--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/polynomial/polyaffine.m	Tue Apr 14 07:19:14 2009 +0200
@@ -0,0 +1,79 @@
+## Copyright (C) 2009  Tony Richardson, Jaroslav Hajek
+##
+## 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 3 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, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} polyaffine (@var{f}, @var{mu})
+## Return the coefficients of the polynomial whose coefficients are given by
+## vector @var{f} after an affine tranformation. If @var{f} is the vector
+## representing the polynomial f(x), then @var{g} = polytrans (@var{f},
+## @var{a}) is the vector representing g(x) = f((x-@var{mu}(1))/@var{mu}(2)).
+## 
+## Here is a simple example that will plot both the original and
+## transformed polynomials.  f is a third order polynomial.
+## g is a polynomial obtained after shifting f one unit to the right
+## and stretching the x axis by 1.2:
+##
+## f = [1/5 4/5 -7/5 -2];
+##
+## g = polyaffine(f, [1, 1.2]);
+##
+## x = linspace(-4,4,100);
+##
+## plot(x,polyval(f,x),x,polyval(g,x));
+##
+## axis([-4 4 -3 5]);
+##
+## grid("on");
+## @seealso{polyval}
+## @end deftypefn
+
+
+function g = polyaffine (f, mu)
+
+   if (nargin != 2)
+      print_usage ();
+   endif
+
+   if (! isvector (f))
+      error ("polyaffine: first argument must be a vector.");
+   endif
+
+   if (! isvector (mu) || length (mu) != 2)
+      error ("polyaffine: second argument must be a two-element vector.");
+   endif
+
+   lf = length (f);
+
+   ## Ensure that f is a row vector
+   if (rows (f) > 1)
+      f = f.';
+   endif
+
+   ## Translate.
+   if (mu(1) != 0)
+     w = (-mu(1)) .^ (0:lf-1);
+     ii = lf:-1:1;
+     g = f(ii) * (toeplitz (w) .* pascal (lf, -1));
+     g = g(ii);
+   else
+     g = f;
+   endif
+
+   ## Scale.
+   if (mu(2) != 1)
+     g = g ./ (mu(2) .^ (lf-1:-1:0));
+   endif
+
+endfunction