%Detects eigenvectors of a sparse stiffness matrix that are localized at ends.

%If end effects propagate along 18 parameters
N=30; %number of base pairs
n=6*N+6*(N-1); %number of parameters
A = constructStiffHom(N);
B = A(1:18,1:18);
C = A(19:30,1:18);
[x,y]=eig(B);
y = diag(y);
nb=[];
for i=1:size(x,2),
	nb=[nb, norm(C*x(:,i))];
end;
th=0.8
findem1 = find(nb<th)
number1 = size(findem1,2)
norms1  = nb(findem1)
vectors1= x(:,findem1)
evalues1= y(findem1)


%End effects propagate along 24 parameters
N=30;
n=6*N+6*(N-1);
A = constructStiffHom(N);
B = A(1:24,1:24);
C = A(25:30,1:24);
[x,y]=eig(B);
y = diag(y);
nb=[];
for i=1:size(x,2),
	nb=[nb, norm(C*x(:,i))];
end;
th=0.5
findem1 = find(nb<th)
number1 = size(findem1,2)
norms1  = nb(findem1)
vectors1= x(:,findem1)
evalues1= y(findem1)
th=0.8
findem1 = find(nb<th)
number1 = size(findem1,2)
norms1  = nb(findem1)
vectors1= x(:,findem1)
evalues1= y(findem1)



%other end
B = A(n-24+1:n,n-24+1:n);
C = A(n-30+1:n-24,n-24+1:n);
[x,y]=eig(B);
y = diag(y);
nb=[];
for i=1:size(x,2),
	nb=[nb, norm(C*x(:,i))];
end;
nb
th=0.5
findem2 = find(nb<th)
number2 = size(findem2,2)
norms2  = nb(findem2)
vectors2= x(:,findem2)
evalues2= y(findem2)
th=0.8
findem2 = find(nb<th)
number2 = size(findem2,2)
norms2  = nb(findem2)
vectors2= x(:,findem2)
evalues2= y(findem2)