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[section hpr2]

[heading Prototype]
There are two prototypes of `hpr2` available, please see below.
``
hpr2( const Scalar >, const VectorX& x, const VectorY& y, MatrixAP& ap );
``

``
hpr2( const Scalar alpha, const VectorX& x, const VectorY& y,
        MatrixAP& ap );
``


[heading Description]

`hpr2` (short for hermitian, packed,  rank-2 update) provides a C++
interface to BLAS routines SSPR2, DSPR2, CHPR2, and ZHPR2. 
`hpr2` performs the hermitian rank 2 operation

A := alpha*x*y**H + conjg( alpha )*y*x**H + A,

where alpha is a scalar, x and y are n element vectors and A is an
n by n hermitian matrix, supplied in packed form.

The selection of the BLAS routine is done during compile-time, 
and is determined by the type of values contained in type `VectorX`.
The type of values is obtained through the `value_type` meta-function
 `typename value_type<VectorX>::type`.
Table X below illustrates to which specific routine this dispatching will take place. 

[table Dispatching of hpr2.
[  [ Value type of VectorX ] [BLAS routine] [CBLAS routine] [CUBLAS routine] ]
[  [`float`][SSPR2][cblas_sspr2][cublasSspr2] ]
[  [`double`][DSPR2][cblas_dspr2][cublasDspr2] ]
[  [`complex<float>`][CHPR2][cblas_chpr2][cublasChpr2] ]
[  [`complex<double>`][ZHPR2][cblas_zhpr2][cublasZhpr2] ]

]

The original routines SSPR2, DSPR2, CHPR2, and ZHPR2 have eight arguments,
whereas `hpr2` requires four arguments.

[table Deduction of arguments of hpr2.
]

[heading Definition]
Defined in header [headerref boost/numeric/bindings/blas/level2/hpr2.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/blas/level2/hpr2.hpp>
using namespace boost::numeric::bindings;

blas::hpr2( 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/blas/sspr2.f sspr2.f], [@http://www.netlib.org/blas/dspr2.f dspr2.f], [@http://www.netlib.org/blas/chpr2.f chpr2.f], and [@http://www.netlib.org/blas/zhpr2.f zhpr2.f] at Netlib.

[endsect]
