedon = u_actedon.get_local()
v = bip.prior.gen_vector()
jac.reduce(v, np.sqrt(bip.misfit.prec) * u)
return bip.prior.rtM * v
metact = _get_metact_misfit
rtmetact = _get_rtmetact_misfit
if whitened:
metact = lambda u: bip.prior.C_act(_get_metact_misfit(
bip.prior.C_act(u, .5, op='C')),
.5,
op='C',
transp=True) # ppGNH
rtmetact = lambda u: bip.prior.C_act(
_get_rtmetact_misfit(u), .5, op='C', transp=True)
if any(s > 1 for s in geom_ord) and len(kwargs) != 0:
if whitened:
# generalized eigen-decomposition (_C^(1/2) F _C^(1/2), M), i.e. _C^(1/2) F _C^(1/2) = M V D V', V' M V = I
def invM(a):
a = bip.prior.gen_vector(a)
invMa = bip.prior.gen_vector()
bip.prior.Msolver.solve(invMa, a)
return invMa
eigs = geigen_RA(metact,
lambda u: bip.prior.M * u,
invM,
dim=bip.pde.V.dim(),
**kwargs)
else:
# generalized eigen-decomposition (F, _C^(-1)), i.e. F = _C^(-1) U D U^(-1), U' _C^(-1) U = I, V = _C^(-1/2) U
eigs = geigen_RA(metact,
lambda u: bip.prior.C_act(u, -1, op='K'),
lambda u: bip.prior.C_act(u, op='K'),
dim=bip.pde.V.dim(),
**kwargs)
if any(s > 1.5 for s in geom_ord):
# adjust the gradient
# update low-rank approximate Gaussian posterior
bip.post_Ga = Gaussian_apx_posterior(bip.prior, eigs=eigs)
Hu = bip.prior.gen_vector()
bip.post_Ga.Hlr.mult(unknown, Hu)
gradlik.axpy(1.0, Hu)
if len(kwargs) == 0:
return loglik, gradlik, metact, rtmetact
else:
return loglik, gradlik, metact, eigs
dll_emul = cnn.gradient(u_img[None, :, :, None], loglik)
t_used[1] += timeit.default_timer() - t_start
# test difference
dif = dll_xact - dll_emul.img2fun(dll_emul, elliptic.pde.V).vector()
print(
'Difference between the calculated and emulated gradients: min ({}), med ({}), max ({})'
.format(dif.min(), np.median(dif.get_local()), dif.max()))
# # check the gradient extracted from emulation
# v=elliptic.prior.sample()
# v_img=fun2img(vec2fun(v,elliptic.pde.V))
# h=1e-4
# dll_emul_fd_v=(loglik(u_img[None,:,:,None]+h*v_img[None,:,:,None])-loglik(u_img[None,:,:,None]))/h
# reldif = abs(dll_emul_fd_v - dll_emul.flatten().dot(v_img.flatten()))/v.norm('l2')
# print('Relative difference between finite difference and extracted results: {}'.format(reldif))
# plot
plt.subplot(121)
u_f.vector().set_local(dll_xact)
df.plot(u_f)
plt.title('Calculated')
plt.subplot(122)
u_f = img2fun(dll_emul)
df.plot(u_f)
plt.title('Emulated')
plt.draw()
plt.pause(1.0 / 30.0)
print(
'Time used to calculate vs emulate gradients: {} vs {}'.format(t_used))
plt.ion()
# plt.show(block=True)
u_f = df.Function(elliptic.pde.V)
for n in range(10):
u = elliptic.prior.sample()
# calculate gradient
t_start = timeit.default_timer()
dll_xact = elliptic.get_geom(u, [0, 1])[1]
t_used[0] += timeit.default_timer() - t_start
# emulate gradient
t_start = timeit.default_timer()
u_img = fun2img(vec2fun(u, elliptic.pde.V))
dll_emul = cnn.gradient(u_img[None, :, :, None], loglik)
t_used[1] += timeit.default_timer() - t_start
# test difference
dif = dll_xact - img2fun(dll_emul, elliptic.pde.V).vector()
print(
'Difference between the calculated and emulated gradients: min ({}), med ({}), max ({})'
.format(dif.min(), np.median(dif.get_local()), dif.max()))
# # check the gradient extracted from emulation
# v=elliptic.prior.sample()
# v_img=fun2img(vec2fun(v,elliptic.pde.V))
# h=1e-4
# dll_emul_fd_v=(loglik(u_img[None,:,:,None]+h*v_img[None,:,:,None])-loglik(u_img[None,:,:,None]))/h
# reldif = abs(dll_emul_fd_v - dll_emul.flatten().dot(v_img.flatten()))/v.norm('l2')
# print('Relative difference between finite difference and extracted results: {}'.format(reldif))
# plot
plt.subplot(121)
u_f.vector().set_local(dll_xact)