Matlab - Curve Fitting Data using lsqcurvefit

07 Dec 2007 Quan Quach 29 comments 13,257 views

Example 1: A Simple 3rd Order Polynomial

In this tutorial, you will learn how to perform a curve fit for nonlinear data using the lsqcurvefit command. This curve fit is performed by minimizing the sum of the error squared. This tutorial will go over two different examples. The first example involves a polynomial function, and the second example involves an asymptotic function. Let’s start with the first example, which consists of a 3rd degree polynomial. (Note: It’s possible to use the polyfit command, but we won’t be doing that here.)

The sample data for this example is shown in the scatter plot below. The goal is to fit the most accurate curve through these data points.

Sample Data

In this example we know beforehand what the model is, but sometimes you might not know this and you may have to propose your own model. This data is characterized by the following equation:

Polynomial Equation

Information we know: the x data and the y data.

Information we do NOT know and wish to find out: the parameters a, b, c, and d.

How can we go about finding this information? Continue onto the next section to find out.

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29 Responses to “Matlab - Curve Fitting Data using lsqcurvefit”

on 20 Jan 2008 at 12:55 pm 1Hong

Thank you so much for this page. Its really helped me out!

All the best in the future,
Hong.
on 23 Jan 2008 at 12:08 pm 2voytek

Quan,

Thanks a lot for putting this tutorial up. It is very robust in the sense that anybody using it for any kind of fitting is able to benefit from it.

Great job.

-voy
on 20 Feb 2008 at 12:34 pm 3Sara

Thanks so much!!!I was looking for an example like that!

;^)
Sara
on 27 Feb 2008 at 9:37 am 4san

thanks a lot
it was very helpful
on 20 Mar 2008 at 6:54 am 5Stephen

matlab gives the value of a certain parameter

can it tell you the error in this parameter?
on 10 Apr 2008 at 6:54 am 6Giovanni

hi

I am very grateful to you.
Your example was very helpful for my data fitting

cheers

Giovanni
on 23 May 2008 at 3:15 am 7Frederic Moisy

Hi,
Perhaps some of you will be interested in
“EzyFit - A free curve fitting toolbox for Matlab”,
check http://www.fast.u-psud.fr/ezyfit/
Comments are welcome!
Frederic Moisy
on 11 Jun 2008 at 9:38 am 8sathya

Is it right to use lsqcurve fit for Gaussian equation of the form

a*exp(b-x) + a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)
on 05 Aug 2008 at 12:47 pm 9darkspirit

I think the line [newParameters,error] = lsqcurvefit(@myCurve, initialConditions,Vin,Vout);
should actually be [newParameters,error] = lsqcurvefit(@limiter, initialConditions,Vin,Vout);
on 05 Aug 2008 at 1:31 pm 10Quan Quach

Darkspirit,

I think you’re right. I have changed the post to reflect thec hange.

Quan
on 05 Aug 2008 at 4:16 pm 11kerry

as Stephen said:

matlab gives the value of a certain parameter

can it tell you the error in this parameter?

please email me if you have the answer. thanks a lot!!!
on 05 Aug 2008 at 5:53 pm 12Quan Quach

kerry,

it only returns the residual error (that is, the sum of the error squared).

Quan
on 08 Aug 2008 at 6:35 am 13d.

Thanks so much for the helpful post. Hope all blogs were this useful.
Cheers
on 27 Aug 2008 at 9:53 am 14Marcio

Please, dear friends

tell me how to perform parameter estimation in a ode system like this:

dy1/dt = a*y1 - b*y2 + c

dy2/dt = y1*y2 - a

I have both vectors, y1 and y2, how do I find a, b and c. What function should I use.

thank you in advance
on 25 Sep 2008 at 11:55 am 15venkar

Hey thanks a lot for the information but can u tell me what is happening with my code i gave some initial conditions and it isn’t working.

“No improvement in search direction: Terminating.”

i used a 6th order equation for 6th order equation
on 25 Sep 2008 at 2:49 pm 16Quan Quach

venkar,

it looks like your initial conditions might be too far off or something is not right with your equation so it is not able to do the curve fit. try adjusting your initial conditions to see if it garners any improvement,

Quan
on 04 Oct 2008 at 12:47 pm 17ased

can i use ”lsqcurvefit” to find the optimal values
for the parameters (tx,ty,sx.sy,θ,v) that appear in the following function:

g(x,y)=(1/(2*pi*sx*sy))*exp(-0.5*[(x'/sx)^2+(y'/sy)^2])*sin(2*pi*v*x’) ,with

x’=cosθ(x-tx)-sinθ(y-ty)
y’=sinθ(x-tx)+cosθ(y-ty) ?

Thanks for your help.
on 14 Oct 2008 at 3:09 pm 18Murat

I have the following code as a Function Argument of the lsqcurvefit. In the equation, there is 100.5 which I want to change. I want to supply that value to following function as an input but when I try to do this it gives error inside the lsqcurvefit. Is it possible to do?
```
 
function speed = equation (initialGuess, time)
B = initialGuess(1);
t0 = initialGuess(2);
 
% Equation which is our model to represent the data
speed = (100.5 / B) * tan( ( 1 - time/t0 ) * atan(B) );
```
on 06 Jan 2009 at 1:53 pm 19Tom Pham

Quan,

If x,y and z are known, will lsqcurvefit be able to find the coefficients (a,b,c,d,e,f) for the following 3D surface?

z(x,y) = a*x^2 + b*y^2 + c*xy + d*x + e*y + f

Any help is much appreciated!

-Tom
on 23 Feb 2009 at 5:35 am 20Tommy

Great explanation of how to do the curvefit, it really helped me out alot!

Thanks,

Tommy
on 05 Mar 2009 at 4:05 am 21glow

hi,

thank you it was helpful but i am using the lsqcurvefit but i am getting some errors can i email you my code ?
on 05 Mar 2009 at 4:06 am 22glow

hi,

thank you it was helpful but i am using the lsqcurvefit but i am getting some errors can i email you my code ? its urgent… :/
on 05 Mar 2009 at 9:32 am 23glow

how do i find a single maximum and minimum value of the fitted curve?
on 11 Apr 2009 at 11:59 am 24Matt

Thanks a lot for a great explanation. This has helped me out quite a bit.

Is there a way to turn off the output of the message:

Optimization terminated: first-order optimality less than OPTIONS.TolFun, and no negative/zero curvature detected in trust region model

?

I’m trying to use lsqcurvefit to loop over several datasets and having the message repeated a few thousand times is not great.

Thanks again for a great post.
on 11 Apr 2009 at 12:14 pm 25Matt

Ok, nevermind. I figured out how to use the options.Display option to get it to turn off output. I was just having trouble because I was trying to use
```
 
x = lsqcurvefit(fun,x0,xdata,ydata,options)
```
but after reading this in MATLAB help (I must have missed it the first time):

x = lsqcurvefit(fun,x0,xdata,ydata,lb,ub,options) minimizes with the optimization options specified in the structure options. Use optimset to set these options. Pass empty matrices for lb and ub if no bounds exist.

I corrected myself and included empty matrices for lb and ub and it worked.

Thanks again and thanks anyway.
on 19 Apr 2009 at 8:57 pm 26spacex

You’re a life saver, bud. Thanks for the well written tutorial!
on 15 May 2009 at 7:02 am 27glow

hello,

i tried the following code:

B = lsqcurvefit(@polsin,A,polang,intensityy,[0 -255 -2*pi],[255 255 2*pi],optimset(’Display’,'off’));

and got this error

??? Error using ==> lsqncommon at 134
Function value and YDATA sizes are incommensurate.

Error in ==> lsqcurvefit at 186
[x,Resnorm,FVAL,EXITFLAG,OUTPUT,LAMBDA,JACOB] = …

Error in ==> newnew at 164
B = lsqcurvefit(@polsin,A,polang,intensityy,[0 -255 -2*pi],[255 255
2*pi],optimset(’Display’,'off’));
bye
on 09 Jun 2009 at 2:22 am 28Aisling

Hi,

Great tutorial! Does anybody know of a way of changing the optimisation criteria? as in, instead of the routine solving for the minimum sum of errors squared, solving it for say the relative error?

Thanks!
on 01 Sep 2009 at 10:04 am 29sz

Hi,
Do you know how to write code for a data set with a curve that goes back on itself? Over time, there is 2 x-points for the same line because it’s like a ‘S’ curve. Any ideas how to take the lower value?

Thanks.

Include MATLAB code in your comment by doing the following:

<pre lang="MATLAB">

%insert code here

</pre>

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