NOX::Abstract::Group Class Reference

NOX pure abstract interface to a "group"; i.e., a solution vector and the corresponding F-vector, Jacobian matrix, gradient vector, and Newton vector. More...

#include <NOX_Abstract_Group.H>

Inheritance diagram for NOX::Abstract::Group:

[legend]
List of all members.

Public Types

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...

Public Member Functions

 Group ()
 Constructor.
virtual ~Group ()
 Destructor.
virtual NOX::Abstract::Groupoperator= (const NOX::Abstract::Group &source)=0
 Copies the source group into this group.
"Compute" functions.
virtual void setX (const NOX::Abstract::Vector &y)=0
 Set the solution vector x to y.
virtual void computeX (const NOX::Abstract::Group &grp, const NOX::Abstract::Vector &d, double step)=0
 Compute x = grp.x + step * d.
virtual NOX::Abstract::Group::ReturnType computeF ()=0
 Compute and store F(x).
virtual NOX::Abstract::Group::ReturnType computeJacobian ()
 Compute and store Jacobian.
virtual NOX::Abstract::Group::ReturnType computeGradient ()
 Compute and store gradient.
virtual 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.

virtual NOX::Abstract::Group::ReturnType applyJacobian (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
 Applies Jacobian to the given input vector and puts the answer in the result.
virtual NOX::Abstract::Group::ReturnType applyJacobianTranspose (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
 Applies Jacobian-Transpose to the given input vector and puts the answer in the result.
virtual 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.
virtual NOX::Abstract::Group::ReturnType applyRightPreconditioning (bool useTranspose, NOX::Parameter::List &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
 Apply right preconditiong to the given input vector.
"Is" functions.
Checks to see if various objects have been computed. Returns true if the corresponding "compute" function has been called since the last change to the solution vector.

virtual bool isF () const =0
 Return true if F is valid.
virtual bool isJacobian () const
 Return true if the Jacobian is valid.
virtual bool isGradient () const
 Return true if the gradient is valid.
virtual 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.

virtual const NOX::Abstract::VectorgetX () const =0
 Return solution vector.
virtual const NOX::Abstract::VectorgetF () const =0
 Return F(x).
virtual double getNormF () const =0
 Return 2-norm of F(x).
virtual const NOX::Abstract::VectorgetGradient () const =0
 Return gradient.
virtual const NOX::Abstract::VectorgetNewton () const =0
 Return Newton direction.
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().
Creating new Groups.
virtual NOX::Abstract::Groupclone (NOX::CopyType type=NOX::DeepCopy) const =0
 Create a new Group of the same derived type as this one by cloning this one, and return a pointer to the new group.

Detailed Description

NOX pure abstract interface to a "group"; i.e., a solution vector and the corresponding F-vector, Jacobian matrix, gradient vector, and Newton vector.

This class is a member of the namespace NOX::Abstract.

The user should implement their own concrete implementation of this class or use one of the implementations provided by us. Typically the implementation is also tied to a particular NOX::Abstract::Vector implementation.

Note:
The group may be implemented so that multiple groups can share underlying memory space. This is particularly important when it comes to the Jacobian, which is often to big to be replicated for every group. Thus, we have included instructions on how shared data should be treated for the operator=() and clone() functions.


Member Enumeration Documentation

enum NOX::Abstract::Group::ReturnType
 

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.

Note:
These return types may be expanded in future releases.
Enumeration values:
Ok  Computation completed successfully.
NotDefined  This function is not implemented.
BadDependency  Data dependencies not satisfied.
NotConverged  Unable to satisfy convergence criteria.
Failed  Any other type of failure.


Constructor & Destructor Documentation

NOX::Abstract::Group::Group  )  [inline]
 

Constructor.

Note:
Constructors for any derived object should always define a default x-value so that getX() is always defined.


Member Function Documentation

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

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

Computes

\[ v = J u, \]

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

Returns:

Reimplemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, and NOX::LAPACK::Group.

NOX::Abstract::Group::ReturnType NOX::Abstract::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 in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ModifiedBorderingGroup, LOCA::Bifurcation::TPBord::NicDayModifiedBorderingGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, and NOX::LAPACK::Group.

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

Applies Jacobian-Transpose to the given input vector and puts the answer in the result.

Computes

\[ v = J^T u, \]

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

Returns:

Reimplemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, and NOX::LAPACK::Group.

NOX::Abstract::Group::ReturnType NOX::Abstract::Group::applyRightPreconditioning bool  useTranspose,
NOX::Parameter::List params,
const NOX::Abstract::Vector input,
NOX::Abstract::Vector result
const [virtual]
 

Apply right preconditiong to the given input vector.

Let $M$ be a right preconditioner for the Jacobian $J$; in other words, $M$ is a matrix such that

\[ JM \approx I. \]

Compute

\[ u = M^{-1} v, \]

where $u$ is the input vector and $v$ is the result vector.

If useTranspose is true, then the transpose of the preconditioner is applied:

\[ u = {M^{-1}}^T v, \]

The transpose preconditioner is currently only required for Tensor methods.

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

\[ \frac{\| M v - u \|_2}{\max \{ 1, \|u\|_2\} } < \mbox{Tolerance} \]

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

Reimplemented in LOCA::Bifurcation::TPBord::ExtendedGroup, NOX::Epetra::Group, and NOX::EpetraNew::Group.

virtual NOX::Abstract::Group* NOX::Abstract::Group::clone NOX::CopyType  type = NOX::DeepCopy  )  const [pure 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.

Implemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ModifiedBorderingGroup, LOCA::Bifurcation::TPBord::NicDayModifiedBorderingGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::HouseholderGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, LOCA::Epetra::Group, LOCA::EpetraNew::Group, LOCA::LAPACK::Group, and NOX::LAPACK::Group.

virtual NOX::Abstract::Group::ReturnType NOX::Abstract::Group::computeF  )  [pure 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:

Implemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::HouseholderGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, LOCA::Epetra::Group, LOCA::EpetraNew::Group, LOCA::LAPACK::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, NOX::Petsc::Group, and NOX::LAPACK::Group.

NOX::Abstract::Group::ReturnType NOX::Abstract::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 in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, NOX::Petsc::Group, and NOX::LAPACK::Group.

NOX::Abstract::Group::ReturnType NOX::Abstract::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 in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, LOCA::Epetra::Group, LOCA::EpetraNew::Group, LOCA::LAPACK::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, NOX::Petsc::Group, and NOX::LAPACK::Group.

NOX::Abstract::Group::ReturnType NOX::Abstract::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 in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::HouseholderGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, and NOX::LAPACK::Group.

virtual void NOX::Abstract::Group::computeX const NOX::Abstract::Group grp,
const NOX::Abstract::Vector d,
double  step
[pure 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

Implemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, and NOX::LAPACK::Group.

virtual double NOX::Abstract::Group::getNormF  )  const [pure virtual]
 

Return 2-norm of F(x).

In other words,

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

Implemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, NOX::Petsc::Group, and NOX::LAPACK::Group.

NOX::Abstract::Group::ReturnType NOX::Abstract::Group::getNormLastLinearSolveResidual double &  residual  )  const [virtual]
 

Return the norm of the last linear solve residual as the result of either a call to computeNewton() or applyJacobianInverse().

Returns:

Reimplemented in NOX::Epetra::Group, and NOX::EpetraNew::Group.

bool NOX::Abstract::Group::isGradient  )  const [virtual]
 

Return true if the gradient is valid.

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

Reimplemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, NOX::Petsc::Group, and NOX::LAPACK::Group.

bool NOX::Abstract::Group::isJacobian  )  const [virtual]
 

Return true if the Jacobian is valid.

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

Reimplemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, NOX::Petsc::Group, and NOX::LAPACK::Group.

bool NOX::Abstract::Group::isNewton  )  const [virtual]
 

Return true if the Newton direction is valid.

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

Reimplemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, NOX::Petsc::Group, and NOX::LAPACK::Group.

virtual NOX::Abstract::Group& NOX::Abstract::Group::operator= const NOX::Abstract::Group source  )  [pure 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.

Implemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ModifiedBorderingGroup, LOCA::Bifurcation::TPBord::NicDayModifiedBorderingGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::ExtendedGroup, LOCA::Continuation::HouseholderGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, LOCA::Epetra::Group, LOCA::EpetraNew::Group, LOCA::LAPACK::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, NOX::Petsc::Group, and NOX::LAPACK::Group.

virtual void NOX::Abstract::Group::setX const NOX::Abstract::Vector y  )  [pure 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

Implemented in LOCA::Bifurcation::HopfBord::ExtendedGroup, LOCA::Bifurcation::PitchforkBord::ExtendedGroup, LOCA::Bifurcation::TPBord::ExtendedGroup, LOCA::Continuation::ArcLengthGroup, LOCA::Continuation::NaturalGroup, LOCA::Homotopy::Group, NOX::Epetra::Group, NOX::EpetraNew::Group, and NOX::LAPACK::Group.


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