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annotate scripts/miscellaneous/bincoeff.m @ 14363:f3d52523cde1
Use Octave coding conventions in all m-file %!test blocks
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interp1q.m, interp2.m, interp3.m, interpft.m, interpn.m, isa.m, isdir.m,
isequal.m, isequalwithequalnans.m, issquare.m, logspace.m, nargchk.m,
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get_first_help_sentence.m, help.m, type.m, unimplemented.m, which.m, imread.m,
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duplication_matrix.m, expm.m, housh.m, isdefinite.m, ishermitian.m,
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qzhess.m, rank.m, rref.m, trace.m, vech.m, ans.m, bincoeff.m, bug_report.m,
bzip2.m, comma.m, compare_versions.m, computer.m, edit.m, fileparts.m,
fullfile.m, getfield.m, gzip.m, info.m, inputname.m, isappdata.m, isdeployed.m,
ismac.m, ispc.m, isunix.m, list_primes.m, ls.m, mexext.m, namelengthmax.m,
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ishghandle.m, ishold.m, isocolors.m, isonormals.m, isosurface.m, isprop.m,
legend.m, line.m, loglog.m, loglogerr.m, meshgrid.m, ndgrid.m, newplot.m,
orient.m, patch.m, plot3.m, plotyy.m, __print_parse_opts__.m, quiver3.m,
refreshdata.m, ribbon.m, semilogx.m, semilogxerr.m, semilogy.m, stem.m,
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deconv.m, mkpp.m, mpoles.m, pchip.m, poly.m, polyaffine.m, polyder.m,
polyfit.m, polygcd.m, polyint.m, polyout.m, polyval.m, polyvalm.m, ppder.m,
ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, intersect.m,
ismember.m, powerset.m, setdiff.m, setxor.m, union.m, unique.m,
autoreg_matrix.m, bartlett.m, blackman.m, detrend.m, fftconv.m, fftfilt.m,
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nchoosek.m, nthroot.m, perms.m, pow2.m, primes.m, reallog.m, realpow.m,
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statistics.m, std.m, table.m, var.m, zscore.m, betacdf.m, betainv.m, betapdf.m,
betarnd.m, binocdf.m, binoinv.m, binopdf.m, binornd.m, cauchy_cdf.m,
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chi2rnd.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, discrete_rnd.m,
empirical_cdf.m, empirical_inv.m, empirical_pdf.m, empirical_rnd.m, expcdf.m,
expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m,
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hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m,
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logistic_inv.m, logistic_pdf.m, logistic_rnd.m, logncdf.m, logninv.m,
lognpdf.m, lognrnd.m, nbincdf.m, nbininv.m, nbinpdf.m, nbinrnd.m, normcdf.m,
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tcdf.m, tinv.m, tpdf.m, trnd.m, unidcdf.m, unidinv.m, unidpdf.m, unidrnd.m,
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wblrnd.m, kolmogorov_smirnov_test.m, kruskal_wallis_test.m, base2dec.m,
bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m,
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strcat.m, strjust.m, strmatch.m, strsplit.m, strtok.m, strtrim.m, strtrunc.m,
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Use Octave coding conventions in all m-file %!test blocks
author | Rik <octave@nomad.inbox5.com> |
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date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 4d917a6a858b |
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rev | line source |
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1 ## Copyright (C) 1995-2012 Kurt Hornik |
3426 | 2 ## |
3922 | 3 ## This file is part of Octave. |
4 ## | |
5 ## Octave is free software; you can redistribute it and/or modify it | |
6 ## under the terms of the GNU General Public License as published by | |
7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
8 ## your option) any later version. | |
3426 | 9 ## |
3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
2538 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
3426 | 13 ## General Public License for more details. |
14 ## | |
2538 | 15 ## You should have received a copy of the GNU General Public License |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
2538 | 18 |
3321 | 19 ## -*- texinfo -*- |
20 ## @deftypefn {Mapping Function} {} bincoeff (@var{n}, @var{k}) | |
21 ## Return the binomial coefficient of @var{n} and @var{k}, defined as | |
22 ## @tex | |
23 ## $$ | |
24 ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!} | |
25 ## $$ | |
26 ## @end tex | |
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27 ## @ifnottex |
3426 | 28 ## |
3321 | 29 ## @example |
30 ## @group | |
31 ## / \ | |
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32 ## | n | n (n-1) (n-2) @dots{} (n-k+1) |
3321 | 33 ## | | = ------------------------- |
34 ## | k | k! | |
35 ## \ / | |
36 ## @end group | |
37 ## @end example | |
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38 ## |
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39 ## @end ifnottex |
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40 ## For example: |
3426 | 41 ## |
3321 | 42 ## @example |
43 ## @group | |
44 ## bincoeff (5, 2) | |
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45 ## @result{} 10 |
3321 | 46 ## @end group |
47 ## @end example | |
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48 ## |
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49 ## In most cases, the @code{nchoosek} function is faster for small |
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50 ## scalar integer arguments. It also warns about loss of precision for |
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51 ## big arguments. |
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52 ## |
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53 ## @seealso{nchoosek} |
3321 | 54 ## @end deftypefn |
2538 | 55 |
5428 | 56 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
2538 | 57 ## Created: 8 October 1994 |
58 ## Adapted-By: jwe | |
59 | |
60 function b = bincoeff (n, k) | |
3426 | 61 |
2538 | 62 if (nargin != 2) |
6046 | 63 print_usage (); |
2538 | 64 endif |
3426 | 65 |
2538 | 66 [retval, n, k] = common_size (n, k); |
67 if (retval > 0) | |
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68 error ("bincoeff: N and K must be of common size or scalars"); |
2538 | 69 endif |
3426 | 70 |
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71 if (iscomplex (n) || iscomplex (k)) |
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72 error ("bincoeff: N and K must not be complex"); |
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73 endif |
3426 | 74 |
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75 b = zeros (size (n)); |
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76 |
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77 ok = (k >= 0) & (k == fix (k)) & (! isnan (n)); |
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78 b(! ok) = NaN; |
2538 | 79 |
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80 n_int = (n == fix (n)); |
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81 idx = n_int & (n < 0) & ok; |
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82 b(idx) = (-1) .^ k(idx) .* exp (gammaln (abs (n(idx)) + k(idx)) |
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83 - gammaln (k(idx) + 1) |
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84 - gammaln (abs (n(idx)))); |
3426 | 85 |
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86 idx = (n >= k) & ok; |
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87 b(idx) = exp (gammaln (n(idx) + 1) |
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88 - gammaln (k(idx) + 1) |
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89 - gammaln (n(idx) - k(idx) + 1)); |
6902 | 90 |
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91 idx = (! n_int) & (n < k) & ok; |
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92 b(idx) = (1/pi) * exp (gammaln (n(idx) + 1) |
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93 - gammaln (k(idx) + 1) |
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94 + gammaln (k(idx) - n(idx)) |
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95 + log (sin (pi * (n(idx) - k(idx) + 1)))); |
6902 | 96 |
97 ## Clean up rounding errors. | |
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98 b(n_int) = round (b(n_int)); |
6902 | 99 |
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100 idx = ! n_int; |
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101 b(idx) = real (b(idx)); |
6902 | 102 |
2538 | 103 endfunction |
104 | |
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105 |
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106 %!assert (bincoeff (4, 2), 6) |
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107 %!assert (bincoeff (2, 4), 0) |
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108 %!assert (bincoeff (-4, 2), 10) |
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109 %!assert (bincoeff (5, 2), 10) |
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110 %!assert (bincoeff (50, 6), 15890700) |
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111 %!assert (bincoeff (0.4, 2), -.12, 8*eps) |
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113 %!assert (bincoeff ([4 NaN 4], [-1, 2, 2.5]), NaN (1, 3)) |
7385 | 114 |
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115 %% Test input validation |
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116 %!error bincoeff () |
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117 %!error bincoeff (1, 2, 3) |
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118 %!error bincoeff (ones (3),ones (2)) |
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119 %!error bincoeff (ones (2),ones (3)) |
7385 | 120 |