tmp/tmp2l7lgpaf/{from.md → to.md}
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#### Symmetric matrix-vector product <a id="linalg.algs.blas2.symv">[[linalg.algs.blas2.symv]]</a>
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[*Note 1*: These functions correspond to the BLAS functions `xSYMV` and
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`xSPMV`. — *end note*]
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The following elements apply to all functions in
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[[linalg.algs.blas2.symv]].
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*Mandates:*
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- If `InMat` has `layout_blas_packed` layout, then the layout’s
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`Triangle` template argument has the same type as the function’s
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`Triangle` template argument;
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- `compatible-static-extents<decltype(A), decltype(A)>(0, 1)` is `true`;
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- `possibly-multipliable<decltype(A), decltype(x), decltype(y)>()` is
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`true`; and
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- `possibly-addable<decltype(x), decltype(y), decltype(z)>()` is `true`
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for those overloads that take a `z` parameter.
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*Preconditions:*
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- `A.extent(0)` equals `A.extent(1)`,
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- `multipliable(A,x,y)` is `true`, and
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- `addable(x,y,z)` is `true` for those overloads that take a `z`
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parameter.
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*Complexity:* 𝑂(`x.extent(0)` × `A.extent(1)`).
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``` cpp
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template<in-matrix InMat, class Triangle, in-vector InVec, out-vector OutVec>
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void symmetric_matrix_vector_product(InMat A, Triangle t, InVec x, OutVec y);
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template<class ExecutionPolicy,
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in-matrix InMat, class Triangle, in-vector InVec, out-vector OutVec>
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void symmetric_matrix_vector_product(ExecutionPolicy&& exec,
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InMat A, Triangle t, InVec x, OutVec y);
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```
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These functions perform an overwriting symmetric matrix-vector product,
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taking into account the `Triangle` parameter that applies to the
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symmetric matrix `A` [[linalg.general]].
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*Effects:* Computes y = A x.
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``` cpp
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template<in-matrix InMat, class Triangle, in-vector InVec1, in-vector InVec2, out-vector OutVec>
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void symmetric_matrix_vector_product(InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z);
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template<class ExecutionPolicy,
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in-matrix InMat, class Triangle, in-vector InVec1, in-vector InVec2, out-vector OutVec>
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void symmetric_matrix_vector_product(ExecutionPolicy&& exec,
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InMat A, Triangle t, InVec1 x, InVec2 y, OutVec z);
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```
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These functions perform an updating symmetric matrix-vector product,
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taking into account the `Triangle` parameter that applies to the
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symmetric matrix `A` [[linalg.general]].
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*Effects:* Computes z = y + A x.
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*Remarks:* `z` may alias `y`.
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