Content

General Matrix
Triangular Matrix
Symmetric Matrix
Hermitian Matrix

BLAS Level 2: mv

mv (defined in namespace flens::blas) computes matrix vector products.

Depending on the involved matrix type specialized variants are defined.

General Matrix

For a general matrix \(A\) and dense vectors \(x\), \(y\) the function computes matrix-vector products of the form \(y \leftarrow \beta y + \alpha \, \text{op}(A) \, x\) where \(\text{op}(X)\) denotes \(X\), \(X^T\) or \(X^H\).

GeMatrix

template <typename ALPHA, typename MA, typename VX, typename BETA, typename VY>
    typename RestrictTo<IsGeMatrix<MA>::value
                     && IsDenseVector<VX>::value
                     && IsDenseVector<VY>::value,
             void>::Type
    mv(Transpose trans, const ALPHA &alpha, const MA &A, const VX &x,
       const BETA &beta, VY &&y);

trans

(input)
Specifiy the operation, i.e.

NoTrans	\(y \leftarrow \beta y + \alpha A x\)
Trans	\(y \leftarrow \beta y + \alpha A^T x\)
ConjTrans	\(y \leftarrow \beta y + \alpha A^H x\)

alpha

(input) real or complex scalar value
Scaling factor \(\alpha\).

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

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

beta

(input)
Scaling factor \(\beta\). If \(\beta\) is zero and \(y\) has length zero then \(y\) gets resized.

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

GeCCSMatrix

template <typename ALPHA, typename MA, typename VX, typename BETA, typename VY>
    typename RestrictTo<IsGeCCSMatrix<MA>::value
                     && IsDenseVector<VX>::value
                     && IsDenseVector<VY>::value,
             void>::Type
    mv(Transpose trans, const ALPHA &alpha, const MA &A, const VX &x,
       const BETA &beta, VY &&y);

trans

(input)
Specifiy the operation, i.e.

NoTrans	\(y \leftarrow \beta y + \alpha A x\)
Trans	\(y \leftarrow \beta y + \alpha A^T x\)
ConjTrans	\(y \leftarrow \beta y + \alpha A^H x\)

alpha

(input) real or complex scalar value
Scaling factor \(\alpha\).

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

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

beta

(input)
Scaling factor \(\beta\). If \(\beta\) is zero and \(y\) has length zero then \(y\) gets resized.

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

GeCRSMatrix

template <typename ALPHA, typename MA, typename VX, typename BETA, typename VY>
    typename RestrictTo<IsGeCRSMatrix<MA>::value
                     && IsDenseVector<VX>::value
                     && IsDenseVector<VY>::value,
             void>::Type
    mv(Transpose trans, const ALPHA &alpha, const MA &A, const VX &x,
       const BETA &beta, VY &&y);

trans

(input)
Specifiy the operation, i.e.

NoTrans	\(y \leftarrow \beta y + \alpha A x\)
Trans	\(y \leftarrow \beta y + \alpha A^T x\)
ConjTrans	\(y \leftarrow \beta y + \alpha A^H x\)

alpha

(input) real or complex scalar value
Scaling factor \(\alpha\).

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

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

beta

(input)
Scaling factor \(\beta\). If \(\beta\) is zero and \(y\) has length zero then \(y\) gets resized.

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

Triangular Matrix

For a triangular matrix \(A\) and a dense vectors \(x\) the function computes matrix-vector products of the form \(x \leftarrow \text{op}(A) \, x\) where \(\text{op}(X)\) denotes \(X\), \(X^T\) or \(X^H\).

template <typename MA, typename VX>
    typename RestrictTo<IsTrMatrix<MA>::value
                     && IsDenseVector<VX>::value,
             void>::Type
    mv(Transpose trans, const MA &A, VX &&x);

trans

(input)
Specifiy the operation, i.e.

NoTrans	\(x \leftarrow A x\)
Trans	\(x \leftarrow A^T x\)
ConjTrans	\(x \leftarrow A^H x\)

(input) real or complex valued TrMatrix
Triangular Matrix \(A\).

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

Symmetric Matrix

For a symmetric matrix \(A\) and dense vectors \(x, y\) the function computes matrix-vector products of the form \(y \leftarrow \beta y + \alpha \, A \, x\).

SyMatrix

template <typename ALPHA, typename MA, typename VX, typename BETA, typename VY>
    typename RestrictTo<IsSyMatrix<MA>::value
                     && IsDenseVector<VX>::value
                     && IsDenseVector<VY>::value,
             void>::Type
    mv(const ALPHA &alpha, const MA &A, const VX &x,
       const BETA &beta, VY &&y);

alpha	`(input) real or complex scalar value` Scaling factor \(\alpha\).
A	`(input) real or complex valued SyMatrix` Symmetric matrix \(A\).
x	`(input) real or complex valued DenseVector` Vector \(x\).
beta	`(input)` Scaling factor \(\beta\). If \(\beta\) is zero and \(y\) has length zero then \(y\) gets resized.
y	`(input/output) real or complex valued DenseVector` Vector \(y\).

SyCCSMatrix

template <typename ALPHA, typename MA, typename VX, typename BETA, typename VY>
    typename RestrictTo<IsSyCCSMatrix<MA>::value
                     && IsDenseVector<VX>::value
                     && IsDenseVector<VY>::value,
             void>::Type
    mv(const ALPHA &alpha, const MA &A, const VX &x, const BETA &beta, VY &&y);

alpha	`(input) real or complex scalar value` Scaling factor \(\alpha\).
A	`(input) real or complex valued SyCCSMatrix` Symmetric matrix \(A\).
x	`(input) real or complex valued DenseVector` Vector \(x\).
beta	`(input)` Scaling factor \(\beta\). If \(\beta\) is zero and \(y\) has length zero then \(y\) gets resized.
y	`(input/output) real or complex valued DenseVector` Vector \(y\).

SyCRSMatrix

template <typename ALPHA, typename MA, typename VX, typename BETA, typename VY>
    typename RestrictTo<IsSyCRSMatrix<MA>::value
                     && IsDenseVector<VX>::value
                     && IsDenseVector<VY>::value,
             void>::Type
    mv(const ALPHA &alpha, const MA &A, const VX &x, const BETA &beta, VY &&y);

alpha	`(input) real or complex scalar value` Scaling factor \(\alpha\).
A	`(input) real or complex valued SyCRSMatrix` Symmetric matrix \(A\).
x	`(input) real or complex valued DenseVector` Vector \(x\).
beta	`(input)` Scaling factor \(\beta\). If \(\beta\) is zero and \(y\) has length zero then \(y\) gets resized.
y	`(input/output) real or complex valued DenseVector` Vector \(y\).

Hermitian Matrix

For a hermitian matrix \(A\) and dense vectors \(x, y\) the function computes matrix-vector products of the form \(y \leftarrow \beta y + \alpha \, A \, x\).

HeMatrix

template <typename ALPHA, typename MA, typename VX, typename BETA, typename VY>
    typename RestrictTo<IsHeMatrix<MA>::value
                     && IsDenseVector<VX>::value
                     && IsDenseVector<VY>::value,
             void>::Type
    mv(const ALPHA &alpha, const MA &A, const VX &x,
       const BETA &beta, VY &&y);

alpha	`(input) real or complex scalar value` Scaling factor \(\alpha\).
A	`(input) real or complex valued HeMatrix` Hermitian matrix \(A\).
x	`(input) real or complex valued DenseVector` Vector \(x\).
beta	`(input)` Scaling factor \(\beta\). If \(\beta\) is zero and \(y\) has length zero then \(y\) gets resized.
y	`(input/output) real or complex valued DenseVector` Vector \(y\).

HeCCSMatrix

template <typename ALPHA, typename MA, typename VX, typename BETA, typename VY>
    typename RestrictTo<IsHeCCSMatrix<MA>::value
                     && IsDenseVector<VX>::value
                     && IsDenseVector<VY>::value,
             void>::Type
    mv(const ALPHA &alpha, const MA &A, const VX &x, const BETA &beta, VY &&y);

alpha	`(input) real or complex scalar value` Scaling factor \(\alpha\).
A	`(input) real or complex valued HeCCSMatrix` Hermitian matrix \(A\).
x	`(input) real or complex valued DenseVector` Vector \(x\).
beta	`(input)` Scaling factor \(\beta\). If \(\beta\) is zero and \(y\) has length zero then \(y\) gets resized.
y	`(input/output) real or complex valued DenseVector` Vector \(y\).