%basis functions

function bf = bf(a);

global nA A
bf = zeros(1,nA);
        
if a <= A(2) 
    bf(1) =  (A(2) - a)/(A(2) - A(1));
    bf(2) =  (a - A(1))/(A(2) - A(1));
elseif a<= A(3)
    bf(2) =  (A(3) - a)/(A(3) - A(2));    
end
        
if a >= A(nA-1) 
    bf(nA-1) =  (A(nA) - a)/(A(nA) - A(nA-1));
    bf(nA) =  (a - A(nA-1))/(A(nA) - A(nA-1));
elseif a>= A(nA-2)
    bf(nA-1) =  (a - A(nA-2))/(A(nA-1) - A(nA-2));    
end     
        
for i=3:nA-2
    if (a >= A(i-1))&(a <= A(i)) 
        bf(i) =  (a - A(i-1))/(A(i) - A(i-1));
    elseif (a >= A(i))&(a <= A(i+1))
        bf(i) =  (A(i+1) - a)/(A(i+1) - A(i));    
    end    
end