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Simplify TeXinfo files by eliminating redundant @iftex followed by @tex construction. spellchecked all .txi and .texi files.
author Rik <rdrider0-list@yahoo.com>
date Sun, 17 May 2009 12:18:06 -0700
parents 5235caf89e12
children 3140cb7a05a1
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1 ## Copyright (C) 1999, 2006, 2007 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}, @var{t})
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22 ##
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23 ## Return the Pascal matrix of order @var{n} if @code{@var{t} = 0}.
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24 ## @var{t} defaults to 0. Return lower triangular Cholesky factor of
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25 ## the Pascal matrix if @code{@var{t} = 1}. This matrix is its own
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26 ## inverse, that is @code{pascal (@var{n}, 1) ^ 2 == eye (@var{n})}.
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27 ## If @code{@var{t} = -1}, return its absolute value. This is the
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28 ## standard pascal triangle as a lower-triangular matrix.
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29 ## If @code{@var{t} = 2}, return a transposed and permuted version of
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30 ## @code{pascal (@var{n}, 1)}, which is the cube-root of the identity
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31 ## matrix. That is @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}.
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32 ##
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33 ## @seealso{hankel, vander, sylvester_matrix, hilb, invhilb, toeplitz
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34 ## hadamard, wilkinson, compan, rosser}
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35 ## @end deftypefn
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36
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37 ## Author: Peter Ekberg
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38 ## (peda)
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39
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40 function retval = pascal (n, t)
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41
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42 if (nargin > 2) || (nargin == 0)
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43 print_usage ();
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44 endif
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45
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46 if (nargin == 1)
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47 t = 0;
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48 endif
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49
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50 if (! isscalar (n) || ! isscalar (t))
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51 error ("pascal: expecting scalar arguments, found something else");
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52 endif
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53
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54 retval = zeros (n);
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55 retval(:,1) = 1;
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56
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57 if (t == -1)
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58 for j = 2:n
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59 retval(j:n,j) = cumsum (retval (j-1:n-1,j-1));
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60 endfor
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61 else
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62 for j = 2:n
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63 retval(j:n,j) = -cumsum (retval (j-1:n-1,j-1));
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64 endfor
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65 endif
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66
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67 if (t == 0)
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68 retval = retval*retval';
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69 elseif (t == 2)
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70 retval = retval';
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71 retval = retval(n:-1:1,:);
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72 retval(:,n) = -retval(:,n);
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73 retval(n,:) = -retval(n,:);
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74 if (rem(n,2) != 1)
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75 retval = -retval;
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76 endif
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77 endif
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78
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79 endfunction