Prototype

There are two prototypes of ggevx available, please see below.

ggevx( const char balanc, const char jobvl, const char jobvr,
        const char sense, MatrixA& a, MatrixB& b, VectorALPHAR& alphar,
        VectorALPHAI& alphai, VectorBETA& beta, MatrixVL& vl, MatrixVR& vr,
        int_t& ilo, int_t& ihi, VectorLSCALE& lscale,
        VectorRSCALE& rscale, Scalar >, Scalar >, VectorRCONDE& rconde,
        VectorRCONDV& rcondv );

ggevx( const char balanc, const char jobvl, const char jobvr,
        const char sense, MatrixA& a, MatrixB& b, VectorALPHA& alpha,
        VectorBETA& beta, MatrixVL& vl, MatrixVR& vr, int_t& ilo,
        int_t& ihi, VectorLSCALE& lscale, VectorRSCALE& rscale,
        Scalar >, Scalar >, VectorRCONDE& rconde, VectorRCONDV& rcondv );

Description

ggevx (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGGEVX, DGGEVX, CGGEVX, and ZGGEVX. ggevx computes for a pair of N-by-N complex nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.

Optionally, it also computes a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors (ILO, IHI, LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for the eigenvalues (RCONDE), and reciprocal condition numbers for the right eigenvectors (RCONDV).

A generalized eigenvalue for a pair of matrices (A,B) is a scalar lambda or a ratio alpha/beta = lambda, such that A - lambda*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0, and even for both being zero.

The right eigenvector v(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies A * v(j) = lambda(j) * B * v(j) . The left eigenvector u(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies u(j)*H * A = lambda(j) * u(j)H * B. where u(j)*H is the conjugate-transpose of u(j).

The selection of the LAPACK routine is done during compile-time, and is determined by the type of values contained in type MatrixA. The type of values is obtained through the value_type meta-function typename value_type<MatrixA>::type. The dispatching table below illustrates to which specific routine the code path will be generated.

Definition

Defined in header boost/numeric/bindings/lapack/driver/ggevx.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/driver/ggevx.hpp>
using namespace boost::numeric::bindings;

lapack::ggevx( x, y, z );

this will output

[5] 0 1 2 3 4 5

Notes

See Also