Fitting data in x,y to a known function

Hi everyone. I have a function that is f = 1/(a+b*x) where a and b are the values to obtain and I have some data:

x1 = linspace(1,32,32);
y1 = [0.01 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.04 0.04 0.05 0.05 0.06 0.07 0.07 0.08 0.10 0.11 0.14 0.14 0.17 0.17 0.16 0.21 0.31 0.31 2.43 2.43 29.53 29.53 29.53];

I need to fit these two variables x1 and y1 into the function above to obtain a and b. How can I do this?

I'm sorry I'm pretty new in Matlab. Thank you.

Answer 1

[Star Strider]

Use the fminsearch function to fit your data:

x1 = linspace(1,32,32);
y1 = [0.01 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.04 0.04 0.05 0.05 0.06 0.07 0.07 0.08 0.10 0.11 0.14 0.14 0.17 0.17 0.16 0.21 0.31 0.31 2.43 2.43 29.53 29.53 29.53];

f = @(p,x) 1./(p(1) + p(2).*x);

P = fminsearch(@(p) norm(y1 - f(p,x1)), rand(2,1));

x1v = linspace(min(x1), max(x1));

figure
plot(x1, y1, 'p')
hold on
plot(x1v, f(P,x1v), '-r')
hold off
grid

producing:

P =
   0.845464263829100
  -0.025490734971736

where ‘P(1)=a’, and ‘P(2)=b’.

The plot appears correct, even though it looks a bit strange.

[Raúl Alonso Merino]

Thank you so much. It worked as I wanted!

[Star Strider]

As always, my pleasure!

Answer 2

[Nicolas B.]

If you have it, I would recommend to use the Curve Fitting Toolbox. You can give it the expected function and it fits the parameters.

Otherwise, the only solution would be to yourself try to fit the function on the samples based on an optimization method but that requires to investigate mathematic fitting.

[Raúl Alonso Merino]

I tried and I get a fitted curve, thank you.

General model:
     myfit(x) = 1/(a+b*x)
     Coefficients (with 95% confidence bounds):
       a =      0.9058  (0.4335, 1.378)
       b =    -0.02738  (-0.04219, -0.01256)

My question now is: is it correct to fit it directly to that function or do I have to fit it to the integral of 1/(a+b*x) which is log(a+b*x)/b + c?