help-octave
[Top][All Lists]

## Re: System of ODE - part III

 From: Przemek Klosowski Subject: Re: System of ODE - part III Date: Wed, 3 Oct 2001 15:46:17 -0400

```       Now,  is there a way to have Octave determine values for multiple
initial constants that are part of my model so that a value from one of
the integrated equations can match a specified value? Basically I want
to curve fit the resulting plots to my actual experimental data and have
Octave determine the best values for the constants that would accomplish
this. In the past I have used Excel's SOLVER function to accomplish this
task but wish to know if Octave can do the same thing.

OK, that's an interesting problem. What you need to do is non-linear fitting
of the solution to your set of differential equation to your data. NOrmally,
a nonlinear fitting problem is set up thusly: there's a function F(x;p)
depending
on an independent variable (or several variables) x, and on some parameters p.
You
also have some data Y measured at some points (x1, x2, ... xN).
You
are trying to find a set of parameters that minimizes the difference between
F and your data: the most-often used formula for this difference is called
chi square:

chisq(p) = sum over all Xi  of  (F(Xi;p) - Y(Xi))^2 / (error of Y(Xi))

Note that chi squared is a function of p. Normally, F is some closed function:
e.g. often people fit gaussian peak shapes to data, where p = [A x0 sig] and
F(x;p) = A exp(-(x-x0)^2/sig)

In your case, F(x;p) is a solution of your differential equation, and p are
the coefficients of the equation; it's just a little more difficult technically,
because there's no closed form formula for F in general--but it's the same
concept.

Octave doesn't yet have built-in minimization package.
http://users.powernet.co.uk/kienzle/octave/optim.html lists several choices;
for starters, you could try to use leastsq.m from
http://cvs.sourceforge.net/cgi-bin/viewcvs.cgi/octave/octave/scripts/numeric/optim/

975-6249
NIST Center for Neutron Research (bldg. 235), E111
National Institute of Standards and Technology
Gaithersburg, MD 20899,      USA

-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.

Octave's home on the web:  http://www.octave.org
How to fund new projects:  http://www.octave.org/funding.html
Subscription information:  http://www.octave.org/archive.html
-------------------------------------------------------------

```