/usr/share/octave/packages/miscellaneous-1.2.1/chebyshevpoly.m is in octave-miscellaneous 1.2.1-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 | ## Copyright (C) 2007 Muthiah Annamalai <muthiah.annamalai@uta.edu>
##
## 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} {@var{coefs}=} chebyshevpoly (@var{kind},@var{order},@var{x})
##
## Compute the coefficients of the Chebyshev polynomial, given the
## @var{order}. We calculate the Chebyshev polynomial using the recurrence
## relations Tn+1(x) = (2*x*Tn(x) - Tn-1(x)). The @var{kind} can be set to
## compute the first or second kind Chebyshev polynomial.
##
## If the value @var{x} is specified, the polynomial is evaluated at @var{x},
## otherwise just the coefficients of the polynomial are returned.
##
## This is NOT the generalized Chebyshev polynomial.
##
## @end deftypefn
function h=chebyshevpoly(kind,order,val)
if nargin < 2, print_usage, endif
h_prev=[0 1];
if kind == 1
h_now=[1 0];
elseif (kind == 2)
h_now=[2 0];
else
error('unknown kind');
endif
if order == 0
h=h_prev;
else
h=h_now;
endif
for ord=2:order
x=[];y=[];
if (length(h_now) < (1+ord))
x=0;
endif
y=zeros(1,(1+ord)-length(h_prev));
p1=[h_now, x];
p3=[y, h_prev];
h=2*p1 -p3;
h_prev=h_now;
h_now=h;
endfor
if nargin == 3
h=polyval(h,val);
endif
endfunction
%!test
%! x = logspace(-2, 2, 30);
%! maxdeg = 10;
%! for n = 1:maxdeg
%! assert( chebyshevpoly(1,n,cos(x)), cos(n*x), 1E3*eps )
%! assert( chebyshevpoly(2,n,cos(x)) .* sin(x), sin((n+1)*x), 1E3*eps )
%! endfor
|