def set_perturbation(self, m_dot):
'''Return another instance of the same class, representing the Control perturbed in a particular
direction m_dot.'''
m_dot = enlist(m_dot)
if not len(self.controls) == len(m_dot):
raise ValueError, "The perturbation m_dot must be a list of the same shape as the control list"
return ListControl([p.set_perturbation(m) for (p, m) in zip(self.controls, m_dot)])
def __init__(self, J, m, warn=True):
self.J = J
self.enlisted_controls = enlist(m)
self.m = ListControl(self.enlisted_controls)
if warn:
backend.info_red("Warning: Hessian computation is still experimental and is known to not work for some problems. Please Taylor test thoroughly.")
def compute_gradient(J, param, forget=True, ignore=[], callback=lambda var, output: None, project=False):
backend.parameters["adjoint"]["stop_annotating"] = True
enlisted_controls = enlist(param)
param = ListControl(enlisted_controls)
dJdparam = enlisted_controls.__class__([None] * len(enlisted_controls))
last_timestep = adjglobals.adjointer.timestep_count
ignorelist = []
for fn in ignore:
if isinstance(fn, backend.Function):
ignorelist.append(adjglobals.adj_variables[fn])
elif isinstance(fn, str):
ignorelist.append(libadjoint.Variable(fn, 0, 0))
else:
ignorelist.append(fn)
for i in range(adjglobals.adjointer.timestep_count):
adjglobals.adjointer.set_functional_dependencies(J, i)
for i in range(adjglobals.adjointer.equation_count)[::-1]:
fwd_var = adjglobals.adjointer.get_forward_variable(i)
if fwd_var in ignorelist:
info("Ignoring the adjoint equation for %s" % fwd_var)
continue
(adj_var, output) = adjglobals.adjointer.get_adjoint_solution(i, J)
callback(adj_var, output.data)
storage = libadjoint.MemoryStorage(output)
storage.set_overwrite(True)
adjglobals.adjointer.record_variable(adj_var, storage)
fwd_var = libadjoint.Variable(adj_var.name, adj_var.timestep, adj_var.iteration)
out = param.equation_partial_derivative(adjglobals.adjointer, output.data, i, fwd_var)
dJdparam = _add(dJdparam, out)
if last_timestep > adj_var.timestep:
# We have hit a new timestep, and need to compute this timesteps' \partial J/\partial m contribution
out = param.functional_partial_derivative(adjglobals.adjointer, J, adj_var.timestep)
dJdparam = _add(dJdparam, out)
last_timestep = adj_var.timestep
if forget is None:
pass
elif forget:
adjglobals.adjointer.forget_adjoint_equation(i)
else:
adjglobals.adjointer.forget_adjoint_values(i)
rename(J, dJdparam, param)
return postprocess(dJdparam, project, list_type=enlisted_controls)
def _taylor_test_multi_control(J, m, Jm, dJdm, HJm, seed, perturbation_direction, value):
if perturbation_direction is None:
perturbation_direction = [None] * len(m.controls)
perturbation_direction = enlist(perturbation_direction)
if value is None:
value = [None] * len(m.controls)
value = enlist(value)
# Create a deep copy of the initial control values
m_cpy = []
for c in m:
if isinstance(c.data(), backend.Function):
m_cpy.append(c.data().copy(deepcopy=True))
elif isinstance(c.data(), backend.MultiMeshFunction):
m_cpy.append(c.data().copy(deepcopy=True))
else:
m_cpy.append(backend.Constant(c.data()))
# Build a objective version restricted to the i'th control
def J_cmp(J, i):
m_values = list(m_cpy)
def out(x):
m_values[i] = x
return J(m_values)
return out
# A Hessian version restricted to the i'th control
if HJm is not None:
HJm_cmp = lambda i: lambda x: HJm.__class__(HJm.J, m[i])(x)
else:
HJm_cmp = lambda i: None
# Perform the Taylor tests for each control
min_conv = 1e10
for i in range(len(m.controls)):
print "\nRunning Taylor test for control {}".format(i)
conv = _taylor_test_single_control(J_cmp(J, i), m[i], Jm, dJdm[i],
HJm_cmp(i), seed, perturbation_direction[i], value[i])
min_conv = min(min_conv, conv)
return min_conv
def derivative(self, forget=True, project=False):
''' Evaluates the derivative of the reduced functional for the most
recently evaluated control value. '''
# Check if we have the gradient already in the cash.
# If so, return the cached value
if self.cache is not None:
hash = value_hash([x.data() for x in self.controls])
fnspaces = [p.data().function_space() if isinstance(p.data(),
Function) else None for p in self.controls]
if hash in self._cache["derivative_cache"]:
info_green("Got a derivative cache hit.")
return cache_load(self._cache["derivative_cache"][hash], fnspaces)
# Call callback
values = [p.data() for p in self.controls]
self.derivative_cb_pre(delist(values, list_type=self.controls))
# Compute the gradient by solving the adjoint equations
dfunc_value = drivers.compute_gradient(self.functional, self.controls, forget=forget, project=project)
dfunc_value = enlist(dfunc_value)
# Reset the checkpointing state in dolfin-adjoint
adjointer.reset_revolve()
# Apply the scaling factor
scaled_dfunc_value = [utils.scale(df, self.scale) for df in list(dfunc_value)]
# Call callback
# We might have forgotten the control values already,
# in which case we can only return Nones
values = []
for c in self.controls:
try:
values.append(p.data())
except libadjoint.exceptions.LibadjointErrorNeedValue:
values.append(None)
if self.current_func_value is not None:
self.derivative_cb_post(self.scale * self.current_func_value,
delist(scaled_dfunc_value, list_type=self.controls),
delist(values, list_type=self.controls))
# Cache the result
if self.cache is not None:
info_red("Got a derivative cache miss")
self._cache["derivative_cache"][hash] = cache_store(scaled_dfunc_value, self.cache)
return scaled_dfunc_value
def derivative(self, forget=True, project=False):
''' Evaluates the derivative of the reduced functional for the most
recently evaluated control value. '''
# Check if we have the gradient already in the cash.
# If so, return the cached value
if self.cache is not None:
hash = value_hash([x.data() for x in self.controls])
fnspaces = [p.data().function_space() if isinstance(p.data(),
Function) else None for p in self.controls]
if hash in self._cache["derivative_cache"]:
info_green("Got a derivative cache hit.")
return cache_load(self._cache["derivative_cache"][hash], fnspaces)
# Compute the gradient by solving the adjoint equations
dfunc_value = drivers.compute_gradient(self.functional, self.controls, forget=forget, project=project)
dfunc_value = enlist(dfunc_value)
# Reset the checkpointing state in dolfin-adjoint
adjointer.reset_revolve()
# Apply the scaling factor
scaled_dfunc_value = [utils.scale(df, self.scale) for df in list(dfunc_value)]
# Call the user-specific callback routine
if self.derivative_cb:
if self.current_func_value is not None:
values = [p.data() for p in self.controls]
self.derivative_cb(self.scale * self.current_func_value,
delist(scaled_dfunc_value, list_type=self.controls),
delist(values, list_type=self.controls))
else:
info_red("Gradient evaluated without functional evaluation, not calling derivative callback function")
# Cache the result
if self.cache is not None:
info_red("Got a derivative cache miss")
self._cache["derivative_cache"][hash] = cache_store(scaled_dfunc_value, self.cache)
return scaled_dfunc_value
def derivative(self, forget=True, project=False):
""" Evaluates the derivative of the reduced functional at the most
recently evaluated control value.
Args:
forget (Optional[bool]): Delete the forward state while solving the
adjoint equations. If you want to reevaluate derivative at the same
point (or the Hessian) you will need to set this to False or None. Defaults to True.
project (Optional[bool]): If True, the returned value will be the L2
Riesz representer, if False it will be the l2 Riesz representative.
The L2 projection requires one additional linear solve.
Defaults to False.
Returns:
The functional derivative. The returned type is the same as the control
type.
"""
# Check if we have the gradient already in the cash.
# If so, return the cached value
if self.cache is not None:
hash = value_hash([x.data() for x in self.controls])
fnspaces = [p.data().function_space() if isinstance(p.data(),
Function) else None for p in self.controls]
if hash in self._cache["derivative_cache"]:
info_green("Got a derivative cache hit.")
return cache_load(self._cache["derivative_cache"][hash], fnspaces)
# Call callback
values = [p.data() for p in self.controls]
self.derivative_cb_pre(delist(values, list_type=self.controls))
# Compute the gradient by solving the adjoint equations
dfunc_value = drivers.compute_gradient(self.functional, self.controls, forget=forget, project=project)
dfunc_value = enlist(dfunc_value)
# Reset the checkpointing state in dolfin-adjoint
adjointer.reset_revolve()
# Apply the scaling factor
scaled_dfunc_value = [utils.scale(df, self.scale) for df in list(dfunc_value)]
# Call callback
# We might have forgotten the control values already,
# in which case we can only return Nones
values = []
for c in self.controls:
try:
values.append(p.data())
except libadjoint.exceptions.LibadjointErrorNeedValue:
values.append(None)
if self.current_func_value is not None:
self.derivative_cb_post(self.scale * self.current_func_value,
delist(scaled_dfunc_value, list_type=self.controls),
delist(values, list_type=self.controls))
# Cache the result
if self.cache is not None:
info_red("Got a derivative cache miss")
self._cache["derivative_cache"][hash] = cache_store(scaled_dfunc_value, self.cache)
return scaled_dfunc_value
def __init__(self, functional, controls, scale=1.0,
eval_cb_pre=lambda *args: None,
eval_cb_post=lambda *args: None,
derivative_cb_pre=lambda *args: None,
derivative_cb_post=lambda *args: None,
replay_cb=lambda *args: None,
hessian_cb=lambda *args: None,
cache=None):
#: The objective functional.
self.functional = functional
#: One, or a list of controls.
self.controls = enlist(controls)
# Check the types of the inputs
self.__check_input_types(functional, self.controls, scale, cache)
#: An optional scaling factor for the functional
self.scale = scale
#: An optional callback function that is executed before each functional
#: evaluation.
#: The interace must be eval_cb_pre(m) where
#: m is the control value at which the functional is evaluated.
self.eval_cb_pre = eval_cb_pre
#: An optional callback function that is executed after each functional
#: evaluation.
#: The interace must be eval_cb_post(j, m) where j is the functional value and
#: m is the control value at which the functional is evaluated.
self.eval_cb_post = eval_cb_post
#: An optional callback function that is executed before each functional
#: gradient evaluation.
#: The interface must be eval_cb_pre(m) where m is the control
#: value at which the gradient is evaluated.
self.derivative_cb_pre = derivative_cb_pre
#: An optional callback function that is executed after each functional
#: gradient evaluation.
#: The interface must be eval_cb_post(j, dj, m) where j and dj are the
#: functional and functional gradient values, and m is the control
#: value at which the gradient is evaluated.
self.derivative_cb_post = derivative_cb_post
#: An optional callback function that is executed after each hessian
#: action evaluation. The interface must be hessian_cb(j, m, mdot, h)
#: where mdot is the direction in which the hessian action is evaluated
#: and h the value of the hessian action.
self.hessian_cb = hessian_cb
#: An optional callback function that is executed after for each forward
#: equation during a (forward) solve. The interface must be
#: replay_cb(var, value, m) where var is the libadjoint variable
#: containing information about the variable, value is the associated
#: dolfin object and m is the control at which the functional is
#: evaluated.
self.replay_cb = replay_cb
#: If not None, caching (memoization) will be activated. The control->ouput pairs
#: are stored on disk in the filename given by cache.
self.cache = cache
if cache is not None:
try:
self._cache = pickle.load(open(cache, "r"))
except IOError: # didn't exist
self._cache = {"functional_cache": {},
"derivative_cache": {},
"hessian_cache": {}}
#: Indicator if the user has overloaded the functional evaluation and
#: hence re-annotates the forward model at every evaluation.
#: By default the ReducedFunctional replays the tape for the
#: evaluation.
self.replays_annotation = True
# Stores the functional value of the latest evaluation
self.current_func_value = None
# Set up the Hessian driver
# Note: drivers.hessian currently only supports one control
try:
self.H = drivers.hessian(functional, delist(controls,
list_type=controls), warn=False)
except libadjoint.exceptions.LibadjointErrorNotImplemented:
# Might fail as Hessian support is currently limited
# to a single control
pass
def __call__(self, value):
""" Evaluates the reduced functional for the given control value.
Args:
value: The point in control space where to perform the Taylor test. Must be of the same type as the Control (e.g. Function, Constant or lists of latter).
Returns:
float: The functional value.
"""
# Make sure we do not annotate
# Reset any cached data in dolfin-adjoint
adj_reset_cache()
#: The control values at which the reduced functional is to be evaluated.
value = enlist(value)
# Call callback
self.eval_cb_pre(delist(value, list_type=self.controls))
# Update the control values on the tape
ListControl(self.controls).update(value)
# Check if the result is already cached
if self.cache:
hash = value_hash(value)
if hash in self._cache["functional_cache"]:
# Found a cache
info_green("Got a functional cache hit")
return self._cache["functional_cache"][hash]
# Replay the annotation and evaluate the functional
func_value = 0.
for i in range(adjointer.equation_count):
(fwd_var, output) = adjointer.get_forward_solution(i)
if isinstance(output.data, Function):
output.data.rename(str(fwd_var), "a Function from dolfin-adjoint")
# Call callback
self.replay_cb(fwd_var, output.data, delist(value, list_type=self.controls))
# Check if we checkpointing is active and if yes
# record the exact same checkpoint variables as
# in the initial forward run
if adjointer.get_checkpoint_strategy() != None:
if str(fwd_var) in mem_checkpoints:
storage = libadjoint.MemoryStorage(output, cs = True)
storage.set_overwrite(True)
adjointer.record_variable(fwd_var, storage)
if str(fwd_var) in disk_checkpoints:
storage = libadjoint.MemoryStorage(output)
adjointer.record_variable(fwd_var, storage)
storage = libadjoint.DiskStorage(output, cs = True)
storage.set_overwrite(True)
adjointer.record_variable(fwd_var, storage)
if not str(fwd_var) in mem_checkpoints and not str(fwd_var) in disk_checkpoints:
storage = libadjoint.MemoryStorage(output)
storage.set_overwrite(True)
adjointer.record_variable(fwd_var, storage)
# No checkpointing, so we record everything
else:
storage = libadjoint.MemoryStorage(output)
storage.set_overwrite(True)
adjointer.record_variable(fwd_var, storage)
if i == adjointer.timestep_end_equation(fwd_var.timestep):
func_value += adjointer.evaluate_functional(self.functional, fwd_var.timestep)
if adjointer.get_checkpoint_strategy() != None:
adjointer.forget_forward_equation(i)
self.current_func_value = func_value
# Call callback
self.eval_cb_post(self.scale * func_value, delist(value,
list_type=self.controls))
if self.cache:
# Add result to cache
info_red("Got a functional cache miss")
self._cache["functional_cache"][hash] = self.scale*func_value
return self.scale*func_value
def __call__(self, m_dot, project=False):
flag = misc.pause_annotation()
hess_action_timer = backend.Timer("Hessian action")
m_p = self.m.set_perturbation(m_dot)
last_timestep = adjglobals.adjointer.timestep_count
m_dot = enlist(m_dot)
Hm = []
for m_dot_cmp in m_dot:
if hasattr(m_dot_cmp, 'function_space'):
Hm.append(backend.Function(m_dot_cmp.function_space()))
elif isinstance(m_dot_cmp, float):
Hm.append(0.0)
else:
raise NotImplementedError("Sorry, don't know how to handle this")
tlm_timer = backend.Timer("Hessian action (TLM)")
# run the tangent linear model
for (tlm, tlm_var) in compute_tlm(m_p, forget=None):
pass
tlm_timer.stop()
# run the adjoint and second-order adjoint equations.
for i in range(adjglobals.adjointer.equation_count)[::-1]:
adj_var = adjglobals.adjointer.get_forward_variable(i).to_adjoint(self.J)
# Only recompute the adjoint variable if we do not have it yet
try:
adj = adjglobals.adjointer.get_variable_value(adj_var)
except (libadjoint.exceptions.LibadjointErrorHashFailed, libadjoint.exceptions.LibadjointErrorNeedValue):
adj_timer = backend.Timer("Hessian action (ADM)")
adj = adjglobals.adjointer.get_adjoint_solution(i, self.J)[1]
adj_timer.stop()
storage = libadjoint.MemoryStorage(adj)
adjglobals.adjointer.record_variable(adj_var, storage)
adj = adj.data
soa_timer = backend.Timer("Hessian action (SOA)")
(soa_var, soa_vec) = adjglobals.adjointer.get_soa_solution(i, self.J, m_p)
soa_timer.stop()
soa = soa_vec.data
def hess_inner(Hm, out):
assert len(out) == len(Hm)
for i in range(len(out)):
if out[i] is not None:
if isinstance(Hm[i], backend.Function):
Hm[i].vector().axpy(1.0, out[i].vector())
elif isinstance(Hm[i], float):
Hm[i] += out[i]
else:
raise ValueError, "Do not know what to do with this"
return Hm
func_timer = backend.Timer("Hessian action (derivative formula)")
# now implement the Hessian action formula.
out = self.m.equation_partial_derivative(adjglobals.adjointer, soa, i, soa_var.to_forward())
Hm = hess_inner(Hm, out)
out = self.m.equation_partial_second_derivative(adjglobals.adjointer, adj, i, soa_var.to_forward(), m_dot)
Hm = hess_inner(Hm, out)
if last_timestep > adj_var.timestep:
# We have hit a new timestep, and need to compute this timesteps' \partial^2 J/\partial m^2 contribution
last_timestep = adj_var.timestep
out = self.m.functional_partial_second_derivative(adjglobals.adjointer, self.J, adj_var.timestep, m_dot)
Hm = hess_inner(Hm, out)
func_timer.stop()
storage = libadjoint.MemoryStorage(soa_vec)
storage.set_overwrite(True)
adjglobals.adjointer.record_variable(soa_var, storage)
for Hm_cmp in Hm:
if isinstance(Hm_cmp, backend.Function):
Hm_cmp.rename("d^2(%s)/d(%s)^2" % (str(self.J), str(self.m)), "a Function from dolfin-adjoint")
misc.continue_annotation(flag)
return postprocess(Hm, project, list_type=self.enlisted_controls)