Re: (again) common problem with FindMinimum and NIntegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg69535] Re: (again) common problem with FindMinimum and NIntegrate
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Fri, 15 Sep 2006 06:44:43 -0400 (EDT)
• Organization: The University of Western Australia
• References: <eebf11\$1iv\$1@smc.vnet.net>

```In article <eebf11\$1iv\$1 at smc.vnet.net>, wtplasar at ehu.es wrote:

> Some people have enquired in the past about how to avoid error
> messages similar to this one I get:
>
> NMinimize::nnum: The function value
> Experimental`NumericalFunction[{Hold[bestchi[om, ol]], Block},
> <<4>>, {None, None}] is not a number at {ol, om} =
> {1.5636149496419025`,0.08724393316032257`}
>
> I have read the documentation and  tried to implement the
> recommendations posted at mathgroup, but to no avail.
>
> Here is my code (it won't take much from your time):
>
> ndat = {1.`, 2.`, 3.`, 4.`, 5.`, 6.`, 7.`, 8.`, 9.`};
> Hobs = {69.`, 83.`, 70.`, 87.`, 117.`, 168.`, 177.`, 140.`, 202.`};
> sH = {12.`, 8.3`, 14.`, 17.4`, 23.4`, 13.4`, 14.2`, 13.5`, 40.4`};
> z = {0.09`, 0.17`, 0.27`, 0.4`, 0.88`, 1.3`, 1.43`, 1.53`, 1.75`};
> H[x_, om_, ol_, H0_] := H0 Sqrt[om (1 + x)^3 + ol + (1 - om - ol)(1 +
> x)^2];
> Hlist[om_, ol_, H0_, mylist_] := Thread[H[#, om, ol, H0]] &[mylist];
> chisq[om_?NumericQ, ol_?NumericQ, H0_?
>       NumericQ] := Switch[Head[N[#]], Real, #, Complex, 10^20] &[Module
> [{vec1 = (Hobs - Hlist[om, ol, H0, z])^2, vec2 = (sH^2)}, Total
> [vec1/vec2]]];
> bestchi[om_?NumericQ, ol_?NumericQ] := -2*Log[NIntegrate[1/(3 Sqrt[2
> Pi])Exp[-
>   Chop[(H0 - 73)]^2/18]Exp[-chisq[om,
>         ol, H0]/2], {H0, 71, 75}, WorkingPrecision -> 20]];
> NMinimize[{bestchi[om, ol], 0.7 > om > 0 && ol > 0}, {
>     om, ol}, Method -> {"RandomSearch"}];
>
> I would appreciate someone posted a reply to show me how to fix it.

I think that the error message is spurious, and not helpful -- there is
no problem with bestchi[om, ol] at

{ol, om} =  {1.5636149496419025`,0.08724393316032257`}

as direct numerical evaluation will show.

First, have a look at a ContourPlot of bestchi:

ContourPlot[bestchi[om, ol], {om, 0, 0.7}, {ol, 0, 1}]

This may give you a clue as to why NMinimize might have a problem. You
are trying to minimize -2 Log[ f ]. The effect of Log will be to flatten
out the function. If you modify bestchi, calling it bestchi2, to
evaluate f instead of -2 Log[ f ] and then do

ContourPlot[bestchi2[om, ol], {om, 0, 0.7}, {ol, 0, 1}]

you can see where to look for the maximum. Then

NMaximize[{bestchi2[om, ol], 0.7 > om > 0 && ol > 0},
{{om, 0.1, 0.3}, {ol, 0.5, 0.7}}, Method -> {"RandomSearch"}]

works without problem.

Cheers,
Paul
>
> Thanks a lot in advance,
>
> Ruth Lazkoz

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul

```

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