power method e pagerank come funzioni esterne

functions/external/costruzioneMatrice.m

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+function A=costruzioneMatrice(G,p)
+% c = out-degree, r = in-degree
+[n,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);
+
+% Solve (I - p*G*D)*x = e
+
+e = ones(n,1);
+I = speye(n,n);
+
+%Conventional power method
+   z = ((1-p)*(c~=0) + (c==0))/n;
+   A = p*G*D + e*z;

functions/external/page_rank_start.m

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+load unisa100.mat 
+% si possono generare mediante 
+%[U,G] = surfer('http://www.xgiovio.com',100);
+p = 0.85;
+A=costruzioneMatrice(G,p)
+
+toll=1e-5;
+x=power_method(A,toll);
+
+% Grafico a barre del page rank.
+
+shg
+bar(x)
+title('Page Rank')
+
+% Stampa degli URLs in ordine di page rank.
+
+[ignore,q] = sort(-x);
+disp('     page-rank  url')
+k = 1;
+n=length(x)
+while (k <= n) & (x(q(k)) >= .005)
+    j = q(k);
+    disp(sprintf(' %3.0f %8.4f %s', ...
+        j,x(j),U{j}))
+    k = k+1;
+end
+

functions/external/surfer.m

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+function [U,G] = surfer(root,n)
+% SURFER  Create the adjacency graph of a portion of the Web.
+%    [U,G] = surfer(root,n) starts at the URL root and follows
+%    Web links until it forms an adjacency graph with n nodes.
+%    U = a cell array of n strings, the URLs of the nodes.
+%    G = an n-by-n sparse matrix with G(i,j)=1 if node j is linked to node i.
+%
+%    Example:  [U,G] = surfer('http://www.harvard.edu',500);
+%    See also PAGERANK.
+%
+%    This function currently has two defects.  (1) The algorithm for
+%    finding links is naive.  We just look for the string 'http:'.
+%    (2) An attempt to read from a URL that is accessible, but very slow,
+%    might take an unacceptably long time to complete.  In some cases,
+%    it may be necessary to have the operating system terminate MATLAB.
+%    Key words from such URLs can be added to the skip list in surfer.m.
+
+% Initialize
+
+clf
+shg
+set(gcf,'doublebuffer','on')
+axis([0 n 0 n])
+axis square
+axis ij
+box on
+set(gca,'position',[.12 .20 .78 .78])
+uicontrol('style','frame','units','normal','position',[.01 .09 .98 .07]);
+uicontrol('style','frame','units','normal','position',[.01 .01 .98 .07]);
+t1 = uicontrol('style','text','units','normal','position',[.02 .10 .94 .04], ...
+   'horiz','left');
+t2 = uicontrol('style','text','units','normal','position',[.02 .02 .94 .04], ...
+   'horiz','left');
+slow = uicontrol('style','toggle','units','normal', ...
+   'position',[.01 .24 .07 .05],'string','slow','value',0);
+quit = uicontrol('style','toggle','units','normal', ...
+   'position',[.01 .17 .07 .05],'string','quit','value',0);
+
+U = cell(n,1);
+hash = zeros(n,1);
+G = logical(sparse(n,n));
+m = 1;
+U{m} = root;
+hash(m) = hashfun(root);
+
+j = 1;
+while j < n & get(quit,'value') == 0
+   
+   % Try to open a page.
+
+   try
+      set(t1,'string',sprintf('%5d %s',j,U{j}))
+      set(t2,'string','');
+      drawnow
+      page = urlread(U{j});
+   catch
+      set(t1,'string',sprintf('fail: %5d %s',j,U{j}))
+      drawnow
+      j = j+1;
+      continue
+   end
+   if get(slow,'value')
+      pause(.25)
+   end
+
+   % Follow the links from the open page.
+
+   for f = findstr('http:',page);
+
+      % A link starts with 'http:' and ends with the next quote.
+
+      e = min([findstr('"',page(f:end)) findstr('''',page(f:end))]);
+      if isempty(e), continue, end
+      url = deblank(page(f:f+e-2));
+      url(url<' ') = '!';   % Nonprintable characters
+      if url(end) == '/', url(end) = []; end
+
+      % Look for links that should be skipped.
+
+      skips = {'.gif','.jpg','.jpeg','.pdf','.css','.asp','.mwc','.ram', ...
+               '.cgi','lmscadsi','cybernet','w3.org','google','yahoo', ...
+               'scripts','netscape','shockwave','webex','fansonly'};
+      skip = any(url=='!') | any(url=='?');
+      k = 0;
+      while ~skip & (k < length(skips))
+         k = k+1;
+         skip = ~isempty(findstr(url,skips{k}));
+      end
+      if skip
+         if isempty(findstr(url,'.gif')) & isempty(findstr(url,'.jpg'))
+            set(t2,'string',sprintf('skip: %s',url))
+            drawnow
+            if get(slow,'value')
+               pause(.25)
+            end
+         end
+         continue
+      end
+
+      % Check if page is already in url list.
+
+      i = 0;
+      for k = find(hash(1:m) == hashfun(url))';
+         if isequal(U{k},url)
+            i = k;
+            break
+         end
+      end
+
+      % Add a new url to the graph there if are fewer than n.
+
+      if (i == 0) & (m < n)
+         m = m+1;
+         U{m} = url;
+         hash(m) = hashfun(url);
+         i = m;
+      end
+
+      % Add a new link.
+
+      if i > 0
+         G(i,j) = 1;
+         set(t2,'string',sprintf('%5d %s',i,url))
+         line(j,i,'marker','.','markersize',6)
+         drawnow
+         if get(slow,'value')
+            pause(.25)
+         end
+      end
+   end
+
+   j = j+1;
+end
+delete(t1)
+delete(t2)
+delete(slow)
+set(quit,'string','close','callback','close(gcf)','value',0)
+
+
+
+%------------------------
+
+function h = hashfun(url)
+% Almost unique numeric hash code for pages already visited.
+h = length(url) + 1024*sum(url);

functions/power_method.m

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+
+
+function [v,a] = power_method (U,toll)
+
+[x,~] = size(U);
+for i=1:x
+    v(i)=1;
+end
+v=v';
+
+err = inf;
+while err > toll
+    
+    v1=U*v;
+    v1=v1./norm(v1,inf);
+    err = norm(v1-v,inf);
+    a = v1./v;
+    v=v1;
+    
+end
+
+
+ 
+end