##### pbtrf

###### Prototype

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

    pbtrf( MatrixAB& ab );

###### Description

`pbtrf` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SPBTRF, DPBTRF, CPBTRF, and ZPBTRF. `pbtrf` computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.

The factorization has the form A = U*H * U, if UPLO = 'U', or A = L * L*H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular.

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 1.264. Dispatching of pbtrf

Value type of MatrixAB | LAPACK routine
--- | ---
`float` | SPBTRF
`double` | DPBTRF
`complex<float>` | CPBTRF
`complex<double>` | ZPBTRF

###### Definition

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

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files spbtrf.f, dpbtrf.f, cpbtrf.f, and zpbtrf.f at Netlib.