tmp/tmpmxjj5wxl/{from.md → to.md}
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| 1 |
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#### Rank-1 (outer product) update of a matrix <a id="linalg.algs.blas2.rank1">[[linalg.algs.blas2.rank1]]</a>
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``` cpp
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template<in-vector InVec1, in-vector InVec2, inout-matrix InOutMat>
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void matrix_rank_1_update(InVec1 x, InVec2 y, InOutMat A);
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template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2, inout-matrix InOutMat>
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void matrix_rank_1_update(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InOutMat A);
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```
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These functions perform a nonsymmetric nonconjugated rank-1 update.
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[*Note 1*: These functions correspond to the BLAS functions `xGER` (for
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real element types) and `xGERU` (for complex element
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types). — *end note*]
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*Mandates:* *`possibly-multipliable`*`<InOutMat, InVec2, InVec1>()` is
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`true`.
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*Preconditions:* *`multipliable`*`(A, y, x)` is `true`.
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*Effects:* Computes a matrix A' such that $A' = A + x y^T$, and assigns
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each element of A' to the corresponding element of A.
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*Complexity:* 𝑂(`x.extent(0)` × `y.extent(0)`).
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``` cpp
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template<in-vector InVec1, in-vector InVec2, inout-matrix InOutMat>
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void matrix_rank_1_update_c(InVec1 x, InVec2 y, InOutMat A);
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template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2, inout-matrix InOutMat>
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void matrix_rank_1_update_c(ExecutionPolicy&& exec, InVec1 x, InVec2 y, InOutMat A);
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```
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These functions perform a nonsymmetric conjugated rank-1 update.
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[*Note 2*: These functions correspond to the BLAS functions `xGER` (for
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real element types) and `xGERC` (for complex element
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types). — *end note*]
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*Effects:*
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- For the overloads without an `ExecutionPolicy` argument, equivalent
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to:
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``` cpp
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matrix_rank_1_update(x, conjugated(y), A);
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```
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- otherwise, equivalent to:
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``` cpp
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matrix_rank_1_update(std::forward<ExecutionPolicy>(exec), x, conjugated(y), A);
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```
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