cppdraft_translate/cppdraft/linalg/algs/blas3/rank2k.md

[linalg.algs.blas3.rank2k]

29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.15 BLAS 3 algorithms [linalg.algs.blas3]

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

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[Note 1:

These functions correspond to the BLAS functionsxSYR2K and xHER2K[bib].

— end note]

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

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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.

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Preconditions:

• (4.1)

addable(A, B, C) is true, and

• (4.2)

A.extent(0) equals A.extent(1).

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Complexity: O(A.extent(0)×A.extent(1)×C.extent(0)).

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template<[in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat1, [in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat2, [possibly-packed-inout-matrix](linalg.helpers.concepts#concept:possibly-packed-inout-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InOutMat, class Triangle> void symmetric_matrix_rank_2k_update(InMat1 A, InMat2 B, InOutMat C, Triangle t); template<class ExecutionPolicy, [in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat1, [in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat2, [possibly-packed-inout-matrix](linalg.helpers.concepts#concept:possibly-packed-inout-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InOutMat, class Triangle> void symmetric_matrix_rank_2k_update(ExecutionPolicy&& exec, InMat1 A, InMat2 B, InOutMat C, Triangle t);

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Effects: Computes a matrix C′ such that C′=C+ABT+BAT, and assigns each element of C′ to the corresponding element of C.

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template<[in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat1, [in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat2, [possibly-packed-inout-matrix](linalg.helpers.concepts#concept:possibly-packed-inout-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InOutMat, class Triangle> void hermitian_matrix_rank_2k_update(InMat1 A, InMat2 B, InOutMat C, Triangle t); template<class ExecutionPolicy, [in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat1, [in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat2, [possibly-packed-inout-matrix](linalg.helpers.concepts#concept:possibly-packed-inout-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InOutMat, class Triangle> void hermitian_matrix_rank_2k_update(ExecutionPolicy&& exec, InMat1 A, InMat2 B, InOutMat C, Triangle t);

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Effects: Computes a matrix C′ such that C′=C+ABH+BAH, and assigns each element of C′ to the corresponding element of C.