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:

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

Public Member Functions

 Group (Interface &i)
 Constructor.
 Group (Interface &i, int m, int n, int ma, int na)
 Constructor with used and allocated dimensions of matrices.
 Group (const NOX::LAPACK::Group &source, NOX::CopyType type=DeepCopy)
 Copy constructor.
 ~Group ()
 Destructor.
NOX::Abstract::Groupoperator= (const NOX::Abstract::Group &source)
 Copies the source group into this group.
NOX::Abstract::Groupoperator= (const NOX::LAPACK::Group &source)
 See above.
virtual NOX::Abstract::Groupclone (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::VectorgetX () const
 Return solution vector.
const NOX::Abstract::VectorgetF () const
 Return F(x).
double getNormF () const
 Return 2-norm of F(x).
const NOX::Abstract::VectorgetGradient () const
 Return gradient.
const NOX::Abstract::VectorgetNewton () 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::InterfaceproblemInterface
 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:
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:

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:

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:

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:

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:
Generated on Thu Sep 18 12:43:32 2008 for NOX by doxygen 1.3.9.1