cppdraft_translate/cppdraft/linalg/algs/blas2/rank2.md

[linalg.algs.blas2.rank2]

29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.14 BLAS 2 algorithms [linalg.algs.blas2]

29.9.14.8 Symmetric and Hermitian rank-2 matrix updates [linalg.algs.blas2.rank2]

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[Note 1:

These functions correspond to the BLAS functionsxSYR2,xSPR2, xHER2 and xHPR2[bib].

— end note]

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The following elements apply to all functions in [linalg.algs.blas2.rank2].

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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)

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

• (3.3)

possibly-multipliable<decltype(A), decltype(x), decltype(y)>() is true.

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Preconditions:

• (4.1)

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

• (4.2)

multipliable(A, x, y) is true.

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Complexity: O(x.extent(0)×y.extent(0)).

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template<[in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec1, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec2, [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_2_update(InVec1 x, InVec2 y, InOutMat A, Triangle t); template<class ExecutionPolicy, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec1, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec2, [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_2_update(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InOutMat A, Triangle t);

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These functions perform a symmetric rank-2 update of the symmetric matrix A, taking into account the Triangle parameter that applies to A ([linalg.general]).

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Effects: Computes A′ such that A′=A+xyT+yxT and assigns each element of A′ to the corresponding element of A.

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template<[in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec1, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec2, [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_2_update(InVec1 x, InVec2 y, InOutMat A, Triangle t); template<class ExecutionPolicy, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec1, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec2, [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_2_update(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InOutMat A, Triangle t);

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These functions perform a Hermitian rank-2 update of the Hermitian matrix A, taking into account the Triangle parameter that applies to A ([linalg.general]).

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Effects: Computes A′ such that A′=A+xyH+yxH and assigns each element of A′ to the corresponding element of A.