!standard G.3.1(1)                                 05-03-09  AI95-00418-01/01
!standard G.3.2(1)
!class amendment 05-03-09
!status work item 05-03-09
!status received 05-03-09
!priority High
!difficulty Easy
!subject Vector norm

!summary

(See proposal.)

!problem

While the packages Generic_Real_Arrays and Generic_Complex_Arrays provide inner
product, they do not provide a related operation that is often used in
practice, the norm. Normalizing a vector is common and it seems unfriendly to
require the user to implement the norm based on the inner product (and
conjugation), especially as intermediate overflows/underflows could occur.

!proposal

Add "abs" operators implementing the L2-norm.

[What the heck is an L2-norm? We can't have terms that poorly defined in the
standard. - ED]

!wording

Add after G.3.1(9):

    function "abs" (Right : Real_Vector) return Real'Base;

Add after G.3.1(39):

function "abs" (Right : Real_Vector) return Real'Base;

This operation returns the L2-norm of Right.  This operation involves an inner
product.

Add after G.3.2(15):

    function "abs" (Right : Complex_Vector) return Real'Base;

Add after G.3.2(73):

function "abs" (Right : Complex_Vector) return Real'Base;

This operation returns the Hermitian L2-norm of Right.  This operation involves
an inner product.

!discussion

(See proposal.)

!example


--!corrigendum

!ACATS test

Test cases should be added to the ACATS tests created for AI-296.

!appendix

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