% Quick MATLAB Tutorial
% Prepared for 605.721.71 Summer 2004 (June 5, 2004)
% John E. Boon, Jr.

% Resources used during preparation:
% Coleman, Thomas F. and Van Loan, C., Handbook for Matrix Computations,
% SIAM, 1988 (third printing 1991).
%
% The MathWorks, Inc.,MATLAB for MS-DOS Personal Computers, User's Guide,
% October 15, 1990.
% 
% MATLAB release 12, online Help, The MathWorks, Inc., 2000.

echo on
% General interface usage notes:
% MATLAB is case sensitive. Any user-introduced name must start with
%   a letter but may contain special characters and numbers later.
%   First 19 characters of a user-introduced name are used by MATLAB.
% non-MATLAB (operating system level) commands are accessed via !
%   !whois jhu.edu
% directory commands can be executed within MATLAB
%   cd matlab
%   dir
%   ls
% to access MATLAB general help or help on a specific topic
%   help
%   help elmat
% help short_MATLAB_tutorial 
%   accesses the initial contiguous comments
% short_MATLAB_tutorial
%   exeuctes this m file if it is in the default
%   MATLABPATH or added to MATLABPATH
% commands ending in ; do not have their results displayed
%   otherwise, results are displayed immediately
% multiple commands can be placed on a single line, each 
%   separated by ,
% to clear the command window and its history use
%   clc
% to clear the command window but retain history use
%   home
% recursive functions can be created in MATLAB
% 
echo off

format short; % see format statements explained later

% Create a string. Note use of single quotes
s = 'hello'
% text is stored as a vector, one character per vector element
% to access the ASCII values of the characters in the string
abs(s)
% set vector to display as text instead of ACSII values
setstr(s)

% Create an m-by-n matrix
% matrix_name = [ {row 1 elements 1..n} ; ... ; {row m elements 1..n} ]
A = [1 2 3; 4 5 6; 7 8 9]
% a vector is a one-dimensional array
r = [10 11 12]
% create an empty matrix
D = []

% "Colon Method" for setting up row vectors
v = 1:3      % v = { start} : { stop }
v = 3:-1:0   % v = { start} : { increment } : { stop }
v = 1:2:10   % v = { start} : { increment } : { stop }

% scalars do not require []
x = pi

% size of a matrix
[m,n] = size(A)

% length of a vector
r_length = length(r)

% checking on a matrix
exist('D')
isempty(D)

% subscripting -- accessing subparts of a matrix
A(1:2, 3)   % first 2 rows of 3rd column of A
A(2:3, 1:2) % last 2 rows and first 2 columns of A
A(:, 3)     % third column of A
A(1:2,:)    % first two rows of A
% b=A(:)    all of the elements of A are moved to a single column vector
% A(:)=b    if A exists, create a matrix with same dimensions as A but with
%           new contents from the righthand side

% information on variables in use
who  % display all variables in use
whos % space used by variables in use

% removing variables
clear r_length % removes a specific variable
clear % removes all variables

% entering complex numbers
B = [1 2; 3 4] + i*[5 6; 7 8]
C = [1+5*i 2+6*i; 3+7*i 4+8*i]

% save a matrix to your default directory
save C.mat C
% show that matrix C is stored in file C.mat in directory
dir
% load matrices from disk
load C.mat C

A=[1 2 3; 4 5 6; 7 8 0];
% transpose a matrix
B=A'

% add matrices
C = A + B

x = [-1 0 2]';
% addition and subtraction defined if one operand is a scalar
y = x - 1

% matrix multiplications examples
x' * y
y * x'

% matrix-vector products
b = A*x

% matrix division
X = A\B  % is a solution to A*x=B
X = B/A  % is a solution to x*A=B

% matrix powers
A^3  % raise A to the 3rd power; A must be square, exponent a scalar

x = 1:3;
y = 4:6;
% Pointwise operations (element-by-element)
z = x.*y  %z(i,j) = x(i,j)y(i,j)
z = x.\y  %z(i,j) = x(i,j)/y(i,j)

% machine precision
eps  % smallest floating point number suc that if x=1+eps then x>1

% IEEE floating point results
1/0      % produces warning and Inf as result
Inf/Inf  % results in NaN
0/0      % produces warning and NaN as result

% output format
%format short
%format long
%format hex
%format +       help in displaying large matrices; (pos, neg, blank) entries

% relational operators
% <  less than
% <= less than or equal
% >  greater than
% >= gretater than or equal
% == equal
% ~= not equal

% logical operators
% & and
% | or
% ~ not
% any(x) returns 1 if any of the elements of the 0-1 vector are non-zero
% all(A) returns 1 if all of the elements of A are non-zero

% LU factorization
% square matrices
% express as the product of two triangular matrices, one of them a permutation
% of the lower triangular matrix and the other an upper triangular matrix
[L,U] = lu(A)
% check that L*U produces A
D = L*U

% QR factorization
% square and rectangular matrices
% express the matrix as the product of an orthonormal matrix and an
% upper triangular matri
[Q,R] = qr(A)

% singular value decomposition
[U,S,V] = svd(A)

% eigenvectors and eigenvalues
[X,D] = eig(A)

%invert a matrix, finds its determinate
inv(A)
det(A)

% Programming control flow in MATLAB
% FOR loops
% for {var} = {row of vector counter values}
%   {statements}
% end
% example:
n = 10;
for i=1:n, x(i) = 0; end, x
% example:
m = 10;
for i=1:m
   for j=1:n
      A(i,j)=1/(i+j-1);
   end
end
A

% WHILE loops
% while {relation}
%   {statements}
% end
% example: What is the first integer n for which n! is a 100 digit number?
n=1;
while prod(1:n) < 1.e100, n=n+1; end
n

% IF statements
% if {relation}
%   {statements}
% end

% example: suppose n is a positive integer and want to set E to the upper
% triangular matrix that has 1's on the diagonal and -1's above the
% diagonal
n = 5;
for i=1:n
   for j=1:n
      if (i<j)
         E(i,j) = -1;
      elseif (i>j)
         E(i,j) = 0;
      else
         E(i,j) = 1;
      end
   end
end


% Break command
% used to terminate a loop
% Example: print all Fibonacci numbers less than 1000
fib(1) = 1;
fib(2) = 1;
for j = 3:1000
   z = fib(j-1) + fib(j-2);
   if z >= 1000
      break
   end
   fib(j) = z;
end
fib

% getting user input
% gives prompt in the text string, waits, then returns the number or
% expression input from the keyboard
% user_entry = input('prompt') 
%   displays prompt as a prompt on the screen, waits for input from the 
%   keyboard, and returns the value entered in user_entry.
% user_entry = input('prompt','s') 
%   returns the entered string as a text variable rather than as a variable 
%   name or numerical value
n = input('Enter a number: ')

% keyboard 
%   when placed in an M-file, stops execution of the file and gives control 
%   to the keyboard. The special status is indicated by a K appearing before 
%   the prompt. You can examine or change variables; all MATLAB commands 
%   are valid. This keyboard mode is useful for debugging your M-files.
%   To terminate the keyboard mode, type the command:
%   return
%   then press the Return key.

% pause
%    by itself, causes M-files to stop and wait for you to press any key before 
%    continuing.
% pause(n) 
%    pauses execution for n seconds before continuing, where n can be any real 
%    number. The resolution of the clock is platform specific. A fractional 
%    pause of 0.01 seconds should be supported on most platforms.
% pause on 
%   allows subsequent pause commands to pause execution.
% pause off 
%  ensures that any subsequent pause or pause(n) statements do not pause 
%  execution. This allows normally interactive scripts to run unattended.