##### hseqr

###### Prototype

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

    hseqr( const char job, const char compz, const int_t ilo,
            const int_t ihi, MatrixH& h, VectorWR& wr, VectorWI& wi,
            MatrixZ& z );

    hseqr( const char job, const char compz, const int_t ilo,
            const int_t ihi, MatrixH& h, VectorW& w, MatrixZ& z );

###### Description

`hseqr` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SHSEQR, DHSEQR, CHSEQR, and ZHSEQR. `hseqr` computes the eigenvalues of a Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors.

Optionally Z may be postmultiplied into an input unitary matrix Q so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the unitary matrix Q: A = QH*Q*H = (QZ)H(QZ)**H.

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

Table 1.228. Dispatching of hseqr

Value type of MatrixH | LAPACK routine
--- | ---
`float` | SHSEQR
`double` | DHSEQR
`complex<float>` | CHSEQR
`complex<double>` | ZHSEQR

###### Definition

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

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files shseqr.f, dhseqr.f, chseqr.f, and zhseqr.f at Netlib.