93 lines
2.3 KiB
Matlab
Executable File
93 lines
2.3 KiB
Matlab
Executable File
function [C,A,b,blk] = sdpt3data(F,h)
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%SDPT3DATA Internal function to convert data to SDPT3 format
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if ~(isempty(F) | isa(F,'lmi'))
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help lmi
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error('First argument (F) should be an lmi object. See help text above');
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end
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if ~(isempty(h) | isa(h,'sdpvar'))
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help solvesdp
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error('Third argument (the objective function h) should be an sdpvar object (or empty). See help text above');
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end
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[ProblemString,real_data] = catsdp(F);
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% This one is used a lot
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nvars = sdpvar('nvars');
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% Convert the objective
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onlyfeasible = 0;
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if isempty(h)
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c=zeros(nvars,1);
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else
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[n,m]=size(h);
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if ~((n==1) & (m==1))
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error('Scalar expression to minimize please.');
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else
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lmi_variables = getvariables(h);
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c = zeros(nvars,1);
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for i=1:length(lmi_variables)
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c(lmi_variables(i))=getbasematrix(h,lmi_variables(i));
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end;
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end
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end
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[F_struc,K] = lmi2sedumistruct(F);
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% Which sdpvar variables are actually in the problem
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used_variables_LMI = find(any(F_struc(:,2:end),1));
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used_variables_obj = find(any(c',1));
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used_variables = uniquestripped([used_variables_LMI used_variables_obj]);
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% Check for unbounded variables
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unbounded_variables = setdiff(used_variables_obj,used_variables_LMI);
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if ~isempty(unbounded_variables)
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% Remove unbounded variable from problem
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used_variables = setdiff(used_variables,unbounded_variables);
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end
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% Pick out the necessary rows
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if length(used_variables)<nvars
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c = c(used_variables);
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F_struc = sparse(F_struc(:,[1 1+[used_variables]]));
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end
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if (K.f>0)
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% Extract the inequalities
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A_equ = F_struc(1:K.f,2:end);
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b_equ = -F_struc(1:K.f,1);
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% Find feasible (turn off annoying warning on PC)
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% Using method from Nocedal-Wright book
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showprogress('Solving equalities',options.ShowProgress);
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[Q,R] = qr(A_equ');
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n = size(R,2);
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Q1 = Q(:,1:n);
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R = R(1:n,:);
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x_equ = Q1*(R'\b_equ);
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% Exit if no consistent solution exist
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if (norm(A_equ*x_equ-b_equ)>sqrt(eps))
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error('Linear constraints inconsistent.');
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return
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end
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% We dont need the rows for equalities anymore
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F_struc = F_struc(K.f+1:end,:);
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K.f = 0;
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% We found a new basis
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H = Q(:,n+1:end); % New basis
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% objective in new basis
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c = H'*c;
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% LMI in new basis
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F_struc = [F_struc*[1;x_equ] F_struc(:,2:end)*H];
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else
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% For simpliciy we introduce a dummy coordinate change
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x_equ = 0;
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H = 1;
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end
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[C,A,b,blk] = sdpt3struct2sdpt3block(F_struc,c,K);
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A = svec(blk,A,ones(size(blk,1),1)); |