%-- 9/03/08  1:18 PM --%
% notice that a % symbol comments out the rest of that line which is not executed
% simple matrix manipulations
x=[1 2 3 4 5]
x=[1 2 3 4 5];
x'
x*x'
x'*x
A=x'*x
% extracting parts of a matrix
A(:,3)
A(3,:)
% using an implied loop
x=1:5
x=1:8
x=1:2:8
x=0:.01:2*pi;
plot(x,sin(x))
plot(x,sin(x),'r--^')
x=0:0.1:2*pi;
plot(x,sin(x),'r--^')
plot(x,sin(x),'r--^','markerfacecolor','r')
plot(x,sin(x),'r--^','markerfacecolor','r','markersize',8)
plot(x,sin(x),'r--^','markerfacecolor','r','markersize',2)
plot(x,sin(x),'r--^','markerfacecolor','r','markersize',3)
xlabel(' this is the x of \beta ')
clear  % clears all the work space
whos
clf
% solve y"= 1 y(0)=0=y(1) by finite differences
x=0:.1:1
N=length(x)
whos
o=ones(N,1)
o=zeros(N,1)
o=zeros(1,N)
A=diag(-2*ones(N-2,1),0)
A=diag(-2*ones(N-2,1),0)+diag(ones(N-3,1),1)
A=diag(-2*ones(N-2,1),0)+diag(ones(N-3,1),1)+diag(ones(N-3,1),-1)
b=ones(N-2,1)
Y=zeros(N,1)
Y(2:N-1)=A\b   % note solution is inserted into part of the vector Y
% oops wrong answer as we forgot the dx^2 factor
dx=0.1
b=b*dx^2
Y(2:N-1)=A\b
plot(x,Y,'b-^',x,0.5*x.*(x-1),'r--o')  % <--- note the .* here

% A slicker piece of code would be (copy and paste the following into the command window and wait and watch):
clear;clf;
dx       = 0.1;
x        = 0:dx:1
N        = length(x)
A        = diag(-2*ones(N-2,1),0)+diag(ones(N-3,1),1)+diag(ones(N-3,1),-1);
b        = dx^2*ones(N-2,1)
Y        = zeros(N,1)
Y(2:N-1) = A\b   % note solution is inserted into part of the vector Y
plot(x,Y,'b-^',x,0.5*x.*(x-1),'r--o')  % <--- note the .* here


% using Matlab help
help eig
eig(A)
[V,D]=eig(A)
whos
clear
% the .* .? and .^ operations
x=1:5
y=2*x
x*y
x.*y
x./y
x.^5
log(x)