       Re: Using NIntegrate in a function

• To: mathgroup at smc.vnet.net
• Subject: [mg130083] Re: Using NIntegrate in a function
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Fri, 8 Mar 2013 06:23:23 -0500 (EST)
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```Dear all,
I am struggling with the following problem, I will explain the problem to you with this simple toy example: I define a function f of a variable a through a numerical integration

f[a_] := NIntegrate[Exp[-((a - 1/3)^2 + 1)*x^4], {x, -1, 1}]

I want to find numerically the maximum of f with respect to a. If I use FindMaximum,

FindMaximum[{f[y], -1 <= y <= 1}, {y, 1/2}]

Then I have some error messages:

NIntegrate::inumr: The integrand E^(x^4 (-1-(-(1/3)+y)^2)) has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,1}}. >>

NIntegrate::inumr: The integrand E^(x^4 (-1-(-(1/3)+y)^2)) has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,1}}. >>

NIntegrate::inumr: The integrand E^(x^4 (-1-(-(1/3)+y)^2)) has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,1}}. >>

General::stop: Further output of NIntegrate::inumr will be suppressed during this calculation. >>

Still, in the end I have got the correct result {1.68968, {y -> 0.333333}}.  NMaximize gives the same error messages.

I have a more complicated example where I have a numerical routine (NDSolve) that needs some parameter q as an input and that is incorporated into a function g[q], just like in the toy example the numerical routine NIntegrate needs the parameter a, and NIntegrate is incorporated into the function f[a]. In this more complicated example, I have got the same kind of complaints, NDSolve::ndnl: "Endpoint q in {x,q,qp} is not a real number.", but in the end when I call NMaximize of FindMaximum to maximize g with respect to q, it crashes and I have got no useful output. Still, the function g[q] is well-defined, and when I call it for any numerical value of q I obtain a number and everything is fine.

Do you have any ideas on how to fix this?

Thanks!
Best
Michele

Hi, Michele

I checked your operators and they worked for me (PC WinXP, Math 9.0.1.0):

f[a_] := NIntegrate[Exp[-((a - 1/3)^2 + 1)*x^4], {x, -1, 1}]
FindMaximum[{f[y], -1 <= y <= 1}, {y, 1/2}]

{1.68968, {y -> 0.333333}}

Without error messages. However, you might try also this:

lst = Table[f[a], {a, -1, 1, 0.01}];
Max[lst]

1.68967

Have fun, Alexei

Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
Office fax:       +352-2454-3566
mobile phone:  +49 151 52 40 66 44

e-mail: alexei.boulbitch at iee.lu

```

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