tmp/tmpqmbqvajq/{from.md → to.md}
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#### Rank-2k update of a symmetric or Hermitian matrix <a id="linalg.algs.blas3.rank2k">[[linalg.algs.blas3.rank2k]]</a>
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[*Note 1*: These functions correspond to the BLAS functions `xSYR2K`
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and `xHER2K`. — *end note*]
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The following elements apply to all functions in
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[[linalg.algs.blas3.rank2k]].
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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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- `possibly-addable<decltype(A), decltype(B), decltype(C)>()` is `true`;
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and
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- `compatible-static-extents<decltype(A), decltype(A)>(0, 1)` is `true`.
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*Preconditions:*
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- `addable(A, B, C)` is `true`, and
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- `A.extent(0)` equals `A.extent(1)`.
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*Complexity:* 𝑂(`A.extent(0)` × `A.extent(1)` × `C.extent(0)`).
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``` cpp
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template<in-matrix InMat1, in-matrix InMat2,
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possibly-packed-inout-matrix InOutMat, class Triangle>
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void symmetric_matrix_rank_2k_update(InMat1 A, InMat2 B, InOutMat C, Triangle t);
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template<class ExecutionPolicy, in-matrix InMat1, in-matrix InMat2,
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possibly-packed-inout-matrix InOutMat, class Triangle>
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void symmetric_matrix_rank_2k_update(ExecutionPolicy&& exec,
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InMat1 A, InMat2 B, InOutMat C, Triangle t);
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```
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*Effects:* Computes a matrix C' such that $C' = C + A B^T + B A^T$, and
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assigns each element of C' to the corresponding element of C.
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``` cpp
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template<in-matrix InMat1, in-matrix InMat2,
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possibly-packed-inout-matrix InOutMat, class Triangle>
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void hermitian_matrix_rank_2k_update(InMat1 A, InMat2 B, InOutMat C, Triangle t);
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template<class ExecutionPolicy,
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in-matrix InMat1, in-matrix InMat2,
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possibly-packed-inout-matrix InOutMat, class Triangle>
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void hermitian_matrix_rank_2k_update(ExecutionPolicy&& exec,
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InMat1 A, InMat2 B, InOutMat C, Triangle t);
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```
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*Effects:* Computes a matrix C' such that $C' = C + A B^H + B A^H$, and
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assigns each element of C' to the corresponding element of C.
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