Re: Does Ada need elemental functions to make it suitable for scientific work?

["Nasser M. Abbasi" <nma@12000.org>]

On 7/10/2012 3:02 AM, gautier.de.montmollin@gmail.com wrote:
> Le mardi 10 juillet 2012 07:22:58 UTC+2, Ada novice a �crit :
>
>> Believe me, for someone who do numerical computations on a daily basis, an operation
>like V**2 is a NECESSITY. It's a pity that Ada does not offer such a facility.
>I do not blame those who stick to Matlab (or Fortran?) for doing numerical computations.
>
> Wait... There are *such* facilities and several built-in operations *like* that:
> http://www.ada-auth.org/standards/12rm/html/RM-G-3-1.html
>
> Apparently it is not enough. But it is possible to make a proposal for
>  the next standard (and short term for the next GNAT version).
>

That is a start. But not enough by any means. All functions should be
vectorized. Even user defined ones.

In Ada, I can't even take the sin of a vector

----------------------
with Ada.Numerics.Elementary_Functions;
use Ada.Numerics.Elementary_Functions;

procedure foo3 is
   type array_t is array(1..5) OF float;
   D : constant array_t :=(0.1,0.2,0.3,0.4,0.5);
   V : array_t;
   
   begin
     -- V := sin(D);  -- ERROR

     for I in D'Range loop  -- must use a LOOP
         V(I) := sin(D(I));
     end loop;
        
end foo3;
--------------------

I can ofcourse overload sin, hide the loop inside my own sine
and then do

    V:= myPackage.sin(D);

All of this is possible in Ada. It is just a little (alot?)
more effort compared to what is out there.

octave/Matlab:
--------------------------
D=[0.1,0.2,0.3,0.4,0.5];
sin(D)

ans =
     0.0998    0.1987    0.2955    0.3894    0.4794
---------------------------

> The snag with that *specific* operation, v**2 meaning "v(i)**2 for each i",
>is that it is counter-intuitive from a linear algebra point of view. You
>would rather expect v**2 = v*v. Now another snag is should "*" be the
>dot or the cross product ?...
>
> These kind of things are thought-out carefully before landing into an Ada standard...
>

But these issue have been solved long time time. (like maybe
30 years ago? and are well defined for all cases:

http://www.mathworks.com/help/techdoc/ref/arithmeticoperators.html

There are element-wise operators, and operators that work
on the whole vector or matrix.

In octave/Matlab world, V.^2 means element-wise. (notice
the ".")

-------------------------
octave:3> V=[1 2 3 4];
octave:4> v.^2
ans =

     1    4    9   16
--------------------------

Otherwise, it becomes standard matrix operation.
A^2 means A*A

------------------------
octave:17> A=[1 2;3 4]
A =
    1   2
    3   4

octave:18> A^2
ans =
     7   10
    15   22

octave:19> A*A
ans =
     7   10
    15   22
---------------------

To do dot product, it has its own operator, called dot() !

----------------------
octave:5> dot(V,V)
ans =  30
-------------------------

To do cross product, it has its own operator, called cross() !

-----------------------
octave:9> D=[1 2 3]; V=[3 4 5]; cross(D,V)
ans =

   -2   4  -2
-------------------

btw, in Mathematica, it is the other way around. V*V does
element by element multiplication, and V.V does matrix product.
It has also Dot[] and Cross[] and all functions are vectorized,
and all user defined functions can be vectorized by simply
giving them the attribute Listable.

--Nasser