28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.13 BLAS 1 algorithms [linalg.algs.blas1] Frobenius norm of a matrix [linalg.algs.blas1.matfrobnorm]

[Note 1: 
These functions exist in the BLAS standard[bib] but are not part of the reference implementation.
— end note]
template<in-matrix InMat, class Scalar> Scalar matrix_frob_norm(InMat A, Scalar init); template<class ExecutionPolicy, in-matrix InMat, class Scalar> Scalar matrix_frob_norm(ExecutionPolicy&& exec, InMat A, Scalar init);
Mandates: Let a be abs-if-needed(declval<typename InMat​::​value_type>()).
Then, decltype(
init + a * a)
is convertible to Scalar.
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]
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.
template<in-matrix InMat> auto matrix_frob_norm(InMat A); template<class ExecutionPolicy, in-matrix InMat> auto matrix_frob_norm(ExecutionPolicy&& exec, InMat A);
Effects: Let a be abs-if-needed(declval<typename InMat​::​value_type>()).
Let T be decltype(a * a).
  • the one-parameter overload is equivalent to: return matrix_frob_norm(A, T{}); and
  • the two-parameter overload is equivalent to: return matrix_frob_norm(std::forward<ExecutionPolicy>(exec), A, T{});