--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/splines/pchip.m	Wed Oct 10 19:54:49 2001 +0000
@@ -0,0 +1,87 @@
+## Copyright (C) 2001  Kai Habel
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; if not, write to the Free Software
+## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{pp} = } pchip (@var{x}, @var{y})
+## @deftypefnx {Function File} {@var{yi} = } pchip (@var{x}, @var{y}, @var{xi})
+## piecewise cubic hermite interpolating polynom.
+## pchip preserves the monotonicity of (x,y)
+##
+## @seealso{ppval, spline, csape}
+## @end deftypefn
+
+## Author:  Kai Habel <kai.habel@gmx.de>
+## Date: 9. mar 2001
+## 2001-04-03 Paul Kienzle
+##   * move (:) from definition of l,r to use of l,r so it works with 2.0
+
+## S_k = a_k + b_k*x + c_k*x^2 + d_k*x^3; (spline polynom)
+##
+## 4 conditions:
+## S_k(x_k) = y_k;
+## S_k(x_k+1) = y_k+1;
+## S_k'(x_k) = y_k';
+## S_k'(x_k+1) = y_k+1';
+##
+## 22. april 2001: Hmm, something is wrong, it seems pchip doesn't 
+## preserve the monotonicity, as expected. So if _you_ know how to
+## do it right, please contact me. Kai
+
+function ret = pchip (x, y, xi)
+
+  if (nargin < 2 || nargin > 3)
+    usage ("pchip (x, y, [xi])");
+  endif
+
+  x = x(:);
+  n = length (x);
+
+  if (columns(y) == n) y = y'; endif
+
+  [ry,cy] = size (y);
+  if (cy > 1)
+    h = kron (diff (x), ones (1, cy));
+  else
+    h = diff (x);
+  endif
+
+  a = y;
+  
+  dy = diff (y) ./ h;
+  t = diff (sign (dy)) == 0;
+  l = dy(1:n - 2, :);
+  r = dy(2:n - 1, :);
+  b = zeros (size (y));
+  s = reshape (0.5 * (l(:) + r(:)), ry - 2, cy);
+  b(2:ry - 1,:) = s .* t;
+
+  c = - (b(2:n, :) + 2 * b(1:n - 1, :)) ./ h + 3 * diff (a) ./ h .^ 2;
+
+  d = (b(1:n - 1, :) + b(2:n, :)) ./ h.^2 - 2 * diff (a) ./ h.^3;
+
+  d = d(1:n - 1, :); c = c(1:n - 1, :);
+  b = b(1:n - 1, :); a = a(1:n - 1, :);
+
+  coeffs = [d(:), c(:), b(:), a(:)];
+  pp = mkpp (x, coeffs);
+
+  if (nargin == 2)
+    ret = pp;
+  else
+    ret = ppval(pp,xi);
+  endif
+
+endfunction