[Octave-bug-tracker] [bug #38063] optim: expfit inaccurate (incorrect)

[Muhali]

URL:
  <http://savannah.gnu.org/bugs/?38063>

                 Summary: optim: expfit inaccurate (incorrect)
                 Project: GNU Octave
            Submitted by: muhali
            Submitted on: Fri 11 Jan 2013 06:15:26 AM PST
                Category: Octave Forge Package
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Inaccurate Result
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: dev
        Operating System: Any

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Details:

I get very bad results from the expfit estimator for exp fitting. The function
has a demo that uses *extremely* low levels of noise. With more realistic
levels the fit becomes useless. In this example


pkg load optim

## expfit
x0 = 0; step = 0.05; xend = 5; x = x0:step:xend;
y = 2*exp(1.3*x)-0.5*exp(2*x);
error = (rand(1,length(y))-0.5)*3e3;
[alpha,c,rms] = expfit(1,x0,step,y+error);

## nonlin_curvefit
fun = @(p,x) p(2)*exp(p(1)*x) ; p0 = [1;-1] ;
[p, fy, cvg, outp] = nonlin_curvefit(fun, p0, x, y+error)

hold on
plot(x, y=y+error, "k.")
plot(x, c*exp(alpha*x), "r-;expfit;")
plot(x, fy, "b-;nonlin_curvefit;")
legend("location", "southwest")
print foo.png


expfit is compared with a more conventional iterative technique, showing the
discrepancies (see attached figure; the demo noise level had to be expanded by
7(!) orders of magnitude).

Apparently expfit is based on Prony's method, a DSP technique similar to
Fourier analysis. Either that method cannot be used for fitting noisy data, or
its implementation in expfit is incorrect. In either case I consider the
expfit function buggy, and recommend not using it.
 



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File Attachments:


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Date: Fri 11 Jan 2013 06:15:26 AM PST  Name: foo.png  Size: 46kB   By: muhali

<http://savannah.gnu.org/bugs/download.php?file_id=27243>

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