Re: Using NIntegrate in a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg130071] Re: Using NIntegrate in a function*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Thu, 7 Mar 2013 22:50:22 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20130307085836.EF08A6468@smc.vnet.net>

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 at 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 > > >

**References**:**Using NIntegrate in a function***From:*michele.castellana@gmail.com