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

*mm* (defined in namespace `flens::blas`) computes matrix-matrix products.


General Matrix
==============
For general matrices $A$, $B$ and $C$ the function computes matrix-matrix
products of the form

  *--[LATEX]------------------------------------------------------*
  |                                                               |
  |   C \leftarrow \beta C + \alpha\,\text{op}(A)\,\text{op}(B)   |
  |                                                               |
  *---------------------------------------------------------------*

where $\text{op}(X)$ denotes $X$, $X^T$ or $X^H$.

*--[CODEREF]------------------------------------------------------------------------*
|                                                                                   |
|  template <typename ALPHA, typename MA, typename MB, typename BETA, typename MC>  |
|      typename RestrictTo<IsGeMatrix<MA>::value                                    |
|                       && IsGeMatrix<MB>::value                                    |
|                       && IsGeMatrix<MC>::value,                                   |
|               void>::Type                                                         |
|      mm(Transpose        transA,                                                  |
|         Transpose        transB,                                                  |
|         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#Tmm#$@N@cxxblas@E@Trans]
                            [pose#S0_#&1t0.0#&1t0.1#&1t0.2#&1t0.3#&t0.4#templatetype]
                            [nameALPHA,typenameMA,typenameMB,typenameBETA,typenameMC]
                            [typenameRestrictToIsGeMatrixMAvalueandIsGeMatrixMBvalue]
                            [andIsGeMatrixMCvalue,voidType                          ]

    transA    `(input)`                                                        +
              Specifiy $\text{op}(A)$:
               NoTrans      $A$
               Trans        $A^T$
               ConjTrans    $A^H$
    transB    `(input)`                                                        +
              Specifiy $\text{op}(B)$:
               NoTrans      $B$
               Trans        $B^T$
               ConjTrans    $B^H$
    alpha     `(input)`                                                        +
              Scaling factor $\alpha$.
    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 GeMatrix`                 +
              On entry the original matrix $C$.                                +
              On exit overwritten with
              $\beta\,C + \alpha\,\text{op}(A)\,\text{op}(B)$.


Triangular Matrix
=================
For a triangular matrix $A$ and a general matrices $B$ the function computes
matrix-matrix products of the form

  *--[LATEX]----------------------------------------*
  |                                                 |
  |   B \leftarrow \alpha\,\text{op}(A)\,B          |
  |                                                 |
  *-------------------------------------------------*

or

  *--[LATEX]----------------------------------------*
  |                                                 |
  |   B \leftarrow \alpha\,B\,\text{op}(A)          |
  |                                                 |
  *-------------------------------------------------*

where $\text{op}(X)$ denotes $X$, $X^T$ or $X^H$.

*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsTrMatrix<MA>::value                            |
|                       && IsGeMatrix<MB>::value,                           |
|               void>::Type                                                 |
|      mm(Side             side,                                            |
|         Transpose        transA,                                          |
|         const ALPHA      &alpha,                                          |
|         const MA         &A,                                              |
|         MB               &&B);                                            |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Tmm#$@N@cxxblas@E@Side]
                         [#$@N@cxxblas@E@Transpose#&1t0.0#&1t0.1#&t0.2#templ]
                         [atetypenameALPHA,typenameMA,typenameMBtypenameRest]
                         [rictToIsTrMatrixMAvalueandIsGeMatrixMBvalue,voidTy]
                         [pe                                                ]

    side      `(input)`                                                        +
              Specify the type of matrix-matrix product:
               Left     $B \leftarrow \alpha\,\text{op}(A)\,B$
               Right    $B \leftarrow \alpha\,B\,\text{op}(A)$
    transA    `(input)`                                                        +
              Specifiy $\text{op}(A)$:
               NoTrans      $A$
               Trans        $A^T$
               ConjTrans    $A^H$
    alpha     `(input)`                                                        +
              Scaling factor $\alpha$.
    A         `(input) real or complex valued GeMatrix`                        +
              Matrix $A$.
    B         `(input/output) real or complex valued GeMatrix`                 +
              On entry the original matrix $B$.                                +
              On exit overwritten with $\alpha\,\text{op}(A)\,B$ or
              $\alpha\,B\,\text{op}(A)$.



Symmetric Matrix
================
For a symmetric matrix $A$ and general matrices $B$ and $C$ the function
computes matrix-matrix products of the form

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

or

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

i.e. the symmetric matrix $A$ can be multiplies from left or right.

*--[CODEREF]------------------------------------------------------------------------*
|                                                                                   |
|  template <typename ALPHA, typename MA, typename MB, typename BETA, typename MC>  |
|      typename RestrictTo<IsSyMatrix<MA>::value                                    |
|                       && IsGeMatrix<MB>::value                                    |
|                       && IsGeMatrix<MC>::value,                                   |
|               void>::Type                                                         |
|      mm(Side             side,                                                    |
|         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#Tmm#$@N@cxxblas@E@Side#]
                            [&1t0.0#&1t0.1#&1t0.2#&1t0.3#&t0.4#templatetypenameALPHA]
                            [,typenameMA,typenameMB,typenameBETA,typenameMCtypenameR]
                            [estrictToIsSyMatrixMAvalueandIsGeMatrixMBvalueandIsGeMa]
                            [trixMCvalue,voidType                                   ]

    side      `(input)`                                                        +
              Specify the type of matrix-matrix product:
               Left     $B \leftarrow \beta\,C + \alpha\,A\,B$
               Right    $B \leftarrow \beta\,C + \alpha\,B\,A$
    alpha     `(input)`                                                        +
              Scaling factor $\alpha$.
    A         `(input) real or complex valued SyMatrix`                         +
              Symmetric 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 GeMatrix`                 +
              On entry the original matrix $C$.                                +
              On exit overwritten with
              $\beta\,C + \alpha\,A\,B$ or $\beta\,C + \alpha\,B\,A$.


Hermitian Matrix
================
For a hermitial matrix $A$ and general matrices $B$ and $C$ the function
computes matrix-matrix products of the form

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

or

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

i.e. the hermitian matrix $A$ can be multiplies from left or right.

*--[CODEREF]------------------------------------------------------------------------*
|                                                                                   |
|  template <typename ALPHA, typename MA, typename MB, typename BETA, typename MC>  |
|      typename RestrictTo<IsHeMatrix<MA>::value                                    |
|                       && IsGeMatrix<MB>::value                                    |
|                       && IsGeMatrix<MC>::value,                                   |
|               void>::Type                                                         |
|      mm(Side             side,                                                    |
|         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#Tmm#$@N@cxxblas@E@Side#]
                            [&1t0.0#&1t0.1#&1t0.2#&1t0.3#&t0.4#templatetypenameALPHA]
                            [,typenameMA,typenameMB,typenameBETA,typenameMCtypenameR]
                            [estrictToIsHeMatrixMAvalueandIsGeMatrixMBvalueandIsGeMa]
                            [trixMCvalue,voidType                                   ]

    side      `(input)`                                                        +
              Specify the type of matrix-matrix product:
               Left     $B \leftarrow \beta\,C + \alpha\,A\,B$
               Right    $B \leftarrow \beta\,C + \alpha\,B\,A$
    alpha     `(input)`                                                        +
              Scaling factor $\alpha$.
    A         `(input) real or complex valued SyMatrix`                         +
              Symmetric 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 GeMatrix`                 +
              On entry the original matrix $C$.                                +
              On exit overwritten with
              $\beta\,C + \alpha\,A\,B$ or $\beta\,C + \alpha\,B\,A$.
################################################################################
#
#  The following CODEREFs are automatically created stubs.
#
################################################################################


*--[CODEREF]------------------------------------------------------------------------*
|                                                                                   |
|  template <typename ALPHA, typename MA, typename MB, typename BETA, typename MC>  |
|      typename RestrictTo<IsGbMatrix<MA>::value                                    |
|                       && IsGeMatrix<MB>::value                                    |
|                       && IsGeMatrix<MC>::value,                                   |
|               void>::Type                                                         |
|      mm(Transpose        transA,                                                  |
|         Transpose        transB,                                                  |
|         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#Tmm#$@N@cxxblas@E@Trans]
                            [pose#S0_#&1t0.0#&1t0.1#&1t0.2#&1t0.3#&t0.4#templatetype]
                            [nameALPHA,typenameMA,typenameMB,typenameBETA,typenameMC]
                            [typenameRestrictToIsGbMatrixMAvalueandIsGeMatrixMBvalue]
                            [andIsGeMatrixMCvalue,voidType                          ]

    Defined in namespace `flens::blas`.
    Function `mm` with 5 template parameters.



*--[CODEREF]------------------------------------------------------------------------*
|                                                                                   |
|  template <typename ALPHA, typename MA, typename MB, typename BETA, typename MC>  |
|      typename RestrictTo<IsGeMatrix<MA>::value                                    |
|                       && IsGbMatrix<MB>::value                                    |
|                       && IsGeMatrix<MC>::value,                                   |
|               void>::Type                                                         |
|      mm(Transpose        transA,                                                  |
|         Transpose        transB,                                                  |
|         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#Tmm#$@N@cxxblas@E@Trans]
                            [pose#S0_#&1t0.0#&1t0.1#&1t0.2#&1t0.3#&t0.4#templatetype]
                            [nameALPHA,typenameMA,typenameMB,typenameBETA,typenameMC]
                            [typenameRestrictToIsGeMatrixMAvalueandIsGbMatrixMBvalue]
                            [andIsGeMatrixMCvalue,voidType                          ]

    Defined in namespace `flens::blas`.
    Function `mm` with 5 template parameters.



*--[CODEREF]------------------------------------------------------------------------*
|                                                                                   |
|  template <typename ALPHA, typename MA, typename MB, typename BETA, typename MC>  |
|      typename RestrictTo<IsHbMatrix<MA>::value                                    |
|                       && IsGeMatrix<MB>::value                                    |
|                       && IsGeMatrix<MC>::value,                                   |
|               void>::Type                                                         |
|      mm(Side             side,                                                    |
|         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#Tmm#$@N@cxxblas@E@Side#]
                            [&1t0.0#&1t0.1#&1t0.2#&1t0.3#&t0.4#templatetypenameALPHA]
                            [,typenameMA,typenameMB,typenameBETA,typenameMCtypenameR]
                            [estrictToIsHbMatrixMAvalueandIsGeMatrixMBvalueandIsGeMa]
                            [trixMCvalue,voidType                                   ]

    Defined in namespace `flens::blas`.
    Function `mm` with 5 template parameters.



*--[CODEREF]------------------------------------------------------------------------*
|                                                                                   |
|  template <typename ALPHA, typename MA, typename MB, typename BETA, typename MC>  |
|      typename RestrictTo<IsSbMatrix<MA>::value                                    |
|                       && IsGeMatrix<MB>::value                                    |
|                       && IsGeMatrix<MC>::value,                                   |
|                   void>::Type                                                     |
|      mm(Side             side,                                                    |
|         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#Tmm#$@N@cxxblas@E@Side#]
                            [&1t0.0#&1t0.1#&1t0.2#&1t0.3#&t0.4#templatetypenameALPHA]
                            [,typenameMA,typenameMB,typenameBETA,typenameMCtypenameR]
                            [estrictToIsSbMatrixMAvalueandIsGeMatrixMBvalueandIsGeMa]
                            [trixMCvalue,voidType                                   ]

    Defined in namespace `flens::blas`.
    Function `mm` with 5 template parameters.



*--[CODEREF]----------------------------------------------------------------*
|                                                                           |
|  template <typename ALPHA, typename MA, typename MB>                      |
|      typename RestrictTo<IsTbMatrix<MA>::value                            |
|                       && IsGeMatrix<MB>::value,                           |
|               void>::Type                                                 |
|      mm(Side             side,                                            |
|         Transpose        transA,                                          |
|         const ALPHA      &alpha,                                          |
|         const MA         &A,                                              |
|         MB               &&B);                                            |
|                                                                           |
*---------------------------------------------------------------------------*
                         [c:@N@flens@N@blas@FT@>3#T#T#Tmm#$@N@cxxblas@E@Side]
                         [#$@N@cxxblas@E@Transpose#&1t0.0#&1t0.1#&t0.2#templ]
                         [atetypenameALPHA,typenameMA,typenameMBtypenameRest]
                         [rictToIsTbMatrixMAvalueandIsGeMatrixMBvalue,voidTy]
                         [pe                                                ]

    Defined in namespace `flens::blas`.
    Function `mm` with 3 template parameters.