core/vnl/algo/vnl_complex_generalized_schur.h File Reference

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

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

Go to the source code of this file.

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

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Detailed Description

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

Author:

Peter Vanroose, ABIS Leuven

Date:

9 Jan 2011 Adapted from vnl_generalized_schur.h/.cxx

Definition in file vnl_complex_generalized_schur.h.

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Function Documentation

template<class T >

vcl_complex<T> vnl_complex_generalized_schur_convert_cast

(

vcl_complex< double >

a

)

Definition at line 51 of file vnl_complex_generalized_schur.h.

template<class T >

bool vnl_generalized_schur	(	vnl_matrix< vcl_complex< T > > *	A,
		vnl_matrix< vcl_complex< T > > *	B,
		vnl_vector< vcl_complex< T > > *	alpha,
		vnl_vector< vcl_complex< T > > *	beta,
		vnl_matrix< vcl_complex< T > > *	L,
		vnl_matrix< vcl_complex< T > > *	R
	)		[inline]

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

This means that A and B become upper triangular, A <-- L^* A R, and B <-- L^* B R. Of course, A and B should be of the same size.

In addition, the function computes the (complex) generalized eigenvalues alpha(k) : beta(k) for k = 0, 1, 2,...

To pass in scalar type T matrices A and B, you'll have to first convert them to complex matrices since they will be overwritten by they (complex) upper triangular decomposition.

Definition at line 54 of file vnl_complex_generalized_schur.h.

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

Definition at line 19 of file vnl_complex_generalized_schur.cxx.