firedrake.adjoint package¶
Submodules¶
firedrake.adjoint.ensemble_reduced_functional module¶
- class firedrake.adjoint.ensemble_reduced_functional.EnsembleReducedFunctional(J, control, ensemble, scatter_control=True, gather_functional=None)[source]¶
Bases:
ReducedFunctional
Enable solving simultaneously reduced functionals in parallel.
Consider a functional \(J\) and its gradient \(\dfrac{dJ}{dm}\), where \(m\) is the control parameter. Let us assume that \(J\) is the sum of \(N\) functionals \(J_i(m)\), i.e.,
\[J = \sum_{i=1}^{N} J_i(m).\]The gradient over a summation is a linear operation. Therefore, we can write the gradient \(\dfrac{dJ}{dm}\) as
\[\frac{dJ}{dm} = \sum_{i=1}^{N} \frac{dJ_i}{dm},\]The
EnsembleReducedFunctional
allows simultaneous evaluation of \(J_i\) and \(\dfrac{dJ_i}{dm}\). After that, the allreduceEnsemble
operation is employed to sum the functionals and their gradients over an ensemble communicator.If gather_functional is present, then all the values of J are communicated to all ensemble ranks, and passed in a list to gather_functional, which is a reduced functional that expects a list of that size of the relevant types.
- Parameters:
J (pyadjoint.OverloadedType) – An instance of an OverloadedType, usually
pyadjoint.AdjFloat
. This should be the functional that we want to reduce.control (pyadjoint.Control or list of pyadjoint.Control) – A single or a list of Control instances, which you want to map to the functional.
ensemble (Ensemble) – An instance of the
Ensemble
. It is used to communicate the functionals and their derivatives between the ensemble members.scatter_control (bool) – Whether scattering a control (or a list of controls) over the ensemble communicator
Ensemble.ensemble comm
.gather_functional (An instance of the
pyadjoint.ReducedFunctional
.) – that takes in all of the Js.
See also
Notes
The functionals \(J_i\) and the control must be defined over a common ensemble.comm communicator. To understand more about how ensemble parallelism works, please refer to the Firedrake manual.
- derivative(adj_input=1.0, options=None)[source]¶
Compute derivatives of a functional with respect to the control parameters.
- hessian(m_dot, options=None)[source]¶
The Hessian is not yet implemented for ensemble reduced functional.
- Raises:
NotImplementedError – This method is not yet implemented for ensemble reduced functional.
firedrake.adjoint.ufl_constraints module¶
- class firedrake.adjoint.ufl_constraints.UFLConstraint(form, control)[source]¶
Bases:
Constraint
Easily implement scalar constraints using UFL.
The form must be a 0-form that depends on a Function control.
- function(m)[source]¶
Evaluate c(m), where c(m) == 0 for equality constraints and c(m) >= 0 for inequality constraints.
c(m) must return a numpy array or a dolfin Function or Constant.
- hessian_action(m, dm, dp, result)[source]¶
Computes the Hessian action of c(m) in direction dm and dp.
Stores the result in result.
- jacobian(m)[source]¶
Returns the full Jacobian matrix as a list of vector-like objects representing the gradient of the constraint function with respect to the parameter m.
The objects returned must be of the same type as m’s data.
- jacobian_action(m, dm, result)[source]¶
Computes the Jacobian action of c(m) in direction dm.
Stores the result in result.
- class firedrake.adjoint.ufl_constraints.UFLEqualityConstraint(form, control)[source]¶
Bases:
UFLConstraint
,EqualityConstraint
- class firedrake.adjoint.ufl_constraints.UFLInequalityConstraint(form, control)[source]¶
Bases:
UFLConstraint
,InequalityConstraint
Module contents¶
The public interface to Firedrake’s adjoint.
To start taping, run:
from firedrake.adjoint import *
continue_annotation()