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	MatrixType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::Index	Index

Public Member Functions
	IterScaling (const MatrixType &matrix)
void	compute (const MatrixType &mat)
	Compute the left and right diagonal matrices to scale the input matrix mat. More...
void	computeRef (MatrixType &mat)
	Compute the left and right vectors to scale the vectors the input matrix is scaled with the computed vectors at output. More...
VectorXd &	LeftScaling ()
	Get the vector to scale the rows of the matrix.
VectorXd &	RightScaling ()
	Get the vector to scale the columns of the matrix.
void	setTolerance (double tol)
	Set the tolerance for the convergence of the iterative scaling algorithm.

Protected Member Functions
void	init ()

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

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

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()

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()

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

• third-party-libs/eigen3/unsupported/Eigen/src/IterativeSolvers/Scaling.h