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1 ## Copyright (C) 1999 Peter Ekberg |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify it |
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4 ## under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this program; see the file COPYING. If not, write to the Free |
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15 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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16 ## 02111-1307, USA. |
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17 |
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18 ## usage: pascal (n, t) |
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19 ## |
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20 ## Return the Pascal matrix of order n if t=0. |
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21 ## t defaults to 0. |
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22 ## Return lower triangular Cholesky factor of the Pascal matrix if t=1. |
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23 ## Return a transposed and permuted version of pascal(n,1) if t=2. |
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24 ## |
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25 ## pascal(n,1)^2 == eye(n) |
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26 ## pascal(n,2)^3 == eye(n) |
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27 ## |
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28 ## See also: hankel, vander, sylvester_matrix, hilb, invhilb, toeplitz |
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29 ## hadamard, wilkinson, rosser, compan |
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30 |
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31 ## Author: peda |
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32 |
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33 function retval = pascal (n, t) |
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34 |
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35 if (nargin > 2) || (nargin == 0) |
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36 usage ("pascal (n, t)"); |
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37 endif |
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38 |
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39 if (nargin == 1) |
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40 t = 0; |
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41 endif |
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42 |
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43 if !is_scalar (n) || !is_scalar (t) |
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44 error ("pascal expecting scalar arguments, found something else"); |
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45 endif |
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46 |
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47 retval = diag((-1).^[0:n-1]); |
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48 retval(:,1) = ones(n, 1); |
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49 |
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50 for j=2:n-1 |
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51 for i=j+1:n |
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52 retval(i,j) = retval(i-1,j) - retval(i-1,j-1); |
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53 endfor |
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54 endfor |
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55 |
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56 if (t==0) |
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57 retval = retval*retval'; |
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58 elseif (t==2) |
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59 retval = retval'; |
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60 retval = retval(n:-1:1,:); |
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61 retval(:,n) = -retval(:,n); |
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62 retval(n,:) = -retval(n,:); |
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63 if (rem(n,2) != 1) |
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64 retval = -retval; |
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65 endif |
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66 endif |
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67 |
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68 endfunction |
