def run_invsigma(config_file):
"""Compute control sigma values from eigendecomposition"""
comm = MPI.comm_world
rank = comm.rank
# Read run config file
params = ConfigParser(config_file)
# Setup logging
log = inout.setup_logging(params)
inout.log_preamble("inv sigma", params)
outdir = params.io.output_dir
diags_dir = params.io.diagnostics_dir
# Load the static model data (geometry, smb, etc)
input_data = inout.InputData(params)
# Eigen decomposition params
phase_suffix_e = params.eigendec.phase_suffix
eigendir = Path(outdir)/params.eigendec.phase_name/phase_suffix_e
lamfile = params.io.eigenvalue_file
vecfile = params.io.eigenvecs_file
threshlam = params.eigendec.eigenvalue_thresh
if len(phase_suffix_e) > 0:
lamfile = params.io.run_name + phase_suffix_e + '_eigvals.p'
vecfile = params.io.run_name + phase_suffix_e + '_vr.h5'
# Get model mesh
mesh = fice_mesh.get_mesh(params)
# Define the model (only need alpha & beta though)
mdl = model.model(mesh, input_data, params, init_fields=True)
# Load alpha/beta fields
mdl.alpha_from_inversion()
mdl.beta_from_inversion()
mdl.bglen_from_data(mask_only=True)
# Setup our solver object
slvr = solver.ssa_solver(mdl, mixed_space=params.inversion.dual)
cntrl = slvr.get_control()[0]
space = slvr.get_control_space()
# sigma_old, sigma_prior_old = [Function(space) for i in range(3)]
x, y, z = [Function(space) for i in range(3)]
# Regularization operator using inversion delta/gamma values
Prior = mdl.get_prior()
reg_op = Prior(slvr, space)
# Load the eigenvalues
with open(os.path.join(eigendir, lamfile), 'rb') as ff:
eigendata = pickle.load(ff)
lam = eigendata[0].real.astype(np.float64)
nlam = len(lam)
# Check if eigendecomposition successfully produced num_eig
# or if some are NaN
if np.any(np.isnan(lam)):
nlam = np.argwhere(np.isnan(lam))[0][0]
lam = lam[:nlam]
# Read in the eigenvectors and check they are normalised
# w.r.t. the prior (i.e. the B matrix in our GHEP)
eps = params.constants.float_eps
W = []
with HDF5File(comm,
os.path.join(eigendir, vecfile), 'r') as hdf5data:
for i in range(nlam):
w = Function(space)
hdf5data.read(w, f'v/vector_{i}')
print(f"Getting eigenvector {i} of {nlam}")
# # Test norm in prior == 1.0
# reg_op.action(w.vector(), y.vector())
# norm_in_prior = w.vector().inner(y.vector())
# assert (abs(norm_in_prior - 1.0) < eps)
W.append(w)
# Which eigenvalues are larger than our threshold?
pind = np.flatnonzero(lam > threshlam)
lam = lam[pind]
W = [W[i] for i in pind]
# this is a diagonal matrix but we only ever address it element-wise
# bit of a waste of space.
D = np.diag(lam / (lam + 1))
# TODO make this a model method
cntrl_names = []
if params.inversion.alpha_active:
cntrl_names.append("alpha")
if params.inversion.beta_active:
cntrl_names.append("beta")
dual = params.inversion.dual
############################################
# Isaac Eq. 20
# P2 = prior
# P1 = WDW
# Note - don't think we're considering the cross terms
# in the posterior covariance.
# Generate patches of cells for computing invsigma
clust_fun, npatches = patch_fun(mesh, params)
# Create standard & mixed DG spaces
dg_space = FunctionSpace(mesh, 'DG', 0)
if(dual):
dg_el = FiniteElement("DG", mesh.ufl_cell(), 0)
mixedEl = dg_el * dg_el
dg_out_space = FunctionSpace(mesh, mixedEl)
else:
dg_out_space = dg_space
sigmas = [Function(dg_space) for i in range(len(cntrl_names))]
sigma_priors = [Function(dg_space) for i in range(len(cntrl_names))]
indic_1 = Function(dg_space)
indic = Function(dg_out_space)
test = TestFunction(space)
neg_flag = 0
for i in range(npatches):
print(f"Working on patch {i+1} of {npatches}")
# Create DG indicator function for patch i
indic_1.vector()[:] = (clust_fun.vector()[:] == i).astype(int)
indic_1.vector().apply("insert")
# Loop alpha & beta as appropriate
for j in range(len(cntrl_names)):
if(dual):
indic.vector()[:] = 0.0
indic.vector().apply("insert")
assign(indic.sub(j), indic_1)
else:
assign(indic, indic_1)
clust_lump = assemble(inner(indic, test)*dx)
patch_area = clust_lump.sum() # Duplicate work here...
clust_lump /= patch_area
# Prior variance
reg_op.inv_action(clust_lump, x.vector())
cov_prior = x.vector().inner(clust_lump)
# P_i^T W D W^T P_i
# P_i is clust_lump
# P_i^T has dims [1 x M], W has dims [M x N]
# where N is num eigs & M is size of ev function space
PiW = np.asarray([clust_lump.inner(w.vector()) for w in W])
# PiW & PiWD are [1 x N]
PiWD = PiW * D.diagonal()
# PiWDWPi, [1 x N] * [N x 1]
PiWDWPi = np.inner(PiWD, PiW) # np.inner OK here because already parallel reduced
cov_reduction = PiWDWPi
cov_post = cov_prior - cov_reduction
if cov_post < 0:
log.warning(f'WARNING: Negative Sigma: {cov_post}')
log.warning('Setting as Zero and Continuing.')
neg_flag = 1
continue
# NB: "+=" here but each DOF will only be contributed to *once*
# Essentially we are constructing the sigmas functions from
# non-overlapping patches.
sigmas[j].vector()[:] += indic_1.vector()[:] * np.sqrt(cov_post)
sigmas[j].vector().apply("insert")
sigma_priors[j].vector()[:] += indic_1.vector()[:] * np.sqrt(cov_prior)
sigma_priors[j].vector().apply("insert")
if neg_flag:
log.warning('Negative value(s) of sigma encountered.'
'Examine the range of eigenvalues and check if '
'the threshlam paramater is set appropriately.')
# # Previous approach for comparison
# #####################################
# # Isaac Eq. 20
# # P2 = prior
# # P1 = WDW
# # Note - don't think we're considering the cross terms
# # in the posterior covariance.
# # TODO - this isn't particularly well parallelised - can it be improved?
# neg_flag = 0
# for j in range(space.dim()):
# # Who owns this DOF?
# own_idx = y.vector().owns_index(j)
# ownership = np.where(comm.allgather(own_idx))[0]
# assert len(ownership) == 1
# idx_root = ownership[0]
# # Prior (P2)
# y.vector().zero()
# y.vector().vec().setValue(j, 1.0)
# y.vector().apply('insert')
# reg_op.inv_action(y.vector(), x.vector())
# P2 = x
# # WDW (P1) ~ lam * V_r**2
# tmp2 = np.asarray([D[i, i] * w.vector().vec().getValue(j) for i, w in enumerate(W)])
# tmp2 = comm.bcast(tmp2, root=idx_root)
# P1 = Function(space)
# for tmp, w in zip(tmp2, W):
# P1.vector().axpy(tmp, w.vector())
# P_vec = P2.vector() - P1.vector()
# # Extract jth component & save
# # TODO why does this need to be communicated here? surely owning proc
# # just inserts?
# dprod = comm.bcast(P_vec.vec().getValue(j), root=idx_root)
# dprod_prior = comm.bcast(P2.vector().vec().getValue(j), root=idx_root)
# if dprod < 0:
# log.warning(f'WARNING: Negative Sigma: {dprod}')
# log.warning('Setting as Zero and Continuing.')
# neg_flag = 1
# continue
# sigma_old.vector().vec().setValue(j, np.sqrt(dprod))
# sigma_prior_old.vector().vec().setValue(j, np.sqrt(dprod_prior))
# sigma_old.vector().apply("insert")
# sigma_prior_old.vector().apply("insert")
# For testing - whole thing at once:
# wdw = (np.matrix(W) * np.matrix(D) * np.matrix(W).T)
# wdw[:,0] == P1 for j = 0
# if neg_flag:
# log.warning('Negative value(s) of sigma encountered.'
# 'Examine the range of eigenvalues and check if '
# 'the threshlam paramater is set appropriately.')
# Write sigma & sigma_prior to files
# sigma_var_name = "_".join((cntrl.name(), "sigma"))
# sigma_prior_var_name = "_".join((cntrl.name(), "sigma_prior"))
# sigma_old.rename(sigma_var_name, "")
# sigma_prior_old.rename(sigma_prior_var_name, "")
# inout.write_variable(sigma_old, params,
# name=sigma_var_name+"_old")
# inout.write_variable(sigma_prior_old, params,
# name=sigma_prior_var_name+"_old")
for i, name in enumerate(cntrl_names):
sigmas[i].rename("sigma_"+name, "")
sigma_priors[i].rename("sigma_prior_"+name, "")
phase_suffix_sigma = params.inv_sigma.phase_suffix
inout.write_variable(sigmas[i], params,
outdir=outdir,
phase_name=params.inv_sigma.phase_name,
phase_suffix=phase_suffix_sigma)
inout.write_variable(sigma_priors[i], params,
outdir=outdir,
phase_name=params.inv_sigma.phase_name,
phase_suffix=phase_suffix_sigma)
mdl.cntrl_sigma = sigmas
mdl.cntrl_sigma_prior = sigma_priors
return mdl
def run_inv(config_file):
"""Run the inversion part of the simulation"""
# Read run config file
params = ConfigParser(config_file)
inout.setup_logging(params)
inout.log_preamble("inverse", params)
# Load the static model data (geometry, smb, etc)
input_data = inout.InputData(params)
# Get the model mesh
mesh = fice_mesh.get_mesh(params)
mdl = model.model(mesh, input_data, params)
# pts_lengthscale = params.obs.pts_len
mdl.gen_alpha()
# Add random noise to Beta field iff we're inverting for it
mdl.bglen_from_data()
mdl.init_beta(mdl.bglen_to_beta(mdl.bglen), pert=False)
# Next line will output the initial guess for alpha fed into the inversion
# File(os.path.join(outdir,'alpha_initguess.pvd')) << mdl.alpha
#####################
# Run the Inversion #
#####################
slvr = solver.ssa_solver(mdl)
slvr.inversion()
##############################################
# Write out variables in outdir and #
# diagnostics folder #
#############################################
phase_name = params.inversion.phase_name
phase_suffix = params.inversion.phase_suffix
outdir = Path(params.io.output_dir) / phase_name / phase_suffix
diag_dir = Path(params.io.diagnostics_dir)
# Required for next phase (HDF5):
invout_file = params.io.inversion_file
phase_suffix = params.inversion.phase_suffix
if len(phase_suffix) > 0:
invout_file = params.io.run_name + phase_suffix + '_invout.h5'
invout = HDF5File(mesh.mpi_comm(), str(outdir / invout_file), 'w')
invout.parameters.add("gamma_alpha", slvr.gamma_alpha)
invout.parameters.add("delta_alpha", slvr.delta_alpha)
invout.parameters.add("gamma_beta", slvr.gamma_beta)
invout.parameters.add("delta_beta", slvr.delta_beta)
invout.parameters.add("delta_beta_gnd", slvr.delta_beta_gnd)
invout.parameters.add("timestamp", str(datetime.datetime.now()))
invout.write(mdl.alpha, 'alpha')
invout.write(mdl.beta, 'beta')
# For visualisation (XML & VTK):
if params.io.write_diagnostics:
inout.write_variable(slvr.U,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(mdl.beta,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
mdl.beta_bgd.rename("beta_bgd", "")
inout.write_variable(mdl.beta_bgd,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(mdl.bed,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
H = project(mdl.H, mdl.M)
H.rename("thick", "")
inout.write_variable(H,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
fl_ex = project(slvr.float_conditional(H), mdl.M)
inout.write_variable(fl_ex,
params,
name='float',
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(mdl.mask_vel_M,
params,
name="mask_vel",
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(mdl.u_obs_Q,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(mdl.v_obs_Q,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(mdl.u_std_Q,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(mdl.v_std_Q,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
U_obs = project((mdl.v_obs_Q**2 + mdl.u_obs_Q**2)**(1.0 / 2.0), mdl.M)
U_obs.rename("uv_obs", "")
inout.write_variable(U_obs,
params,
name="uv_obs",
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(mdl.alpha,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
Bglen = project(slvr.beta_to_bglen(slvr.beta), mdl.M)
Bglen.rename("Bglen", "")
inout.write_variable(Bglen,
params,
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(slvr.bmelt,
params,
name="bmelt",
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(slvr.smb,
params,
name="smb",
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
inout.write_variable(mdl.surf,
params,
name="surf",
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=phase_suffix)
return mdl
def run_errorprop(config_file):
# Read run config file
params = ConfigParser(config_file)
log = inout.setup_logging(params)
inout.log_preamble("errorprop", params)
outdir = params.io.output_dir
# Load the static model data (geometry, smb, etc)
input_data = inout.InputData(params)
lamfile = params.io.eigenvalue_file
vecfile = params.io.eigenvecs_file
threshlam = params.eigendec.eigenvalue_thresh
dqoi_h5file = params.io.dqoi_h5file
# Get model mesh
mesh = fice_mesh.get_mesh(params)
# Define the model
mdl = model.model(mesh, input_data, params)
# Load alpha/beta fields
mdl.alpha_from_inversion()
mdl.beta_from_inversion()
# Regularization operator using inversion delta/gamma values
# TODO - this won't handle dual inversion case
if params.inversion.alpha_active:
delta = params.inversion.delta_alpha
gamma = params.inversion.gamma_alpha
cntrl = mdl.alpha
elif params.inversion.beta_active:
delta = params.inversion.delta_beta
gamma = params.inversion.gamma_beta
cntrl = mdl.beta
if params.inversion.alpha_active and params.inversion.beta_active:
log.warning(
"Dual inversion but error propagation isn't implemented yet!"
"Doing alpha only!")
reg_op = prior.laplacian(delta, gamma, cntrl.function_space())
space = cntrl.function_space()
x, y, z = [Function(space) for i in range(3)]
# Loads eigenvalues from file
with open(os.path.join(outdir, lamfile), 'rb') as ff:
eigendata = pickle.load(ff)
lam = eigendata[0].real.astype(np.float64)
nlam = len(lam)
# and eigenvectors from .h5 file
eps = params.constants.float_eps
W = []
with HDF5File(MPI.comm_world, os.path.join(outdir, vecfile),
'r') as hdf5data:
for i in range(nlam):
w = Function(space)
hdf5data.read(w, f'v/vector_{i}')
# Test norm in prior == 1.0
reg_op.action(w.vector(), y.vector())
norm_in_prior = w.vector().inner(y.vector())
assert (abs(norm_in_prior - 1.0) < eps)
W.append(w)
# take only the largest eigenvalues
pind = np.flatnonzero(lam > threshlam)
lam = lam[pind]
W = [W[i] for i in pind]
D = np.diag(lam / (lam + 1)) # D_r Isaac 20
# File containing dQoi_dCntrl (i.e. Jacobian of parameter to observable (Qoi))
hdf5data = HDF5File(MPI.comm_world, os.path.join(outdir, dqoi_h5file), 'r')
dQ_cntrl = Function(space)
run_length = params.time.run_length
num_sens = params.time.num_sens
t_sens = np.flip(np.linspace(run_length, 0, num_sens))
sigma = np.zeros(num_sens)
sigma_prior = np.zeros(num_sens)
for j in range(num_sens):
hdf5data.read(dQ_cntrl, f'dQd{cntrl.name()}/vector_{j}')
# TODO - is a mass matrix operation required here?
# qd_cntrl - should be gradients
tmp1 = np.asarray([w.vector().inner(dQ_cntrl.vector()) for w in W])
tmp2 = np.dot(D, tmp1)
P1 = Function(space)
for tmp, w in zip(tmp2, W):
P1.vector().axpy(tmp, w.vector())
reg_op.inv_action(dQ_cntrl.vector(), x.vector())
P2 = x # .vector().get_local()
P_vec = P2.vector() - P1.vector()
variance = P_vec.inner(dQ_cntrl.vector())
sigma[j] = np.sqrt(variance)
# Prior only
variance_prior = P2.vector().inner(dQ_cntrl.vector())
sigma_prior[j] = np.sqrt(variance_prior)
# Test that eigenvectors are prior inverse orthogonal
# y.vector().set_local(W[:,398])
# y.vector().apply('insert')
# reg_op.action(y.vector(), x.vector())
# #mass.mult(x.vector(),z.vector())
# q = np.dot(y.vector().get_local(),x.vector().get_local())
# Output model variables in ParaView+Fenics friendly format
sigma_file = params.io.sigma_file
sigma_prior_file = params.io.sigma_prior_file
pickle.dump([sigma, t_sens], open(os.path.join(outdir, sigma_file), "wb"))
pickle.dump([sigma_prior, t_sens],
open(os.path.join(outdir, sigma_prior_file), "wb"))
# This simplifies testing - is it OK? Should we hold all data in the solver object?
mdl.Q_sigma = sigma
mdl.Q_sigma_prior = sigma_prior
mdl.t_sens = t_sens
return mdl
def run_forward(config_file):
# Read run config file
params = ConfigParser(config_file)
log = inout.setup_logging(params)
inout.log_preamble("forward", params)
outdir = params.io.output_dir
diag_dir = params.io.diagnostics_dir
phase_name = params.time.phase_name
# Load the static model data (geometry, smb, etc)
input_data = inout.InputData(params)
# Get model mesh
mesh = fice_mesh.get_mesh(params)
# Define the model
mdl = model.model(mesh, input_data, params)
mdl.alpha_from_inversion()
mdl.beta_from_inversion()
# Solve
slvr = solver.ssa_solver(mdl, mixed_space=params.inversion.dual)
slvr.save_ts_zero()
cntrl = slvr.get_control()
qoi_func = slvr.get_qoi_func()
# TODO here - cntrl now returns a list - so compute_gradient returns a list of tuples
# Run the forward model
Q = slvr.timestep(adjoint_flag=1, qoi_func=qoi_func)
# Run the adjoint model, computing gradient of Qoi w.r.t cntrl
dQ_ts = compute_gradient(Q, cntrl) # Isaac 27
# Output model variables in ParaView+Fenics friendly format
# Output QOI & DQOI (needed for next steps)
inout.write_qval(slvr.Qval_ts, params)
inout.write_dqval(dQ_ts, [var.name() for var in cntrl], params)
# Output final velocity, surface & thickness (visualisation)
inout.write_variable(slvr.U,
params,
name="U_fwd",
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=params.time.phase_suffix)
inout.write_variable(mdl.surf,
params,
name="surf_fwd",
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=params.time.phase_suffix)
H = project(mdl.H, mdl.Q)
inout.write_variable(H,
params,
name="H_fwd",
outdir=diag_dir,
phase_name=phase_name,
phase_suffix=params.time.phase_suffix)
return mdl
def run_invsigma(config_file):
"""Compute control sigma values from eigendecomposition"""
comm = MPI.comm_world
rank = comm.rank
# Read run config file
params = ConfigParser(config_file)
# Setup logging
log = inout.setup_logging(params)
inout.log_preamble("inv sigma", params)
outdir = params.io.output_dir
# Load the static model data (geometry, smb, etc)
input_data = inout.InputData(params)
eigendir = outdir
lamfile = params.io.eigenvalue_file
vecfile = params.io.eigenvecs_file
threshlam = params.eigendec.eigenvalue_thresh
# Get model mesh
mesh = fice_mesh.get_mesh(params)
# Define the model (only need alpha & beta though)
mdl = model.model(mesh, input_data, params, init_fields=False)
# Load alpha/beta fields
mdl.alpha_from_inversion()
mdl.beta_from_inversion()
# Regularization operator using inversion delta/gamma values
# TODO - this won't handle dual inversion case
if params.inversion.alpha_active:
delta = params.inversion.delta_alpha
gamma = params.inversion.gamma_alpha
cntrl = mdl.alpha
elif params.inversion.beta_active:
delta = params.inversion.delta_beta
gamma = params.inversion.gamma_beta
cntrl = mdl.beta
space = cntrl.function_space()
sigma, sigma_prior, x, y, z = [Function(space) for i in range(5)]
reg_op = prior.laplacian(delta, gamma, space)
# Load the eigenvalues
with open(os.path.join(eigendir, lamfile), 'rb') as ff:
eigendata = pickle.load(ff)
lam = eigendata[0].real.astype(np.float64)
nlam = len(lam)
# Read in the eigenvectors and check they are normalised
# w.r.t. the prior (i.e. the B matrix in our GHEP)
eps = params.constants.float_eps
W = []
with HDF5File(comm, os.path.join(eigendir, vecfile), 'r') as hdf5data:
for i in range(nlam):
w = Function(space)
hdf5data.read(w, f'v/vector_{i}')
# Test norm in prior == 1.0
reg_op.action(w.vector(), y.vector())
norm_in_prior = w.vector().inner(y.vector())
assert (abs(norm_in_prior - 1.0) < eps)
W.append(w)
# Which eigenvalues are larger than our threshold?
pind = np.flatnonzero(lam > threshlam)
lam = lam[pind]
W = [W[i] for i in pind]
D = np.diag(lam / (lam + 1))
neg_flag = 0
# Isaac Eq. 20
# P2 = prior
# P1 = WDW
# Note - don't think we're considering the cross terms
# in the posterior covariance.
# TODO - this isn't particularly well parallelised - can it be improved?
for j in range(space.dim()):
# Who owns this index?
own_idx = y.vector().owns_index(j)
ownership = np.where(comm.allgather(own_idx))[0]
assert len(ownership) == 1
idx_root = ownership[0]
y.vector().zero()
y.vector().vec().setValue(j, 1.0)
y.vector().apply('insert')
tmp2 = np.asarray(
[D[i, i] * w.vector().vec().getValue(j) for i, w in enumerate(W)])
tmp2 = comm.bcast(tmp2, root=idx_root)
P1 = Function(space)
for tmp, w in zip(tmp2, W):
P1.vector().axpy(tmp, w.vector())
reg_op.inv_action(y.vector(), x.vector())
P2 = x
P_vec = P2.vector() - P1.vector()
dprod = comm.bcast(P_vec.vec().getValue(j), root=idx_root)
dprod_prior = comm.bcast(P2.vector().vec().getValue(j), root=idx_root)
if dprod < 0:
log.warning(f'WARNING: Negative Sigma: {dprod}')
log.warning('Setting as Zero and Continuing.')
neg_flag = 1
continue
sigma.vector().vec().setValue(j, np.sqrt(dprod))
sigma_prior.vector().vec().setValue(j, np.sqrt(dprod_prior))
sigma.vector().apply("insert")
sigma_prior.vector().apply("insert")
# For testing - whole thing at once:
# wdw = (np.matrix(W) * np.matrix(D) * np.matrix(W).T)
# wdw[:,0] == P1 for j = 0
if neg_flag:
log.warning('Negative value(s) of sigma encountered.'
'Examine the range of eigenvalues and check if '
'the threshlam paramater is set appropriately.')
# Write sigma & sigma_prior to files
sigma_var_name = "_".join((cntrl.name(), "sigma"))
sigma_prior_var_name = "_".join((cntrl.name(), "sigma_prior"))
sigma.rename(sigma_var_name, "")
sigma_prior.rename(sigma_prior_var_name, "")
inout.write_variable(sigma, params, name=sigma_var_name)
inout.write_variable(sigma_prior, params, name=sigma_prior_var_name)
mdl.cntrl_sigma = sigma
mdl.cntrl_sigma_prior = sigma_prior
return mdl
def run_errorprop(config_file):
# Read run config file
params = ConfigParser(config_file)
log = inout.setup_logging(params)
inout.log_preamble("errorprop", params)
outdir = params.io.output_dir
# Load the static model data (geometry, smb, etc)
input_data = inout.InputData(params)
#Eigen value params
phase_eigen = params.eigendec.phase_name
phase_suffix_e = params.eigendec.phase_suffix
lamfile = params.io.eigenvalue_file
vecfile = params.io.eigenvecs_file
threshlam = params.eigendec.eigenvalue_thresh
# Qoi forward params
phase_time = params.time.phase_name
phase_suffix_qoi = params.time.phase_suffix
dqoi_h5file = params.io.dqoi_h5file
if len(phase_suffix_e) > 0:
lamfile = params.io.run_name + phase_suffix_e + '_eigvals.p'
vecfile = params.io.run_name + phase_suffix_e + '_vr.h5'
if len(phase_suffix_qoi) > 0:
dqoi_h5file = params.io.run_name + phase_suffix_qoi + '_dQ_ts.h5'
# Get model mesh
mesh = fice_mesh.get_mesh(params)
# Define the model
mdl = model.model(mesh, input_data, params)
# Load alpha/beta fields
mdl.alpha_from_inversion()
mdl.beta_from_inversion()
mdl.bglen_from_data(mask_only=True)
# Setup our solver object
slvr = solver.ssa_solver(mdl, mixed_space=params.inversion.dual)
cntrl = slvr.get_control()[0]
space = slvr.get_control_space()
# Regularization operator using inversion delta/gamma values
Prior = mdl.get_prior()
reg_op = Prior(slvr, space)
x, y, z = [Function(space) for i in range(3)]
# Loads eigenvalues from file
outdir_e = Path(outdir) / phase_eigen / phase_suffix_e
with open(outdir_e / lamfile, 'rb') as ff:
eigendata = pickle.load(ff)
lam = eigendata[0].real.astype(np.float64)
nlam = len(lam)
# Check if eigendecomposition successfully produced num_eig
# or if some are NaN
if np.any(np.isnan(lam)):
nlam = np.argwhere(np.isnan(lam))[0][0]
lam = lam[:nlam]
# and eigenvectors from .h5 file
eps = params.constants.float_eps
W = []
with HDF5File(MPI.comm_world, str(outdir_e / vecfile), 'r') as hdf5data:
for i in range(nlam):
w = Function(space)
hdf5data.read(w, f'v/vector_{i}')
# Test norm in prior == 1.0
reg_op.action(w.vector(), y.vector())
norm_in_prior = w.vector().inner(y.vector())
assert (abs(norm_in_prior - 1.0) < eps)
W.append(w)
# take only the largest eigenvalues
pind = np.flatnonzero(lam > threshlam)
lam = lam[pind]
nlam = len(lam)
W = [W[i] for i in pind]
D = np.diag(lam / (lam + 1)) # D_r Isaac 20
# File containing dQoi_dCntrl (i.e. Jacobian of parameter to observable (Qoi))
outdir_qoi = Path(outdir) / phase_time / phase_suffix_qoi
hdf5data = HDF5File(MPI.comm_world, str(outdir_qoi / dqoi_h5file), 'r')
dQ_cntrl = Function(space)
run_length = params.time.run_length
num_sens = params.time.num_sens
t_sens = np.flip(np.linspace(run_length, 0, num_sens))
sigma = np.zeros(num_sens)
sigma_prior = np.zeros(num_sens)
for j in range(num_sens):
hdf5data.read(dQ_cntrl, f'dQd{cntrl.name()}/vector_{j}')
# TODO - is a mass matrix operation required here?
# qd_cntrl - should be gradients
tmp1 = np.asarray([w.vector().inner(dQ_cntrl.vector()) for w in W])
tmp2 = np.dot(D, tmp1)
P1 = Function(space)
for tmp, w in zip(tmp2, W):
P1.vector().axpy(tmp, w.vector())
reg_op.inv_action(dQ_cntrl.vector(), x.vector())
P2 = x # .vector().get_local()
P_vec = P2.vector() - P1.vector()
variance = P_vec.inner(dQ_cntrl.vector())
sigma[j] = np.sqrt(variance)
# Prior only
variance_prior = P2.vector().inner(dQ_cntrl.vector())
sigma_prior[j] = np.sqrt(variance_prior)
# Look at the last sampled time and check how sigma QoI converges
# with addition of more eigenvectors
sigma_conv = []
sigma_steps = []
P1 = Function(space)
# How many steps?
conv_res = 100
conv_int = int(np.ceil(nlam / conv_res))
for i in range(0, nlam, conv_int):
# Reuse tmp1/tmp2 from above because its the last sens
for j in range(i, min(i + conv_int, nlam)):
P1.vector().axpy(tmp2[j], W[j].vector())
P_vec = P2.vector() - P1.vector()
variance = P_vec.inner(dQ_cntrl.vector())
sigma_conv.append(np.sqrt(variance))
sigma_steps.append(min(i + conv_int, nlam))
# Save plots in diagnostics
phase_err = params.error_prop.phase_name
phase_suffix_err = params.error_prop.phase_suffix
diag_dir = Path(params.io.diagnostics_dir) / phase_err / phase_suffix_err
outdir_err = Path(params.io.output_dir) / phase_err / phase_suffix_err
# if(MPI.comm_world.rank == 0):
plt.semilogy(sigma_steps, sigma_conv)
plt.title("Convergence of sigmaQoI")
plt.ylabel("sigma QoI")
plt.xlabel("Num eig")
plt.savefig(
os.path.join(
str(diag_dir), "_".join(
(params.io.run_name, phase_suffix_err + "sigmaQoI_conv.pdf"))))
plt.close()
sigmaqoi_file = os.path.join(
str(outdir_err), "_".join(
(params.io.run_name,
phase_suffix_err + "sigma_qoi_convergence.p")))
with open(sigmaqoi_file, 'wb') as pfile:
pickle.dump([sigma_steps, sigma_conv], pfile)
# Test that eigenvectors are prior inverse orthogonal
# y.vector().set_local(W[:,398])
# y.vector().apply('insert')
# reg_op.action(y.vector(), x.vector())
# #mass.mult(x.vector(),z.vector())
# q = np.dot(y.vector().get_local(),x.vector().get_local())
# Output model variables in ParaView+Fenics friendly format
sigma_file = params.io.sigma_file
sigma_prior_file = params.io.sigma_prior_file
if len(phase_suffix_err) > 0:
sigma_file = params.io.run_name + phase_suffix_err + '_sigma.p'
sigma_prior_file = params.io.run_name + phase_suffix_err + '_sigma_prior.p'
with open(os.path.join(outdir_err, sigma_file), "wb") as sigfile:
pickle.dump([sigma, t_sens], sigfile)
with open(os.path.join(outdir_err, sigma_prior_file), "wb") as sigpfile:
pickle.dump([sigma_prior, t_sens], sigpfile)
# This simplifies testing - is it OK? Should we hold all data in the solver object?
mdl.Q_sigma = sigma
mdl.Q_sigma_prior = sigma_prior
mdl.t_sens = t_sens
return mdl
def run_forward(config_file):
#Read run config file
params = ConfigParser(config_file)
log = inout.setup_logging(params)
inout.log_preamble("forward", params)
outdir = params.io.output_dir
# Load the static model data (geometry, smb, etc)
input_data = inout.InputData(params)
# Get model mesh
mesh = fice_mesh.get_mesh(params)
# Define the model
mdl = model.model(mesh, input_data, params)
mdl.alpha_from_inversion()
mdl.beta_from_inversion()
# Solve
slvr = solver.ssa_solver(mdl)
slvr.save_ts_zero()
cntrl = slvr.get_control()
qoi_func = slvr.get_qoi_func()
#TODO here - cntrl now returns a list - so compute_gradient returns a list of tuples
#Run the forward model
Q = slvr.timestep(adjoint_flag=1, qoi_func=qoi_func)
#Run the adjoint model, computing gradient of Qoi w.r.t cntrl
dQ_ts = compute_gradient(Q, cntrl) #Isaac 27
#Uncomment for Taylor Verification, Comment above two lines
# param['num_sens'] = 1
# J = slvr.timestep(adjoint_flag=1, cst_func=slvr.comp_Q_vaf)
# dJ = compute_gradient(J, slvr.alpha)
#
#
# def forward_ts(alpha_val=None):
# slvr.reset_ts_zero()
# if alpha_val:
# slvr.alpha = alpha_val
# return slvr.timestep(adjoint_flag=1, cst_func=slvr.comp_Q_vaf)
#
#
# min_order = taylor_test(lambda alpha : forward_ts(alpha_val = alpha), slvr.alpha,
# J_val = J.value(), dJ = dJ, seed = 1e-2, size = 6)
# sys.exit(os.EX_OK)
# Output model variables in ParaView+Fenics friendly format
outdir = params.io.output_dir
# Output QOI & DQOI (needed for next steps)
inout.write_qval(slvr.Qval_ts, params)
inout.write_dqval(dQ_ts, [var.name() for var in cntrl], params)
# Output final velocity, surface & thickness (visualisation)
inout.write_variable(slvr.U, params, name="U_fwd")
inout.write_variable(mdl.surf, params, name="surf_fwd")
H = project(mdl.H, mdl.Q)
inout.write_variable(H, params, name="H_fwd")
return mdl
def run_eigendec(config_file):
"""
Run the eigendecomposition phase of the model.
1. Define the model domain & fields
2. Runs the forward model w/ alpha/beta from run_inv
3. Computes the Hessian of the *misfit* cost functional (J)
4. Performs the generalized eigendecomposition with
A = H_mis, B = prior_action
"""
# Read run config file
params = ConfigParser(config_file)
log = inout.setup_logging(params)
inout.log_preamble("eigendecomp", params)
dd = params.io.input_dir
outdir = params.io.output_dir
# Load the static model data (geometry, smb, etc)
input_data = inout.InputData(params)
# Get model mesh
mesh = fice_mesh.get_mesh(params)
# Define the model
mdl = model.model(mesh, input_data, params)
# Load alpha/beta fields
mdl.alpha_from_inversion()
mdl.beta_from_inversion()
# Setup our solver object
slvr = solver.ssa_solver(mdl)
# TODO generalise - get_control returns a list
cntrl = slvr.get_control()[0]
space = cntrl.function_space()
msft_flag = params.eigendec.misfit_only
if msft_flag:
slvr.zero_inv_params()
# Hessian Action
slvr.set_hessian_action(cntrl)
# Mass matrix solver
xg, xb = Function(space), Function(space)
# test, trial = TestFunction(space), TrialFunction(space)
# mass = assemble(inner(test, trial) * slvr.dx)
# mass_solver = KrylovSolver("cg", "sor")
# mass_solver.parameters.update({"absolute_tolerance": 1.0e-32,
# "relative_tolerance": 1.0e-14})
# mass_solver.set_operator(mass)
# Regularization operator using inversion delta/gamma values
# TODO - this won't handle dual inversion case
if params.inversion.alpha_active:
delta = params.inversion.delta_alpha
gamma = params.inversion.gamma_alpha
elif params.inversion.beta_active:
delta = params.inversion.delta_beta
gamma = params.inversion.gamma_beta
reg_op = prior.laplacian(delta, gamma, space)
# Uncomment to get low-level SLEPc/PETSc output
# set_log_level(10)
@count_calls()
# @timer
def ghep_action(x):
"""Hessian action w/o preconditioning"""
_, _, ddJ_val = slvr.ddJ.action(cntrl, x)
# reg_op.inv_action(ddJ_val.vector(), xg.vector()) <- gnhep_prior
return function_get_values(ddJ_val)
@count_calls()
def prior_action(x):
"""Define the action of the B matrix (prior)"""
reg_op.action(x.vector(), xg.vector())
return function_get_values(xg)
def prior_approx_action(x):
"""Only used for checking B' orthonormality"""
reg_op.approx_action(x.vector(), xg.vector())
return function_get_values(xg)
def slepc_config_callback(config):
log.info("Got to the callback")
# KSP corresponds to B-matrix inversion
# Set it to precondition only because we
# supply the inverse in LaplacianPC
ksp = config.getST().getKSP()
ksp.setType(PETSc.KSP.Type.PREONLY)
pc = ksp.getPC()
pc.setType(PETSc.PC.Type.PYTHON)
pc.setPythonContext(prior.LaplacianPC(reg_op))
# A_matrix already defined so just grab it
A_matrix, _ = config.getOperators()
(n, N), (n_col, N_col) = A_matrix.getSizes()
assert n == n_col
assert N == N_col
del n_col, N_col
comm = A_matrix.getComm()
B_matrix = PETSc.Mat().createPython(((n, N), (n, N)),
PythonMatrix(prior_action, space),
comm=comm)
B_matrix.setUp()
config.view() # TODO - should this go to log?
config.setOperators(A_matrix, B_matrix)
# opts = {'prior': gnhep_prior_action, 'mass': gnhep_mass_action}
# gnhep_func = opts[params.eigendec.precondition_by]
num_eig = params.eigendec.num_eig
n_iter = params.eigendec.power_iter # <- not used yet
# Hessian eigendecomposition using SLEPSc
eig_algo = params.eigendec.eig_algo
if eig_algo == "slepc":
# Eigendecomposition
lam, vr = eigendecompose(
space,
ghep_action,
tolerance=1.0e-10,
N_eigenvalues=num_eig,
problem_type=SLEPc.EPS.ProblemType.GHEP,
# solver_type=SLEPc.EPS.Type.ARNOLDI,
configure=slepc_config_callback)
# Check orthonormality of EVs
if num_eig is not None and num_eig < 100:
# Check for B (not B') orthogonality & normalisation
for i in range(num_eig):
reg_op.action(vr[i].vector(), xg.vector())
norm = xg.vector().inner(Vector(vr[i].vector()))**0.5
print("EV %s norm %s" % (i, norm))
for i in range(num_eig):
reg_op.action(vr[i].vector(), xg.vector())
for j in range(i + 1, num_eig):
inn = xg.vector().inner(Vector(vr[j].vector()))
print("EV %s %s inner %s" % (i, j, inn))
# Uses extreme amounts of disk space; suitable for ismipc only
# #Save eigenfunctions
# vtkfile = File(os.path.join(outdir,'vr.pvd'))
# for v in vr:
# v.rename('v', v.label())
# vtkfile << v
#
# vtkfile = File(os.path.join(outdir,'vi.pvd'))
# for v in vi:
# v.rename('v', v.label())
# vtkfile << v
ev_file = params.io.eigenvecs_file
with HDF5File(slvr.mesh.mpi_comm(), os.path.join(outdir, ev_file),
'w') as hdf5file:
for i, v in enumerate(vr):
hdf5file.write(v, 'v', i)
hdf5file.parameters.add("num_eig", num_eig)
hdf5file.parameters.add("eig_algo", eig_algo)
hdf5file.parameters.add("timestamp", str(datetime.datetime.now()))
else:
raise NotImplementedError
slvr.eigenvals = lam
slvr.eigenfuncs = vr
# Save eigenvals and some associated info - TODO HDF5File?
fileout = params.io.eigenvalue_file
pfile = open(os.path.join(outdir, fileout), "wb")
pickle.dump([lam, num_eig, n_iter, eig_algo, msft_flag, outdir, dd], pfile)
pfile.close()
# Plot of eigenvals
lamr = lam.real
lpos = np.argwhere(lamr > 0)
lneg = np.argwhere(lamr < 0)
lind = np.arange(0, len(lamr))
plt.semilogy(lind[lpos], lamr[lpos], '.')
plt.semilogy(lind[lneg], np.abs(lamr[lneg]), '.')
plt.savefig(os.path.join(outdir, 'lambda.pdf'))
# Note - for now this does nothing, but eventually if the whole series
# of runs were done without re-initializing solver, it'd be important to
# put the inversion params back
if msft_flag:
slvr.set_inv_params()
return mdl
def run_eigendec(config_file):
"""
Run the eigendecomposition phase of the model.
1. Define the model domain & fields
2. Runs the forward model w/ alpha/beta from run_inv
3. Computes the Hessian of the *misfit* cost functional (J)
4. Performs the generalized eigendecomposition with
A = H_mis, B = prior_action
"""
# Read run config file
params = ConfigParser(config_file)
log = inout.setup_logging(params)
inout.log_preamble("eigendecomp", params)
# Load the static model data (geometry, smb, etc)
input_data = inout.InputData(params)
# Get mesh & define model
mesh = fice_mesh.get_mesh(params)
mdl = model.model(mesh, input_data, params)
# Load alpha/beta fields
mdl.alpha_from_inversion()
mdl.beta_from_inversion()
mdl.bglen_from_data(mask_only=True)
# Setup our solver object
slvr = solver.ssa_solver(mdl, mixed_space=params.inversion.dual)
cntrl = slvr.get_control()[0]
space = slvr.get_control_space()
# Regularization operator using inversion delta/gamma values
Prior = mdl.get_prior()
reg_op = Prior(slvr, space)
msft_flag = params.eigendec.misfit_only
if msft_flag:
slvr.zero_inv_params()
# Hessian Action
slvr.set_hessian_action(cntrl)
# Mass matrix solver
xg, xb = Function(space), Function(space)
# test, trial = TestFunction(space), TrialFunction(space)
# mass = assemble(inner(test, trial) * slvr.dx)
# mass_solver = KrylovSolver("cg", "sor")
# mass_solver.parameters.update({"absolute_tolerance": 1.0e-32,
# "relative_tolerance": 1.0e-14})
# mass_solver.set_operator(mass)
# Uncomment to get low-level SLEPc/PETSc output
# set_log_level(10)
@count_calls()
# @timer
def ghep_action(x):
"""Hessian action w/o preconditioning"""
_, _, ddJ_val = slvr.ddJ.action(cntrl, x)
# reg_op.inv_action(ddJ_val.vector(), xg.vector()) <- gnhep_prior
return function_get_values(ddJ_val)
@count_calls()
def prior_action(x):
"""Define the action of the B matrix (prior)"""
reg_op.action(x.vector(), xg.vector())
return function_get_values(xg)
# opts = {'prior': gnhep_prior_action, 'mass': gnhep_mass_action}
# gnhep_func = opts[params.eigendec.precondition_by]
num_eig = params.eigendec.num_eig
n_iter = params.eigendec.power_iter # <- not used yet
# Hessian eigendecomposition using SLEPSc
eig_algo = params.eigendec.eig_algo
if eig_algo == "slepc":
results = {
} # Create this empty dict & pass it to slepc_monitor_callback to fill
# Eigendecomposition
import slepc4py.SLEPc as SLEPc
esolver = eigendecompose(
space,
ghep_action,
tolerance=params.eigendec.tol,
max_it=params.eigendec.max_iter,
N_eigenvalues=num_eig,
problem_type=SLEPc.EPS.ProblemType.GHEP,
solver_type=SLEPc.EPS.Type.KRYLOVSCHUR,
configure=slepc_config_callback(reg_op, prior_action, space),
monitor=slepc_monitor_callback(params, space, results))
log.info("Finished eigendecomposition")
vr = results['vr']
lam = results['lam']
# Check the eigenvectors & eigenvalues
if (params.eigendec.test_ed):
ED.test_eigendecomposition(esolver, results, space, params)
if num_eig > 100:
log.warning(
"Requesting inner product of more than 100 EVs, this is expensive!"
)
# Check for B (not B') orthogonality & normalisation
for i in range(num_eig):
reg_op.action(vr[i].vector(), xg.vector())
norm = xg.vector().inner(Vector(vr[i].vector()))**0.5
if (abs(1.0 - norm) > params.eigendec.tol):
raise Exception(f"Eigenvector norm is {norm}")
for i in range(num_eig):
reg_op.action(vr[i].vector(), xg.vector())
for j in range(i + 1, num_eig):
inn = xg.vector().inner(Vector(vr[j].vector()))
if (abs(inn) > params.eigendec.tol):
raise Exception(
f"Eigenvectors {i} & {j} inner product nonzero: {inn}"
)
# Uses extreme amounts of disk space; suitable for ismipc only
# #Save eigenfunctions
# vtkfile = File(os.path.join(outdir,'vr.pvd'))
# for v in vr:
# v.rename('v', v.label())
# vtkfile << v
#
# vtkfile = File(os.path.join(outdir,'vi.pvd'))
# for v in vi:
# v.rename('v', v.label())
# vtkfile << v
else:
raise NotImplementedError
slvr.eigenvals = lam
slvr.eigenfuncs = vr
# Plot of eigenvals
lpos = np.argwhere(lam > 0)
lneg = np.argwhere(lam < 0)
lind = np.arange(0, len(lam))
plt.semilogy(lind[lpos], lam[lpos], '.')
plt.semilogy(lind[lneg], np.abs(lam[lneg]), '.')
diag_dir = Path(
params.io.diagnostics_dir
) / params.eigendec.phase_name / params.eigendec.phase_suffix
plt.savefig(diag_dir / 'lambda.pdf')
plt.close()
# Note - for now this does nothing, but eventually if the whole series
# of runs were done without re-initializing solver, it'd be important to
# put the inversion params back
if msft_flag:
slvr.set_inv_params()
return mdl