octave-nkf: scripts/specfun/ellipke.m annotate

annotate scripts/specfun/ellipke.m @ 19840:c5270263d466 gui-release

close gui-release branch

author	John W. Eaton <jwe@octave.org>
date	Fri, 30 Jan 2015 17:41:50 -0500
parents	d63878346099
children	0850b5212619

rev	line source
17744 d63878346099 maint: Update copyright notices for release. John W. Eaton <jwe@octave.org> parents: 17371 diff changeset	1 ## Copyright (C) 2001, 2013 David Billinghurst
d63878346099 maint: Update copyright notices for release. John W. Eaton <jwe@octave.org> parents: 17371 diff changeset	2 ## Copyright (C) 2001, 2013 Paul Kienzle
d63878346099 maint: Update copyright notices for release. John W. Eaton <jwe@octave.org> parents: 17371 diff changeset	3 ## Copyright (C) 2003, 2013 Jaakko Ruohio
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	4 ##
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	5 ## This file is part of Octave.
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	6 ##
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	7 ## Octave is free software; you can redistribute it and/or modify it
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	8 ## under the terms of the GNU General Public License as published by
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	9 ## the Free Software Foundation; either version 3 of the License, or (at
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	10 ## your option) any later version.
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	11 ##
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	12 ## Octave is distributed in the hope that it will be useful, but
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	13 ## WITHOUT ANY WARRANTY; without even the implied warranty of
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	15 ## General Public License for more details.
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	16 ##
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	17 ## You should have received a copy of the GNU General Public License
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	18 ## along with Octave; see the file COPYING. If not, see
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	19 ## <http://www.gnu.org/licenses/>.
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	20
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	21 ## -- texinfo --
17370 c7c0dad2f9ac doc: Use Octave citation style for references in ellipj, ellipke. Rik <rik@octave.org> parents: 17336 diff changeset	22 ## @deftypefn {Function File} {@var{k} =} ellipke (@var{m})
c7c0dad2f9ac doc: Use Octave citation style for references in ellipj, ellipke. Rik <rik@octave.org> parents: 17336 diff changeset	23 ## @deftypefnx {Function File} {@var{k} =} ellipke (@var{m}, @var{tol})
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	24 ## @deftypefnx {Function File} {[@var{k}, @var{e}] =} ellipke (@dots{})
17370 c7c0dad2f9ac doc: Use Octave citation style for references in ellipj, ellipke. Rik <rik@octave.org> parents: 17336 diff changeset	25 ## Compute complete elliptic integrals of the first K(@var{m}) and second
16587 a3fdd6041e64 Fix ellipj, ellipke, and expint docstrings Mike Miller <mtmiller@ieee.org> parents: 16586 diff changeset	26 ## E(@var{m}) kind.
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	27 ##
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	28 ## @var{m} must be a scalar or real array with -Inf @leq{} @var{m} @leq{} 1.
17370 c7c0dad2f9ac doc: Use Octave citation style for references in ellipj, ellipke. Rik <rik@octave.org> parents: 17336 diff changeset	29 ##
c7c0dad2f9ac doc: Use Octave citation style for references in ellipj, ellipke. Rik <rik@octave.org> parents: 17336 diff changeset	30 ## The optional input @var{tol} is currently ignored (@sc{matlab} uses this
c7c0dad2f9ac doc: Use Octave citation style for references in ellipj, ellipke. Rik <rik@octave.org> parents: 17336 diff changeset	31 ## to allow a faster, less accurate approximation).
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	32 ##
17370 c7c0dad2f9ac doc: Use Octave citation style for references in ellipj, ellipke. Rik <rik@octave.org> parents: 17336 diff changeset	33 ## Called with only one output, elliptic integrals of the first kind are
c7c0dad2f9ac doc: Use Octave citation style for references in ellipj, ellipke. Rik <rik@octave.org> parents: 17336 diff changeset	34 ## returned.
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	35 ##
17370 c7c0dad2f9ac doc: Use Octave citation style for references in ellipj, ellipke. Rik <rik@octave.org> parents: 17336 diff changeset	36 ## Reference: Milton Abramowitz and Irene A. Stegun,
c7c0dad2f9ac doc: Use Octave citation style for references in ellipj, ellipke. Rik <rik@octave.org> parents: 17336 diff changeset	37 ## @cite{Handbook of Mathematical Functions}, Chapter 17, Dover, 1965.
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	38 ## @seealso{ellipj}
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	39 ## @end deftypefn
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	40
16768 e2de3c8882be copyright notice fixes John W. Eaton <jwe@octave.org> parents: 16587 diff changeset	41 ## Author: David Billinghurst <David.Billinghurst@riotinto.com>
e2de3c8882be copyright notice fixes John W. Eaton <jwe@octave.org> parents: 16587 diff changeset	42 ## Author: Paul Kienzle <pkienzle@users.sf.net>
e2de3c8882be copyright notice fixes John W. Eaton <jwe@octave.org> parents: 16587 diff changeset	43 ## Author: Jaakko Ruohio
e2de3c8882be copyright notice fixes John W. Eaton <jwe@octave.org> parents: 16587 diff changeset	44
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	45 function [k, e] = ellipke (m)
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	46
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	47 if (nargin < 1 \|\| nargin > 2)
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	48 print_usage ();
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	49 endif
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	50
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	51 m = m(:);
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	52 if (! isreal (m))
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	53 error ("ellipke: M must be real");
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	54 elseif (any (m > 1))
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	55 error ("ellipke: M must be <= 1");
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	56 endif
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	57
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	58 k = e = zeros (size (m));
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	59
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	60 ## Handle extreme values
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	61 idx_1 = (m == 1);
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	62 k(idx_1) = Inf;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	63 e(idx_1) = 1;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	64
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	65 idx_neginf = (m == -Inf);
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	66 k(idx_neginf) = 0;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	67 e(idx_neginf) = Inf;
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	68
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	69 ## Arithmetic-Geometric Mean (AGM) algorithm
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	70 ## ( Abramowitz and Stegun, Section 17.6 )
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	71 Nmax = 16;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	72 idx = !idx_1 & !idx_neginf;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	73 if (any (idx))
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	74 idx_neg = find (m < 0 & !idx_neginf);
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	75 mult_k = 1./sqrt (1 - m(idx_neg));
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	76 mult_e = sqrt (1 - m(idx_neg));
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	77 m(idx_neg) = -m(idx_neg) ./ (1 - m(idx_neg));
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	78 a = ones (sum (idx), 1);
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	79 b = sqrt (1 - m(idx));
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	80 c = sqrt (m(idx));
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	81 f = 0.5;
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	82 sum = f*c.^2;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	83 n = 2;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	84 do
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	85 t = (a + b)/2;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	86 c = (a - b)/2;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	87 b = sqrt (a.*b);
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	88 a = t;
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	89 f *= 2;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	90 sum += f*c.^2;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	91 until (all (c./a < eps) \|\| (++n > Nmax))
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	92 if (n >= Nmax)
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	93 error ("ellipke: algorithm did not converge in %d iterations", Nmax);
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	94 endif
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	95 k(idx) = 0.5*pi ./ a;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	96 e(idx) = 0.5pi(1 - sum) ./ a;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	97 k(idx_neg) = mult_k .* k(idx_neg);
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	98 e(idx_neg) = mult_e .* e(idx_neg);
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	99 endif
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	100
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	101 endfunction
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	102
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16933 diff changeset	103
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16933 diff changeset	104 ## Test complete elliptic functions of first and second kind
b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16933 diff changeset	105 ## against "exact" solution from Mathematica 3.0
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	106 %!test
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	107 %! m = [0.0; 0.01; 0.1; 0.5; 0.9; 0.99; 1.0];
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	108 %! [k,e] = ellipke (m);
16584 2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge Mike Miller <mtmiller@ieee.org> parents: diff changeset	109 %!
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	110 %! k_exp = [1.5707963267948966192;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	111 %! 1.5747455615173559527;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	112 %! 1.6124413487202193982;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	113 %! 1.8540746773013719184;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	114 %! 2.5780921133481731882;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	115 %! 3.6956373629898746778;
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	116 %! Inf ];
16586 f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	117 %! e_exp = [1.5707963267948966192;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	118 %! 1.5668619420216682912;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	119 %! 1.5307576368977632025;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	120 %! 1.3506438810476755025;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	121 %! 1.1047747327040733261;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	122 %! 1.0159935450252239356;
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	123 %! 1.0 ];
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	124 %! assert (k, k_exp, 8*eps);
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m Mike Miller <mtmiller@ieee.org> parents: 16585 diff changeset	125 %! assert (e, e_exp, 8*eps);
16585 1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	126
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16933 diff changeset	127 ## Test against A&S Table 17.1
16585 1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	128 %!test
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	129 %! m = [0:5:50]'/100;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	130 %! k_exp = [1.570796326794897;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	131 %! 1.591003453790792;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	132 %! 1.612441348720219;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	133 %! 1.635256732264580;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	134 %! 1.659623598610528;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	135 %! 1.685750354812596;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	136 %! 1.713889448178791;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	137 %! 1.744350597225613;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	138 %! 1.777519371491253;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	139 %! 1.813883936816983;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	140 %! 1.854074677301372 ];
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	141 %! e_exp = [1.570796327;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	142 %! 1.550973352;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	143 %! 1.530757637;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	144 %! 1.510121831;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	145 %! 1.489035058;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	146 %! 1.467462209;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	147 %! 1.445363064;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	148 %! 1.422691133;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	149 %! 1.399392139;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	150 %! 1.375401972;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	151 %! 1.350643881 ];
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	152 %! [k,e] = ellipke (m);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	153 %! assert (k, k_exp, 1e-15);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	154 %! assert (e, e_exp, 1e-8);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	155
17371 f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	156 ## Test negative values against "exact" solution from Mathematica.
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	157 %! m = [-0.01; -1; -5; -100; -1000; -Inf];
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	158 %! [k,e] = ellipke (m);
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	159 %!
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	160 %! k_exp = [1.5668912730681963584;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	161 %! 1.3110287771460599052;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	162 %! 0.9555039270640439337;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	163 %! 0.3682192486091410329;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	164 %! 0.1530293349884987857;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	165 %! 0];
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	166 %! e_exp = [1.5747159850169884130;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	167 %! 1.9100988945138560089;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	168 %! 2.8301982463458773125;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	169 %! 10.209260919814572009;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	170 %! 31.707204053711259719;
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	171 %! Inf ];
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	172 %! assert (k, k_exp, 8*eps);
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	173 %! assert (e, e_exp, 8*eps (e_exp));
f9e8544ce66d ellipke.m: Overhaul function. Rik <rik@octave.org> parents: 17370 diff changeset	174
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16933 diff changeset	175 ## Test input validation
16585 1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	176 %!error ellipke ()
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint Mike Miller <mtmiller@ieee.org> parents: 16584 diff changeset	177 %!error ellipke (1,2,3)
17336 b81b9d079515 Use '##' for comments which stand alone on a line. Rik <rik@octave.org> parents: 16933 diff changeset	178

Mercurial > hg > octave-nkf

annotate scripts/specfun/ellipke.m @ 19840:c5270263d466 gui-release