From ddbda84923b5d948c94e47264e3fdede5f44785b Mon Sep 17 00:00:00 2001 From: Apostolof Date: Thu, 13 Sep 2018 21:53:05 +0300 Subject: [PATCH] Rebase serial implementation, Add header file for serial, Add dataset, Add matlab package --- datasets/toronto_death_penalty_refined_adj | 1800 ++++++++++++++++++++ matlab/package/cs-stanford.mat | Bin 0 -> 170401 bytes matlab/package/pagerank.m | 893 ++++++++++ matlab/package/pagerank_gs_mult.c | 109 ++ matlab/package/pagerank_gs_mult.mexa64 | Bin 0 -> 10765 bytes matlab/package/pagerank_gs_mult.mexglx | Bin 0 -> 7799 bytes matlab/package/pagerank_mult.c | 128 ++ matlab/package/pagerank_mult.mexa64 | Bin 0 -> 10825 bytes matlab/package/pagerank_mult.mexglx | Bin 0 -> 8163 bytes matlab/package/spmatvec_mult.c | 78 + matlab/package/spmatvec_mult.mexa64 | Bin 0 -> 9893 bytes matlab/package/spmatvec_mult.mexglx | Bin 0 -> 7551 bytes matlab/package/spmatvec_transmult.c | 82 + matlab/package/spmatvec_transmult.mexa64 | Bin 0 -> 9914 bytes matlab/package/spmatvec_transmult.mexglx | Bin 0 -> 7548 bytes serial.c | 88 - serial/Makefile | 36 + serial/pagerank | Bin 0 -> 25344 bytes serial/serial_gs_pagerank.c | 32 + serial/serial_gs_pagerank_functions.c | 286 ++++ serial/serial_gs_pagerank_functions.h | 75 + 21 files changed, 3519 insertions(+), 88 deletions(-) create mode 100644 datasets/toronto_death_penalty_refined_adj create mode 100644 matlab/package/cs-stanford.mat create mode 100644 matlab/package/pagerank.m create mode 100644 matlab/package/pagerank_gs_mult.c create mode 100644 matlab/package/pagerank_gs_mult.mexa64 create mode 100644 matlab/package/pagerank_gs_mult.mexglx create mode 100644 matlab/package/pagerank_mult.c create mode 100644 matlab/package/pagerank_mult.mexa64 create mode 100644 matlab/package/pagerank_mult.mexglx create mode 100644 matlab/package/spmatvec_mult.c create mode 100644 matlab/package/spmatvec_mult.mexa64 create mode 100644 matlab/package/spmatvec_mult.mexglx create mode 100644 matlab/package/spmatvec_transmult.c create mode 100644 matlab/package/spmatvec_transmult.mexa64 create mode 100644 matlab/package/spmatvec_transmult.mexglx delete mode 100644 serial.c create mode 100644 serial/Makefile create mode 100644 serial/pagerank create mode 100644 serial/serial_gs_pagerank.c create mode 100644 serial/serial_gs_pagerank_functions.c create mode 100644 serial/serial_gs_pagerank_functions.h diff --git a/datasets/toronto_death_penalty_refined_adj b/datasets/toronto_death_penalty_refined_adj new file mode 100644 index 0000000..3b4fc82 --- /dev/null +++ b/datasets/toronto_death_penalty_refined_adj @@ -0,0 +1,1800 @@ +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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The return +% from the algorithm are a set of cell arrays where +% p = cell(5,1), flag = cell(5,1), hist = cell(5,1), dt = cell(5,1) +% and each cell contains the result from one algorithm. +% p{1} is the vector computed from the 'power' algorithm +% p{2} is the vector computed from the 'gs' algorithm +% p{3} is the vector computed from the 'arnoldi' algorithm +% p{4} is the vector computed from the 'linsys' algorithm with bicgstab +% p{5} is the vector comptued from the 'linsys' algorithm with gmres +% the other outputs all match these indices. +% +% pagerank(A,options) specifies optional parameters +% options.c: the teleportation coefficient [double | {0.85}] +% options.tol: the stopping tolerance [double | {1e-7}] +% options.v: the personalization vector [vector | {uniform: 1/n}] +% options.maxiter maximum number of iterations [integer | {500}] +% options.verbose: extra output information [{0} | 1] +% options.x0: the initial vector [vector | {options.v}] +% options.alg: force the algorithm type +% ['gs' | 'power' | 'linsys' | 'dense' | {'arnoldi'} | ... +% 'approx' | 'eval'] +% +% options.linsys_solver: a function handle for the linear solver used +% with the linsys option [fh | {@(f,v,tol,its) bicgstab(f,v,tol,its)}] +% options.arnoldi_k: use a k dimensional arnoldi basis [intger | {8}] +% options.approx_bp: boundary probability to expand [float | 1e-3] +% options.approx_boundary: when to expand on the boundary [1 | {inf}] +% options.approx_subiter: number of subiterations of power iterations +% [integer | {5}] +% +% Example: +% load cs-stanford; +% p = pagerank(A); +% p = pagerank(A,struct('alg','linsys',... +% 'linsys_solver',@(f,v,tol,its) gmres(f,v,[],tol, its))); +% pagerank(A,struct('alg','eval')); + + +% +% pagerank.m +% David Gleich +% + +% +% 21 February 2006 +% -- added approximate PageRank +% +% Revision 1.10 +% 28 January 2006 +% -- added different computational modes and timing information +% +% Revision 1.00 +% 19 Octoboer 2005 +% + +% +% The driver does mainly parameter checking, then sends things off to one +% of the computational routines. +% + +[m n] = size(A); +if (m ~= n) + error('pagerank:invalidParameter', 'the matrix A must be square'); +end; + +options = struct('tol', 1e-7, 'maxiter', 500, 'v', ones(n,1)./n, ... + 'c', 0.85, 'verbose', 0, 'alg', 'arnoldi', ... + 'linsys_solver', @(f,v,tol,its) bicgstab(f,v,tol,its), ... + 'arnoldi_k', 8, 'approx_bp', 1e-3, 'approx_boundary', inf,... + 'approx_subiter', 5); + +if (nargin > 1) + options = merge_structs(optionsu, options); +end; + + +if (size(options.v) ~= size(A,1)) + error('pagerank:invalidParameter', ... + 'the vector v must have the same size as A'); +end; + +if (~issparse(A)) + A = sparse(A); +end; + +% normalize the matrix +P = normout(A); + +switch (options.alg) + case 'dense' + [x flag hist dt] = pagerank_dense(P, options); + case 'linsys' + [x flag hist dt] = pagerank_linsys(P, options); + case 'gs' + [x flag hist dt] = pagerank_gs(P, options); + case 'power' + [x flag hist dt] = pagerank_power(P, options); + case 'arnoldi' + [x flag hist dt] = pagerank_arnoldi(P, options); + case 'approx' + [x flag hist dt] = pagerank_approx(P, options); + case 'eval' + [x flag hist dt] = pagerank_eval(P, options); + otherwise + error('pagerank:invalidParameter', ... + 'invalid computation mode specified.'); +end; + + + +% =================================== +% pagerank_linsys +% =================================== + +function [x flag hist dt] = pagerank_linsys(P, options) + +if (options.verbose > 0) + fprintf('linear system computation...\n'); +end; + +tol = options.tol; +v = options.v; +maxiter = options.maxiter; +c = options.c; + +solver = options.linsys_solver; + +% transpose P (see pagerank_linsys_mult docs) +P = P'; + +f = @(x,varargin) pagerank_linsys_mult(x,P,c,length(varargin)); + +tic; +[x flag ignore1 ignore2 hist] = solver(f,v,tol,maxiter); +dt = toc; + +% renormalize the vector to have norm 1 +x = x./norm(x,1); + + + +function y = pagerank_linsys_mult(x,P,c,tflag) +% compute the matrix vector product for the linear system. This function +% includes the transpose flag (tflag > 0) to indicate a transpose multiply. +% Because many of the algorithms just use A*x (and not A'*x) the matrix P +% should have already been transposed. +if (tflag > 0) + %y = x - c*P'*x; + y = x - c*spmatvec_transmult(P,x); +else + %y = x - c*P*x; + y = x - c*spmatvec_mult(P,x); +end; + + +% =================================== +% pagerank_dense +% =================================== + +function [x flag hist dt] = pagerank_dense(P, options) +% solve as a dense linear system + +if (options.verbose > 0) + fprintf('dense computation...\n'); +end; + +v = options.v; +c = options.c; + +n = size(P,1); + +P = eye(n) - c*full(P)'; + +tic; +x = P \ v; +dt = toc; + +hist = norm(P*x - v,1); +flag = 0; + +% renormalize the vector to have norm 1 +x = x./norm(x,1); + + +% =================================== +% pagerank_gs +% =================================== +function [x flag hist dt] = pagerank_gs(P, options) +% use gauss-seidel computation + +if (options.verbose > 0) + fprintf('gauss-seidel computation...\n'); +end; + +tol = options.tol; +v = options.v; +maxiter = options.maxiter; +c = options.c; + +x = v; +if (isfield(options, 'x0')) + x = options.x0; +else + % this is dumb, but we need to make sure + % we actually get x it's own memory... + + % right now, Matlab just has a ``shadow copy'' + x(1) = x(1)-1.0; + x(1) = x(1)+1.0; +end; + +delta = 1; +iter = 0; +P = -c*P; + +hist = zeros(maxiter,1); + +dt = 0; +while (delta > tol && iter < maxiter) + tic; + xold = pagerank_gs_mult(P,x,(1-c)*v); + dt = dt + toc; + + delta = norm(x - xold,1); + hist(iter+1) = delta; + + if (options.verbose > 0) + fprintf('iter=%d; delta=%f\n', iter, delta); + end; + + iter = iter + 1; +end; + +% resize hist +hist = hist(1:iter); + +% renormalize the vector to have norm 1 +x = x./norm(x,1); + +% default is convergence +flag = 0; + +if (delta > tol && iter == maxiter) + warning('pagerank:didNotConverge', ... + 'The PageRank algorithm did not converge after %i iterations', ... + maxiter); + flag = 1; +end; + +% =================================== +% pagerank_power +% =================================== + +function [x flag hist dt] = pagerank_power(P, options) +% use the power iteration algorithm + +if (options.verbose > 0) + fprintf('power iteration computation...\n'); +end; + + +tol = options.tol; +v = options.v; +maxiter = options.maxiter; +c = options.c; + +x = v; +if (isfield(options, 'x0')) + x = options.x0; +end; + +hist = zeros(maxiter,1); +delta = 1; +iter = 0; +dt = 0; +while (delta > tol && iter < maxiter) + tic; + y =c* spmatvec_transmult(P,x); + w = 1 - norm(y,1); + y = y + w*v; + dt = dt + toc; + + delta = norm(x - y,1); + + hist(iter+1) = delta; + + tic; + x = y; + dt = dt + toc; + + if (options.verbose > 0) + fprintf('iter=%d; delta=%f\n', iter, delta); + end; + + iter = iter + 1; +end; + +% resize hist +hist = hist(1:iter); + +flag = 0; + +if (delta > tol && iter == maxiter) + warning('pagerank:didNotConverge', ... + 'The PageRank algorithm did not converge after %i iterations', ... + maxiter); + flag = 1; +end; + +% =================================== +% pagerank_arnoldi +% =================================== + +function [x flag hist dt] = pagerank_arnoldi(P, options) +% use the power iteration algorithm + +if (options.verbose > 0) + fprintf('arnoldi method computation...\n'); +end; + + +tol = options.tol; +v = options.v; +maxiter = options.maxiter; +c = options.c; +k = options.arnoldi_k; + +x = v; +if (isfield(options, 'x0')) + x = options.x0; +end; + +hist = zeros(maxiter,1); + +d = dangling(P); +d = double(d); +P = P'; + +%f = @(x) pagerank_arnoldi_mult(x,P,c,d,v); +f = @(x) pagerank_mult(x,P,c,d,v); + +iter = 0; +dt = 0; +delta = 1; +while (delta > tol && iter < maxiter) + tic; + [Q H] = pagerank_arnoldi_fact(f,x,k); + [u,s,v]=svd(H-[speye(k);zeros(1,k)]); + x=Q(:,1:k)*v(:,k); + dt = dt + toc; + + % for statistics purposes only + delta=norm(f(x)-x,1)/norm(x,1); + + hist(iter+1) = delta; + + if (options.verbose > 0) + fprintf('iter=%d; delta=%f\n', iter, delta); + end; + + iter = iter + 1; +end; + +% ensure correct normalization +x = sign(sum(x))*x; +x = x/norm(x,1); + +% resize hist +hist = hist(1:iter); + +flag = 0; + +if (delta > tol && iter == maxiter) + warning('pagerank:didNotConverge', ... + 'The PageRank algorithm did not converge after %i iterations', ... + maxiter); + flag = 1; +end; + + +function [V,H] = pagerank_arnoldi_fact(A,V,k) +% [Q,H] = ARNOLDI7(A,Q0,K,c,d,e,v) +% +% ARNOLDI: Reduce an n x n matrix A to upper Hessenberg form. +% [Q,H] = ARNOLDI(A,Q0,K) computes (k+1) x k upper +% Hessenberg matrix H and n x k matrix Q with orthonormal +% columns and Q(:,1) = Q0/NORM(Q0), such that +% Q(:,1:k+1)'*A*Q(:,1:k) = H. +% +% A can also be a function_handle to return A*x +% + +% +% Written by Chen Grief +% modified by David Gleich +% + +V(:,1) = V(:,1)/norm(V(:,1)); +if (~isa(A,'function_handle')) + f = @(x) A*x; + A = f; +end; + +w = A(V(:,1)); +alpha=V(:,1)'*w; +H(1,1)=alpha; +f(:,1)=w-V(:,1)*alpha; +for j=1:k-1 + beta=norm(f(:,j)); + V(:,j+1)=f(:,j)/beta; + ejt=[zeros(1,j-1) beta]; + Hhat=[H; ejt]; + w=A(V(:,j+1)); + h=V(:,1:j+1)'*w; + f(:,j+1)=w-V(:,1:j+1)*h; + H=[Hhat h]; +end + +% Extend Arnoldi factorization +beta=norm(f(:,k)); +V(:,k+1) = f(:,k)/beta; +ejt=[zeros(1,k-1) beta]; +H=[H ;ejt]; + +% =================================== +% pagerank_approx +% =================================== + +function [x flag hist dt] = pagerank_approx(A, options) +% use the power iteration algorithm + +if (options.verbose > 0) + fprintf('approximate computation...\n'); +end; + + +tol = options.tol; +v = options.v; +maxiter = options.maxiter; +c = options.c; +bp = options.approx_bp; +subiter = options.approx_subiter; +boundary = options.approx_boundary; + + +n = size(A,1); + +%x = v; +%if (isfield(options, 'x0')) +% x = options.x0; +%end; + +if (length(find(v)) ~= n) + global_pr = 0; +else + global_pr = 1; + error('pagerank:invalidParameter',... + 'approximation computations are not implemented for global pagerank yet'); +end; + + +hist = zeros(maxiter,1); +delta = 1; +iter = 0; +dt = 0; + +% set the initial set of seed pages +if (global_pr) + if (isfield(options, 'x0')) + % the seed pages come from the x0 vector if provided + p = find(options.x0); + x = x0(p); + else + % the seed pages come from the x0 vector (otherwise, choose random) + p = unique(ceil(rand(250,1)*size(P,1))); + x = ones(length(p),1)./length(p); + end; +else + % the seed pages come from the x0 vector + p = find(v); + x = ones(length(p),1)./length(p); + v = v(p); +end; + +local = []; +active = p; +frontier = p; + +tic; +while (iter <= maxiter && delta > tol) + % expand all pages + if (boundary == 1) + + % if we are running the boundary algorithm... + + [ignore sp] = sort(-x); + cs = cumsum(x(sp)); + spactive = active(sp); + allexpand_ind = cs < (1-bp); + % actually, we need to add the first 0 after the last 1 in + % allexpand_ind because we need cumsum to be larger than 1-bp + allexpand_ind(min(find(allexpand_ind == 0))) = ~0; + allexpand = spactive(allexpand_ind); + toexpand = setdiff(allexpand,local); + else + % + % otherwise, just expand all pages with a sufficient tolerance + % + allexpand = active(x > bp); + toexpand = setdiff(allexpand,local); + end; + + if (length(toexpand) > 0) + xp = zeros(n,1); + xp([local frontier]) = x; + + local = [local toexpand]; + frontier = setdiff(find(sum(A(local,:),1)), local); + active = [local frontier]; + + x = xp(local); + else + xp = zeros(n,1); + xp([local frontier]) = x; + x = xp(local); + end; + + Lp = A(local,active); + outdegree = full(sum(Lp,2)); + outdegree = [outdegree; zeros(length(frontier),1)]; + + siter = 0; + L = [Lp; sparse(length(frontier),length(active))]; + x2 = [x; xp(frontier)]; + while (siter < subiter) + y = full(c*L'*(invzero(outdegree).*x2)); + omega = 1 - norm(y,1); + + % the ordering of local is preseved, so these are always the + % correct vertices + y(1:length(p)) = y(1:length(p)) + omega*v; + + x2 = y; + + siter = siter+1; + end; + + + x2 = [x; xp(frontier)]; + + delta = norm(y-x2,1); + hist(iter+1) = delta; + + if (options.verbose > 0) + fprintf('iter=%02i; delta=%0.03e expand=%i\n', iter, delta, length(toexpand)); + end + + x = y; + iter = iter + 1; +end; +dt = toc; +% resize hist +hist = hist(1:iter); + +xpartial = x; +x = zeros(n,1); +x([local frontier]) = xpartial; + +flag = 0; + +if (delta > tol && iter == maxiter) + warning('pagerank:didNotConverge', ... + 'The PageRank algorithm did not converge after %i iterations', ... + maxiter); + flag = 1; +end; + +no% =================================== +% pagerank_eval +% =================================== +function [x flag hist dt] = pagerank_eval(P,options) + +algs = {'power', 'gs', 'arnoldi', 'linsys', 'linsys'}; +extra_opts = {struct(''), struct(''), struct(''), struct(''), ... + struct('linsys_solver',@(f,v,tol,its) gmres(f,v,8,tol, its))}; +names = {'power', 'gs', 'arnoldi8', 'bicgstab', 'gmres8'}; + +v = options.v; +c = options.c; + +x = cell(5,1); +flag = cell(5,1); +hist = cell(5,1); +dt = cell(5,1); + +web('text://Generating PageRank report...','-noaddressbox'); + +htmlend = ''; +s = {}; +s{1} = 'PageRank runtime report

PageRank Report

'; + +stemp = s; +stemp{end+1} = '

Generating graph statistics...

'; +stemp{end+1} = htmlend; + +A = spones(P); +d = dangling(P); + +npages = size(P,1); +nedges = nnz(P); +ndangling = sum(d); +maxindeg = full(max(sum(A,1))); +maxoutdeg = full(max(sum(A,2))); +ncomp = components(A); + +s{end+1} = '

Graph statistics

'; +s{end+1} = ''; +s{end+1} = sprintf('', ... + 'Number of pages', npages); +s{end+1} = sprintf('', ... + 'Number of edges', nedges); +s{end+1} = sprintf('', ... + 'Number of dangling nodes', ndangling); +s{end+1} = sprintf('', ... + 'Max in-degree', maxindeg); +s{end+1} = sprintf('', ... + 'Max out-degree', maxoutdeg); +s{end+1} = sprintf('', ... + 'Number of strong components:', ncomp); +s{end+1} = '
%s:%i
%s:%i
%s:%i
%s:%i
%s:%i
%s:%i
'; + +sOut = [stemp{:}]; +web(['text://' sOut],'-noaddressbox'); + +s{end+1} = '

Algorithm performance

'; +s{end+1} = ''; +s{end+1} = sprintf('', ... + 'c = ', c); +s{end+1} = sprintf('', ... + 'tol = ', options.tol); +s{end+1} = sprintf('', ... + 'maxiter = ', options.maxiter); +s{end+1} = '
%s%0.3f
%s%2.2e
%s%i
'; + +s{end+1} = ''; +s{end+1} = ['' ... + '' ... + '' ... + '' ... + '']; + +for (ii=1:length(algs)) + alg = algs{ii}; + extra_opt = extra_opts{ii}; + name = names{ii}; + + stemp = s; + stemp{end+1} = '
AlgorithmTimeIterationsError
'; + stemp{end+1} = sprintf('

Solving for PageRank with %s...

', char(name)); + stemp{end+1} = htmlend; + + sOut = [stemp{:}]; + web(['text://' sOut],'-noaddressbox'); + + extra_opt = merge_structs(struct('alg',char(alg)),extra_opt); + + [pi flagi histi dti] = pagerank(P, merge_structs(extra_opt,options)); + + p{ii} = pi; + flag{ii} = flagi; + hist{ii} = histi; + dt{ii} = dti; + + err = norm(pi - c*(pi'*P)' - c*(d'*pi)*v - (1-c)*v,1); + + if (mod(ii,2) == 0) + s{end+1} = sprintf('%s%.2f%i%2.2e',... + char(name), dti, length(histi), err); + else + s{end+1} = sprintf('%s%.2f%i%2.2e',... + char(name), dti, length(histi), err); + end; +end + +s{end+1} = ''; + + +s{end+1} = htmlend; +sOut = [s{:}]; +web(['text://' sOut],'-noaddressbox'); + +s{end+1} = sprintf('%s',char(name)); + +% +% plot the time histogram +% +figure(1); +close(1); +figure(1); + +dts = cell2mat(dt); +flags = cell2mat(flag); + +h2 = bar(dts.*(flags==0)); + + set(h2,'FaceColor',[1 1 1]); + set(h2,'LineWidth',2.0); + + set(gca,'XTick', 1:length(algs)); + set(gca,'XTickLabel',names); + ylabel('time (sec)'); + + +% +% plot the history results +% +figure(2); +close(2); +figure(2); +lso = get(0,'DefaultAxesLineStyleOrder'); +lsc = get(0,'DefaultAxesColorOrder'); + +lso = {'o-', 'x:', '+-.', 's--', 'd-'}; + + nlso = length(lso); + curlso = 0; + nlsc = length(lsc); + curlsc = 0; + + for ii=1:length(algs) + histi = hist{ii}; + %legendname = fn{ii}; + %line(1:length(mrval.hist), mrval.hist); + semilogy(1:length(histi),histi,... + lso{mod(curlso,nlso)+1}, ... + 'Color',lsc(mod(curlsc,nlsc)+1,:),... + 'MarkerSize',3); + hold on; + curlso = curlso+1; + curlsc = curlsc+1; + end; + + title('PageRank algorithm convergence (WARNING: DIFFERENT Y-SCALES)'); + xlabel('iteration')'; + ylabel('convergence measure'); + + legend(names{:}); + + +function S = merge_structs(A, B) +% MERGE_STRUCTS Merge two structures. +% +% S = merge_structs(A, B) makes the structure S have all the fields from A +% and B. Conflicts are resolved by using the value in A. +% + +% +% merge_structs.m +% David Gleich +% +% Revision 1.00 +% 19 Octoboer 2005 +% + +S = A; + +fn = fieldnames(B); + +for ii = 1:length(fn) + if (~isfield(A, fn{ii})) + S.(fn{ii}) = B.(fn{ii}); + end; +end; + +function P = normout(A) +% NORMOUT Normalize the outdegrees of the matrix A. +% +% P = normout(A) +% +% P has the same non-zero structure as A, but is normalized such that the +% sum of each row is 1, assuming that A has non-negative entries. +% + +% +% normout.m +% David Gleich +% +% Revision 1.00 +% 19 Octoboer 2005 +% + +% compute the row-sums/degrees +d = full(sum(A,2)); + +% invert the non-zeros in the data +id = invzero(d); + +% scale the rows of the matrix +P = diag(sparse(id))*A; + +function v = invzero(v) +% INVZERO Compute the inverse elements of a vector with zero entries. +% +% iv = invzero(v) +% +% iv is 1./v except where v = 0, in which case it is 0. +% + +% +% invzero.m +% David Gleich +% +% Revision 1.00 +% 19 Octoboer 2005 +% + +% sparse input are easy to handle +if (issparse(v)) + [m n] = size(v); + [i j val] = find(v); + val = 1./val; + v = sparse(i,j,val,m,n); + return; +end; + +% so are dense input + +% compute the 0 mask +zm = abs(v) > eps(1); + +% invert all non-zeros +v(zm) = 1./v(zm); + +function dmask = dangling(A) +% DANGLING Compute the indicator vector for dangling links for webgraph A +% +% d = dangling(A) +% + +d = full(sum(A,2)); +dmask = d == 0; + +function [k,sizes]=components(A) + +% based on components.m from (MESHPART Toolkit) +% which had +% John Gilbert, Xerox PARC, 8 June 1992. +% Copyright (c) 1990-1996 by Xerox Corporation. All rights reserved. +% HELP COPYRIGHT for complete copyright and licensing notice + +[p,p,r,r] = dmperm(A|speye(size(A))); +sizes = diff(r); +k = length(sizes); \ No newline at end of file diff --git a/matlab/package/pagerank_gs_mult.c b/matlab/package/pagerank_gs_mult.c new file mode 100644 index 0000000..e71d0f5 --- /dev/null +++ b/matlab/package/pagerank_gs_mult.c @@ -0,0 +1,109 @@ +/* + * ============================================================= + * pagerank_gs_mult.c Compute the matrix vector multiplication + * for the gauss seidel iteration in an efficient manner + * (that is, by overwriting the vector x in place.) + * + * David Gleich + * Stanford University + * 28 January 2006 + * ============================================================= + */ + +#include "mex.h" + +/* + * The mex function just computes one matrix-vector product. + */ +void mexFunction(int nlhs, mxArray *plhs[], + int nrhs, const mxArray *prhs[]) +{ + int i, j, k; + int n, mrows, ncols; + + /* sparse matrix */ + int A_nz; + int *A_row, *A_col; + double *A_val; + + double *x, *b; + double *xold; + + if (nrhs != 3) + { + mexErrMsgTxt("Three inputs required."); + } + else if (nlhs > 1) + { + mexErrMsgTxt("Too many output arguments"); + } + + mrows = mxGetM(prhs[0]); + ncols = mxGetN(prhs[0]); + if (mrows != ncols || + !mxIsSparse(prhs[0]) || + !mxIsDouble(prhs[0]) || + mxIsComplex(prhs[0])) + { + mexErrMsgTxt("Input must be a noncomplex square sparse matrix."); + } + + /* okay, the first input passes */ + n = mrows; + + /* The second input must be a vector. */ + if (mxGetM(prhs[1])*mxGetN(prhs[1]) != n || + mxIsSparse(prhs[1]) || !mxIsDouble(prhs[1])) + { + mexErrMsgTxt("Invalid vector."); + } + + /* The third input must be a vector. */ + if (mxGetM(prhs[2])*mxGetN(prhs[2]) != n || + mxIsSparse(prhs[2]) || !mxIsDouble(prhs[2])) + { + mexErrMsgTxt("Invalid vector."); + } + + /* Get the sparse matrix */ + A_nz = mxGetNzmax(prhs[0]); + A_val = mxGetPr(prhs[0]); + A_row = mxGetIr(prhs[0]); + A_col = mxGetJc(prhs[0]); + + /* Get the vector x */ + x = mxGetPr(prhs[1]); + + /* Get the vector b */ + b = mxGetPr(prhs[2]); + + /* if they request x old, then we need to copy x to xold */ + if (nlhs > 0) + { + plhs[0] = mxDuplicateArray(prhs[1]); + } + + /* Update x in place, this means we have to iterate over columns + * of the matrix A. */ + + for (i = 0; i < n; i++) + { + /* we actually compute one iteration for the + * system (I+A')x = b */ + double aself = 1.0; + double xnew = b[i]; + + + for (j = A_col[i]; j < A_col[i+1]; ++j) + { + /* add to aself only if the row = i (the column) */ + aself += A_val[j]*(A_row[j] == i); + + /* add to xnew only if row != i */ + xnew -= A_val[j]*x[A_row[j]]*(A_row[j] != i); + } + + x[i] = xnew/aself; + } +} + diff --git a/matlab/package/pagerank_gs_mult.mexa64 b/matlab/package/pagerank_gs_mult.mexa64 new file mode 100644 index 0000000000000000000000000000000000000000..215b8d7997cbe1d41c7be6aca9fcf6752d8c9c84 GIT binary patch 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c*Pt*x + (c*(d'*x))*v + (1-c)*sum(x)*v; + */ +void mexFunction(int nlhs, mxArray *plhs[], + int nrhs, const mxArray *prhs[]) +{ + int i, j, k; + int n, mrows, ncols; + + /* sparse matrix */ + int *A_row, *A_col; + double *A_val; + + double *x, *d, *v; + double c; + double *y; + + double sum_x; + double dtx; + double xval; + + + if (nrhs != 5) + { + mexErrMsgTxt("5 inputs required."); + } + else if (nlhs > 1) + { + mexErrMsgTxt("Too many output arguments"); + } + + mrows = mxGetM(prhs[1]); + ncols = mxGetN(prhs[1]); + if (mrows != ncols || + !mxIsSparse(prhs[1]) || + !mxIsDouble(prhs[1]) || + mxIsComplex(prhs[1])) + { + mexErrMsgTxt("Input must be a noncomplex square sparse matrix."); + } + + /* okay, the second input passes */ + n = mrows; + + /* The first input must be a vector. */ + if (mxGetM(prhs[0])*mxGetN(prhs[0]) != n || + mxIsSparse(prhs[0]) || !mxIsDouble(prhs[0])) + { + mexErrMsgTxt("Invalid vector 1."); + } + + /* The third input must be a scalar. */ + if (mxGetM(prhs[2])*mxGetN(prhs[2]) != 1 || !mxIsDouble(prhs[0])) + { + mxErrMsgTxt("Invalid scalar 3."); + } + + /* The fourth input must be a scalar. */ + if (mxGetM(prhs[3])*mxGetN(prhs[3]) != n || + mxIsSparse(prhs[3]) || !mxIsDouble(prhs[3])) + { + mexErrMsgTxt("Invalid vector 4."); + } + + /* The fifth input must be a scalar. */ + if (mxGetM(prhs[4])*mxGetN(prhs[4]) != n || + mxIsSparse(prhs[4]) || !mxIsDouble(prhs[4])) + { + mexErrMsgTxt("Invalid vector 5."); + } + + /* Get the sparse matrix */ + A_val = mxGetPr(prhs[1]); + A_row = mxGetIr(prhs[1]); + A_col = mxGetJc(prhs[1]); + + /* Get the vector x */ + x = mxGetPr(prhs[0]); + + /* Get the vector d */ + d = mxGetPr(prhs[3]); + + /* Get the vector v */ + v = mxGetPr(prhs[4]); + + c = mxGetScalar(prhs[2]); + + plhs[0] = mxCreateDoubleMatrix(n,1,mxREAL); + y = mxGetPr(plhs[0]); + + sum_x = 0.0; + dtx = 0.0; + + for (i = 0; i < n; i++) + { + xval = x[i]; + sum_x += xval; + dtx += d[i]*xval; + + for (j = A_col[i]; j < A_col[i+1]; ++j) 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+#include "mex.h" + +/* + * The mex function just computes one matrix-vector product. + * + * function y = A*x; + */ +void mexFunction(int nlhs, mxArray *plhs[], + int nrhs, const mxArray *prhs[]) +{ + int i, j, k; + int mrows, ncols; + + /* sparse matrix */ + int *A_row, *A_col; + double *A_val; + + double *x; + double *y; + + double xval; + + if (nrhs != 2) + { + mexErrMsgTxt("2 inputs required."); + } + else if (nlhs > 1) + { + mexErrMsgTxt("Too many output arguments"); + } + + mrows = mxGetM(prhs[0]); + ncols = mxGetN(prhs[0]); + if (!mxIsSparse(prhs[0]) || + !mxIsDouble(prhs[0]) || + mxIsComplex(prhs[0])) + { + mexErrMsgTxt("Input must be a noncomplex sparse matrix."); + } + + /* The first input must be a vector. */ + if (mxGetM(prhs[1])*mxGetN(prhs[1]) != ncols || + mxIsSparse(prhs[1]) || !mxIsDouble(prhs[1])) + { + mexErrMsgTxt("Invalid vector."); + } + + /* Get the sparse matrix */ + A_val = mxGetPr(prhs[0]); + A_row = mxGetIr(prhs[0]); + A_col = mxGetJc(prhs[0]); + + /* Get 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============================================================= + */ + +#include "mex.h" + +/* + * The mex function just computes one matrix-vector product. + * + * function y = A'*x + */ +void mexFunction(int nlhs, mxArray *plhs[], + int nrhs, const mxArray *prhs[]) +{ + int i, j, k; + int mrows, ncols; + + /* sparse matrix */ + int *A_row, *A_col; + double *A_val; + + double *x; + double *y; + + double yval; + + if (nrhs != 2) + { + mexErrMsgTxt("2 inputs required."); + } + else if (nlhs > 1) + { + mexErrMsgTxt("Too many output arguments"); + } + + mrows = mxGetM(prhs[0]); + ncols = mxGetN(prhs[0]); + if (!mxIsSparse(prhs[0]) || + !mxIsDouble(prhs[0]) || + mxIsComplex(prhs[0])) + { + mexErrMsgTxt("Input must be a noncomplex sparse matrix."); + } + + /* The second input must be a vector. */ + if (mxGetM(prhs[1])*mxGetN(prhs[1]) != mrows || + mxIsSparse(prhs[1]) || !mxIsDouble(prhs[1])) + { + mexErrMsgTxt("Invalid vector 2."); + } + + /* Get the sparse matrix */ + A_val = mxGetPr(prhs[0]); + A_row = mxGetIr(prhs[0]); + A_col = mxGetJc(prhs[0]); + + /* Get the vector x */ + x = mxGetPr(prhs[1]); + + plhs[0] = mxCreateDoubleMatrix(ncols,1,mxREAL); + y = mxGetPr(plhs[0]); + + for (i = 0; i < ncols; i++) + { + yval = 0.0; + + for (j = A_col[i]; j < A_col[i+1]; ++j) + { + yval += A_val[j]*x[A_row[j]]; + } + + y[i] = yval; + } +} + diff --git a/matlab/package/spmatvec_transmult.mexa64 b/matlab/package/spmatvec_transmult.mexa64 new file mode 100644 index 0000000000000000000000000000000000000000..45cfcb80e0d00615834cc48d347d626da3172332 GIT binary patch literal 9914 zcmdT~eQaCR6~FdNQWuiODYWa_0$!n00o6&<(4}1d+%|s zZ){OjOxjNJeD3+3bME)oyZ1fN+PTZ^axo%i;9dWcpx)J;^z4IkXuLc|_t`!ho1vFW1t zvV1$KUIyfLP%V^H8qlYx-xS){u(Ps%6ynR-xuW<=cBopdDdA;6s~y$w6sV{k(Q2JA zWwwS>{ay|ozJ|Sm=WajdjsnjnUUEwewGuwv1BY-a8rGJEWSXvVSA%`q#Ju`?`g5AVt*!cH`q zz;J6i-IW>W8+KTHxXpID1lt3wJ=2@A(ixivTawvOOaz;g@l?zn7KYtv!P_O@9R|5M zZCj2lT)HeL9R*{1_$E7@!9-)xP<+^*N%DZ54_OXj!2MfLn{guHYp>0VDQ6HOj-XtJ 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"serial_gs_pagerank_functions.h" + +struct timeval startwtime, endwtime; +double seq_time; + +int main(int argc, char **argv) { + int **directedWebGraph; + double **transitionMatrix, *pagerankVector; + Parameters parameters; + + parseArguments(argc, argv, ¶meters); + + initialize(&directedWebGraph, &transitionMatrix, &pagerankVector, ¶meters); + + //Starts wall-clock timer + gettimeofday (&startwtime, NULL); + + int iterations = pagerank(&transitionMatrix, &pagerankVector, parameters); + if (parameters.verbose) { + printf("\n----- Results -----\ + \nTotal iterations = %d\n", iterations); + } + + //Stops wall-clock timer + gettimeofday (&endwtime, NULL); + double seq_time = (double)((endwtime.tv_usec - startwtime.tv_usec)/1.0e6 + + endwtime.tv_sec - startwtime.tv_sec); + printf("%s wall clock time = %f\n","Pagerank (Gauss-Seidel method), serial implementation", + seq_time); +} diff --git a/serial/serial_gs_pagerank_functions.c b/serial/serial_gs_pagerank_functions.c new file mode 100644 index 0000000..380a3a1 --- /dev/null +++ b/serial/serial_gs_pagerank_functions.c @@ -0,0 +1,286 @@ +#include "serial_gs_pagerank_functions.h" + +const char *CONVERGENCE_ARGUMENT = "-c"; +const char *MAX_ITERATIONS_ARGUMENT = "-m"; +const char *DAMPING_FACTOR_ARGUMENT = "-a"; +const char *VERBAL_OUTPUT_ARGUMENT = "-v"; +const int NUMERICAL_BASE = 10; + +void validUsage(char *programName) { + printf("%s [-c convergence] [-m max_iterations] [-a alpha] [-v] \ + \n-c convergence\ + \n\tthe convergence criterion\ + \n-m max_iterations\ + \n\tmaximum number of iterations to perform\ + \n-a alpha\ + \n\tthe damping factor\ + \n-v enable verbal output\ + \n", programName); + exit(EXIT_FAILURE); +} + +int checkIncrement(int previousIndex, int maxIndex, char *programName) { + if (previousIndex == maxIndex) { + validUsage(programName); + exit(EXIT_FAILURE); + } + return ++previousIndex; +} + +void parseArguments(int argumentCount, char **argumentVector, Parameters *parameters) { + if (argumentCount < 2 || argumentCount > 10) { + validUsage(argumentVector[0]); + } + + (*parameters).numberOfPages = 0; + (*parameters).maxIterations = 0; + (*parameters).convergenceCriterion = 1; + (*parameters).dampingFactor = 0.85; + (*parameters).verbose = false; + + char *endPointer; + int argumentIndex = 1; + + while (argumentIndex < argumentCount) { + if (!strcmp(argumentVector[argumentIndex], CONVERGENCE_ARGUMENT)) { + argumentIndex = checkIncrement(argumentIndex, argumentCount, argumentVector[0]); + + double convergenceInput = strtod(argumentVector[argumentIndex], &endPointer); + if (convergenceInput == 0) { + printf("Invalid convergence argument\n"); + exit(EXIT_FAILURE); + } + (*parameters).convergenceCriterion = convergenceInput; + } else if (!strcmp(argumentVector[argumentIndex], MAX_ITERATIONS_ARGUMENT)) { + argumentIndex = checkIncrement(argumentIndex, argumentCount, argumentVector[0]); + + size_t iterationsInput = strtol(argumentVector[argumentIndex], &endPointer, NUMERICAL_BASE); + if (iterationsInput == 0 && endPointer) { + printf("Invalid iterations argument\n"); + exit(EXIT_FAILURE); + } + (*parameters).maxIterations = iterationsInput; + } else if (!strcmp(argumentVector[argumentIndex], DAMPING_FACTOR_ARGUMENT)) { + argumentIndex = checkIncrement(argumentIndex, argumentCount, argumentVector[0]); + + double alphaInput = strtod(argumentVector[argumentIndex], &endPointer); + if ((alphaInput == 0 || alphaInput > 1) && endPointer) { + printf("Invalid alpha argument\n"); + exit(EXIT_FAILURE); + } + (*parameters).dampingFactor = alphaInput; + } else if (!strcmp(argumentVector[argumentIndex], VERBAL_OUTPUT_ARGUMENT)) { + (*parameters).verbose = true; + } else if (argumentIndex == argumentCount - 1) { + (*parameters).graphFilename = argumentVector[argumentIndex]; + } else { + validUsage(argumentVector[0]); + exit(EXIT_FAILURE); + } + ++argumentIndex; + } +} + +void readGraphFromFile(int ***directedWebGraph, Parameters *parameters) { + FILE *graphFile; + + // Opens the file for reading + graphFile = fopen((*parameters).graphFilename, "r+"); + if (!graphFile) { + printf("Error opening file \n"); + exit(EXIT_FAILURE); + } + + // Reads the dimensions of the (square) array from the file + int readChar, numberOfLines=0; + while((readChar = fgetc(graphFile))) { + // Breaks if end of file + if (readChar == EOF) break; + // Otherwise, if the character is a break line, adds one to the count of lines + if (readChar == '\n') { + ++numberOfLines; + } + } + + if ((*parameters).verbose) { + printf("Line count of file is %d \n", numberOfLines); + } + + // Each line of the file represents one page of the graph + (*parameters).numberOfPages = numberOfLines; + rewind(graphFile); + + // Allocates memory and loads values into directedWebGraph (matrix A) + // Allocates memory for the rows + (*directedWebGraph) = (int **) malloc((*parameters).numberOfPages * sizeof(int *)); + + for (int i=0; i<(*parameters).numberOfPages; ++i) { + // Allocates memory for the columns of this row + (*directedWebGraph)[i] = (int *) malloc((*parameters).numberOfPages * sizeof(int)); + // Reads values from the file + for (int j=0; j<(*parameters).numberOfPages; ++j) { + if (!fscanf(graphFile, "%d ", &(*directedWebGraph)[i][j])) { + break; + } + //printf("directedWebGraph[%d][%d] = %d", i , j, (*directedWebGraph)[i][j]); + } + } + + fclose(graphFile); +} + +void generateNormalizedTransitionMatrix(double ***transitionMatrix, + int **directedWebGraph, Parameters parameters) { + // Allocates memory for the transitionMatrix rows + (*transitionMatrix) = (double **) malloc(parameters.numberOfPages * sizeof(double *)); + + for (int i=0; i parameters.convergenceCriterion && + (parameters.maxIterations != 0 || iterations < parameters.maxIterations)); + + return iterations; +} \ No newline at end of file diff --git a/serial/serial_gs_pagerank_functions.h b/serial/serial_gs_pagerank_functions.h new file mode 100644 index 0000000..9eea0e1 --- /dev/null +++ b/serial/serial_gs_pagerank_functions.h @@ -0,0 +1,75 @@ +#ifndef SERIAL_GS_PAGERANK_FUNCTIONS_H /* Include guard */ +#define SERIAL_GS_PAGERANK_FUNCTIONS_H + +#include +#include +#include +#include + +/* + * Constant strings that store the command line options available. +*/ +extern const char *CONVERGENCE_ARGUMENT; +extern const char *MAX_ITERATIONS_ARGUMENT; +extern const char *DAMPING_FACTOR_ARGUMENT; +extern const char *VERBAL_OUTPUT_ARGUMENT; + +// This is the numerical base used when parsing the numerical command line +// arguments. +extern const int NUMERICAL_BASE; + +// Declares a data structure to conveniently hold the algorithm's parameters +typedef struct parameters { + int numberOfPages, maxIterations; + double convergenceCriterion, dampingFactor; + bool verbose; + char* graphFilename; +} Parameters; + +// Function validUsage outputs the correct way to use the program with command +// line arguments. +void validUsage(char *programName); + +// Function checkIncrement is a helper function used in parseArguments (see +// bellow). +int checkIncrement(int previousIndex, int maxIndex, char *programName); + +// Function parseArguments parses command line arguments. +void parseArguments(int argumentCount, char **argumentVector, Parameters *parameters); + +// Function readGraphFromFile loads the graph stored in the file provided in the +// command line arguments to the array directedWebGraph. +void readGraphFromFile(int ***directedWebGraph, Parameters *parameters); + +// Function generateNormalizedTransitionMatrix generates the normalized transition +// matrix from the graph data. +void generateNormalizedTransitionMatrix(double ***transitionMatrix, + int **directedWebGraph, Parameters parameters); + +// Function makeIrreducible introduces teleportation to the transition matrix, +// making it irreducible. +void makeIrreducible(double ***transitionMatrix, Parameters parameters); + +// Function transposeMatrix transposes a matrix. +void transposeMatrix(double ***matrix, int rows, int columns); + +// Function initialize allocates required memory for arrays, reads the dataset +// from the file and creates the transition probability distribution matrix. +void initialize( + int ***directedWebGraph, /*This is matrix G (web graph)*/ + double ***transitionMatrix, /*This is matrix A (transition probability distribution matrix)*/ + double **pagerankVector, /*This is the resulting pagerank vector*/ + Parameters *parameters + ); + +// Function vectorFirstNorm calculates the first norm of a vector. +double vectorFirstNorm(double *vector, int vectorSize); + +// Function nextProbabilityDistribution calculates the product of the transition +// matrix and the pagerank vector. +void nextProbabilityDistribution(double ***transitionMatrix, double *previousPagerankVector, + double **newPagerankVector, Parameters parameters); + +int pagerank(double ***transitionMatrix, double **pagerankVector, Parameters parameters); + +#endif // SERIAL_GS_PAGERANK_FUNCTIONS_H \ No newline at end of file