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 functions xSYMV 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.
4
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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: .
🔗
template<in-matrix InMat, class Triangle, in-vector InVec, out-vector OutVec> void symmetric_matrix_vector_product(InMat A, Triangle t, InVec x, OutVec y); template<class ExecutionPolicy, in-matrix InMat, class Triangle, in-vector InVec, out-vector 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 .
🔗
template<in-matrix InMat, class Triangle, in-vector InVec1, in-vector InVec2, out-vector OutVec> void symmetric_matrix_vector_product(InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z); template<class ExecutionPolicy, in-matrix InMat, class Triangle, in-vector InVec1, in-vector InVec2, out-vector 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 .
10
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Remarks: z may alias y.