##### gees

###### 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.

Table 1.151. Dispatching of gees

Value type of MatrixA | LAPACK routine
--- | ---
`float` | SGEES
`double` | DGEES
`complex<float>` | CGEES
`complex<double>` | ZGEES

###### Definition

Defined in header `boost/numeric/bindings/lapack/driver/gees.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/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

- Originating Fortran source files sgees.f, dgees.f, cgees.f, and zgees.f at Netlib.