load beijing.mat;
load beijing_angles.mat;
load beijing_graph.mat;
load beijing_config.mat;

cov = [ 0.25, 0, 0; 0, 0.25, 0; 0, 0, 0.01];

factors = Pose2Graph;
factors2 = Pose2Graph;
ord2 = Ordering();

[rows cols] = find(tree);
for i=length(edge_order):-1:1
    if mod(i,500) == 0
        fprintf(1, 'processing edge %d\n', i);
    end
    
    id1 = rows(edge_order(i));
    id2 = cols(edge_order(i));
    key1 = sprintf('x%d', id1);
    key2 = sprintf('x%d', id2);
    
    delta_x = points(id1,:) - points(id2,:);
    delta_angle = angles(id1) - angles(id2);
    measured = Pose2(delta_x(1), delta_x(2), delta_angle);
    
    if pred(id1) == id2 || pred(id2) == id1 %% in the spanning tree
        factor=Pose2Factor(key1,key2,measured, cov);
        factors.push_back(factor);
    else %% not in the spanning tree
        factors2.push_back(Pose2Factor(key1,key2,measured, cov));
        ord2.push_back(key1);
        ord2.push_back(key2);
    end
end
ord2.unique();

if 1
    config=Pose2Config();
    n=size(points,1);
    for j=1:n
        pose=Pose2(points(j,1),points(j,2),angles(j));
        key = sprintf('x%d', j);
        config.insert(key,pose);
        if mod(j,1000) == 0
            key
        end
    end
    save('beijing_config.mat','config');
end

% Spanning tree with bottom-up ordering
ord = bottom_up_ordering(pred);
LFG=factors.linearize_(config);
ijs=LFG.sparse(ord);
A=sparse(ijs(1,:),ijs(2,:),ijs(3,:)); 
figure(1)
spy(A);
%save('beijing_factors.mat', 'factors');

% LFG2=factors2.linearize_(config);
% ijs2=LFG2.sparse(ord2);
% A2=sparse(ijs2(1,:),ijs2(2,:),ijs2(3,:)); 
% figure(2)
% spy(A2);

% show R factor
R = qr(A,0);
figure(3)
spy(R)

% show re-ordered R factor
% P = colamd(A);
% figure(4)
% spy(A(:,P))
% R = qr(A(:,P),0);
% figure(5)
% spy(R)