How to find max and min of fuction of 2 independent variables?
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Faris Hajdarpasic
on 20 Feb 2019
Commented: Walter Roberson
on 21 Feb 2019
My question is how can I find minimum and maximum of this function, and then tag them with 'o' in function graph?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/205130/image.png)
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')
8 Comments
Walter Roberson
on 21 Feb 2019
[~, 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+');
Accepted Answer
Asad Mirza
on 20 Feb 2019
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')
![localmaxmin.jpg](https://www.mathworks.com/matlabcentral/answers/uploaded_files/205133/localmaxmin.jpeg)
6 Comments
Asad Mirza
on 21 Feb 2019
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)
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