69 lines
2.0 KiB
Mathematica
69 lines
2.0 KiB
Mathematica
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%%*******************************************************
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%% thetaproblem: Lovasz theta number.
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%%
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%% (primal) min Tr C*X
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%% s.t. X(i,j) = 0 if (i,j) is an edge of G,
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%% Tr(X) = 1.
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%% b = e1,
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%% C = -ones(n),
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%% A1 = eye(n), Ak = ei*ej' + ej*ei', if (i,j) is an edge.
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%%-------------------------------------------------------
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%%
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%% [blk,Avec,C,b,X0,y0,Z0,objval,X] = thetaproblem(G,feas,solve);
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%%
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%% G: adjacency matrix of a graph.
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%% feas = 1 if want feasible starting point
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%% = 0 if otherwise.
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%% solve = 0 just to initialize
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%% = 1 if want to solve the problem.
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%%
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%% See graph.m --- generate random adjacency matrix.
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%%*****************************************************************
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%% SDPT3: version 4.0
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%% Copyright (c) 1997 by
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%% Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu
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%% Last Modified: 16 Sep 2004
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%%*****************************************************************
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function [blk,Avec,C,b,X0,y0,Z0,objval,X] = thetaproblem(G,feas,solve);
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if (nargin < 2); feas = 0; end
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if (nargin < 3); solve = 0; end
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if isempty(feas); feas = 0; end
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if ~isreal(G); error('only real G allowed'); end;
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n = length(G);
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m = sum(sum(triu(G,1))) + 1;
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e1 = [1 zeros(1,m-1)]';
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C{1} = -ones(n);
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b = e1;
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blk{1,1} = 's'; blk{1,2} = n;
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A = cell(1,m); A{1} = speye(n);
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cnt = 2;
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for i = 1:n
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idx = find(G(i,i+1:n));
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idx = idx+i; %% adjust index.
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for j = 1:length(idx)
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A{1,cnt} = sparse([i idx(j)],[idx(j) i],[1 1],n,n);
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cnt = cnt + 1;
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end
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end
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Avec = svec(blk,A,ones(size(blk,1),1));
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if (feas == 1)
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y0 = -2*n*e1;
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Z0 = 2*n*eye(n)+C{1};
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X0 = eye(n)/n;
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elseif (feas == 0);
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[X0,y0,Z0] = infeaspt(blk,Avec,C,b);
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end
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if (solve)
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[obj,X,y,Z] = sqlp(blk,Avec,C,b,[],X0,y0,Z0);
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objval = obj(1);
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else
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objval = []; X = [];
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end
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%%=======================================================
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