28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.14 BLAS 2 algorithms [linalg.algs.blas2]

28.9.14.2 Symmetric matrix-vector product [linalg.algs.blas2.symv]

[Note 1:

These functions correspond to the BLAS functions xSYMV and xSPMV[bib].

— end note]

The following elements apply to all functions in [linalg.algs.blas2.symv].

Mandates:

(3.1)
If InMat has layout_blas_packed layout, then the layout's Triangle template argument has the same type as the function's Triangle template argument;
(3.2)
compatible-static-extents<decltype(A), decltype(A)>(0, 1) is true;
(3.3)
possibly-multipliable<decltype(A), decltype(x), decltype(y)>() is true; and
(3.4)
possibly-addable<decltype(x), decltype(y), decltype(z)>() is true for those overloads that take a z parameter.

Preconditions:

(4.1)
A.extent(0) equals A.extent(1),
(4.2)
multipliable(A,x,y) is true, and
(4.3)
addable(x,y,z) is true for those overloads that take a z parameter.

Complexity:

O (x.extent(0) \times A.extent(1))

🔗

template<in-matrix InMat, class Triangle, in-vector InVec, out-vector OutVec>
  void symmetric_matrix_vector_product(InMat A, Triangle t, InVec x, OutVec y);
template<class ExecutionPolicy,
         in-matrix InMat, class Triangle, in-vector InVec, out-vector OutVec>
  void symmetric_matrix_vector_product(ExecutionPolicy&& exec,
                                       InMat A, Triangle t, InVec x, OutVec y);

These functions perform an overwriting symmetric matrix-vector product, taking into account the Triangle parameter that applies to the symmetric matrix A ([linalg.general]).

Effects: Computes

y = A x

🔗

template<in-matrix InMat, class Triangle, in-vector InVec1, in-vector InVec2, out-vector OutVec>
  void symmetric_matrix_vector_product(InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z);
template<class ExecutionPolicy,
         in-matrix InMat, class Triangle, in-vector InVec1, in-vector InVec2, out-vector OutVec>
  void symmetric_matrix_vector_product(ExecutionPolicy&& exec,
                                       InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z);

These functions perform an updating symmetric matrix-vector product, taking into account the Triangle parameter that applies to the symmetric matrix A ([linalg.general]).

Effects: Computes

z = y + A x

Remarks: z may alias y.