% This file is a tutorial "script" 
% it is a "script" as opposed to a "function"
%  .. typing its name (without the .m) at the matlab prompt
%  will just execute all the lines of this script in order.

% you can try typing all these to see what happens
% tip: not ending a line in a semicolon displays the result

% clear all variables in matlab memory
clear all;

a = 3;    % save a variable
b = 3;    % and another
whos      % see which variables are there
clear a;  % clear just a from memory
whos      % see which variables are there (only b)
clear all; % clear everything again

% basic arithmetic
3 * 3      % can multiply
3 ^ 3      % exponentiate
mod(5,3)   % compute 5 mod 3
0 < 1      % compare numbers
0 < inf    % compare to infinity
0 < -inf   % or negative infinity
nan < inf  % nan will not satisfy any inequality

% matrices

% manual entry
M = 2;             % "1x1" matrix
N = [ 2 ; 2 ];     % 2x1 matrix -- semicolon = new row
O = [ 1 2 ; 3 4 ]; % spaces are new columns 
P = [ 1 2          % can also use a newline to create new row
      3 4 ];

% usual initialization functions
% NOTE: If you have a hard time remembering what a 3x4 matrix
% is, (whether 3 columns or 3 rows), remember "Roman Catholic":
% Rows, then Columns!
a = ones(3);     % 3x3 matrix of all ones
b = zeros(3,4);  % 3x4 matrix of all zeros
c = ones(2,2,2); % 2x2x2 matrix of all ones
d = eye(4);      % 4x4 identity matrix 
e = rand(2);     % 2x2 random uniform matrix
f = randn(2);    % 2x2 random zero-mean unit-std gaussian matrix

% iterator examples
g = [ 1 : 5 ];          % two operands
h = [ 10 : -2.5 : 0 ];  % three operands

% linspace
i = linspace(0,10,9);   % 9 values evenly spaced in [0,10]

% repmat
j = repmat( ones(2) , [ 1 2 ] ); % 2 x 4 matrix 
k = repmat( ones(2) , [ 2 1 ] ); % 4 x 2 matrix
l = repmat( ones(2) , [ 2 2 ] ); % 4 x 4 matrix

% matrix concatentation examples
m = zeros(4,4);     % 4 x 4 all zeros
m(:) = 1 : 16;      % assign the values 1:16 to elements of m
m(eye(4)==1)=0;     % set diagonal elements to 0
n = -m';            % n is negative transpose (') of m
mcatn = [ m n ];          
maboven = [ m ; n ];
ocatz = [ ones(3,3) ; zeros(3,3) ];

% structures

% just declare a "structure" named "o" and give it some "fields"
o.name = 'alice'; % introduced a string
o.name(1)         % the character 'a'
o.height = 70;    

% cell arrays, use curly brace instead of parentheses to index
p{1} = rand(2,2); % each element of the cell array can be anything at all
p{2} = o;
p{3} = -1;

save aandm.mat a m  % save variables a and m to disk

amstruct = load('aandm.mat'); % load a and m into struct named amstruct
% note, if we had just used:
% load('aandm.mat')
% the variables 'a' and 'm' would have appeared in our matlab environment
% without any container struct (e.g. 'amstruct' above)

% basic matrix arithmetic

m % no semicolon, so this variable is displayed
n % and this

npm = n + m;         % you can add matrices
ndivm = n / m;       % or divide
ninvm = n * inv(m);  % which is same as multiplying by the inverse
npwdivm = n ./ m;    % divide matrices, element by element
npwmulm = n .* m;    % pointwise multiply
nm = n * m;          % full matrix multiplication