Prototype

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

ggesx( const char jobvsl, const char jobvsr, const char sort,
        external_fp selctg, const char sense, MatrixA& a, MatrixB& b,
        int_t& sdim, VectorALPHAR& alphar, VectorALPHAI& alphai,
        VectorBETA& beta, MatrixVSL& vsl, MatrixVSR& vsr,
        VectorRCONDE& rconde, VectorRCONDV& rcondv );

ggesx( const char jobvsl, const char jobvsr, const char sort,
        external_fp selctg, const char sense, MatrixA& a, MatrixB& b,
        int_t& sdim, VectorALPHA& alpha, VectorBETA& beta,
        MatrixVSL& vsl, MatrixVSR& vsr, VectorRCONDE& rconde,
        VectorRCONDV& rcondv );

Description

ggesx (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGGESX, DGGESX, CGGESX, and ZGGESX. ggesx computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T), and, optionally, the left and/or right matrices of Schur vectors (VSL and VSR). This gives the generalized Schur factorization

(A,B) = ( (VSL) S (VSR)*H, (VSL) T (VSR)*H )

where (VSR)**H is the conjugate-transpose of VSR.

Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper triangular matrix S and the upper triangular matrix T; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right and left deflating subspaces corresponding to the selected eigenvalues (RCONDV). The leading columns of VSL and VSR then form an orthonormal basis for the corresponding left and right eigenspaces (deflating subspaces).

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

A pair of matrices (S,T) is in generalized complex Schur form if T is upper triangular with non-negative diagonal and S is upper triangular.

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/ggesx.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also