function [QQ]=schur_invssts_qq(G,ord)

% SCHUR_INVSSTS_QQ      Generates the Generalised Schur's complement of the
% Hermitian matrix, R, such that
%
%     [ T+(v/a)I    T  I ]
% R = [     T       0  I ]
%     [     0       I  0 ]
%
% where T is a positive-definite strongly Toeplitz-like Block  matrix. Note
% that no hyperbolic rotation is implemented.
%
%   QQ = SCHUR_INVSSTS_QQ(G,ord)
%
% Inputs:
%           G   : generating matrix, size (3n)x(2rk)
%           ord : order of matrix
%
% Outputs:
%           QQ  = returns N*{ (v/a)*inv(T*T) + inv(T) }*N'
%
% such that N is a transformation matrix, defined by ord.
%
%
% (C) Gaussian Process SSTS Toolbox 1.0
% (C) Copyright 2006-2007, Keith Neo <keith.neo@nuim.ie>
%                          http://www.hamilton.ie

n=size(G,1);
n3=n/3;
rk=size(G,2)/2;
d0=ceil(n3/(ord+1));
ind=(ord+1)*ones(d0,1);
ind(1,1)=1;
ind=cumsum(ind);
dx=1;
QQ=zeros(d0);
pc=n3+1;

for k=1:2*n3
    g=G(1,:);
    %l=G*J*g';
    l=G*[g(1,1:rk)'; -g(1,rk+1:end)'];
    d=l(1,1);

    if k>n3
        pp=k-n3;
        pa=1+pc-pp;
%         pb=1+n-k;

        if dx<d0
            if pp==ind(dx+1)
                dx=dx+1;
            end
        end
        u=l(pa:pc,1);
        for r=1:dx
            tx=u(ind(r))/d;
            for s=1:r
                QQ(r,s)=QQ(r,s)-tx*u(ind(s));
            end
        end

%         trq2=trq2-(l(pa:pc,1)'*l(pa:pc,1))/d;
%         tmp=(l(pa:pc,1)'*b(1:pp,1))/d;
%         dQb=dQb-tmp*l(pa:pb,1);
    end
    
    tmp=l*(g/d);
    G=G+blaschke_potapov_3(tmp,n3);
    G=G(2:end,:);
end
for r=2:d0
    for s=1:(r-1)
        QQ(s,r)=QQ(r,s);
    end
end

function X=blaschke_potapov_3(Gmp,n2)
N=size(Gmp,1);
rk=size(Gmp,2);

tmp=[zeros(1,rk);Gmp(1:end-1,:)];
tmp(N-n2+1,:)=zeros(1,rk);
if N>2*n2
    tmp(N-2*n2+1,:)=zeros(1,rk);
end
X=tmp-Gmp;