```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 sinceit uses a numerical technique (NIntegrate); consequently, restrict itsdefinition 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 HanlonOn 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>>>
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