=================
BLAS Level 3: r2k                                                      [TOC]
=================

*r2k* (defined in namespace `flens::blas`) computes hermitian or symmetric
rank $2k$ operations.


Hermitian Rank $2k$ Operations
==============================
For a hermitian matrix $C$ and general matrices $A$ and $B$ the function
computes rank $2k$ operations

  *--[LATEX]------------------------------------------------------*
  |                                                               |
  |  C \leftarrow \beta\,C + \alpha\,A\,B^H + \alpha\,B\,A^H      |
  |                                                               |
  *---------------------------------------------------------------*

or

  *--[LATEX]------------------------------------------------------*
  |                                                               |
  |  C \leftarrow \beta\,C + \alpha\,A^H\,B + \alpha\,B^H\,A.     |
  |                                                               |
  *---------------------------------------------------------------*

$C$ is an $n \times n$ hermitian matrix and  $A$ and $B$ are $n \times k$
matrices in the first case and $k \times n$ matrices in the second case.


*--[CODEREF]------------------------------------------------------------------------*
|                                                                                   |
|  template <typename ALPHA, typename MA, typename MB, typename BETA, typename MC>  |
|      typename RestrictTo<IsGeMatrix<MA>::value                                    |
|                       && IsGeMatrix<MB>::value                                    |
|                       && IsHeMatrix<MC>::value,                                   |
|               void>::Type                                                         |
|      r2k(Transpose       trans,                                                   |
|          const ALPHA     &alpha,                                                  |
|          const MA        &A,                                                      |
|          const MB        &B,                                                      |
|          const BETA      &beta,                                                   |
|          MC              &&C);                                                    |
|                                                                                   |
*-----------------------------------------------------------------------------------*
                            [c:@N@flens@N@blas@FT@>5#T#T#T#T#Tr2k#$@N@cxxblas@E@Tran]
                            [spose#&1t0.0#&1t0.1#&1t0.2#&1t0.3#&t0.4#templatetypenam]
                            [eALPHA,typenameMA,typenameMB,typenameBETA,typenameMCtyp]
                            [enameRestrictToIsGeMatrixMAvalueandIsGeMatrixMBvalueand]
                            [IsHeMatrixMCvalue,voidType                             ]

    trans     `(input)`                                                        +
              Specifies the operation to be performed as follows
              NoTrans    $C \leftarrow \beta\,C + \alpha\,A\,B^H
                         + \alpha\,B\,A^H$
              Trans      $C \leftarrow \beta\,C + \alpha\,A^H\,B
                         + \alpha\,B^H\,A$
    A         `(input) real or complex valued GeMatrix`                        +
              Matrix $A$.
    B         `(input) real or complex valued GeMatrix`                        +
              Matrix $B$.
    beta      `(input)`                                                        +
              Scaling factor $\beta$. If $\beta$ is zero and $C$ has zero rows
              or columns then $C$ gets resized.
    C         `(input/output) complex valued HeMatrix`                         +
              On entry the original matrix $C$.                                +
              On exit overwritten with
              $\beta\,C + \alpha\,A\,B^H + \alpha\,B\,A^H$ or
              $\beta\,C + \alpha\,A^H\,B + \alpha\,B^H\,A$.


Symmetric Rank $2k$ Operations
==============================
For a symmetric matrix $C$ and general matrices $A$ and $B$ the function
computes rank $2k$ operations

  *--[LATEX]------------------------------------------------------*
  |                                                               |
  |  C \leftarrow \beta\,C + \alpha\,A\,B^T + \alpha\,B\,A^T      |
  |                                                               |
  *---------------------------------------------------------------*

or

  *--[LATEX]------------------------------------------------------*
  |                                                               |
  |  C \leftarrow \beta\,C + \alpha\,A^T\,B + \alpha\,B^T\,A.     |
  |                                                               |
  *---------------------------------------------------------------*

$C$ is an $n \times n$ symmetric matrix and  $A$ and $B$ are $n \times k$
matrices in the first case and $k \times n$ matrices in the second case.

*--[CODEREF]------------------------------------------------------------------------*
|                                                                                   |
|  template <typename ALPHA, typename MA, typename MB, typename BETA, typename MC>  |
|      typename RestrictTo<IsGeMatrix<MA>::value                                    |
|                       && IsGeMatrix<MB>::value                                    |
|                       && IsSyMatrix<MC>::value,                                   |
|               void>::Type                                                         |
|      r2k(Transpose       trans,                                                   |
|          const ALPHA     &alpha,                                                  |
|          const MA        &A,                                                      |
|          const MB        &B,                                                      |
|          const BETA      &beta,                                                   |
|          MC              &&C);                                                    |
|                                                                                   |
*-----------------------------------------------------------------------------------*
                            [c:@N@flens@N@blas@FT@>5#T#T#T#T#Tr2k#$@N@cxxblas@E@Tran]
                            [spose#&1t0.0#&1t0.1#&1t0.2#&1t0.3#&t0.4#templatetypenam]
                            [eALPHA,typenameMA,typenameMB,typenameBETA,typenameMCtyp]
                            [enameRestrictToIsGeMatrixMAvalueandIsGeMatrixMBvalueand]
                            [IsSyMatrixMCvalue,voidType                             ]

    trans     `(input)`                                                        +
              Specifies the operation to be performed as follows
              NoTrans    $C \leftarrow \beta\,C + \alpha\,A\,B^T
                         + \alpha\,B\,A^T$
              Trans      $C \leftarrow \beta\,C + \alpha\,A^T\,B
                         + \alpha\,B^T\,A$
    A         `(input) real or complex valued GeMatrix`                        +
              Matrix $A$.
    B         `(input) real or complex valued GeMatrix`                        +
              Matrix $B$.
    beta      `(input)`                                                        +
              Scaling factor $\beta$. If $\beta$ is zero and $C$ has zero rows
              or columns then $C$ gets resized.
    C         `(input/output) real or complex valued SyMatrix`                 +
              On entry the original matrix $C$.                                +
              On exit overwritten with
              $\beta\,C + \alpha\,A\,B^T + \alpha\,B\,A^T$ or
              $\beta\,C + \alpha\,A^T\,B + \alpha\,B^T\,A$.