NOX::LAPACK::Group Class Reference

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

#include <NOX_LAPACK_Group.H>

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List of all members.

Public Member Functions

 Group (Interface &i)
 Constructor.
 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 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.
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 (Teuchos::ParameterList &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 (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.
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.
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::LinearSolver< double > jacSolver
 Jacobian Matrix & LAPACK solver.
NOX::LAPACK::InterfaceproblemInterface
 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


Detailed Description

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

Definition at line 63 of file NOX_LAPACK_Group.H.


Constructor & Destructor Documentation

NOX::LAPACK::Group::Group ( Interface i  ) 

Constructor.

Definition at line 48 of file NOX_LAPACK_Group.C.

References resetIsValid(), and NOX::ShapeCopy.

NOX::LAPACK::Group::Group ( const NOX::LAPACK::Group source,
NOX::CopyType  type = DeepCopy 
)

Copy constructor.

Definition at line 59 of file NOX_LAPACK_Group.C.

References NOX::DeepCopy, resetIsValid(), and NOX::ShapeCopy.

NOX::LAPACK::Group::~Group (  )  [virtual]

Destructor.

Reimplemented from NOX::Abstract::Group.

Reimplemented in LOCA::LAPACK::Group.

Definition at line 89 of file NOX_LAPACK_Group.C.


Member Function Documentation

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.

Definition at line 110 of file NOX_LAPACK_Group.C.

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

See above.

Reimplemented in LOCA::LAPACK::Group.

Definition at line 115 of file NOX_LAPACK_Group.C.

References fVector, gradientVector, jacSolver, newtonVector, and xVector.

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.

Definition at line 147 of file NOX_LAPACK_Group.C.

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

See above.

Definition at line 152 of file NOX_LAPACK_Group.C.

References resetIsValid(), and xVector.

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.

Definition at line 158 of file NOX_LAPACK_Group.C.

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

See above.

Definition at line 168 of file NOX_LAPACK_Group.C.

References resetIsValid(), and xVector.

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.

Definition at line 174 of file NOX_LAPACK_Group.C.

References NOX::LAPACK::Interface::computeF(), NOX::Abstract::Group::Failed, fVector, NOX::Abstract::Group::Ok, problemInterface, and xVector.

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.

Definition at line 184 of file NOX_LAPACK_Group.C.

References NOX::LAPACK::Interface::computeJacobian(), NOX::Abstract::Group::Failed, NOX::LAPACK::LinearSolver< T >::getMatrix(), jacSolver, NOX::Abstract::Group::Ok, problemInterface, and xVector.

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.

Definition at line 196 of file NOX_LAPACK_Group.C.

References NOX::LAPACK::LinearSolver< T >::apply(), NOX::Abstract::Group::BadDependency, fVector, gradientVector, isF(), isJacobian(), jacSolver, and NOX::Abstract::Group::Ok.

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:

Reimplemented from NOX::Abstract::Group.

Definition at line 221 of file NOX_LAPACK_Group.C.

References fVector, isF(), isJacobian(), isNewton(), newtonVector, NOX::Abstract::Group::Ok, and NOX::LAPACK::Vector::scale().

NOX::Abstract::Group::ReturnType NOX::LAPACK::Group::applyJacobian ( const NOX::Abstract::Vector input,
NOX::Abstract::Vector result 
) const [virtual]

See above.

Reimplemented from NOX::Abstract::Group.

Definition at line 247 of file NOX_LAPACK_Group.C.

NOX::Abstract::Group::ReturnType NOX::LAPACK::Group::applyJacobianTranspose ( const NOX::Abstract::Vector input,
NOX::Abstract::Vector result 
) const [virtual]

See above.

Reimplemented from NOX::Abstract::Group.

Definition at line 269 of file NOX_LAPACK_Group.C.

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:
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.

Definition at line 291 of file NOX_LAPACK_Group.C.

NOX::Abstract::Group::ReturnType NOX::LAPACK::Group::applyJacobianInverseMultiVector ( Teuchos::ParameterList &  params,
const NOX::Abstract::MultiVector input,
NOX::Abstract::MultiVector result 
) const [virtual]

bool NOX::LAPACK::Group::isF (  )  const [virtual]

Return true if F is valid.

Implements NOX::Abstract::Group.

Definition at line 362 of file NOX_LAPACK_Group.C.

Referenced by computeGradient(), and computeNewton().

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.

Definition at line 367 of file NOX_LAPACK_Group.C.

Referenced by applyJacobianInverseMultiVector(), LOCA::LAPACK::Group::applyJacobianTransposeInverse(), LOCA::LAPACK::Group::applyJacobianTransposeInverseMultiVector(), computeGradient(), and computeNewton().

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.

Definition at line 372 of file NOX_LAPACK_Group.C.

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.

Definition at line 377 of file NOX_LAPACK_Group.C.

Referenced by computeNewton().

const NOX::Abstract::Vector & NOX::LAPACK::Group::getX (  )  const [virtual]

Return solution vector.

Implements NOX::Abstract::Group.

Definition at line 382 of file NOX_LAPACK_Group.C.

References xVector.

const NOX::Abstract::Vector & NOX::LAPACK::Group::getF (  )  const [virtual]

Return F(x).

Implements NOX::Abstract::Group.

Definition at line 387 of file NOX_LAPACK_Group.C.

References fVector.

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.

Definition at line 392 of file NOX_LAPACK_Group.C.

References fVector, and NOX::LAPACK::Vector::norm().

const NOX::Abstract::Vector & NOX::LAPACK::Group::getGradient (  )  const [virtual]

Return gradient.

Implements NOX::Abstract::Group.

Definition at line 404 of file NOX_LAPACK_Group.C.

References gradientVector.

const NOX::Abstract::Vector & NOX::LAPACK::Group::getNewton (  )  const [virtual]

Return Newton direction.

Implements NOX::Abstract::Group.

Definition at line 409 of file NOX_LAPACK_Group.C.

References newtonVector.

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.

Definition at line 103 of file NOX_LAPACK_Group.C.

void NOX::LAPACK::Group::print (  )  const

Print out the group.

Definition at line 415 of file NOX_LAPACK_Group.C.

References fVector, and xVector.

void NOX::LAPACK::Group::resetIsValid (  )  [protected]

resets the isValid flags to false

Reimplemented in LOCA::LAPACK::Group.

Definition at line 93 of file NOX_LAPACK_Group.C.

References jacSolver, and NOX::LAPACK::LinearSolver< T >::reset().

Referenced by computeX(), Group(), and setX().


Member Data Documentation

Right-hand-side vector (function evaluation).

Definition at line 191 of file NOX_LAPACK_Group.H.

Referenced by computeF(), computeGradient(), computeNewton(), getF(), getNormF(), operator=(), and print().

Newton direction vector.

Definition at line 193 of file NOX_LAPACK_Group.H.

Referenced by computeNewton(), getNewton(), and operator=().

Gradient vector (steepest descent vector).

Definition at line 195 of file NOX_LAPACK_Group.H.

Referenced by computeGradient(), getGradient(), and operator=().

Problem interface.

Definition at line 203 of file NOX_LAPACK_Group.H.

Referenced by computeF(), and computeJacobian().


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

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