94 lines
2.9 KiB
Mathematica
94 lines
2.9 KiB
Mathematica
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%%******************************************************************
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%% randlowranksdp.m : creates random feasible SDP problems where the
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%% constraint matrices are low-rank matrices of the
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%% form V*diag(d)*V'.
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%%
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%% [blk2,At2,C,b,blk,At] = randlowranksdp(n,m1,m2,r);
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%%
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%% blk2,At2: data with low-rank structure coded.
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%% blk, At: data without taking low-rank structure into account.
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%%
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%% n = size of the sdp variable
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%% m1 = number of general constraints
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%% m2 = number of low-rank constraints
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%% r = rank of each constraint 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 [blk2,At2,C,b,blk,At] = randlowranksdp(n,m1,m2,r)
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blk = cell(1,2);
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if (m1 > 0)
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[blk,At0,C,b0] = randsdp(n,[],[],m1);
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else
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b0 = []; At0 = cell(1);
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end
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if (m2 > 0)
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if (nargout > 4)
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[blk2,At2,C,b2,blk,At1] = randlowranksdpfun(n,m2,r);
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else
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[blk2,At2,C,b2] = randlowranksdpfun(n,m2,r);
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end
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else
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b2 = []; At1 = cell(1); blk2 = blk;
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end
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b = [b0; b2];
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if (nargout > 4)
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At{1} = [At0{1}, At1{1}];
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end
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At2{1,1} = At0{1};
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%%******************************************************************
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%%******************************************************************
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function [blk2,At2,C,b,blk,At] = randlowranksdpfun(n,m,r)
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randn('state',0);
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blk{1,1} = 's'; blk{1,2} = n;
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blk2{1,1} = 's'; blk2{1,2} = n; blk2{1,3} = r*ones(1,m);
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%%
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%% construct data with low rank structure
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%%
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At2 = cell(1,3);
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b = zeros(m,1);
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X0 = randn(n); X0 = X0*X0'; X0 = 0.5*(X0+X0');
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ss = [0,cumsum(blk2{1,3})];
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V = randn(n,m*r);
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dd = [];
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for k = 1:length(blk2{1,3})
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idx = [ss(k)+1 : ss(k+1)];
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len = blk2{1,3}(k);
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Dk = randn(len,len); Dk = 0.5*(Dk+Dk');
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[ii,jj,vv] = find(Dk);
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numnz = length(ii);
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dd = [dd; k*ones(numnz,1),ii,jj,vv]; %% each row has the form [constr,i,j,val]
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tmp1 = X0*V(:,idx);
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tmp2 = V(:,idx)*Dk;
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b(k) = sum(sum(tmp1.*tmp2));
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end
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At2{1,2} = V; At2{1,3} = dd;
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Z0 = X0;
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y0 = randn(m,1);
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Aty = At2{1,2}*spdiags(mexexpand(blk2{1,3},y0),0,r*m,r*m)*At2{1,2}';
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C{1} = Z0 + norm(Aty,'fro')*speye(n,n) + Aty;
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C{1} = 0.5*(C{1}+C{1}');
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%%
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%% construct data without exploiting low rank structure
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%%
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if (nargout > 4)
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idxD = [0; find(diff(dd(:,1))); size(dd,1)];
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for k = 1:m
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idx = [ss(k)+1 : ss(k+1)];
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Vk = At2{1,2}(:,idx);
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len = blk2{1,3}(k);
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idx2 = [idxD(k)+1:idxD(k+1)];
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Dk = spconvert([dd(idx2,2:4); len,len,0]);
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A{k} = Vk*Dk*Vk';
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end
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At = svec(blk,A);
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end
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%%******************************************************************
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