def __init__(self, functional, controls, solver, parameters):
# For consistency with the dolfin-adjoint API.
self.scale = parameters.scale
self.solver = solver
if not isinstance(solver, Solver):
raise ValueError, "solver argument of wrong type."
self.functional = functional
if not isinstance(functional, PrototypeFunctional):
raise ValueError, "invalid functional argument."
# Create the default parameters
self.parameters = parameters
# Hidden attributes
self._solver_params = solver.parameters
self._problem_params = solver.problem.parameters
self._time_integrator = None
self._automatic_scaling_factor = None
# Caching variables that store which controls the last forward run was
# performed
self.last_m = None
if self.solver.parameters.dump_period > 0:
turbine_filename = os.path.join(solver.parameters.output_dir,
"turbines.pvd")
self.turbine_file = File(turbine_filename, "compressed")
if self._solver_params.output_turbine_power:
power_filename = os.path.join(solver.parameters.output_dir,
"power.pvd")
self.power_file = File(power_filename, "compressed")
# dolfin-adjoint requires the ReducedFunctional to have a member
# variable `parameter` which must be a list comprising an instance of a
# class (here, TurbineFarmControl) which has a method named `data`
# which returns a numpy.ndarray of the parameters used for optimisation,
# e.g. the turbine frictions and positions.
if not hasattr(controls, "__getitem__"):
controls = [controls]
self.controls = controls
self._compute_functional_mem = MemoizeMutable(self._compute_functional)
self._compute_gradient_mem = MemoizeMutable(self._compute_gradient)
# Load checkpoints from file
if self.parameters.load_checkpoints:
self._load_checkpoint()
if self._solver_params.print_individual_turbine_power:
# if this is enabled, we need to instantiate the relevant helper
# and pass this to the solver
output_writer = helpers.OutputWriter(self.functional)
self._solver_params.output_writer = output_writer
def __init__(self, functional, controls, solver, parameters):
# For consistency with the dolfin-adjoint API.
self.scale = parameters.scale
self.solver = solver
if not isinstance(solver, Solver):
raise ValueError, "solver argument of wrong type."
self.functional = functional
if not isinstance(functional, PrototypeFunctional):
raise ValueError, "invalid functional argument."
# Create the default parameters
self.parameters = parameters
# Hidden attributes
self._solver_params = solver.parameters
self._problem_params = solver.problem.parameters
self._time_integrator = None
self._automatic_scaling_factor = None
# Caching variables that store which controls the last forward run was
# performed
self.last_m = None
if self.solver.parameters.dump_period > 0:
turbine_filename = os.path.join(solver.parameters.output_dir, "turbines.pvd")
self.turbine_file = File(turbine_filename, "compressed")
if self._solver_params.output_turbine_power:
power_filename = os.path.join(solver.parameters.output_dir, "power.pvd")
self.power_file = File(power_filename, "compressed")
# dolfin-adjoint requires the ReducedFunctional to have a member
# variable `parameter` which must be a list comprising an instance of a
# class (here, TurbineFarmControl) which has a method named `data`
# which returns a numpy.ndarray of the parameters used for optimisation,
# e.g. the turbine frictions and positions.
if not hasattr(controls, "__getitem__"):
controls = [controls]
self.controls = controls
self._compute_functional_mem = MemoizeMutable(self._compute_functional)
self._compute_gradient_mem = MemoizeMutable(self._compute_gradient)
# Load checkpoints from file
if self.parameters.load_checkpoints:
self._load_checkpoint()
if self._solver_params.print_individual_turbine_power:
# if this is enabled, we need to instantiate the relevant helper
# and pass this to the solver
output_writer = helpers.OutputWriter(self.functional)
self._solver_params.output_writer = output_writer
class ReducedFunctional(ReducedFunctionalPrototype):
"""
Following parameters are expected:
:ivar functional: a :class:`PrototypeFunctional` class.
:ivar controls: a :class:`TurbineFarmControl` or :class:`dolfin_adjoint.DolfinAdjointControl` class.
:ivar solver: a :class:`Solver` object.
:ivar parameters: a :class:`ReducedFunctionalParameters` object.
This class has a parameter attribute for further adjustments.
"""
def __init__(self, functional, controls, solver, parameters):
# For consistency with the dolfin-adjoint API.
self.scale = parameters.scale
self.solver = solver
if not isinstance(solver, Solver):
raise ValueError, "solver argument of wrong type."
self.functional = functional
if not isinstance(functional, PrototypeFunctional):
raise ValueError, "invalid functional argument."
# Create the default parameters
self.parameters = parameters
# Hidden attributes
self._solver_params = solver.parameters
self._problem_params = solver.problem.parameters
self._time_integrator = None
self._automatic_scaling_factor = None
# Caching variables that store which controls the last forward run was
# performed
self.last_m = None
if self.solver.parameters.dump_period > 0:
turbine_filename = os.path.join(solver.parameters.output_dir, "turbines.pvd")
self.turbine_file = File(turbine_filename, "compressed")
if self._solver_params.output_turbine_power:
power_filename = os.path.join(solver.parameters.output_dir, "power.pvd")
self.power_file = File(power_filename, "compressed")
# dolfin-adjoint requires the ReducedFunctional to have a member
# variable `parameter` which must be a list comprising an instance of a
# class (here, TurbineFarmControl) which has a method named `data`
# which returns a numpy.ndarray of the parameters used for optimisation,
# e.g. the turbine frictions and positions.
if not hasattr(controls, "__getitem__"):
controls = [controls]
self.controls = controls
self._compute_functional_mem = MemoizeMutable(self._compute_functional)
self._compute_gradient_mem = MemoizeMutable(self._compute_gradient)
# Load checkpoints from file
if self.parameters.load_checkpoints:
self._load_checkpoint()
if self._solver_params.print_individual_turbine_power:
# if this is enabled, we need to instantiate the relevant helper
# and pass this to the solver
output_writer = helpers.OutputWriter(self.functional)
self._solver_params.output_writer = output_writer
@staticmethod
def default_parameters():
""" Return the default parameters for the :class:`ReducedFunctional`.
"""
return ReducedFunctionalParameters()
def _compute_gradient(self, m, forget=True):
""" Compute the functional gradient for the turbine positions/frictions array """
farm = self.solver.problem.parameters.tidal_farm
# If any of the parameters changed, the forward model needs to be re-run
if numpy.any(m != self.last_m):
self._compute_functional(m, annotate=True)
J = self.time_integrator.dolfin_adjoint_functional()
# Output power
if self.solver.parameters.dump_period > 0:
if self._solver_params.output_turbine_power:
turbines = farm.turbine_cache["turbine_field"]
power = self.functional.power(self.solver.current_state, turbines)
self.power_file << project(power,
farm._turbine_function_space,
annotate=False)
if farm.turbine_specification.controls.dynamic_friction:
parameters = []
for i in xrange(len(farm._parameters["friction"])):
parameters.append(
FunctionControl("turbine_friction_cache_t_%i" % i))
else:
parameters = FunctionControl("turbine_friction_cache")
djdtf = dolfin_adjoint.compute_gradient(J, parameters, forget=forget)
dolfin.parameters["adjoint"]["stop_annotating"] = False
# Decide if we need to apply the chain rule to get the gradient of
# interest.
if farm.turbine_specification.smeared:
# We are looking for the gradient with respect to the friction
dj = dolfin_adjoint.optimization.get_global(djdtf)
else:
# Let J be the functional, m the parameter and u the solution of the
# PDE equation F(u) = 0.
# Then we have
# dJ/dm = (\partial J)/(\partial u) * (d u) / d m + \partial J / \partial m
# = adj_state * \partial F / \partial u + \partial J / \partial m
# In this particular case m = turbine_friction, J = \sum_t(ft)
dj = []
if farm.turbine_specification.controls.friction:
# Compute the derivatives with respect to the turbine friction
for tfd in farm.turbine_cache["turbine_derivative_friction"]:
farm.update()
dj.append(djdtf.vector().inner(tfd.vector()))
elif farm.turbine_specification.controls.dynamic_friction:
# Compute the derivatives with respect to the turbine friction
for djdtf_arr, t in zip(djdtf, farm.turbine_cache["turbine_derivative_friction"]):
for tfd in t:
farm.update()
dj.append(djdtf_arr.vector().inner(tfd.vector()))
if farm.turbine_specification.controls.position:
# Compute the derivatives with respect to the turbine position
for d in farm.turbine_cache["turbine_derivative_pos"]:
for var in ('turbine_pos_x', 'turbine_pos_y'):
farm.update()
tfd = d[var]
dj.append(djdtf.vector().inner(tfd.vector()))
dj = numpy.array(dj)
return dj
def _compute_functional(self, m, annotate=True):
""" Compute the functional of interest for the turbine positions/frictions array """
self.last_m = m
self._update_turbine_farm(m)
farm = self.solver.problem.parameters.tidal_farm
# Configure dolfin-adjoint
adj_reset()
dolfin.parameters["adjoint"]["record_all"] = True
self._set_revolve_parameters()
# Solve the shallow water system and integrate the functional of
# interest.
final_only = (not self.solver.problem._is_transient or
self._problem_params.functional_final_time_only)
self.time_integrator = TimeIntegrator(self.solver.problem, self.functional,
final_only)
for sol in self.solver.solve(annotate=annotate):
self.time_integrator.add(sol["time"], sol["state"], sol["tf"],
sol["is_final"])
return self.time_integrator.integrate()
def _set_revolve_parameters(self):
if (hasattr(self._solver_params, "revolve_parameters")
and self._solver_params.revolve_parameters is not None):
(strategy,
snaps_on_disk,
snaps_in_ram,
verbose) = self._farm.params['revolve_parameters']
adj_checkpointing(
strategy,
self._problem_params.finish_time/self._problem_params.dt,
snaps_on_disk=snaps_on_disk,
snaps_in_ram=snaps_in_ram,
verbose=verbose)
def _update_turbine_farm(self, m):
""" Update the turbine farm from the flattened parameter array m. """
farm = self.solver.problem.parameters.tidal_farm
if farm.turbine_specification.smeared:
farm._parameters["friction"] = m
else:
controlled_by = farm.turbine_specification.controls
shift = 0
if controlled_by.friction:
shift = len(farm._parameters["friction"])
farm._parameters["friction"] = m[:shift]
elif controlled_by.dynamic_friction:
shift = len(numpy.reshape(farm._parameters["friction"],-1))
nb_turbines = len(farm._parameters["position"])
farm._parameters["friction"] = (
numpy.reshape(m[:shift], (-1, nb_turbines)).tolist())
if controlled_by.position:
m_pos = m[shift:]
farm._parameters["position"] = (
numpy.reshape(m_pos, (-1,2)).tolist())
# Update the farm cache.
farm.update()
def _save_checkpoint(self):
""" Checkpoint the reduced functional from which can be used to restart
the turbine optimisation. """
base_filename = self.parameters.checkpoints_basefilename
base_path = os.path.join(self._solver_params.output_dir, base_filename)
self._compute_functional_mem.save_checkpoint(base_path + "_fwd.dat")
self._compute_gradient_mem.save_checkpoint(base_path + "_adj.dat")
def _load_checkpoint(self):
""" Checkpoint the reduceduced functional from which can be used to
restart the turbine optimisation. """
base_filename = self.parameters.checkpoints_basefilename
base_path = os.path.join(self._solver_params.output_dir, base_filename)
self._compute_functional_mem.load_checkpoint(base_path + "_fwd.dat")
self._compute_gradient_mem.load_checkpoint(base_path + "_adj.dat")
def evaluate(self, m, annotate=True):
""" Return the functional value for the given parameter array. """
log(INFO, 'Start evaluation of j')
timer = dolfin.Timer("j evaluation")
j = self._compute_functional_mem(m, annotate=annotate)
timer.stop()
if self.parameters.save_checkpoints:
self._save_checkpoint()
log(INFO, 'Runtime: %f s.' % timer.value())
log(INFO, 'j = %e.' % float(j))
self.last_j = j
if self.parameters.automatic_scaling:
if self._automatic_scaling_factor is None:
# Computing dj will set the automatic scaling factor.
log(INFO, ("Computing derivative to determine the automatic "
"scaling factor"))
self._dj(m, forget=False, new_optimisation_iteration=False)
return j*self.scale*self._automatic_scaling_factor
else:
return j*self.scale
def _dj(self, m, forget, new_optimisation_iteration=True):
""" This memoised function returns the gradient of the functional for the parameter choice m. """
log(INFO, 'Start evaluation of dj')
timer = dolfin.Timer("dj evaluation")
dj = self._compute_gradient_mem(m, forget)
# We assume that the gradient is computed at and only at the beginning
# of each new optimisation iteration. Hence, this is the right moment
# to store the turbine friction field and to increment the optimisation
# iteration counter.
if new_optimisation_iteration:
self.solver.optimisation_iteration += 1
farm = self.solver.problem.parameters.tidal_farm
if (self.solver.parameters.dump_period > 0 and
farm is not None):
# A cache hit skips the turbine cache update, so we need
# trigger it manually.
if self._compute_gradient_mem.has_cache(m, forget):
self._update_turbine_farm(m)
if farm.turbine_specification.controls.dynamic_friction:
log(WARNING, ("Turbine VTU output not yet implemented for "
" dynamic turbine control"))
else:
self.turbine_file << farm.turbine_cache["turbine_field"]
# Compute the total amount of friction due to turbines
if farm.turbine_specification.smeared:
log(INFO, "Total amount of friction: %f" %
assemble(farm.turbine_cache["turbine_field"]*dx))
if self.parameters.save_checkpoints:
self._save_checkpoint()
log(INFO, "Runtime: " + str(timer.stop()) + " s")
log(INFO, "|dj| = " + str(numpy.linalg.norm(dj)))
if self.parameters.automatic_scaling:
self._set_automatic_scaling_factor(dj)
return dj*self.scale*self._automatic_scaling_factor
else:
return dj*self.scale
def _set_automatic_scaling_factor(self, dj):
""" Compute the scaling factor if never done before. """
if self._automatic_scaling_factor is None:
farm = self.solver.problem.parameters.tidal_farm
if not farm.turbine_specification.controls.position:
raise NotImplementedError("Automatic scaling only works if "
"the turbine positions are control "
"parameters")
if (farm.turbine_specification.controls.friction or
farm.turbine_specification.controls.dynamic_friction):
assert(len(dj) % 3 == 0)
# Exclude the first third from the automatic scaling as it
# contains the friction coefficients.
djl2 = max(abs(dj[len(dj) / 3:]))
else:
djl2 = max(abs(dj))
if djl2 == 0:
log(ERROR, ("Automatic scaling failed: The gradient at the "
"parameter point is zero."))
else:
self._automatic_scaling_factor = abs(
self.parameters.automatic_scaling*
farm.turbine_specification.diameter/
djl2/
self.scale)
log(INFO, "Set automatic scaling factor to %e." %
self._automatic_scaling_factor)
def derivative(self, m_array, forget=True, **kwargs):
""" Computes the first derivative of the functional with respect to its
parameters by solving the adjoint equations. """
return self._dj(m_array, forget)
def __init__(self, functional, controls, solver, parameters):
# For consistency with the dolfin-adjoint API.
self.scale = parameters.scale
self.rf = self
self.solver = solver
if not isinstance(solver, Solver):
raise ValueError, "solver argument of wrong type."
self.functional = functional
if not isinstance(functional, PrototypeFunctional):
raise ValueError, "invalid functional argument."
# Create the default parameters
self.parameters = parameters
# Hidden attributes
self._solver_params = solver.parameters
self._problem_params = solver.problem.parameters
self._time_integrator = None
self._automatic_scaling_factor = None
# For storing the friction function for each time step as one changing
# function and not as multiple functions
if (isinstance(self.solver.problem.parameters.tidal_farm.\
friction_function, list)):
self._friction_plot_function = self.solver.problem.parameters\
.tidal_farm.friction_function[0]
else:
self._friction_plot_function = self.solver.problem.parameters\
.tidal_farm.friction_function
# Caching variables that store which controls the last forward run was
# performed
self.last_m = None
if self.solver.parameters.dump_period > 0:
turbine_filename = os.path.join(solver.parameters.output_dir, "turbines.pvd")
self.turbine_file = File(turbine_filename, "compressed")
if self._solver_params.output_turbine_power:
power_filename = os.path.join(solver.parameters.output_dir, "power.pvd")
self.power_file = File(power_filename, "compressed")
# Just to clean any 'j.txt' files from previous simulations.
if self._solver_params.output_j:
dir = os.path.join(self.solver.parameters.output_dir,
"iter_{}".format(self.solver.optimisation_iteration))
if not os.path.exists(dir):
os.mkdir(dir)
filename = os.path.join(dir, "j.txt")
j_file = open(filename, 'w')
j_file.close()
# dolfin-adjoint requires the ReducedFunctional to have a member
# variable `parameter` which must be a list comprising an instance of a
# class (here, TurbineFarmControl) which has a method named `data`
# which returns a numpy.ndarray of the parameters used for optimisation,
# e.g. the turbine frictions and positions.
if not hasattr(controls, "__getitem__"):
controls = [controls]
self.controls = controls
self._compute_functional_mem = MemoizeMutable(self._compute_functional)
self._compute_gradient_mem = MemoizeMutable(self._compute_gradient)
# Load checkpoints from file
if self.parameters.load_checkpoints:
self._load_checkpoint()
if (self._solver_params.print_individual_turbine_power
or ((self.solver.parameters.dump_period > 0)
and self._solver_params.output_turbine_power)):
# if this is enabled, we need to instantiate the relevant helper
# and pass this to the solver
output_writer = helpers.OutputWriter(self.functional)
self._solver_params.output_writer = output_writer
def __init__(self, functional, controls, solver, parameters):
# For consistency with the dolfin-adjoint API.
self.scale = parameters.scale
self.rf = self
self.solver = solver
if not isinstance(solver, Solver):
raise ValueError, "solver argument of wrong type."
self.functional = functional
if not isinstance(functional, PrototypeFunctional):
raise ValueError, "invalid functional argument."
# Create the default parameters
self.parameters = parameters
# Hidden attributes
self._solver_params = solver.parameters
self._problem_params = solver.problem.parameters
self._time_integrator = None
self._automatic_scaling_factor = None
# For storing the friction function for each time step as one changing
# function and not as multiple functions
if (isinstance(self.solver.problem.parameters.tidal_farm.\
friction_function, list)):
self._friction_plot_function = self.solver.problem.parameters\
.tidal_farm.friction_function[0]
else:
self._friction_plot_function = self.solver.problem.parameters\
.tidal_farm.friction_function
# Caching variables that store which controls the last forward run was
# performed
self.last_m = None
if self.solver.parameters.dump_period > 0:
turbine_filename = os.path.join(solver.parameters.output_dir, "turbines.pvd")
self.turbine_file = File(turbine_filename, "compressed")
if self._solver_params.output_turbine_power:
power_filename = os.path.join(solver.parameters.output_dir, "power.pvd")
self.power_file = File(power_filename, "compressed")
# Just to clean any 'j.txt' files from previous simulations.
if self._solver_params.output_j:
dir = os.path.join(self.solver.parameters.output_dir,
"iter_{}".format(self.solver.optimisation_iteration))
if not os.path.exists(dir):
os.mkdir(dir)
filename = os.path.join(dir, "j.txt")
j_file = open(filename, 'w')
j_file.close()
# dolfin-adjoint requires the ReducedFunctional to have a member
# variable `parameter` which must be a list comprising an instance of a
# class (here, TurbineFarmControl) which has a method named `data`
# which returns a numpy.ndarray of the parameters used for optimisation,
# e.g. the turbine frictions and positions.
if not hasattr(controls, "__getitem__"):
controls = [controls]
self.controls = controls
self._compute_functional_mem = MemoizeMutable(self._compute_functional)
self._compute_gradient_mem = MemoizeMutable(self._compute_gradient)
# Load checkpoints from file
if self.parameters.load_checkpoints:
self._load_checkpoint()
if (self._solver_params.print_individual_turbine_power
or ((self.solver.parameters.dump_period > 0)
and self._solver_params.output_turbine_power)):
# if this is enabled, we need to instantiate the relevant helper
# and pass this to the solver
output_writer = helpers.OutputWriter(self.functional)
self._solver_params.output_writer = output_writer
class ReducedFunctional(ReducedFunctionalPrototype):
"""
Following parameters are expected:
:ivar functional: a :class:`PrototypeFunctional` class.
:ivar controls: a :class:`TurbineFarmControl` or :class:`dolfin_adjoint.DolfinAdjointControl` class.
:ivar solver: a :class:`Solver` object.
:ivar parameters: a :class:`ReducedFunctionalParameters` object.
This class has a parameter attribute for further adjustments.
"""
def __init__(self, functional, controls, solver, parameters):
# For consistency with the dolfin-adjoint API.
self.scale = parameters.scale
self.rf = self
self.solver = solver
if not isinstance(solver, Solver):
raise ValueError, "solver argument of wrong type."
self.functional = functional
if not isinstance(functional, PrototypeFunctional):
raise ValueError, "invalid functional argument."
# Create the default parameters
self.parameters = parameters
# Hidden attributes
self._solver_params = solver.parameters
self._problem_params = solver.problem.parameters
self._time_integrator = None
self._automatic_scaling_factor = None
# For storing the friction function for each time step as one changing
# function and not as multiple functions
if (isinstance(self.solver.problem.parameters.tidal_farm.\
friction_function, list)):
self._friction_plot_function = self.solver.problem.parameters\
.tidal_farm.friction_function[0]
else:
self._friction_plot_function = self.solver.problem.parameters\
.tidal_farm.friction_function
# Caching variables that store which controls the last forward run was
# performed
self.last_m = None
if self.solver.parameters.dump_period > 0:
turbine_filename = os.path.join(solver.parameters.output_dir, "turbines.pvd")
self.turbine_file = File(turbine_filename, "compressed")
if self._solver_params.output_turbine_power:
power_filename = os.path.join(solver.parameters.output_dir, "power.pvd")
self.power_file = File(power_filename, "compressed")
# Just to clean any 'j.txt' files from previous simulations.
if self._solver_params.output_j:
dir = os.path.join(self.solver.parameters.output_dir,
"iter_{}".format(self.solver.optimisation_iteration))
if not os.path.exists(dir):
os.mkdir(dir)
filename = os.path.join(dir, "j.txt")
j_file = open(filename, 'w')
j_file.close()
# dolfin-adjoint requires the ReducedFunctional to have a member
# variable `parameter` which must be a list comprising an instance of a
# class (here, TurbineFarmControl) which has a method named `data`
# which returns a numpy.ndarray of the parameters used for optimisation,
# e.g. the turbine frictions and positions.
if not hasattr(controls, "__getitem__"):
controls = [controls]
self.controls = controls
self._compute_functional_mem = MemoizeMutable(self._compute_functional)
self._compute_gradient_mem = MemoizeMutable(self._compute_gradient)
# Load checkpoints from file
if self.parameters.load_checkpoints:
self._load_checkpoint()
if (self._solver_params.print_individual_turbine_power
or ((self.solver.parameters.dump_period > 0)
and self._solver_params.output_turbine_power)):
# if this is enabled, we need to instantiate the relevant helper
# and pass this to the solver
output_writer = helpers.OutputWriter(self.functional)
self._solver_params.output_writer = output_writer
@staticmethod
def default_parameters():
""" Return the default parameters for the :class:`ReducedFunctional`.
"""
return ReducedFunctionalParameters()
def _compute_gradient(self, m, forget=True):
""" Compute the functional gradient for the turbine positions/frictions array """
farm = self.solver.problem.parameters.tidal_farm
# If any of the parameters changed, the forward model needs to be re-run
if self.last_m is None or numpy.any(m != self.last_m):
self._compute_functional(m, annotate=True)
J = self.time_integrator.dolfin_adjoint_functional(self.solver.state)
# Output power
if self.solver.parameters.dump_period > 0:
if self._solver_params.output_turbine_power:
turbines = farm.turbine_cache["turbine_field"]
power = self.functional.power(self.solver.state, turbines)
self.power_file << project(power,
farm._turbine_function_space,
annotate=False)
if farm.turbine_specification.controls.dynamic_friction:
parameters = []
for i in xrange(len(farm._parameters["friction"])):
parameters.append(
FunctionControl("turbine_friction_cache_t_%i" % i))
else:
parameters = FunctionControl("turbine_friction_cache")
djdtf = dolfin_adjoint.compute_gradient(J, parameters, forget=forget)
dolfin.parameters["adjoint"]["stop_annotating"] = False
# Decide if we need to apply the chain rule to get the gradient of
# interest.
if farm.turbine_specification.smeared:
# We are looking for the gradient with respect to the friction
dj = dolfin_adjoint.optimization.get_global(djdtf)
else:
# Let J be the functional, m the parameter and u the solution of the
# PDE equation F(u) = 0.
# Then we have
# dJ/dm = (\partial J)/(\partial u) * (d u) / d m + \partial J / \partial m
# = adj_state * \partial F / \partial u + \partial J / \partial m
# In this particular case m = turbine_friction, J = \sum_t(ft)
dj = []
if farm.turbine_specification.controls.friction:
# Compute the derivatives with respect to the turbine friction
for tfd in farm.turbine_cache["turbine_derivative_friction"]:
farm.update()
dj.append(djdtf.vector().inner(tfd.vector()))
elif farm.turbine_specification.controls.dynamic_friction:
# Compute the derivatives with respect to the turbine friction
for djdtf_arr, t in zip(djdtf,
farm.turbine_cache["turbine_derivative_friction"]):
for tfd in t:
farm.update()
dj.append(djdtf_arr.vector().inner(tfd.vector()))
if (farm.turbine_specification.controls.position):
if (farm.turbine_specification.controls.dynamic_friction):
# Compute the derivatives with respect to the turbine position
farm.update()
turb_deriv_pos = farm.turbine_cache["turbine_derivative_pos"]
n_time_steps =len(turb_deriv_pos)
for n in xrange(farm.number_of_turbines):
for var in ('turbine_pos_x', 'turbine_pos_y'):
dj_t = 0
for t in xrange(n_time_steps):
tfd_t = turb_deriv_pos[t][n][var]
dj_t += djdtf_arr.vector().inner(tfd_t.vector())
dj.append(dj_t)
else:
# Compute the derivatives with respect to the turbine position
for d in farm.turbine_cache["turbine_derivative_pos"]:
for var in ('turbine_pos_x', 'turbine_pos_y'):
farm.update()
tfd = d[var]
dj.append(djdtf.vector().inner(tfd.vector()))
dj = numpy.array(dj)
return dj
def _compute_functional(self, m, annotate=True):
""" Compute the functional of interest for the turbine positions/frictions array """
self.last_m = m
self._update_turbine_farm(m)
farm = self.solver.problem.parameters.tidal_farm
# Configure dolfin-adjoint
adj_reset()
dolfin.parameters["adjoint"]["record_all"] = True
self._set_revolve_parameters()
# Solve the shallow water system and integrate the functional of
# interest.
final_only = (not self.solver.problem._is_transient or
self._problem_params.functional_final_time_only)
self.time_integrator = TimeIntegrator(self.solver.problem, self.functional,
final_only)
for sol in self.solver.solve(annotate=annotate):
self.time_integrator.add(sol["time"], sol["state"], sol["tf"],
sol["is_final"])
log(INFO, "Temporal breakdown of functional evaluation")
log(INFO, "----------------------------------")
for time, val in zip(self.time_integrator.times, self.time_integrator.vals):
log(INFO, "Time: {} s\t Value: {}.".format(float(time), val))
log(INFO, "----------------------------------")
if ((self.solver.parameters.dump_period > 0)
and self._solver_params.output_temporal_breakdown_of_j):
dir = self.solver.get_optimisation_and_search_directory()
filename = os.path.join(dir, "temporal_breakdown_of_j.txt")
numpy.savetxt(filename, self.time_integrator.vals)
j = float(self.time_integrator.integrate())
if ((self.solver.parameters.dump_period > 0)
and self._solver_params.output_j):
dir = os.path.join(self.solver.parameters.output_dir,
"iter_{}".format(self.solver.optimisation_iteration))
if not os.path.exists(dir):
os.mkdir(dir)
filename = os.path.join(dir, "j.txt")
j_file = open(filename, 'a')
numpy.savetxt(j_file, [j])
j_file.close()
self.solver.search_iteration += 1
return j
def _set_revolve_parameters(self):
if (hasattr(self._solver_params, "revolve_parameters")
and self._solver_params.revolve_parameters is not None):
(strategy,
snaps_on_disk,
snaps_in_ram,
verbose) = self._farm.params['revolve_parameters']
adj_checkpointing(
strategy,
self._problem_params.finish_time/self._problem_params.dt,
snaps_on_disk=snaps_on_disk,
snaps_in_ram=snaps_in_ram,
verbose=verbose)
def _update_turbine_farm(self, m):
""" Update the turbine farm from the flattened parameter array m. """
farm = self.solver.problem.parameters.tidal_farm
if farm.turbine_specification.smeared:
farm._parameters["friction"] = m
else:
controlled_by = farm.turbine_specification.controls
shift = 0
if controlled_by.friction:
shift = len(farm._parameters["friction"])
farm._parameters["friction"] = m[:shift]
elif controlled_by.dynamic_friction:
shift = len(numpy.reshape(farm._parameters["friction"],-1))
nb_turbines = len(farm._parameters["position"])
farm._parameters["friction"] = (
numpy.reshape(m[:shift], (-1, nb_turbines)).tolist())
if controlled_by.position:
m_pos = m[shift:]
farm._parameters["position"] = (
numpy.reshape(m_pos, (-1,2)).tolist())
# Update the farm cache.
farm.update()
def _save_checkpoint(self):
""" Checkpoint the reduced functional from which can be used to restart
the turbine optimisation. """
base_filename = self.parameters.checkpoints_basefilename
base_path = os.path.join(self._solver_params.output_dir, base_filename)
self._compute_functional_mem.save_checkpoint(base_path + "_fwd.dat")
self._compute_gradient_mem.save_checkpoint(base_path + "_adj.dat")
def _load_checkpoint(self):
""" Checkpoint the reduceduced functional from which can be used to
restart the turbine optimisation. """
base_filename = self.parameters.checkpoints_basefilename
base_path = os.path.join(self._solver_params.output_dir, base_filename)
self._compute_functional_mem.load_checkpoint(base_path + "_fwd.dat")
self._compute_gradient_mem.load_checkpoint(base_path + "_adj.dat")
def evaluate(self, m, annotate=True):
""" Return the functional value for the given parameter array. """
log(INFO, 'Start evaluation of j')
timer = dolfin.Timer("j evaluation")
j = self._compute_functional_mem(m, annotate=annotate)
timer.stop()
if self.parameters.save_checkpoints:
self._save_checkpoint()
log(INFO, 'Runtime: %f s.' % timer.elapsed()[0])
log(INFO, 'j = %e.' % float(j))
self.last_j = j
if ((self.solver.parameters.dump_period > 0)
and self.solver.parameters.output_control_array):
dir = self.solver.get_optimisation_and_search_directory()
filename = os.path.join(dir, "control_array.txt")
numpy.savetxt(filename, m)
if self.parameters.automatic_scaling:
if self._automatic_scaling_factor is None:
# Computing dj will set the automatic scaling factor.
log(INFO, ("Computing derivative to determine the automatic "
"scaling factor"))
self._dj(m, forget=False, new_optimisation_iteration=False)
return j*self.scale*self._automatic_scaling_factor
else:
return j*self.scale
def _dj(self, m, forget, new_optimisation_iteration=True):
""" This memoised function returns the gradient of the functional for the parameter choice m. """
log(INFO, 'Start evaluation of dj')
timer = dolfin.Timer("dj evaluation")
dj = self._compute_gradient_mem(m, forget)
# We assume that the gradient is computed at and only at the beginning
# of each new optimisation iteration. Hence, this is the right moment
# to store the turbine friction field and to increment the optimisation
# iteration counter.
if new_optimisation_iteration:
farm = self.solver.problem.parameters.tidal_farm
if (self.solver.parameters.dump_period > 0 and
farm is not None):
# A cache hit skips the turbine cache update, so we need
# trigger it manually.
if self._compute_gradient_mem.has_cache(m, forget):
self._update_turbine_farm(m)
if farm.turbine_specification.controls.dynamic_friction:
dir = self.solver.get_optimisation_and_search_directory()
filename = os.path.join(dir, "turbine_friction.pvd")
friction_file = File(filename)
for timestep in range(0,len(farm.friction_function)):
self._friction_plot_function.assign(
farm.friction_function[timestep])
friction_file << self._friction_plot_function
else:
self.turbine_file << farm.turbine_cache["turbine_field"]
# Compute the total amount of friction due to turbines
if farm.turbine_specification.smeared:
log(INFO, "Total amount of friction: %f" %
assemble(farm.turbine_cache["turbine_field"]*dx))
self.solver.optimisation_iteration += 1
self.solver.search_iteration = 0
if self.parameters.save_checkpoints:
self._save_checkpoint()
log(INFO, "Runtime: " + str(timer.stop()) + " s")
log(INFO, "|dj| = " + str(numpy.linalg.norm(dj)))
if self.parameters.automatic_scaling:
self._set_automatic_scaling_factor(dj)
return dj*self.scale*self._automatic_scaling_factor
else:
return dj*self.scale
def _set_automatic_scaling_factor(self, dj):
""" Compute the scaling factor if never done before. """
if self._automatic_scaling_factor is None:
farm = self.solver.problem.parameters.tidal_farm
if not farm.turbine_specification.controls.position:
raise NotImplementedError("Automatic scaling only works if "
"the turbine positions are control "
"parameters")
if (farm.turbine_specification.controls.friction or
farm.turbine_specification.controls.dynamic_friction):
assert(len(dj) % 3 == 0)
# Exclude the first third from the automatic scaling as it
# contains the friction coefficients.
djl2 = max(abs(dj[len(dj) / 3:]))
else:
djl2 = max(abs(dj))
if djl2 == 0:
log(ERROR, ("Automatic scaling failed: The gradient at the "
"parameter point is zero."))
else:
self._automatic_scaling_factor = abs(
self.parameters.automatic_scaling*
farm.turbine_specification.diameter/
djl2/
self.scale)
log(INFO, "Set automatic scaling factor to %e." %
self._automatic_scaling_factor)
def derivative(self, m_array, forget=True, **kwargs):
""" Computes the first derivative of the functional with respect to its
parameters by solving the adjoint equations. """
return self._dj(m_array, forget)
def derivative_with_check(self, m, seed=0.1, tol=1.8, forget=True):
''' This function checks the correctness and returns the gradient of
the functional for the parameter choice m. '''
log(INFO, "Checking derivative at m = " + str(m))
p = numpy.random.rand(len(m))
minconv = helpers.test_gradient_array(self.evaluate,
self._dj,
m,
seed=seed,
perturbation_direction=p)
if minconv < tol:
log(INFO, "The gradient taylor remainder test failed.")
sys.exit(1)
else:
log(INFO, "The gradient taylor remainder test passed.")
return self._dj(m, forget)
def mpi_comm(self):
return mpi_comm_world()