Find Coefficients of an equation

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Learning
Learning on 18 Feb 2024
Answered: Star Strider on 18 Feb 2024
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!
  2 Comments
Torsten
Torsten on 18 Feb 2024
Why three columns and not two ? Do you have two independent variables in your equation:
column3 = f(column1,column2)
?
Learning
Learning on 18 Feb 2024
Thanks for responding. Yes I have 2 independent variables.

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Answers (1)

Star Strider
Star Strider on 18 Feb 2024
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.
.

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