NOX::LAPACK::Group Class Reference

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

#include <NOX_LAPACK_Group.H>

Inheritance diagram for NOX::LAPACK::Group:

[legend]Collaboration diagram for NOX::LAPACK::Group:[legend]List of all members.


Public Member Functions
	Group (Interface &i)
	Constructor.
	Group (Interface &i, int m, int n)
	Constructor with used and allocated dimensions of matrices.
	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.
NOX::Abstract::Group &	operator= (const NOX::LAPACK::Group &source)
	See above.
virtual 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 pointer to the new group.
void	print () const
	Print out the group.
"Compute" functions.
void	setX (const NOX::Abstract::Vector &y)
	Set the solution vector x to y.
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.
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).
NOX::Abstract::Group::ReturnType	computeJacobian ()
	Compute and store Jacobian.
NOX::Abstract::Group::ReturnType	computeGradient ()
	Compute and store gradient.
NOX::Abstract::Group::ReturnType	computeNewton (NOX::Parameter::List &params)
	Compute the Newton direction, using parameters for the linear solve.
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 (NOX::Parameter::List &params, const NOX::LAPACK::Vector &input, Vector &result) const
NOX::Abstract::Group::ReturnType	applyJacobianInverse (NOX::Parameter::List &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.
"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.
bool	isGradient () const
	Return true if the gradient is valid.
bool	isNewton () const
	Return true if the Newton direction is valid.
"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).
const NOX::Abstract::Vector &	getGradient () const
	Return gradient.
const NOX::Abstract::Vector &	getNewton () const
	Return Newton direction.
Protected Member Functions
void	resetIsValid ()
	resets the isValid flags to false
Protected Attributes
NOX::LAPACK::Matrix	jacobianMatrix
	Jacobian Matrix.
NOX::LAPACK::Matrix	jacobianLUFact
	LU factorization of Jacobian Matrix.
vector< int >	pivots
	Pivot array for LU factorization.
NOX::LAPACK::Interface &	problemInterface
	Problem interface.
double	normF
	Norm of F.
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
bool	isValidJacobianLUFact

Detailed Description

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

Member Function Documentation

NOX::Abstract::Group::ReturnType NOX::LAPACK::Group::applyJacobianInverse ( NOX::Parameter::List & 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 $J$ 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.

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 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". 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.

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.
Reimplemented in LOCA::LAPACK::Group.

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 $F$ or $J$ 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.

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 taken 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.
Reimplemented in LOCA::LAPACK::Group.

NOX::Abstract::Group::ReturnType NOX::LAPACK::Group::computeNewton ( NOX::Parameter::List & 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 $F$ or $J$ 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.

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.
Reimplemented in LOCA::LAPACK::Group.

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

Generated on Thu Sep 18 12:40:50 2008 for NOX by

1.3.9.1

NOX::LAPACK::Group Class Reference

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation