28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.14 BLAS 2 algorithms [linalg.algs.blas2]

28.9.14.8 Symmetric and Hermitian rank-2 matrix updates [linalg.algs.blas2.rank2]

[Note 1:

These functions correspond to the BLAS functions xSYR2,xSPR2, xHER2 and xHPR2[bib].

— end note]

The following elements apply to all functions in [linalg.algs.blas2.rank2].

Mandates:

(3.1)
If InOutMat 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; and
(3.3)
possibly-multipliable<decltype(A), decltype(x), decltype(y)>() is true.

Preconditions:

(4.1)
A.extent(0) equals A.extent(1), and
(4.2)
multipliable(A, x, y) is true.

Complexity:

O (x.extent(0) \times y.extent(0))

🔗

template<in-vector InVec1, in-vector InVec2,
         possibly-packed-inout-matrix InOutMat, class Triangle>
  void symmetric_matrix_rank_2_update(InVec1 x, InVec2 y, InOutMat A, Triangle t);
template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2,
         possibly-packed-inout-matrix InOutMat, class Triangle>
  void symmetric_matrix_rank_2_update(ExecutionPolicy&& exec,
                                      InVec1 x, InVec2 y, InOutMat A, Triangle t);

These functions perform a symmetric rank-2 update of the symmetric matrix A, taking into account the Triangle parameter that applies to A ([linalg.general]).

Effects: Computes

A^{'}

such that

A^{'} = A + x y^{T} + y x^{T}

and assigns each element of

A^{'}

to the corresponding element of A.

🔗

template<in-vector InVec1, in-vector InVec2,
         possibly-packed-inout-matrix InOutMat, class Triangle>
  void hermitian_matrix_rank_2_update(InVec1 x, InVec2 y, InOutMat A, Triangle t);
template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2,
         possibly-packed-inout-matrix InOutMat, class Triangle>
  void hermitian_matrix_rank_2_update(ExecutionPolicy&& exec,
                                      InVec1 x, InVec2 y, InOutMat A, Triangle t);

These functions perform a Hermitian rank-2 update of the Hermitian matrix A, taking into account the Triangle parameter that applies to A ([linalg.general]).

Effects: Computes

A^{'}

such that

A^{'} = A + x y^{H} + y x^{H}

and assigns each element of

A^{'}

to the corresponding element of A.