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.

acxpy (defined in namespace flens::blas) is a variant with conjugation that computes \(y \leftarrow y +\alpha \bar{x}\) where \(x, y\) are vectors and \(\alpha\) is a constant scalar. acxpy is short for alpha times conjugate 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 \(y\).

Vector Variant with Conjugation

template <typename ALPHA, typename VX, typename VY>
    typename RestrictTo<IsDenseVector<VX>::value
                     && IsDenseVector<VY>::value,
             void>::Type
    acxpy(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 \(x\).

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

(input/output) real or complex valued GeMatrix
Matrix \(B\).