How to find max and min of fuction of 2 independent variables?

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Faris Hajdarpasic 2019-2-20

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/446105-how-to-find-max-and-min-of-fuction-of-2-independent-variables

评论： Walter Roberson 2019-2-21

采纳的回答： Asad Mirza

在 MATLAB Online 中打开

My question is how can I find minimum and maximum of this function, and then tag them with 'o' in function graph?

This is my code so far:

   function funkcija(intervalpox,intervalpoy,korak,crtanje)
    x=0:korak:intervalpox;
    y=0:korak:intervalpoy; 
    [X,Y] = meshgrid(x,y);
    Z = (sin(sqrt(X.^2 + Y.^2)) ./ (sqrt(X.^2 + Y.^2)));
        mesh(X,Y,Z)
        grid on
        xlabel('.x.')
        ylabel('.y.')
        zlabel('.z.')
        title('mesh')

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Faris Hajdarpasic 2019-2-20

编辑：Faris Hajdarpasic 2019-2-20

But what if i want it on plot3?

Walter Roberson 2019-2-21

在 MATLAB Online 中打开

[~, location_of_max] = max(Z(:));
[~, location_of_min] = min(Z(:));
x_at_max = X(location_of_max);
y_at_max = Y(location_of_max);
z_at_max = Z(location_of_max);
x_at_min = X(location_of_min);
y_at_min = Y(location_of_min);
z_at_min = Z(location_of_min)
plot3(x_at_max, y_at_max, z_at_max, 'go', x_at_min, y_at_min, z_at_min,'r+');

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采纳的回答

Asad Mirza 2019-2-20

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/446105-how-to-find-max-and-min-of-fuction-of-2-independent-variables#answer_361955

在 MATLAB Online 中打开

You could use a similar formulation as found here.

What it boils down to is using imregionalmax on your Z matrix to find the local maximums.

MaxVals = find(imregionalmax(Z));
plot3(X(MaxVals),Y(MaxVals),Z(MaxVals),'ro','MarkerSize',30)

Now this will find you your local maximums but to find the minimums you could just flip Z upside down and then run imregionalmax again.

Zupsidedown=-Z;
MinVals = find(imregionalmax(Zupsidedown));
plot3(X(MinVals),Y(MinVals),Z(MinVals),'go','MarkerSize',30)

This will allow you to find the local max and mins across the entire surface.

clear;clc;close all
korak=.1;
intervalpox=10;
intervalpoy=10;
x=korak:korak:intervalpox;
y=korak:korak:intervalpoy;
[X,Y] = meshgrid(x,y);
Z = (sin(sqrt(X.^2 + Y.^2)) ./ (sqrt(X.^2 + Y.^2)));
Zupsidedown=-Z;
MaxVals = find(imregionalmax(Z));
MinVals = find(imregionalmax(Zupsidedown));
plot3(X(MaxVals),Y(MaxVals),Z(MaxVals),'r.','MarkerSize',30)
hold on
plot3(X(MinVals),Y(MinVals),Z(MinVals),'g.','MarkerSize',30)
mesh(X,Y,Z)
grid on
xlabel('.x.')
ylabel('.y.')
zlabel('.z.')
title('mesh')

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Faris Hajdarpasic 2019-2-20

One more question. There is multiple red and green dots. And what if I want only one maximum and only one minimum(the highest/lowest one). How to achieve that?

Asad Mirza 2019-2-21

在 MATLAB Online 中打开

That's just using max() and min() on the resulting vector output of imregionalmax:

clear;clc;close all
korak=.1;
intervalpox=10;
intervalpoy=10;
x=korak:korak:intervalpox;
y=korak:korak:intervalpoy;
[X,Y] = meshgrid(x,y);
Z = (sin(sqrt(X.^2 + Y.^2)) ./ (sqrt(X.^2 + Y.^2)));
Zupsidedown=-Z;
MaxVals = find(imregionalmax(Z));
[~, ZGlobalMaxInd]=max(Z(MaxVals));
MinVals = find(imregionalmax(Zupsidedown));
[~, ZGlobalMinInd]=min(Zupsidedown(MinVals));
% plot3(X(MaxVals),Y(MaxVals),Z(MaxVals),'r.','MarkerSize',30)
% hold on
% plot3(X(MinVals),Y(MinVals),Z(MinVals),'g.','MarkerSize',30)
plot3(X(ZGlobalMaxInd),Y(ZGlobalMaxInd),Z(ZGlobalMaxInd),'r.','MarkerSize',30)
hold on
plot3(X(ZGlobalMinInd),Y(ZGlobalMinInd),Z(ZGlobalMinInd),'g.','MarkerSize',30)
mesh(X,Y,Z)
grid on
xlabel('.x.')
ylabel('.y.')
zlabel('.z.')
title('mesh')
view(45,12)