Prototype

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

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

gees( const char jobvs, const char sort, external_fp select, MatrixA& a,
        int_t& sdim, VectorW& w, MatrixVS& vs );

Description

gees (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGEES, DGEES, CGEES, and ZGEES. gees 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. The leading columns of Z then form an orthonormal basis for the invariant subspace corresponding to the selected eigenvalues.

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/gees.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also