128 lines
4.3 KiB
Mathematica
128 lines
4.3 KiB
Mathematica
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%%*****************************************************************
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%% detect_lblk: detect diagonal blocks in the SDP data.
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%%
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%% [blk,At,C,diagblkinfo,blockchange,parbarrier,X,Z] = ...
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%% detect_lblk(blk,At,C,b,parbarrier,X,Z);
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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,At,C,diagblkinfo,blockchange,parbarrier,X,Z] = ...
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detect_lblk(blk,At,C,b,parbarrier,X,Z,printlevel);
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if (nargin < 8); printlevel = 1; end
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%%
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%% Acum = abs(C) + sum_{k=1}^m abs(Ak)
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%% but with diagonal elements removed.
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%%
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blkold = blk;
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m = length(b);
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ee = ones(m,1);
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numdiagelt = 0;
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numblknew = 0;
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blockchange = zeros(size(blk,1),1);
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Acum = cell(size(blk,1),1);
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diagblkinfo = cell(size(blk,1),3);
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for p=1:size(blk,1)
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pblk = blk(p,:);
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n = sum(pblk{2});
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if strcmp(pblk{1},'s') & (length(pblk{2}) == 1) & (size(At{p,1},2)==m)
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Acumtmp = smat(blk(p,:),abs(At{p})*ee,1) + abs(C{p});
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Acum{p} = Acumtmp - spdiags(diag(Acumtmp),0,n,n);
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rownorm = sqrt(sum(Acum{p}.*Acum{p}))';
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idxdiag = find(rownorm < 1e-15);
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if ~isempty(idxdiag)
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blockchange(p) = 1;
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numdiagelt = numdiagelt + length(idxdiag);
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idxnondiag = setdiff([1:n]',idxdiag);
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diagblkinfo{p,2} = idxdiag;
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diagblkinfo{p,3} = idxnondiag;
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if ~isempty(idxnondiag)
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numblknew = numblknew + 1;
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diagblkinfo{p,1} = numblknew;
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end
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else
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numblknew = numblknew + 1;
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diagblkinfo{p,1} = numblknew;
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end
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else
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numblknew = numblknew + 1;
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diagblkinfo{p,1} = numblknew;
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end
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end
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%%
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%% extract diagonal sub-blocks in nondiagonal blocks
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%% into a single linear block
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%%
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if any(blockchange)
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numblk = size(blkold,1);
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idx_keepblk = [];
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Atmp = cell(1,m);
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Adiag = cell(1,m);
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C(numblk+1,1) = cell(1,1);
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Cdiag = []; Xdiag = []; Zdiag = [];
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parbarrierdiag = [];
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for p = 1:numblk
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n = sum(blkold{p,2});
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if (blockchange(p)==1)
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idxdiag = diagblkinfo{p,2};
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idxnondiag = diagblkinfo{p,3};
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if ~isempty(idxdiag);
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blk{p,2} = length(idxnondiag);
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len = length(idxdiag);
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for k = 1:m;
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Ak = mexsmat(blkold,At,1,p,k);
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tmp = diag(Ak);
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Atmp{k} = Ak(idxnondiag,idxnondiag);
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Adiag{k} = [Adiag{k}; tmp(idxdiag)];
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end
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tmp = diag(C{p,1});
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Cdiag = [Cdiag; tmp(idxdiag)];
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C{p,1} = C{p,1}(idxnondiag,idxnondiag);
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At(p) = svec(blk(p,:),Atmp,1);
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if (nargin >= 7)
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parbarrierdiag = [parbarrierdiag, parbarrier{p}*ones(1,len)];
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tmp = diag(X{p,1});
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Xdiag = [Xdiag; tmp(idxdiag)];
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tmp = diag(Z{p,1});
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Zdiag = [Zdiag; tmp(idxdiag)];
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X{p,1} = X{p,1}(idxnondiag,idxnondiag);
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Z{p,1} = Z{p,1}(idxnondiag,idxnondiag);
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end
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end
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if ~isempty(idxnondiag)
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idx_keepblk = [idx_keepblk, p];
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else
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if (printlevel)
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fprintf(' %2.0dth semidefinite block is actually diagonal\n',p);
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end
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end
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else
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idx_keepblk = [idx_keepblk, p];
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end
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end
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blk{numblk+1,1} = 'l';
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blk{numblk+1,2} = numdiagelt;
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C{numblk+1,1} = Cdiag;
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At(numblk+1,1) = svec(blk(numblk+1,:),Adiag,1);
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idx_keepblk = [idx_keepblk, numblk+1];
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blk = blk(idx_keepblk,:);
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C = C(idx_keepblk,:);
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At = At(idx_keepblk,:);
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if (nargin >= 7)
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parbarrier{numblk+1,1} = parbarrierdiag;
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X{numblk+1,1} = Xdiag;
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Z{numblk+1,1} = Zdiag;
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parbarrier = parbarrier(idx_keepblk);
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X = X(idx_keepblk);
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Z = Z(idx_keepblk);
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end
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end
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%%******************************************************************
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