91 lines
3.2 KiB
Mathematica
91 lines
3.2 KiB
Mathematica
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%%*****************************************************************
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%% sqlpu2lblk: decide whether to convert ublk to lblk
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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,X,Z,ublk2lblk,ublkidx] = sqlpu2lblk(blk,At,C,X,Z,par,convertlen)
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%%
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ublk2lblk = zeros(size(blk,1),1);
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ublkidx = cell(size(blk,1),2);
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for p = 1:size(blk,1)
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pblk = blk(p,:); n0 = sum(pblk{2});
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if strcmp(pblk{1},'u') & (pblk{2} > 0)
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ublk2lblk(p) = 1;
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if (pblk{2} > convertlen); continue; end
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AAt = At{p}*At{p}';
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mexschurfun(AAt,1e-15*max(1,diag(AAt)));
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indef = 0;
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[L.R,indef,L.perm] = chol(AAt,'vector');
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L.d = full(diag(L.R)).^2;
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if (~indef) & (max(L.d)/min(L.d) < 1e6)
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ublk2lblk(p) = 0;
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msg = '*** no conversion for ublk';
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if (par.printlevel); fprintf(' %s',msg); end
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else
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dd(L.perm,1) = abs(L.d);
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idxN = find(dd < 1e-11*mean(L.d));
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idxB = setdiff([1:n0]',idxN);
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ddB = dd(idxB);
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ddN = dd(idxN);
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if ~isempty(ddN) & ~isempty(ddB) & (min(ddB)/max(ddN) < 10)
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idxN = []; idxB = [1:n0]';
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end
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ublkidx{p,1} = n0; ublkidx{p,2} = idxN;
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if ~isempty(idxN)
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restol = 1e-8;
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[W,resnorm] = findcoeff(At{p}',idxB,idxN);
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resnorm(2) = norm(C{p}(idxN) - W'*C{p}(idxB));
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if (max(resnorm) < restol)
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feasible = 1;
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blk{p,2} = length(idxB);
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Atmp = At{p}';
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At{p} = Atmp(:,idxB)';
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C{p} = C{p}(idxB);
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X{p} = X{p}(idxB); Z{p} = Z{p}(idxB);
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msg = 'removed dependent columns in constraint matrix for ublk';
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if (par.printlevel); fprintf('\n %s\n',msg); end
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end
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end
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end
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end
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end
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%%***************************************************************************
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%%***************************************************************************
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%% findcoeff:
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%%
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%% [W,resnorm] = findcoeff(A,idXB,idXN);
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%%
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%% idXB = indices of independent columns of A.
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%% idxN = indices of dependent columns of A.
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%%
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%% AB = A(:,idxB); AN = A(:,idxN) = AB*W
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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 [W,resnorm] = findcoeff(A,idxB,idxN);
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AB = A(:,idxB);
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AN = A(:,idxN);
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[m,n] = size(AB);
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%%
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%%-----------------------------------------
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%% find W so that AN = AB*W
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%%-----------------------------------------
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%%
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[L,U,P,Q] = lu(sparse(AB));
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rhs = P*AN;
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Lhat = L(1:n,:);
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W = Q*( U \ (Lhat \ rhs(1:n,:)));
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resnorm = norm(AN-AB*W,'fro')/max(1,norm(AN,'fro'));
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%%***************************************************************************
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