Re: Boolean Integral

• To: mathgroup at smc.vnet.net
• Subject: [mg62399] Re: Boolean Integral
• From: dh <dh at metrohm.ch>
• Date: Wed, 23 Nov 2005 01:12:14 -0500 (EST)
• References: <dlupfj\$nb2\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Roberto,
If your function does not behave too exotic, an increase of the number
of sample points may help: GaussPoints->n, where n is big enough (see
the manual).

If your function is slightly pathologic, you may help NIntegrate by
splitting the integral region into pieces, where the function behaves well.

Plot has an adaptive algorithm to determine the plot points. As a last
resort, you could get the

Daniel

Brambilla Roberto Luigi (CESI-PGE) wrote:
> Hi,
>
> I have defined the following support function:
>
> chi[func_,y1_,y2_]:=Boole[yi<func<y2]
>
> that gives 1 if yi<func<y2 and 0 otherwise. It works well with Plot :
>
> (*example*)
> foo[x_]:=-BesselJ[1,x]
> y1=.12;
> y2=.16;
> Plot[{foo[x],chi[foo[x]],y1,y2],y1,y2},{x,0,20},
> PlotRange->All,PlotStyle->{Black,Red,Blue,Blue}]
>
> but if I want to *measure* the sum of intervals where y1<foo<y2, the answer is wrong:  the integral
>
> NIntegrate[chi[foo[x],y1,y2],{x,0,20}]
>
> often gives 0 since x-sample points (Gauss points) of a numerical method may fall into intervals where chi=0.
> If I use Method->MonteCarlo the results is rather slow (10 sec.) and change a little bit at every execution
>
> NIntegrate[chi[foo[x],y1,y2],{x,0,20},Method->MonteCarlo]
> 1.3668
>
> There are other NIntegrate settings to obtain the wright result more quicly?
> (I would like to avoid to use FindRoot and to fragment the integral etc...)
>
> Any help well accepted.
> Thank You.
> Rob.
>
>
>
>
>
>
>
> CESI SpA ha adottato il Modello Organizzativo ai sensi del D.Lgs.231/2001, in forza del quale l'assunzione di obbligazioni da parte della SocietÃ  avviene con firma di un procuratore, munito di idonei poteri.
> CESI adopts a Compliance Programme under the Italian Law (D.Lgs.231/2001). According to this CESI Compliance Programme, any commitment of CESI is taken by the signature of one Representative granted by a proper Power of Attorney.
>
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```

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