29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.15 BLAS 3 algorithms [linalg.algs.blas3]

29.9.15.3 In-place triangular matrix-matrix product [linalg.algs.blas3.trmm]

These functions perform an in-place matrix-matrix multiply, taking into account the Triangle and DiagonalStorage parameters that apply to the triangular matrix A ([linalg.general]).

[Note 1:

These functions correspond to the BLAS function xTRMM[bib].

— end note]

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template<in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
  void triangular_matrix_left_product(InMat A, Triangle t, DiagonalStorage d, InOutMat C);
template<class ExecutionPolicy,
         in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
  void triangular_matrix_left_product(ExecutionPolicy&& exec,
                                      InMat A, Triangle t, DiagonalStorage d, InOutMat C);

Mandates:

(2.1)
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;
(2.2)
possibly-multipliable<InMat, InOutMat, InOutMat>() is true; and
(2.3)
compatible-static-extents<InMat, InMat>(0, 1) is true.

Preconditions:

(3.1)
multipliable(A, C, C) is true, and
(3.2)
A.extent(0) == A.extent(1) is true.

Effects: Computes a matrix

C^{'}

such that

C^{'} = A C

and assigns each element of

C^{'}

to the corresponding element of C.

Complexity:

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

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template<in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
  void triangular_matrix_right_product(InMat A, Triangle t, DiagonalStorage d, InOutMat C);
template<class ExecutionPolicy,
         in-matrix InMat, class Triangle, class DiagonalStorage, inout-matrix InOutMat>
  void triangular_matrix_right_product(ExecutionPolicy&& exec,
                                       InMat A, Triangle t, DiagonalStorage d, InOutMat C);