imstk::NonLinearSolver< SystemMatrix > Class Template Reference

Base class for non-linear solvers. More...

#include <imstkNonLinearSolver.h>

Inheritance diagram for imstk::NonLinearSolver< SystemMatrix >:

Collaboration diagram for imstk::NonLinearSolver< SystemMatrix >:

Public Types
using	JacobianType = std::function< const SystemMatrix &(const Vectord &)>
using	UpdateIterateType = std::function< void(const Vectord &, Vectord &)>
using	FunctionType = NonLinearSystem< SparseMatrixd >::VectorFunctionType

Public Member Functions
virtual void	solveGivenState (Vectord &x)=0
	Main solve routine.
virtual void	solve () override=0
double	armijo (const Vectord &dx, Vectord &x, const double previousFnorm)
	Backtracking line search method based on the Armijo-Goldstein condition. More...
void	parabolicModel (const std::array< double, 3 > &fnorm, std::array< double, 3 > &lambda)
	Three-point safeguarded parabolic model for a line search. Upon return lambda[0] will contain the new value of lambda given by the parabolic model. More...
void	setSigma (const std::array< double, 2 > &newSigma)
	Set/Get Sigma. Safeguard parameter for the the line search method. More...
const std::array< double, 2 > &	getSigma () const
void	setAlpha (const double newAlpha)
	Set/Get Alpha. Parameter to measure sufficient decrease in the line search. More...
double	getAlpha () const
void	setArmijoMax (const size_t newArmijoMax)
	Set/Get ArmijoMax. Maximum number of step length reductions. More...
size_t	getArmijoMax () const
void	setSystem (std::shared_ptr< NonLinearSystem< SystemMatrix >> newSystem)
	Sets the system. System of nonlinear equations. More...
std::shared_ptr< NonLinearSystem< SystemMatrix > >	getSystem () const
void	setUpdateIterate (const UpdateIterateType &newUpdateIterate)
	Set a customized iterate update function. More...
virtual void	setToFullyImplicit ()
	Set the Newton solver to be fully implicit.
virtual void	setToSemiImplicit ()
	Set the Newton solver to be fully implicit.

Protected Attributes
std::array< double, 2 >	m_sigma
	Safeguarding bounds for the line search.
double	m_alpha
	Parameter to measure decrease.
size_t	m_armijoMax
	Maximum number of step length reductions.
std::shared_ptr< NonLinearSystem< SystemMatrix > >	m_nonLinearSystem
	System of non-linear equations.
UpdateIterateType	m_updateIterate
	Update iteration function.
bool	m_isSemiImplicit = false
	Semi-Implicit solver.

Additional Inherited Members
Public Attributes inherited from imstk::SolverBase
std::shared_ptr< DataTracker >	m_dataTracker

Detailed Description

template<typename SystemMatrix>
class imstk::NonLinearSolver< SystemMatrix >

Base class for non-linear solvers.

Definition at line 24 of file imstkNonLinearSolver.h.

Member Function Documentation

armijo()

template<typename SystemMatrix >

double imstk::NonLinearSolver< SystemMatrix >::armijo	(	const Vectord &	dx,
		Vectord &	x,
		const double	previousFnorm
	)

Backtracking line search method based on the Armijo-Goldstein condition.

Parameters

dx	Computed direction.
x	Current iterate.

Temporaries used in the line search

Initialize temporaries

Todo:

log this

Todo:

Log this

Update x and keep books on lambda

Todo:

Log this

Update function norms

Apply the three point parabolic model

Todo:

Add to logger

Definition at line 27 of file imstkNonLinearSolver.cpp.

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parabolicModel()

template<typename SystemMatrix >

void imstk::NonLinearSolver< SystemMatrix >::parabolicModel	(	const std::array< double, 3 > &	fnorm,
		std::array< double, 3 > &	lambda
	)

Three-point safeguarded parabolic model for a line search. Upon return lambda[0] will contain the new value of lambda given by the parabolic model.

Parameters

lambda[1]	Current step length lambda[2] Previous step length
fnorm[0]	Value of |F(x)|^2 fnorm[1] Value of |F(x + lambda[1]*dx)|^2 fnorm[2] Value of |F(x + lambda[2]*dx)|^2

Compute the coefficients for the interpolation polynomial: p(lambda) = fnorm[0] + (b*lambda + a*lambda^2)/d1, where d1 = (lambda[1] - lambda[2])*lambda[1]*lambda[2] < 0 if a > 0, then we have a concave up curvature and lambda defaults to: lambda = sigma[0]*lambda

Definition at line 88 of file imstkNonLinearSolver.cpp.

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setAlpha()

template<typename SystemMatrix >

void imstk::NonLinearSolver< SystemMatrix >::setAlpha

(

const double

newAlpha

)

Set/Get Alpha. Parameter to measure sufficient decrease in the line search.

Parameters

newAlpha

New alpha parameter.

Definition at line 137 of file imstkNonLinearSolver.cpp.

setArmijoMax()

template<typename SystemMatrix >

void imstk::NonLinearSolver< SystemMatrix >::setArmijoMax

(

const size_t

newArmijoMax

)

Set/Get ArmijoMax. Maximum number of step length reductions.

Parameters

newArmijoMax

New iteration parameter.

Definition at line 151 of file imstkNonLinearSolver.cpp.

setSigma()

template<typename SystemMatrix >

void imstk::NonLinearSolver< SystemMatrix >::setSigma

(

const std::array< double, 2 > &

newSigma

)

Set/Get Sigma. Safeguard parameter for the the line search method.

Parameters

newSigma

New sigma parameter.

Definition at line 123 of file imstkNonLinearSolver.cpp.

setSystem()

template<typename SystemMatrix >

void imstk::NonLinearSolver< SystemMatrix >::setSystem

(

std::shared_ptr< NonLinearSystem< SystemMatrix >>

newSystem

)

Sets the system. System of nonlinear equations.

Parameters

newSystem

Non-linear system replacement.

Definition at line 165 of file imstkNonLinearSolver.cpp.

setUpdateIterate()

template<typename SystemMatrix >

void imstk::NonLinearSolver< SystemMatrix >::setUpdateIterate ( const UpdateIterateType &  newUpdateIterate )

inline

Set a customized iterate update function.

Parameters

newUpdateIterate

Function used to update iterates. Default: x+=dx.

Definition at line 98 of file imstkNonLinearSolver.h.

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

• Source/Solvers/imstkNonLinearSolver.h
• Source/Solvers/imstkNonLinearSolver.cpp