[scilab-Users] Strange problem with "integrate" : "Convergence problem..." error 24 (Scilab 4.1.2)

[Michaël Baudin]

Oh, and by the way, this is exactly the method used by integrate, so
you can use it with several step instead of only one :

x0=0.;
step = 2*%pi/10
x1=0:step:2*%pi;
integrate("sin(x)",'x',x0,x1)

The value you search for is the last one : 2.d-17 ~ 0

Regards,

Michaël

Michaël Baudin a écrit :
> Hi Remi,
>
> I inquired your problem and it seems to me that all is fine,
> that is, the problem you face is a limitation of the computationnal
> method and not a bug.
>
> The "integrate" command is a Scilab macro which is
> based on the "intg" Scilab primitive.
>
> Now try the following Scilab script :
>
> function y=f(x)
>  y=sin(x)
> endfunction
> a = 0;
> b=2*%pi;
> computed = intg(a,b,f);
>
> The expected result in that case is 0., since -cos(x) is periodic
> on the [0,2 PI] range.
> The same error message appears.
> The following is the call stack, which shows how the quapro library
> is used to compute the integral based on a "21-point gauss-kronrod 
> approximation".
>
> differential_equations/sci_gateway/c/sci_intg
> > differential_equations/sci_gateway/fortran/intg.f
> > differential_equations/src/fortran/dqag0.f
> > dqags > quarul
>
> By doing a step-by-step check of the process, it
> appears that the numerical integration is correctly computed (near the
> machine's epsilon), but a secondary check sets a boolean flag to a
> value indicating that the error for that computation is too large.
>
> A simple workaround for your problem may be to decompose the
> range in two parts :
>
> i1 = intg(0,%pi,f);
> i2 = intg(%pi,2*%pi,f);
>
> then the expected result is the sum of i1 and i2.
> Other solutions include traditionnal ode solver (like dassl ) or 
> Monte-Carlo methods.
>
> Best regards,
>
> Michaël Baudin
>
> Remi G. a écrit :
>> Hello!
>>
>> I'm facing a strange problem with the function "integrate" (and also 
>> with "intg") with Scilab 4.1.2 :
>>
>> If I want to integrate x^5 between -%pi and %pi, it works (hopefully) :
>>  integrate('t^5','t',-%pi,%pi)
>>
>> But if replace 5 by a variable k (that I've defined before of course) 
>> it will not work for k>=5!
>>  i=5
>>  integrate('t^i','t',-%pi,%pi)
>>
>> Here is the error message I get :
>>    !--error 24
>>  convergence problem...
>>  At line      26 of function integrate called by :
>>  integrate('t^i','t',-%pi,%pi)
>>
>> That's really annoying because I can't code my least square 
>> approximation procedure which is... for tomorrow!
>> If someone could give me a way to go through this issue!
>> Thank you very much!
>>
>> Rémi.
>