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BLAS Level 3: mm

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

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

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

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);

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

\[ B \leftarrow \alpha\,\text{op}(A)\,B \]

or

\[ B \leftarrow \alpha\,B\,\text{op}(A) \]

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

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);

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

\[ C \leftarrow \beta C + \alpha\,A\,B \]

or

\[ C \leftarrow \beta C + \alpha\,B\,A, \]

i.e. the symmetric matrix \(A\) can be multiplies from left or right.

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);

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

\[ C \leftarrow \beta C + \alpha\,A\,B \]

or

\[ C \leftarrow \beta C + \alpha\,B\,A, \]

i.e. the hermitian matrix \(A\) can be multiplies from left or right.

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);

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 \(\beta\,C + \alpha\,B\,A\).
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