##### hsein

###### Prototype

There are two prototypes of `hsein` available, please see below.

    hsein( const Side side, const char eigsrc, const char initv,
            VectorSELECT& select, const MatrixH& h, VectorWR& wr,
            const VectorWI& wi, MatrixVL& vl, MatrixVR& vr,
            const int_t mm, int_t& m,
            VectorIFAILL& ifaill, VectorIFAILR& ifailr );

    hsein( const Side side, const char eigsrc, const char initv,
            const VectorSELECT& select, const MatrixH& h, VectorW& w,
            MatrixVL& vl, MatrixVR& vr, const int_t mm,
            int_t& m, VectorIFAILL& ifaill, VectorIFAILR& ifailr );

###### Description

`hsein` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SHSEIN, DHSEIN, CHSEIN, and ZHSEIN. `hsein` uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H.

The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by:

H * x = w * x, y*h * H = w * y*h

where y**h denotes the conjugate transpose of the vector y.

The selection of the LAPACK routine is done during compile-time, and is determined by the type of values contained in type `VectorSELECT`. The type of values is obtained through the `value_type` meta-function `typename value_type<VectorSELECT>::type`. The dispatching table below illustrates to which specific routine the code path will be generated.

Table 1.227. Dispatching of hsein

Value type of VectorSELECT | LAPACK routine
--- | ---
`float` | SHSEIN
`double` | DHSEIN
`complex<float>` | CHSEIN
`complex<double>` | ZHSEIN

###### Definition

Defined in header `boost/numeric/bindings/lapack/computational/hsein.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/computational/hsein.hpp>
    using namespace boost::numeric::bindings;

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files shsein.f, dhsein.f, chsein.f, and zhsein.f at Netlib.