79 lines
2.3 KiB
Matlab
Executable File
79 lines
2.3 KiB
Matlab
Executable File
%%********************************************************************
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%% scaling: scale the SDP data so that A_k,C,b have unit norm.
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%%
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%% [At,C,b,normA,normC,normb,X0,y0,Z0] = scaling(blk,At,C,b,X0,y0,Z0);
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%%
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%% The linear objective function value is unchanged under
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%% the scaling.
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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 [At,C,b,normA,normC,normb,X0,y0,Z0] = scaling(blk,At,C,b,X0,y0,Z0);
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m = length(b);
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numblk = size(blk,1);
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normA = cell(numblk,1);
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for p = 1:numblk
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pblk = blk(p,:);
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if strcmp(pblk{1},'s')
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m1 = size(At{p,1},2);
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if (m1 > 0)
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normAp2 = sum(sum(At{p,1}.*At{p,1}));
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else
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normAp2 = 0;
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end
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if (length(pblk) > 2) %% for low rank constraints
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dd = At{p,3};
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m2 = m-m1;
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ss = [0,cumsum(pblk{3})];
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for k=1:m2
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idx = [ss(k)+1:ss(k+1)];
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V = At{p,2}(:,idx);
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ii = dd(idx,1)-ss(k); %% undo cumulative indexing
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jj = dd(idx,2)-ss(k);
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len = pblk{3}(k);
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D = spconvert([ii,jj,dd(idx,3); len,len,0]);
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tmp = V'*V*D;
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normAp2 = normAp2 + sum(sum(tmp.*tmp'));
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end
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end
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else
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normAp2 = sum(sum(At{p,1}.*At{p,1}));
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end
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normAp = sqrt(normAp2);
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normA{p} = max(1,sqrt(normAp));
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end
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%%
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normb = max(1,norm(b));
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normC = 0;
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for p = 1:numblk
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normC = max(normC,norm(C{p},'fro'));
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end
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normC = max(1,normC);
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%%
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for p = 1:numblk
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pblk = blk(p,:);
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if strcmp(pblk{1},'s')
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m1 = size(At{p,1},2);
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m2 = m - m1;
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At{p,1} = At{p,1}/normA{p};
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if (m2 > 0) %% for low rank constaints
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At{p,3}(:,3) = At{p,3}(:,3)/normA{p};
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end
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else
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At{p,1} = At{p,1}/normA{p};
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end
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C{p} = C{p}/(normC*normA{p});
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if (nargin == 7)
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X0{p} = X0{p}*normA{p};
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Z0{p} = Z0{p}/(normC*normA{p});
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end
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end
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b = b/normb;
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%%********************************************************************
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