MATLAB: Error calculation perfect fit

matlab error fit

Hi guys, so I have experimental data in column matrix y. And I want to use the equation below to find x as a function of y. This means have constant b adjusted from 0 to 2 and hence want to obtain the ideal b value.

I'm thinking of using a double for loop however would anyone know how to calculate for error and set a desirable tolerance. Or tips on how to solve for it effectively?

Thanks in advance. The equation is:

y= (1-0.05*x^(b))/(1-0.03*x^b)^2

Best Answer

I would use nlinfit and nlparci to estimate ‘b’, and use a few values of ‘x’ and ‘y’ to provide an initial estimate, with:

b = log(20*(1-1./y))./log(x);

Noting the assumptions and restrictions that I mentioned earlier.

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MATLAB: Fit 2 parameters with fminsearch and use ODE15s to solve single differential equation

Using that model of the Gompertz equation, your code is correct.

If you want to avoid negative rate constants, use lsqcurvefit instead, with constraints on the lower limits of the parameters:

B = lsqcurvefit(@fit_GompModel, p0, t, y, [0 0])

producing:

B =
          68.5834500164402
      6.38601980323603e-12

This give a straight line, however that is likely the best you can do. I doubt that ga (genetic algorithm) or other solvers will produce any different result, although I did not try them.

MATLAB: Fsolve interchangeable with nlinfit, but how

It’s not exactly interchangable, however it’s possible to use it to estimate the parameters.

Example —

x = linspace(0, 10, 10);
y = exp(x.*0.2)+randn(size(x))/10
objfcn = @(b,x) b(1) + b(2).*exp(x.*b(3));
B = fsolve(@(b) norm(y - objfcn(b,x)), rand(3,1));
figure
plot(x, y, 'p')
hold on
plot(x, objfcn(B,x), '-r')
hold off
grid
text(1.5,6,sprintf('y = %.3f + %.3f\\cdote^{%.3f\\cdotx}',B))

producing (with this set of random values):

Experiment with this approach with your own data.

Best Answer

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MATLAB: Fit 2 parameters with fminsearch and use ODE15s to solve single differential equation

MATLAB: Fsolve interchangeable with nlinfit, but how

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