Iterative solvers module

Detailed Description

This module aims to provide various iterative linear and non linear solver algorithms. It currently provides:

• a constrained conjugate gradient
• a Householder GMRES implementation

  #include <unsupported/Eigen/IterativeSolvers>

Classes
class	Eigen::IterationController
	Controls the iterations of the iterative solvers. More...
class	Eigen::IterScaling< _MatrixType >
	iterative scaling algorithm to equilibrate rows and column norms in matrices More...

Functions
template<typename TMatrix, typename CMatrix, typename VectorX, typename VectorB, typename VectorF>
void	Eigen::internal::constrained_cg (const TMatrix &A, const CMatrix &C, VectorX &x, const VectorB &b, const VectorF &f, IterationController &iter)
template<typename CMatrix, typename CINVMatrix>
void	Eigen::internal::pseudo_inverse (const CMatrix &C, CINVMatrix &CINV)

Function Documentation

constrained_cg()

template<typename TMatrix, typename CMatrix, typename VectorX, typename VectorB, typename VectorF>

void Eigen::internal::constrained_cg	(	const TMatrix &	A,
		const CMatrix &	C,
		VectorX &	x,
		const VectorB &	b,
		const VectorF &	f,
		IterationController &	iter )

Constrained conjugate gradient

Computes the minimum of \( 1/2((Ax).x) - bx \) under the contraint \( Cx \le f \)

pseudo_inverse()

template<typename CMatrix, typename CINVMatrix>

void Eigen::internal::pseudo_inverse	(	const CMatrix &	C,
		CINVMatrix &	CINV )

Compute the pseudo inverse of the non-square matrix C such that \( CINV = (C * C^T)^{-1} * C \) based on a conjugate gradient method.

This function is internally used by constrained_cg.