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BLAS Level 1: axpy

axpy (defined in namespace flens::blas) computes \(y \leftarrow y +\alpha x\) where \(x, y\) are vectors and \(\alpha\) is a constant scalar. axpy is short for alpha times x plus y.

We also provide a variant that does the computation for matrices instead of vectors.

Vector Variant

template <typename ALPHA, typename VX, typename VY>
    typename RestrictTo<IsDenseVector<VX>::value
                     && IsDenseVector<VY>::value,
             void>::Type
    axpy(const ALPHA &alpha, const VX &x, VY &&y);

alpha

(input) real scalar
Scaling factor for the values in \(x\).

x

(input) real or complex valued DenseVector
Vector \(x\).

y

(input/output) real or complex valued DenseVector
Vector \(y\).

Matrix Variant (Level 1 Extension)

template <typename ALPHA, typename MA, typename MB>
    typename RestrictTo<IsGeMatrix<MA>::value
                     && IsGeMatrix<MB>::value,
             void>::Type
    axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);

trans

(input)
Specifiy the operation, i.e.

NoTrans

\(B \leftarrow B + \alpha\, A\)

Trans

\(B \leftarrow B + \alpha\, A^T\)

ConjTrans

\(B \leftarrow B + \alpha\, A^H\)

alpha

(input) real scalar
Scaling factor for the values in \(x\).

A

(input) real or complex valued GeMatrix
Matrix \(A\).

B

(input/output) real or complex valued GeMatrix
Matrix \(B\).
template <typename ALPHA, typename VX, typename VY>
    typename RestrictTo<IsTinyVector<VX>::value
                     && IsTinyVector<VY>::value,
             void>::Type
    axpy(const ALPHA &alpha, const VX &x, VY &&y);

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

template <typename ALPHA, typename MA, typename MB>
    typename RestrictTo<IsGbMatrix<MA>::value
                     && IsGbMatrix<MB>::value,
             void>::Type
    axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);

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

template <typename ALPHA, typename MA, typename MB>
    typename RestrictTo<IsGeTinyMatrix<MA>::value
                     && IsGeTinyMatrix<MB>::value,
             void>::Type
    axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);

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

template <typename ALPHA, typename MA, typename MB>
    typename RestrictTo<IsHbMatrix<MA>::value
                     && IsHbMatrix<MB>::value,
             void>::Type
    axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);

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

template <typename ALPHA, typename MA, typename MB>
    typename RestrictTo<IsHpMatrix<MA>::value
                     && IsHpMatrix<MB>::value,
             void>::Type
    axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);

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

template <typename ALPHA, typename MA, typename MB>
    typename RestrictTo<IsSbMatrix<MA>::value
                     && IsSbMatrix<MB>::value,
             void>::Type
    axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);

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

template <typename ALPHA, typename MA, typename MB>
    typename RestrictTo<IsSpMatrix<MA>::value
                     && IsSpMatrix<MB>::value,
             void>::Type
    axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);

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

template <typename ALPHA, typename MA, typename MB>
    typename RestrictTo<IsTbMatrix<MA>::value
                     && IsTbMatrix<MB>::value,
             void>::Type
    axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);

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

template <typename ALPHA, typename MA, typename MB>
    typename RestrictTo<IsTpMatrix<MA>::value
                     && IsTpMatrix<MB>::value,
             void>::Type
    axpy(Transpose trans, const ALPHA &alpha, const MA &A, MB &&B);

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

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