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[linalg.algs.blas1.dot]

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+ #### Dot product of two vectors <a id="linalg.algs.blas1.dot">[[linalg.algs.blas1.dot]]</a>
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+
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+ [*Note 1*: The functions in this section correspond to the BLAS
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+ functions `xDOT`, `xDOTU`, and `xDOTC`. — *end note*]
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+
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+ The following elements apply to all functions in
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+ [[linalg.algs.blas1.dot]].
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+
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+ *Mandates:* `compatible-static-extents<InVec1, InVec2>(0, 0)` is `true`.
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+
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+ *Preconditions:* `v1.extent(0)` equals `v2.extent(0)`.
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+
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+ ``` cpp
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+ template<in-vector InVec1, in-vector InVec2, class Scalar>
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+ Scalar dot(InVec1 v1, InVec2 v2, Scalar init);
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+ template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2, class Scalar>
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+ Scalar dot(ExecutionPolicy&& exec,
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+ InVec1 v1, InVec2 v2, Scalar init);
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+ ```
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+
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+ These functions compute a non-conjugated dot product with an explicitly
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+ specified result type.
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+
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+ *Returns:* Let `N` be `v1.extent(0)`.
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+
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+ - `init` if `N` is zero;
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+ - otherwise, *GENERALIZED_SUM*(plus\<\>(), init, v1\[0\]\*v2\[0\], …,
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+ v1\[N-1\]\*v2\[N-1\]).
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+
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+ *Remarks:* If `InVec1::value_type`, `InVec2::value_type`, and `Scalar`
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+ are all floating-point types or specializations of `complex`, and if
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+ `Scalar` has higher precision than `InVec1::value_type` or
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+ `InVec2::value_type`, then intermediate terms in the sum use `Scalar`’s
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+ precision or greater.
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+
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+ ``` cpp
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+ template<in-vector InVec1, in-vector InVec2>
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+ auto dot(InVec1 v1, InVec2 v2);
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+ template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2>
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+ auto dot(ExecutionPolicy&& exec,
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+ InVec1 v1, InVec2 v2);
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+ ```
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+
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+ These functions compute a non-conjugated dot product with a default
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+ result type.
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+
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+ *Effects:* Let `T` be
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+ `decltype(declval<typename InVec1::value_type>() * declval<typename InVec2::value_type>())`.
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+ Then,
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+
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+ - the two-parameter overload is equivalent to:
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+ ``` cpp
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+ return dot(v1, v2, T{});
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+ ```
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+
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+ and
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+ - the three-parameter overload is equivalent to:
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+ ``` cpp
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+ return dot(std::forward<ExecutionPolicy>(exec), v1, v2, T{});
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+ ```
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+
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+ ``` cpp
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+ template<in-vector InVec1, in-vector InVec2, class Scalar>
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+ Scalar dotc(InVec1 v1, InVec2 v2, Scalar init);
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+ template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2, class Scalar>
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+ Scalar dotc(ExecutionPolicy&& exec,
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+ InVec1 v1, InVec2 v2, Scalar init);
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+ ```
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+
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+ These functions compute a conjugated dot product with an explicitly
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+ specified result type.
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+
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+ *Effects:*
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+
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+ - The three-parameter overload is equivalent to:
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+ ``` cpp
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+ return dot(conjugated(v1), v2, init);
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+ ```
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+
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+ and
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+ - the four-parameter overload is equivalent to:
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+ ``` cpp
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+ return dot(std::forward<ExecutionPolicy>(exec), conjugated(v1), v2, init);
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+ ```
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+
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+ ``` cpp
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+ template<in-vector InVec1, in-vector InVec2>
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+ auto dotc(InVec1 v1, InVec2 v2);
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+ template<class ExecutionPolicy, in-vector InVec1, in-vector InVec2>
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+ auto dotc(ExecutionPolicy&& exec,
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+ InVec1 v1, InVec2 v2);
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+ ```
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+
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+ These functions compute a conjugated dot product with a default result
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+ type.
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+
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+ *Effects:* Let `T` be
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+ `decltype(`*`conj-if-needed`*`(declval<typename InVec1::value_type>()) * declval<typename InVec2::value_type>())`.
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+ Then,
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+
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+ - the two-parameter overload is equivalent to:
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+ ``` cpp
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+ return dotc(v1, v2, T{});
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+ ```
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+
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+ and
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+ - the three-parameter overload is equivalent to
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+ ``` cpp
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+ return dotc(std::forward<ExecutionPolicy>(exec), v1, v2, T{});
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+ ```
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+