# How to write function for two variables

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Faizan Lali on 22 Feb 2023
Commented: Faizan Lali on 23 Feb 2023
I am trying to write down the function to predict "y" having two independent variables "x1 & x2". Here is my code for the function;
function y=Project_func(beta0,x1,x2)
y=100./(1+exp((-beta0(1).*(-2.4-(39.7*(1+x1).^(-2.8))))+(beta0(2).*(-2.4-(39.7*(1+x1).^(-2.8))).*log10(100.*x2))));
end;
but once I run the code it does not spit the y values as desired because I have predicted values taken from the excel. I want to solve it in the Matlab. Here are the equations. C1 & C2 are parameters having intial guess.
Faizan Lali on 23 Feb 2023
Yeah, i am sorry for not providing the data vectors, as data sheet is kind a mess and you wont understand untill explain. i can attach excel sheet and my code for you if you want, but let me explain to make it clear.
Xp vector is 50x50x2, means it contains two parameter of the functions. Now I want to plot each parameter Xp1 and Xp2 against two variables X and Y. Also I want to plot function value as Z above them. So total of 3 surfaces on a meshgrid against X and Y. I did it by another way i can share the part of code and the figure for your reference.
So normally in 2D handle option works well while plotting over each other and then playing with the properties of the figure as you mentioned, but I am not sure how it will work for meshgrid.
Moreover, once I go to change the color scheme for each surface generated it dosen,t let me do it.
Now I figure it out this way
ypred=fnameFOR(beta0,X,Y);
Xp1=Xp(:,:,1);
Xp2=Xp(:,:,2);
figure;
mesh(X,Y,Xp1);
hold on
mesh(X,Y,Xp2);
mesh(X,Y,ypred);
legend('\beta_1*\partialY/\partial(\beta_1)','\beta_2*\partialY/\partial(\beta_2)','Y');
xlabel('X'); ylabel('Y'); zlabel('Parameters and Z');

dpb on 22 Feb 2023
I'd approach writing the functional something more like--
function y=Y(C,x1,x2)
% Magic function Y=fn(C, x1, x2) from unknown source
% C is 2-vector of C1, C2 per Eqn 1
C1=C(1); C2=C(2); % convenience in writing expression w/o subscripts
C2S=@(x) -2.40874-39.748*(1+x).^-2.856; % define C2* as anonymous function(x)
y=100./(1+exp(-C1.*C2S(x1)+C2.*C2S(x1).*log10(100*x2))); % the function (x1,x2) for input C
end;
If we had the experimental or other data, be interesting to see how well it would fit...but, we're pretty much hamstrung at this point.

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