/usr/share/octave/packages/specfun-1.1.0/ellipke.m is in octave-specfun 1.1.0-1build1.
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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 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 | ## Copyright (C) 2001 David Billinghurst
##
## 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{k}, @var{e}] =} ellipke (@var{m}[,@var{tol}])
## Compute complete elliptic integral of first K(@var{m}) and second E(@var{m}).
##
## @var{m} is either real array or scalar with 0 <= m <= 1
##
## @var{tol} will be ignored (@sc{Matlab} uses this to allow faster, less
## accurate approximation)
##
## Ref: Abramowitz, Milton and Stegun, Irene A. Handbook of Mathematical
## Functions, Dover, 1965, Chapter 17.
## @seealso{ellipj}
## @end deftypefn
## Author: David Billinghurst <David.Billinghurst@riotinto.com>
## Created: 31 January 2001
## 2001-02-01 Paul Kienzle
## * vectorized
## * included function name in error messages
## 2003-1-18 Jaakko Ruohio
## * extended for m < 0
function [k,e] = ellipke( m )
if (nargin < 1 || nargin > 2)
print_usage;
endif
k = e = zeros(size(m));
m = m(:);
if any(~isreal(m))
error("ellipke must have real m");
endif
if any(m>1)
error("ellipke must have m <= 1");
endif
Nmax = 16;
idx = find(m == 1);
if (!isempty(idx))
k(idx) = Inf;
e(idx) = 1.0;
endif
idx = find(m == -Inf);
if (!isempty(idx))
k(idx) = 0.0;
e(idx) = Inf;
endif
## Arithmetic-Geometric Mean (AGM) algorithm
## ( Abramowitz and Stegun, Section 17.6 )
idx = find(m != 1 & m != -Inf);
if (!isempty(idx))
idx_neg = find(m < 0 & m != -Inf);
mult_k = 1./sqrt(1-m(idx_neg));
mult_e = sqrt(1-m(idx_neg));
m(idx_neg) = -m(idx_neg)./(1-m(idx_neg));
a = ones(length(idx),1);
b = sqrt(1.0-m(idx));
c = sqrt(m(idx));
f = 0.5;
sum = f*c.*c;
for n = 2:Nmax
t = (a+b)/2;
c = (a-b)/2;
b = sqrt(a.*b);
a = t;
f = f * 2;
sum = sum + f*c.*c;
if all(c./a < eps), break; endif
endfor
if n >= Nmax, error("ellipke: not enough workspace"); endif
k(idx) = 0.5*pi./a;
e(idx) = 0.5*pi.*(1.0-sum)./a;
k(idx_neg) = mult_k.*k(idx_neg);
e(idx_neg) = mult_e.*e(idx_neg);
endif
endfunction
%!test
%! ## Test complete elliptic functions of first and second kind
%! ## against "exact" solution from Mathematica 3.0
%! ##
%! ## David Billinghurst <David.Billinghurst@riotinto.com>
%! ## 1 February 2001
%! m = [0.0; 0.01; 0.1; 0.5; 0.9; 0.99; 1.0 ];
%! [k,e] = ellipke(m);
%!
%! # K(1.0) is really infinity - see below
%! K = [
%! 1.5707963267948966192;
%! 1.5747455615173559527;
%! 1.6124413487202193982;
%! 1.8540746773013719184;
%! 2.5780921133481731882;
%! 3.6956373629898746778;
%! 0.0 ];
%! E = [
%! 1.5707963267948966192;
%! 1.5668619420216682912;
%! 1.5307576368977632025;
%! 1.3506438810476755025;
%! 1.1047747327040733261;
%! 1.0159935450252239356;
%! 1.0 ];
%! if k(7)==Inf, k(7)=0.0; endif;
%! assert(K,k,8*eps);
%! assert(E,e,8*eps);
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