%
% ex1.m is an example matlab program 
%

% ----- save output to file ----- %

clear all
diary ex1.mout
diary off
delete ex1.mout
diary ex1.mout

% ----- display date and time of computation ----- %

format short
date
time0 = clock;

% ----- enter matrices ----- %

a  = [5;
      4;
      2]; 

b  = [1;
      1;
      2]; 

AA = [2 1 3; 
      1 3 2; 
      3 2 5]; 

% - to print matrices just list them - %

a, b, AA

a 
b 
AA

% ----- create special matrices in matlabl ----- %

iota = ones(10,1);
ident = eye(10);

iota, ident

% ----- use of the addtion, multiplication, and transpose operators ----- %

temp = a'+b';  
temp1 = (a+b)'; 
 
temp, temp1

temp = a'*AA;
temp1 = AA*AA;
temp2 = AA^2;

temp, temp1, temp2 

% ----- enter data into matrices ----- %

y = [89.2121;
     89.8565;
     90.4337;
     89.6069;
     90.8523;
     89.1211;
     90.7312; 
     89.9642; 
     90.1163;
     88.8782];

x = [1 11;
     1 13;
     1 22;
     1 12;
     1 24;
     1 10;
     1 9; 
     1 8; 
     1 17;
     1 22 ];

% ----- compute eigenvalues/vectors ---- %

P = [.9 .1 ;
     .3 .7];

pie = [.5 ; .5];

y = [1 ; 5]

L2a = pie(1,1)*P(1,2)*P(2,1)*P(1,2)*P(2,1)
P2d = pie'*y
P2e = P*y
P2e = P^2*y
P2e = P^3*y
F2g = inv( eye(2) - 0.9*P) * y

% - note V is eigenvectors - %

[V,D] = eig(P');

V, D

test = V(:,1)
test1 = V(1,:)
test2 = V(1,1:2)
test3 = V(1,1:1)

% ----- compute some traces ----- %

trace(P)
trace(P')
trace(P*P')
trace(P'*P)

% ----- turn off diary ----- %

comptime = etime(clock, time0)
diary off