28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.13 BLAS 1 algorithms [linalg.algs.blas1]

28.9.13.8 Scaled sum of squares of a vector's elements [linalg.algs.blas1.ssq]

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

[Note 1:

These functions correspond to the LAPACK function xLASSQ[bib].

— end note]

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

Effects: Returns a value result such that

(3.1)
result.scaling_factor is the maximum of init.scaling_factor and abs-if-needed(x[i]) for all i in the domain of v; and
(3.2)
let s2init be init.scaling_factor * init.scaling_factor * init.scaled_sum_of_squares then result.scaling_factor * result.scaling_factor * result.scaled_sum_of_squares equals the sum of s2init and the squares of abs-if-needed(x[i]) for all i in the domain of v.

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.