Extension of the NOX::Epetra::Group to LOCA. More...

#include <LOCA_Epetra_Group.H>

Inheritance diagram for LOCA::Epetra::Group:

Collaboration diagram for LOCA::Epetra::Group:

Public Member Functions
	Group (const Teuchos::RCP< LOCA::GlobalData > &global_data, Teuchos::ParameterList &printingParams, const Teuchos::RCP< LOCA::Epetra::Interface::Required > &i, NOX::Epetra::Vector &initialGuess, const LOCA::ParameterVector &p)
	Constructor with NO linear system (VERY LIMITED).
	Group (const Teuchos::RCP< LOCA::GlobalData > &global_data, Teuchos::ParameterList &printingParams, const Teuchos::RCP< LOCA::Epetra::Interface::Required > &i, NOX::Epetra::Vector &initialGuess, const Teuchos::RCP< NOX::Epetra::LinearSystem > &linSys, const LOCA::ParameterVector &p)
	Standard Constructor enabling most LOCA support.
	Group (const Teuchos::RCP< LOCA::GlobalData > &global_data, Teuchos::ParameterList &printingParams, const Teuchos::RCP< LOCA::Epetra::Interface::TimeDependent > &i, NOX::Epetra::Vector &initialGuess, const Teuchos::RCP< NOX::Epetra::LinearSystem > &linSys, const Teuchos::RCP< NOX::Epetra::LinearSystem > &shiftedLinSys, const LOCA::ParameterVector &p)
	Constructor with time-dependent interface and shifted linear system.
	Group (const Teuchos::RCP< LOCA::GlobalData > &global_data, Teuchos::ParameterList &printingParams, const Teuchos::RCP< LOCA::Epetra::Interface::TimeDependentMatrixFree > &i, NOX::Epetra::Vector &initialGuess, const Teuchos::RCP< NOX::Epetra::LinearSystem > &linSys, const Teuchos::RCP< NOX::Epetra::LinearSystem > &shiftedLinSys, const LOCA::ParameterVector &p)
	Constructor with time-dependent matrix-free interface and shifted linear system.
	Group (const Group &source, NOX::CopyType type=NOX::DeepCopy)
	Copy constructor. If type is DeepCopy, takes ownership of valid shared Jacobian and shared preconditioning matrix.
virtual	~Group ()
	Destructor.
virtual Group &	operator= (const Group &source)
	Assignment operator.
virtual void	setFreeEnergyInterface (const Teuchos::RCP< LOCA::Epetra::Interface::FreeEnergy > &iFE)
	Method to inject an interface for calucatiuong the free energy.
void	declareSeparateMatrixMemory (bool separateMem=true)
	Method for calling code to guarantee to LOCA that separate matrix.
virtual Teuchos::RCP < NOX::Epetra::Interface::Required >	getUserInterface ()
	Return the userInterface.
virtual void	printSolution (const NOX::Epetra::Vector &x, const double conParam) const
	Call the user interface print() routine, any vector.
void	setScaleVector (const NOX::Abstract::Vector &s)
	Sets the scale vector.
void	setJacobianOperatorForSolve (const Teuchos::RCP< const Epetra_Operator > &op) const
	Sets the Jacobian operator.
virtual Teuchos::RCP< const NOX::Epetra::LinearSystem >	getComplexLinearSystem () const
	Return the Linear System.
virtual Teuchos::RCP < NOX::Epetra::LinearSystem >	getComplexLinearSystem ()
	Return the Linear System.
virtual void	getComplexMaps (Teuchos::RCP< const Epetra_BlockMap > &baseMap, Teuchos::RCP< const Epetra_BlockMap > &globalMap) const
Overloaded NOX::Epetra::Group methods.
virtual NOX::Abstract::Group &	operator= (const NOX::Abstract::Group &source)
	Assignment operator.
virtual NOX::Abstract::Group &	operator= (const NOX::Epetra::Group &source)
	Assignment operator.
virtual Teuchos::RCP < NOX::Abstract::Group >	clone (NOX::CopyType type=NOX::DeepCopy) const
	Cloning function.
virtual NOX::Abstract::Group::ReturnType	computeF ()
	Overloaded computeF()
virtual NOX::Abstract::Group::ReturnType	computeJacobian ()
	Overloaded computeJacobian()
Implementation of LOCA::Abstract::TransposeSolveGroup methods.
virtual NOX::Abstract::Group::ReturnType	applyJacobianTransposeInverse (Teuchos::ParameterList &params, const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Solve Jacobian-tranpose system.
virtual NOX::Abstract::Group::ReturnType	applyJacobianTransposeInverseMultiVector (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Solve Jacobian-tranpose system with multiple right-hand sides.
Implementation of LOCA::MultiContinuation::AbstractGroup virtual methods.
virtual void	copy (const NOX::Abstract::Group &source)
	Copy.
virtual void	setParams (const ParameterVector &p)
	Set the parameters.
virtual void	setParam (int paramID, double val)
	Set parameter indexed by paramID.
virtual void	setParam (std::string paramID, double val)
	Set parameter indexed by paramID.
const LOCA::ParameterVector &	getParams () const
	Return a const reference to the ParameterVector owned by the group.
virtual double	getParam (int paramID) const
	Return copy of parameter indexed by paramID.
virtual double	getParam (std::string paramID) const
	Return copy of parameter indexed by paramID.
virtual void	preProcessContinuationStep (LOCA::Abstract::Iterator::StepStatus stepStatus)
	Perform any preprocessing before a continuation step starts.
virtual void	postProcessContinuationStep (LOCA::Abstract::Iterator::StepStatus stepStatus)
	Perform any postprocessing after a continuation step finishes.
virtual void	projectToDraw (const NOX::Abstract::Vector &x, double *px) const
	Projects solution to a few scalars for multiparameter continuation.
virtual int	projectToDrawDimension () const
	Returns the dimension of the project to draw array.
virtual double	computeScaledDotProduct (const NOX::Abstract::Vector &a, const NOX::Abstract::Vector &b) const
	Compute a scaled dot product.
virtual void	printSolution (const double conParam) const
	Call the user interface print() routine, solution vector.
virtual void	printSolution (const NOX::Abstract::Vector &x, const double conParam) const
	Call the user interface print() routine, any vector.
virtual void	scaleVector (NOX::Abstract::Vector &x) const
	Scales a vector using scaling vector.
Implementation of LOCA::Homotopy::AbstractGroup virtual methods.
virtual NOX::Abstract::Group::ReturnType	augmentJacobianForHomotopy (double a, double b)
	Replace Jacobian by where is the identity matrix.
Implementation of LOCA::TimeDependent::AbstractGroup virtual methods.
virtual NOX::Abstract::Group::ReturnType	computeShiftedMatrix (double alpha, double beta)
	Compute the shifted matrix.
virtual NOX::Abstract::Group::ReturnType	applyShiftedMatrix (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Multiply the shifted matrix by a vector.
virtual NOX::Abstract::Group::ReturnType	applyShiftedMatrixMultiVector (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Multiply the shifted matrix by a multi-vector.
virtual NOX::Abstract::Group::ReturnType	applyShiftedMatrixInverseMultiVector (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Apply the inverse of the shifted matrix by a multi-vector, as needed by the shift-and-invert and generalized Cayley transformations.
virtual NOX::Abstract::Group::ReturnType	computeSecondShiftedMatrix (double alpha, double beta)
	Compute the second shifted matrix (uses different memory then Shifted matrix)
virtual NOX::Abstract::Group::ReturnType	applySecondShiftedMatrix (const NOX::Abstract::Vector &input, NOX::Abstract::Vector &result) const
	Multiply the second shifted matrix by a vector.
virtual NOX::Abstract::Group::ReturnType	applySecondShiftedMatrixMultiVector (const NOX::Abstract::MultiVector &input, NOX::Abstract::MultiVector &result) const
	Multiply the second shifted matrix by a multi-vector.
Implementation of LOCA::Hopf::MooreSpence::AbstractGroup virtual methods.
virtual bool	isComplex () const
	Is $J+i\omega B$ valid.
virtual NOX::Abstract::Group::ReturnType	computeComplex (double frequency)
	Compute $J+i\omega B$ .
virtual NOX::Abstract::Group::ReturnType	applyComplex (const NOX::Abstract::Vector &input_real, const NOX::Abstract::Vector &input_imag, NOX::Abstract::Vector &result_real, NOX::Abstract::Vector &result_imag) const
	Compute $(J+i\omega B)(y+iz)$ .
virtual NOX::Abstract::Group::ReturnType	applyComplexMultiVector (const NOX::Abstract::MultiVector &input_real, const NOX::Abstract::MultiVector &input_imag, NOX::Abstract::MultiVector &result_real, NOX::Abstract::MultiVector &result_imag) const
	Compute $(J+i\omega B)(y+iz)$ .
virtual NOX::Abstract::Group::ReturnType	applyComplexInverseMultiVector (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input_real, const NOX::Abstract::MultiVector &input_imag, NOX::Abstract::MultiVector &result_real, NOX::Abstract::MultiVector &result_imag) const
	Solve $(J+i\omega B)(y+iz) = a+ib$ .
Implementation of LOCA::Hopf::MinimallyAugmented::AbstractGroup virtual methods.
virtual NOX::Abstract::Group::ReturnType	applyComplexTranspose (const NOX::Abstract::Vector &input_real, const NOX::Abstract::Vector &input_imag, NOX::Abstract::Vector &result_real, NOX::Abstract::Vector &result_imag) const
virtual NOX::Abstract::Group::ReturnType	applyComplexTransposeMultiVector (const NOX::Abstract::MultiVector &input_real, const NOX::Abstract::MultiVector &input_imag, NOX::Abstract::MultiVector &result_real, NOX::Abstract::MultiVector &result_imag) const
virtual NOX::Abstract::Group::ReturnType	applyComplexTransposeInverseMultiVector (Teuchos::ParameterList &params, const NOX::Abstract::MultiVector &input_real, const NOX::Abstract::MultiVector &input_imag, NOX::Abstract::MultiVector &result_real, NOX::Abstract::MultiVector &result_imag) const
	Solve $(J+i\omega B)^H (x + iy) = a+ib$ .
Implementation of LOCA::PhseTransition::AbstractGroup virtual methods.
virtual double	computeFreeEnergy ()
	Computes the free energy at the current solution and parameter values.
Protected Member Functions
virtual void	resetIsValid ()
	resets the isValid flags to false
Protected Attributes
Teuchos::RCP< LOCA::GlobalData >	globalData
	Global data.
Teuchos::ParameterList &	printParams
	Printing parameters.
LOCA::ParameterVector	params
	Parameter vector.
Teuchos::RCP < LOCA::Epetra::Interface::Required >	userInterface
	Reference to the user supplied interface functions.
Teuchos::RCP < LOCA::Epetra::Interface::TimeDependent >	userInterfaceTime
	Interface for shifted-matrix.
Teuchos::RCP < LOCA::Epetra::Interface::TimeDependentMatrixFree >	userInterfaceTimeMF
	Interface for matrix-free shifted-matrix.
Teuchos::RCP < LOCA::Epetra::Interface::FreeEnergy >	userInterfaceFreeEnergy
	Interface for free enerfgy calculation for phase transitions.
Teuchos::RCP < NOX::SharedObject < NOX::Epetra::LinearSystem, LOCA::Epetra::Group > >	shiftedSharedLinearSystem
	Shared shifted linear system.
bool	isValidShiftedPrec
	Is preconditioner for shifted matrix valid.
double	alpha_
	$\alpha$ for matrix-free shifted matrix
double	beta_
	$\beta$ for matrix-free shifted matrix
Teuchos::RCP< Epetra_Vector >	tmpVectorPtr2
	Extra vector needed for intermediate calculations of LOCA routines.
Teuchos::RCP < NOX::Abstract::Vector >	scaleVecPtr
	Stores a pointer to the scale vector.
Teuchos::RCP < LOCA::Epetra::TransposeLinearSystem::AbstractStrategy >	tls_strategy
	Stores transpose linear solver strategy.
Teuchos::RCP < NOX::SharedObject < NOX::Epetra::LinearSystem, LOCA::Epetra::Group > >	complexSharedLinearSystem
	Shared complex system.
Teuchos::RCP < EpetraExt::BlockCrsMatrix >	complexMatrix
	Complex matrix.
Teuchos::RCP < EpetraExt::BlockVector >	complexVec
	Complex vector.
bool	isValidComplex
	Is complex matrix valid.
bool	isValidComplexPrec
	Is complex matrix preconditioner valid.
bool	separateMatrixMemoryDeclared
	Is complex matrix valid.

Detailed Description

Extension of the NOX::Epetra::Group to LOCA.

This class extends the NOX::Epetra::Group to LOCA enabling continuation and bifurcation capabilities using Epetra. It is derived from the NOX::Epetra::Group (basic Epetra support), the LOCA::Abstract::Group (brings in all LOCA abstract base classes), and the LOCA::Abstract::TransposeSolveGroup (for applyJacobianTransposeInverse() methods). It stores a parameter vector for setting/retrieving parameter values and overloads the computeF() and computeJacobian() methods of the NOX::Epetra::Group parent class to set the entire contents of the parameter vector in the problem interface before calling the NOX::Epetra::Group computeF() and computeJacobian().

Since it is derived from the LOCA::Abstract::Group (which is in turn derived from all FiniteDifference groups), it uses the finite-difference implementations for all parameter derivatives and second derivatives. However this behavior can be modified by calling the setDerivUtils() method of the LOCA::MultiContinuation::FiniteDifferenceGroup parent class.

This class provides complete support for all continuation and bifurcation methods including shift-invert and Cayley methods for computing eigenvalues and Hopf bifurcations. However this support is only enabled by calling the appropriate constructor described below.

Constructor & Destructor Documentation

LOCA::Epetra::Group::Group	(	const Teuchos::RCP< LOCA::GlobalData > &	global_data,
		Teuchos::ParameterList &	printingParams,
		const Teuchos::RCP< LOCA::Epetra::Interface::Required > &	i,
		NOX::Epetra::Vector &	initialGuess,
		const LOCA::ParameterVector &	p
	)

Constructor with NO linear system (VERY LIMITED).

WARNING: If this constructor is used, then methods that require a Jacobian or preconditioning will not be available. You will be limited to simple algorithms like nonlinear-CG with no preconditioning.

LOCA::Epetra::Group::Group	(	const Teuchos::RCP< LOCA::GlobalData > &	global_data,
		Teuchos::ParameterList &	printingParams,
		const Teuchos::RCP< LOCA::Epetra::Interface::Required > &	i,
		NOX::Epetra::Vector &	initialGuess,
		const Teuchos::RCP< NOX::Epetra::LinearSystem > &	linSys,
		const LOCA::ParameterVector &	p
	)

Standard Constructor enabling most LOCA support.

This is the most commonly used constructor and provides support for all LOCA algorithms except shift-invert and Cayley transformations and Hopf bifurcations.

LOCA::Epetra::Group::Group	(	const Teuchos::RCP< LOCA::GlobalData > &	global_data,
		Teuchos::ParameterList &	printingParams,
		const Teuchos::RCP< LOCA::Epetra::Interface::TimeDependent > &	i,
		NOX::Epetra::Vector &	initialGuess,
		const Teuchos::RCP< NOX::Epetra::LinearSystem > &	linSys,
		const Teuchos::RCP< NOX::Epetra::LinearSystem > &	shiftedLinSys,
		const LOCA::ParameterVector &	p
	)

Constructor with time-dependent interface and shifted linear system.

Use this constructor to enable shift-invert and Cayley transformations or Hopf bifurcations. It requires another interface to compute the shifted matrix $\alpha J + \beta M$ where $J$ is the Jacobian matrix and $M$ is the mass matrix, and a linear system object to solve this system. Setting linSys = shiftedLinSys is a valid option for passing the shifted solver, but this will cause the shifted matrix to overwrite the Jacobian possibly resulting in more matrix fills. See declareSeparateMatrixMemory() method below to assert separate memory.

References Teuchos::rcp(), and shiftedSharedLinearSystem.

LOCA::Epetra::Group::Group	(	const Teuchos::RCP< LOCA::GlobalData > &	global_data,
		Teuchos::ParameterList &	printingParams,
		const Teuchos::RCP< LOCA::Epetra::Interface::TimeDependentMatrixFree > &	i,
		NOX::Epetra::Vector &	initialGuess,
		const Teuchos::RCP< NOX::Epetra::LinearSystem > &	linSys,
		const Teuchos::RCP< NOX::Epetra::LinearSystem > &	shiftedLinSys,
		const LOCA::ParameterVector &	p
	)

Constructor with time-dependent matrix-free interface and shifted linear system.

This constructor may also be used for shift-invert and Cayley transformations, but should be only be used for a matrix-free method for solving the shifted system.

References Teuchos::rcp(), and shiftedSharedLinearSystem.

Member Function Documentation

NOX::Abstract::Group::ReturnType LOCA::Epetra::Group::applyComplexTranspose	(	const NOX::Abstract::Vector &	input_real,
		const NOX::Abstract::Vector &	input_imag,
		NOX::Abstract::Vector &	result_real,
		NOX::Abstract::Vector &	result_imag
	)		const `[virtual]`

Computes conjugate-tranpose matrix vector product $(J+i\omega B)^H (x + iy)$ .

Reimplemented from LOCA::Abstract::Group.

References NOX::Abstract::Group::BadDependency, NOX::Epetra::Vector::getEpetraVector(), and NOX::Abstract::Group::Ok.

NOX::Abstract::Group::ReturnType LOCA::Epetra::Group::applyComplexTransposeMultiVector	(	const NOX::Abstract::MultiVector &	input_real,
		const NOX::Abstract::MultiVector &	input_imag,
		NOX::Abstract::MultiVector &	result_real,
		NOX::Abstract::MultiVector &	result_imag
	)		const `[virtual]`

Computes conjugate-tranpose matrix vector product $(J+i\omega B)^H (x + iy)$ .

Reimplemented from LOCA::Abstract::Group.

References NOX::Abstract::MultiVector::numVectors(), and NOX::Abstract::Group::Ok.

NOX::Abstract::Group::ReturnType LOCA::Epetra::Group::applyJacobianTransposeInverse	(	Teuchos::ParameterList &	params,
		const NOX::Abstract::Vector &	input,
		NOX::Abstract::Vector &	result
	)		const `[virtual]`

Solve Jacobian-tranpose system.

In addition to all regular linear solver parameters, this method references the following additional parameters:

"Transpose Solver Method" -- [string] (default: "Transpose Preconditioner") Method for preconditioning the transpose linear system (LOCA::Epetra::TransposeLinearSystem::Factory). Available choices are:
- "Transpose Preconditioner" -- Use the transpose of the preconditioner for the original system.
- "Left Preconditioning" -- Use the transpose of the preconditioner, and apply using left preconditioning.
- "Explicit Transpose" -- Form the transpose of the matrix and compute the preconditioner. This method is available only if Trilinos is configured with EpetraExt support (--enable-epetraext).

Implements LOCA::Abstract::TransposeSolveGroup.

References LOCA::Epetra::TransposeLinearSystem::Factory::create(), LOCA::Epetra::TransposeLinearSystem::AbstractStrategy::createJacobianTranspose(), NOX::Epetra::LinearSystem::destroyPreconditioner(), NOX::Epetra::LinearSystem::getJacobianOperator(), NOX::Abstract::Group::NotConverged, NOX::Abstract::Group::Ok, Teuchos::rcp(), and NOX::Epetra::LinearSystem::setJacobianOperatorForSolve().

NOX::Abstract::Group::ReturnType LOCA::Epetra::Group::applyJacobianTransposeInverseMultiVector	(	Teuchos::ParameterList &	params,
		const NOX::Abstract::MultiVector &	input,
		NOX::Abstract::MultiVector &	result
	)		const `[virtual]`

Solve Jacobian-tranpose system with multiple right-hand sides.

In addition to all regular linear solver parameters, this method references the following additional parameters:

"Transpose Solver Method" -- [string] (default: "Transpose Preconditioner") Method for preconditioning the transpose linear system (LOCA::Epetra::TransposeLinearSystem::Factory). Available choices are:
- "Transpose Preconditioner" -- Use the transpose of the preconditioner for the original system.
- "Left Preconditioning" -- Use the transpose of the preconditioner, and apply using left preconditioning.
- "Explicit Transpose" -- Form the transpose of the matrix and compute the preconditioner. This method is available only if Trilinos is configured with EpetraExt support (--enable-epetraext).

Implements LOCA::Abstract::TransposeSolveGroup.

References LOCA::Epetra::TransposeLinearSystem::Factory::create(), LOCA::Epetra::TransposeLinearSystem::AbstractStrategy::createJacobianTranspose(), NOX::Epetra::LinearSystem::destroyPreconditioner(), NOX::Epetra::LinearSystem::getJacobianOperator(), NOX::Abstract::Group::NotConverged, NOX::Abstract::MultiVector::numVectors(), NOX::Abstract::Group::Ok, Teuchos::rcp(), and NOX::Epetra::LinearSystem::setJacobianOperatorForSolve().

NOX::Abstract::Group::ReturnType LOCA::Epetra::Group::computeComplex ( double frequency ) [virtual]

Compute $J+i\omega B$ .

The argument frequency stores $\omega$ .

Reimplemented from LOCA::Abstract::Group.

References NOX::Abstract::Group::BadDependency, NOX::Epetra::Vector::CreateView, NOX::Abstract::Group::Ok, Teuchos::rcp(), and NOX::Epetra::LinearSystem::setJacobianOperatorForSolve().

NOX::Abstract::Group::ReturnType LOCA::Epetra::Group::computeF ( ) [virtual]

Overloaded computeF()

Calls LOCA::Epetra::Interface::setParams before evalulating F.

Reimplemented from NOX::Epetra::Group.

References NOX::Epetra::Group::computeF(), and NOX::Abstract::Group::Ok.

NOX::Abstract::Group::ReturnType LOCA::Epetra::Group::computeJacobian ( ) [virtual]

Overloaded computeJacobian()

Calls LOCA::Epetra::Interface::setParams before evalulating J.

Reimplemented from NOX::Epetra::Group.

References NOX::Epetra::Group::computeJacobian(), and NOX::Abstract::Group::Ok.

double LOCA::Epetra::Group::computeScaledDotProduct	(	const NOX::Abstract::Vector &	a,
		const NOX::Abstract::Vector &	b
	)		const `[virtual]`

Compute a scaled dot product.

The implementation here uses the scaling vector $s$ if one is supplied:

$\sum_{i=1}^n a_i*b_i*s_i*s_i.$

If the scaling vector is not provided, the standard dot product is used.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

References as(), NOX::Abstract::Vector::clone(), NOX::DeepCopy, NOX::Abstract::Vector::innerProduct(), NOX::Abstract::Vector::length(), and NOX::Abstract::Vector::scale().

void LOCA::Epetra::Group::postProcessContinuationStep ( LOCA::Abstract::Iterator::StepStatus stepStatus ) [virtual]

Perform any postprocessing after a continuation step finishes.

The stepStatus argument indicates whether the step was successful. The implementation here is to call the corresponding method in the interface.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

void LOCA::Epetra::Group::preProcessContinuationStep ( LOCA::Abstract::Iterator::StepStatus stepStatus ) [virtual]

Perform any preprocessing before a continuation step starts.

The stepStatus argument indicates whether the previous step was successful. The implementation here is to call the corresponding method in the interface.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

void LOCA::Epetra::Group::projectToDraw	(	const NOX::Abstract::Vector &	x,
		double *	px
	)		const `[virtual]`

Projects solution to a few scalars for multiparameter continuation.

This method is called every time a solution is saved by the multiparameter continuation code MF for later visualization and should project the solution vector down to a few scalars. The array px will be preallocated to the proper length given by projectToDrawDimension().

The implementation here is to call the corresponding method in the interface.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

int LOCA::Epetra::Group::projectToDrawDimension ( ) const [virtual]

Returns the dimension of the project to draw array.

The implementation here is to call the corresponding method in the interface.

Reimplemented from LOCA::MultiContinuation::AbstractGroup.

void LOCA::Epetra::Group::scaleVector ( NOX::Abstract::Vector & x ) const [virtual]

Scales a vector using scaling vector.

The implementation here uses the scaling vector $s$ if one is supplied:

$x_i = a_i*s_i.$