28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.15 BLAS 3 algorithms [linalg.algs.blas3]

28.9.15.5 Rank-2k update of a symmetric or Hermitian matrix [linalg.algs.blas3.rank2k]

[Note 1:

These functions correspond to the BLAS functions xSYR2K and xHER2K[bib].

— end note]

The following elements apply to all functions in [linalg.algs.blas3.rank2k].

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)
possibly-addable<decltype(A), decltype(B), decltype(C)>() is true; and
(3.3)
compatible-static-extents<decltype(A), decltype(A)>(0, 1) is true.

Preconditions:

(4.1)
addable(A, B, C) is true, and
(4.2)
A.extent(0) equals A.extent(1).

Complexity:

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

🔗

template<in-matrix InMat1, in-matrix InMat2,
         possibly-packed-inout-matrix InOutMat, class Triangle>
  void symmetric_matrix_rank_2k_update(InMat1 A, InMat2 B, InOutMat C, Triangle t);
template<class ExecutionPolicy, in-matrix InMat1, in-matrix InMat2,
         possibly-packed-inout-matrix InOutMat, class Triangle>
  void symmetric_matrix_rank_2k_update(ExecutionPolicy&& exec,
                                       InMat1 A, InMat2 B, InOutMat C, Triangle t);

Effects: Computes a matrix

C^{'}

such that

C^{'} = C + A B^{T} + B A^{T}

, and assigns each element of

C^{'}

to the corresponding element of C.

🔗

template<in-matrix InMat1, in-matrix InMat2,
         possibly-packed-inout-matrix InOutMat, class Triangle>
  void hermitian_matrix_rank_2k_update(InMat1 A, InMat2 B, InOutMat C, Triangle t);
template<class ExecutionPolicy,
         in-matrix InMat1, in-matrix InMat2,
         possibly-packed-inout-matrix InOutMat, class Triangle>
  void hermitian_matrix_rank_2k_update(ExecutionPolicy&& exec,
                                       InMat1 A, InMat2 B, InOutMat C, Triangle t);

Effects: Computes a matrix

C^{'}

such that

C^{'} = C + A B^{H} + B A^{H}

, and assigns each element of

C^{'}

to the corresponding element of C.