/usr/share/octave/packages/3.2/miscellaneous-1.0.11/legendrepoly.m is in octave-miscellaneous 1.0.11-1.
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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 59 60 61 | ## 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 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, write to the Free Software
## Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
## -*- texinfo -*-
## @deftypefn {Function File} {@var{coefs}=} legendrepoly (@var{order},@var{x})
##
## Compute the coefficients of the Legendre polynomial, given the
## @var{order}. We calculate the Legendre polynomial using the recurrence
## relations, Pn+1(x) = inv(n+1)*((2n+1)*x*Pn(x) - nPn-1(x)).
##
## If the value @var{x} is specified, the polynomial is also evaluated,
## otherwise just the return the coefficients of the polynomial are returned.
##
## This is NOT the generalized Legendre polynomial.
##
## @end deftypefn
function h=legendrepoly(order,val)
if nargin < 1, error('usage: legendrepoly(order,val)'), end
h_prev=[0 1];
h_now=[1 0];
if order == 0
h=h_prev;
else
h=h_now;
end
for ord=2:order
x=[];y=[];
if (length(h_now) < (1+ord))
x=0;
end;
y=zeros(1,(1+ord)-length(h_prev));
p1=[h_now, x];
p3=[y, h_prev];
h=((2*ord -1).*p1 -(ord -1).*p3)./(ord);
h_prev=h_now;
h_now=h;
end
if nargin == 2
h=polyval(h,val);
end
return
end
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