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

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


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

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

or

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

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

*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename BETA, typename MC>       |
|      typename RestrictTo<IsGeMatrix<MA>::value                            |
|                       && IsHeMatrix<MC>::value,                           |
|               void>::Type                                                 |
|      rk(Transpose        trans,                                           |
|         const ALPHA      &alpha,                                          |
|         const MA         &A,                                              |
|         const BETA       &beta,                                           |
|         MC               &&C);                                            |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>4#T#T#T#Trk#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&1t0.2#&t0.3#templatetypenam]
                         [eALPHA,typenameMA,typenameBETA,typenameMCtypenameR]
                         [estrictToIsGeMatrixMAvalueandIsHeMatrixMCvalue,voi]
                         [dType                                             ]

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


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

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

or

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

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

*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename BETA, typename MC>       |
|      typename RestrictTo<IsGeMatrix<MA>::value                            |
|                       && IsSyMatrix<MC>::value,                           |
|               void>::Type                                                 |
|      rk(Transpose        trans,                                           |
|         const ALPHA      &alpha,                                          |
|         const MA         &A,                                              |
|         const BETA       &beta,                                           |
|         MC               &&C);                                            |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>4#T#T#T#Trk#$@N@cxxblas@E@Tr]
                         [anspose#&1t0.0#&1t0.1#&1t0.2#&t0.3#templatetypenam]
                         [eALPHA,typenameMA,typenameBETA,typenameMCtypenameR]
                         [estrictToIsGeMatrixMAvalueandIsSyMatrixMCvalue,voi]
                         [dType                                             ]

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