Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / miscellaneous-1.1.0 / laguerrepoly.m

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+## Copyright (C) 2007 Muthiah Annamalai <muthiah.annamalai@mavs.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}=} laguerrepoly (@var{order},@var{x})
+## 
+## Compute the coefficients of the Laguerre polynomial, given the 
+## @var{order}. We calculate the Laguerre polynomial using the recurrence
+## relations, Ln+1(x) = inv(n+1)*((2n+1-x)Ln(x) - nLn-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 Laguerre polynomial.
+##
+## @end deftypefn
+
+function h = laguerrepoly (order, val)
+  if (nargin < 1 || nargin > 2)
+    print_usage
+  endif
+
+  h_prev=[0 1];
+  h_now=[-1 1];
+
+  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];
+    p2=[x, h_now];
+    p3=[y, h_prev];
+    h=((2*ord -1).*p2 -p1 -(ord -1).*p3)./(ord);
+    h_prev=h_now;
+    h_now=h;
+  endfor
+
+  if nargin == 2
+    h=polyval(h,val);
+  endif
+
+endfunction