Local minima of an interpolant fit

Hello, I have a 2d interpolant fit (linear, but any interpolant type will do) for a scatter plot, for which i need to locate the local minimas, meaning multiple minimas. How would one proceed to do that?

Using islocalmin on the plot the fit is fitted on, results in too many false positives.

I was thinking to contruct a function made up of all the coefficients the fit uses to construct the piecewise like fit, but i'm not sure how to do so.

Answer 1

[Torsten]

Pass the evaluating function for the interpolant as objective function to fminsearch or another optimizer (fmincon,...).

E.g.

x = 0:0.02:1;
f = (x-0.5).^2;
fun = @(u)interp1(x,f,u,'spline');
sol = fminsearch(fun,0.1)

sol = 0.5000

[Sh_]

it only returns one minima, i need all of them (there's like 8), and i need to repeat this processes for multiple fits (that's why i dont try to do it manually), do you maybe have another solution?

[Torsten]

Use different guess values (in the above case 0.1) in the neighbourhood of the points where you suspect from visual inspection that the local minima are located.

If this is too much work for you, you will have to ressort to islocalmin or findpeaks(-data).

[Sh_]

I need the process to be automated, such that I dont really need to look at the graph.

[Torsten]

Ok, if you don't want to invest that effort, you will have to stick to the "old" solution.

Or you try "MultiStart" for the optimizer.