3d data fitting from three 1D vector

Hi

I want to obtained fitting function Delta_n = f(width,gap, thick). I have run the EM simulation of particular device and obtained the value of Delta_n by varying width, gap and thickness. There is no mathematical model that I can use to fit. The data directily came from EM simulations. I have attached the data in case you want to look into it. The data contain three vectors width_j (1x11), gap_i (1x11) and thick_k (1x10), I have stored the value of Delta_n (11 x 11 x 10) using three nested loop as shown below.

delta_n = matrix (length(gap_i),length(width_j),length(thick_k)); 

for (kk=1:length(thick_k))
{
for (ii=1:length(gap_i))
{
    for(jj=1:length(width_j)) 
    {
    delta_n(ii,jj,kk) =  EM Simulation (width_i(jj), gap_j(ii), thick_k(kk)) % I have used third party EM simulator here.
    }}}

I have gone through several MATLAB answer mostly recommends to use scatteredInterpolant or polyfitn. But here I think is the problem data arrangement. Can anyone please help to obtained the fitting function delta_n=f(width,gap,thick)? I can't use cftool interactive app as it only supports only 2D fucntions.

Answer 1

[Ameer Hamza]

You first need to create a grid from the three input variables and then apply scatteredInterpolant

[W, G, T] = ndgrid(width_j, gap_i, thick_k);
Model = scatteredInterpolant(W(:), G(:), T(:), delta_n(:))

[Abi Waqas]

Dear Ameer Hamza

Thank you so much for the response. I really appreciate the help.

The code seems to working. How can I extract the fittting function from it? As I have to use it do further simulation in 3rd party software. Or I can only use it in MATLAB by storing the Model and re-load it every time? Is there any other way to build the function out of it that I can use it every time?

[Ameer Hamza]

I don't think that there is a method to get an equation from it. In fact, it does not even fit a single surface. It uses local interpolation by using neighboring points. The documentation page refers to a research paper, and you may need to study that to see how scatteredInterpolant works.

[Ameer Hamza]

It also does not support code generation, so it seems that Mathworks does not intend it to be interfaced with other software. If you want a closed-form expression, then you need to use the Curve-Fitting toolbox.

[Abi Waqas]

cftool box doesn't not support to fit 3D data. It only works upto 2D data.

[Ameer Hamza]

yes, cftool does not support more than two independent variables, but you can programmatically call fit() function. There is no restriction on the number of independent variables.