28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.13 BLAS 1 algorithms [linalg.algs.blas1] Euclidean norm of a vector [linalg.algs.blas1.nrm2]

template<in-vector InVec, class Scalar> Scalar vector_two_norm(InVec v, Scalar init); template<class ExecutionPolicy, in-vector InVec, class 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: 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 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.
[Note 3: 
An implementation of this function for floating-point types T can use the scaled_sum_of_squares result from vector_sum_of_squares(x, {.scaling_factor=1.0, .scaled_sum_of_squares=init}).
— end note]
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).
  • the one-parameter overload is equivalent to: return vector_two_norm(v, T{}); and
  • the two-parameter overload is equivalent to: return vector_two_norm(std::forward<ExecutionPolicy>(exec), v, T{});