BLAS Level 3: rk

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

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

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

\(C\) 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.

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);

trans

(input)
Specifies the operation to be performed as follows

NoTrans	\(C \leftarrow \beta\,C + \alpha\,A\,A^H\)
Trans	\(C \leftarrow \beta\,C + \alpha\,A^H\,A\)

(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.

(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

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

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

\(C\) 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.

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);

trans

(input)
Specifies the operation to be performed as follows

NoTrans	\(C \leftarrow \beta\,C + \alpha\,A\,A^T\)
Trans	\(C \leftarrow \beta\,C + \alpha\,A^T\,A\)

(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.

(input/output) real or complex valued SyMatrix
On entry the original matrix \(C\).
On exit overwritten with \(\beta\,C + \alpha\,A\,A^T\) or \(\beta\,C + \alpha\,A^T\,A\).