73 lines
2.1 KiB
Mathematica
73 lines
2.1 KiB
Mathematica
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%%*******************************************************
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%% gpp: pgraph partitioning problem.
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%%
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%% (primal problem) min Tr C*X
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%% s.t. Tr(ee'*X) = alpha,
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%% diag(X) = e,
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%%
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%% C = -(diag(B*e)-B).
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%%
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%% (dual problem) max alpha*y1 + e'*y
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%% s.t. y1*e*e^T + diag(y) + Z = C.
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%%-------------------------------------------------------
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%%
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%% [blk,Avec,C,b,X0,y0,Z0,objval,X] = gpp(B,alpha,feas,solve);
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%%
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%% B: weighted adjacency matrix of a graph with n nodes.
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%% alpha: any real number,
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%% for alpha in (0,n^2), primal problem is strictly feasible.
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%% in {0,n^2}, primal problem is feasible but not strictly.
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%% outside [0,n^2], primal problem is infeasible.
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%% [default = 1].
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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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%%*****************************************************************
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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] = gpp(B,alpha,feas,solve);
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if nargin < 2; alpha = 1; end;
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if nargin < 3; feas = 0; end;
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if nargin < 4; solve = 0; end;
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if ~isreal(B); error('only real B allowed'); end;
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n = length(B); e = ones(n,1);
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C = -(spdiags(B*e,0,n,n)-B);
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b = [alpha; e];
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blk{1,1} = 's'; blk{1,2} = n;
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A = cell(1,n+1);
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A{1} = e*e';
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for k = 1:n; A{k+1} = sparse(k,k,1,n,n); 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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error('feas = 1, this option is not avaliable');
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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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