Nonlinear solver based on Anderson Acceleration. More...

#include <NOX_Solver_AndersonAcceleration.H>

Inheritance diagram for NOX::Solver::AndersonAcceleration:

Collaboration diagram for NOX::Solver::AndersonAcceleration:

Public Member Functions
	AndersonAcceleration (const Teuchos::RCP< NOX::Abstract::Group > &grp, const Teuchos::RCP< NOX::StatusTest::Generic > &tests, const Teuchos::RCP< Teuchos::ParameterList > &params)
	Constructor.
virtual	~AndersonAcceleration ()
	Destructor.
virtual void	reset ()
	Resets the solver for another solve. This resets the counters and status only. Uses the final solution from the last solve as the initial guess for the next solve.
virtual void	reset (const NOX::Abstract::Vector &initialGuess)
	Resets the solver and sets a new initial guess.
virtual void	reset (const NOX::Abstract::Vector &initialGuess, const Teuchos::RCP< NOX::StatusTest::Generic > &tests)
	Resets the solver, sets a new status test, and sets a new initial guess.
virtual NOX::StatusTest::StatusType	step ()
	Do one nonlinear step in the iteration sequence and return status.
virtual NOX::StatusTest::StatusType	solve ()
	Solve the nonlinear problem and return final status.
virtual const NOX::Abstract::Group &	getSolutionGroup () const
	Return a reference to the current solution group.
virtual const NOX::Abstract::Group &	getPreviousSolutionGroup () const
	Return a reference to the previous solution group.
virtual NOX::StatusTest::StatusType	getStatus () const
	Returns the current status of the solver.
virtual int	getNumIterations () const
	Get number of iterations.
virtual const Teuchos::ParameterList &	getList () const
	Return a reference to the solver parameters.
virtual double	getStepSize () const
virtual Teuchos::RCP< const NOX::Abstract::Group >	getSolutionGroupPtr () const
	Return a RCP to the solution group.
virtual Teuchos::RCP< const NOX::Abstract::Group >	getPreviousSolutionGroupPtr () const
	Return a RCP to the previous solution group.
virtual Teuchos::RCP< const Teuchos::ParameterList >	getListPtr () const
	Return a RCP to the solver parameters.
virtual Teuchos::RCP< const NOX::SolverStats >	getSolverStatistics () const
	Return a RCP to the solver statistics.
Public Member Functions inherited from NOX::Solver::Generic
	Generic ()
	Constructor (does nothing).
virtual	~Generic ()
	Destructor (does nothing).

Protected Member Functions
virtual void	init ()
	Print out initialization information and calcuate the RHS.
virtual void	printUpdate ()
	Prints the current iteration information.
void	qrAdd (NOX::Abstract::Vector &newCol)
	Updates QR factors by addition of a column.
void	qrDelete ()
	Updates QR factors by deletion of a column.
void	reorthogonalize ()
	Reorthogonalized columns of Q and updates factorization.

Protected Attributes
Teuchos::RCP< NOX::GlobalData >	globalDataPtr
	Pointer to the global data object.
Teuchos::RCP< NOX::Utils >	utilsPtr
	Utils.
Teuchos::RCP< NOX::Abstract::Group >	solnPtr
	Current solution.
Teuchos::RCP< NOX::Abstract::Group >	oldSolnPtr
	Previous solution pointer.
Teuchos::RCP< NOX::StatusTest::Generic >	testPtr
	Stopping test.
Teuchos::RCP< Teuchos::ParameterList >	paramsPtr
	Input parameters.
Teuchos::RCP< NOX::LineSearch::Generic >	lineSearchPtr
	Linesearch.
bool	precond
	Flag for preconditioning.
bool	recomputeJacobian
	Flag to recompute Jacobian each iterate. Needed if Jacobian required to apply preconditioner.
Teuchos::RCP< NOX::Abstract::Vector >	workVec
	Vector for temporary storage.
Teuchos::RCP< NOX::Abstract::Vector >	precF
	Current preconditioned function value.
Teuchos::RCP< NOX::Abstract::Vector >	oldPrecF
	Previous preconditioned function value.
int	storeParam
	Maximum storage depth.
int	nStore
	Current storage depth.
double	mixParam
	Mixing parameter.
double	stepSize
	Current step.
std::vector< Teuchos::RCP< NOX::Abstract::Vector > >	xMat
	"Matrix" of successive iterate differences
std::vector< Teuchos::RCP< NOX::Abstract::Vector > >	qMat
	Q factor the for least-squares problem.
Teuchos::SerialDenseMatrix< int, double >	rMat
	R factor for the least-squares problem.
int	nIter
	Number of nonlinear iterations.
int	orthoFrequency
	Frequency for reorthogonalization of QR factors. If nonpositive, we never reorthogonalize.
NOX::StatusTest::StatusType	status
	Status of nonlinear solver.
NOX::StatusTest::CheckType	checkType
	Type of check to use for status tests. See NOX::StatusTest for more details.
Teuchos::RCP< NOX::Observer >	observer
	Pointer to a user defined NOX::Observer object.
std::vector< double >	WORK
	Scratch space for condition number estimation using LAPACK.
std::vector< int >	IWORK
	Scratch space for condition number estimation using LAPACK.
bool	adjustForConditionNumber
	If true, the QR matrix will be resized if the condiiton number is greater than the dropTolerance.
double	dropTolerance
	Value of the condition number above which the QR matrix is resized.
int	accelerationStartIteration
	The nonlinear iteration where Anderson Acceleration will start.
bool	disableChecksForUnitTesting
	Disables the storage depth size check - used for unit testing corner cases only.

Detailed Description

Nonlinear solver based on Anderson Acceleration.

Solves $F(x)=0$ using Anderson Acceleration.

This method requires a mixing parameter $\beta$ and a preconditioner $M(x)$ . If preconditioning is not supported, it is taken to be the identity.

For the first iteration, the solver computes $x_1 = x_0 + \beta M(x_0)F(x_0)$ .

Each iteration afterward, the solver does the following.

Set $m_k = \min\{m,k\}$ , where is a parameter that determines the maximum number of iterates for which we store iterate and function values in addition to the current iterate. represents the number of previous iterates stored currently.
Solve the least-squares problem: $\min_{\gamma}\|\sum_{i=0}^{m_k} \alpha_iM(x_{k-i})F(x_{k-i}) \|$ , such that $\sum_{i=1}^{m_k} \alpha_i = 1$ . In this implementation, we solve an equivalent unconstrained problem for which the QR factors are stored and updated.
Calculate the new iterate: $x_{k+1} = \sum_{i=0}^{m_k} \alpha_i[x_{k-i} + \beta M(x_{k-i})F(x_{k-i})]$.

The iterations progress until the status tests (see NOX::StatusTest) determine either failure or convergence.

Input Parameters

The following parameter list entries are valid for this solver:

"Anderson Parameters" - Sublist of parameters specific to AA
"Line Search" - Sublist of the line search parameters, passed to the NOX::LineSearch::Manager constructor. Defaults to an empty list.
"Solver Options" - Sublist of general solver options.
- "User Defined Pre/Post Operator" is supported. See NOX::Parameter::PrePostOperator for more details.

Output Parameters

Every time solve() is called, a sublist for output parameters called "Output" will be created and contain the following parameters.

"Output":

"Nonlinear Iterations" - Number of nonlinear iterations
"2-Norm of Residual" - Two-norm of final residual

Author: Alex Toth and Roger Pawlowski

Constructor & Destructor Documentation

◆ AndersonAcceleration()

NOX::Solver::AndersonAcceleration::AndersonAcceleration	(	const Teuchos::RCP< NOX::Abstract::Group > &	grp,
		const Teuchos::RCP< NOX::StatusTest::Generic > &	tests,
		const Teuchos::RCP< Teuchos::ParameterList > &	params )

Constructor.

See reset(NOX::Abstract::Group&, NOX::StatusTest::Generic&, Teuchos::ParameterList&) for description

References NOX::DeepCopy, globalDataPtr, init(), observer, oldPrecF, oldSolnPtr, paramsPtr, NOX::Solver::parseObserver(), precF, NOX::ShapeCopy, solnPtr, testPtr, utilsPtr, NOX::Solver::validateSolverOptionsSublist(), and workVec.

Member Function Documentation

◆ getList()

const Teuchos::ParameterList & NOX::Solver::AndersonAcceleration::getList ( ) const

virtual

Return a reference to the solver parameters.

Implements NOX::Solver::Generic.

References paramsPtr.

◆ getListPtr()

virtual Teuchos::RCP< const Teuchos::ParameterList > NOX::Solver::AndersonAcceleration::getListPtr ( ) const

inlinevirtual

Return a RCP to the solver parameters.

Implements NOX::Solver::Generic.

References paramsPtr.

◆ getNumIterations()

int NOX::Solver::AndersonAcceleration::getNumIterations ( ) const

virtual

Get number of iterations.

Implements NOX::Solver::Generic.

References nIter.

◆ getPreviousSolutionGroup()

const NOX::Abstract::Group & NOX::Solver::AndersonAcceleration::getPreviousSolutionGroup ( ) const

virtual

Return a reference to the previous solution group.

Implements NOX::Solver::Generic.

References oldSolnPtr.

◆ getPreviousSolutionGroupPtr()

virtual Teuchos::RCP< const NOX::Abstract::Group > NOX::Solver::AndersonAcceleration::getPreviousSolutionGroupPtr ( ) const

inlinevirtual

Return a RCP to the previous solution group.

Implements NOX::Solver::Generic.

References oldSolnPtr.

◆ getSolutionGroup()

const NOX::Abstract::Group & NOX::Solver::AndersonAcceleration::getSolutionGroup ( ) const

virtual

Return a reference to the current solution group.

Implements NOX::Solver::Generic.

References solnPtr.

◆ getSolutionGroupPtr()

virtual Teuchos::RCP< const NOX::Abstract::Group > NOX::Solver::AndersonAcceleration::getSolutionGroupPtr ( ) const

inlinevirtual

Return a RCP to the solution group.

Implements NOX::Solver::Generic.

References solnPtr.

◆ getSolverStatistics()

Teuchos::RCP< const NOX::SolverStats > NOX::Solver::AndersonAcceleration::getSolverStatistics ( ) const

virtual

Return a RCP to the solver statistics.

Implements NOX::Solver::Generic.

References globalDataPtr.

◆ getStatus()

NOX::StatusTest::StatusType NOX::Solver::AndersonAcceleration::getStatus ( ) const

virtual

Returns the current status of the solver.

Implements NOX::Solver::Generic.

References status.

◆ init()

void NOX::Solver::AndersonAcceleration::init ( )

protectedvirtual

Print out initialization information and calcuate the RHS.

References accelerationStartIteration, adjustForConditionNumber, checkType, disableChecksForUnitTesting, dropTolerance, NOX::Utils::fill(), globalDataPtr, lineSearchPtr, mixParam, nIter, nStore, orthoFrequency, NOX::Utils::Parameters, paramsPtr, NOX::Solver::parseStatusTestCheckType(), precond, qMat, recomputeJacobian, NOX::ShapeCopy, solnPtr, status, stepSize, storeParam, NOX::StatusTest::Unconverged, utilsPtr, workVec, and xMat.

Referenced by AndersonAcceleration().

◆ printUpdate()

void NOX::Solver::AndersonAcceleration::printUpdate ( )

protectedvirtual

Prints the current iteration information.

References NOX::StatusTest::Converged, NOX::StatusTest::Failed, NOX::Utils::fill(), nIter, NOX::Utils::OuterIteration, NOX::Utils::OuterIterationStatusTest, solnPtr, status, stepSize, testPtr, NOX::StatusTest::Unconverged, and utilsPtr.

Referenced by step().

◆ qrAdd()

void NOX::Solver::AndersonAcceleration::qrAdd ( NOX::Abstract::Vector & newCol )

protected

Updates QR factors by addition of a column.

References disableChecksForUnitTesting, NOX::Abstract::Vector::norm(), nStore, qMat, rMat, NOX::Abstract::Vector::scale(), and NOX::Abstract::Vector::update().

Referenced by step().

◆ qrDelete()

void NOX::Solver::AndersonAcceleration::qrDelete ( )

protected

Updates QR factors by deletion of a column.

References nStore, qMat, rMat, and workVec.

Referenced by step().

◆ reorthogonalize()

void NOX::Solver::AndersonAcceleration::reorthogonalize ( )

protected

Reorthogonalized columns of Q and updates factorization.

References disableChecksForUnitTesting, nStore, qMat, and rMat.

Referenced by step().

◆ reset() [1/3]

void NOX::Solver::AndersonAcceleration::reset ( )

virtual

Resets the solver for another solve. This resets the counters and status only. Uses the final solution from the last solve as the initial guess for the next solve.

NOTE: All NOX solvers will call reset() automatically at teh beginning of the solve() method. We add the reset() method to the solver interface for the application to call in case the application needs to reset counters and status manually before the next call to solve() is made.

Implements NOX::Solver::Generic.

References globalDataPtr, nIter, nStore, status, NOX::StatusTest::Unconverged, and workVec.

Referenced by solve().

◆ reset() [2/3]

void NOX::Solver::AndersonAcceleration::reset ( const NOX::Abstract::Vector & initial_guess )

virtual

Resets the solver and sets a new initial guess.

Implements NOX::Solver::Generic.

References globalDataPtr, nIter, nStore, solnPtr, status, NOX::StatusTest::Unconverged, and workVec.

◆ reset() [3/3]

void NOX::Solver::AndersonAcceleration::reset	(	const NOX::Abstract::Vector &	initial_guess,
		const Teuchos::RCP< NOX::StatusTest::Generic > &	test )

virtual

Resets the solver, sets a new status test, and sets a new initial guess.

Implements NOX::Solver::Generic.

References globalDataPtr, nIter, nStore, solnPtr, status, stepSize, testPtr, NOX::StatusTest::Unconverged, and workVec.

◆ solve()

NOX::StatusTest::StatusType NOX::Solver::AndersonAcceleration::solve ( )

virtual

Solve the nonlinear problem and return final status.

By "solve", we call iterate() until the NOX::StatusTest value is either NOX::StatusTest::Converged or NOX::StatusTest::Failed.

Implements NOX::Solver::Generic.

References nIter, observer, paramsPtr, reset(), solnPtr, status, step(), and NOX::StatusTest::Unconverged.

◆ step()

NOX::StatusTest::StatusType NOX::Solver::AndersonAcceleration::step ( )

virtual

Do one nonlinear step in the iteration sequence and return status.

Implements NOX::Solver::Generic.

References accelerationStartIteration, adjustForConditionNumber, checkType, NOX::StatusTest::Converged, NOX::Utils::Details, dropTolerance, NOX::StatusTest::Failed, globalDataPtr, IWORK, lineSearchPtr, mixParam, nIter, nStore, observer, NOX::Abstract::Group::Ok, oldPrecF, oldSolnPtr, orthoFrequency, paramsPtr, precF, precond, printUpdate(), qMat, qrAdd(), qrDelete(), recomputeJacobian, reorthogonalize(), rMat, solnPtr, status, stepSize, storeParam, testPtr, NOX::StatusTest::Unconverged, utilsPtr, NOX::Utils::Warning, WORK, workVec, and xMat.

Referenced by solve().

Member Data Documentation

◆ accelerationStartIteration

int NOX::Solver::AndersonAcceleration::accelerationStartIteration

protected

The nonlinear iteration where Anderson Acceleration will start.

Referenced by init(), and step().

◆ adjustForConditionNumber

bool NOX::Solver::AndersonAcceleration::adjustForConditionNumber

protected

If true, the QR matrix will be resized if the condiiton number is greater than the dropTolerance.

Referenced by init(), and step().

◆ checkType

NOX::StatusTest::CheckType NOX::Solver::AndersonAcceleration::checkType

protected

Type of check to use for status tests. See NOX::StatusTest for more details.

Referenced by init(), and step().

◆ disableChecksForUnitTesting

bool NOX::Solver::AndersonAcceleration::disableChecksForUnitTesting

protected

Disables the storage depth size check - used for unit testing corner cases only.

Referenced by init(), qrAdd(), and reorthogonalize().

◆ dropTolerance

double NOX::Solver::AndersonAcceleration::dropTolerance

protected

Value of the condition number above which the QR matrix is resized.

Referenced by init(), and step().

◆ globalDataPtr

Teuchos::RCP<NOX::GlobalData> NOX::Solver::AndersonAcceleration::globalDataPtr

protected

Pointer to the global data object.

Referenced by AndersonAcceleration(), getSolverStatistics(), init(), reset(), reset(), reset(), and step().

◆ IWORK

std::vector<int> NOX::Solver::AndersonAcceleration::IWORK

protected

Scratch space for condition number estimation using LAPACK.

Referenced by step().

◆ lineSearchPtr

Teuchos::RCP<NOX::LineSearch::Generic> NOX::Solver::AndersonAcceleration::lineSearchPtr

protected

Linesearch.

Referenced by init(), and step().

◆ mixParam

double NOX::Solver::AndersonAcceleration::mixParam

protected

Mixing parameter.

Referenced by init(), and step().

◆ nIter

int NOX::Solver::AndersonAcceleration::nIter

protected

Number of nonlinear iterations.

Referenced by getNumIterations(), init(), printUpdate(), reset(), reset(), reset(), solve(), and step().

◆ nStore

int NOX::Solver::AndersonAcceleration::nStore

protected

Current storage depth.

Referenced by init(), qrAdd(), qrDelete(), reorthogonalize(), reset(), reset(), reset(), and step().

◆ observer

Teuchos::RCP<NOX::Observer> NOX::Solver::AndersonAcceleration::observer

protected

Pointer to a user defined NOX::Observer object.

Referenced by AndersonAcceleration(), solve(), and step().

◆ oldPrecF

Teuchos::RCP<NOX::Abstract::Vector> NOX::Solver::AndersonAcceleration::oldPrecF

protected

Previous preconditioned function value.

Referenced by AndersonAcceleration(), and step().

◆ oldSolnPtr

Teuchos::RCP<NOX::Abstract::Group> NOX::Solver::AndersonAcceleration::oldSolnPtr

protected

Previous solution pointer.

Referenced by AndersonAcceleration(), getPreviousSolutionGroup(), getPreviousSolutionGroupPtr(), and step().

◆ orthoFrequency

int NOX::Solver::AndersonAcceleration::orthoFrequency

protected

Frequency for reorthogonalization of QR factors. If nonpositive, we never reorthogonalize.

Referenced by init(), and step().

◆ paramsPtr

Teuchos::RCP<Teuchos::ParameterList> NOX::Solver::AndersonAcceleration::paramsPtr

protected

Input parameters.

Referenced by AndersonAcceleration(), getList(), getListPtr(), init(), solve(), and step().

◆ precF

Teuchos::RCP<NOX::Abstract::Vector> NOX::Solver::AndersonAcceleration::precF

protected

Current preconditioned function value.

Referenced by AndersonAcceleration(), and step().

◆ precond

bool NOX::Solver::AndersonAcceleration::precond

protected

Flag for preconditioning.

Referenced by init(), and step().

◆ qMat

std::vector< Teuchos::RCP<NOX::Abstract::Vector> > NOX::Solver::AndersonAcceleration::qMat

protected

Q factor the for least-squares problem.

Referenced by init(), qrAdd(), qrDelete(), reorthogonalize(), and step().

◆ recomputeJacobian

bool NOX::Solver::AndersonAcceleration::recomputeJacobian

protected

Flag to recompute Jacobian each iterate. Needed if Jacobian required to apply preconditioner.

Referenced by init(), and step().

◆ rMat

Teuchos::SerialDenseMatrix<int,double> NOX::Solver::AndersonAcceleration::rMat

protected

R factor for the least-squares problem.

Referenced by qrAdd(), qrDelete(), reorthogonalize(), and step().

◆ solnPtr

Teuchos::RCP<NOX::Abstract::Group> NOX::Solver::AndersonAcceleration::solnPtr

protected

Current solution.

Referenced by AndersonAcceleration(), getSolutionGroup(), getSolutionGroupPtr(), init(), printUpdate(), reset(), reset(), solve(), and step().

◆ status

NOX::StatusTest::StatusType NOX::Solver::AndersonAcceleration::status

protected

Status of nonlinear solver.

Referenced by getStatus(), init(), printUpdate(), reset(), reset(), reset(), solve(), and step().

◆ stepSize

double NOX::Solver::AndersonAcceleration::stepSize

protected

Current step.

Referenced by init(), printUpdate(), reset(), and step().

◆ storeParam

int NOX::Solver::AndersonAcceleration::storeParam

protected

Maximum storage depth.

Referenced by init(), and step().

◆ testPtr

Teuchos::RCP<NOX::StatusTest::Generic> NOX::Solver::AndersonAcceleration::testPtr

protected

Stopping test.

Referenced by AndersonAcceleration(), printUpdate(), reset(), and step().

◆ utilsPtr

Teuchos::RCP<NOX::Utils> NOX::Solver::AndersonAcceleration::utilsPtr

protected

Utils.

Referenced by AndersonAcceleration(), init(), printUpdate(), and step().

◆ WORK

std::vector<double> NOX::Solver::AndersonAcceleration::WORK

protected

Scratch space for condition number estimation using LAPACK.

Referenced by step().

◆ workVec

Teuchos::RCP<NOX::Abstract::Vector> NOX::Solver::AndersonAcceleration::workVec

protected

Vector for temporary storage.

Referenced by AndersonAcceleration(), init(), qrDelete(), reset(), reset(), reset(), and step().

◆ xMat

std::vector< Teuchos::RCP<NOX::Abstract::Vector> > NOX::Solver::AndersonAcceleration::xMat

protected

"Matrix" of successive iterate differences

Referenced by init(), and step().

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

NOX_Solver_AndersonAcceleration.H
NOX_Solver_AndersonAcceleration.C

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ AndersonAcceleration()

Member Function Documentation

◆ getList()

◆ getListPtr()

◆ getNumIterations()

◆ getPreviousSolutionGroup()

◆ getPreviousSolutionGroupPtr()

◆ getSolutionGroup()

◆ getSolutionGroupPtr()

◆ getSolverStatistics()

◆ getStatus()

◆ init()

◆ printUpdate()

◆ qrAdd()

◆ qrDelete()

◆ reorthogonalize()

◆ reset() [1/3]

◆ reset() [2/3]

◆ reset() [3/3]

◆ solve()

◆ step()

Member Data Documentation

◆ accelerationStartIteration

◆ adjustForConditionNumber

◆ checkType

◆ disableChecksForUnitTesting

◆ dropTolerance

◆ globalDataPtr

◆ IWORK

◆ lineSearchPtr

◆ mixParam

◆ nIter

◆ nStore

◆ observer

◆ oldPrecF

◆ oldSolnPtr

◆ orthoFrequency

◆ paramsPtr

◆ precF

◆ precond

◆ qMat

◆ recomputeJacobian

◆ rMat

◆ solnPtr

◆ status

◆ stepSize

◆ storeParam

◆ testPtr

◆ utilsPtr

◆ WORK

◆ workVec

◆ xMat