125 lines
3.6 KiB
Mathematica
125 lines
3.6 KiB
Mathematica
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%%*****************************************************************
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%% convertcmpsdp: convert SDP with complex data into one
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%% with real data by converting
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%%
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%% C - sum_{k=1}^m yk*Ak psd
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%% to
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%% [CR,-CI] - sum ykR*[AkR,-AkI] psd
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%% [CI, CR] [AkI, AkR]
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%%
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%% ykI = 0 for k = 1:m
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%%
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%% [bblk,AAt,CC,bb] = convertcmpsdp(blk,A,C,b);
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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 [bblk,AAt,CC,bb,iscmp] = convertcmpsdp(blk,A,C,b);
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m = length(b);
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[pp,mm] = size(A);
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if (pp ~= size(blk,1))
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error('blk and A not compatible');
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end
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numblk = size(blk,1);
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iscmp = zeros(numblk,m+1);
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for p = 1:size(blk,1)
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pblk = blk(p,:);
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len = size(A(p),2);
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for k = 1:len
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if ~isempty(A{p,k})
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iscmp(p,k) = 1-isreal(A{p,k});
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end
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end
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iscmp(p,m+1) = 1-isreal(C{p});
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end
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iscmp = norm(iscmp,'fro');
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%%
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if (iscmp == 0)
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%% data is real
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bblk = blk; AAt = A; CC = C; bb = b;
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return;
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end
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%%
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bb = [real(b)];
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bblk = cell(size(blk,1),2);
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for p = 1:size(blk,1)
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pblk = blk(p,:);
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if (size(pblk{2},1) > size(pblk{2},2))
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pblk{2} = pblk{2}';
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end
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if strcmp(pblk{1},'s')
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ss = [0,cumsum(pblk{2})];
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ss2 = [0,cumsum(2*pblk{2})];
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n = sum(pblk{2});
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n2 = sum(pblk{2}.*(pblk{2}+1))/2;
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AR = cell(1,m); Ctmp = sparse(2*n,2*n);
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if (size(A{p},1)==n2 & size(A{p},2)==m);
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Atype = 1;
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elseif (size(A(p),1)==1 & size(A(p),2)==1);
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Atype = 2;
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else
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error('convertcmp: At is not properly coded');
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end
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for k = 0:m
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if (k == 0)
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Ak = C{p};
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else
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if (Atype == 1)
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Ak = smat(pblk,A{p}(:,k),1);
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elseif (Atype == 2)
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Ak = A{p,k};
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end
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end
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Atmp = sparse(2*n,2*n);
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if (length(pblk{2}) == 1)
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tmp = [real(Ak),-imag(Ak); imag(Ak), real(Ak)];
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if (k==0)
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Ctmp = tmp;
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else
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Atmp = tmp;
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end
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else
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for j = 1:length(pblk{2})
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idx = [ss(j)+1: ss(j+1)];
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Akj = Ak(idx,idx);
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tmp = [real(Akj),-imag(Akj); imag(Akj), real(Akj)];
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idx2 = [ss2(j)+1: ss2(j+1)];
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if (k==0)
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Ctmp(idx2,idx2) = tmp;
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else
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Atmp(idx2,idx2) = tmp;
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end
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end
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end
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if (k==0);
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CC{p,1} = Ctmp;
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else
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AR{k} = Atmp;
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end
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end
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bblk{p,1} = 's'; bblk{p,2} = 2*pblk{2};
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AAt(p,1) = svec(bblk(p,:),AR);
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elseif strcmp(pblk{1},'q');
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error('SOCP block with complex data is currently not allowed');
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elseif strcmp(pblk{1},'l');
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if isreal(A{p}) & isreal(C{p})
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bblk(p,:) = blk(p,:);
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AAt{p,1} = A{p}; CC{p,1} = C{p};
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else
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error('data for linear block must be real');
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end
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elseif strcmp(pblk{1},'u');
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if isreal(A{p}) & isreal(C{p})
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bblk(p,:) = blk(p,:);
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AAt{p,1} = A{p}; CC{p,1} = C{p};
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else
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error('data for unrestricted block must be real');
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end
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end
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end
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%%*********************************************************
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