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:
  • 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;
  • compatible-static-extents<decltype(A), decltype(A)>(0, 1) is true;
  • compatible-static-extents<decltype(C), decltype(C)>(0, 1) is true; and
  • compatible-static-extents<decltype(A), decltype(C)>(0, 0) is true.
Preconditions:
  • A.extent(0) equals A.extent(1),
  • C.extent(0) equals C.extent(1), and
  • A.extent(0) equals C.extent(0).
Complexity: .
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 such that , where the scalar α is alpha, and assigns each element of 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 such that , and assigns each element of 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 such that , where the scalar α is alpha, and assigns each element of 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 such that , and assigns each element of to the corresponding element of C.