Re: small example, using complex variables in Ada

[Ludovic Brenta <ludovic@ludovic-brenta.org>]

On Jun 9, 12:49 pm, "Nasser M. Abbasi" <n...@12000.org> wrote:
> I never used complex variables before in Ada, so for the last 3 hrs I
> was learning how to do it. I wrote a simple program, to find the DFT of
> an array of 3 elements {1,2,3} (DFT=discrete Fourier transform).
>
> The definition of DFT is one equation with summation, here it is, first
> equation you'll see:
>
> http://en.wikipedia.org/wiki/Discrete_Fourier_transform
>
> Since I have not programmed in Ada nor in FORTRAN for a looong time, I
> am very rusty, I program in Mathematica and sometimes in matlab these
> days, but I wanted to try Ada on complex numbers.
>
> I also wrote a FORTRAN equivalent of the small Ada function.  Here is
> below the Ada code, and the FORTRAN code.  Again, do not scream too much
> if it is not good code, I just learned this now, I am sure this can be
> improved a lot.
>
> And for comparing, I show the Matlab and the Mathematica output just to
> make sure.
>
> ====== START ADA ============
> --
> -- dtf.adb, compiled with GNAT 4.3.4 20090804 (release) 1
> -- under CYGWIN 1.7.5
> -- gnatmake dft.adb
> --
> -- ./dft.exe
> -- ( 6.00000E+00, 0.00000E+00)
> -- (-1.50000E+00, 8.66026E-01)
> -- (-1.50000E+00,-8.66025E-01)
> -- $
>
> with Ada.Text_IO; use Ada.Text_IO;
> with Ada.Numerics.Complex_Types; use  Ada.Numerics.Complex_Types;
>
> with Ada.Numerics; use  Ada.Numerics;
>
> with Ada.Numerics.Complex_Elementary_Functions;
> use  Ada.Numerics.Complex_Elementary_Functions;
>
> with Ada.Complex_Text_IO; use Ada.Complex_Text_IO;
>
> procedure dft is
>      N : positive := 3;
>      J : constant complex :=(0.0,1.0);  -- SQRT(-1)
>      X : array(0 .. N-1) of Complex  := (others=>(0.0,0.0));
>      data : array(0 .. N-1) of float :=(1.0,2.0,3.0);
>
> begin
>      FOR k in X'range LOOP
>          FOR m in data'range LOOP
>              X(k) := X(k) + data(m) * exp(- J*(2.0*Pi)/float(N) *
> float(m*k) );
>          END LOOP;
>          put(X(k)); new_line;
>      END LOOP;
>
> end dft;
> ================== END ADA ==============
>
> ======= FORTRAN code ===========
> ! dtf.f90, compiled with GCC 4.3.4
> ! under CYGWIN 1.7.5
> ! gfortran -Wall dft.f90
> ! ./a.exe
> ! (  6.0000000    ,  0.0000000    )
> ! ( -1.4999999    , 0.86602557    )
> ! ( -1.5000005    ,-0.86602497    )
> !
>
> PROGRAM dft
>
>    IMPLICIT NONE
>
>    INTEGER, PARAMETER :: N = 3
>    COMPLEX, parameter :: J =(0,1)
>
>    REAL, parameter :: Pi = ACOS(-1.0)
>    INTEGER :: k,m
>    COMPLEX, dimension(N) :: X
>    REAL, dimension(N) :: data=(/1.0,2.0,3.0/)
>
> DO k=1,N
>     X(k)=(0,0)
>     DO m=1,N
>        X(k) = X(k) + data(m) * EXP(-1.0*J*2.0*Pi/N *(m-1)*(k-1) )
>     END DO
>     print *,X(k)
>
> END DO
>
> END PROGRAM dft
> ==================================
>
> ==== Matlab code ====
> EDU>> fft([1,2,3])'
>
> ans =
>
>     6.0000
>    -1.5000 - 0.8660i
>    -1.5000 + 0.8660i
> ===============================
>
> === Mathematica ====
> In[5]:= Chop[Fourier[{1, 2, 3}, FourierParameters -> {1, -1}]]
>
> Out[5]= {6., -1.5 + 0.8660254037844386*I,  -1.5 - 0.8660254037844386*I}
> =========================
>
> Conclusion:
> I actually liked the Ada implementation more than FORTRAN because:
>
> 1. In Ada, I did not have to change the index of m and k in the
> summation to reflect the 1-off per the definition of DFT.
> DFT starts from 0 to N-1. In Ada, using 'Range and defining the arrays
> to go from 0 .. N-1 solved the problem.
>
> 2. In Ada, the compiler complained more times more about types being
> mixed up. I placed float() around the places it complained about.
>
> 3. It actually took me less time to do the Ada function than the FORTRAN
> one, even though I am equally not familiar with both at this time :)
>
> ok, this was a fun learning exercise

You should use constants and named numbers instead of variables
wherever possible; this simplifies your Ada program. Also, i and j are
predefined so you do not need to declare a "new" value for J:

with Ada.Text_IO; use Ada.Text_IO;
with Ada.Numerics.Complex_Types; use  Ada.Numerics.Complex_Types;

with Ada.Numerics; use  Ada.Numerics;

with Ada.Numerics.Complex_Elementary_Functions;
use  Ada.Numerics.Complex_Elementary_Functions;

with Ada.Complex_Text_IO; use Ada.Complex_Text_IO;

procedure dft is
     N : constant := 3; -- named number, no conversion to Float needed
     X : array(0 .. N-1) of Complex  := (others=>(0.0,0.0));
     data : constant array(0 .. N-1) of float :=(1.0,2.0,3.0);
     Two_Pi_Over_N : constant := 2 * Pi / N;
      -- named number, outside the loop, like in ARM 3.3.2(9)
begin
     FOR k in X'range LOOP
         FOR m in data'range LOOP
             X(k) := X(k) + data(m) * exp(- J*Two_Pi_Over_N *
float(m*k) );
         END LOOP;
         put(X(k)); new_line;
     END LOOP;
end dft;

--
Ludovic Brenta.