##### syr2k

###### Prototype

There are two prototypes of `syr2k` available, please see below.

    syr2k( const Scalar >, const MatrixA& a, const MatrixB& b,
            const Scalar >, MatrixC& c );

    syr2k( const Scalar alpha, const MatrixA& a, const MatrixB& b,
            const Scalar beta, MatrixC& c );

###### Description

`syr2k` (short for symmetric rank-2k update) provides a C++ interface to BLAS routines SSYR2K, DSYR2K, CSYR2K, and ZSYR2K. `syr2k` performs one of the symmetric rank 2k operations

C := alpha*A*B' + alpha*B*A' + beta*C,

or

C := alpha*A'*B + alpha*B'*A + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

The selection of the BLAS 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`. Table X below illustrates to which specific routine this dispatching will take place.

Table 1.92. Dispatching of syr2k.

Value type of MatrixA | BLAS routine | CBLAS routine | CUBLAS routine
--- | --- | --- | ---
`float` | SSYR2K | cblas_ssyr2k | cublasSsyr2k
`double` | DSYR2K | cblas_dsyr2k | cublasDsyr2k
`complex<float>` | CSYR2K | cblas_csyr2k | cublasCsyr2k
`complex<double>` | ZSYR2K | cblas_zsyr2k | Unavailable

The original routines SSYR2K, DSYR2K, CSYR2K, and ZSYR2K have twelve arguments, whereas `syr2k` requires five arguments.

Table 1.93. Deduction of arguments of syr2k.

###### Definition

Defined in header `boost/numeric/bindings/blas/level3/syr2k.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/blas/level3/syr2k.hpp>
    using namespace boost::numeric::bindings;

    blas::syr2k( x, y, z );

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files ssyr2k.f, dsyr2k.f, csyr2k.f, and zsyr2k.f at Netlib.