Continuation Core and Toolboxes (COCO) Code

function [ A B C D ] = sfh3coeff( x0, t0, x1, t1 )
%SFH3COEFF Scale free Hermite polynomial coefficients.

dx = x1-x0;

t00 = t0'*t0;
t01 = t0'*t1;
t11 = t1'*t1;
dx0 = dx'*t0;
dx1 = dx'*t1;

if 1-t01 > 1.0e-12
	% qubic spline with
	% [C'*C' + 9*D'*D](al) = Min!
	AA = [ 13*t00 11*t01 ; 11*t01 10*t11 ];
	bb = [ 24*dx0 ; 21*dx1 ];
	al = AA\bb;

	A = x0;
	B = al(1)*t0;
	D = al(2)*t1 + B - 2*dx;
	C = dx - B - D;
else
	% linear interpolation
	A = x0;
	B = dx;
	C = zeros(size(x0));
	D = C;
end