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

[linalg.algs.blas2.symv]

29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.14 BLAS 2 algorithms [linalg.algs.blas2]

29.9.14.2 Symmetric matrix-vector product [linalg.algs.blas2.symv]

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[Note 1:

These functions correspond to the BLAS functionsxSYMV and xSPMV[bib].

— end note]

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

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Mandates:

• (3.1)

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;

• (3.2)

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

• (3.3)

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

• (3.4)

possibly-addable<decltype(x), decltype(y), decltype(z)>() is true for those overloads that take a z parameter.

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Preconditions:

• (4.1)

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

• (4.2)

multipliable(A,x,y) is true, and

• (4.3)

addable(x,y,z) is true for those overloads that take a z parameter.

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

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template<[in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat, class Triangle, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec, [out-vector](linalg.helpers.concepts#concept:out-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") OutVec> void symmetric_matrix_vector_product(InMat A, Triangle t, InVec x, OutVec y); template<class ExecutionPolicy, [in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat, class Triangle, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec, [out-vector](linalg.helpers.concepts#concept:out-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") OutVec> void symmetric_matrix_vector_product(ExecutionPolicy&& exec, InMat A, Triangle t, InVec x, OutVec y);

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These functions perform an overwriting symmetric matrix-vector product, taking into account the Triangle parameter that applies to the symmetric matrix A ([linalg.general]).

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Effects: Computes y=Ax.

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template<[in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat, class Triangle, [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, [out-vector](linalg.helpers.concepts#concept:out-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") OutVec> void symmetric_matrix_vector_product(InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z); template<class ExecutionPolicy, [in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat, class Triangle, [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, [out-vector](linalg.helpers.concepts#concept:out-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") OutVec> void symmetric_matrix_vector_product(ExecutionPolicy&& exec, InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z);

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These functions perform an updating symmetric matrix-vector product, taking into account the Triangle parameter that applies to the symmetric matrix A ([linalg.general]).

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Effects: Computes z=y+Ax.

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Remarks: z may alias y.