octave: scripts/general/bincoeff.m annotate

annotate scripts/general/bincoeff.m @ 28886:d8318c12d903

test: remove unnecessary BIST tests in m-files checking for excessive number of inputs. Remove BIST tests now that interpreter enforces calling function with no more than the number of arguments defined in the function prototype. * makeUniqueStrings.m, makeValidName.m, base64decode.m, base64encode.m, record.m, sound.m, soundsc.m, acosd.m, acot.m, acotd.m, acoth.m, acsc.m, acscd.m, acsch.m, asec.m, asecd.m, asech.m, asind.m, atan2d.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, accumdim.m, bincoeff.m, bitget.m, bitset.m, cell2mat.m, circshift.m, cplxpair.m, cumtrapz.m, deg2rad.m, flip.m, fliplr.m, flipud.m, int2str.m, interpft.m, logspace.m, num2str.m, postpad.m, prepad.m, rad2deg.m, rot90.m, rotdim.m, shift.m, subsindex.m, trapz.m, rotx.m, roty.m, rotz.m, getappdata.m, getpixelposition.m, guidata.m, isappdata.m, waitforbuttonpress.m, __gripe_missing_component__.m, bessel.m, hsv2rgb.m, ind2gray.m, rgb2gray.m, rgb2hsv.m, rgbplot.m, fileread.m, javachk.m, usejava.m, findstr.m, genvarname.m, isdir.m, vectorize.m, cond.m, cross.m, duplication_matrix.m, expm.m, isbanded.m, isdefinite.m, isdiag.m, ishermitian.m, issymmetric.m, istril.m, istriu.m, trace.m, vech.m, vecnorm.m, cast.m, citation.m, compare_versions.m, grabcode.m, inputname.m, isfile.m, isfolder.m, ismac.m, ispc.m, isunix.m, list_primes.m, methods.m, news.m, open.m, run.m, swapbytes.m, tar.m, verLessThan.m, zip.m, odeget.m, optimget.m, stemleaf.m, allchild.m, ancestor.m, close.m, groot.m, hgsave.m, isaxes.m, isfigure.m, isgraphics.m, ishandle.m, isprop.m, linkaxes.m, rotate.m, saveas.m, conv.m, poly.m, polyint.m, polyreduce.m, ppval.m, roots.m, addpref.m, getpref.m, ispref.m, rmpref.m, setpref.m, profile.m, profshow.m, powerset.m, autoreg_matrix.m, bartlett.m, blackman.m, detrend.m, fftconv.m, fftfilt.m, fftshift.m, hamming.m, hanning.m, ifftshift.m, sinewave.m, spectral_adf.m, spectral_xdf.m, unwrap.m, nonzeros.m, spconvert.m, sprand.m, sprandn.m, beta.m, betainc.m, betaln.m, cosint.m, expint.m, factorial.m, legendre.m, nchoosek.m, nthroot.m, perms.m, pow2.m, primes.m, reallog.m, realpow.m, realsqrt.m, sinint.m, hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, toeplitz.m, vander.m, wilkinson.m, center.m, corr.m, cov.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, empirical_cdf.m, empirical_inv.m, empirical_pdf.m, iqr.m, kendall.m, kurtosis.m, mad.m, meansq.m, median.m, moment.m, prctile.m, quantile.m, range.m, run_count.m, skewness.m, spearman.m, statistics.m, std.m, var.m, base2dec.m, bin2dec.m, blanks.m, dec2base.m, dec2bin.m, dec2hex.m, endsWith.m, erase.m, hex2dec.m, index.m, isletter.m, isstring.m, isstrprop.m, mat2str.m, ostrsplit.m, rindex.m, startsWith.m, strtrunc.m, substr.m, fail.m, addtodate.m, asctime.m, ctime.m, date.m, datestr.m, eomday.m, etime.m, is_leap_year.m, now.m: remove unnecessary BIST tests in m-files checking for excessive number of inputs.

author	Rik <rik@octave.org>
date	Fri, 09 Oct 2020 13:28:53 -0700
parents	9f9ac219896d
children	7854d5752dd2

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) 1995-2020 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/>.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	7 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	8 ## This file is part of Octave.
38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	9 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	11 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## (at your option) any later version.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	14 ##
3922 38c61cbf086c [project @ 2002-05-01 06:48:35 by jwe] jwe parents: 3458 diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	18 ## GNU General Public License for more details.
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	19 ##
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6902 diff changeset	21 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 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 ########################################################################
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	25
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	26 ## -- texinfo --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 19833 diff changeset	27 ## @deftypefn {} {} bincoeff (@var{n}, @var{k})
25106 d7ad543255c5 doc: Shorten very long first sentences of docstrings (bug #53388). Rik <rik@octave.org> parents: 25054 diff changeset	28 ## Return the binomial coefficient of @var{n} and @var{k}.
d7ad543255c5 doc: Shorten very long first sentences of docstrings (bug #53388). Rik <rik@octave.org> parents: 25054 diff changeset	29 ##
d7ad543255c5 doc: Shorten very long first sentences of docstrings (bug #53388). Rik <rik@octave.org> parents: 25054 diff changeset	30 ## The binomial coefficient is defined as
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	31 ## @tex
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	32 ## $$
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	33 ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!}
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	34 ## $$
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	35 ## @end tex
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 8435 diff changeset	36 ## @ifnottex
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	37 ##
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	38 ## @example
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	39 ## @group
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	40 ## / \
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	41 ## \| n \| n (n-1) (n-2) @dots{} (n-k+1)
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	42 ## \| \| = -------------------------
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	43 ## \| k \| k!
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	44 ## \ /
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	45 ## @end group
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	46 ## @end example
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	47 ##
8517 81d6ab3ac93c Allow documentation tobe built for other formats than tex and info sh@sh-laptop parents: 8435 diff changeset	48 ## @end ifnottex
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	49 ## For example:
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	50 ##
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	51 ## @example
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	52 ## @group
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	53 ## bincoeff (5, 2)
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	54 ## @result{} 10
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	55 ## @end group
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	56 ## @end example
8435 69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	57 ##
69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	58 ## In most cases, the @code{nchoosek} function is faster for small
69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	59 ## scalar integer arguments. It also warns about loss of precision for
69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	60 ## big arguments.
69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	61 ##
69e27978114a bincoeff.m: make reference to nchoosek Francesco PotortÃ¬ <pot@gnu.org> parents: 7385 diff changeset	62 ## @seealso{nchoosek}
3321 6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe] jwe parents: 2538 diff changeset	63 ## @end deftypefn
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	64
6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	65 function b = bincoeff (n, k)
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	66
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	67 if (nargin != 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5961 diff changeset	68 print_usage ();
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	69 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	70
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	71 [retval, n, k] = common_size (n, k);
6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	72 if (retval > 0)
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 10821 diff changeset	73 error ("bincoeff: N and K must be of common size or scalars");
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	74 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	75
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	76 if (iscomplex (n) \|\| iscomplex (k))
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	77 error ("bincoeff: N and K must not be complex");
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	78 endif
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	79
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	80 b = zeros (size (n));
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	81
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	82 ok = (k >= 0) & (k == fix (k)) & (! isnan (n));
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	83 b(! ok) = NaN;
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	84
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	85 n_int = (n == fix (n));
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	86 idx = n_int & (n < 0) & ok;
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	87 b(idx) = (-1) .^ k(idx) .* exp (gammaln (abs (n(idx)) + k(idx))
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	88 - gammaln (k(idx) + 1)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	89 - gammaln (abs (n(idx))));
3426 f8dde1807dee [project @ 2000-01-13 08:40:00 by jwe] jwe parents: 3321 diff changeset	90
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	91 idx = (n >= k) & ok;
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	92 b(idx) = exp (gammaln (n(idx) + 1)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	93 - gammaln (k(idx) + 1)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	94 - gammaln (n(idx) - k(idx) + 1));
6902 d6d19fcc51b0 [project @ 2007-09-14 19:34:12 by jwe] jwe parents: 6046 diff changeset	95
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	96 idx = (! n_int) & (n < k) & ok;
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	97 b(idx) = (1/pi) * exp (gammaln (n(idx) + 1)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	98 - gammaln (k(idx) + 1)
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	99 + gammaln (k(idx) - n(idx))
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	100 + log (sin (pi * (n(idx) - k(idx) + 1))));
6902 d6d19fcc51b0 [project @ 2007-09-14 19:34:12 by jwe] jwe parents: 6046 diff changeset	101
d6d19fcc51b0 [project @ 2007-09-14 19:34:12 by jwe] jwe parents: 6046 diff changeset	102 ## Clean up rounding errors.
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	103 b(n_int) = round (b(n_int));
6902 d6d19fcc51b0 [project @ 2007-09-14 19:34:12 by jwe] jwe parents: 6046 diff changeset	104
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	105 idx = ! n_int;
078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	106 b(idx) = real (b(idx));
6902 d6d19fcc51b0 [project @ 2007-09-14 19:34:12 by jwe] jwe parents: 6046 diff changeset	107
2538 6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	108 endfunction
6f71af650490 [project @ 1996-11-19 21:41:48 by jwe] jwe parents: diff changeset	109
13169 078729410a0d bincoeff.m: 15% speed improvement and better input validation Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	110
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	111 %!assert (bincoeff (4, 2), 6)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	112 %!assert (bincoeff (2, 4), 0)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	113 %!assert (bincoeff (-4, 2), 10)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	114 %!assert (bincoeff (5, 2), 10)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	115 %!assert (bincoeff (50, 6), 15890700)
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	116 %!assert (bincoeff (0.4, 2), -.12, 8*eps)
7385 8b7b4f58199f [project @ 2008-01-15 20:49:09 by jwe] jwe parents: 7017 diff changeset	117
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	118 %!assert (bincoeff ([4 NaN 4], [-1, 2, 2.5]), NaN (1, 3))
7385 8b7b4f58199f [project @ 2008-01-15 20:49:09 by jwe] jwe parents: 7017 diff changeset	119
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	120 ## Test input validation
28886 d8318c12d903 test: remove unnecessary BIST tests in m-files checking for excessive number of inputs. Rik <rik@octave.org> parents: 27985 diff changeset	121 %!error <Invalid call> bincoeff ()
d8318c12d903 test: remove unnecessary BIST tests in m-files checking for excessive number of inputs. Rik <rik@octave.org> parents: 27985 diff changeset	122 %!error <Invalid call> bincoeff (1)
d8318c12d903 test: remove unnecessary BIST tests in m-files checking for excessive number of inputs. Rik <rik@octave.org> parents: 27985 diff changeset	123 %!error bincoeff (ones (3), ones (2))
d8318c12d903 test: remove unnecessary BIST tests in m-files checking for excessive number of inputs. Rik <rik@octave.org> parents: 27985 diff changeset	124 %!error bincoeff (ones (2), ones (3))

Mercurial > octave

annotate scripts/general/bincoeff.m @ 28886:d8318c12d903