##### gbsv

###### Prototype

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

    gbsv( MatrixAB& ab, VectorIPIV& ipiv, MatrixB& b );

###### Description

`gbsv` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGBSV, DGBSV, CGBSV, and ZGBSV. `gbsv` computes the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U, where L is a product of permutation and unit lower triangular matrices with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals. The factored form of A is then used to solve the system of equations A * X = B.

The selection of the LAPACK routine is done during compile-time, and is determined by the type of values contained in type `MatrixAB`. The type of values is obtained through the `value_type` meta-function `typename value_type<MatrixAB>::type`. The dispatching table below illustrates to which specific routine the code path will be generated.

Table 1.126. Dispatching of gbsv

Value type of MatrixAB | LAPACK routine
--- | ---
`float` | SGBSV
`double` | DGBSV
`complex<float>` | CGBSV
`complex<double>` | ZGBSV

###### Definition

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

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files sgbsv.f, dgbsv.f, cgbsv.f, and zgbsv.f at Netlib.