NIntegrate::inum continued

• To: mathgroup at smc.vnet.net
• Subject: [mg59119] NIntegrate::inum continued
• From: wtplasar at lg.ehu.es
• Date: Fri, 29 Jul 2005 00:42:01 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

I have these code which is a modification on a code which was improved
by one of the mathgroup members (see the original message below). When
I evaluate it a get a Recursion Limit problem. Can you help me?

In[1]:=
datanw={{0.04`,36.38`,0.19`},{0.05`,36.84`,0.21`},
{0.0307`,35.9`,0.2`}};

In[2]:=
ndat=3;

In[3]:=
Nn = ndat;

In[4]:=
z =datanw[[#1,1]]  & ; mi = datanw[[#1,2]] & ;
smi =datanw[[#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];

Para: mathgroup at smc.vnet.net
Asunto: NIntegrate::inum
De: <wtplasar at lg.ehu.es>
Fecha: Thu, 28 Jul 2005 02:35:51 +0200 (CEST)

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 ¡Ü om ¡Ü 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}}}