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Re: Using NIntegrate in a function
Posted:
Mar 7, 2013 10:47 PM


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 nonnumerical 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 nonnumerical 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 nonnumerical 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 welldefined, 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 > > >



