/usr/share/octave/packages/signal-1.3.2/cheb.m is in octave-signal 1.3.2-1+b1.
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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 | ## Copyright (C) 2002 André Carezia <acarezia@uol.com.br>
##
## 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} {} cheb (@var{n}, @var{x})
## Returns the value of the nth-order Chebyshev polynomial calculated at
## the point x. The Chebyshev polynomials are defined by the equations:
##
## @example
## @group
## / cos(n acos(x), |x| <= 1
## Tn(x) = |
## \ cosh(n acosh(x), |x| > 1
## @end group
## @end example
##
## If x is a vector, the output is a vector of the same size, where each
## element is calculated as y(i) = Tn(x(i)).
## @end deftypefn
function T = cheb (n, x)
if (nargin != 2)
print_usage;
elseif !(isscalar (n) && (n == round(n)) && (n >= 0))
error ("cheb: n has to be a positive integer");
endif
if (max(size(x)) == 0)
T = [];
endif
## avoid resizing latencies
T = zeros(size(x));
ind = abs (x) <= 1;
if (max(size(ind)))
T(ind) = cos(n*acos(x(ind)));
endif
ind = abs (x) > 1;
if (max(size(ind)))
T(ind) = cosh(n*acosh(x(ind)));
endif
T = real(T);
endfunction
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