cppdraft_translate/cppdraft/linalg/algs/blas1/asum.md

[linalg.algs.blas1.asum]

29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.13 BLAS 1 algorithms [linalg.algs.blas1]

29.9.13.10 Sum of absolute values of vector elements [linalg.algs.blas1.asum]

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template<[in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec, class Scalar> Scalar vector_abs_sum(InVec v, Scalar init); template<class ExecutionPolicy, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec, class Scalar> Scalar vector_abs_sum(ExecutionPolicy&& exec, InVec v, Scalar init);

1

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[Note 1:

These functions correspond to the BLAS functionsSASUM, DASUM, SCASUM, and DZASUM[bib].

— end note]

2

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Mandates: decltype(init + abs-if-needed(real-if-needed(declval())) +abs-if-needed(imag-if-needed(declval()))) is convertible to Scalar.

3

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Returns: Let N be v.extent(0).

• (3.1)

init if N is zero;

• (3.2)

otherwise, if InVec​::​value_type is an arithmetic type,GENERALIZED_SUM(plus<>(), init, abs-if-needed(v[0]), …, abs-if-needed(v[N-1]))

• (3.3)

otherwise,GENERALIZED_SUM(plus<>(), init, abs-if-needed(real-if-needed(v[0])) + abs-if-needed(imag-if-needed(v[0])), …, abs-if-needed(real-if-needed(v[N-1])) + abs-if-needed(imag-if-needed(v[N-1])))

4

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Remarks: If InVec​::​value_type and Scalar are all floating-point types or specializations of complex, and if Scalar has higher precision than InVec​::​value_type, then intermediate terms in the sum use Scalar's precision or greater.

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template<[in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec> auto vector_abs_sum(InVec v); template<class ExecutionPolicy, [in-vector](linalg.helpers.concepts#concept:in-vector "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InVec> auto vector_abs_sum(ExecutionPolicy&& exec, InVec v);

5

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Effects: Let T be typename InVec​::​value_type.

Then,

• (5.1)

the one-parameter overload is equivalent to:return vector_abs_sum(v, T{}); and

• (5.2)

the two-parameter overload is equivalent to:return vector_abs_sum(std::forward(exec), v, T{});