octave: scripts/specfun/betaincinv.m annotate

annotate scripts/specfun/betaincinv.m @ 27923:bd51beb6205e

update formatting of copyright notices * Use <https://octave.org/copyright/> instead of <https://octave.org/COPYRIGHT.html/>. * For consistency with other comments in the Octave sources, use C++-style comments for copyright blocks in C and C++ files. * Use delimiters above and below copyright blocks that are appropriate for the language used in the file. * Eliminate extra spacing inside copyright blocks. * lex.ll (looks_like_copyright): Also allow newlines and carriage returns before the word "Copyright". * scripts/mk-doc.pl (gethelp): Also skip empty comment lines. * bp-table.cc, type.m: Adjust tests.

author	John W. Eaton <jwe@octave.org>
date	Wed, 08 Jan 2020 11:59:41 -0500
parents	1891570abac8
children	a4268efb7334

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ########################################################################
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 ##
27919 1891570abac8 update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 27918 diff changeset	3 ## Copyright (C) 2017-2020 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	4 ##
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 ## distribution or <https://octave.org/copyright/>.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	7 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	8 ## This file is part of Octave.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	9 ##
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	11 ## under the terms of the GNU General Public License as published by
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	13 ## (at your option) any later version.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	14 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	18 ## GNU General Public License for more details.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	19 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	21 ## along with Octave; see the file COPYING. If not, see
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	22 ## <https://www.gnu.org/licenses/>.
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 ##
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ########################################################################
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	25
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	26 ## Author: Michele Ginesi <michele.ginesi@gmail.com>
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	27
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	28 ## -- texinfo --
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	29 ## @deftypefn {} {} betaincinv (@var{y}, @var{a}, @var{b})
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	30 ## @deftypefnx {} {} betaincinv (@var{y}, @var{a}, @var{b}, "lower")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	31 ## @deftypefnx {} {} betaincinv (@var{y}, @var{a}, @var{b}, "upper")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	32 ## Compute the inverse of the normalized incomplete beta function.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	33 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	34 ## The normalized incomplete beta function is defined as
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	35 ## @tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	36 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	37 ## I_x (a, b) = {1 \over {B(a,b)}} \displaystyle{\int_0^x t^{a-1} (1-t)^{b-1} dt}
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	38 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	39 ## @end tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	40 ## @ifnottex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	41 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	42 ## @example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	43 ## @group
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	44 ## x
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	45 ## /
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	46 ## \|
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	47 ## I_x (a, b) = \| t^(a-1) (1-t)^(b-1) dt
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	48 ## \|
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	49 ## /
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	50 ## 0
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	51 ## @end group
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	52 ## @end example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	53 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	54 ## @end ifnottex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	55 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	56 ## If two inputs are scalar, then @code{betaincinv (@var{y}, @var{a}, @var{b})}
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	57 ## is returned for each of the other inputs.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	58 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	59 ## If two or more inputs are not scalar, the sizes of them must agree, and
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	60 ## @code{betaincinv} is applied element-by-element.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	61 ##
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	62 ## The variable @var{y} must be in the interval [0,1], while @var{a} and
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	63 ## @var{b} must be real and strictly positive.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	64 ##
25579 07c2c42f457e doc: Miscellaneous documentation fixes all over the manual (bug #54288). Rik <rik@octave.org> parents: 25054 diff changeset	65 ## By default, @var{tail} is @qcode{"lower"} and the inverse of the incomplete
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	66 ## beta function integrated from 0 to @var{x} is computed. If @var{tail} is
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	67 ## @qcode{"upper"} then the complementary function integrated from @var{x} to 1
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	68 ## is inverted.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	69 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	70 ## The function is computed by standard Newton's method, by solving
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	71 ## @tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	72 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	73 ## y - I_x (a, b) = 0
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	74 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	75 ## @end tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	76 ## @ifnottex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	77 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	78 ## @example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	79 ## @var{y} - betainc (@var{x}, @var{a}, @var{b}) = 0
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	80 ## @end example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	81 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	82 ## @end ifnottex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	83 ##
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	84 ## @seealso{betainc, beta, betaln}
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	85 ## @end deftypefn
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	86
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	87 function x = betaincinv (y, a, b, tail = "lower")
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	88
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	89 if (nargin < 3 \|\| nargin > 4)
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	90 print_usage ();
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	91 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	92
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	93 [err, y, a, b] = common_size (y, a, b);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	94 if (err > 0)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	95 error ("betaincinv: Y, A, and B must be of common size or scalars");
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	96 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	97
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	98 if (iscomplex (y) \|\| iscomplex (a) \|\| iscomplex (b))
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	99 error ("betaincinv: all inputs must be real");
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	100 endif
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	101
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	102 ## FIXME: Should there be isnumeric checking? Right now it accepts char
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	103 ## arrays, but then produces a weird error later on.
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	104
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	105 ## Remember original shape of data, but convert to column vector for calcs.
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	106 orig_sz = size (y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	107 y = y(:);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	108 a = a(:);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	109 b = b(:);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	110
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	111 if (any ((y < 0) \| (y > 1)))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	112 error ("betaincinv: Y must be in the range [0, 1]");
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	113 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	114
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	115 if (any (a <= 0))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	116 error ("betaincinv: A must be strictly positive");
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	117 endif
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	118
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	119 if (any (b <= 0))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	120 error ("betaincinv: B must be strictly positive");
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	121 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	122
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	123 ## If any of the arguments is single then the output should be as well.
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	124 if (strcmp (class (y), "single") \|\| strcmp (class (a), "single")
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	125 \|\| strcmp (class (b), "single"))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	126 y = single (y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	127 a = single (a);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	128 b = single (b);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	129 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	130
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	131 ## Convert to floating point if necessary
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	132 if (isinteger (y))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	133 y = double (y);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	134 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	135 if (isinteger (a))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	136 a = double (a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	137 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	138 if (isinteger (b))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	139 b = double (b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	140 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	141
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	142 ## Initialize output array
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	143 x = zeros (size (y), class (y));
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	144
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	145 ## Parameters for the Newton method
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	146 maxit = 20;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	147 tol = eps (class (y));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	148
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	149 if (strcmpi (tail, "lower"))
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	150 p = y;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	151 q = 1 - y;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	152 x(y == 0) = 0;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	153 x(y == 1) = 1;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	154 elseif (strcmpi (tail, "upper"))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	155 p = 1 - y;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	156 q = y;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	157 x(y == 0) = 1;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	158 x(y == 1) = 0;
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	159 else
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	160 error ("betaincinv: invalid value for TAIL")
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	161 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	162
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	163 ## Special values have been already computed.
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	164 todo = (y != 0) & (y != 1);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	165
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	166 ## We will invert the lower version for p < 0.5 and the upper otherwise.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	167 i_low = (p < 0.5);
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	168 i_upp = (! i_low);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	169
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	170 idx = todo & i_low;
26268 6dd232798997 maint: Remove useless ';' from end of for, if, while, etc. statements. Rik <rik@octave.org> parents: 25579 diff changeset	171 if (any (idx))
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	172 n = nnz (idx);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	173 ## Function and derivative of the lower version.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	174 F = @(x, a, b, y) y - betainc (x, a, b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	175 JF = @(x, a, b) - real (exp ((a-1) .* log (x) + (b-1) .* log1p (-x) + ...
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	176 gammaln (a+b) - gammaln (a) - gammaln (b)));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	177
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	178 ## Compute the initial guess with a bisection method of 10 steps.
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	179 x0 = bisection_method (F, zeros (n,1), ones (n,1), ...
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	180 a(i_low), b(i_low), p(i_low), 10);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	181
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	182 ## Use Newton's method to iteratively find solution.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	183 x(i_low) = newton_method (F, JF, x0, a(i_low), b(i_low), p(i_low), ...
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	184 tol, maxit);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	185 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	186
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	187 idx = todo & i_upp;
26268 6dd232798997 maint: Remove useless ';' from end of for, if, while, etc. statements. Rik <rik@octave.org> parents: 25579 diff changeset	188 if (any (idx))
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	189 n = nnz (idx);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	190 ## Function and derivative of the upper version.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	191 F = @(x, a, b, y) y - betainc (x, a, b, "upper");
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	192 JF = @(x, a, b) real (exp ((a-1) .* log (x) + (b-1) .* log1p (-x) + ...
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	193 gammaln (a+b) - gammaln (a) - gammaln (b)));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	194
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	195 ## Compute the initial guess with a bisection method of 10 steps.
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	196 x0 = bisection_method (F, zeros (n,1), ones (n,1), ...
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	197 a(i_upp), b(i_upp), q(i_upp), 10);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	198
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	199 ## Use Newton's method to iteratively find solution.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	200 x(i_upp) = newton_method (F, JF, x0, a(i_upp), b(i_upp), q(i_upp), ...
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	201 tol, maxit);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	202 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	203
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	204 ## Restore original shape
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	205 x = reshape (x, orig_sz);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	206
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	207 endfunction
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	208
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	209
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	210 ## Subfunctions: Bisection and Newton Methods
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	211 function xc = bisection_method (F, xl, xr, a, b, y, maxit)
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	212 F_l = F (xl, a, b, y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	213 F_r = F (xr, a, b, y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	214 for it = 1:maxit
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	215 xc = (xl + xr) / 2;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	216 F_c = F (xc, a, b, y);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	217 flag_l = ((F_c .* F_r) < 0);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	218 flag_r = ((F_c .* F_l) < 0);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	219 flag_c = (F_c == 0);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	220 xl(flag_l) = xc(flag_l);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	221 xr(flag_r) = xc(flag_r);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	222 xl(flag_c) = xr(flag_c) = xc(flag_c);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	223 F_l(flag_l) = F_c(flag_l);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	224 F_r(flag_r) = F_c(flag_r);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	225 F_l(flag_c) = F_r(flag_c) = 0;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	226 endfor
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	227 endfunction
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	228
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	229 function x = newton_method (F, JF, x0, a, b, y, tol, maxit);
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	230 l = numel (y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	231 res = -F (x0, a, b, y) ./ JF (x0, a, b);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	232 todo = (abs(res) >= tol * abs (x0));
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	233 x = x0;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	234 it = 0;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	235 while (any (todo) && (it < maxit))
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	236 it++;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	237 x(todo) += res(todo);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	238 res(todo) = -F(x(todo), a(todo), b(todo), y(todo)) ...
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	239 ./ JF (x(todo), a(todo), b(todo));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	240 todo = (abs(res) >= tol * abs (x));
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	241 endwhile
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	242 x += res;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	243 endfunction
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	244
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	245
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	246 %!test
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	247 %! x = linspace (0.1, 0.9, 11);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	248 %! a = [2, 3, 4];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	249 %! [x,a,b] = ndgrid (x,a,a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	250 %! xx = betaincinv (betainc (x, a, b), a, b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	251 %! assert (xx, x, 3e-15);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	252
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	253 %!test
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	254 %! x = linspace (0.1, 0.9, 11);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	255 %! a = [2, 3, 4];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	256 %! [x,a,b] = ndgrid (x,a,a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	257 %! xx = betaincinv (betainc (x, a, b, "upper"), a, b, "upper");
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	258 %! assert (xx, x, 3e-15);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	259
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	260 %!test
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	261 %! x = linspace (0.1, 0.9, 11);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	262 %! a = [0.1:0.1:1];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	263 %! [x,a,b] = ndgrid (x,a,a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	264 %! xx = betaincinv (betainc (x, a, b), a, b);
24996 f80e68529bbf test: relax tolerances on specfun tests to pass on i386 (bug #53437) Mike Miller <mtmiller@octave.org> parents: 24927 diff changeset	265 %! assert (xx, x, 5e-15);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	266
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	267 %!test
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	268 %! x = linspace (0.1, 0.9, 11);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	269 %! a = [0.1:0.1:1];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	270 %! [x,a,b] = ndgrid (x,a,a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	271 %! xx = betaincinv (betainc (x, a, b, "upper"), a, b, "upper");
24996 f80e68529bbf test: relax tolerances on specfun tests to pass on i386 (bug #53437) Mike Miller <mtmiller@octave.org> parents: 24927 diff changeset	272 %! assert (xx, x, 5e-15);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	273
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	274 ## Test the conservation of the input class
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	275 %!assert (class (betaincinv (0.5, 1, 1)), "double")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	276 %!assert (class (betaincinv (single (0.5), 1, 1)), "single")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	277 %!assert (class (betaincinv (0.5, single (1), 1)), "single")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	278 %!assert (class (betaincinv (int8 (0), 1, 1)), "double")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	279 %!assert (class (betaincinv (0.5, int8 (1), 1)), "double")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	280 %!assert (class (betaincinv (int8 (0), single (1), 1)), "single")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	281 %!assert (class (betaincinv (single (0.5), int8 (1), 1)), "single")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	282
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	283 ## Test input validation
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	284 %!error betaincinv ()
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	285 %!error betaincinv (1)
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	286 %!error betaincinv (1,2)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	287 %!error betaincinv (1,2,3,4,5)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	288 %!error <must be of common size or scalars>
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	289 %! betaincinv (ones (2,2), ones (1,2), 1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	290 %!error <all inputs must be real> betaincinv (0.5i, 1, 2)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	291 %!error <all inputs must be real> betaincinv (0, 1i, 1)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	292 %!error <all inputs must be real> betaincinv (0, 1, 1i)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	293 %!error <Y must be in the range \[0, 1\]> betaincinv (-0.1,1,1)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	294 %!error <Y must be in the range \[0, 1\]> betaincinv (1.1,1,1)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	295 %!error <Y must be in the range \[0, 1\]>
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	296 %! y = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	297 %! y(1,1,2) = -1;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	298 %! betaincinv (y,1,1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	299 %!error <A must be strictly positive> betaincinv (0.5,0,1)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	300 %!error <A must be strictly positive>
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	301 %! a = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	302 %! a(1,1,2) = 0;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	303 %! betaincinv (1,a,1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	304 %!error <B must be strictly positive> betaincinv (0.5,1,0)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	305 %!error <B must be strictly positive>
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	306 %! b = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	307 %! b(1,1,2) = 0;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	308 %! betaincinv (1,1,b);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	309 %!error <invalid value for TAIL> betaincinv (1,2,3, "foobar")

Mercurial > octave

annotate scripts/specfun/betaincinv.m @ 27923:bd51beb6205e