97 lines
2.4 KiB
Mathematica
97 lines
2.4 KiB
Mathematica
|
function [C,A,b,blk] = dsdpdata(F,h)
|
||
|
|
%DSDPDATA Internal function create DSDP data
|
||
|
|
|
||
|
|
if ~(isempty(F) | isa(F,'lmi'))
|
||
|
|
help lmi
|
||
|
|
error('First argument (F) should be an lmi object. See help text above');
|
||
|
|
end
|
||
|
|
|
||
|
|
if ~(isempty(h) | isa(h,'sdpvar'))
|
||
|
|
help solvesdp
|
||
|
|
error('Third argument (the objective function h) should be an sdpvar object (or empty). See help text above');
|
||
|
|
end
|
||
|
|
|
||
|
|
[ProblemString,real_data] = catsdp(F);
|
||
|
|
if (real_data == 0)
|
||
|
|
error('DSDP does not support complex data')
|
||
|
|
end
|
||
|
|
|
||
|
|
% This one is used a lot
|
||
|
|
nvars = sdpvar('nvars');
|
||
|
|
|
||
|
|
% Convert the objective
|
||
|
|
onlyfeasible = 0;
|
||
|
|
if isempty(h)
|
||
|
|
c=zeros(nvars,1);
|
||
|
|
else
|
||
|
|
[n,m]=size(h);
|
||
|
|
if ~((n==1) & (m==1))
|
||
|
|
error('Scalar expression to minimize please.');
|
||
|
|
else
|
||
|
|
lmi_variables = getvariables(h);
|
||
|
|
c = zeros(nvars,1);
|
||
|
|
for i=1:length(lmi_variables)
|
||
|
|
c(lmi_variables(i))=getbasematrix(h,lmi_variables(i));
|
||
|
|
end;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
[F_struc,K,F_blksz] = lmi2spstruct(F);
|
||
|
|
|
||
|
|
% Which sdpvar variables are actually in the problem
|
||
|
|
used_variables_LMI = find(any(F_struc(:,2:end),1));
|
||
|
|
used_variables_obj = find(any(c',1));
|
||
|
|
used_variables = uniquestripped([used_variables_LMI used_variables_obj]);
|
||
|
|
|
||
|
|
% Check for unbounded variables
|
||
|
|
unbounded_variables = setdiff(used_variables_obj,used_variables_LMI);
|
||
|
|
if ~isempty(unbounded_variables)
|
||
|
|
% Remove unbounded variable from problem
|
||
|
|
used_variables = setdiff(used_variables,unbounded_variables);
|
||
|
|
end
|
||
|
|
|
||
|
|
% Pick out the necessary rows
|
||
|
|
if length(used_variables)<nvars
|
||
|
|
c = c(used_variables);
|
||
|
|
F_struc = sparse(F_struc(:,[1 1+[used_variables]]));
|
||
|
|
end
|
||
|
|
|
||
|
|
|
||
|
|
if (K.f>0)
|
||
|
|
% Extract the inequalities
|
||
|
|
A_equ = F_struc(1:K.f,2:end);
|
||
|
|
b_equ = -F_struc(1:K.f,1);
|
||
|
|
|
||
|
|
% Find feasible (turn off annoying warning on PC)
|
||
|
|
% Using method from Nocedal-Wright book
|
||
|
|
showprogress('Solving equalities',options.ShowProgress);
|
||
|
|
[Q,R] = qr(A_equ');
|
||
|
|
n = size(R,2);
|
||
|
|
Q1 = Q(:,1:n);
|
||
|
|
R = R(1:n,:);
|
||
|
|
x_equ = Q1*(R'\b_equ);
|
||
|
|
% Exit if no consistent solution exist
|
||
|
|
if (norm(A_equ*x_equ-b_equ)>sqrt(eps))
|
||
|
|
error('Linear constraints inconsistent.');
|
||
|
|
return
|
||
|
|
end
|
||
|
|
% We dont need the rows for equalities anymore
|
||
|
|
F_struc = F_struc(K.f+1:end,:);
|
||
|
|
K.f = 0;
|
||
|
|
|
||
|
|
% We found a new basis
|
||
|
|
H = Q(:,n+1:end); % New basis
|
||
|
|
|
||
|
|
% objective in new basis
|
||
|
|
c = H'*c;
|
||
|
|
% LMI in new basis
|
||
|
|
F_struc = [F_struc*[1;x_equ] F_struc(:,2:end)*H];
|
||
|
|
else
|
||
|
|
% For simpliciy we introduce a dummy coordinate change
|
||
|
|
x_equ = 0;
|
||
|
|
H = 1;
|
||
|
|
end
|
||
|
|
|
||
|
|
% Convert from SP format (same format as SDPT3-2.3)
|
||
|
|
[C,A,b,blk] = sp2sdpt323(F_struc,F_blksz,c);
|