Mercurial > octave-libtiff
annotate scripts/special-matrix/pascal.m @ 30875:5d3faba0342e
doc: Ensure documentation lists output argument when it exists for all m-files.
For new users of Octave it is best to show explicit calling forms
in the documentation and to show a return argument when it exists.
* bp-table.cc, shift.m, accumarray.m, accumdim.m, bincoeff.m, bitcmp.m,
bitget.m, bitset.m, blkdiag.m, celldisp.m, cplxpair.m, dblquad.m, flip.m,
fliplr.m, flipud.m, idivide.m, int2str.m, interpft.m, logspace.m, num2str.m,
polyarea.m, postpad.m, prepad.m, randi.m, repmat.m, rng.m, rot90.m, rotdim.m,
structfun.m, triplequad.m, uibuttongroup.m, uicontrol.m, uipanel.m,
uipushtool.m, uitoggletool.m, uitoolbar.m, waitforbuttonpress.m, help.m,
__additional_help_message__.m, hsv.m, im2double.m, im2frame.m, javachk.m,
usejava.m, argnames.m, char.m, formula.m, inline.m, __vectorize__.m, findstr.m,
flipdim.m, strmatch.m, vectorize.m, commutation_matrix.m, cond.m, cross.m,
duplication_matrix.m, expm.m, orth.m, rank.m, rref.m, trace.m, vech.m, cast.m,
compare_versions.m, delete.m, dir.m, fileattrib.m, grabcode.m, gunzip.m,
inputname.m, license.m, list_primes.m, ls.m, mexext.m, movefile.m,
namelengthmax.m, nargoutchk.m, nthargout.m, substruct.m, swapbytes.m, ver.m,
verLessThan.m, what.m, fminunc.m, fsolve.m, fzero.m, optimget.m, __fdjac__.m,
matlabroot.m, savepath.m, campos.m, camroll.m, camtarget.m, camup.m, camva.m,
camzoom.m, clabel.m, diffuse.m, legend.m, orient.m, rticks.m, specular.m,
thetaticks.m, xlim.m, xtickangle.m, xticklabels.m, xticks.m, ylim.m,
ytickangle.m, yticklabels.m, yticks.m, zlim.m, ztickangle.m, zticklabels.m,
zticks.m, ellipsoid.m, isocolors.m, isonormals.m, stairs.m, surfnorm.m,
__actual_axis_position__.m, __pltopt__.m, close.m, graphics_toolkit.m, pan.m,
print.m, printd.m, __ghostscript__.m, __gnuplot_print__.m, __opengl_print__.m,
rotate3d.m, subplot.m, zoom.m, compan.m, conv.m, poly.m, polyaffine.m,
polyder.m, polyint.m, polyout.m, polyreduce.m, polyvalm.m, roots.m, prefdir.m,
prefsfile.m, profexplore.m, profexport.m, profshow.m, powerset.m, unique.m,
arch_rnd.m, arma_rnd.m, autoreg_matrix.m, bartlett.m, blackman.m, detrend.m,
durbinlevinson.m, fftconv.m, fftfilt.m, fftshift.m, fractdiff.m, hamming.m,
hanning.m, hurst.m, ifftshift.m, rectangle_lw.m, rectangle_sw.m, triangle_lw.m,
sinc.m, sinetone.m, sinewave.m, spectral_adf.m, spectral_xdf.m, spencer.m,
ilu.m, __sprand__.m, sprand.m, sprandn.m, sprandsym.m, treelayout.m, beta.m,
betainc.m, betaincinv.m, betaln.m, cosint.m, expint.m, factorial.m, gammainc.m,
gammaincinv.m, lcm.m, nthroot.m, perms.m, reallog.m, realpow.m, realsqrt.m,
sinint.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, pascal.m, rosser.m,
toeplitz.m, vander.m, wilkinson.m, center.m, corr.m, cov.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, kendall.m, kurtosis.m,
mad.m, mean.m, meansq.m, median.m, mode.m, moment.m, range.m, ranks.m,
run_count.m, skewness.m, spearman.m, statistics.m, std.m, base2dec.m,
bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m,
hex2dec.m, index.m, regexptranslate.m, rindex.m, strcat.m, strjust.m,
strtrim.m, strtrunc.m, substr.m, untabify.m, __have_feature__.m,
__prog_output_assert__.m, __run_test_suite__.m, example.m, fail.m, asctime.m,
calendar.m, ctime.m, date.m, etime.m:
Add return arguments to @deftypefn macros where they were missing. Rename
variables in functions (particularly generic "retval") to match documentation.
Rename some return variables for (hopefully) better clarity (e.g., 'ax' to 'hax'
to indicate it is a graphics handle to an axes object).
author | Rik <rik@octave.org> |
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date | Wed, 30 Mar 2022 20:40:27 -0700 |
parents | 796f54d4ddbf |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 1999-2022 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
5827 | 7 ## |
8 ## This file is part of Octave. | |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
5827 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
5827 | 14 ## |
15 ## Octave is distributed in the hope that it will be useful, but | |
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
5827 | 19 ## |
20 ## You should have received a copy of the GNU General Public License | |
7016 | 21 ## along with Octave; see the file COPYING. If not, see |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
5827 | 25 |
26 ## -*- texinfo -*- | |
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27 ## @deftypefn {} {@var{P} =} pascal (@var{n}) |
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28 ## @deftypefnx {} {@var{P} =} pascal (@var{n}, @var{t}) |
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29 ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}. |
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30 ## |
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31 ## The default value of @var{t} is 0. |
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32 ## |
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33 ## When @code{@var{t} = 1}, return the pseudo-lower triangular |
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34 ## Cholesky@tie{}factor of the Pascal matrix (The sign of some columns may be |
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35 ## negative). This matrix is its own inverse, that is |
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36 ## @code{pascal (@var{n}, 1) ^ 2 == eye (@var{n})}. |
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37 ## |
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38 ## If @code{@var{t} = -1}, return the true Cholesky@tie{}factor with strictly |
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39 ## positive values on the diagonal. |
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40 ## |
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41 ## If @code{@var{t} = 2}, return a transposed and permuted version of |
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42 ## @code{pascal (@var{n}, 1)}, which is the cube root of the identity matrix. |
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43 ## That is, @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}. |
5827 | 44 ## |
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45 ## @seealso{chol} |
5827 | 46 ## @end deftypefn |
47 | |
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48 function P = pascal (n, t = 0) |
5827 | 49 |
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50 if (nargin < 1) |
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51 print_usage (); |
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52 elseif (! (isscalar (n) && isscalar (t))) |
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53 error ("pascal: N and T must be scalars"); |
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54 elseif (! any (t == [-1, 0, 1, 2])) |
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55 error ("pascal: T must be -1, 0, 1, or 2, found %d", t); |
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56 endif |
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57 |
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58 P = zeros (n); |
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59 if (n > 0) |
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60 P(:,1) = 1; |
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61 endif |
5827 | 62 |
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63 if (t == -1) |
9096 | 64 for j = 2:n |
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65 P(j:n,j) = cumsum (P(j-1:n-1,j-1)); |
5827 | 66 endfor |
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67 else |
9096 | 68 for j = 2:n |
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69 P(j:n,j) = -cumsum (P(j-1:n-1,j-1)); |
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70 endfor |
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71 endif |
5827 | 72 |
73 if (t == 0) | |
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74 P = P*P'; |
5827 | 75 elseif (t == 2) |
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76 P = rot90 (P, 3); |
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77 if (rem (n,2) != 1) |
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78 P *= -1; |
5827 | 79 endif |
80 endif | |
81 | |
82 endfunction | |
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83 |
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84 |
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85 %!assert (pascal (3,-1), [1,0,0;1,1,0;1,2,1]) |
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86 %!assert (pascal (3,0), [1,1,1;1,2,3;1,3,6]) |
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87 %!assert (pascal (3,0), pascal (3)) |
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88 %!assert (pascal (3,1), [1,0,0;1,-1,0;1,-2,1]) |
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89 %!assert (pascal (3,2), [1,1,1;-2,-1,0;1,0,0]) |
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90 %!assert (pascal (0,2), []) |
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91 |
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92 ## Test input validation |
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93 %!error <Invalid call> pascal () |
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94 %!error <N and T must be scalars> pascal ([1 2]) |
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95 %!error <N and T must be scalars> pascal (1, [1 2]) |
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96 %!error <T must be -1> pascal (3,-2) |
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97 %!error <T must be .* or 2> pascal (3,4) |