#include <SVDLinearSolver.h>

Inheritance diagram for sofa::component::linearsolver::direct::SVDLinearSolver< TMatrix, TVector >:

Detailed Description

template<class TMatrix, class TVector>
class sofa::component::linearsolver::direct::SVDLinearSolver< TMatrix, TVector >

Linear system solver using the JacobiSVD decomposition of the Eigen library (http://eigen.tuxfamily.org/ , see also an excellent introduction in Numerical Recipes.) The Singular Value Decomposition is probably the most robust (and the slowest !) matrix factoring for linear equation solution. It works only for dense matrices (FullMatrix). The equation system Ax=b is solved using a decomposition of A=USV^T, where U is a n-by-n unitary, V is a p-by-p unitary, and S is a n-by-p real positive matrix which is zero outside of its main diagonal; the diagonal entries of S are known as the singular values of A and the columns of U and V are known as the left and right singular vectors of A respectively. In case of indefinite matrix, there is at least one null singular value, and there is no solution to the equation system except for special right-hand terms. The SVD solver solves the equation in the least-square sense: it finds the pseudo-solution x which minimizes Ax-b. The condition number of the matrix is a byproduct of the solution, written in attribute "conditionNumber" by method solve (Matrix& M, Vector& x, Vector& b).

Public Attributes
Data< bool >	f_verbose
	Dump system state at each iteration. More...

Data< Real >	f_minSingularValue
	Thershold under which a singular value is set to 0, for the stabilization of ill-conditioned system. More...

Data< Real >	f_conditionNumber
	Condition number of the matrix: ratio between the largest and smallest singular values. Computed in method solve. More...

Public Member Functions
	SOFA_CLASS (SOFA_TEMPLATE2(SVDLinearSolver, TMatrix, TVector), SOFA_TEMPLATE2(sofa::component::linearsolver::MatrixLinearSolver, TMatrix, TVector))

void	solve (Matrix &M, Vector &x, Vector &b) override
	Solve Mx=b. More...

bool	supportNonSymmetricSystem () const override

Public Member Functions inherited from sofa::component::linearsolver::MatrixLinearSolver< TMatrix, TVector >
void	resetSystem ()

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API void	resetSystem ()

void	resizeSystem (Size n)

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API void	resizeSystem (Size)

void	setSystemMBKMatrix (const core::MechanicalParams *mparams)

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API void	setSystemMBKMatrix (const core::MechanicalParams *mparams)

void	rebuildSystem (SReal, SReal)

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API void	rebuildSystem (SReal massFactor, SReal forceFactor)

void	setSystemLHVector (core::MultiVecDerivId v)

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API void	setSystemLHVector (core::MultiVecDerivId v)

void	applySystemSolution ()

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API void	applySystemSolution ()

void	applyConstraintForce (const sofa::core::ConstraintParams , sofa::core::MultiVecDerivId, const linearalgebra::BaseVector )

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API void	applyConstraintForce (const sofa::core::ConstraintParams , sofa::core::MultiVecDerivId, const linearalgebra::BaseVector )

void	computeResidual (const core::ExecParams , linearalgebra::BaseVector )

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API void	computeResidual (const core::ExecParams params, linearalgebra::BaseVector f)

GraphScatteredVector *	createPersistentVector ()

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API GraphScatteredVector *	createPersistentVector ()

linearalgebra::BaseMatrix *	getSystemBaseMatrix ()

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API linearalgebra::BaseMatrix *	getSystemBaseMatrix ()

linearalgebra::BaseVector *	getSystemRHBaseVector ()

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API linearalgebra::BaseVector *	getSystemRHBaseVector ()

linearalgebra::BaseVector *	getSystemLHBaseVector ()

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API linearalgebra::BaseVector *	getSystemLHBaseVector ()

void	checkLinearSystem ()

SOFA_COMPONENT_LINEARSOLVER_ITERATIVE_API void	checkLinearSystem ()

bool	addJMInvJtLocal (GraphScatteredMatrix M, MatrixLinearSolver< GraphScatteredMatrix, GraphScatteredVector, NoThreadManager >::ResMatrixType result, const MatrixLinearSolver< GraphScatteredMatrix, GraphScatteredVector, NoThreadManager >::JMatrixType *J, const SReal fact)