[37] | 1 | function varargout = dissect(X); |
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| 2 | % DISSECT Dissect SDP constraint |
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| 3 | % |
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| 4 | % G = unblkdiag(F) Converts SDP to several smaller SDPs with more variables |
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| 5 | % |
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| 6 | % See also UNBLKDIAG |
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| 7 | |
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| 8 | % Author Johan Löfberg |
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| 9 | % $Id: dissect.m,v 1.7 2006/05/10 10:07:02 joloef Exp $ |
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| 10 | |
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| 11 | |
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| 12 | switch class(X) |
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| 13 | case 'sdpvar' |
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| 14 | % Get sparsity pattern |
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| 15 | Z=spy(X); |
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| 16 | |
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| 17 | % Partition as |
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| 18 | % [A1 0 C1 |
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| 19 | % 0 A2 C2 |
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| 20 | % C1' C2' E] |
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| 21 | |
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| 22 | % Find a dissection |
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| 23 | try |
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| 24 | sep = metismex('NodeBisect',Z); |
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| 25 | catch |
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| 26 | error('You have to install the MATLAB interface to METIS, http://www.cerfacs.fr/algor/Softs/MESHPART/'); |
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| 27 | end |
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| 28 | |
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| 29 | % Indicies for elements in Ai |
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| 30 | s = setdiff(1:length(Z),sep); |
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| 31 | |
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| 32 | % re-order Ais to get diagonal blocks |
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| 33 | Z = Z(s,s); |
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| 34 | AB = X(s,s); |
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| 35 | CD = X(s,sep); |
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| 36 | [v,dummy,r,dummy2]=dmperm(Z); |
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| 37 | |
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| 38 | for i = 1:length(r)-1 |
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| 39 | A{i} = AB(v(r(i):r(i+1)-1),v(r(i):r(i+1)-1)); |
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| 40 | C{i}= CD(v(r(i):r(i+1)-1),:); |
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| 41 | end |
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| 42 | E = X(sep,sep); |
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| 43 | varargout{1} = A; |
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| 44 | varargout{2} = C; |
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| 45 | varargout{3} = E; |
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| 46 | |
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| 47 | case 'lmi' |
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| 48 | Fnew=set([]); |
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| 49 | % decompose trivial block diagonal stuff |
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| 50 | X = unblkdiag(X); |
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| 51 | for i = 1:length(X) |
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| 52 | if is(X(i),'sdp') & length(sdpvar(X(i))) |
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| 53 | if 0 |
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| 54 | [A,B,C,D,E]=dissect(sdpvar(X(i))); |
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| 55 | if ~isempty(B) |
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| 56 | S=sdpvar(size(E,1)); |
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| 57 | S = S.*inversesparsity(E,D,B); |
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| 58 | Fnew=Fnew+set([A C;C' S])+set([E-S D';D B]); |
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| 59 | else |
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| 60 | Fnew = Fnew + X(i); |
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| 61 | end |
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| 62 | |
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| 63 | else |
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| 64 | [A,C,E]=dissect(sdpvar(X(i))); |
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| 65 | if length(A)>1 |
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| 66 | allS = 0; |
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| 67 | for i = 1:length(A)-1 |
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| 68 | S{i}=sdpvar(size(E,1)); |
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| 69 | S{i} = S{i}.*inversesparsity(E,C{i},A{i}); |
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| 70 | allS = allS + S{i}; |
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| 71 | Fnew=Fnew+set([A{i} C{i};C{i}' S{i}]); |
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| 72 | end |
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| 73 | i = i + 1; |
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| 74 | S{i}=E-allS; |
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| 75 | S{i} = S{i}.*inversesparsity(E,C{i},A{i}); |
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| 76 | Fnew=Fnew+set([A{i} C{i};C{i}' S{i}]); |
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| 77 | else |
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| 78 | Fnew = Fnew + X(i); |
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| 79 | end |
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| 80 | |
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| 81 | end |
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| 82 | |
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| 83 | else |
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| 84 | Fnew=Fnew+X(i); |
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| 85 | end |
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| 86 | end |
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| 87 | varargout{1} = Fnew; |
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| 88 | end |
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| 89 | |
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| 90 | |
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| 91 | function S = inversesparsity(E,D,B) |
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| 92 | |
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| 93 | if isa(E,'sdpvar') |
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| 94 | E = spy(E).*randn(size(E)); |
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| 95 | else |
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| 96 | E = E.*randn(size(E)); |
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| 97 | end |
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| 98 | if isa(D,'sdpvar') |
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| 99 | D = spy(D).*randn(size(D)); |
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| 100 | else |
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| 101 | D = D.*randn(size(D)); |
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| 102 | end |
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| 103 | if isa(B,'sdpvar') |
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| 104 | B = spy(B).*randn(size(B)); |
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| 105 | else |
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| 106 | B = B.*randn(size(B)); |
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| 107 | end |
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| 108 | S = E-D'*inv(B)*D; |
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| 109 | S = S | S'; |
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| 110 | |
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| 111 | |
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