Some examples of plotting 2d functions in Matlab.

How would you make a graph of on in Matlab? You would

1. Create vector x of gridpoints with linspace
2. Evaluate on gridpoints using dot operations on x
3. Use plot(x,f) to draw the graph

For example,

plot1d.m

% Plot 1d graph of f(x) = (x-1)^2 on -3 < x < 3
 
x = linspace(-3, 3, 100); % create vector x of gridpoints
f = (x-1).^2;             % evaluate f(x) on gridpoints
plot(x,f)                 % plot  the graph
 
xlabel('x')
ylabel('f(x) = (x-1)^2')

produces

Graphing a 2d function is very similar. For example, to make a graph of the function on

1. Create vectors x and y of gridpoints on and axes with linspace
2. Create matrices X and Y of gridpoints on 2d mesh with meshgrid
3. Evaluate on mesh of gridpoints using dot operations on X,Y
4. Use pcolor(x,y,f) to draw the graph (or contour, contourf, surf, surfc)

For example,

plot2d.m

% Plot f(x,y) = 2*(x-1)^2 + (y-1)^2 on -4 < x < 4, -4 < y < 4
 
x = linspace(-4,4,30);     % create 1d gridpoints on x and y axes
y = linspace(-4,4,30);
 
[X,Y] = meshgrid(x,y);     % create 2d mesh of gridpoints over x,y
 
F = 2*(X-1).^2 + (Y-1).^2; % evaluate the function f(x,y) over mesh
 
pcolor(x,y,F);             % or contour(X,Y,F), surf(x,y,F), etc. 
colorbar()                 % plot a colorbar
 
xlabel('x');
ylabel('y');
title('f(x,y) = 2(x-1)^2 + (y-1)^2')
 
shading interp   % or faceted, flat

The function has gradient

Here's the Matlab code to make a contour plot of with its gradient superimposed as a quiver plot.

plotgradient.m

% Plot f(x,y) = x e^(-x^2 - y^2) with contours and its gradient as arrows.
x = linspace(-2, 2, 30);
y = linspace(-2, 2, 30);
 
[X,Y] = meshgrid(x,y);
 
F = X .* exp(-X.^2 - Y.^2);  % evaluate f(x,y) on mesh
contour(x,y,F);              % draw contour plot of f
 
% let dfdy = y component of grad F = df/dy
 
dfdx = (1-2*X.^2) .* exp(-X.^2 - Y.^2); % evaluate dfdx on mesh
dfdy = -2*X.*Y .* exp(-X.^2 - Y.^2);    % evaluate dfdy on mesh
 
hold on
quiver(x,y,dfdx,dfdy);       % draw quiver plot
 
xlabel('x')
ylabel('y')
title('f(x,y) = x e^{-x^2 - y^2} with \nabla f arrow plot')
colorbar()