Pfthb

I want to use octave to plot fairly simple functions with two variables like : f(x,y) = x^2 + 3y . It is very easy to plot single variable functions, but I am having alot of trouble finding out how to do two variable functions. Does anyone know the best way of doing this? I would really appreciate any suggestions.

Thanks,
Zach

Plotting a function of two variables would normally mean a 3-dimensional plot - in MATLAB you would use the function plot3 for that. To plot your function f(x,y) in the interval [-10,10] for both X and Y, you could use the following commands:

x = [-10:.1:10];
y = [-10:.1:10];
plot3(x, y, x.^2 + 3*y)
grid on

In case it may help someone out there... I ran in Octave the code in the accepted answer and I got this plot:

But I really wanted the function for every point in the Cartesian product of x and y, not just along the diagonal, so I used the function mesh to get this 3D plot with the projected contour lines in the x,y plane:

x = [-10:.1:10];
y = [-10:.1:10];
[xx, yy] = meshgrid (x, y);
z = xx.^2 + 3*yy;
mesh(x, y, z)
meshc(xx,yy,z) 
xlabel ("x");
ylabel ("y");
zlabel ("f(x,y)");
title ("f(x,y) = x^2 + 3y");
grid on

To get rid of the mesh-wire texture of the plot, the function surf did the trick:

x = [-10:.1:10]; 
y = [-10:.1:10];
[xx, yy] = meshgrid (x, y);
z = xx.^2 + 3*yy;
h = surf(xx,yy,z);
colormap hsv;
set(h,'linestyle','none');
xlabel ("x");
ylabel ("y");
zlabel ("f(x,y)");
title ("f(x,y) = x^2 + 3y");

Another way to plot is as a heatmap with contour lines:

x = [-10:.1:10];
y = [-10:.1:10];
[xx, yy] = meshgrid (x, y);
z = xx.^2 + yy.*3;
contourf(xx,yy,z);
colormap hsv;
xlabel ("x");
ylabel ("y");
zlabel ("f(x,y)");
title ("f(x,y) = x^2 + 3y");
grid on

And for completeness, the levels can be labeled:

x = [-10:.1:10];
y = [-10:.1:10];
[xx, yy] = meshgrid (x, y);
z = xx.^2 + 3*yy;
[C,h] = contour(xx,yy,z);
clabel(C,h)
xlabel ("x");
ylabel ("y");
zlabel ("f(x,y)");
title ("f(x,y) = x^2 + 3y");
grid on

In addition to the excellent answers from @Toni and @esskov, for future plotters of functions with two variables, the contour and contourf functions are useful for some applications.

MATLAB Code (2018b):

x = [-10:.1:10]; 
y = [-20:.1:20];
[xx, yy] = meshgrid (x, y);
z = xx.^2 + 3*yy; % Borrowed 4 lines from @Toni

figure
s(1) = subplot(1,2,1), hold on % Left Plot
 [M,c] = contour(xx,yy,z); % Contour Plot
 c.ShowText = 'on'; % Label Contours
 c.LineWidth = 1.2; % Contour Line Width
 xlabel('X')
 ylabel('Y')
 box on
s(2) = subplot(1,2,2), hold on % Right Plot
 [M2,c2] = contourf(xx,yy,z);
 colorbar % Add Colorbar
 xlabel('X')
 ylabel('Y')
 box on
title(s(1),'Contour Plot')
title(s(2),'Filled Contour Plot')

Update: Added example of surfc

h = surfc(xx,yy,z)