[scilab-Users] Atan function

[Samuel GOUGEON]

  Hi,

----- Message d'origine -----
De : Laurent Berger
Date : 10/05/2011 14:38:
> In this program
>
> clear;
> N=256;
> n=0:N-1;
> Xr=zeros(1,N);
> f0=2;
> Xr(f0+1)=1/(2*%i);
> Xr(N-(f0+1)+2)=-1/(2*%i);
> Xr=Xr.*exp(%i*%pi*2*6*n/N);
> xr=ifft(Xr);
> disp (atan(imag(Xr(11:12)),real(Xr(11:12))))
> disp (Xr(11)-Xr(12))
>
> results are
>  0.    3.1415927
>
>     0
>
> I don't understand why two numbers with a difference of 0 can have a numerical 
> phase of 0 or pi .
> In matlab results are
> 0 0
> 0
This result is mathematically possible, since the phase of the origin 0 -- that 
is here considered --
is undefined (or conventional). So any phase is possible, provided that the 
modulus is zero.

The issue is that both Xr(11) and Xr(12) are apparently (complex: ok) (really) 
null, with the same
actually null real parts and imaginary parts, with no epsilon-machine residues:

-->format("e",15)
-->real(Xr(11:12))
  ans  =
     0.00000000D+00    0.00000000D+00
-->imag(Xr(11:12))
  ans  =
     0.00000000D+00    0.00000000D+00
-->imag(Xr(11:12))==[0 0]
  ans  =
   T T
-->real(Xr(11:12))==[0 0]
  ans  =
   T T
// BUT
-->atan(imag(Xr(11:12)),real(Xr(11:12)))
  ans  =
     0.00000000D+00    3.14159265D+00
// whereas
-->atan([0 0],[0 0])
  ans  =
     0.00000000D+00    0.00000000D+00
// !!!!!

The issue may come from real() or/and imag(), instead of atan().
Or from somewhere else.

Regards
Samuel