A simple example of a group structure, based on BLAS/LAPACK. More...

#include <NOX_LAPACK_Group.H>

Inheritance diagram for NOX::LAPACK::Group:

Collaboration diagram for NOX::LAPACK::Group:

Public Member Functions
	Group (Interface &i)
	Constructor.

	Group (const NOX::LAPACK::Group &source, NOX::CopyType type=DeepCopy)
	Copy constructor.

	~Group ()
	Destructor.

NOX::Abstract::Group &	operator= (const NOX::Abstract::Group &source)
	Copies the source group into this group. More...

NOX::Abstract::Group &	operator= (const NOX::LAPACK::Group &source)
	See above.

virtual Teuchos::RCP < NOX::Abstract::Group >	clone (NOX::CopyType type=NOX::DeepCopy) const
	Create a new Group of the same derived type as this one by cloning this one, and return a ref count pointer to the new group. More...

void	print () const
	Print out the group.

"Compute" functions.
void	setX (const NOX::Abstract::Vector &y)
	Set the solution vector x to y. More...

void	setX (const NOX::LAPACK::Vector &y)
	See above.

void	computeX (const NOX::Abstract::Group &grp, const NOX::Abstract::Vector &d, double step)
	Compute x = grp.x + step * d. More...

void	computeX (const NOX::LAPACK::Group &grp, const NOX::LAPACK::Vector &d, double step)
	See above.

NOX::Abstract::Group::ReturnType	computeF ()
	Compute and store F(x). More...

NOX::Abstract::Group::ReturnType	computeJacobian ()
	Compute and store Jacobian. More...

NOX::Abstract::Group::ReturnType	computeGradient ()
	Compute and store gradient. More...

NOX::Abstract::Group::ReturnType	computeNewton (Teuchos::ParameterList &params)
	Compute the Newton direction, using parameters for the linear solve. More...

Jacobian operations.
Operations using the Jacobian matrix. These may not be defined in matrix-free scenarios.
NOX::Abstract::Group::ReturnType	applyJacobian (const NOX::LAPACK::Vector &input, NOX::LAPACK::Vector &result) const

NOX::Abstract::Group::ReturnType	applyJacobian (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	See above.

NOX::Abstract::Group::ReturnType	applyJacobianTranspose (const NOX::LAPACK::Vector &input, NOX::LAPACK::Vector &result) const

NOX::Abstract::Group::ReturnType	applyJacobianTranspose (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	See above.

NOX::Abstract::Group::ReturnType	applyJacobianInverse (Teuchos::ParameterList &params, const NOX::LAPACK::Vector &input, Vector &result) const

NOX::Abstract::Group::ReturnType	applyJacobianInverse (Teuchos::ParameterList &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Applies the inverse of the Jacobian matrix to the given input vector and puts the answer in result. More...

virtual NOX::Abstract::Group::ReturnType	applyJacobianInverseMultiVector (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	applyJacobianInverse for multiple right-hand sides

"Is" functions
Checks to see if various objects have been computed. Returns true if the corresponding "compute" function has been called since the last update to the solution vector (via instantiation or computeX).
bool	isF () const
	Return true if F is valid.

bool	isJacobian () const
	Return true if the Jacobian is valid. More...

bool	isGradient () const
	Return true if the gradient is valid. More...

bool	isNewton () const
	Return true if the Newton direction is valid. More...

"Get" functions
Note that these function do not check whether or not the vectors are valid. Must use the "Is" functions for that purpose.
const NOX::Abstract::Vector &	getX () const
	Return solution vector.

const NOX::Abstract::Vector &	getF () const
	Return F(x)

double	getNormF () const
	Return 2-norm of F(x). More...

const NOX::Abstract::Vector &	getGradient () const
	Return gradient.

const NOX::Abstract::Vector &	getNewton () const
	Return Newton direction.

Teuchos::RCP< const NOX::Abstract::Vector >	getXPtr () const
	Return RCP to solution vector.

Teuchos::RCP< const NOX::Abstract::Vector >	getFPtr () const
	Return RCP to F(x)

Teuchos::RCP< const NOX::Abstract::Vector >	getGradientPtr () const
	Return RCP to gradient.

Teuchos::RCP< const NOX::Abstract::Vector >	getNewtonPtr () const
	Return RCP to Newton direction.

Public Member Functions inherited from NOX::Abstract::Group
	Group ()
	Constructor. More...

virtual NOX::Abstract::Group::ReturnType	applyRightPreconditioning (bool useTranspose, Teuchos::ParameterList &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Apply right preconditiong to the given input vector. More...

virtual NOX::Abstract::Group::ReturnType	applyJacobianMultiVector (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	applyJacobian for multiple right-hand sides More...

virtual NOX::Abstract::Group::ReturnType	applyJacobianTransposeMultiVector (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	applyJacobianTranspose for multiple right-hand sides More...

virtual NOX::Abstract::Group::ReturnType	applyRightPreconditioningMultiVector (bool useTranspose, Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	applyRightPreconditioning for multiple right-hand sides More...

virtual const NOX::Abstract::Vector &	getScaledX () const

virtual void	logLastLinearSolveStats (NOX::SolverStats &stats) const
	Adds statistics from last linear solve to the SovlerStats object.

virtual NOX::Abstract::Group::ReturnType	getNormLastLinearSolveResidual (double &residual) const
	Return the norm of the last linear solve residual as the result of either a call to computeNewton() or applyJacobianInverse(). More...

Protected Member Functions
void	resetIsValid ()
	resets the isValid flags to false

Protected Attributes
NOX::LAPACK::LinearSolver< double >	jacSolver
	Jacobian Matrix & LAPACK solver.

NOX::LAPACK::Interface &	problemInterface
	Problem interface.

Vectors
NOX::LAPACK::Vector	xVector
	Solution vector.

NOX::LAPACK::Vector	fVector
	Right-hand-side vector (function evaluation).

NOX::LAPACK::Vector	newtonVector
	Newton direction vector.

NOX::LAPACK::Vector	gradientVector
	Gradient vector (steepest descent vector).

IsValid flags
True if the current solution is up-to-date with respect to the currect xVector.
bool	isValidF

bool	isValidJacobian

bool	isValidGradient

bool	isValidNewton

Additional Inherited Members
Public Types inherited from NOX::Abstract::Group
enum	ReturnType { Ok, NotDefined, BadDependency, NotConverged, Failed }
	The computation of, say, the Newton direction in computeNewton() may fail in many different ways, so we have included a variety of return codes to describe the failures. Of course, we also have a code for success. More...

Detailed Description

A simple example of a group structure, based on BLAS/LAPACK.

Member Function Documentation

NOX::Abstract::Group::ReturnType NOX::LAPACK::Group::applyJacobianInverse	(	Teuchos::ParameterList &	params,
		const NOX::Abstract::Vector &	input,
		NOX::Abstract::Vector &	result
	)		const

virtual

Applies the inverse of the Jacobian matrix to the given input vector and puts the answer in result.

Computes

$v = J^{-1} u,$

where $ J$ is the Jacobian, $ u$ is the input vector, and $ v$ is the result vector.

The "Tolerance" parameter specifies that the solution should be such that

$\frac{\| J v - u \|_2}{\max \{ 1, \|u\|_2\} } < \mbox{Tolerance}$

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::BadDependency - If has not been computed
NOX::Abstract::Group::NotConverged - If the linear solve fails to satisfy the "Tolerance" specified in params
NOX::Abstract::Group::Failed - If the computation fails
NOX::Abstract::Group::Ok - Otherwise

The parameter "Tolerance" may be added/modified in the list of parameters - this is the ideal solution tolerance for an iterative linear solve.

Reimplemented from NOX::Abstract::Group.

Teuchos::RCP< NOX::Abstract::Group > NOX::LAPACK::Group::clone ( NOX::CopyType type = NOX::DeepCopy ) const

virtual

Create a new Group of the same derived type as this one by cloning this one, and return a ref count pointer to the new group.

If type is NOX::DeepCopy, then we need to create an exact replica of "this". Otherwise, if type is NOX::ShapeCopy, we need only replicate the shape of "this" (only the memory is allocated, the values are not copied into the vectors and Jacobian). Returns NULL if clone is not supported.

Note: Any shared data should have its ownership transfered to this group from the source for a NOX::DeepCopy.

Implements NOX::Abstract::Group.

Reimplemented in LOCA::LAPACK::Group.

References Teuchos::rcp().

NOX::Abstract::Group::ReturnType NOX::LAPACK::Group::computeF ( )

virtual

Compute and store F(x).

Note: It's generally useful to also compute and store the 2-norm of F(x) at this point for later access by the getNormF() function.

Returns

NOX::Abstract::Group::Failed - If the computation fails in any way
NOX::Abstract::Group::Ok - Otherwise

Implements NOX::Abstract::Group.

References NOX::Abstract::Group::Failed, and NOX::Abstract::Group::Ok.

Referenced by LOCA::LAPACK::Group::computeF().

NOX::Abstract::Group::ReturnType NOX::LAPACK::Group::computeGradient ( )

virtual

Compute and store gradient.

We can pose the nonlinear equation problem $ F(x) = 0$ as an optimization problem as follows:

$\min f(x) \equiv \frac{1}{2} \|F(x)\|_2^2.$

In that case, the gradient (of $ f$ ) is defined as

$g \equiv J^T F.$

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::BadDependency - If either or has not been computed
NOX::Abstract::Group::Failed - If the computation fails in any other way
NOX::Abstract::Group::Ok - Otherwise

Reimplemented from NOX::Abstract::Group.

References NOX::Abstract::Group::BadDependency, and NOX::Abstract::Group::Ok.

NOX::Abstract::Group::ReturnType NOX::LAPACK::Group::computeJacobian ( )

virtual

Compute and store Jacobian.

Recall that

$F(x) = \left[ \begin{array}{c} F_1(x) \\ F_2(x) \\ \vdots \\ F_n(x) \\ \end{array} \right].$

The Jacobian is denoted by $ J$ and defined by

$J_{ij} = \frac{\partial F_i}{\partial x_j} (x).$

Note: If this is a shared object, this group should take ownership of the Jacobian before it computes it.

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::Failed - If the computation fails in any other way
NOX::Abstract::Group::Ok - Otherwise

Reimplemented from NOX::Abstract::Group.

References NOX::Abstract::Group::Failed, and NOX::Abstract::Group::Ok.

Referenced by LOCA::LAPACK::Group::computeJacobian().

NOX::Abstract::Group::ReturnType NOX::LAPACK::Group::computeNewton ( Teuchos::ParameterList & params )

virtual

Compute the Newton direction, using parameters for the linear solve.

The Newton direction is the solution, s, of

$J s = -F.$

The parameters are from the "Linear %Solver" sublist of the "Direction" sublist that is passed to solver during construction.

The "Tolerance" parameter may be added/modified in the sublist of "Linear Solver" parameters that is passed into this function. The solution should be such that

$\frac{\| J s - (-F) \|_2}{\max \{ 1, \|F\|_2\} } < \mbox{Tolerance}$

Returns

NOX::Abstract::Group::NotDefined - Returned by default implementation in NOX::Abstract::Group
NOX::Abstract::Group::BadDependency - If either or has not been computed
NOX::Abstract::Group::NotConverged - If the linear solve fails to satisfy the "Tolerance" specified in params
NOX::Abstract::Group::Failed - If the computation fails in any other way
NOX::Abstract::Group::Ok - Otherwise

Reimplemented from NOX::Abstract::Group.

References NOX::Abstract::Group::Ok.

void NOX::LAPACK::Group::computeX	(	const NOX::Abstract::Group &	grp,
		const NOX::Abstract::Vector &	d,
		double	step
	)

virtual

Compute x = grp.x + step * d.

Let $ x$ denote this group's solution vector. Let $\hat x$ denote the result of grp.getX(). Then set

$x = \hat x + \mbox{step} \; d.$

Note: This should invalidate the function value, Jacobian, gradient, and Newton direction.; Throw an error if the copy fails.

Returns: Reference to this object

Implements NOX::Abstract::Group.

double NOX::LAPACK::Group::getNormF ( ) const

virtual

Return 2-norm of F(x).

In other words,

$\sqrt{\sum_{i=1}^n F_i^2}$

Implements NOX::Abstract::Group.

bool NOX::LAPACK::Group::isGradient ( ) const

virtual

Return true if the gradient is valid.

Note: Default implementation in NOX::Abstract::Group returns false.

Reimplemented from NOX::Abstract::Group.

bool NOX::LAPACK::Group::isJacobian ( ) const

virtual

Return true if the Jacobian is valid.

Note: Default implementation in NOX::Abstract::Group returns false.

Reimplemented from NOX::Abstract::Group.

bool NOX::LAPACK::Group::isNewton ( ) const

virtual

Return true if the Newton direction is valid.

Note: Default implementation in NOX::Abstract::Group returns false.

Reimplemented from NOX::Abstract::Group.

NOX::Abstract::Group & NOX::LAPACK::Group::operator= ( const NOX::Abstract::Group & source )

virtual

Copies the source group into this group.

Note: Any shared data owned by the source should have its ownership transfered to this group. This may result in a secret modification to the source object.

Implements NOX::Abstract::Group.

Referenced by LOCA::LAPACK::Group::operator=().

void NOX::LAPACK::Group::setX ( const NOX::Abstract::Vector & y )

virtual

Set the solution vector x to y.

Note: This should invalidate the function value, Jacobian, gradient, and Newton direction.; Throw an error if the copy fails.

Returns: Reference to this object

Implements NOX::Abstract::Group.

The documentation for this class was generated from the following files:

NOX_LAPACK_Group.H
NOX_LAPACK_Group.C

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation