%Matlab primer 1 - mprim1.m
%In this document, I want to illustrate simple Matlab functions, including:
%data i/o, plotting, etc.

%Some helpful hints:
%1) Matlab stands for ``Matrix Laboratory'' - this means that Matlab is
%designed to work well with matrices.  As such, it is much faster to use
%intrinsic matrix routines to operate on matrices rather than writing
%elementary code (a la FORTRAN).  For example, if we want to multiply two
%conformable matrics A, B together to form C, we can simply write C = A*B
%in Matlab.

A = [1 2; 3 4]
B = eye(2);

C = A*B
pause
%The above statement is true for other algebraic operations as well.  Note
%that a semicolon suppresses output.

C = A + B
C = A - B

pause
%We can do matrix inverses in two ways:

C = inv(A)

C =  A \ B

pause
%I have been told that method 2 is faster as it uses a faster algorithm
%than inv(), but that could be bunk.  Suppose we want to multiply a matrix
%by a scalar.

lambda = 10;
C = lambda * A

%Easy, right?  Suppose now we want to add a matrix of ones to A.  We can do
%this in three ways.

C = A + ones(2)

C = A + repmat(1,2,2)

C = A + 1

pause

%The third technique is nice as it shows us that Matlab will automatically
%make a scalar conformable to a matrix for algebraic operations.  Matlab
%has to ways of operating on matrices:  all full matrices or
%element-by-element.  For example, if we want to compute A*A = A^2, we simply
%write:

C = A^2

%If however we want to compute the matrix of squares of each element of A,
%we write:

C = A.^2

pause

C = A.*B
%Functions like exp, log, sin, etc. work element-wise in Matlab.

C = log(A)
C = exp(A)
C = sin(A)

pause

%You can write do/while loops in Matlab if you please, they are done in the
%following manner.
B = eye(2);
[na,ma] = size(A)
[nb,mb] = size(B)

if (ma ~= nb)
    disp('Houston, we have a problem:  A and B are not conformable')
    break
else
    for i = 1:na
        for j = 1:mb
            C(i,j) = A(i,:) * B(:,j);
        end;
    end;
    disp(C)
end;
    
%In general, the above way to compute A*B is inefficient - use A*B instead

pause

%Since we are now comfortable with the basic methods of using Matlab, lets
%do some plotting.  The easiest way to do this is via the ``plot''
%function.  

tvec = [0:100]';
svec = sin(tvec/100*2*pi);
plot(tvec,svec)

pause 
%Now let's plot the cosine function instead
cvec = cos(tvec/100*2*pi);
plot(tvec,cvec)

%Note that the old plot has been overwritten by the new plot.  If we wanted
%to plot them both together, we can do so by doing:
pause

plot(tvec,svec,tvec,cvec)
legend('sin','cos')

%or

plot(tvec,svec, 'bo')
hold on
plot(tvec,cvec,'g+')
legend('sin','cos')
hold off

%There are a TON of plot options - type help plot in the Command Window to
%see.  If you want to plot the above two functions in separate figures,
%there are two ways to do this.
%close
pause
figure
hold on
box on
plot(tvec,svec)
title('sin')
xlabel('t')
ylabel('sin(t)')
hold off

figure
hold on
box on
plot(tvec,cvec)
title('cos')
xlabel('t')
ylabel('cos(t)')
hold off

%or
pause

figure
subplot(2,1,1)
hold on
box on
plot(tvec,svec)
title('sin')
xlabel('t')
ylabel('sin(t)')
hold off

subplot(2,1,2)
hold on
box on
plot(tvec,cvec)
title('cos')
xlabel('t')
ylabel('cos(t)')
hold off