Solves the generalized eigenproblem det(t A - s B) = 0. More...

#include <vnl/vnl_matrix.h>
#include <vnl/vnl_vector.h>
#include <vcl_algorithm.h>

Functions
template<class T >
bool	vnl_generalized_schur (vnl_matrix< T > A, vnl_matrix< T > B, vnl_vector< T > alphar, vnl_vector< T > alphai, vnl_vector< T > beta, vnl_matrix< T > L, vnl_matrix< T > *R)
	For a real scalar type T, this function uses orthogonal matrices L, R to reduce the (square) matrices A, B to generalized (real) Schur form.
VCL_DEFINE_SPECIALIZATION bool	vnl_generalized_schur (vnl_matrix< double > A, vnl_matrix< double > B, vnl_vector< double > alphar, vnl_vector< double > alphai, vnl_vector< double > beta, vnl_matrix< double > L, vnl_matrix< double > *R)
template<class T >
T	vnl_generalized_schur_convert_cast (double a)

Detailed Description

Solves the generalized eigenproblem det(t A - s B) = 0.

Author:: fsm, Oxford RRG

Date:: 2 Oct 2001

Definition in file vnl_generalized_schur.h.

Function Documentation

template<class T >

bool vnl_generalized_schur	(	vnl_matrix< T > *	A,
		vnl_matrix< T > *	B,
		vnl_vector< T > *	alphar,
		vnl_vector< T > *	alphai,
		vnl_vector< T > *	beta,
		vnl_matrix< T > *	L,
		vnl_matrix< T > *	R
	)		`[inline]`

For a real scalar type T, this function uses orthogonal matrices L, R to reduce the (square) matrices A, B to generalized (real) Schur form.

This means that B is upper triangular and A is block upper triangular with blocks of size at most 2x2 such that the 2x2 blocks B corresponding to 2x2 blocks of A are diagonal. E.g.:

                  [ * * * * * ]
                  [   * * * * ]
   A <- L^* A R = [   * * * * ]
                  [       * * ]
                  [       * * ]
  
                  [ * * * * * ]
                  [   *   * * ]
   B <- L^* B R = [     * * * ]
                  [       *   ]
                  [         * ]

In addition, the function computes the generalized eigenvalues (alphar(k) + i alphai(k) : beta(k) for k = 0, 1, 2,...

Definition at line 63 of file vnl_generalized_schur.h.

VCL_DEFINE_SPECIALIZATION bool vnl_generalized_schur	(	vnl_matrix< double > *	A,
		vnl_matrix< double > *	B,
		vnl_vector< double > *	alphar,
		vnl_vector< double > *	alphai,
		vnl_vector< double > *	beta,
		vnl_matrix< double > *	L,
		vnl_matrix< double > *	R
	)

Definition at line 19 of file vnl_generalized_schur.cxx.

template<class T >

T vnl_generalized_schur_convert_cast ( double a )

Definition at line 60 of file vnl_generalized_schur.h.

Functions

Detailed Description

Function Documentation