Done 5.1, check 5.2 impl (convergence error is a bit high)

This commit is contained in:
Claudio Maggioni 2020-09-22 13:34:48 +02:00
parent 1bcce91807
commit 7355b27cd3
3 changed files with 156 additions and 22 deletions

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@ -1,22 +0,0 @@
%[U,G] = surfer('https://www.usi.ch',500);
% pagerank(U,G);
% A = (1/40) * [1 1 1 35 1 1;
% 18 1 1 1 1 1;
% 18 18 1 1 1 1;
% 1 18 35 1 1 1;
% 1 1 1 1 1 35;
% 1 1 1 1 35 1];
A = (1/40) * [
0 0 0 40 0 0;
20 0 0 0 0 0;
20 20 0 0 0 0;
0 20 40 0 0 0;
0 0 0 0 0 40;
0 0 0 0 40 0];
[v,d] = eig(A);
display(d);
display(v);

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function x = pagerank1(U,G,p)
% PAGERANK Google's PageRank
% pagerank(U,G,p) uses the URLs and adjacency matrix produced by SURFER,
% together with a damping factory p, (default is .85), to compute and plot
% a bar graph of page rank, and print the dominant URLs in page rank order.
% x = pagerank(U,G,p) returns the page ranks instead of printing.
% See also SURFER, SPY.
if nargin < 3, p = .85; end
% Eliminate any self-referential links
%G = G - diag(diag(G));
% c = out-degree, r = in-degree
[~,n] = size(G);
c = sum(G,1);
r = sum(G,2);
% Scale column sums to be 1 (or 0 where there are no out links).
k = find(c~=0);
D = sparse(k,k,1./c(k),n,n);
e = ones(n,1);
% ----------------------------- POWER METHOD ------------------------------
disp('Using power method implementation\n');
x = ones(n, 1) * 1/n;
G = p * G * D;
z = ((1 - p) * (c ~= 0) + (c == 0))/n;
it = 0;
new_x = x;
old_norm = -1;
no = +Inf;
while old_norm == -1 || old_norm > no
x = new_x;
old_norm = no;
new_x = G * x + e * (z * x);
new_x = new_x/sum(new_x);
it = it + 1;
no = norm(new_x - x, 2);
end
% -------------------------------------------------------------------------
% Normalize so that sum(x) == 1.
x = x/sum(x);
% Bar graph of page rank.
shg
bar(x)
title('Page Rank')
% Print URLs in page rank order.
if nargout < 1
[~,q] = sort(-x);
disp(' page-rank in out url')
k = 1;
maxN = length(U);
while (k <= maxN) && (x(q(k)) >= .005)
disp(k)
j = q(k);
temp1 = r(j);
temp2 = c(j);
disp(fprintf(' %3.0f %8.4f %4.0f %4.0f %s', j,x(j),full(temp1),full(temp2),U{j}))
k = k+1;
end
end

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function x = pagerank2(U,G,p)
% PAGERANK Google's PageRank
% pagerank(U,G,p) uses the URLs and adjacency matrix produced by SURFER,
% together with a damping factory p, (default is .85), to compute and plot
% a bar graph of page rank, and print the dominant URLs in page rank order.
% x = pagerank(U,G,p) returns the page ranks instead of printing.
% See also SURFER, SPY.
if nargin < 3, p = .85; end
% Eliminate any self-referential links
%G = G - diag(diag(G));
% c = out-degree, r = in-degree
[~,n] = size(G);
c = sum(G,1);
r = sum(G,2);
% Scale column sums to be 1 (or 0 where there are no out links).
k = find(c~=0);
D = sparse(k,k,1./c(k),n,n);
e = ones(n,1);
I = speye(n,n);
% ---------------------------- INVERSE ITERATION --------------------------
disp('Using inverse iteration implementation\n');
z = ((1 - p) * (c ~= 0) + (c == 0)) / n;
A = p * G * D + e * z;
x = e/n;
% Check if B will be a singular matrix. If so, change it
alpha = 1;
while rcond(A - alpha * I) <= eps
alpha = alpha + 0.01;
end
display(alpha);
B = (A - alpha * I);
old_x = zeros(n, 1);
old_norm = -1;
no = +Inf;
it = 0;
while old_norm == -1 || old_norm > no
old_norm = no;
old_x = x;
x = B \ x;
x = x/norm(x, 2);
it = it + 1;
no = norm(x - old_x, 2);
end
x = old_x;
display(it);
% -------------------------------------------------------------------------
% Normalize so that sum(x) == 1.
x = x/sum(x);
% Bar graph of page rank.
shg
bar(x)
title('Page Rank')
% Print URLs in page rank order.
if nargout < 1
[~,q] = sort(-x);
disp(' page-rank in out url')
k = 1;
maxN = length(U);
while (k <= maxN) && (x(q(k)) >= .005)
disp(k)
j = q(k);
temp1 = r(j);
temp2 = c(j);
disp(fprintf(' %3.0f %8.4f %4.0f %4.0f %s', j,x(j),full(temp1),full(temp2),U{j}))
k = k+1;
end
end