fitting equation with condition on 1 parameter

I have to fit an equation over my data. Equation has two unknows parameters to be found i.e a and b...but if i deliberately want that the b value should lie betweem 0.2 and 2 and then find 'a' and 'b'...how can i do that???

Answer 1

[Matt J]

Here is a simple script for fitting a Gaussian f(z) = a*exp(-b*z^2) using LSQCURVEFIT subject to bounds a>=0, 0<=b<=7. You should run it, study it, and adapt it to your needs.

f=@(p,z) p(1)*exp(-p(2)*z.^2); 

   x=linspace(0,2,10); 
   y=f([1,2],x)+rand(size(x))/10; %simulated data

p=lsqcurvefit( f, [.5,.5], x,y, [0,0],[inf,7]); %perform fit

   plot(x,y,'*', x, f(p,x)) ;

You should also, of course, read "doc lsqcurvefit" to understand the input syntax and know what additional options you have.

[aditi]

thanks matt...

but could u please explain the equation :

p=lsqcurvefit( f, [.5,.5], x,y, [0,0],[inf,7]);

what is [.5,.5] and if i dont want to give any condition for a???

[Matt J]

[.5,.5] is my initial guess of the parameters. You should see an explanation of that in "doc lsqcurvefit".

Bounds on individual parameters can be set to inf and -inf if you effectively want them unconstrained. You can see in my example that I set upper and lower bounds on a of 0 and inf, meaning that a is not bounded from above, but is constrained to be >=0.

[aditi]

hey matt... oh okay....i tried this...n found almost d correct results...i will try for other data sets...thanks a lot

but 1 thing...when we plot its showing discontinous curve...how to smoothen it...i mean like in cfools we get the smooth fit curve...similarly how to do here???

[Matt J]

The curve isn't discontinuous. You're just not plotting it at very many points.

[aditi]

ha right...i meant that only... so how to smoothen it...??

[Matt J]

Plot at more densely spaced points.

[aditi]

I have only 5 data points...for x and y...so how to plot both the data points and fit curve both(the smoothed one) on the same plot...

Answer 2

[Amit]

You can use fmincon.

I would think that these a and b are from you previous post, where fminsearch were used. fmincon is similar to fminsearch but support bounds. More details on fmincon is here http://www.mathworks.com/help/optim/ug/fmincon.html

[aditi]

hey amit...yes...the same question... could you plz explain it according to my problem plz...as u know the problem completely ...

[Matt J]

lsqnonlin or lsqcurvefit would be better, if the only constraints are bounds.

[Amit]

Actually MAtt's idea is better.

[aditi]

Matt could you please explain how to use it...

Answer 3

[Alan Weiss]

There are some documentation examples that show how to fit equations. Adding bound constraints is easy for lsqnonlin or lsqcurvefit.

Nonlinear Data Fitting

Nonlinear Curve Fitting with lsqcurvefit

Hope this helps,

Alan Weiss

MATLAB mathematical toolbox documentation