Prototype

There is one prototype of gghrd available, please see below.

gghrd( const char compq, const char compz, const int_t ilo,
        MatrixA& a, MatrixB& b, MatrixQ& q, MatrixZ& z );

Description

gghrd (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGGHRD, DGGHRD, CGGHRD, and ZGGHRD. gghrd reduces a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular. The form of the generalized eigenvalue problem is A*x = lambda*B*x, and B is typically made upper triangular by computing its QR factorization and moving the unitary matrix Q to the left side of the equation.

This subroutine simultaneously reduces A to a Hessenberg matrix H: Q**HA*Z = H and transforms B to another upper triangular matrix T: Q*H*B*Z = T in order to reduce the problem to its standard form H*y = lambdaT*y where y = Z*H*x.

The unitary matrices Q and Z are determined as products of Givens rotations. They may either be formed explicitly, or they may be postmultiplied into input matrices Q1 and Z1, so that Q1 * A * Z1**H = (Q1*Q) * H * (Z1Z)H Q1 * B * Z1*H = (Q1*Q) * T * (Z1Z)*H If Q1 is the unitary matrix from the QR factorization of B in the original equation A*x = lambda*B*x, then gghrd reduces the original problem to generalized Hessenberg form.

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/computational/gghrd.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/computational/gghrd.hpp>
using namespace boost::numeric::bindings;

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also