# HG changeset patch
# User Anthony Richardson <ar63@evansville.edu>
# Date 1239044129 -7200
# Node ID 705c24e3db58ee53f4054509a16252c1574903ca
# Parent  5235caf89e12fbd0c533c828631fe2c620c27124
implement polyscale and polytrans

diff -r 5235caf89e12 -r 705c24e3db58 scripts/ChangeLog
--- a/scripts/ChangeLog	Mon Apr 06 20:50:54 2009 +0200
+++ b/scripts/ChangeLog	Mon Apr 06 20:55:29 2009 +0200
@@ -1,3 +1,8 @@
+2009-04-06  Jaroslav Hajek <highegg@gmail.com>
+
+	* polynomial/polyscale.m: New function.
+	* polynomial/polytrans.m: New function.
+
 2009-04-06  Jaroslav Hajek  <highegg@gmail.com>
 
 	* special-matrix/pascal.m: Fix, optimize & extend.
diff -r 5235caf89e12 -r 705c24e3db58 scripts/polynomial/polyscale.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/polynomial/polyscale.m	Mon Apr 06 20:55:29 2009 +0200
@@ -0,0 +1,69 @@
+## Copyright (C) 2009  Tony Richardson
+##
+## 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, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} polyscale (@var{f}, @var{a})
+## Return the coefficients of the scaled polynomial whose
+## coefficients are given by vector @var{f}.  If @var{f} is the
+## vector representing the polynomial f(x), then 
+## @var{g} = polyscale (@var{f}, @var{a}) is the vector
+## representing g(x) = f(x*a).
+##
+## Here is a simple example that will plot both the original and
+## translated (shifted) polynomials.  f is a third order polynomial.
+## g is a polynomial obtained after scaling f by 2 (compression):
+##
+## f = [1/5 4/5 -7/5 -2];
+##
+## g = polyscale(f, 2);
+##
+## x = linspace(-4,4,100);
+##
+## plot(x,polyval(f,x),x,polyval(g,x));
+##
+## axis([-4 4 -3 5]);
+##
+## grid("on");
+## @seealso{polytranslate}
+## @end deftypefn
+
+## Author: Tony Richardson <richardson@evansville.edu)
+## Created: April 2009
+## adapted by: jh
+
+function g = polyscale (f, a)
+
+   if (nargin != 2)
+      print_usage ();
+   endif
+
+   if (! isvector (f))
+      error ("polyscale: first argument must be a vector.");
+   endif
+
+   if (! isscalar (a))
+      error ("polyscale: second argument must be a scalar.");
+   endif
+
+   lf = length(f);
+
+   # Ensure that f is a row vector
+   if (rows (f) > 1)
+      f = reshape (a, 1, lf);
+   endif
+
+   g = f .* (a .^ linspace (lf-1, 0, lf));
+
+endfunction
diff -r 5235caf89e12 -r 705c24e3db58 scripts/polynomial/polytrans.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/polynomial/polytrans.m	Mon Apr 06 20:55:29 2009 +0200
@@ -0,0 +1,70 @@
+## Copyright (C) 2009  Tony Richardson
+##
+## 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, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} polytrans (@var{f}, @var{a})
+## Return the coefficients of the shifted polynomial whose
+## coefficients are given by vector @var{f}.  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+a).
+## 
+## Here is a simple example that will plot both the original and
+## translated (shifted) polynomials.  f is a third order polynomial.
+## g is a polynomial obtained after shifting f one unit to the right:
+##
+## f = [1/5 4/5 -7/5 -2];
+##
+## g = polytrans(f, -1);
+##
+## x = linspace(-4,4,100);
+##
+## plot(x,polyval(f,x),x,polyval(g,x));
+##
+## axis([-4 4 -3 5]);
+##
+## grid("on");
+## @seealso{polyscale}
+## @end deftypefn
+
+## Author: Tony Richardson <richardson@evansville.edu)
+## Created: April 2009
+
+function g = polytrans (f, a)
+
+   if (nargin != 2)
+      print_usage ();
+   endif
+
+   if (! isvector (f))
+      error ("polytrans: first argument must be a vector.");
+   endif
+
+   if (! isscalar (a))
+      error ("polytrans: second argument must be a scalar.");
+   endif
+
+   lf = length (f);
+
+   # Ensure that f is a row vector
+   if (rows (f) > 1)
+      f = f.';
+   endif
+
+   p = linspace (0, lf-1, lf)';
+   ii = lf:-1:1;
+   g = f(ii) * (toeplitz (a .^ p) .* pascal (lf, -1));
+   g = g(ii);
+endfunction