Best matlab curve fitting functions?

I have the following set of data:

x=[0 .1579 .3158 .4737 .6316 .7895 .9474 1.1053 1.2632 1.4211 1.5789 1.7368 1.8947 2.0526 2.2105 2.3684 2.5263 2.6842 2.8421 3]';
fx=[-.3637 .3164 -1.1263 -1.0672 .1076 1.8249 -.1899 1.3484 1.2583 3.2179 1.7378 3.6954 5.1611 6.7646 8.3733 8.1898 7.9968 10.2402 11.5248 16.6505]';

I have to fit a curve to this data, without using matlabs curve fitting toolbox. What are the best built in matlab functions to fit data like this?

Answer 1

[Star Strider]

There are three other functions you can use to fit nonlinear data: nlinfit (Statistics Toolbox), lsqcurvefit (Optimization Toolbox), and fminsearch (built-in MATLAB function).

Do you have a model you want to fit? (It looks like a noisy exponential function, but the process that created it dictates the model you fit to it.)

[the cyclist]

... or polyfit if you want to assume that fx is a polynomial function of x.

[Andrew]

No, I just have the data provided. I've used polyfit, interp1, and regress already.

[Image Analyst]

What do you want once you're all done: a formula (equation), or a smoothed or interpolated set of numbers? If you want numbers, you can use Savitzky-Golay (Signal Processing Toolbox) or conv() (base MATLAB) - either will smooth the data. If you want a formula you can use polyfit to get coefficients, and then use polyval to get actual numbers.

[Andrew]

I want a curve that somewhat accurately fits the curve. It doesn't have to be exact, but the closer the fit the better. I just can't use the curve fitting toolbox.

[Star Strider]

This produces an acceptable fit:

x=[0 .1579 .3158 .4737 .6316 .7895 .9474 1.1053 1.2632 1.4211 1.5789 1.7368 1.8947 2.0526 2.2105 2.3684 2.5263 2.6842 2.8421 3]';
fx=[-.3637 .3164 -1.1263 -1.0672 .1076 1.8249 -.1899 1.3484 1.2583 3.2179 1.7378 3.6954 5.1611 6.7646 8.3733 8.1898 7.9968 10.2402 11.5248 16.6505]';

fitfn = @(b,x) b(1).*exp(b(2).*x)+b(3);
B0 = rand(3,1);
B = nlinfit(x, fx, fitfn, B0);

figure(1)
plot(x, fx, 'pb')
hold on
plot(x, fitfn(B,x), '-r')
hold off
grid

The ‘B’ vector are the estimated parameters. If you need statistics on the parameters or the fit, you can ask nlinfit for the appropriate outputs and use nlparci and nlpredci. You can also use fitnlm with ‘fitfn’ and get even more statistics as part of the process without having to do anything else.

[Andrew]

That's what I was looking for. Thanks a lot

[Star Strider]

My pleasure!

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