octave-nkf: scripts/statistics/distributions/cauchy

annotate scripts/statistics/distributions/cauchy_inv.m @ 20643:d6d04088ac9e

nbininv.m: Increase speed (85X) and accuracy of function (bug #34363). * nbininv.m: Call new function scalar_nbininv to calculate nbininv for scalar. If there are still uncalculated values then call bin_search_nbininv. Call bin_search_nbininv directly for vectors. Add more BIST tests. * nbininv.m (scalar_binoinv): New subfunction to calculate nbininv for scalar x. Stops when x > 1000. * nbininv.m (bin_search_nbininv): New subfunction to do binary search for nbininv.

author	Lachlan Andrew <lachlanbis@gmail.com>
date	Sun, 11 Oct 2015 20:33:37 -0700
parents	d9341b422488
children

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 13171 diff changeset	1 ## Copyright (C) 2012 Rik Wehbring
19731 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 17744 diff changeset	2 ## Copyright (C) 1995-2015 Kurt Hornik
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	3 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	4 ## This file is part of Octave.
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	5 ##
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	7 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	8 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	9 ## your option) any later version.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	10 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3456 diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	14 ## General Public License for more details.
f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	15 ##
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	16 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	17 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	18 ## <http://www.gnu.org/licenses/>.
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	19
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	20 ## -- texinfo --
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	21 ## @deftypefn {Function File} {} cauchy_inv (@var{x})
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	22 ## @deftypefnx {Function File} {} cauchy_inv (@var{x}, @var{location}, @var{scale})
20209 d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19867 diff changeset	23 ## For each element of @var{x}, compute the quantile (the inverse of the CDF)
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19867 diff changeset	24 ## at @var{x} of the Cauchy distribution with location parameter
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19867 diff changeset	25 ## @var{location} and scale parameter @var{scale}.
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19867 diff changeset	26 ##
d9341b422488 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19867 diff changeset	27 ## Default values are @var{location} = 0, @var{scale} = 1.
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	28 ## @end deftypefn
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	29
5428 2a16423e4aa0 [project @ 2005-08-23 18:38:27 by jwe] jwe parents: 5307 diff changeset	30 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
3456 434790acb067 [project @ 2000-01-19 06:58:51 by jwe] jwe parents: 3426 diff changeset	31 ## Description: Quantile function of the Cauchy distribution
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	32
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	33 function inv = cauchy_inv (x, location = 0, scale = 1)
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	34
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	35 if (nargin != 1 && nargin != 3)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5428 diff changeset	36 print_usage ();
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	37 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	38
19867 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19731 diff changeset	39 if (! isscalar (location) \|\| ! isscalar (scale))
4854 4b0f3b055331 [project @ 2004-04-07 02:37:05 by jwe] jwe parents: 3922 diff changeset	40 [retval, x, location, scale] = common_size (x, location, scale);
4b0f3b055331 [project @ 2004-04-07 02:37:05 by jwe] jwe parents: 3922 diff changeset	41 if (retval > 0)
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	42 error ("cauchy_inv: X, LOCATION, and SCALE must be of common size or scalars");
4854 4b0f3b055331 [project @ 2004-04-07 02:37:05 by jwe] jwe parents: 3922 diff changeset	43 endif
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	44 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	45
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	46 if (iscomplex (x) \|\| iscomplex (location) \|\| iscomplex (scale))
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	47 error ("cauchy_inv: X, LOCATION, and SCALE must not be complex");
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	48 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	49
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	50 if (isa (x, "single") \|\| isa (location, "single") \|\| isa (scale, "single"))
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	51 inv = NaN (size (x), "single");
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	52 else
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	53 inv = NaN (size (x));
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	54 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	55
19867 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19731 diff changeset	56 ok = ! isinf (location) & (scale > 0) & (scale < Inf);
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	57
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	58 k = (x == 0) & ok;
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	59 inv(k) = -Inf;
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	60
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	61 k = (x == 1) & ok;
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	62 inv(k) = Inf;
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	63
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	64 k = (x > 0) & (x < 1) & ok;
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	65 if (isscalar (location) && isscalar (scale))
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	66 inv(k) = location - scale * cot (pi * x(k));
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	67 else
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	68 inv(k) = location(k) - scale(k) .* cot (pi * x(k));
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	69 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3191 diff changeset	70
3191 e4f4b2d26ee9 [project @ 1998-10-23 05:43:59 by jwe] jwe parents: diff changeset	71 endfunction
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	72
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	73
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	74 %!shared x
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	75 %! x = [-1 0 0.5 1 2];
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	76 %!assert (cauchy_inv (x, ones (1,5), 2*ones (1,5)), [NaN -Inf 1 Inf NaN], eps)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	77 %!assert (cauchy_inv (x, 1, 2*ones (1,5)), [NaN -Inf 1 Inf NaN], eps)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	78 %!assert (cauchy_inv (x, ones (1,5), 2), [NaN -Inf 1 Inf NaN], eps)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	79 %!assert (cauchy_inv (x, [1 -Inf NaN Inf 1], 2), [NaN NaN NaN NaN NaN])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	80 %!assert (cauchy_inv (x, 1, 2*[1 0 NaN Inf 1]), [NaN NaN NaN NaN NaN])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	81 %!assert (cauchy_inv ([x(1:2) NaN x(4:5)], 1, 2), [NaN -Inf NaN Inf NaN])
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	82
19867 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19731 diff changeset	83 ## Test class of input preserved
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	84 %!assert (cauchy_inv ([x, NaN], 1, 2), [NaN -Inf 1 Inf NaN NaN], eps)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	85 %!assert (cauchy_inv (single ([x, NaN]), 1, 2), single ([NaN -Inf 1 Inf NaN NaN]), eps ("single"))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	86 %!assert (cauchy_inv ([x, NaN], single (1), 2), single ([NaN -Inf 1 Inf NaN NaN]), eps ("single"))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	87 %!assert (cauchy_inv ([x, NaN], 1, single (2)), single ([NaN -Inf 1 Inf NaN NaN]), eps ("single"))
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	88
19867 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19731 diff changeset	89 ## Test input validation
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	90 %!error cauchy_inv ()
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	91 %!error cauchy_inv (1,2)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	92 %!error cauchy_inv (1,2,3,4)
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	93 %!error cauchy_inv (ones (3), ones (2), ones (2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	94 %!error cauchy_inv (ones (2), ones (3), ones (2))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	95 %!error cauchy_inv (ones (2), ones (2), ones (3))
13171 19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	96 %!error cauchy_inv (i, 2, 2)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	97 %!error cauchy_inv (2, i, 2)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	98 %!error cauchy_inv (2, 2, i)
19b9f17d22af Overhaul of statistical distribution functions Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	99

Mercurial > octave-nkf

annotate scripts/statistics/distributions/cauchy_inv.m @ 20643:d6d04088ac9e