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.

Definition

Defined in header boost/numeric/bindings/lapack/computational/hseqr.hpp.

Parameters or Requirements on Types

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