73 lines
2.5 KiB
Mathematica
73 lines
2.5 KiB
Mathematica
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%%*******************************************************************
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%% schurmat_sblk: compute Schur complement matrix corresponding to
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%% SDP blocks.
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%%
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%% symm = 0, HKM
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%% = 1, NT
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%%
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%% SDPT3: version 3.0
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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: 2 Feb 01
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%%*******************************************************************
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function schur = schurmat_sblk(blk,At,par,schur,p,X,Y);
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global smallblkdim
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if (nargin == 7); symm = 0; else; symm = 1; Y = X; end;
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m = length(schur);
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pblk = blk(p,:);
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%%
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if (max(pblk{2}) > smallblkdim)
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%%
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%% compute schur for matrices that are very sparse.
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%%
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if issparse(schur); schur = full(schur); end;
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J = max(find(par.nzlistA{p,1} < inf)) -1;
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if (J > 0)
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if issparse(X{p}) & ~issparse(Y{p}); X{p} = full(X{p}); end
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if ~issparse(X{p}) & issparse(Y{p}); Y{p} = full(Y{p}); end
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nnzspschur = mexschur(pblk,At{p},par.nzlistA{p,1},...
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par.nzlistA{p,2},par.permA(p,:),Y{p},X{p},J,symm,schur);
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end
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%%
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%% compute schur for matrices that are not so sparse or dense.
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%%
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L = max(find(par.nzlistAsum{p,1} < inf)) -1;
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if (J < L)
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len = par.nzlistAsum{p,1}(J+1); list = par.nzlistAsum{p,2}(1:len,:);
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end
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for k = J+1:m
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isspAk = par.isspA(p,k);
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Ak = mexsmat(blk,At,isspAk,p,k);
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if (k <= L)
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idx1 = par.nzlistAsum{p,1}(k)+1; idx2 = par.nzlistAsum{p,1}(k+1);
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list = [list; par.nzlistAsum{p,2}(idx1:idx2,:)];
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list = sortrows(list,[2 1]);
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tmp = Prod3(pblk,X{p},Ak,Y{p},symm,list);
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else
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tmp = Prod3(pblk,X{p},Ak,Y{p},symm);
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end
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if ~symm
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tmp = 0.5*(mexsvec(pblk,tmp) + mexsvec(pblk,tmp,[],1));
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else
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tmp = mexsvec(pblk,tmp);
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end
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permk = par.permA(p,k);
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idx = par.permA(p,1:k);
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tmp2 = schur(idx,permk) + mexinprod(blk,At,tmp,k,p);
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schur(idx,permk) = tmp2;
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schur(permk,idx) = tmp2';
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end
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else
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if issparse(X{p}) & ~issparse(Y{p}); Y{p} = sparse(Y{p}); end
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if ~issparse(X{p}) & issparse(Y{p}); X{p} = sparse(X{p}); end
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tmp = mexskron(pblk,X{p},Y{p});
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Perm = spconvert([(1:m)' par.permA(p,:)' ones(m,1)]);
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schurtmp = At{p}'*tmp*At{p};
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schurtmp = 0.5*(schurtmp + schurtmp');
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schur = schur + Perm'*schurtmp*Perm;
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end
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%%*******************************************************************
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