Exp Fit Error: Inf computed by model function, fitting cannot continue. Try using or tightening upper and lower bounds on coefficients.

I have successfully fit multiple similar sets with no problem but the attached data gives the error in the title. I tried fitting both first and second order exponentials but they both fail. If anyone can tell me what to do to resolve this I would greatly appreciate it.

Answer 1

[John D'Errico]

You need to look at your data. THINK about what is happening. Don't just throw a modeling tool at it and expect magic to always work.

[min(x),max(x)]
ans =
       1.3776       1.3811

So your data is over a TINY range. But exponentials tend to have problems with huge numbers. So you also need to be VERY careful as to the multiplier of x in there.

min(y)
ans =
      -6.4096

If you plot log(y - 6.45), as a function of x, except for some crap down at the bottom, the fit is pretty good. So a simple exponential model will do pretty well, IF you are careful.

polyfit(x,log(y + 6.45),1)
ans =
      -1514.5       2091.1

This tells us that a model something like this is a good idea.

y = a + b*exp(-c*(x-1.38))

where a good starting value for c is approximately 1500.

I've subtracted 1.38 off, since exp(-1500*1.38) will fail in double precision. This is surely why you are having problems. Well, it does not fail. But it underflows. You get a pure zero as a result.

exp(-1500*1.38)
ans =
     0

So you very much need to shift the problem. If you do that, and then use 1500 as a starting value for the multiplier, you can get a model of

y = -4.208 + 2.0602*exp(-1670.7*(x-1.38))

This fits your data fairly well.

plot(x,y,'o',x,-4.208 + 2.0602*exp(-1670.7*(x-1.38)),'b-')

So, hey, you don't need to do these things. But if you want to find a valid model that fits your data, it is a good idea. Otherwise, garbage will result.

[Craig Siebe]

Thank you so much for your reply John D'Errico. Sadly I don't know much about curve fitting.

Mostly I wanted to create a smooth curve to help define the widths of hundreds of impulse response peaks inside a code.

[halo]

Can you explain the logic behind how you are deriving your inferences like 1500 is a good starting point for c?