tmp/tmpmj3djfj4/{from.md → to.md}
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| 1 |
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#### Symmetric or Hermitian Rank-1 (outer product) update of a matrix <a id="linalg.algs.blas2.symherrank1">[[linalg.algs.blas2.symherrank1]]</a>
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[*Note 1*: These functions correspond to the BLAS functions `xSYR`,
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`xSPR`, `xHER`, and `xHPR`. They have overloads taking a scaling factor
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`alpha`, because it would be impossible to express the update
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$A = A - x x^T$ otherwise. — *end note*]
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The following elements apply to all functions in
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[[linalg.algs.blas2.symherrank1]].
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*Mandates:*
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- If `InOutMat` 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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and
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- `compatible-static-extents<decltype(A), decltype(x)>(0, 0)` is `true`.
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*Preconditions:*
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- `A.extent(0)` equals `A.extent(1)`, and
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- `A.extent(0)` equals `x.extent(0)`.
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*Complexity:* 𝑂(`x.extent(0)` × `x.extent(0)`).
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``` cpp
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template<class Scalar, in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle>
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void symmetric_matrix_rank_1_update(Scalar alpha, InVec x, InOutMat A, Triangle t);
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template<class ExecutionPolicy,
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class Scalar, in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle>
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void symmetric_matrix_rank_1_update(ExecutionPolicy&& exec,
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Scalar alpha, InVec x, InOutMat A, Triangle t);
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```
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These functions perform a symmetric rank-1 update of the symmetric
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matrix `A`, taking into account the `Triangle` parameter that applies to
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`A` [[linalg.general]].
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*Effects:* Computes a matrix A' such that $A' = A + \alpha x x^T$, where
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the scalar α is `alpha`, and assigns each element of A' to the
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corresponding element of A.
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``` cpp
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template<in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle>
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void symmetric_matrix_rank_1_update(InVec x, InOutMat A, Triangle t);
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template<class ExecutionPolicy,
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in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle>
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void symmetric_matrix_rank_1_update(ExecutionPolicy&& exec, InVec x, InOutMat A, Triangle t);
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```
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These functions perform a symmetric rank-1 update of the symmetric
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matrix `A`, taking into account the `Triangle` parameter that applies to
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`A` [[linalg.general]].
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*Effects:* Computes a matrix A' such that $A' = A + x x^T$ and assigns
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each element of A' to the corresponding element of A.
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``` cpp
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template<class Scalar, in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle>
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void hermitian_matrix_rank_1_update(Scalar alpha, InVec x, InOutMat A, Triangle t);
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template<class ExecutionPolicy,
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class Scalar, in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle>
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void hermitian_matrix_rank_1_update(ExecutionPolicy&& exec,
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Scalar alpha, InVec x, InOutMat A, Triangle t);
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```
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These functions perform a Hermitian rank-1 update of the Hermitian
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matrix `A`, taking into account the `Triangle` parameter that applies to
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`A` [[linalg.general]].
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*Effects:* Computes A' such that $A' = A + \alpha x x^H$, where the
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scalar α is `alpha`, and assigns each element of A' to the corresponding
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element of A.
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``` cpp
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template<in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle>
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void hermitian_matrix_rank_1_update(InVec x, InOutMat A, Triangle t);
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template<class ExecutionPolicy,
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in-vector InVec, possibly-packed-inout-matrix InOutMat, class Triangle>
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void hermitian_matrix_rank_1_update(ExecutionPolicy&& exec, InVec x, InOutMat A, Triangle t);
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```
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These functions perform a Hermitian rank-1 update of the Hermitian
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matrix `A`, taking into account the `Triangle` parameter that applies to
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`A` [[linalg.general]].
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*Effects:* Computes a matrix A' such that $A' = A + x x^H$ and assigns
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each element of A' to the corresponding element of A.
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