# I tried to show effect of uncertain parameters on bi-variate function with color map and aslo highlight changes to max and min,I am not sure the function I wrote is right!!!

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sogol bandekian on 21 May 2022
Commented: sogol bandekian on 24 May 2022
for i=1:length(x)
x=lhsdesign(10,1,"iterations",2);
for j=1:length(y)
y=lhsnorm(50,10,10,"on");
Z=[x,y];
Z(i,j)=2.*x(i).^3+y(j).^3-3.*x(i).^2-12.*x(i)-3.*y(j);
end
end
options = optimset('Display','iter','PlotFcns',@optimplotfval);
x0=[x(1),y(1)]
[xmin,fval]=fminsearch(@(xy)Z(xy(1),xy(2)),x0,options); %min
[xmax ,fval]=fminsearch(@(xy) -1 *Z(xy(1),xy(2)),x0,options); %max
[X,Y]=meshgrid(x,y);
surf(X,Y,Z(i,j),'EdgeColor',"interp","FaceAlpha",0.5);
hold on
plot(xmin(1),xmin(2), f(xmin(1),xmin(2)),'MarkerSize',6);
hold on
plot(xmax(1),xmax(2), f(xmax(1),xmax(2)),'MarkerSize',6);
hold off
xlabel("optimum valeus for x")
ylabel("optimum valeus for y")
colormap(parula(6));%default colormap with 6 colors
colorbar
can anyone help me for correcting this function?
Torsten on 23 May 2022
No. It's a search for a minimum or maximum of a functrion on a discrete set of (x/y) values. The function is evaluated on a (fine enough) grid and the point where this evaluation is minimal (or maximal) is taken as the minimum (or maximum) of the function. It's an alternative to fminsearch and other optimizers if the region where minimum (or maximum) is is approximately known and if the function is badly behaved (not differentiable etc).

Walter Roberson on 22 May 2022
y=lhsnorm(50,10,10,"on");
[xmin,fval]=fminsearch(@(x)Z(x,y),x0,options) %min
The y referred to there is being "captured" from the workspace variable y which is the lhsnorm that you defined earlier.
With y being non-scalar, your multinomial Z function is going to return multiple values for each input x value, but for fminsearch you need to return a vector.
Perhaps what you need is
[xmin,fval]=fminsearch(@(xy)Z(xy(1),xy(2)),x0,options) %min
sogol bandekian on 24 May 2022
thank you so much