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Re: Non linear model fitting with an integral model

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  • Subject: [mg125427] Re: Non linear model fitting with an integral model
  • From: Darren Glosemeyer <darreng at>
  • Date: Tue, 13 Mar 2012 03:07:55 -0500 (EST)
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On 3/12/2012 4:07 AM, Juan Baselga wrote:
> Hello, I'm new user of Mathemetica. I'm trying to fit data to a model, that is defined by an integral, using NonlinearModelFit. The integral contains the parameter I'm looking for. When I set a particular value for the parameter, NIntegrate works well giving an estimate of the integral value; but when I define the model within the fitting algorithm, the integral cannot be numerically evaluated since it contains the non-numerical parameter giving the "inumr" error message. Do anyone know how to fit data with model parameters contained in an integral that must be numerically evaluated?

The place to start is using a definition for the model that will only 
evaluate when all quantities that need to be numeric are numeric. 
Compare the results when using f1 and f2 in the following:

data = Table[{i, i^2/2}, {i, 5}];

f1[a_, y_] := NIntegrate[a*x, {x, 0, y}]

f1[a, y]

NonlinearModelFit[data, f1[a, y], a, y];

f2[a_?NumericQ, y_?NumericQ] := NIntegrate[a*x, {x, 0, y}]

f2[a, y]

NonlinearModelFit[data, f2[a, y], a, y]

?NumericQ restrictions like those in f2 are most likely what you need in 
your example.

Darren Glosemeyer
Wolfram Research

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