29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.15 BLAS 3 algorithms [linalg.algs.blas3]

29.9.15.4 Rank-k update of a symmetric or Hermitian matrix [linalg.algs.blas3.rankk]

[Note 1:

These functions correspond to the BLAS functions xSYRK and xHERK[bib].

— end note]

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

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;
(3.3)
compatible-static-extents<decltype(C), decltype(C)>(0, 1) is true; and
(3.4)
compatible-static-extents<decltype(A), decltype(C)>(0, 0) is true.

Preconditions:

(4.1)
A.extent(0) equals A.extent(1),
(4.2)
C.extent(0) equals C.extent(1), and
(4.3)
A.extent(0) equals C.extent(0).

Complexity:

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

🔗

  template<class Scalar, in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
    void symmetric_matrix_rank_k_update(Scalar alpha, InMat A, InOutMat C, Triangle t);
  template<class ExecutionPolicy, class Scalar,
           in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
    void symmetric_matrix_rank_k_update(ExecutionPolicy&& exec,
                                        Scalar alpha, InMat A, InOutMat C, Triangle t);

Effects: Computes a matrix

C^{'}

such that

C^{'} = C + α A A^{T}

, where the scalar α is alpha, and assigns each element of

C^{'}

to the corresponding element of C.

🔗

template<in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
  void symmetric_matrix_rank_k_update(InMat A, InOutMat C, Triangle t);
template<class ExecutionPolicy,
         in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
  void symmetric_matrix_rank_k_update(ExecutionPolicy&& exec,
                                      InMat A, InOutMat C, Triangle t);

Effects: Computes a matrix

C^{'}

such that

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

, and assigns each element of

C^{'}

to the corresponding element of C.

🔗

template<class Scalar, in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
  void hermitian_matrix_rank_k_update(Scalar alpha, InMat A, InOutMat C, Triangle t);
template<class ExecutionPolicy,
         class Scalar, in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
  void hermitian_matrix_rank_k_update(ExecutionPolicy&& exec,
                                      Scalar alpha, InMat A, InOutMat C, Triangle t);

Effects: Computes a matrix

C^{'}

such that

C^{'} = C + α A A^{H}

, where the scalar α is alpha, and assigns each element of

C^{'}

to the corresponding element of C.

🔗

template<in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
  void hermitian_matrix_rank_k_update(InMat A, InOutMat C, Triangle t);
template<class ExecutionPolicy,
         in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
  void hermitian_matrix_rank_k_update(ExecutionPolicy&& exec,
                                      InMat A, InOutMat C, Triangle t);

Effects: Computes a matrix

C^{'}

such that

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

, and assigns each element of

C^{'}

to the corresponding element of C.