tmp/tmpisawm1et/{from.md → to.md}
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| 1 |
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#### Sum of absolute values of vector elements <a id="linalg.algs.blas1.asum">[[linalg.algs.blas1.asum]]</a>
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``` cpp
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template<in-vector InVec, class Scalar>
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Scalar vector_abs_sum(InVec v, Scalar init);
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template<class ExecutionPolicy, in-vector InVec, class Scalar>
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Scalar vector_abs_sum(ExecutionPolicy&& exec, InVec v, Scalar init);
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```
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[*Note 1*: These functions correspond to the BLAS functions `SASUM`,
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`DASUM`, `SCASUM`, and `DZASUM`. — *end note*]
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*Mandates:*
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``` cpp
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decltype(init + abs-if-needed(real-if-needed(declval<typename InVec::value_type>())) +
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abs-if-needed(imag-if-needed(declval<typename InVec::value_type>())))
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```
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is convertible to `Scalar`.
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*Returns:* Let `N` be `v.extent(0)`.
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- `init` if `N` is zero;
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- otherwise, if `InVec::value_type` is an arithmetic type,
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``` cpp
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GENERALIZED_SUM(plus<>(), init, abs-if-needed(v[0]), …, abs-if-needed(v[N-1]))
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```
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- otherwise,
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``` cpp
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GENERALIZED_SUM(plus<>(), init,
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abs-if-needed(real-if-needed(v[0])) + abs-if-needed(imag-if-needed(v[0])),
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…,
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abs-if-needed(real-if-needed(v[N-1])) + abs-if-needed(imag-if-needed(v[N-1])))
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```
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*Remarks:* If `InVec::value_type` and `Scalar` are all floating-point
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types or specializations of `complex`, and if `Scalar` has higher
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precision than `InVec::value_type`, then intermediate terms in the sum
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use `Scalar`’s precision or greater.
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``` cpp
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template<in-vector InVec>
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auto vector_abs_sum(InVec v);
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template<class ExecutionPolicy, in-vector InVec>
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auto vector_abs_sum(ExecutionPolicy&& exec, InVec v);
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```
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*Effects:* Let `T` be `typename InVec::value_type`. Then,
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- the one-parameter overload is equivalent to:
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``` cpp
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return vector_abs_sum(v, T{});
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```
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and
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- the two-parameter overload is equivalent to:
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``` cpp
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return vector_abs_sum(std::forward<ExecutionPolicy>(exec), v, T{});
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```
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