ROL
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#include <example_01.hpp>
Public Member Functions | |
Normalization_Constraint (int n, Real dx) | |
void | value (Vector< Real > &c, const Vector< Real > &psi, Real &tol) |
Evaluate \(c[\psi]\). More... | |
void | applyJacobian (Vector< Real > &jv, const Vector< Real > &v, const Vector< Real > &psi, Real &tol) |
Evaluate \(c'[\psi]v\). More... | |
void | applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &psi, Real &tol) |
Evaluate \((c'[\psi])^\ast v\). More... | |
void | applyAdjointHessian (Vector< Real > &ahuv, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &psi, Real &tol) |
Evaluate \(((c''[\psi])^\ast v)u\). More... | |
Normalization_Constraint (int n, Real dx, Teuchos::RCP< FiniteDifference< Real > > fd, bool exactsolve) | |
void | value (Vector< Real > &c, const Vector< Real > &psi, Real &tol) |
Evaluate \(c[\psi]\). More... | |
void | applyJacobian (Vector< Real > &jv, const Vector< Real > &v, const Vector< Real > &psi, Real &tol) |
Evaluate \(c'[\psi]v\). More... | |
void | applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &psi, Real &tol) |
Evaluate \((c'[\psi])^\ast v\). More... | |
void | applyAdjointHessian (Vector< Real > &ahuv, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &psi, Real &tol) |
Evaluate \(((c''[\psi])^\ast v)u\). More... | |
std::vector< Real > | solveAugmentedSystem (Vector< Real > &v1, Vector< Real > &v2, const Vector< Real > &b1, const Vector< Real > &b2, const Vector< Real > &psi, Real &tol) |
Normalization_Constraint (Teuchos::RCP< InnerProductMatrix< Real > > mass) | |
void | value (Vector< Real > &c, const Vector< Real > &psi, Real &tol) |
Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\). More... | |
void | applyJacobian (Vector< Real > &jv, const Vector< Real > &v, const Vector< Real > &psi, Real &tol) |
Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\). More... | |
void | applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &psi, Real &tol) |
Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^*, \mathcal{X}^*)\), to vector \(v\). More... | |
void | applyAdjointHessian (Vector< Real > &ahuv, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &psi, Real &tol) |
Apply the derivative of the adjoint of the constraint Jacobian at \(x\) to vector \(u\) in direction \(v\), according to \( v \mapsto c''(x)(v,\cdot)^*u \). More... | |
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virtual | ~EqualityConstraint () |
virtual void | applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &dualv, Real &tol) |
Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^*, \mathcal{X}^*)\), to vector \(v\). More... | |
virtual void | applyPreconditioner (Vector< Real > &pv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &g, Real &tol) |
Apply a constraint preconditioner at \(x\), \(P(x) \in L(\mathcal{C}, \mathcal{C}^*)\), to vector \(v\). Ideally, this preconditioner satisfies the following relationship:
\[ \left[c'(x) \circ R \circ c'(x)^* \circ P(x)\right] v = v \,, \] where R is the appropriate Riesz map in \(L(\mathcal{X}^*, \mathcal{X})\). It is used by the solveAugmentedSystem method. More... | |
EqualityConstraint (void) | |
virtual void | update (const Vector< Real > &x, bool flag=true, int iter=-1) |
Update constraint functions. x is the optimization variable, flag = true if optimization variable is changed, iter is the outer algorithm iterations count. More... | |
virtual bool | isFeasible (const Vector< Real > &v) |
Check if the vector, v, is feasible. More... | |
void | activate (void) |
Turn on constraints. More... | |
void | deactivate (void) |
Turn off constraints. More... | |
bool | isActivated (void) |
Check if constraints are on. More... | |
virtual std::vector < std::vector< Real > > | checkApplyJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &jv, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1) |
Finite-difference check for the constraint Jacobian application. More... | |
virtual std::vector < std::vector< Real > > | checkApplyJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &jv, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1) |
Finite-difference check for the constraint Jacobian application. More... | |
virtual std::vector < std::vector< Real > > | checkApplyAdjointJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &c, const Vector< Real > &ajv, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS) |
Finite-difference check for the application of the adjoint of constraint Jacobian. More... | |
virtual Real | checkAdjointConsistencyJacobian (const Vector< Real > &w, const Vector< Real > &v, const Vector< Real > &x, const bool printToStream=true, std::ostream &outStream=std::cout) |
virtual Real | checkAdjointConsistencyJacobian (const Vector< Real > &w, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &dualw, const Vector< Real > &dualv, const bool printToStream=true, std::ostream &outStream=std::cout) |
virtual std::vector < std::vector< Real > > | checkApplyAdjointHessian (const Vector< Real > &x, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &hv, const std::vector< Real > &step, const bool printToScreen=true, std::ostream &outStream=std::cout, const int order=1) |
Finite-difference check for the application of the adjoint of constraint Hessian. More... | |
virtual std::vector < std::vector< Real > > | checkApplyAdjointHessian (const Vector< Real > &x, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &hv, const bool printToScreen=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1) |
Finite-difference check for the application of the adjoint of constraint Hessian. More... | |
Private Types | |
typedef std::vector< Real > | svec |
typedef StdVector< Real > | rvec |
typedef Teuchos::RCP< const svec > | pcsv |
typedef Teuchos::RCP< svec > | psv |
Private Attributes | |
int | nx_ |
Real | dx_ |
Teuchos::RCP< FiniteDifference < Real > > | fd_ |
bool | exactsolve_ |
Teuchos::RCP < InnerProductMatrix< Real > > | mass_ |
Constraint class
Definition at line 225 of file gross-pitaevskii/example_01.hpp.
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Definition at line 228 of file gross-pitaevskii/example_01.hpp.
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Definition at line 231 of file gross-pitaevskii/example_01.hpp.
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Definition at line 234 of file gross-pitaevskii/example_01.hpp.
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Definition at line 237 of file gross-pitaevskii/example_01.hpp.
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Definition at line 244 of file gross-pitaevskii/example_01.hpp.
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Definition at line 568 of file gross-pitaevskii/example_02.hpp.
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Definition at line 527 of file gross-pitaevskii/example_03.hpp.
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Evaluate \(c[\psi]\).
\[ c[\psi]= \int\limits_0^1 |\psi|^2\,\mathrm{d}x - 1 \]
where the integral is approximated with the trapezoidal rule and the derivative is approximated using finite differences. This constraint is a scalar
Implements ROL::EqualityConstraint< Real >.
Definition at line 251 of file gross-pitaevskii/example_01.hpp.
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Evaluate \(c'[\psi]v\).
\[ c'[\psi]v= 2 \int\limits_0^1 \psi v\,\mathrm{d}x \]
The action of the Jacobian on a vector produces a scalar
Reimplemented from ROL::EqualityConstraint< Real >.
Definition at line 268 of file gross-pitaevskii/example_01.hpp.
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Evaluate \((c'[\psi])^\ast v\).
\[ (c'[\psi])^\ast v = 2 \int\limits_0^1 \psi v\,\mathrm{d}x \]
The action of the Jacobian adjoint on a scalar produces a vector
Reimplemented from ROL::EqualityConstraint< Real >.
Definition at line 288 of file gross-pitaevskii/example_01.hpp.
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Evaluate \(((c''[\psi])^\ast v)u\).
\[ ((c''[\psi])^\ast v)u = 2 v u \]
The action of the Hessian adjoint on a on a vector v in a direction u produces a vector of the same size as \(\psi\)
Reimplemented from ROL::EqualityConstraint< Real >.
Definition at line 308 of file gross-pitaevskii/example_01.hpp.
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Evaluate \(c[\psi]\).
\[ c[\psi]= \int\limits_0^1 |\psi|^2\,\mathrm{d}x - 1 \]
where the integral is approximated with the trapezoidal rule and the derivative is approximated using finite differences. This constraint is a scalar
Implements ROL::EqualityConstraint< Real >.
Definition at line 576 of file gross-pitaevskii/example_02.hpp.
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Evaluate \(c'[\psi]v\).
\[ c'[\psi]v= 2 \int\limits_0^1 \psi v\,\mathrm{d}x \]
The action of the Jacobian on a vector produces a scalar
Reimplemented from ROL::EqualityConstraint< Real >.
Definition at line 596 of file gross-pitaevskii/example_02.hpp.
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Evaluate \((c'[\psi])^\ast v\).
\[ (c'[\psi])^\ast v = 2 \int\limits_0^1 \psi v\,\mathrm{d}x \]
The action of the Jacobian adjoint on a scalar produces a vector
Reimplemented from ROL::EqualityConstraint< Real >.
Definition at line 619 of file gross-pitaevskii/example_02.hpp.
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Evaluate \(((c''[\psi])^\ast v)u\).
\[ ((c''[\psi])^\ast v)u = 2 v u \]
The action of the Hessian adjoint on a on a vector v in a direction u produces a vector of the same size as \(\psi\)
Reimplemented from ROL::EqualityConstraint< Real >.
Definition at line 642 of file gross-pitaevskii/example_02.hpp.
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Solve the system
\[ \begin{\pmatrix} K & c'^\ast(\psi)\\ c'(\psi) & 0 \end{pmatrix} \begin{pmatrix} v_1\\v_2 \end{pmatrix}=\begin{pmatrix} b_1\\b_2\end{pmatrix}\]
In this example, \(K\) is the finite difference Laplacian the constraint is a scalar and the Jacobian is a vector and the exact inverse can be computed using the Schur complement method
Reimplemented from ROL::EqualityConstraint< Real >.
Definition at line 669 of file gross-pitaevskii/example_02.hpp.
References ROL::Vector< Real >::plus(), ROL::Vector< Real >::scale(), ROL::Vector< Real >::set(), and ROL::EqualityConstraint< Real >::solveAugmentedSystem().
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Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\).
[out] | c | is the result of evaluating the constraint operator at x; a constraint-space vector |
[in] | x | is the constraint argument; an optimization-space vector |
[in,out] | tol | is a tolerance for inexact evaluations; currently unused |
On return, \(\mathsf{c} = c(x)\), where \(\mathsf{c} \in \mathcal{C}\), \(\mathsf{x} \in \mathcal{X}\).
Implements ROL::EqualityConstraint< Real >.
Definition at line 530 of file gross-pitaevskii/example_03.hpp.
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Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\).
[out] | jv | is the result of applying the constraint Jacobian to v at x; a constraint-space vector |
[in] | v | is an optimization-space vector |
[in] | x | is the constraint argument; an optimization-space vector |
[in,out] | tol | is a tolerance for inexact evaluations; currently unused |
On return, \(\mathsf{jv} = c'(x)v\), where \(v \in \mathcal{X}\), \(\mathsf{jv} \in \mathcal{C}\).
The default implementation is a finite-difference approximation.
Reimplemented from ROL::EqualityConstraint< Real >.
Definition at line 543 of file gross-pitaevskii/example_03.hpp.
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Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^*, \mathcal{X}^*)\), to vector \(v\).
[out] | ajv | is the result of applying the adjoint of the constraint Jacobian to v at x; a dual optimization-space vector |
[in] | v | is a dual constraint-space vector |
[in] | x | is the constraint argument; an optimization-space vector |
[in,out] | tol | is a tolerance for inexact evaluations; currently unused |
On return, \(\mathsf{ajv} = c'(x)^*v\), where \(v \in \mathcal{C}^*\), \(\mathsf{ajv} \in \mathcal{X}^*\).
The default implementation is a finite-difference approximation.
Reimplemented from ROL::EqualityConstraint< Real >.
Definition at line 559 of file gross-pitaevskii/example_03.hpp.
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Apply the derivative of the adjoint of the constraint Jacobian at \(x\) to vector \(u\) in direction \(v\), according to \( v \mapsto c''(x)(v,\cdot)^*u \).
[out] | ahuv | is the result of applying the derivative of the adjoint of the constraint Jacobian at x to vector u in direction v; a dual optimization-space vector |
[in] | u | is the direction vector; a dual constraint-space vector |
[in] | v | is an optimization-space vector |
[in] | x | is the constraint argument; an optimization-space vector |
[in,out] | tol | is a tolerance for inexact evaluations; currently unused |
On return, \( \mathsf{ahuv} = c''(x)(v,\cdot)^*u \), where \(u \in \mathcal{C}^*\), \(v \in \mathcal{X}\), and \(\mathsf{ahuv} \in \mathcal{X}^*\).
The default implementation is a finite-difference approximation based on the adjoint Jacobian.
Reimplemented from ROL::EqualityConstraint< Real >.
Definition at line 578 of file gross-pitaevskii/example_03.hpp.
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Definition at line 240 of file gross-pitaevskii/example_01.hpp.
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Definition at line 241 of file gross-pitaevskii/example_01.hpp.
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Definition at line 564 of file gross-pitaevskii/example_02.hpp.
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Definition at line 565 of file gross-pitaevskii/example_02.hpp.
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Definition at line 524 of file gross-pitaevskii/example_03.hpp.