29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.13 BLAS 1 algorithms [linalg.algs.blas1]

29.9.13.8 Euclidean norm of a vector [linalg.algs.blas1.nrm2]

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

[Note 1:

These functions correspond to the BLAS function xNRM2[bib].

— end note]

Mandates: InVec::value_type and Scalar are either a floating-point type, or a specialization of complex.

Let a be abs-if-needed(declval<typename InVec::value_type>()).

Then, decltype(init + a * a is convertible to Scalar.

Returns: The square root of the sum of the square of init and the squares of the absolute values of the elements of v.

[Note 2:

For init equal to zero, this is the Euclidean norm (also called 2-norm) of the vector v.

— end note]

Remarks: If Scalar has higher precision than InVec::value_type, then intermediate terms in the sum use Scalar's precision or greater.

🔗

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

Effects: Let a be abs-if-needed(declval<typename InVec::value_type>()).

Let T be decltype(a * a).

Then,

(5.1)
the one-parameter overload is equivalent to: return vector_two_norm(v, T{}); and
(5.2)
the two-parameter overload is equivalent to: return vector_two_norm(std::forward<ExecutionPolicy>(exec), v, T{});