source: proiecte/pmake3d/make3d_original/Make3dSingleImageStanford_version0.1/third_party/opt/yalmip/extras/sdpt3data.m @ 37

function [C,A,b,blk] = sdpt3data(F,h)
%SDPT3DATA Internal function to convert data to SDPT3 format

% Author Johan Löfberg
% $Id: sdpt3data.m,v 1.3 2004/11/24 09:13:05 johanl Exp $

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);

% 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] = lmi2sedumistruct(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

[C,A,b,blk] = sdpt3struct2sdpt3block(F_struc,c,K);
A = svec(blk,A,ones(size(blk,1),1));