Matlab pchiptx

function v = pchiptx(x,y,u)%PCHIPTX  Textbook piecewise cubic Hermite interpolation.%  v = pchiptx(x,y,u) finds the shape-preserving piecewise cubic%  interpolant P(x), with P(x(j)) = y(j), and returns v(k) = P(u(k)).%%  See PCHIP, SPLINETX. %  First derivatives    h = diff(x);   delta = diff(y)./h;   d = pchipslopes(h,delta);%  Piecewise polynomial coefficients   n = length(x);   c = (3*delta - 2*d(1:n-1) - d(2:n))./h;   b = (d(1:n-1) - 2*delta + d(2:n))./h.^2;%  Find subinterval indices k so that x(k) <= u < x(k+1)   k = ones(size(u));   for j = 2:n-1      k(x(j) <= u) = j;   end%  Evaluate interpolant   s = u - x(k);   v = y(k) + s.*(d(k) + s.*(c(k) + s.*b(k)));% -------------------------------------------------------function d = pchipslopes(h,delta)%  PCHIPSLOPES  Slopes for shape-preserving Hermite cubic%  interpolation.  pchipslopes(h,delta) computes d(k) = P'(x(k)).%  Slopes at interior points%  delta = diff(y)./diff(x).%  d(k) = 0 if delta(k-1) and delta(k) have opposites signs%         or either is zero.%  d(k) = weighted harmonic mean of delta(k-1) and delta(k)%         if they have the same sign.   n = length(h)+1;   d = zeros(size(h));   k = find(sign(delta(1:n-2)).*sign(delta(2:n-1)) > 0) + 1;   w1 = 2*h(k)+h(k-1);   w2 = h(k)+2*h(k-1);   d(k) = (w1+w2)./(w1./delta(k-1) + w2./delta(k));%  Slopes at endpoints   d(1) = pchipendpoint(h(1),h(2),delta(1),delta(2));   d(n) = pchipendpoint(h(n-1),h(n-2),delta(n-1),delta(n-2));% -------------------------------------------------------function d = pchipendpoint(h1,h2,del1,del2)%  Noncentered, shape-preserving, three-point formula.   d = ((2*h1+h2)*del1 - h1*del2)/(h1+h2);   if sign(d) ~= sign(del1)      d = 0;   elseif (sign(del1) ~= sign(del2)) & (abs(d) > abs(3*del1))      d = 3*del1;   end