Mercurial > octave
annotate scripts/specfun/gammaincinv.m @ 28789:28de41192f3c
Eliminate unneeded verification of nargin, nargout in m-files.
* FIRfilter.m, FIRfilter_aggregation.m, get.m, polynomial.m,
polynomial_superiorto.m, polynomial2.m, makeUniqueStrings.m, base64decode.m,
base64encode.m, cd.m, lin2mu.m, record.m, sound.m, soundsc.m, accumarray.m,
accumdim.m, bitcmp.m, bitset.m, cart2pol.m, celldisp.m, circshift.m,
cplxpair.m, cumtrapz.m, flip.m, idivide.m, interpft.m, logspace.m, pol2cart.m,
polyarea.m, postpad.m, prepad.m, rat.m, rot90.m, rotdim.m, shift.m, shiftdim.m,
sortrows.m, trapz.m, dsearch.m, dsearchn.m, getappdata.m, getpixelposition.m,
guidata.m, guihandles.m, isappdata.m, listfonts.m, uigetdir.m,
waitforbuttonpress.m, __makeinfo__.m, doc.m, get_first_help_sentence.m,
autumn.m, bone.m, brighten.m, cmpermute.m, cmunique.m, colorcube.m, contrast.m,
cool.m, copper.m, cubehelix.m, flag.m, gray.m, gray2ind.m, hot.m, hsv.m,
im2double.m, im2frame.m, imformats.m, jet.m, lines.m, ocean.m, pink.m, prism.m,
rainbow.m, rgbplot.m, spinmap.m, spring.m, summer.m, viridis.m, white.m,
winter.m, beep.m, importdata.m, is_valid_file_id.m, javachk.m, javaclasspath.m,
findstr.m, genvarname.m, strmatch.m, bandwidth.m, commutation_matrix.m, cond.m,
cross.m, isdefinite.m, ishermitian.m, issymmetric.m, krylov.m, linsolve.m,
logm.m, lscov.m, null.m, ordeig.m, orth.m, rank.m, rref.m, vecnorm.m,
bunzip2.m, citation.m, computer.m, copyfile.m, dir.m, dos.m, fileattrib.m,
gunzip.m, inputParser.m, inputname.m, ismac.m, ispc.m, isunix.m, license.m,
list_primes.m, methods.m, mkdir.m, movefile.m, nargchk.m, news.m,
orderfields.m, recycle.m, tar.m, unix.m, unpack.m, untar.m, unzip.m, ver.m,
version.m, what.m, zip.m, decic.m, fminbnd.m, fminunc.m, fsolve.m, fzero.m,
glpk.m, humps.m, lsqnonneg.m, optimget.m, pqpnonneg.m, sqp.m, pathdef.m,
camlookat.m, hidden.m, specular.m, plotmatrix.m, smooth3.m, sombrero.m,
stemleaf.m, __gnuplot_drawnow__.m, __opengl_info__.m, ancestor.m, cla.m,
close.m, closereq.m, copyobj.m, gca.m, gcf.m, ginput.m, graphics_toolkit.m,
groot.m, hgload.m, hgsave.m, isgraphics.m, ishold.m, linkaxes.m, meshgrid.m,
newplot.m, refresh.m, refreshdata.m, rotate.m, saveas.m, struct2hdl.m, conv.m,
mkpp.m, mpoles.m, padecoef.m, pchip.m, polyder.m, polyfit.m, polygcd.m,
polyint.m, polyout.m, polyval.m, ppder.m, ppint.m, getpref.m, ispref.m,
rmpref.m, profexport.m, profshow.m, powerset.m, arch_fit.m, arma_rnd.m,
blackman.m, detrend.m, diffpara.m, fftconv.m, fftfilt.m, filter2.m, freqz.m,
freqz_plot.m, hamming.m, hanning.m, sinetone.m, sinewave.m, spectral_adf.m,
spectral_xdf.m, stft.m, unwrap.m, gplot.m, ichol.m, ilu.m, spdiags.m, sprand.m,
sprandn.m, spstats.m, svds.m, treelayout.m, treeplot.m, betainc.m,
betaincinv.m, ellipke.m, gammainc.m, gammaincinv.m, legendre.m, pow2.m,
hankel.m, pascal.m, rosser.m, toeplitz.m, bounds.m, corr.m, cov.m, histc.m,
kendall.m, kurtosis.m, mad.m, mode.m, moment.m, prctile.m, quantile.m, range.m,
ranks.m, run_count.m, skewness.m, spearman.m, std.m, var.m, zscore.m,
dec2base.m, dec2bin.m, dec2hex.m, index.m, mat2str.m, native2unicode.m,
ostrsplit.m, strjoin.m, strjust.m, strtok.m, substr.m, unicode2native.m,
untabify.m, __debug_octave__.m, demo.m, example.m, fail.m, oruntests.m,
dump_demos.m, speed.m, test.m, date.m, datenum.m, datestr.m, datevec.m,
is_leap_year.m, now.m, weekday.m:
Eliminate unneeded verification of nargin, nargout in m-files now that
the interpreter checks these values.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 24 Sep 2020 14:44:58 -0700 |
parents | b09432b20a84 |
children | 90fea9cc9caa |
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:
27800
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/>. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
7 ## |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
8 ## This file is part of Octave. |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
9 ## |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
10 ## Octave is free software: you can redistribute it and/or modify it |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
11 ## under the terms of the GNU General Public License as published by |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
12 ## the Free Software Foundation; either version 3 of the License, or |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
13 ## (at your option) any later version. |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
14 ## |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
15 ## Octave is distributed in the hope that it will be useful, but |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
18 ## GNU General Public License for more details. |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
19 ## |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
20 ## You should have received a copy of the GNU General Public License |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
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:
24905
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 ######################################################################## |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
25 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
26 ## -*- texinfo -*- |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
27 ## @deftypefn {} {} gammaincinv (@var{y}, @var{a}) |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
28 ## @deftypefnx {} {} gammaincinv (@var{y}, @var{a}, @var{tail}) |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
29 ## Compute the inverse of the normalized incomplete gamma function. |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
30 ## |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
31 ## The normalized incomplete gamma function is defined as |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
32 ## @tex |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
33 ## $$ |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
34 ## \gamma (x, a) = {1 \over {\Gamma (a)}}\displaystyle{\int_0^x t^{a-1} e^{-t} dt} |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
35 ## $$ |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
36 ## @end tex |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
37 ## @ifnottex |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
38 ## |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
39 ## @example |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
40 ## @group |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
41 ## x |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
42 ## 1 / |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
43 ## gammainc (x, a) = --------- | exp (-t) t^(a-1) dt |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
44 ## gamma (a) / |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
45 ## t=0 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
46 ## @end group |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
47 ## @end example |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
48 ## |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
49 ## @end ifnottex |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
50 ## |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
51 ## and @code{gammaincinv (gammainc (@var{x}, @var{a}), @var{a}) = @var{x}} |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
52 ## for each non-negative value of @var{x}. If @var{a} is scalar then |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
53 ## @code{gammaincinv (@var{y}, @var{a})} is returned for each element of |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
54 ## @var{y} and vice versa. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
55 ## |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
56 ## If neither @var{y} nor @var{a} is scalar then the sizes of @var{y} and |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
57 ## @var{a} must agree, and @code{gammaincinv} is applied element-by-element. |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
58 ## The variable @var{y} must be in the interval @math{[0,1]} while @var{a} must |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
59 ## be real and positive. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
60 ## |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
61 ## By default, @var{tail} is @qcode{"lower"} and the inverse of the incomplete |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
62 ## gamma 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:
24905
diff
changeset
|
63 ## @qcode{"upper"}, then the complementary function integrated from @var{x} to |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
64 ## infinity is inverted. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
65 ## |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
66 ## The function is computed with Newton's method by solving |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
67 ## @tex |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
68 ## $$ |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
69 ## y - \gamma (x, a) = 0 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
70 ## $$ |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
71 ## @end tex |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
72 ## @ifnottex |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
73 ## |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
74 ## @example |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
75 ## @var{y} - gammainc (@var{x}, @var{a}) = 0 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
76 ## @end example |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
77 ## |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
78 ## @end ifnottex |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
79 ## |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
80 ## Reference: @nospell{A. Gil, J. Segura, and N. M. Temme}, @cite{Efficient and |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
81 ## accurate algorithms for the computation and inversion of the incomplete |
27800
5a6a19a4e3da
doc: Use Texinfo non-sentence ending periods in citations.
Rik <rik@octave.org>
parents:
27411
diff
changeset
|
82 ## gamma function ratios}, @nospell{SIAM J. Sci.@: Computing}, pp.@: |
5a6a19a4e3da
doc: Use Texinfo non-sentence ending periods in citations.
Rik <rik@octave.org>
parents:
27411
diff
changeset
|
83 ## A2965--A2981, Vol 34, 2012. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
84 ## |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
85 ## @seealso{gammainc, gamma, gammaln} |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
86 ## @end deftypefn |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
87 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
88 function x = gammaincinv (y, a, tail = "lower") |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
89 |
28789
28de41192f3c
Eliminate unneeded verification of nargin, nargout in m-files.
Rik <rik@octave.org>
parents:
27984
diff
changeset
|
90 if (nargin < 2) |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
91 print_usage (); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
92 endif |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
93 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
94 [err, y, a] = common_size (y, a); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
95 if (err > 0) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
96 error ("gammaincinv: Y and A must be of common size or scalars"); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
97 endif |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
98 |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
99 if (iscomplex (y) || iscomplex (a)) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
100 error ("gammaincinv: all inputs must be real"); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
101 endif |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
102 |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
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:
24905
diff
changeset
|
104 orig_sz = size (y); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
105 y = y(:); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
106 a = a(:); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
107 |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
108 if (any ((y < 0) | (y > 1))) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
109 error ("gammaincinv: Y must be in the range [0, 1]"); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
110 endif |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
111 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
112 if (any (a <= 0)) |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
113 error ("gammaincinv: A must be strictly positive"); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
114 endif |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
115 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
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:
24905
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:
24905
diff
changeset
|
118 y = single (y); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
119 a = single (a); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
120 endif |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
121 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
122 ## Convert to floating point if necessary |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
123 if (isinteger (y)) |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
124 y = double (y); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
125 endif |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
126 if (isinteger (a)) |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
127 a = double (a); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
128 endif |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
129 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
130 ## Initialize output array |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
131 x = zeros (size (y), class (y)); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
132 |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
133 maxit = 20; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
134 tol = eps (class (y)); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
135 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
136 ## Special cases, a = 1 or y = 0, 1. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
137 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
138 if (strcmpi (tail, "lower")) |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
139 x(a == 1) = - log1p (- y(a == 1)); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
140 x(y == 0) = 0; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
141 x(y == 1) = Inf; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
142 p = y; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
143 q = 1 - p; |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
144 elseif (strcmpi (tail, "upper")) |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
145 x(a == 1) = - log (y(a == 1)); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
146 x(y == 0) = Inf; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
147 x(y == 1) = 0; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
148 q = y; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
149 p = 1 - q; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
150 else |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
151 error ("gammaincinv: invalid value for TAIL") |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
152 endif |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
153 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
154 todo = (a != 1) & (y != 0) & (y != 1); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
155 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
156 ## Case 1: p small. |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
157 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
158 i_flag_1 = todo & (p < ((0.2 * (1 + a)) .^ a) ./ gamma (1 + a)); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
159 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
160 if (any (i_flag_1)) |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
161 aa = a(i_flag_1); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
162 pp = p(i_flag_1); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
163 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
164 ## Initial guess. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
165 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
166 r = (pp .* gamma (1 + aa)) .^ (1 ./ aa); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
167 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
168 c2 = 1 ./ (aa + 1); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
169 c3 = (3 * aa + 5) ./ (2 * (aa + 1) .^2 .* (aa + 2)); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
170 c4 = (8 * aa .^ 2 + 33 * aa + 31) ./ (3 * (aa + 1) .^ 3 .* (aa + 2) .* ... |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
171 (aa + 3)); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
172 c5 = (125 * aa .^ 4 + 1179 * aa .^ 3 + 3971 * aa.^2 + 5661 * aa + 2888) ... |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
173 ./ (24 * (1 + aa) .^4 .* (aa + 2) .^ 2 .* (aa + 3) .* (aa + 4)); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
174 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
175 ## FIXME: Would polyval() be better here for more accuracy? |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
176 x0 = r + c2 .* r .^ 2 + c3 .* r .^ 3 + c4 .* r .^4 + c5 .* r .^ 5; |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
177 |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
178 ## For this case we invert the lower version. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
179 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
180 F = @(p, a, x) p - gammainc (x, a, "lower"); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
181 JF = @(a, x) - exp (- gammaln (a) - x + (a - 1) .* log (x)); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
182 x(i_flag_1) = newton_method (F, JF, pp, aa, x0, tol, maxit); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
183 endif |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
184 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
185 todo(i_flag_1) = false; |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
186 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
187 ## Case 2: q small. |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
188 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
189 i_flag_2 = (q < exp (- 0.5 * a) ./ gamma (1 + a)) & (a > 0) & (a < 10); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
190 i_flag_2 &= todo; |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
191 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
192 if (any (i_flag_2)) |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
193 aa = a(i_flag_2); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
194 qq = q(i_flag_2); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
195 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
196 ## Initial guess. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
197 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
198 x0 = (-log (qq) - gammaln (aa)); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
199 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
200 ## For this case, we invert the upper version. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
201 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
202 F = @(q, a, x) q - gammainc (x, a, "upper"); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
203 JF = @(a, x) exp (- gammaln (a) - x) .* x .^ (a - 1); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
204 x(i_flag_2) = newton_method (F, JF, qq, aa, x0, tol, maxit); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
205 endif |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
206 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
207 todo(i_flag_2) = false; |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
208 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
209 ## Case 3: a small. |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
210 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
211 i_flag_3 = todo & ((a > 0) & (a < 1)); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
212 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
213 if (any (i_flag_3)) |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
214 aa = a(i_flag_3); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
215 pp = p(i_flag_3); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
216 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
217 ## Initial guess |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
218 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
219 xl = (pp .* gamma (aa + 1)) .^ (1 ./ aa); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
220 x0 = xl; |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
221 |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
222 ## For this case, we invert the lower version. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
223 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
224 F = @(p, a, x) p - gammainc (x, a, "lower"); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
225 JF = @(a, x) - exp (-gammaln (a) - x) .* x .^ (a - 1); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
226 x(i_flag_3) = newton_method (F, JF, pp, aa, x0, tol, maxit); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
227 endif |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
228 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
229 todo(i_flag_3) = false; |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
230 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
231 ## Case 4: a large. |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
232 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
233 i_flag_4 = todo; |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
234 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
235 if (any (i_flag_4)) |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
236 aa = a(i_flag_4); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
237 qq = q(i_flag_4); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
238 |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
239 ## Initial guess |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
240 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
241 d = 1 ./ (9 * aa); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
242 t = 1 - d + sqrt (2) * erfcinv (2 * qq) .* sqrt (d); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
243 x0 = aa .* (t .^ 3); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
244 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
245 ## For this case, we invert the upper version. |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
246 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
247 F = @(q, a, x) q - gammainc (x, a, "upper"); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
248 JF = @(a, x) exp (- gammaln (a) - x + (a - 1) .* log (x)); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
249 x(i_flag_4) = newton_method (F, JF, qq, aa, x0, tol, maxit); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
250 endif |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
251 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
252 ## Restore original shape |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
253 x = reshape (x, orig_sz); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
254 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
255 endfunction |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
256 |
27984
b09432b20a84
maint: Remove special cases of old version control keywords in code base.
Rik <rik@octave.org>
parents:
27978
diff
changeset
|
257 ## subfunction: Newton's Method |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
258 function x = newton_method (F, JF, y, a, x0, tol, maxit); |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
259 l = numel (y); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
260 res = -F (y, a, x0) ./ JF (a, x0); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
261 todo = (abs (res) >= tol * abs (x0)); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
262 x = x0; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
263 it = 0; |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
264 while (any (todo) && (it++ < maxit)) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
265 x(todo) += res(todo); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
266 res(todo) = -F (y(todo), a(todo), x(todo)) ./ JF (a(todo), x(todo)); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
267 todo = (abs (res) >= tol * abs (x)); |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
268 endwhile |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
269 x += res; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
270 endfunction |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
271 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
272 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
273 %!test |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
274 %! x = [1e-10, 1e-09, 1e-08, 1e-07]; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
275 %! a = [2, 3, 4]; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
276 %! [x, a] = ndgrid (x, a); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
277 %! xx = gammainc (gammaincinv (x, a), a); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
278 %! assert (xx, x, -3e-14); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
279 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
280 %!test |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
281 %! x = [1e-10, 1e-09, 1e-08, 1e-07]; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
282 %! a = [2, 3, 4]; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
283 %! [x, a] = ndgrid (x, a); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
284 %! xx = gammainc (gammaincinv (x, a, "upper"), a, "upper"); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
285 %! assert (xx, x, -3e-14); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
286 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
287 %!test |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
288 %! x = linspace (0, 1)'; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
289 %! a = [linspace(0.1, 1, 10), 2:5]; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
290 %! [x, a] = ndgrid (x, a); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
291 %! xx = gammainc (gammaincinv (x, a), a); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
292 %! assert (xx, x, -1e-13); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
293 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
294 %!test |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
295 %! x = linspace (0, 1)'; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
296 %! a = [linspace(0.1, 1, 10), 2:5]; |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
297 %! [x, a] = ndgrid (x, a); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
298 %! xx = gammainc (gammaincinv (x, a, "upper"), a, "upper"); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
299 %! assert (xx, x, -1e-13); |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
300 |
27411
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
301 %!test <*56453> |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
302 %! assert (gammaincinv (1e-15, 1) * 2, 2e-15, -1e-15); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
303 %! assert (gammaincinv (1e-16, 1) * 2, 2e-16, -1e-15); |
9a946e34553c
gammaincinv.m: Improve accuracy for gammaincinv (bug #56453).
Michele Ginesi <michele.ginesi@gmail.com>
parents:
26376
diff
changeset
|
304 |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
305 ## Test the conservation of the input class |
24905
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
306 %!assert (class (gammaincinv (0.5, 1)), "double") |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
307 %!assert (class (gammaincinv (single (0.5), 1)), "single") |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
308 %!assert (class (gammaincinv (0.5, single (1))), "single") |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
309 %!assert (class (gammaincinv (int8 (0), 1)), "double") |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
310 %!assert (class (gammaincinv (0.5, int8 (1))), "double") |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
311 %!assert (class (gammaincinv (int8 (0), single (1))), "single") |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
312 %!assert (class (gammaincinv (single (0.5), int8 (1))), "single") |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
313 |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
314 ## Test input validation |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
315 %!error gammaincinv () |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
316 %!error gammaincinv (1) |
662faf9de127
Added the inverse of the incomplete gamma function (see bug #48036)
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
317 %!error gammaincinv (1, 2, 3, 4) |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
318 %!error <must be of common size or scalars> |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
319 %! gammaincinv (ones (2,2), ones (1,2), 1); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
320 %!error <all inputs must be real> gammaincinv (0.5i, 1) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
321 %!error <all inputs must be real> gammaincinv (0, 1i) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
322 %!error <Y must be in the range \[0, 1\]> gammaincinv (-0.1,1) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
323 %!error <Y must be in the range \[0, 1\]> gammaincinv (1.1,1) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
324 %!error <Y must be in the range \[0, 1\]> |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
325 %! y = ones (1, 1, 2); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
326 %! y(1,1,2) = -1; |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
327 %! gammaincinv (y,1); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
328 %!error <A must be strictly positive> gammaincinv (0.5, 0) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
329 %!error <A must be strictly positive> |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
330 %! a = ones (1, 1, 2); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
331 %! a(1,1,2) = 0; |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
332 %! gammaincinv (1,a,1); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24905
diff
changeset
|
333 %!error <invalid value for TAIL> gammaincinv (1,2, "foobar") |