##### ggevx

###### 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.

Table 1.105. Dispatching of ggevx

Value type of MatrixA | LAPACK routine
--- | ---
`float` | SGGEVX
`double` | DGGEVX
`complex<float>` | CGGEVX
`complex<double>` | ZGGEVX

###### Definition

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

###### Parameters or Requirements on Types

Parameters

MatrixA

  The definition of term 1

MatrixB

  The definition of term 2

MatrixC

  The definition of term 3.

  Definitions may contain paragraphs.

###### 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

- Originating Fortran source files sggevx.f, dggevx.f, cggevx.f, and zggevx.f at Netlib.