% Math22 matlab session example code, alex barnett, 7/25/06

% comments come after the % symbol and are ignored by matlab

% Please use text editor to paste chunks of this code into matlab command
% window.

A = [1 2 3; 4 5 6]
% fill the A matrix
b = [2;4];
A'*b            % matrix mult
transpose(A)*b

5*A      % scalar mult
C = [-1 1 -1;1 -1 1];
A.*C        % elementwise mult (note .* not *)

A = rand(40,60);               % rectangular matrix of random numbers in [0,1]
U = rref(U);                   % compute its REF form
spy(U);                        % show diagram of nonzero entries
imagesc(U); colorbar;          % show color-scale (density) plot of matrix

% handling the workspace:
whos
save temp.mat
clear
load temp.mat

% LISTS: the colon notation gives a row vector
y = 1:10
y = 1:2:10
y = (1:10)'         % this gives a column vector


% LOOPS

% simple loop doing something many times.
A = [.9 .1; .1 .9];
x = [1;0];
for i=1:20
  x = A*x;
end
% show the final value of x:
x

format long g             % display more decimal digits!

% Problem: we lost all the intermediate values. The next version stores them

% Better version, store the complete evolution of x...
x = zeros(2,20); % 20 columns since we want x_0, x_1, ..., x_20
x(:,1) = [1;0];  % set the initial values
for i=1:19
  x(:,i+1) = A*x(:,i);
end

x
% now x has complete history, useful, can plot it...
figure; plot(1:20, x(1,:), '+-'); 

% make a labelled plot with both populations as a function of iterations...
figure; plot(1:20, x, '+-'); xlabel('time in yrs'); label('pop in millions');