%Beginners Introduction to MATLAB WORKSHOP
%Given by Michael Cohen University of Connecticut, Agricultural and
%Resource Economics, Food Marketing Policy Center. Novermber 2, 2007
%The m-file
clear all
%make comment on suppressing output
x=1+1;
y=2*2^2;
z=sin(y);
w=log(x) %sqrt exp

%vectors
v=[1 4 log(y)];
vprime=v';
q=v(1);
t=[q;v'];
tsq=t.^2;
%string vector
a=['mike'];
b=['went'];
c=['fishing'];
sentance=[a ' ' b ' ' c]';
disp(sentance)
%plotting functions
%make grid on which to evaluate
N=10;
h=1/N;
x=0:h:N;
f=cos(x);
plot(x,f,'k:')
title('cos(x)')
ylabel('f(x)')
xlabel('x')
%text(3,.8,'f=cos(x)')
%%matricies
%%goto excel and create a data file
M=dlmread('mydata1.txt','\t',1,0);
save M
P=M*M;
[r c]=size(P);
Q=P(:,1:2);
Z=[P(:,1) P(:,3)];
A=Q*Z';
H=A.*ones(3,3);
B=A.*eye(3);
steve=diag(B);
C=A.*zeros(3,3);
W=[H B C ones(3,3)];
i=ones(2,1);
j=eye(3);
K=kron(i,j);
Y=reshape(K,2,9);
U=repmat(j,2,3);
S=inv(randn(3,3));
%make a quick comment on generalized inverse

%User defined functions
fac3=fac(3);
disp(['Three Factorial' '    ' num2str(fac3)])

%Example of how clever use of matlab functions can dramatically speed up
%computation time.
tic
n=100;
v=ones(n,1);
it=1;
ij=sqrt(n);
for i=1:sqrt(n)
    x(i)=sum(v(it:ij));
    it=ij+1;
    ij=(i+1)*sqrt(n);
end
toc

tic
n=100;
t=sqrt(n);
x1=reshape(v,t,t);
x2=sum(x1,1);
toc

%an example useing the while function
%Newton-Raphson algorithum for finding zeros (roots) of a function 
syms x %command sysms ques symbolic package and x denotes the symbol/var
f=x^2+5*x;
j=jacobian(f,x);
h=jacobian(j,x);
epsilon=.00001;
x0=1;   %initial guess
dif=1;
while abs(dif)>epsilon
    x=x0;
    je=eval(h); %evaluates the jacobian at the guess
    fe=eval(j); %evaluate FOC at guess
    x1=x0-inv(je)*fe;
    dif=x1-x0; %distance from guess and new value    
    x0=x1; %update guess
    it=it+1; 
end
disp(x1)