[37] | 1 | function [C,A,b,blk] = dsdpdata(F,h) |
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| 2 | %DSDPDATA Internal function create DSDP data |
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| 3 | |
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| 4 | % Author Johan Löfberg |
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| 5 | % $Id: dsdpdata.m,v 1.3 2004/11/24 09:13:05 johanl Exp $ |
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| 6 | |
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| 7 | if ~(isempty(F) | isa(F,'lmi')) |
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| 8 | help lmi |
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| 9 | error('First argument (F) should be an lmi object. See help text above'); |
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| 10 | end |
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| 11 | |
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| 12 | if ~(isempty(h) | isa(h,'sdpvar')) |
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| 13 | help solvesdp |
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| 14 | error('Third argument (the objective function h) should be an sdpvar object (or empty). See help text above'); |
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| 15 | end |
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| 16 | |
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| 17 | [ProblemString,real_data] = catsdp(F); |
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| 18 | if (real_data == 0) |
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| 19 | error('DSDP does not support complex data') |
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| 20 | end |
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| 21 | |
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| 22 | % This one is used a lot |
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| 23 | nvars = sdpvar('nvars'); |
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| 24 | |
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| 25 | % Convert the objective |
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| 26 | onlyfeasible = 0; |
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| 27 | if isempty(h) |
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| 28 | c=zeros(nvars,1); |
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| 29 | else |
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| 30 | [n,m]=size(h); |
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| 31 | if ~((n==1) & (m==1)) |
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| 32 | error('Scalar expression to minimize please.'); |
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| 33 | else |
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| 34 | lmi_variables = getvariables(h); |
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| 35 | c = zeros(nvars,1); |
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| 36 | for i=1:length(lmi_variables) |
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| 37 | c(lmi_variables(i))=getbasematrix(h,lmi_variables(i)); |
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| 38 | end; |
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| 39 | end |
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| 40 | end |
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| 41 | |
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| 42 | [F_struc,K,F_blksz] = lmi2spstruct(F); |
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| 43 | |
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| 44 | % Which sdpvar variables are actually in the problem |
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| 45 | used_variables_LMI = find(any(F_struc(:,2:end),1)); |
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| 46 | used_variables_obj = find(any(c',1)); |
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| 47 | used_variables = uniquestripped([used_variables_LMI used_variables_obj]); |
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| 48 | |
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| 49 | % Check for unbounded variables |
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| 50 | unbounded_variables = setdiff(used_variables_obj,used_variables_LMI); |
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| 51 | if ~isempty(unbounded_variables) |
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| 52 | % Remove unbounded variable from problem |
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| 53 | used_variables = setdiff(used_variables,unbounded_variables); |
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| 54 | end |
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| 55 | |
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| 56 | % Pick out the necessary rows |
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| 57 | if length(used_variables)<nvars |
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| 58 | c = c(used_variables); |
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| 59 | F_struc = sparse(F_struc(:,[1 1+[used_variables]])); |
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| 60 | end |
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| 61 | |
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| 62 | |
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| 63 | if (K.f>0) |
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| 64 | % Extract the inequalities |
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| 65 | A_equ = F_struc(1:K.f,2:end); |
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| 66 | b_equ = -F_struc(1:K.f,1); |
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| 67 | |
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| 68 | % Find feasible (turn off annoying warning on PC) |
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| 69 | % Using method from Nocedal-Wright book |
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| 70 | showprogress('Solving equalities',options.ShowProgress); |
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| 71 | [Q,R] = qr(A_equ'); |
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| 72 | n = size(R,2); |
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| 73 | Q1 = Q(:,1:n); |
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| 74 | R = R(1:n,:); |
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| 75 | x_equ = Q1*(R'\b_equ); |
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| 76 | % Exit if no consistent solution exist |
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| 77 | if (norm(A_equ*x_equ-b_equ)>sqrt(eps)) |
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| 78 | error('Linear constraints inconsistent.'); |
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| 79 | return |
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| 80 | end |
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| 81 | % We dont need the rows for equalities anymore |
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| 82 | F_struc = F_struc(K.f+1:end,:); |
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| 83 | K.f = 0; |
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| 84 | |
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| 85 | % We found a new basis |
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| 86 | H = Q(:,n+1:end); % New basis |
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| 87 | |
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| 88 | % objective in new basis |
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| 89 | c = H'*c; |
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| 90 | % LMI in new basis |
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| 91 | F_struc = [F_struc*[1;x_equ] F_struc(:,2:end)*H]; |
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| 92 | else |
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| 93 | % For simpliciy we introduce a dummy coordinate change |
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| 94 | x_equ = 0; |
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| 95 | H = 1; |
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| 96 | end |
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| 97 | |
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| 98 | % Convert from SP format (same format as SDPT3-2.3) |
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| 99 | [C,A,b,blk] = sp2sdpt323(F_struc,F_blksz,c); |
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