TR-mbed 1.0
Loading...
Searching...
No Matches
Public Types | Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
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 ()
 
 IterScaling (const MatrixType &matrix)
 
 ~IterScaling ()
 
void compute (const MatrixType &mat)
 
void computeRef (MatrixType &mat)
 
VectorXd & LeftScaling ()
 
VectorXd & RightScaling ()
 
void setTolerance (double tol)
 

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);
n
int n
Definition BiCGSTAB_simple.cpp:1
b
Scalar * b
Definition benchVecAdd.cpp:17
A
Matrix< SCALARA, Dynamic, Dynamic, opt_A > A
Definition bench_gemm.cpp:48
Eigen::IterScaling
iterative scaling algorithm to equilibrate rows and column norms in matrices
Definition Scaling.h:49
Eigen::IterScaling::computeRef
void computeRef(MatrixType &mat)
Definition Scaling.h:149
Eigen::Matrix
The matrix class, also used for vectors and row-vectors.
Definition Matrix.h:180
Eigen::SparseMatrix
A versatible sparse matrix representation.
Definition SparseMatrix.h:98
x
set noclip points set clip one set noclip two set bar set border lt lw set xdata set ydata set zdata set x2data set y2data set boxwidth set dummy x
Definition gnuplot_common_settings.hh:12
scal
int EIGEN_BLAS_FUNC() scal(int *n, RealScalar *palpha, RealScalar *px, int *incx)
Definition level1_impl.h:117
Template Parameters
_MatrixTypethe 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 Typedef Documentation

◆ Index

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

◆ MatrixType

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

◆ Scalar

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

Constructor & Destructor Documentation

◆ IterScaling() [1/2]

template<typename _MatrixType >
Eigen::IterScaling< _MatrixType >::IterScaling ( )
inline

◆ IterScaling() [2/2]

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

◆ ~IterScaling()

template<typename _MatrixType >
Eigen::IterScaling< _MatrixType >::~IterScaling ( )
inline

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()

◆ init()

template<typename _MatrixType >
void Eigen::IterScaling< _MatrixType >::init ( )
inlineprotected

◆ LeftScaling()

template<typename _MatrixType >
VectorXd & Eigen::IterScaling< _MatrixType >::LeftScaling ( )
inline

Get the vector to scale the rows of the matrix

◆ RightScaling()

template<typename _MatrixType >
VectorXd & Eigen::IterScaling< _MatrixType >::RightScaling ( )
inline

Get the vector to scale the columns of the matrix

◆ setTolerance()

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

Set the tolerance for the convergence of the iterative scaling algorithm

Member Data Documentation

◆ m_info

template<typename _MatrixType >
ComputationInfo Eigen::IterScaling< _MatrixType >::m_info
mutableprotected

◆ m_isInitialized

template<typename _MatrixType >
bool Eigen::IterScaling< _MatrixType >::m_isInitialized
protected

◆ m_left

template<typename _MatrixType >
VectorXd Eigen::IterScaling< _MatrixType >::m_left
protected

◆ m_matrix

template<typename _MatrixType >
MatrixType Eigen::IterScaling< _MatrixType >::m_matrix
protected

◆ m_maxits

template<typename _MatrixType >
int Eigen::IterScaling< _MatrixType >::m_maxits
protected

◆ m_right

template<typename _MatrixType >
VectorXd Eigen::IterScaling< _MatrixType >::m_right
protected

◆ m_tol

template<typename _MatrixType >
double Eigen::IterScaling< _MatrixType >::m_tol
protected
The documentation for this class was generated from the following file:
Generated by doxygen 1.9.8