Starting diary file diary-18-Oct-2010.txt

A = [.95 .5 ; .05 .5]
sum(A)

x = [.5;.5]
A*x
xx = x
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx
xx = A* xx

x =[ 1 ; 0]
xx = x
xx = A* xx
xx = A* xx  % I repeated this about 20 times; you can do it in a loop!
x = [0 ; 1]
xx = x
xx = A* xx
xx = A* xx  % ...

S = [ .75 .1 ; .25 .9]
x = [.5;.5]
xx = x
xx = S*xx
xx = S*xx
xx = S*xx  % about 20 times ...

clear
load harvard500
whos
U
size(G)
spy(G)
full(sum(G))

clc
p = .85
c = sum(G)
whos
c = full(c)

clc
whos
D = diag( 1./c)     % oops, this is dense and has Inf's in it....

clc
K = find(c~=0)
size(K)
nnz(c)

[n,n] = size(G)

% The next line has the bug that took us so long to find in class...
% it should have been 1./c(K), not just c(K).
%
D = sparse( K, K, c(K), n, n);   

size(D)
nnz(D)
length(K)
whos
nnz(D)
D

e = ones(n,1)
whos

z = ( (c==0)   +   (1-p)*(c~=0)    ) / n;
size(z)
z
whos

A = p * G * D  +  e * z;
size(A)
sum(A)   % Here's where we noticed the problem ... the sums aren't equal to 1!

clc
s = sum(A);
full(s)
s(1)

clc
D   % Aha!  The entries of D should be less than 1, not integers.

D = sparse( K, K, 1 ./ c(K), n, n);
D
max(max(D))
min(min(D))

A = p * G * D  +  e * z;

full(sum(A))
s = sum(A);
max(s)
min(s)

x = e/n;
xx = x;
for i=1:100,plot(xx,'.'),pause,xx = A*xx;end;
sum(xx)
min(xx)
max(xx)

help sort
y = sort(xx);
y = sort(xx,1,'descend');
y

whos
[y,p] = sort(xx,1,'descend');
p'

clc
U(p)

diary off