function [b, c, d] = ccspline(x, a, dfL, dfR)
% Clamped Cubic Spline
% Interpolate the data points x(i),a(i) using a clamped cubic spline,
% with derivatives at the left end = dfL and at the right end = dfR
% See Burden & Faires for desription of coefficients

x = x(:)'; a = a(:)'; % Make sure inputs are row vectors

h = diff(x);
n = length(x)-1;

% Form tridiagonal matrix for clambed cubic splines
A = sparse(2:n+1, 1:n, h, n+1, n+1) + ...
    sparse(1:n, 2:n+1, h, n+1, n+1) + ...
    sparse(2:n, 2:n, 2*(h(1:n-1) + h(2:n)), n+1, n+1);
A(1,1) = 2*h(1);
A(n+1,n+1) = 2*h(n);

% Note: This is the b in the right-hand side of Ax = b in Burden & Faires
b = [3./h(1)*(a(2) - a(1)) - 3*dfL, ...
     3./h(2:n).*(a(3:n+1) - a(2:n)) - 3./h(1:n-1).*(a(2:n) - a(1:n-1)), ...
     3*dfR - 3/h(n)*(a(n+1) - a(n))]';
c = (A\b)';

% Note: This is the b in the actual spline coefficients
b = (a(2:n+1) - a(1:n))./h - h./3.*(2*c(1:n) + c(2:n+1));
d = (c(2:n+1) - c(1:n))./(3*h);
c = c(1:n);
