# HG changeset patch # User Jaroslav Hajek # Date 1239686354 -7200 # Node ID 79e90381b4022fb280bf344c42882f6b8371de56 # Parent 4bb94a71913b97b802634e7b5fc77fcdd8ae882a merge polytrans & polyscale -> polyaffine, make compatible with polyval diff -r 4bb94a71913b -r 79e90381b402 scripts/ChangeLog --- a/scripts/ChangeLog Sun Apr 12 20:40:53 2009 -0400 +++ b/scripts/ChangeLog Tue Apr 14 07:19:14 2009 +0200 @@ -1,3 +1,9 @@ +2009-04-14 Jaroslav Hajek + + * polynomial/polyaffine.m: New function. + * polynomial/polyscale.m: Remove. + * polynomial/polytrans.m: Remove. + 2009-04-12 Ben Abbott * plot/__gnuplot_open_stream__.m: New function. diff -r 4bb94a71913b -r 79e90381b402 scripts/polynomial/Makefile.in --- a/scripts/polynomial/Makefile.in Sun Apr 12 20:40:53 2009 -0400 +++ b/scripts/polynomial/Makefile.in Tue Apr 14 07:19:14 2009 +0200 @@ -34,9 +34,9 @@ INSTALL_DATA = @INSTALL_DATA@ SOURCES = compan.m conv.m convn.m deconv.m mkpp.m mpoles.m \ - pchip.m poly.m polyder.m polyderiv.m polyfit.m polygcd.m \ - polyint.m polyout.m polyreduce.m polyval.m polyvalm.m \ - ppval.m residue.m roots.m spline.m unmkpp.m + pchip.m poly.m polyaffine.m polyder.m polyderiv.m polyfit.m \ + polygcd.m polyint.m polyout.m polyreduce.m polyval.m \ + polyvalm.m ppval.m residue.m roots.m spline.m unmkpp.m DISTFILES = $(addprefix $(srcdir)/, Makefile.in $(SOURCES)) diff -r 4bb94a71913b -r 79e90381b402 scripts/polynomial/polyaffine.m --- /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 . + +## -*- 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 diff -r 4bb94a71913b -r 79e90381b402 scripts/polynomial/polyscale.m --- a/scripts/polynomial/polyscale.m Sun Apr 12 20:40:53 2009 -0400 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,69 +0,0 @@ -## 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 . - -## -*- 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 1) - f = reshape (a, 1, lf); - endif - - g = f .* (a .^ linspace (lf-1, 0, lf)); - -endfunction diff -r 4bb94a71913b -r 79e90381b402 scripts/polynomial/polytrans.m --- a/scripts/polynomial/polytrans.m Sun Apr 12 20:40:53 2009 -0400 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,70 +0,0 @@ -## 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 . - -## -*- 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 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