Poisson material inversion. More...

#include <ROL_PoissonInversion.hpp>

Inheritance diagram for ROL::ZOO::Objective_PoissonInversion< Real >:

Public Member Functions
	Objective_PoissonInversion (uint nz=32, Real alpha=1.e-4)

Real	reg_value (const Vector< Real > &z)

void	reg_gradient (Vector< Real > &g, const Vector< Real > &z)

void	reg_hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &z)

void	apply_mass (Vector< Real > &Mf, const Vector< Real > &f)

void	solve_poisson (Vector< Real > &u, const Vector< Real > &z, Vector< Real > &b)

Real	evaluate_target (Real x)

void	apply_linearized_control_operator (Vector< Real > &Bd, const Vector< Real > &z, const Vector< Real > &d, const Vector< Real > &u)

void	apply_transposed_linearized_control_operator (Vector< Real > &Bd, const Vector< Real > &z, const Vector< Real > &d, const Vector< Real > &u)

void	apply_transposed_linearized_control_operator_2 (Vector< Real > &Bd, const Vector< Real > &z, const Vector< Real > &v, const Vector< Real > &d, const Vector< Real > &u)

void	solve_state_equation (Vector< Real > &u, const Vector< Real > &z)

void	solve_adjoint_equation (Vector< Real > &p, const Vector< Real > &u, const Vector< Real > &z)

void	solve_state_sensitivity_equation (Vector< Real > &w, const Vector< Real > &v, const Vector< Real > &u, const Vector< Real > &z)

void	solve_adjoint_sensitivity_equation (Vector< Real > &q, const Vector< Real > &w, const Vector< Real > &v, const Vector< Real > &p, const Vector< Real > &u, const Vector< Real > &z)

Real	value (const Vector< Real > &z, Real &tol)
	Compute value. More...

void	gradient (Vector< Real > &g, const Vector< Real > &z, Real &tol)
	Compute gradient. More...

void	invHessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply inverse Hessian approximation to vector. More...

Public Member Functions inherited from ROL::Objective< Real >
virtual	~Objective ()

	Objective ()

virtual void	update (const Vector< Real > &x, UpdateType type, int iter=-1)
	Update objective function. More...

virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update objective function. More...

virtual Real	dirDeriv (const Vector< Real > &x, const Vector< Real > &d, Real &tol)
	Compute directional derivative. More...

virtual void	hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply Hessian approximation to vector. More...

virtual void	precond (Vector< Real > &Pv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply preconditioner to vector. More...

virtual void	prox (Vector< Real > &Pv, const Vector< Real > &v, Real t, Real &tol)
	Compute the proximity operator. More...

virtual void	proxJacVec (Vector< Real > &Jv, const Vector< Real > &v, const Vector< Real > &x, Real t, Real &tol)
	Apply the Jacobian of the proximity operator. More...

virtual std::vector < std::vector< Real > >	checkGradient (const Vector< Real > &x, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference gradient check. More...

virtual std::vector < std::vector< Real > >	checkGradient (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference gradient check. More...

virtual std::vector < std::vector< Real > >	checkGradient (const Vector< Real > &x, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference gradient check with specified step sizes. More...

virtual std::vector < std::vector< Real > >	checkGradient (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference gradient check with specified step sizes. More...

virtual std::vector < std::vector< Real > >	checkHessVec (const Vector< Real > &x, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference Hessian-applied-to-vector check. More...

virtual std::vector < std::vector< Real > >	checkHessVec (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference Hessian-applied-to-vector check. More...

virtual std::vector < std::vector< Real > >	checkHessVec (const Vector< Real > &x, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference Hessian-applied-to-vector check with specified step sizes. More...

virtual std::vector < std::vector< Real > >	checkHessVec (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference Hessian-applied-to-vector check with specified step sizes. More...

virtual std::vector< Real >	checkHessSym (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &w, const bool printToStream=true, std::ostream &outStream=std::cout)
	Hessian symmetry check. More...

virtual std::vector< Real >	checkHessSym (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &w, const bool printToStream=true, std::ostream &outStream=std::cout)
	Hessian symmetry check. More...

virtual std::vector < std::vector< Real > >	checkProxJacVec (const Vector< Real > &x, const Vector< Real > &v, Real t=Real(1), bool printToStream=true, std::ostream &outStream=std::cout, int numSteps=ROL_NUM_CHECKDERIV_STEPS)
	Finite-difference proximity operator Jacobian-applied-to-vector check. More...

virtual void	setParameter (const std::vector< Real > &param)

Private Types
typedef std::vector< Real >	vector

typedef Vector< Real >	V

typedef StdVector< Real >	SV

typedef vector::size_type	uint

Private Member Functions
ROL::Ptr< const vector >	getVector (const V &x)

ROL::Ptr< vector >	getVector (V &x)

Private Attributes
uint	nu_

uint	nz_

Real	hu_

Real	hz_

Real	alpha_

Real	eps_

int	reg_type_

Additional Inherited Members
Protected Member Functions inherited from ROL::Objective< Real >
const std::vector< Real >	getParameter (void) const

Detailed Description

template<class Real>
class ROL::ZOO::Objective_PoissonInversion< Real >

Poisson material inversion.

Definition at line 34 of file ROL_PoissonInversion.hpp.

Member Typedef Documentation

template<class Real>

typedef std::vector<Real> ROL::ZOO::Objective_PoissonInversion< Real >::vector

private

Definition at line 36 of file ROL_PoissonInversion.hpp.

template<class Real>

typedef Vector<Real> ROL::ZOO::Objective_PoissonInversion< Real >::V

private

Definition at line 37 of file ROL_PoissonInversion.hpp.

template<class Real>

typedef StdVector<Real> ROL::ZOO::Objective_PoissonInversion< Real >::SV

private

Definition at line 38 of file ROL_PoissonInversion.hpp.

template<class Real>

typedef vector::size_type ROL::ZOO::Objective_PoissonInversion< Real >::uint

private

Definition at line 40 of file ROL_PoissonInversion.hpp.

Constructor & Destructor Documentation

template<class Real>

ROL::ZOO::Objective_PoissonInversion< Real >::Objective_PoissonInversion	(	uint	nz = `32`,
		Real	alpha = `1.e-4`
	)

inline

Definition at line 67 of file ROL_PoissonInversion.hpp.

Member Function Documentation

template<class Real>

ROL::Ptr<const vector> ROL::ZOO::Objective_PoissonInversion< Real >::getVector ( const V & x )

inlineprivate

Definition at line 54 of file ROL_PoissonInversion.hpp.

template<class Real>

ROL::Ptr<vector> ROL::ZOO::Objective_PoissonInversion< Real >::getVector ( V & x )

inlineprivate

Definition at line 59 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::getVector().

template<class Real>

Real ROL::ZOO::Objective_PoissonInversion< Real >::reg_value ( const Vector< Real > & z )

inline

Definition at line 72 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::alpha_, ROL::ZOO::Objective_PoissonInversion< Real >::eps_, ROL::ZOO::Objective_PoissonInversion< Real >::getVector(), ROL::ZOO::Objective_PoissonInversion< Real >::hz_, ROL::ZOO::Objective_PoissonInversion< Real >::nz_, and ROL::ZOO::Objective_PoissonInversion< Real >::reg_type_.

Referenced by ROL::ZOO::Objective_PoissonInversion< Real >::value().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::reg_gradient	(	Vector< Real > &	g,
		const Vector< Real > &	z
	)

inline

Definition at line 94 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::alpha_, ROL::ZOO::Objective_PoissonInversion< Real >::eps_, ROL::ZOO::Objective_PoissonInversion< Real >::getVector(), ROL::ZOO::Objective_PoissonInversion< Real >::hz_, ROL::ZOO::Objective_PoissonInversion< Real >::nz_, ROL::ZOO::Objective_PoissonInversion< Real >::reg_type_, ROL::Vector< Real >::scale(), and ROL::Vector< Real >::set().

Referenced by ROL::ZOO::Objective_PoissonInversion< Real >::gradient().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::reg_hessVec	(	Vector< Real > &	hv,
		const Vector< Real > &	v,
		const Vector< Real > &	z
	)

inline

Definition at line 133 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::alpha_, ROL::ZOO::Objective_PoissonInversion< Real >::eps_, ROL::ZOO::Objective_PoissonInversion< Real >::getVector(), ROL::ZOO::Objective_PoissonInversion< Real >::hz_, ROL::ZOO::Objective_PoissonInversion< Real >::nz_, ROL::ZOO::Objective_PoissonInversion< Real >::reg_type_, ROL::Vector< Real >::scale(), and ROL::Vector< Real >::set().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::apply_mass	(	Vector< Real > &	Mf,
		const Vector< Real > &	f
	)

inline

Definition at line 180 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::getVector(), ROL::ZOO::Objective_PoissonInversion< Real >::hu_, and ROL::ZOO::Objective_PoissonInversion< Real >::nu_.

Referenced by ROL::ZOO::Objective_PoissonInversion< Real >::solve_adjoint_equation(), ROL::ZOO::Objective_PoissonInversion< Real >::solve_adjoint_sensitivity_equation(), and ROL::ZOO::Objective_PoissonInversion< Real >::value().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::solve_poisson	(	Vector< Real > &	u,
		const Vector< Real > &	z,
		Vector< Real > &	b
	)

inline

Definition at line 199 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::getVector(), ROL::ZOO::Objective_PoissonInversion< Real >::hu_, ROL::ZOO::Objective_PoissonInversion< Real >::nu_, and ROL::Vector< Real >::set().

Referenced by ROL::ZOO::Objective_PoissonInversion< Real >::solve_adjoint_equation(), ROL::ZOO::Objective_PoissonInversion< Real >::solve_adjoint_sensitivity_equation(), ROL::ZOO::Objective_PoissonInversion< Real >::solve_state_equation(), and ROL::ZOO::Objective_PoissonInversion< Real >::solve_state_sensitivity_equation().

template<class Real>

Real ROL::ZOO::Objective_PoissonInversion< Real >::evaluate_target ( Real x )

inline

Definition at line 226 of file ROL_PoissonInversion.hpp.

Referenced by ROL::ZOO::Objective_PoissonInversion< Real >::solve_adjoint_equation(), and ROL::ZOO::Objective_PoissonInversion< Real >::value().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::apply_linearized_control_operator	(	Vector< Real > &	Bd,
		const Vector< Real > &	z,
		const Vector< Real > &	d,
		const Vector< Real > &	u
	)

inline

Definition at line 230 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::getVector(), ROL::ZOO::Objective_PoissonInversion< Real >::hu_, and ROL::ZOO::Objective_PoissonInversion< Real >::nu_.

Referenced by ROL::ZOO::Objective_PoissonInversion< Real >::solve_adjoint_sensitivity_equation(), and ROL::ZOO::Objective_PoissonInversion< Real >::solve_state_sensitivity_equation().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::apply_transposed_linearized_control_operator	(	Vector< Real > &	Bd,
		const Vector< Real > &	z,
		const Vector< Real > &	d,
		const Vector< Real > &	u
	)

inline

Definition at line 256 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::getVector(), ROL::ZOO::Objective_PoissonInversion< Real >::hu_, and ROL::ZOO::Objective_PoissonInversion< Real >::nz_.

Referenced by ROL::ZOO::Objective_PoissonInversion< Real >::gradient().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::apply_transposed_linearized_control_operator_2	(	Vector< Real > &	Bd,
		const Vector< Real > &	z,
		const Vector< Real > &	v,
		const Vector< Real > &	d,
		const Vector< Real > &	u
	)

inline

Definition at line 278 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::getVector(), ROL::ZOO::Objective_PoissonInversion< Real >::hu_, and ROL::ZOO::Objective_PoissonInversion< Real >::nz_.

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::solve_state_equation	(	Vector< Real > &	u,
		const Vector< Real > &	z
	)

inline

Definition at line 301 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::hu_, ROL::ZOO::Objective_PoissonInversion< Real >::nu_, and ROL::ZOO::Objective_PoissonInversion< Real >::solve_poisson().

Referenced by ROL::ZOO::Objective_PoissonInversion< Real >::gradient(), and ROL::ZOO::Objective_PoissonInversion< Real >::value().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::solve_adjoint_equation	(	Vector< Real > &	p,
		const Vector< Real > &	u,
		const Vector< Real > &	z
	)

inline

Definition at line 327 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::apply_mass(), ROL::ZOO::Objective_PoissonInversion< Real >::evaluate_target(), ROL::ZOO::Objective_PoissonInversion< Real >::getVector(), ROL::ZOO::Objective_PoissonInversion< Real >::hu_, ROL::ZOO::Objective_PoissonInversion< Real >::nu_, and ROL::ZOO::Objective_PoissonInversion< Real >::solve_poisson().

Referenced by ROL::ZOO::Objective_PoissonInversion< Real >::gradient().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::solve_state_sensitivity_equation	(	Vector< Real > &	w,
		const Vector< Real > &	v,
		const Vector< Real > &	u,
		const Vector< Real > &	z
	)

inline

Definition at line 344 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::apply_linearized_control_operator(), ROL::ZOO::Objective_PoissonInversion< Real >::nu_, and ROL::ZOO::Objective_PoissonInversion< Real >::solve_poisson().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::solve_adjoint_sensitivity_equation	(	Vector< Real > &	q,
		const Vector< Real > &	w,
		const Vector< Real > &	v,
		const Vector< Real > &	p,
		const Vector< Real > &	u,
		const Vector< Real > &	z
	)

inline

Definition at line 353 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::apply_linearized_control_operator(), ROL::ZOO::Objective_PoissonInversion< Real >::apply_mass(), ROL::StdVector< Real, Element >::axpy(), ROL::ZOO::Objective_PoissonInversion< Real >::nu_, and ROL::ZOO::Objective_PoissonInversion< Real >::solve_poisson().

template<class Real>

Real ROL::ZOO::Objective_PoissonInversion< Real >::value	(	const Vector< Real > &	x,
		Real &	tol
	)

inlinevirtual

Compute value.

This function returns the objective function value.

Parameters

[in]	x	is the current iterate.
[in]	tol	is a tolerance for inexact objective function computation.

Implements ROL::Objective< Real >.

Definition at line 367 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::apply_mass(), ROL::StdVector< Real, Element >::clone(), ROL::ZOO::Objective_PoissonInversion< Real >::evaluate_target(), ROL::ZOO::Objective_PoissonInversion< Real >::hu_, ROL::ZOO::Objective_PoissonInversion< Real >::nu_, ROL::ZOO::Objective_PoissonInversion< Real >::reg_value(), and ROL::ZOO::Objective_PoissonInversion< Real >::solve_state_equation().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::gradient	(	Vector< Real > &	g,
		const Vector< Real > &	x,
		Real &	tol
	)

inlinevirtual

Compute gradient.

This function returns the objective function gradient.

Parameters

[out]	g	is the gradient.
[in]	x	is the current iterate.
[in]	tol	is a tolerance for inexact objective function computation.

The default implementation is a finite-difference approximation based on the function value. This requires the definition of a basis \(\{\phi_i\}\) for the optimization vectors x and the definition of a basis \(\{\psi_j\}\) for the dual optimization vectors (gradient vectors g). The bases must be related through the Riesz map, i.e., \( R \{\phi_i\} = \{\psi_j\}\), and this must be reflected in the implementation of the ROL::Vector::dual() method.

Reimplemented from ROL::Objective< Real >.

Definition at line 391 of file ROL_PoissonInversion.hpp.

References ROL::ZOO::Objective_PoissonInversion< Real >::apply_transposed_linearized_control_operator(), ROL::ZOO::Objective_PoissonInversion< Real >::nu_, ROL::ZOO::Objective_PoissonInversion< Real >::nz_, ROL::Vector< Real >::plus(), ROL::ZOO::Objective_PoissonInversion< Real >::reg_gradient(), ROL::ZOO::Objective_PoissonInversion< Real >::solve_adjoint_equation(), and ROL::ZOO::Objective_PoissonInversion< Real >::solve_state_equation().

template<class Real>

void ROL::ZOO::Objective_PoissonInversion< Real >::invHessVec	(	Vector< Real > &	hv,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol
	)

inlinevirtual

Apply inverse Hessian approximation to vector.

This function applies the inverse Hessian of the objective function to the vector \(v\).

Parameters

[out]	hv	is the action of the inverse Hessian on \(v\).
[in]	v	is the direction vector.
[in]	x	is the current iterate.
[in]	tol	is a tolerance for inexact objective function computation.