Find Coefficients of an equation

Hi, I have a table containing 3 columns of data. I also have an equation with 4 unknown coefficients. How do I fit/solve the equation using the table data to obtain the unknown coefficients using Matlab?

Thanks!

[Torsten]

Why three columns and not two ? Do you have two independent variables in your equation:

column3 = f(column1,column2) 

?

[Learning]

Thanks for responding. Yes I have 2 independent variables.

Answer 1

[Star Strider]

Using two independent variables is relatively straightforward. You need to concatenate them, then refer to them individually inside the objective function.

Data = randn(10,3);
objfcn = @(b, xy) b(1).*exp(-((xy(:,1)-b(2)).^2+(xy(:,2)-b(3)).^2)*b(4));
xy = Data(:,[1 2]);
[B,resnrm] = fminsearch(@(b)norm(Data(:,3) - objfcn(b,xy)), rand(4,1))

 
Exiting: Maximum number of function evaluations has been exceeded
         - increase MaxFunEvals option.
         Current function value: 2.628093 

B = 4×1

-2.9726 1.7228 0.1193 9.6214

resnrm = 2.6281

N = 25;
x = linspace(min(Data(:,1)), max(Data(:,1)), N);
y = linspace(min(Data(:,2)), max(Data(:,2)), N);
[X,Y] = ndgrid(x,y);
fitfcn = @(b,X,Y) b(1).*exp(-((X-b(2)).^2+(Y-b(3)).^2)*b(4));
Z = fitfcn(B,X,Y);

figure
scatter3(Data(:,1), Data(:,2), Data(:,3), 'filled')
hold on
surf(X, Y, Z, 'FaceAlpha',0.5)
hold off
colormap(turbo)

This is a random example.

.