28 Numerics library [numerics]

28.9 Basic linear algebra algorithms [linalg]

28.9.13 BLAS 1 algorithms [linalg.algs.blas1]

28.9.13.13 One norm of a matrix [linalg.algs.blas1.matonenorm]

[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_one_norm(InMat A, Scalar init);
template<class ExecutionPolicy, in-matrix InMat, class Scalar>
  Scalar matrix_one_norm(ExecutionPolicy&& exec, InMat A, Scalar init);

Mandates: decltype(abs-if-needed(declval<typename InMat::value_type>())) is convertible to Scalar.

Returns:

(3.1)
init if A.extent(1) is zero;
(3.2)
otherwise, the sum of init and the one norm of the matrix A.

[Note 2:

The one norm of the matrix A is the maximum over all columns of A, of the sum of the absolute values of the elements of the column.

— 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_one_norm(InMat A);
template<class ExecutionPolicy, in-matrix InMat>
  auto matrix_one_norm(ExecutionPolicy&& exec, InMat A);

Effects: Let T be decltype(abs-if-needed(declval<typename InMat::value_type>()).

Then,

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