Done 5.1, check 5.2 impl (convergence error is a bit high)
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3 changed files with 156 additions and 22 deletions
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@ -1,22 +0,0 @@
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%[U,G] = surfer('https://www.usi.ch',500);
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% pagerank(U,G);
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% A = (1/40) * [1 1 1 35 1 1;
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% 18 1 1 1 1 1;
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% 18 18 1 1 1 1;
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% 1 18 35 1 1 1;
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% 1 1 1 1 1 35;
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% 1 1 1 1 35 1];
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A = (1/40) * [
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0 0 0 40 0 0;
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20 0 0 0 0 0;
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20 20 0 0 0 0;
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0 20 40 0 0 0;
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0 0 0 0 0 40;
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0 0 0 0 40 0];
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[v,d] = eig(A);
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display(d);
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display(v);
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72
mp1/files_data/pagerank1.m
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72
mp1/files_data/pagerank1.m
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@ -0,0 +1,72 @@
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function x = pagerank1(U,G,p)
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% PAGERANK Google's PageRank
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% pagerank(U,G,p) uses the URLs and adjacency matrix produced by SURFER,
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% together with a damping factory p, (default is .85), to compute and plot
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% a bar graph of page rank, and print the dominant URLs in page rank order.
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% x = pagerank(U,G,p) returns the page ranks instead of printing.
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% See also SURFER, SPY.
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if nargin < 3, p = .85; end
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% Eliminate any self-referential links
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%G = G - diag(diag(G));
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% c = out-degree, r = in-degree
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[~,n] = size(G);
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c = sum(G,1);
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r = sum(G,2);
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% Scale column sums to be 1 (or 0 where there are no out links).
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k = find(c~=0);
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D = sparse(k,k,1./c(k),n,n);
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e = ones(n,1);
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% ----------------------------- POWER METHOD ------------------------------
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disp('Using power method implementation\n');
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x = ones(n, 1) * 1/n;
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G = p * G * D;
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z = ((1 - p) * (c ~= 0) + (c == 0))/n;
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it = 0;
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new_x = x;
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old_norm = -1;
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no = +Inf;
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while old_norm == -1 || old_norm > no
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x = new_x;
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old_norm = no;
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new_x = G * x + e * (z * x);
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new_x = new_x/sum(new_x);
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it = it + 1;
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no = norm(new_x - x, 2);
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end
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% -------------------------------------------------------------------------
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% Normalize so that sum(x) == 1.
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x = x/sum(x);
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% Bar graph of page rank.
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shg
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bar(x)
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title('Page Rank')
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% Print URLs in page rank order.
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if nargout < 1
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[~,q] = sort(-x);
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disp(' page-rank in out url')
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k = 1;
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maxN = length(U);
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while (k <= maxN) && (x(q(k)) >= .005)
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disp(k)
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j = q(k);
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temp1 = r(j);
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temp2 = c(j);
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disp(fprintf(' %3.0f %8.4f %4.0f %4.0f %s', j,x(j),full(temp1),full(temp2),U{j}))
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k = k+1;
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end
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end
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84
mp1/files_data/pagerank2.m
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84
mp1/files_data/pagerank2.m
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@ -0,0 +1,84 @@
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function x = pagerank2(U,G,p)
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% PAGERANK Google's PageRank
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% pagerank(U,G,p) uses the URLs and adjacency matrix produced by SURFER,
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% together with a damping factory p, (default is .85), to compute and plot
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% a bar graph of page rank, and print the dominant URLs in page rank order.
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% x = pagerank(U,G,p) returns the page ranks instead of printing.
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% See also SURFER, SPY.
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if nargin < 3, p = .85; end
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% Eliminate any self-referential links
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%G = G - diag(diag(G));
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% c = out-degree, r = in-degree
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[~,n] = size(G);
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c = sum(G,1);
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r = sum(G,2);
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% Scale column sums to be 1 (or 0 where there are no out links).
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k = find(c~=0);
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D = sparse(k,k,1./c(k),n,n);
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e = ones(n,1);
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I = speye(n,n);
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% ---------------------------- INVERSE ITERATION --------------------------
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disp('Using inverse iteration implementation\n');
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z = ((1 - p) * (c ~= 0) + (c == 0)) / n;
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A = p * G * D + e * z;
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x = e/n;
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% Check if B will be a singular matrix. If so, change it
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alpha = 1;
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while rcond(A - alpha * I) <= eps
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alpha = alpha + 0.01;
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end
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display(alpha);
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B = (A - alpha * I);
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old_x = zeros(n, 1);
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old_norm = -1;
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no = +Inf;
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it = 0;
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while old_norm == -1 || old_norm > no
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old_norm = no;
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old_x = x;
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x = B \ x;
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x = x/norm(x, 2);
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it = it + 1;
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no = norm(x - old_x, 2);
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end
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x = old_x;
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display(it);
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% -------------------------------------------------------------------------
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% Normalize so that sum(x) == 1.
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x = x/sum(x);
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% Bar graph of page rank.
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shg
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bar(x)
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title('Page Rank')
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% Print URLs in page rank order.
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if nargout < 1
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[~,q] = sort(-x);
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disp(' page-rank in out url')
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k = 1;
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maxN = length(U);
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while (k <= maxN) && (x(q(k)) >= .005)
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disp(k)
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j = q(k);
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temp1 = r(j);
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temp2 = c(j);
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disp(fprintf(' %3.0f %8.4f %4.0f %4.0f %s', j,x(j),full(temp1),full(temp2),U{j}))
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k = k+1;
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end
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end
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