Mercurial > octave
annotate scripts/special-matrix/pascal.m @ 29359:7854d5752dd2
maint: merge stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 10 Feb 2021 10:10:40 -0500 |
parents | d8318c12d903 0a5b15007766 |
children | 796f54d4ddbf |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 1999-2021 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 {} {} pascal (@var{n}) |
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28 ## @deftypefnx {} {} 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 retval = 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 retval = zeros (n); |
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59 if (n > 0) |
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60 retval(:,1) = 1; |
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61 endif |
5827 | 62 |
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63 if (t == -1) |
9096 | 64 for j = 2:n |
13904 | 65 retval(j:n,j) = cumsum (retval(j-1:n-1,j-1)); |
5827 | 66 endfor |
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67 else |
9096 | 68 for j = 2:n |
13904 | 69 retval(j:n,j) = -cumsum (retval(j-1:n-1,j-1)); |
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70 endfor |
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71 endif |
5827 | 72 |
73 if (t == 0) | |
74 retval = retval*retval'; | |
75 elseif (t == 2) | |
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76 retval = rot90 (retval, 3); |
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77 if (rem (n,2) != 1) |
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78 retval *= -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) |