tmp/tmpx5ztyxau/{from.md → to.md}
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| 1 |
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#### Triangular matrix-vector product <a id="linalg.algs.blas2.trmv">[[linalg.algs.blas2.trmv]]</a>
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[*Note 1*: These functions correspond to the BLAS functions `xTRMV` and
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`xTPMV`. — *end note*]
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The following elements apply to all functions in
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[[linalg.algs.blas2.trmv]].
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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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- `compatible-static-extents<decltype(A), decltype(y)>(0, 0)` is `true`;
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- `compatible-static-extents<decltype(A), decltype(x)>(0, 0)` is `true`
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for those overloads that take an `x` parameter; and
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- `compatible-static-extents<decltype(A), decltype(z)>(0, 0)` 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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- `A.extent(0)` equals `y.extent(0)`,
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- `A.extent(0)` equals `x.extent(0)` for those overloads that take an
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`x` parameter, and
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- `A.extent(0)` equals `z.extent(0)` for those overloads that take a `z`
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parameter.
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``` cpp
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template<in-matrix InMat, class Triangle, class DiagonalStorage, in-vector InVec,
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out-vector OutVec>
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void triangular_matrix_vector_product(InMat A, Triangle t, DiagonalStorage d, InVec x, OutVec y);
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template<class ExecutionPolicy,
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in-matrix InMat, class Triangle, class DiagonalStorage, in-vector InVec,
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out-vector OutVec>
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void triangular_matrix_vector_product(ExecutionPolicy&& exec,
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InMat A, Triangle t, DiagonalStorage d, InVec x, OutVec y);
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```
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These functions perform an overwriting triangular matrix-vector product,
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taking into account the `Triangle` and `DiagonalStorage` parameters that
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apply to the triangular matrix `A` [[linalg.general]].
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*Effects:* Computes y = A x.
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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, class DiagonalStorage, inout-vector InOutVec>
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void triangular_matrix_vector_product(InMat A, Triangle t, DiagonalStorage d, InOutVec y);
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template<class ExecutionPolicy,
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in-matrix InMat, class Triangle, class DiagonalStorage, inout-vector InOutVec>
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void triangular_matrix_vector_product(ExecutionPolicy&& exec,
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InMat A, Triangle t, DiagonalStorage d, InOutVec y);
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```
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These functions perform an in-place triangular matrix-vector product,
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taking into account the `Triangle` and `DiagonalStorage` parameters that
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apply to the triangular matrix `A` [[linalg.general]].
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[*Note 1*: Performing this operation in place hinders parallelization.
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However, other `ExecutionPolicy` specific optimizations, such as
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vectorization, are still possible. — *end note*]
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*Effects:* Computes a vector y' such that y' = A y, and assigns each
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element of y' to the corresponding element of y.
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*Complexity:* 𝑂(`y.extent(0)` × `A.extent(1)`).
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``` cpp
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template<in-matrix InMat, class Triangle, class DiagonalStorage,
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in-vector InVec1, in-vector InVec2, out-vector OutVec>
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void triangular_matrix_vector_product(InMat A, Triangle t, DiagonalStorage d,
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InVec1 x, InVec2 y, OutVec z);
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template<class ExecutionPolicy, in-matrix InMat, class Triangle, class DiagonalStorage,
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in-vector InVec1, in-vector InVec2, out-vector OutVec>
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void triangular_matrix_vector_product(ExecutionPolicy&& exec,
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InMat A, Triangle t, DiagonalStorage d,
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InVec1 x, InVec2 y, OutVec z);
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```
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These functions perform an updating triangular matrix-vector product,
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taking into account the `Triangle` and `DiagonalStorage` parameters that
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apply to the triangular matrix `A` [[linalg.general]].
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*Effects:* Computes z = y + A x.
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*Complexity:* 𝑂(`x.extent(0)` × `A.extent(1)`).
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*Remarks:* `z` may alias `y`.
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