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

mp1/files_data/ex2.m

@@ -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);
-

mp1/files_data/pagerank1.m

@@ -0,0 +1,72 @@
+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

mp1/files_data/pagerank2.m

@@ -0,0 +1,84 @@
+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