##### hbgvd

###### Prototype

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

    hbgvd( const char jobz, MatrixAB& ab, MatrixBB& bb, VectorW& w,
            MatrixZ& z );

###### Description

`hbgvd` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SSBGVD, DSBGVD, CHBGVD, and ZHBGVD. `hbgvd` computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

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 1.107. Dispatching of hbgvd

Value type of MatrixAB | LAPACK routine
--- | ---
`float` | SSBGVD
`double` | DSBGVD
`complex<float>` | CHBGVD
`complex<double>` | ZHBGVD

###### Definition

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

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files ssbgvd.f, dsbgvd.f, chbgvd.f, and zhbgvd.f at Netlib.