# Evaluation of self-defined functions

I defined a function that I call disc which I want to minimize later. The function is defined as

disc[dt_]:=Total[(Log[vDat] - Log[(x'[tDat -dt] /. nsol)])^2]


and it quantifies the discrepancy between measured data (the time series {tDat,vDat}) and the solution to a differential equation that was obtained with NDSolve.

My problem is that this function works great sometimes:

but fails in other applications:

I tried hard to get to the bottom of this, but I just can't understand what's wrong. Suggestions?

Clarification: disc[1] returns a number and not a {number}.

• Change the definition of disc[]: disc[dt_?NumericQ] := (* stuff *). Aug 14, 2012 at 10:24
• Yes, I was thinking of something else, so I removed that section. Unfortunately, I don't think we can be more helpful unless you at least show us your tDat, vDat, and nsol... Aug 14, 2012 at 10:34
• A general remark is that defining functions which implicitly depend on global variables is, for most cases, a recipe for disaster. It may be also the case for your function. Check this answer for more details. Aug 14, 2012 at 11:11
• Thanks for this remark. I know that, and my function is actually disc[sol_,dt_] and I have to give it the interpolating function too. I omitted that in the post for clarity. Aug 14, 2012 at 11:26
• Always try to post a running (and minimal) example of your problem. Otherwise you most probably will get right answers for the wrong problem Aug 14, 2012 at 12:03

I think the problem is that you use the same variable symbol for the function returned by NDSolve and for the functions Plot and FindMinimum.

Here is a simplified example I tried. This is just an example equation from the documentation:

nsol = First@NDSolve[{x'[t] == x[t] Cos[t + x[t]], x[0] == 1}, x, {t, 0, 30}]


Here is a minimal definition of disc that demonstrates the problem:

disc[dt_] := x'[dt] /. nsol


Using the variable t the functions Plot and FindMinimum work fine:
But using the variable x (the same name as the function solved for by NDSolve) I get similar problems to what you got: