75 lines
2.5 KiB
Mathematica
75 lines
2.5 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 3.0
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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: 10 Jun 02
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%%*******************************************************************
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function [schur,UU,VV] = schurmat_qblk(blk,At,schur,UU,VV,p,dd,ee,xx);
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if (nargin == 9); options = 0; else; options = 1; end;
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pblk = blk(p,:); n = sum(pblk{2}); numblk = length(pblk{2});
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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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decolidx = checkdense(Ae);
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ddsch = dd{p};
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if ~isempty(decolidx);
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spcolidx = setdiff([1:numblk],decolidx);
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s = 1 + [0 cumsum(pblk{2})];
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idx = s(decolidx);
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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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UU = [UU Ax(:,decolidx) Ae(:,decolidx) Ad];
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VV = [VV Ae(:,decolidx) Ax(:,decolidx) -Ad];
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Ax = Ax(:,spcolidx); Ae = Ae(:,spcolidx);
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schur = schur + Ax*Ae'+ Ae*Ax';
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else
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UU = [UU Ae(:,decolidx) Ad];
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VV = [VV Ae(:,decolidx) -Ad];
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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
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if (options == 0)
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schur = schur + Ax*Ae'+ Ae*Ax';
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else
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schur = schur + Ae*Ae';
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end
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end
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decolidx = checkdense(At{p}');
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if ~isempty(decolidx);
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len = length(decolidx);
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tmp = (spdiags(sqrt(abs(ddsch(decolidx))),0,len,len)*At{p}(decolidx,:))';
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UU = [UU tmp];
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VV = [VV tmp*spdiags(sign(ddsch(decolidx)),0,len,len)];
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ddsch(decolidx) = zeros(len,1);
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end
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schur = schur + At{p}' *spdiags(ddsch,0,n,n) *At{p};
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%%*******************************************************************
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