Date: Mar 7, 2013 10:47 PM Author: Bob Hanlon Subject: Re: Using NIntegrate in a function The function f can only be evaluated if its argument is numeric since

it uses a numerical technique (NIntegrate); consequently, restrict its

definition to numeric arguments.

f[a_?NumericQ] :=

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

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

{1.68968, {y -> 0.33333}}

Whereas,

f2[a_] = Integrate[Exp[-((a - 1/3)^2 + 1)*x^4], {x, -1, 1}];

FindMaximum[{f2[y], -1 <= y <= 1}, {y, 1/2}]

{1.68968, {y -> 0.333333}}

Bob Hanlon

On Thu, Mar 7, 2013 at 3:58 AM, <michele.castellana@gmail.com> wrote:

> 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

>

>

>