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1 ## Copyright (C) 1999 Peter Ekberg |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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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} = 2}, return a transposed and permuted version of |
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28 ## @code{pascal (@var{n}, 1)}, which is the cube-root of the identity |
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29 ## matrix. That is @code{pascal (@var{n}, 2) ^ 3 == eye (@var{n})}. |
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30 ## |
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31 ## @seealso{hankel, vander, sylvester_matrix, hilb, invhilb, toeplitz |
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32 ## hadamard, wilkinson, compan, rosser} |
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33 ## @end deftypefn |
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34 |
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35 ## Author: Peter Ekberg |
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36 ## (peda) |
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37 |
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38 function retval = pascal (n, t) |
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39 |
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40 if (nargin > 2) || (nargin == 0) |
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41 print_usage (); |
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42 endif |
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43 |
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44 if (nargin == 1) |
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45 t = 0; |
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46 endif |
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47 |
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48 if (! is_scalar (n) || ! is_scalar (t)) |
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49 error ("pascal: expecting scalar arguments, found something else"); |
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50 endif |
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51 |
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52 retval = diag ((-1).^[0:n-1]); |
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53 retval(:,1) = ones (n, 1); |
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54 |
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55 for j = 2:n-1 |
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56 for i = j+1:n |
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57 retval(i,j) = retval(i-1,j) - retval(i-1,j-1); |
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58 endfor |
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59 endfor |
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60 |
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61 if (t == 0) |
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62 retval = retval*retval'; |
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63 elseif (t == 2) |
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64 retval = retval'; |
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65 retval = retval(n:-1:1,:); |
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66 retval(:,n) = -retval(:,n); |
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67 retval(n,:) = -retval(n,:); |
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68 if (rem(n,2) != 1) |
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69 retval = -retval; |
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70 endif |
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71 endif |
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72 |
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73 endfunction |
