cppdraft_translate/cppdraft/linalg/algs/blas2/symherrank1.md

[linalg.algs.blas2.symherrank1]

29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.14 BLAS 2 algorithms [linalg.algs.blas2]

29.9.14.7 Symmetric or Hermitian Rank-1 (outer product) update of a matrix [linalg.algs.blas2.symherrank1]

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[Note 1:

These functions correspond to the BLAS functionsxSYR, xSPR, xHER, and xHPR[bib].

They have overloads taking a scaling factor alpha, because it would be impossible to express the updateA=A−xxT otherwise.

— end note]

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The following elements apply to all functions in [linalg.algs.blas2.symherrank1].

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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)

compatible-static-extents<decltype(A), decltype(x)>(0, 0) is true.

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Preconditions:

• (4.1)

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

• (4.2)

A.extent(0) equals x.extent(0).

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

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template<class Scalar, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec, [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_1_update(Scalar alpha, InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, class Scalar, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec, [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_1_update(ExecutionPolicy&& exec, Scalar alpha, InVec x, InOutMat A, Triangle t);

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These functions perform a symmetric rank-1 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 matrix A′ such thatA′=A+αxxT, where the scalar α is alpha, 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]") InVec, [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_1_update(InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec, [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_1_update(ExecutionPolicy&& exec, InVec x, InOutMat A, Triangle t);

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These functions perform a symmetric rank-1 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 matrix A′ such that A′=A+xxT and assigns each element of A′ to the corresponding element of A.

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template<class Scalar, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec, [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_1_update(Scalar alpha, InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, class Scalar, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec, [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_1_update(ExecutionPolicy&& exec, Scalar alpha, InVec x, InOutMat A, Triangle t);

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These functions perform a Hermitian rank-1 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 thatA′=A+αxxH, where the scalar α is alpha, 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]") InVec, [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_1_update(InVec x, InOutMat A, Triangle t); template<class ExecutionPolicy, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec, [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_1_update(ExecutionPolicy&& exec, InVec x, InOutMat A, Triangle t);

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These functions perform a Hermitian rank-1 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 matrix A′ such that A′=A+xxH and assigns each element of A′ to the corresponding element of A.