Mercurial > octave
annotate scripts/special-matrix/pascal.m @ 23219:3ac9f9ecfae5 stable
maint: Update copyright dates.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 22 Feb 2017 12:39:29 -0500 |
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1 ## Copyright (C) 1999-2017 Peter Ekberg |
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2 ## Copyright (C) 2009 VZLU Prague |
5827 | 3 ## |
4 ## This file is part of Octave. | |
5 ## | |
6 ## Octave is free software; you can redistribute it and/or modify it | |
7 ## under the terms of the GNU General Public License as published by | |
7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
9 ## your option) any later version. | |
5827 | 10 ## |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
15 ## | |
16 ## You should have received a copy of the GNU General Public License | |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
5827 | 19 |
20 ## -*- texinfo -*- | |
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21 ## @deftypefn {} {} pascal (@var{n}) |
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22 ## @deftypefnx {} {} pascal (@var{n}, @var{t}) |
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23 ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}. |
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24 ## |
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25 ## The default value of @var{t} is 0. |
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26 ## |
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27 ## When @code{@var{t} = 1}, return the pseudo-lower triangular |
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28 ## Cholesky@tie{}factor of the Pascal matrix (The sign of some columns may be |
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29 ## negative). This matrix is its own inverse, that is |
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30 ## @code{pascal (@var{n}, 1) ^ 2 == eye (@var{n})}. |
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31 ## |
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32 ## If @code{@var{t} = -1}, return the true Cholesky@tie{}factor with strictly |
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33 ## positive values on the diagonal. |
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34 ## |
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35 ## If @code{@var{t} = 2}, return a transposed and permuted version of |
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36 ## @code{pascal (@var{n}, 1)}, which is the cube root of the identity matrix. |
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37 ## That is, @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}. |
5827 | 38 ## |
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39 ## @seealso{chol} |
5827 | 40 ## @end deftypefn |
41 | |
42 ## Author: Peter Ekberg | |
43 ## (peda) | |
44 | |
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45 function retval = pascal (n, t = 0) |
5827 | 46 |
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47 if (nargin < 1 || nargin > 2) |
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48 print_usage (); |
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49 elseif (! (isscalar (n) && isscalar (t))) |
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50 error ("pascal: N and T must be scalars"); |
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51 elseif (! any (t == [-1, 0, 1, 2])) |
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52 error ("pascal: T must be -1, 0, 1, or 2, found %d", t); |
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53 endif |
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54 |
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55 retval = zeros (n); |
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56 if (n > 0) |
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57 retval(:,1) = 1; |
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58 endif |
5827 | 59 |
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60 if (t == -1) |
9096 | 61 for j = 2:n |
13904 | 62 retval(j:n,j) = cumsum (retval(j-1:n-1,j-1)); |
5827 | 63 endfor |
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64 else |
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13904 | 66 retval(j:n,j) = -cumsum (retval(j-1:n-1,j-1)); |
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67 endfor |
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68 endif |
5827 | 69 |
70 if (t == 0) | |
71 retval = retval*retval'; | |
72 elseif (t == 2) | |
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73 retval = rot90 (retval, 3); |
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74 if (rem (n,2) != 1) |
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75 retval *= -1; |
5827 | 76 endif |
77 endif | |
78 | |
79 endfunction | |
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80 |
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81 |
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82 %!assert (pascal (3,-1), [1,0,0;1,1,0;1,2,1]) |
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83 %!assert (pascal (3,0), [1,1,1;1,2,3;1,3,6]) |
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84 %!assert (pascal (3,0), pascal (3)) |
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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 (3,2), [1,1,1;-2,-1,0;1,0,0]) |
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87 %!assert (pascal (0,2), []) |
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88 |
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89 ## Test input validation |
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90 %!error pascal () |
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91 %!error pascal (1,2,3) |
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92 %!error <N and T must be scalars> pascal ([1 2]) |
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93 %!error <N and T must be scalars> pascal (1, [1 2]) |
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94 %!error <T must be -1> pascal (3,-2) |
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95 %!error <T must be .* or 2> pascal (3,4) |