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BLAS Level 3: r2k

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

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

or

\[ C \leftarrow \beta\,C + \alpha\,A^H\,B + \alpha\,B^H\,A. \]

\(C\) 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.

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);

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

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

or

\[ C \leftarrow \beta\,C + \alpha\,A^T\,B + \alpha\,B^T\,A. \]

\(C\) 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.

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);

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