cppdraft_translate/cppdraft/linalg/algs/blas1/nrm2.md

[linalg.algs.blas1.nrm2]

29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.13 BLAS 1 algorithms [linalg.algs.blas1]

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

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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_two_norm(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_two_norm(ExecutionPolicy&& exec, InVec v, Scalar init);

1

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[Note 1:

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

— end note]

2

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Mandates: Let a beabs-if-needed(declval<typename InVec​::​value_type>()).

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

3

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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]

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.

[Note 3:

An implementation of this function for floating-point types T can use the scaled_sum_of_squares result fromvector_sum_of_squares(x, {.scaling_factor=1.0, .scaled_sum_of_squares=init}).

— end note]

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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_two_norm(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_two_norm(ExecutionPolicy&& exec, InVec v);

5

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Effects: Let a beabs-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(exec), v, T{});