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]

template<in-vector InVec, class Scalar>
  Scalar vector_abs_sum(InVec v, Scalar init);
template<class ExecutionPolicy, in-vector InVec, class Scalar>
  Scalar vector_abs_sum(ExecutionPolicy&& exec, InVec v, Scalar init);

[Note 1:

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

— end note]

Mandates: decltype(init + abs-if-needed(real-if-needed(declval<typename InVec::value_type>())) + abs-if-needed(imag-if-needed(declval<typename InVec::value_type>()))) is convertible to Scalar.

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])))

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 InVec>
  auto vector_abs_sum(InVec v);
template<class ExecutionPolicy, in-vector InVec>
  auto vector_abs_sum(ExecutionPolicy&& exec, InVec v);

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<ExecutionPolicy>(exec), v, T{});