Least square curve fitting to 2 -input 1-ouput 2D matrices

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Salman
Salman am 26 Feb. 2016
Hi,
I have two input variables (x1,x2) one output variable (Y) for a model. The function is as follows, Y = a*exp(b*x1) + c*exp(d*x2)
The input-output variables and are all matrices of 400x400 size. I need to determine the coefficients a,b,c,d that best describe the relationship between (x1,x2) and Y. With single input single output, the lsqcurvefit method is straightforward, but I am not finding the right way to deal with 2-inputs.
Here is what I have done so far. Let x1 and x2 be 400x400 matrices which produce a 400x400 Y matrix.
Z = [x1 x2];
fun = @(x,Z)(x(1)*exp(x(2)*Z(:,1:400))+ x(3)*exp(x(4)*Z(:,401:800)));
x0 = [1,1,1,1];
lb = [0 0 0 0];
ub = [10 10 10 10];
x_ans = lsqcurvefit(fun,x0,Z,Y,lb,ub)
I am not sure if I am setting Z correctly and also if this method will work properly as the coefficients are not providing the best fit.
Please advise.
Regards, Salman

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