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[section ggbal]

[heading 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 );
``


[heading 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. 

[table Dispatching of ggbal
[  [ Value type of MatrixA ] [LAPACK routine] ]
[  [`float`][SGGBAL] ]
[  [`double`][DGGBAL] ]
[  [`complex<float>`][CGGBAL] ]
[  [`complex<double>`][ZGGBAL] ]

]


[heading Definition]
Defined in header [headerref boost/numeric/bindings/lapack/computational/ggbal.hpp].


[heading Parameters or Requirements on Types]

[variablelist Parameters
    [[MatrixA] [The definition of term 1]]
    [[MatrixB] [The definition of term 2]]
    [[MatrixC] [
    The definition of term 3.

    Definitions may contain paragraphs.
    ]]
]


[heading Complexity]


[heading 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
``



[heading Notes]


[heading See Also]

* Originating Fortran source files [@http://www.netlib.org/lapack/single/sggbal.f sggbal.f], [@http://www.netlib.org/lapack/double/dggbal.f dggbal.f], [@http://www.netlib.org/lapack/complex/cggbal.f cggbal.f], and [@http://www.netlib.org/lapack/complex16/zggbal.f zggbal.f] at Netlib.

[endsect]
