81 lines
2.5 KiB
Mathematica
81 lines
2.5 KiB
Mathematica
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%%*****************************************************************
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%% blkeig: compute eigenvalue decomposition of a cell array
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%% whose contents are square matrices or the diagonal
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%% of a diagonal matrix.
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%%
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%% [d,V] = blkeig(blk,X);
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%%*****************************************************************
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%% SDPT3: version 4.0
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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: 16 Sep 2004
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%%*****************************************************************
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function [d,V] = blkeig(blk,X);
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spdensity = 0.5;
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if ~iscell(X);
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if strcmp(blk{1},'s');
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blktmp = blk{2};
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if (length(blktmp) == 1);
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if (nargout == 1);
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d = eig(full(X));
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elseif (nargout == 2);
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[V,d] = eig(full(X));
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d = diag(d);
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end
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else
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if (nargout == 2);
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V = sparse(length(X),length(X));
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end
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d = zeros(sum(blktmp),1);
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xx = mexsvec(blk,X,0);
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blktmp2 = blktmp.*(blktmp+1)/2;
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s2 = [0, cumsum(blktmp2)];
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blksub{1,1} = 's'; blksub{1,2} = 0;
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s = [0, cumsum(blktmp)];
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for i = 1:length(blktmp)
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pos = [s(i)+1 : s(i+1)];
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blksub{2} = blktmp(i);
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Xsub = mexsmat(blksub,xx(s2(i)+1:s2(i+1)),0);
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if (nargout == 1);
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lam = eig(Xsub);
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elseif (nargout == 2);
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[evec,lam] = eig(Xsub);
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lam = diag(lam);
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V(pos,pos) = sparse(evec);
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end
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d(pos,1) = lam;
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end
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end
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n2 = sum(blktmp.*blktmp);
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if (nargout == 2);
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if (nnz(V) <= spdensity*n2);
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V = sparse(V);
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else
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V = full(V);
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end
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end
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elseif strcmp(blk{1},'l');
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if (nargout == 2);
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V = ones(size(X)); d = X;
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elseif (nargout == 1);
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d = X;
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end
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end
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else
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if (nargout == 2);
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V = cell(size(X)); d = cell(size(X));
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for p = 1:size(blk,1);
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[d{p},V{p}] = blkeig(blk(p,:),X{p});
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end
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elseif (nargout == 1);
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d = cell(size(X));
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for p = 1:size(blk,1);
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d{p} = blkeig(blk(p,:),X{p});
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end
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end
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end
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%%***************************************************************************
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