[scilab-Users] Convergence problem

[Michaël Baudin]

  Hi,

I guess that you are expecting too much from the solver. The exact 
mathematical result of the integral is 0. Now, the mathematical sin 
function is approximated by a floating point implementation, which is so 
that :

-->sin(2*%pi)
  ans  =
   - 2.449D-16

See the script :

for atol = [1.e-1 1.e-2 1.e-4 1.e-8 1.e-10 1.e-12 1.e-14]
   instr = "I = integrate(""sin(x)"",""x"",0,2*%pi,atol);";
   ierr = execstr(instr,"errcatch");
   if ( ierr == 0 ) then
     mprintf("atol=%e, I=%.17e\n",atol,I)
   else
     mprintf("atol=%e, I=XXX\n",atol)
   end
end

This produces :

atol=1.000000e-001, I=2.26062574420357380e-016
atol=1.000000e-002, I=2.26062574420357380e-016
atol=1.000000e-004, I=2.26062574420357380e-016
atol=1.000000e-008, I=2.26062574420357380e-016
atol=1.000000e-010, I=2.26062574420357380e-016
atol=1.000000e-012, I=2.26062574420357380e-016
atol=1.000000e-014, I=XXX

Hence, it suffices to reduce the request for the absolute error to get 
an answer.

Best regards,

Michaël Baudin

PS-1
I admit that there might not be enough informations provided by Scilab 
in the gateway.
The various output of the solvers are described in the ier variable of :

http://www.netlib.org/quadpack/dqags.f

There are 6 different causes of failures, all of them being represented 
by the single "Convergence problem".

PS-2
A similar problem was discussed at :

http://bugzilla.scilab.org/show_bug.cgi?id=5728

PS-3
There are issues with the integrate function, with the management of 
default input arguments:

http://bugzilla.scilab.org/show_bug.cgi?id=8351

Le 18/10/2010 16:25, José Luis Volta Grau a écrit :
> Hi Jean:
> Change the tolerance and you will get the result of 
> integrate('sin(x)','x',0,2*%pi,1e-5)
> -->integrate('sin(x)','x',0,2*%pi,1e-5)
>  ans  =
>
>     2.222D-16
> which is almost zero.
> J.L.
>
>     ----- Original Message -----
>     *From:* jean podlecki <mailto:jean.podlecki at sfr.fr>
>     *To:* users at lists.scilab.org <mailto:users at lists.scilab.org>
>     *Sent:* Monday, October 18, 2010 9:22 AM
>     *Subject:* [scilab-Users] Convergence problem
>
>     God afternoon,
>
>     Here's my problem.
>
>     -------------------------------------------------
>
>     -->integrate('sin(x)','x',0,2*%pi)
>      !--error 24
>     Problème de convergence ...
>
>     at line      70 of function integrate called by :
>     integrate('sin(x)','x',0,2*%pi)
>
>     -------------------------------------------------
>
>     Is it right ? How can I get the correct answer ?
>
>     Jean.
>


-- 
Michaël Baudin
Ingénieur de développement
michael.baudin at scilab.org
-------------------------
Consortium Scilab - Digiteo
Domaine de Voluceau - Rocquencourt
B.P. 105 - 78153 Le Chesnay Cedex
Tel. : 01 39 63 56 87 - Fax : 01 39 63 55 94


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