112 lines
2.8 KiB
Mathematica
112 lines
2.8 KiB
Mathematica
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function varargout = dissect_internal(X);
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% DISSECT_INTERNAL Dissect SDP constraint
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%
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% G = unblkdiag(F) Converts SDP to several smaller SDPs with more variables
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%
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% See also UNBLKDIAG
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if isa(X,'constraint')
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X = lmi(X);
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end
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switch class(X)
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case 'sdpvar'
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% Get sparsity pattern
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Z=spy(X);
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% Partition as
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% [A1 0 C1
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% 0 A2 C2
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% C1' C2' E]
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% Find a dissection
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try
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sep = metismex('NodeBisect',Z);
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catch
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error('You have to install the MATLAB interface to METIS, http://www.cerfacs.fr/algor/Softs/MESHPART/');
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end
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% Indicies for elements in Ai
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s = setdiff(1:length(Z),sep);
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% re-order Ais to get diagonal blocks
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Z = Z(s,s);
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AB = X(s,s);
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CD = X(s,sep);
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[v,dummy,r,dummy2]=dmperm(Z);
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for i = 1:length(r)-1
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A{i} = AB(v(r(i):r(i+1)-1),v(r(i):r(i+1)-1));
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C{i}= CD(v(r(i):r(i+1)-1),:);
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end
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E = X(sep,sep);
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varargout{1} = A;
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varargout{2} = C;
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varargout{3} = E;
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case 'lmi'
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Fnew=([]);
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% decompose trivial block diagonal stuff
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X = unblkdiag(X);
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for i = 1:length(X)
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if is(X(i),'sdp') & length(sdpvar(X(i)))
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if 0
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[A,B,C,D,E]=dissect(sdpvar(X(i)));
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if ~isempty(B)
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S=sdpvar(size(E,1));
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S = S.*inversesparsity(E,D,B);
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Fnew=Fnew+([A C;C' S]>=0)+([E-S D';D B]>=0);
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else
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Fnew = Fnew + X(i);
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end
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else
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[A,C,E]=dissect(sdpvar(X(i)));
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if length(A)>1
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allS = 0;
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for i = 1:length(A)-1
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S{i}=sdpvar(size(E,1));
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S{i} = S{i}.*inversesparsity(E,C{i},A{i});
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allS = allS + S{i};
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Fnew=Fnew+([A{i} C{i};C{i}' S{i}]>=0);
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end
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i = i + 1;
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S{i}=E-allS;
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S{i} = S{i}.*inversesparsity(E,C{i},A{i});
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Fnew=Fnew+([A{i} C{i};C{i}' S{i}]>=0);
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else
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Fnew = Fnew + X(i);
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end
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end
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else
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Fnew=Fnew+X(i);
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end
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end
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varargout{1} = Fnew;
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end
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function S = inversesparsity(E,D,B)
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if isa(E,'sdpvar')
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E = spy(E).*randn(size(E));
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else
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E = E.*randn(size(E));
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end
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if isa(D,'sdpvar')
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D = spy(D).*randn(size(D));
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else
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D = D.*randn(size(D));
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end
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if isa(B,'sdpvar')
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B = spy(B).*randn(size(B));
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else
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B = B.*randn(size(B));
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end
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S = E-D'*inv(B)*D;
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S = S | S';
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