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maint: update copyright notices for 2012
author John W. Eaton <jwe@octave.org>
date Mon, 02 Jan 2012 14:25:41 -0500
parents 755f6b340453
children d63878346099
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14138
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1 ## Copyright (C) 1999-2012 Peter Ekberg
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2 ## Copyright (C) 2009 VZLU Prague
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {} pascal (@var{n})
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22 ## @deftypefnx {Function File} {} pascal (@var{n}, @var{t})
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23 ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}. @var{t}
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24 ## defaults to 0. Return the pseudo-lower triangular Cholesky@tie{}factor of
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25 ## the Pascal matrix if @code{@var{t} = 1} (The sign of some columns may be
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26 ## negative). This matrix is its own inverse, that is @code{pascal (@var{n},
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27 ## 1) ^ 2 == eye (@var{n})}. If @code{@var{t} = -1}, return the true
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28 ## Cholesky@tie{}factor with strictly positive values on the diagonal. If
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29 ## @code{@var{t} = 2}, return a transposed and permuted version of @code{pascal
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30 ## (@var{n}, 1)}, which is the cube root of the identity matrix. That is,
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31 ## @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}.
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32 ##
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33 ## @seealso{chol}
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34 ## @end deftypefn
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35
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36 ## Author: Peter Ekberg
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37 ## (peda)
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38
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39 function retval = pascal (n, t = 0)
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40
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41 if (nargin < 1 || nargin > 2)
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42 print_usage ();
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43 elseif (! (isscalar (n) && isscalar (t)))
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44 error ("pascal: N and T must be scalars");
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45 elseif (! any (t == [-1, 0, 1, 2]))
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46 error ("pascal: expecting T to be -1, 0, 1, or 2, found %d", t);
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47 endif
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48
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49 retval = zeros (n);
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50 if (n > 0)
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51 retval(:,1) = 1;
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52 endif
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53
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54 if (t == -1)
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55 for j = 2:n
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56 retval(j:n,j) = cumsum (retval(j-1:n-1,j-1));
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57 endfor
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58 else
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59 for j = 2:n
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60 retval(j:n,j) = -cumsum (retval(j-1:n-1,j-1));
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61 endfor
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62 endif
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63
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64 if (t == 0)
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65 retval = retval*retval';
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66 elseif (t == 2)
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67 retval = rot90 (retval, 3);
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68 if (rem (n,2) != 1)
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69 retval *= -1;
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70 endif
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71 endif
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72
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73 endfunction
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74
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75
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76 %!assert (pascal (3,-1), [1,0,0;1,1,0;1,2,1])
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77 %!assert (pascal (3,0), [1,1,1;1,2,3;1,3,6])
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78 %!assert (pascal (3,0), pascal (3))
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79 %!assert (pascal (3,1), [1,0,0;1,-1,0;1,-2,1])
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80 %!assert (pascal (3,2), [1,1,1;-2,-1,0;1,0,0])
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81 %!assert (pascal (0,2), [])
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82
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83 %% Test input validation
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84 %!error pascal ()
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85 %!error pascal (1,2,3)
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86 %!error <N and T must be scalars> pascal ([1 2])
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87 %!error <N and T must be scalars> pascal (1, [1 2])
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88 %!error <expecting T to be> pascal (3,-2)
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89 %!error <expecting T to be> pascal (3,4)
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90