Prototype

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

geesx( const char jobvs, const char sort, external_fp select,
        const char sense, MatrixA& a, int_t& sdim, VectorWR& wr,
        VectorWI& wi, MatrixVS& vs, Scalar >, Scalar > );

geesx( const char jobvs, const char sort, external_fp select,
        const char sense, MatrixA& a, int_t& sdim, VectorW& w,
        MatrixVS& vs, Scalar >, Scalar > );

Description

geesx (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGEESX, DGEESX, CGEESX, and ZGEESX. geesx computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization A = ZT(Z**H).

Optionally, it also orders the eigenvalues on the diagonal of the Schur form so that selected eigenvalues are at the top left; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right invariant subspace corresponding to the selected eigenvalues (RCONDV). The leading columns of Z form an orthonormal basis for this invariant subspace.

For further explanation of the reciprocal condition numbers RCONDE and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where these quantities are called s and sep respectively).

A complex matrix is in Schur form if it 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/geesx.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also