Poly Spline Interpolation with Pth Continuous Derivatives

This function fits a polynomial splines of order m with pth continuous derivatives to a given data (x,y).

% polysplinefitc
% This function fits a polynomial splines of order m with pth continuous
% derivatives to a given data (x,y).
% it is valid for one dimension only.
% the function uses interpolation approach so it is not suitable for
% noisy data
% ----------------------------------------------
% inputs
% x x data must be increasing. ex x = [1,2,3]
% y f(x)
% m polynomial order for each spline
% p number of continuous derivatives
% cond the addition conditions needed to compute the splines
% it's given by spline initial derivative values
% for the first and last spline only.
% cond rows number = spline order - 1.
% ploty 1 to show plots of the splines and their derivatives
%
% cond form is [spline,derivative_order,value_of_the_derivative]
% spline : 1 for the first spline
% 2 for the last splines
% ex:
% cond = [1 1 0;2 1 0]
% this means that the value of the first derivative of the first spline
% is zero and the value of the first derivative of the last spline is zero
%
% ---------------------------------------------------------------------
% output
% sol spline between each x
% ---------------------------------------------------------------------
% example
% x = [0 2 4 6 8];
% y = [0 2.2484 2.3164 2.5413 2.8626];
% m = 4;
% p = 2;
% cond = [1 1 0;2 1 0;1 2 0;2 2 0];
% sol = polysplinefitc(x,y,m,p,cond,0)
%
% All copyrights goes to Mohammad Al-Fetyani
% University of Jordan