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1 ## Copyright (C) 1995, 1996 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it 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 file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {} duplication_matrix (@var{n}) |
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19 ## Return the duplication matrix |
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20 ## @iftex |
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21 ## @tex |
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22 ## $D_n$ |
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23 ## @end tex |
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24 ## @end iftex |
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25 ## @ifinfo |
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26 ## @var{D}_@var{n} |
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27 ## @end ifinfo |
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28 ## which is the unique |
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29 ## @iftex |
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30 ## @tex |
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31 ## $n^2 \times n(n+1)/2$ |
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32 ## @end tex |
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33 ## @end iftex |
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34 ## @ifinfo |
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35 ## @var{n}^2 by @var{n}*(@var{n}+1)/2 |
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36 ## @end ifinfo |
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37 ## matrix such that |
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38 ## @iftex |
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39 ## @tex |
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40 ## $D_n * {\rm vech} (A) = {\rm vec} (A)$ |
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41 ## @end tex |
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42 ## @end iftex |
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43 ## @ifinfo |
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44 ## @var{D}_@var{n} \cdot vech (@var{A}) = vec (@var{A}) |
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45 ## @end ifinfo |
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46 ## for all symmetric |
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47 ## @iftex |
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48 ## @tex |
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49 ## $n \times n$ |
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50 ## @end tex |
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51 ## @end iftex |
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52 ## @ifinfo |
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53 ## @var{n} by @var{n} |
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54 ## @end ifinfo |
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55 ## matrices |
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56 ## @iftex |
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57 ## @tex |
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58 ## $A$. |
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59 ## @end tex |
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60 ## @end iftex |
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61 ## @ifinfo |
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62 ## @var{A}. |
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63 ## @end ifinfo |
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64 ## |
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65 ## See Magnus and Neudecker (1988), Matrix differential calculus with |
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66 ## applications in statistics and econometrics. |
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67 ## @end deftypefn |
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68 |
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69 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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70 ## Created: 8 May 1995 |
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71 ## Adapged-By: jwe |
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72 |
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73 function d = duplication_matrix (n) |
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74 |
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75 if (nargin != 1) |
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76 usage ("duplication_matrix (n)"); |
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77 endif |
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78 |
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79 if (! (is_scalar (n) && n == round (n) && n > 0)) |
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80 error ("duplication_matrix: n must be a positive integer"); |
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81 endif |
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82 |
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83 d = zeros (n * n, n * (n + 1) / 2); |
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84 |
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85 ## It is clearly possible to make this a LOT faster! |
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86 count = 0; |
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87 for j = 1 : n |
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88 d ((j - 1) * n + j, count + j) = 1; |
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89 for i = (j + 1) : n |
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90 d ((j - 1) * n + i, count + i) = 1; |
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91 d ((i - 1) * n + j, count + i) = 1; |
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92 endfor |
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93 count = count + n - j; |
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94 endfor |
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95 |
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96 endfunction |
