RWBalanceDecomp< TypeT > Class Template Reference

Encapsulates the decomposition implicit in the permutation and balance transformations on a nonsymmetric matrix before computing its eigenvalues. More...

#include <rw/lapack/bal.h>

Public Member Functions
	RWBalanceDecomp ()
	RWBalanceDecomp (const RWGenMat< TypeT > &A, bool permute=true, bool scale=true)
const RWBalanceTransform< TypeT > &	B () const
const RWGenMat< TypeT >	C () const
unsigned	cols () const
unsigned	rows () const

Detailed Description

template<class TypeT>
class RWBalanceDecomp< TypeT >

A permutation and balance transformation is often performed on a nonsymmetric matrix before computing its eigenvalues. The permutation attempts to break the matrix into three independent blocks such that the first and last block are triangular, and the balance transformation is a diagonal scaling transformation that attempts to make the row and column norms close to each other. The class RWBalanceDecomp encapsulates the decomposition:

\[ A = BCB^{-1} \]

where B=PD, an amalgamation of the permutation and balance transformations. This decomposition is used internally by the nonsymmetric eigenvalue decomposition classes, including the Schur and Hessenberg decomposition classes.

Synopsis

#include <rw/lapack/bal.h>
 
RWBalanceDecomp<double> bal(A);  // A is a RWGenMat<double>

Constructor & Destructor Documentation

RWBalanceDecomp() [1/2]

template<class TypeT >

RWBalanceDecomp< TypeT >::RWBalanceDecomp

(

)

Constructs an empty decomposition.

RWBalanceDecomp() [2/2]

template<class TypeT >

RWBalanceDecomp< TypeT >::RWBalanceDecomp ( const RWGenMat< TypeT > & A, bool permute = true, bool scale = true )

explicit

Constructs a decomposition of the matrix A. The boolean parameters control whether permutation, scaling (balancing), both, or neither are done. The matrix must be square.

Member Function Documentation

B()

template<class TypeT >

const RWBalanceTransform< TypeT > & RWBalanceDecomp< TypeT >::B ( ) const

inline

Returns a representation of the balance transformation computed.

C()

template<class TypeT >

const RWGenMat< TypeT > RWBalanceDecomp< TypeT >::C ( ) const

inline

Returns the balanced matrix.

cols()

template<class TypeT >

unsigned RWBalanceDecomp< TypeT >::cols ( ) const

inline

Returns the number of columns in the decomposition.

rows()

template<class TypeT >

unsigned RWBalanceDecomp< TypeT >::rows ( ) const

inline

Returns the number of rows in the decomposition.