115 lines
3.9 KiB
Mathematica
115 lines
3.9 KiB
Mathematica
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%%*******************************************************************
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%% schurmat_qblk: compute schur matrix corresponding to SOCP blocks.
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%%
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%% HKM direction: output = schur + Ax*Ae' + Ae*Ax' - Ad*Ad'
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%% NT direction: output = schur + Ae*Ae' - Ad*Ad'
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%%
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%% where schur = A*D*A', and Ad is the modification to ADA'
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%% so that the latter is positive definite.
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%%
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%% [schur,UU,EE] = schurmat_qblk(blk,At,schur,UU,EE,p,dd,ee,xx);
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%%
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%% UU: stores the dense columns of Ax, Ae, Ad, and possibly
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%% those of A*D^{1/2}. It has the form UU = [Ax Ae Ad].
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%% EE: stores the assocaited (2,2) block matrix when the
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%% output matrix is expressed as an augmented matrix.
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%% It has the form EE = [0 -lam 0; -lam 0 0; 0 0 I].
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%%
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%% options = 0, HKM
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%% = 1, NT
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%%
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%% SDPT3: version 3.1
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%% Copyright (c) 1997 by
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%% K.C. Toh, M.J. Todd, R.H. Tutuncu
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%% Last Modified: 16 Sep 2004
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%%*******************************************************************
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function [schur,UU,EE] = schurmat_qblk(blk,At,par,schur,UU,EE,p,dd,ee,xx);
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global idxdenAq nnzschur_qblk
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if (nargin == 10); options = 0; else; options = 1; end;
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iter = par.iter;
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if isempty(EE)
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count = 0;
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else
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count = max(max(EE(:,2)),max(EE(:,1)));
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end
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pblk = blk(p,:); n = sum(pblk{2}); numblk = length(pblk{2});
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%%
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Ae = qprod(pblk,At{p}',ee{p});
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if (options == 0)
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Ax = qprod(pblk,At{p}',xx{p});
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end
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idxden = checkdense(Ae);
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ddsch = dd{p};
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if ~isempty(idxden); % separate sparse and dense handling
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spcolidx = setdiff([1:numblk],idxden);
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s = 1 + [0, cumsum(pblk{2})];
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idx = s(idxden);
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tmp = zeros(n,1);
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tmp(idx) = sqrt(2*abs(ddsch(idx)));
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Ad = qprod(pblk,At{p}',tmp);
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ddsch(idx) = abs(ddsch(idx));
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if (options == 0)
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len = length(idxden);
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gamzsub = par.gamz{p}(idxden);
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lam = gamzsub.*gamzsub;
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UU = [UU, Ax(:,idxden), Ae(:,idxden)*spdiags(lam,0,len,len), Ad(:,idxden)];
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tmp = count+[1:len]';
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EE = [EE; [tmp, len+tmp, -lam; len+tmp, tmp, -lam; ...
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2*len+tmp, 2*len+tmp, ones(len,1)] ];
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count = count+3*len;
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Ax = Ax(:,spcolidx); Ae = Ae(:,spcolidx);
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tmp2 = Ax*Ae';
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schur = schur + (tmp2 + tmp2');
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else
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len = length(idxden);
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w2 = par.gamz{p}./par.gamx{p};
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lam = w2(idxden);
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UU = [UU, Ae(:,idxden)*spdiags(sqrt(lam),0,len,len), Ad(:,idxden)];
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tmp = count+[1:len]';
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EE = [EE; [tmp, tmp, -lam; len+tmp, len+tmp, ones(len,1)] ];
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count = count + 2*len;
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Ae = Ae(:,spcolidx);
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schur = schur + Ae*Ae';
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end
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else %% either all sparse or all dense
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if (nnz(Ae)>0.2*numel(Ae))
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Ae = full(Ae);
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end
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if (options == 0)
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if (nnz(Ax)>0.2*numel(Ax))
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Ax = full(Ax);
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end
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tmp = Ax*Ae';
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schur = schur + (tmp+tmp');
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else
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tmp = Ae*Ae';
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schur = schur + tmp;
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end
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end
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if (iter==1)
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idxdenAq{p} = checkdense(At{p}');
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end
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if ~isempty(idxdenAq{p});
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idxden = idxdenAq{p};
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len = length(idxden);
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Ad = At{p}(idxden,:)'*spdiags(sqrt(abs(ddsch(idxden))),0,len,len);
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UU = [UU, Ad];
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tmp = count+[1:len]';
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EE = [EE; [tmp, tmp, -sign(ddsch(idxden))]];
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count = count + len;
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ddsch(idxden) = zeros(len,1);
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elseif (nnz(At{p})>0.2*numel(At{p})) % heuristic from sedumi
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At{p}=full(At{p});
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end
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if (issparse(At{p}) && exist('spmm','file')==3)
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schurtmp = spmm(At{p}',spmm(spdiags(ddsch,0,n,n),At{p}));
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else
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schurtmp = At{p}' *spdiags(ddsch,0,n,n) *At{p};
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end
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schur = sparse(schur + schurtmp);
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%%*******************************************************************
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