##### gebal

###### Prototype

There is one prototype of `gebal` available, please see below.

    gebal( const char job, MatrixA& a, int_t& ilo,
            int_t& ihi, VectorSCALE& scale );

###### Description

`gebal` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGEBAL, DGEBAL, CGEBAL, and ZGEBAL. `gebal` balances a general complex matrix A. This involves, first, permuting A by a similarity transformation 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 matrix, and improve the accuracy of the computed eigenvalues and/or eigenvectors.

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 1.225. Dispatching of gebal

Value type of MatrixA | LAPACK routine
--- | ---
`float` | SGEBAL
`double` | DGEBAL
`complex<float>` | CGEBAL
`complex<double>` | ZGEBAL

###### Definition

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

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files sgebal.f, dgebal.f, cgebal.f, and zgebal.f at Netlib.