Eigen::IterScaling< _MatrixType > Class Template Reference

iterative scaling algorithm to equilibrate rows and column norms in matrices More...

#include <Scaling.h>

Public Types
typedef MatrixType::Index	Index
typedef _MatrixType	MatrixType
typedef MatrixType::Scalar	Scalar

Public Member Functions
void	compute (const MatrixType &mat)
void	computeRef (MatrixType &mat)
	IterScaling ()
	IterScaling (const MatrixType &matrix)
VectorXd &	LeftScaling ()
VectorXd &	RightScaling ()
void	setTolerance (double tol)
	~IterScaling ()

Protected Member Functions
void	init ()

Protected Attributes
ComputationInfo	m_info
bool	m_isInitialized
VectorXd	m_left
MatrixType	m_matrix
int	m_maxits
VectorXd	m_right
double	m_tol

Detailed Description

template<typename _MatrixType>
class Eigen::IterScaling< _MatrixType >

iterative scaling algorithm to equilibrate rows and column norms in matrices

This class can be used as a preprocessing tool to accelerate the convergence of iterative methods

This feature is useful to limit the pivoting amount during LU/ILU factorization The scaling strategy as presented here preserves the symmetry of the problem NOTE It is assumed that the matrix does not have empty row or column,

Example with key steps

VectorXd x(n), b(n);
SparseMatrix<double> A;
// fill A and b;
IterScaling<SparseMatrix<double> > scal; 
// Compute the left and right scaling vectors. The matrix is equilibrated at output
scal.computeRef(A); 
// Scale the right hand side
b = scal.LeftScaling().cwiseProduct(b); 
// Now, solve the equilibrated linear system with any available solver

// Scale back the computed solution
x = scal.RightScaling().cwiseProduct(x); 

Template Parameters

_MatrixType

the type of the matrix. It should be a real square sparsematrix

References : D. Ruiz and B. Ucar, A Symmetry Preserving Algorithm for Matrix Scaling, INRIA Research report RR-7552

See also

IncompleteLUT

Definition at line 48 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

Member Typedef Documentation

Index

template<typename _MatrixType >

typedef MatrixType::Index Eigen::IterScaling< _MatrixType >::Index

Definition at line 53 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

MatrixType

template<typename _MatrixType >

typedef _MatrixType Eigen::IterScaling< _MatrixType >::MatrixType

Definition at line 51 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

Scalar

template<typename _MatrixType >

typedef MatrixType::Scalar Eigen::IterScaling< _MatrixType >::Scalar

Definition at line 52 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

Constructor & Destructor Documentation

IterScaling() [1/2]

template<typename _MatrixType >

Eigen::IterScaling< _MatrixType >::IterScaling ( )

inline

Definition at line 56 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

IterScaling() [2/2]

template<typename _MatrixType >

Eigen::IterScaling< _MatrixType >::IterScaling ( const MatrixType &  matrix )

inline

Definition at line 58 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

~IterScaling()

template<typename _MatrixType >

Eigen::IterScaling< _MatrixType >::~IterScaling ( )

inline

Definition at line 64 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

Member Function Documentation

compute()

template<typename _MatrixType >

void Eigen::IterScaling< _MatrixType >::compute ( const MatrixType &  mat )

inline

Compute the left and right diagonal matrices to scale the input matrix mat

FIXME This algorithm will be modified such that the diagonal elements are permuted on the diagonal.

See also

LeftScaling() RightScaling()

Definition at line 73 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

computeRef()

template<typename _MatrixType >

void Eigen::IterScaling< _MatrixType >::computeRef ( MatrixType &  mat )

inline

Compute the left and right vectors to scale the vectors the input matrix is scaled with the computed vectors at output

See also

compute()

Definition at line 149 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

init()

template<typename _MatrixType >

void Eigen::IterScaling< _MatrixType >::init ( )

inlineprotected

Definition at line 177 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

LeftScaling()

template<typename _MatrixType >

VectorXd& Eigen::IterScaling< _MatrixType >::LeftScaling ( )

inline

Get the vector to scale the rows of the matrix

Definition at line 156 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

RightScaling()

template<typename _MatrixType >

VectorXd& Eigen::IterScaling< _MatrixType >::RightScaling ( )

inline

Get the vector to scale the columns of the matrix

Definition at line 163 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

setTolerance()

template<typename _MatrixType >

void Eigen::IterScaling< _MatrixType >::setTolerance ( double  tol )

inline

Set the tolerance for the convergence of the iterative scaling algorithm

Definition at line 170 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

Member Data Documentation

m_info

template<typename _MatrixType >

ComputationInfo Eigen::IterScaling< _MatrixType >::m_info

mutableprotected

Definition at line 185 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

m_isInitialized

template<typename _MatrixType >

bool Eigen::IterScaling< _MatrixType >::m_isInitialized

protected

Definition at line 186 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

m_left

template<typename _MatrixType >

VectorXd Eigen::IterScaling< _MatrixType >::m_left

protected

Definition at line 187 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

m_matrix

template<typename _MatrixType >

MatrixType Eigen::IterScaling< _MatrixType >::m_matrix

protected

Definition at line 184 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

m_maxits

template<typename _MatrixType >

int Eigen::IterScaling< _MatrixType >::m_maxits

protected

Definition at line 190 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

m_right

template<typename _MatrixType >

VectorXd Eigen::IterScaling< _MatrixType >::m_right

protected

Definition at line 188 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

m_tol

template<typename _MatrixType >

double Eigen::IterScaling< _MatrixType >::m_tol

protected

Definition at line 189 of file unsupported/Eigen/src/IterativeSolvers/Scaling.h.

---

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

• unsupported/Eigen/src/IterativeSolvers/Scaling.h