octave: scripts/specfun/betaincinv.m annotate

annotate scripts/specfun/betaincinv.m @ 28896:90fea9cc9caa

test: Add expected error message <Invalid call> to BIST tests for nargin. * acosd.m, acot.m, acotd.m, acoth.m, acsc.m, acscd.m, acsch.m, asec.m, asecd.m, asech.m, asind.m, atand.m, cosd.m, cot.m, cotd.m, coth.m, csc.m, cscd.m, csch.m, sec.m, secd.m, sech.m, sind.m, tand.m, cart2pol.m, cart2sph.m, celldisp.m, common_size.m, deal.m, del2.m, fliplr.m, integral2.m, interp1.m, isequal.m, isequaln.m, nextpow2.m, pol2cart.m, quad2d.m, quadl.m, quadv.m, randi.m, rat.m, repelem.m, rescale.m, shiftdim.m, sortrows.m, sph2cart.m, xor.m, convhull.m, delaunay.m, delaunayn.m, griddata.m, griddatan.m, inpolygon.m, voronoi.m, voronoin.m, listdlg.m, msgbox.m, questdlg.m, rmappdata.m, setappdata.m, __gripe_missing_component__.m, get_first_help_sentence.m, type.m, which.m, cmpermute.m, cmunique.m, gray2ind.m, imfinfo.m, imshow.m, imwrite.m, ind2rgb.m, movie.m, rgb2ind.m, importdata.m, bandwidth.m, condeig.m, gls.m, housh.m, linsolve.m, logm.m, lscov.m, normest.m, normest1.m, ols.m, ordeig.m, planerot.m, qzhess.m, rref.m, copyfile.m, delete.m, dos.m, fileparts.m, getfield.m, menu.m, mkdir.m, movefile.m, orderfields.m, publish.m, setfield.m, substruct.m, unix.m, unpack.m, decic.m, ode23.m, ode23s.m, ode45.m, fminsearch.m, lsqnonneg.m, pqpnonneg.m, sqp.m, annotation.m, lighting.m, shading.m, area.m, compass.m, contourc.m, feather.m, fplot.m, hist.m, isocaps.m, isocolors.m, isonormals.m, isosurface.m, ostreamtube.m, pie.m, pie3.m, reducepatch.m, reducevolume.m, rose.m, smooth3.m, stairs.m, stem.m, stem3.m, stream2.m, stream3.m, streamline.m, streamribbon.m, streamtube.m, surfnorm.m, trimesh.m, trisurf.m, colstyle.m, hgload.m, linkprop.m, meshgrid.m, ndgrid.m, padecoef.m, polyfit.m, polyval.m, unmkpp.m, profexport.m, ismember.m, unique.m, movfun.m, movslice.m, periodogram.m, sinc.m, spdiags.m, sprandsym.m, betaincinv.m, ellipke.m, factor.m, gammainc.m, gammaincinv.m, isprime.m, lcm.m, gallery.m, hadamard.m, bounds.m, corrcoef.m, discrete_rnd.m, empirical_rnd.m, histc.m, mode.m, movmad.m, movmax.m, movmean.m, movmedian.m, movmin.m, movprod.m, movstd.m, movsum.m, movvar.m, ranks.m, runlength.m, zscore.m, str2num.m, strchr.m, strsplit.m, strtok.m, untabify.m, assert.m, demo.m, example.m, speed.m, test.m, datenum.m, datevec.m, webread.m, webwrite.m: Add expected error message <Invalid call> to BIST tests for nargin. Remove redundant tests for nargin greater than the number of declared inputs which are now handled by interpreter.

author	Rik <rik@octave.org>
date	Sun, 11 Oct 2020 21:59:35 -0700
parents	28de41192f3c
children	0de38a6ef693

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 ## -- texinfo --
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	27 ## @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	28 ## @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	29 ## @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	30 ## 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	31 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	32 ## 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	33 ## @tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	34 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	35 ## I_x (a, b) = {1 \over {B(a,b)}} \displaystyle{\int_0^x t^{a-1} (1-t)^{b-1} dt}
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	36 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	37 ## @end tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	38 ## @ifnottex
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 ## @example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	41 ## @group
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	42 ## x
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	43 ## /
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	44 ## \|
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	45 ## 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	46 ## \|
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	47 ## /
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	48 ## 0
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	49 ## @end group
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	50 ## @end example
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 ## @end ifnottex
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 ## 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	55 ## 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	56 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	57 ## 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	58 ## @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	59 ##
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	60 ## 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	61 ## @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	62 ##
25579 07c2c42f457e doc: Miscellaneous documentation fixes all over the manual (bug #54288). Rik <rik@octave.org> parents: 25054 diff changeset	63 ## 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	64 ## 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	65 ## @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	66 ## is inverted.
24907 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 ## 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	69 ## @tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	70 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	71 ## y - I_x (a, b) = 0
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	72 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	73 ## @end tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	74 ## @ifnottex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	75 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	76 ## @example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	77 ## @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	78 ## @end example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	79 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	80 ## @end ifnottex
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 ## @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	83 ## @end deftypefn
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	84
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	85 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	86
28789 28de41192f3c Eliminate unneeded verification of nargin, nargout in m-files. Rik <rik@octave.org> parents: 27984 diff changeset	87 if (nargin < 3)
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	88 print_usage ();
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
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	91 [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	92 if (err > 0)
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	93 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	94 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	95
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	96 if (iscomplex (y) \|\| iscomplex (a) \|\| iscomplex (b))
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	97 error ("betaincinv: all inputs must be real");
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	98 endif
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	99
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	100 ## 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	101 ## 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	102
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	103 ## 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	104 orig_sz = size (y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	105 y = y(:);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	106 a = a(:);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	107 b = b(:);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	108
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	109 if (any ((y < 0) \| (y > 1)))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	110 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	111 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	112
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	113 if (any (a <= 0))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	114 error ("betaincinv: A must be strictly positive");
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	115 endif
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	116
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	117 if (any (b <= 0))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	118 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	119 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	120
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	121 ## 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	122 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	123 \|\| strcmp (class (b), "single"))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	124 y = single (y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	125 a = single (a);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	126 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	127 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	128
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	129 ## 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	130 if (isinteger (y))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	131 y = double (y);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	132 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	133 if (isinteger (a))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	134 a = double (a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	135 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	136 if (isinteger (b))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	137 b = double (b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	138 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	139
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	140 ## Initialize output array
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	141 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	142
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	143 ## 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	144 maxit = 20;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	145 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	146
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	147 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	148 p = y;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	149 q = 1 - y;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	150 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	151 x(y == 1) = 1;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	152 elseif (strcmpi (tail, "upper"))
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	153 p = 1 - y;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	154 q = y;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	155 x(y == 0) = 1;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	156 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	157 else
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	158 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	159 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	160
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	161 ## Special values have been already computed.
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	162 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	163
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	164 ## 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	165 i_low = (p < 0.5);
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	166 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	167
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	168 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	169 if (any (idx))
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	170 n = nnz (idx);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	171 ## 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	172 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	173 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	174 gammaln (a+b) - gammaln (a) - gammaln (b)));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	175
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	176 ## 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	177 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	178 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	179
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	180 ## 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	181 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	182 tol, maxit);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	183 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	184
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	185 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	186 if (any (idx))
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	187 n = nnz (idx);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	188 ## 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	189 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	190 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	191 gammaln (a+b) - gammaln (a) - gammaln (b)));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	192
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	193 ## 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	194 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	195 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	196
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	197 ## 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	198 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	199 tol, maxit);
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	200 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	201
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	202 ## Restore original shape
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	203 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	204
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	205 endfunction
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
27984 b09432b20a84 maint: Remove special cases of old version control keywords in code base. Rik <rik@octave.org> parents: 27978 diff changeset	208 ## subfunctions: Bisection and Newton Methods
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	209 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	210 F_l = F (xl, a, b, y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	211 F_r = F (xr, a, b, y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	212 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	213 xc = (xl + xr) / 2;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	214 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	215 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	216 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	217 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	218 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	219 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	220 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	221 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	222 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	223 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	224 endfor
24907 bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	225 endfunction
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	226
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	227 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	228 l = numel (y);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	229 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	230 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	231 x = x0;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	232 it = 0;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	233 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	234 it++;
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	235 x(todo) += res(todo);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	236 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	237 ./ JF (x(todo), a(todo), b(todo));
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	238 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	239 endwhile
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	240 x += res;
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	241 endfunction
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	242
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	243
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	244 %!test
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	245 %! 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	246 %! 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	247 %! [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	248 %! 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	249 %! 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	250
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	251 %!test
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	252 %! 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	253 %! 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	254 %! [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	255 %! 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	256 %! 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	257
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	258 %!test
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	259 %! 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	260 %! 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	261 %! [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	262 %! 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	263 %! 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	264
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	265 %!test
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	266 %! 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	267 %! 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	268 %! [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	269 %! 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	270 %! 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	271
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	272 ## 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	273 %!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	274 %!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	275 %!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	276 %!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	277 %!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	278 %!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	279 %!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	280
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and Michele Ginesi <michele.ginesi@gmail.com> parents: diff changeset	281 ## Test input validation
28896 90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 28789 diff changeset	282 %!error <Invalid call> betaincinv ()
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 28789 diff changeset	283 %!error <Invalid call> betaincinv (1)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 28789 diff changeset	284 %!error <Invalid call> betaincinv (1,2)
24927 c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	285 %!error <must be of common size or scalars>
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	286 %! betaincinv (ones (2,2), ones (1,2), 1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	287 %!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	288 %!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	289 %!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	290 %!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	291 %!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	292 %!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	293 %! y = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	294 %! y(1,1,2) = -1;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	295 %! betaincinv (y,1,1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	296 %!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	297 %!error <A must be strictly positive>
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	298 %! a = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	299 %! a(1,1,2) = 0;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	300 %! betaincinv (1,a,1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	301 %!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	302 %!error <B must be strictly positive>
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	303 %! b = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	304 %! b(1,1,2) = 0;
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	305 %! betaincinv (1,1,b);
c280560d9c96 Overhaul special functions modified by GSOC2018 project. Rik <rik@octave.org> parents: 24907 diff changeset	306 %!error <invalid value for TAIL> betaincinv (1,2,3, "foobar")

Mercurial > octave

annotate scripts/specfun/betaincinv.m @ 28896:90fea9cc9caa