Re: NIntegrate::inum

• To: mathgroup at smc.vnet.net
• Subject: [mg59122] Re: NIntegrate::inum
• From: Peter Pein <petsie at dordos.net>
• Date: Fri, 29 Jul 2005 00:42:05 -0400 (EDT)
• References: <dca01n\$cul\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```wtplasar at lg.ehu.es schrieb:
> Hi,
>
> I have to minimize a function which is defined through a numerical
> integral. I get the "NIntegrate::inum .." error message. I know I can
> switch it off, but I wonder if there is a more elegant way to deal
> with the problem.
>
> These my input and output lines:
> In[1]:=
> Do[z[i] = i, {i, 1, 50}]
> Do[mi[i] = i^2, {i, 1, 50}]
> Do[smi[i] = i^3, {i, 1, 50}]
>
> In[4]:=
> f[x_, om_, w_] := 1/Sqrt[om (1 + x)^3 + (1 - om)(1 + x)^(3*(1 + w))];=

> rr[zz_?NumberQ, om_, w_] := NIntegrate[f[x, om, w], {x, 0, zz}];
> ff[zz_?NumberQ, om_, w_] := 5*Log[10, rr[zz, om, w]*(1 + zz)];
> Nn = 50;
>
> In[8]:=
> ci = Sum[1/smi[i]^2, {i, 1, 50}];
>
> In[9]:=
> chi2f2[om_, w_] := Sum[(mi[i] - ff[z[i], om, w])^2/smi[i]^2, {i, 1,
> Nn}] -
> (Sum[(mi[i] - ff[z[i], om, w])/smi[i]^2, {i, 1, Nn}])^2/ci
>
> In[10]:=
> Timing[NMinimize[{chi2f2[om, w], 0 =A1=DC om =A1=DC 1}, {om, w}]]
>
> NIntegrate::inum: Integrand ..... is not numerical at {x} = {0.5}
>
> Out[10]=
> {38.966 Second, {0.26337, {om -> 0.999998, w -> 0.0738109}}}
>
>
>
> Ruth Lazkoz
>
Hi Ruth,

this is, what I get with your input after some NIntegrate::inum messages:=

Out[14]= {15.922*Second,
{0.26337014333139525,
{om -> 0.9999982304774572,
w ->  0.07381086751638463}}}

But if I redefine chi2f2 to evaluate only numeric arguments, results
change dramatically:

In[15]:=
Clear[chi2f2];
chi2f2[(om_)?NumericQ, (w_)?NumericQ] :=
In[17]:= Timing[NMinimize[{chi2f2[om, w], 0 <= om <= 1}, {om, w}]]
Out[17]=
{277.25*Second,
{0.14928592347858327,
{om -> 5.870827547618156*^-8,
w -> -2.43876283722217}}}

OK, it seems to be necessary to experiment with this function - let's
speed it up a bit:

z = #1 & ; mi = #1^2 & ; smi = #1^3 & ;
SetAttributes[smi, Listable];
f[x_, om_, w_] :=
1/Sqrt[om*(1 + x)^3 + (1 - om)*(1 + x)^(3*(1 + w))];
rr[1, om_, w_] :=
rr[1, om, w] = NIntegrate[f[x, om, w], {x, 0, 1}];
rr[zz_, om_, w_] :=
rr[zz, om, w] = NIntegrate[f[x, om, w], {x, zz - 1, zz}] +
rr[zz - 1, om, w];
ff[zz_, om_, w_] := 5*Log[10, rr[zz, om, w]*(1 + zz)];
ci = Sum[1/smi[i]^2, {i, 1, Nn}];
chi2f2[(om_)?NumericQ, (w_)?NumericQ] :=
Module[{vec = ((mi[#1] - ff[z[#1], om, w])/smi[#1] & ) /@ Range[Nn]},=

vec . vec - Total[vec/smi[Range[Nn]]]^2/ci];

In[10]:=
Nn = 50;
Timing[NMinimize[{chi2f2[om, w], 0 <= om <= 1}, {om, w}]]
Out[11]=
{17.375*Second,
{0.1492859234785726,
{om -> 5.870827547618156*^-8,
w -> -2.43876283722217}}}

In[12]:=
Nn = 1000; chi2f2[0., -2.5424]
Out[12]=
0.16636080313033652
In[13]:=
NMinimize[chi2f2[0, w], w]
Out[13]=
{0.1663608031303223,
{w -> -2.542400491622037}}
In[14]:= (*let's have a look at om==1*)
NMinimize[chi2f2[1, w], w]
Out[14]=
{0.2821141395387428,
{w -> 704.7500004178966}}
In[15]:=
Nn = 50;
NMinimize[chi2f2[1, w], w]
Out[16]=
{0.2633701352226361,
{w -> 704.7500004178966}}

Are there any expected results?

--
Peter Pein
Berlin

```

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