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

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')

[Walter Roberson]

max() and min() can have two outputs instead of 1...

[Faris Hajdarpasic]

I dont understand you

[Walter Roberson]

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

[Faris Hajdarpasic]

What ~ means here?

[Walter Roberson]

[ThisOutputWillNeverBeUsed, location_of_max] = max(Z(:));
clear ThisOutputWillNeverBeUsed
[ThisOutputWillNeverBeUsedEither, location_of_min] = min(Z(:));
clear ThisOutputWillNeverBeUsedEither
x_at_max = ... and so on

[Faris Hajdarpasic]

aaaa okayyy now i got it

[Faris Hajdarpasic]

But what if i want it on plot3?

[Walter Roberson]

[~, 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+');

Answer 1

[Asad Mirza]

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')

[Faris Hajdarpasic]

Thanks a lot!!!!

[Faris Hajdarpasic]

What I dont understand is this:

why you need to change korak to korak=.1, and why x an y starts from korak and not from 0(it doesent work with 0)

[Asad Mirza]

This is because it appears that your function evaluates to NaN at x,y of 0,0 which makes the imregionalmax function not work. The slight workaround I did for this was just start at korak instead of 0. Another fix could be to find any NaNs in your Z matrix beforehand and replace them first with 0 let's say and then do imregionalmax.

[Faris Hajdarpasic]

Oh yes you are correct. Thanks once again

[Faris Hajdarpasic]

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]

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)