Prototype

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

ggbal( const char job, MatrixA& a, MatrixB& b, int_t& ilo,
        int_t& ihi, VectorLSCALE& lscale, VectorRSCALE& rscale );

Description

ggbal (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGGBAL, DGGBAL, CGGBAL, and ZGGBAL. ggbal balances a pair of general complex matrices (A,B). This involves, first, permuting A and B by similarity transformations to isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional.

Balancing may reduce the 1-norm of the matrices, and improve the accuracy of the computed eigenvalues and/or eigenvectors in the generalized eigenvalue problem A*x = lambda*B*x.

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/ggbal.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also