octave: scripts/specfun/betaincinv.m annotate

annotate scripts/specfun/betaincinv.m @ 25579:07c2c42f457e stable

doc: Miscellaneous documentation fixes all over the manual (bug #54288). * embedded.cc, defaults.cc, error.cc, hex2num.cc, load-save.cc, integral2.m, integral3.m, quad2d.m, warning_ids.m, decic.m, lsqnonneg.m, pqpnonneg.m, bicg.m, betaincinv.m: Removal of duplicate words and redundant ')' and ';' characters. Added missing '"', ')' characters. Renamed variables to match other occurrences in docstring. Use '*' instead of 'x' for multiply. Surround variables with @var{}.

author	Rik <rik@octave.org>
date	Wed, 11 Jul 2018 08:40:07 -0700
parents	6652d3823428
children	6dd232798997

rev	line source
25054 6652d3823428 maint: Update copyright dates in all source files. John W. Eaton <jwe@octave.org> parents: 24996 diff changeset	1 ## Copyright (C) 2017-2018 Michele Ginesi
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	2 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	3 ## 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	4 ##
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	5 ## 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	6 ## 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	7 ## 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	8 ## (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	9 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	10 ## 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	11 ## 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	12 ## 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	13 ## 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	14 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	15 ## 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	16 ## 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	17 ## <https://www.gnu.org/licenses/>.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	18
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	19 ## 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	20
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	21 ## -- texinfo --
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	22 ## @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	23 ## @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	24 ## @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	25 ## 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	26 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	27 ## 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	28 ## @tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	29 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	30 ## I_x (a, b) = {1 \over {B(a,b)}} \displaystyle{\int_0^x t^{a-1} (1-t)^{b-1} dt}
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	31 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	32 ## @end tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	33 ## @ifnottex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	34 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	35 ## @example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	36 ## @group
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	37 ## x
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 ## \|
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	40 ## 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	41 ## \|
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	42 ## /
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	43 ## 0
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	44 ## @end group
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	45 ## @end example
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 ## @end ifnottex
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 ## 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	50 ## 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	51 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	52 ## 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	53 ## @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	54 ##
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	55 ## 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	56 ## @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	57 ##
25579 07c2c42f457e doc: Miscellaneous documentation fixes all over the manual (bug #54288). Rik <rik@octave.org> parents: 25054 diff changeset	58 ## 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	59 ## 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	60 ## @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	61 ## is inverted.
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	62 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	63 ## 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	64 ## @tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	65 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	66 ## y - I_x (a, b) = 0
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	67 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	68 ## @end tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	69 ## @ifnottex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	70 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	71 ## @example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	72 ## @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	73 ## @end example
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 ifnottex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	76 ##
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	77 ## @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	78 ## @end deftypefn
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	79
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	80 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	81
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	82 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	83 print_usage ();
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	84 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	85
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	86 [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	87 if (err > 0)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	88 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	89 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	90
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	91 if (iscomplex (y) \|\| iscomplex (a) \|\| iscomplex (b))
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	92 error ("betaincinv: all inputs must be real");
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	93 endif
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	94
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	95 ## 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	96 ## 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	97
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	98 ## 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	99 orig_sz = size (y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	100 y = y(:);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	101 a = a(:);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	102 b = b(:);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	103
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	104 if (any ((y < 0) \| (y > 1)))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	105 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	106 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	107
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	108 if (any (a <= 0))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	109 error ("betaincinv: A must be strictly positive");
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	110 endif
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	111
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	112 if (any (b <= 0))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	113 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	114 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	115
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	116 ## 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	117 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	118 \|\| strcmp (class (b), "single"))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	119 y = single (y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	120 a = single (a);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	121 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	122 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	123
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	124 ## 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	125 if (isinteger (y))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	126 y = double (y);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	127 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	128 if (isinteger (a))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	129 a = double (a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	130 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	131 if (isinteger (b))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	132 b = double (b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	133 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	134
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	135 ## Initialize output array
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	136 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	137
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	138 ## 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	139 maxit = 20;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	140 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	141
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	142 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	143 p = y;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	144 q = 1 - y;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	145 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	146 x(y == 1) = 1;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	147 elseif (strcmpi (tail, "upper"))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	148 p = 1 - y;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	149 q = y;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	150 x(y == 0) = 1;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	151 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	152 else
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	153 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	154 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	155
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	156 ## Special values have been already computed.
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	157 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	158
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	159 ## 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	160 i_low = (p < 0.5);
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	161 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	162
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	163 idx = todo & i_low;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	164 if (any (idx));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	165 n = nnz (idx);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	166 ## 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	167 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	168 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	169 gammaln (a+b) - gammaln (a) - gammaln (b)));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	170
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	171 ## 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	172 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	173 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	174
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	175 ## 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	176 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	177 tol, maxit);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	178 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	179
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	180 idx = todo & i_upp;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	181 if (any (idx));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	182 n = nnz (idx);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	183 ## 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	184 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	185 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	186 gammaln (a+b) - gammaln (a) - gammaln (b)));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	187
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	188 ## 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	189 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	190 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	191
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	192 ## 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	193 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	194 tol, maxit);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	195 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	196
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	197 ## Restore original shape
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	198 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	199
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	200 endfunction
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	201
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	202
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	203 ## 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	204 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	205 F_l = F (xl, a, b, y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	206 F_r = F (xr, a, b, y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	207 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	208 xc = (xl + xr) / 2;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	209 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	210 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	211 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	212 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	213 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	214 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	215 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	216 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	217 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	218 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	219 endfor
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	220 endfunction
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	221
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	222 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	223 l = numel (y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	224 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	225 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	226 x = x0;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	227 it = 0;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	228 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	229 it++;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	230 x(todo) += res(todo);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	231 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	232 ./ JF (x(todo), a(todo), b(todo));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	233 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	234 endwhile
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	235 x += res;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	236 endfunction
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	237
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	238
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	239 %!test
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	240 %! 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	241 %! 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	242 %! [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	243 %! 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	244 %! 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	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, "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	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 = [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	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), 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	258 %! 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	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, "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	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
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	267 ## 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	268 %!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	269 %!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	270 %!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	271 %!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	272 %!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	273 %!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	274 %!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	275
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	276 ## Test input validation
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	277 %!error betaincinv ()
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	278 %!error betaincinv (1)
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	279 %!error betaincinv (1,2)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	280 %!error betaincinv (1,2,3,4,5)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	281 %!error <must be of common size or scalars>
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	282 %! betaincinv (ones (2,2), ones (1,2), 1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	283 %!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	284 %!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	285 %!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	286 %!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	287 %!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	288 %!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	289 %! y = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	290 %! y(1,1,2) = -1;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	291 %! betaincinv (y,1,1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	292 %!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	293 %!error <A must be strictly positive>
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	294 %! a = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	295 %! a(1,1,2) = 0;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	296 %! betaincinv (1,a,1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	297 %!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	298 %!error <B must be strictly positive>
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	299 %! b = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	300 %! b(1,1,2) = 0;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	301 %! betaincinv (1,1,b);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	302 %!error <invalid value for TAIL> betaincinv (1,2,3, "foobar")

Mercurial > octave

annotate scripts/specfun/betaincinv.m @ 25579:07c2c42f457e stable