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

[linalg.algs.blas1.matfrobnorm]

29 Numerics library [numerics]

29.9 Basic linear algebra algorithms [linalg]

29.9.13 BLAS 1 algorithms [linalg.algs.blas1]

29.9.13.12 Frobenius norm of a matrix [linalg.algs.blas1.matfrobnorm]

1

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[Note 1:

These functions exist in the BLAS standard[bib] but are not part of the reference implementation.

— end note]

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template<[in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat, class Scalar> Scalar matrix_frob_norm(InMat A, Scalar init); template<class ExecutionPolicy, [in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat, class Scalar> Scalar matrix_frob_norm(ExecutionPolicy&& exec, InMat A, Scalar init);

2

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

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

3

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

[Note 2:

For init equal to zero, this is the Frobenius norm of the matrix A.

— end note]

4

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Remarks: If InMat​::​value_type and Scalar are all floating-point types or specializations of complex, and if Scalar has higher precision than InMat​::​value_type, then intermediate terms in the sum use Scalar's precision or greater.

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template<[in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat> auto matrix_frob_norm(InMat A); template<class ExecutionPolicy, [in-matrix](linalg.helpers.concepts#concept:in-matrix "29.9.7.5 Argument concepts [linalg.helpers.concepts]") InMat> auto matrix_frob_norm(ExecutionPolicy&& exec, InMat A);

5

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

Let T bedecltype(a * a).

Then,

• (5.1)

the one-parameter overload is equivalent to:return matrix_frob_norm(A, T{}); and

• (5.2)

the two-parameter overload is equivalent to:return matrix_frob_norm(std::forward(exec), A, T{});