tmp/tmp8t4wgnwj/{from.md → to.md}
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#### General matrix-matrix product <a id="linalg.algs.blas3.gemm">[[linalg.algs.blas3.gemm]]</a>
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[*Note 1*: These functions correspond to the BLAS function
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`xGEMM`. — *end note*]
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The following elements apply to all functions in
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[[linalg.algs.blas3.gemm]] in addition to function-specific elements.
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*Mandates:*
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`possibly-multipliable<decltype(A), decltype(B), decltype(C)>()` is
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`true`.
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*Preconditions:* `multipliable(A, B, C)` is `true`.
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*Complexity:* 𝑂(`A.extent(0)` × `A.extent(1)` × `B.extent(1)`).
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``` cpp
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template<in-matrix InMat1, in-matrix InMat2, out-matrix OutMat>
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void matrix_product(InMat1 A, InMat2 B, OutMat C);
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template<class ExecutionPolicy, in-matrix InMat1, in-matrix InMat2, out-matrix OutMat>
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void matrix_product(ExecutionPolicy&& exec, InMat1 A, InMat2 B, OutMat C);
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```
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*Effects:* Computes C = A B.
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``` cpp
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template<in-matrix InMat1, in-matrix InMat2, in-matrix InMat3, out-matrix OutMat>
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void matrix_product(InMat1 A, InMat2 B, InMat3 E, OutMat C);
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template<class ExecutionPolicy,
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in-matrix InMat1, in-matrix InMat2, in-matrix InMat3, out-matrix OutMat>
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void matrix_product(ExecutionPolicy&& exec, InMat1 A, InMat2 B, InMat3 E, OutMat C);
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```
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*Mandates:* *`possibly-addable`*`<InMat3, InMat3, OutMat>()` is `true`.
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*Preconditions:* *`addable`*`(E, E, C)` is `true`.
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*Effects:* Computes C = E + A B.
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*Remarks:* `C` may alias `E`.
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