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I am trying to numerically evaluate an integral. I have a function to be integrated, ftbI[s,a] with undetermined variable(s) a. I create a function that evaluates the integral, given the value of this variable, i.e. :

FI[a]:=Nintegrate[ftbI[s,a],{s,slower,supper}]

Now, inside of ftbI are other functions. One of these functions is an interpolation between some data points. The integral will integrate up to Inf , so extrapolation will be used, but this is okay.

If I try to evaluate FI[a], the integral gets stuck and doesn't seem to progress. So I try to evaluate just the function ftbI[s,a] at some point, and I get the attached result. Evaluating ftbI

You'll see that there are a bunch of these "interpolatingFunctions" floating around. I am assuming that this is the problem with my Nintegrate. So my question is, what are these interpolatingfunctions? I've tried evaluating the part of ftbI that is the interpolation part that I mentioned above, and it seems to give me a real number anywhere within the region of integration, so I am unclear why my ftbI can't be evaluated properly.

Any guesses as to what is going on here, or things I can try to further explore issue are greatly appreciated. I might be wrong as to the issue of my integration, what I have said is just my guess. Thank you

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    $\begingroup$ A numeric integration requires all variables to have numeric values, e.g., FI[a_?NumericQ] := Nintegrate[ftbI[s, a], {s, slower, supper}] However, the cause of your problems cannot be determined without the appropriate definitions/code. $\endgroup$
    – Bob Hanlon
    Jul 1 at 22:45
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    – bbgodfrey
    Jul 2 at 3:34
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The problem (as seen in the image of the output) is that you are passing a complex number as an argument to an InterpolatingFunction, which is defined only for real inputs.

Example:

Interpolation[Range[5]^2][1 + I]

This returns

Note that InterpolatingFunction does not evaluate to a number, which resembles what appears in the OP's image.

This indicates that the most likely source of the problem is a simple mistake in the definition of ftbI[].

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  • $\begingroup$ I see. Is there any sneaky reason you know of that could cause this? I can't figure out how my function is evaluating at a complex point. The function looks approximately like ftbI[x] =...+ Interpolation[x]+.... I am not using complex numbers at all, and x is a real number that I determine. I can provide more details if interested but I am not sure how useful it would be $\endgroup$ Jul 4 at 19:23
  • $\begingroup$ @PhysicsPerson I don't recall seeing it come up before. So it's either in your code or in a latent definition. (A variable's definition will persist until the kernel is Quit[] or the definition is Clear[]-ed. If that's the problem, quitting and restarting the kernel would fix it, unless the definition is in your init.m file.) $\endgroup$
    – Michael E2
    Jul 4 at 19:57

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