Prototype

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

ggev( const char jobvl, const char jobvr, MatrixA& a, MatrixB& b,
        VectorALPHAR& alphar, VectorALPHAI& alphai, VectorBETA& beta,
        MatrixVL& vl, MatrixVR& vr );

ggev( const char jobvl, const char jobvr, MatrixA& a, MatrixB& b,
        VectorALPHA& alpha, VectorBETA& beta, MatrixVL& vl, MatrixVR& vr );

Description

ggev (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGGEV, DGGEV, CGGEV, and ZGGEV. ggev 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.

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 generalized eigenvector v(j) corresponding to the generalized eigenvalue lambda(j) of (A,B) satisfies

A * v(j) = lambda(j) * B * v(j).

The left generalized eigenvector u(j) corresponding to the generalized eigenvalues 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/ggev.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also