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 hessian(self, m_dot, project=False):
""" Evaluates the Hessian action at the most recently evaluated control
value in direction m_dot.
Args:
m_dot: The direction in control space in which to compute the
Hessian. Must be of the same type as the Control (e.g. Function,
Constant or lists of latter).
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 directional second derivative. The returned type is the same as the control
type.
Note: Hessian evaluations never delete the forward state.
"""
# 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] + [m_dot])
fnspaces = [p.data().function_space() if isinstance(p.data(),
Function) else None for p in self.controls]
if hash in self._cache["hessian_cache"]:
info_green("Got a Hessian cache hit.")
return cache_load(self._cache["hessian_cache"][hash], fnspaces)
else:
info_red("Got a Hessian cache miss")
# Compute the Hessian action by solving the second order adjoint equations
Hm = self.H(m_dot, project=project)
# Apply the scaling factor
scaled_Hm = utils.scale(Hm, self.scale)
# Call callback
control_data = [p.data() for p in self.controls]
if self.current_func_value is not None:
current_func_value = self.scale * self.current_func_value
else:
current_func_value = None
self.hessian_cb(current_func_value,
delist(control_data, list_type=self.controls),
m_dot, scaled_Hm)
# Cache the result
if self.cache is not None:
self._cache["hessian_cache"][hash] = cache_store(scaled_Hm, self.cache)
return scaled_Hm
def postprocess(dJdparam, project, list_type):
if isinstance(dJdparam, list):
return delist([postprocess(x, project, list_type) for x in dJdparam], list_type=list_type)
else:
if project:
dJdparam = project_test(dJdparam)
if isinstance(dJdparam, float):
dJdparam = backend.Constant(dJdparam)
return dJdparam
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 hessian(self, m_dot, project=False):
''' Evaluates the Hessian action in direction m_dot. '''
assert(len(self.controls) == 1)
# 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] + [m_dot])
fnspaces = [p.data().function_space() if isinstance(p.data(),
Function) else None for p in self.controls]
if hash in self._cache["hessian_cache"]:
info_green("Got a Hessian cache hit.")
return cache_load(self._cache["hessian_cache"][hash], fnspaces)
else:
info_red("Got a Hessian cache miss")
# Compute the Hessian action by solving the second order adjoint equations
if isinstance(m_dot, list):
assert len(m_dot) == 1
Hm = self.H(m_dot[0], project=project)
else:
Hm = self.H(m_dot, project=project)
# Apply the scaling factor
scaled_Hm = [utils.scale(Hm, self.scale)]
# Call callback
control_data = [p.data() for p in self.controls]
if self.current_func_value is not None:
current_func_value = self.scale * self.current_func_value
else:
current_func_value = None
self.hessian_cb(current_func_value,
delist(control_data, list_type=self.controls),
m_dot, scaled_Hm[0])
# Cache the result
if self.cache is not None:
self._cache["hessian_cache"][hash] = cache_store(scaled_Hm, self.cache)
return scaled_Hm
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