% 1. basic plots
t = 0:0.01:2*pi;
c = cos(t);
plot(t,c)
hold on % to keep the current plot
plot(t,c,'g+')
% to plot a coarser range
s = 0:0.3:2*pi;
c2 = cos(s);
plot(s,c2,'rx')
plot(s,c2,'--')
hold off % clear for new plot
c3 = cos(3*s);
plot(s,c3)
figure
c4 = cos(3*t);
plot(t,c4)
% in plotting we plot x and y values
% if we want to add to figure 1,
% we type
figure(1)
hold on
plot(t,c4,'r')
axis([0,2*pi,-2,2])
% 2. polar plots
% spiral have very natural representations
% in polar coordinates
angle = 0:0.01:10;
r = 0.01*angle.^2 -0.02;
% Observe the . in front of the ^ operator
polar(angle,r)
clf
polar(angle,r)
% to illustrate the componentwise multiplication
a = rand(2,2); b = rand(2,2);
c = a*b

c =

    0.5276    0.2963
    0.6619    0.7518

d = a.*b

d =

    0.5152    0.0354
    0.0884    0.4995

% The first a*b is the matrix multiplication
% The a.*b is the componentwise multiplication
% 3. Three dimensional plots
% Suppose we want to plot z = cos(x*y)
% for x and y both in the interval [-2,2].
% First we determine how many samples we take:
xa = -2:0.01:+2; ya = -2:0.01:+2;
% Secondly, we must setup the grid:
[x,y] = meshgrid(xa,ya);
% Thirdly: we sample z = cos(x*y):
z = cos(x.*y); % observe the .*
% Fourth: we render the plot
figure
mesh(x,y,z)
view([-34,50]);
view(3)
% we can make subplots
figure
subplot(2,2,1)
mesh(x,y,z)
subplot(2,2,2)
mesh(x,y,z)
view([10,10])
subplot(2,2,3)
mesh(x,y,z)
view([10,70])
subplot(2,2,4)
mesh(x,y,z)
view([10,-30])
% to restore the default view for
% the top right plot
subplot(2,2,2)
view(3)
% For a space curve we use the plot3 command
% example the helix defined by
% x = cos(t), y = sin(t), z = t
t = 0:0.01:20*pi;
x = cos(t); y = sin(t); z = t;
figure
plot3(x,y,z)
% contour plots
% we will plot the surface z = exp(-x^2-y^2)
% for x and y ranging from -2 to +2
% We still have the x and y from before,
% which is not true!  We have to remake
% x and y from the xa and ya we had before:
[x,y] = meshgrid(xa,ya);
z = exp(-x.^2 - y.^2);
% this is the surface z = exp(-x^2 - y^2)
figure
subplot(2,1,1)
mesh(x,y,z)
subplot(2,1,2)
contour(z)
diary off