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.
 
%   Copyright 2014 Cleve Moler
%   Copyright 2014 The MathWorks, Inc.

%  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
%  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) = pchipend(h(1),h(2),delta(1),delta(2));
   d(n) = pchipend(h(n-1),h(n-2),delta(n-1),delta(n-2));

% -------------------------------------------------------

function d = pchipend(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