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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Newsgroups: comp.lang.ada
Subject: Re: Does Ada need elemental functions to make it suitable for
 scientific work?
Date: Tue, 10 Jul 2012 11:50:38 +0200
Organization: cbb software GmbH
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Date: 2012-07-10T11:50:38+02:00
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On Tue, 10 Jul 2012 04:21:17 -0500, Nasser M. Abbasi wrote:

> On 7/10/2012 4:07 AM, Dmitry A. Kazakov wrote:
>> On Tue, 10 Jul 2012 03:39:58 -0500, Nasser M. Abbasi wrote:
>>
>>> That is a start. But not enough by any means. All functions should be
>>> vectorized.
>>
>> It is ill-defined. E.g. exp(A), where A is a matrix. Is exp(A) a matrix of
>> exponents or exponent matrix?

[...]

> Just like when I read a paper, I first look for the definitions
> of symbols and terms used by the author.

Exactly. This is how you define it, it is not how LaTeX or TeX does. Since
there is no unambiguous semantics of f(), the language shall not introduce
them.

If you want scalar f() to apply to a matrix in some certain way, just
define that in Ada. You can even do it in generic way:

1. Using generics:

generic
   with function Scalar_F (X : Float) return Float;
function Generic_Vector_F (X : Vector) return Vector;

function Generic_Vector_F (X : Vector) return Vector is
begin
   return Result : Vector (X'Range) do
      for I in X'Range loop
         Result (I) := Scalar_F (X (I));
      end loop;
   end return;
end Generic_Vector_F;
 
function Sin is new Generic_Vector_F (Sin);
function Cos is new Generic_Vector_F (Cos);
...
-------------------------------------------------------------
2. Using functional composition:

function "*"
   (  F : not null access function (X : Float) return Float;
      X : Vector
   )  return Vector is
begin
   return Result : Vector (X'Range) do
      for I in X'Range loop
         Result (I) := F (X (I));
      end loop;
   end return;
end "*";

Used as:

sin'Access * V  -- Applies sin to V

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de