function [] = QF_Solver()
%Given QTAB nq, ns, and the system F=K*Q, transforms to similar system H=C*D
%The essential boundary conditions are in the upper part of D via D=T*Q
%Then C=T*K*T' and H=T*F. H=C*D is solved for D by partitions
%Reverse transformation gives Q=T'*D and F=T'*H
global QTAB F K Q nq ns
 
%In truth table I, I(i) is 1 if Q(i) is an essential displacement in QTAB.
I=zeros(ns,1);
for i=1:nq
    I(QTAB(i,1))=1;
end
I
%Copy the indices of the essential displacenemts from QTAB to V(1:nq)
V=zeros(ns,1);
V(1:nq,1) = QTAB(:,1);
%Write the remaining indices in V(nq+1:ns)
j=nq+1;
for i=1:ns
    if I(i)==0
        V(j)=i;
        j=j+1;
    end
end
V
%Make transform T from the indices in V. 
T=zeros(ns)
for i=1:ns
    T(i,V(i))=1;
end
T
%find the similar system H=CD using the transform matrix T
D=T*Q
H=T*F
C=T*K*T';
%Solve by partitions. The free displacements are DF=inv(CF)*(HF-CEF'*DE)
DE=D(1:nq);
CE=C(1:nq,1:nq);
CF=C(nq+1:ns,nq+1:ns);
CEF=C(1:nq,nq+1:ns);
HF=H(nq+1:ns);
DF=inv(CF)*(HF-CEF'*DE);
%The Reactions are HE=CE*DE+CEF*DF. Insert parts DF in D and HE in H
HE=CE*DE+CEF*DF;
D(nq+1:ns)=DF
H(1:nq)=HE
%Transform the results back to the original
Q=T'*D
F=T'*H
return;
%==========