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1 ## Copyright (C) 1995, 1996 Kurt Hornik |
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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 3 of the License, or (at |
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8 ## your option) 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, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {} commutation_matrix (@var{m}, @var{n}) |
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21 ## Return the commutation matrix |
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22 ## @iftex |
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23 ## @tex |
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24 ## $K_{m,n}$ |
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25 ## @end tex |
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26 ## @end iftex |
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27 ## @ifinfo |
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28 ## K(m,n) |
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29 ## @end ifinfo |
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30 ## which is the unique |
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31 ## @iftex |
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32 ## @tex |
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33 ## $m n \times m n$ |
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34 ## @end tex |
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35 ## @end iftex |
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36 ## @ifinfo |
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37 ## @var{m}*@var{n} by @var{m}*@var{n} |
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38 ## @end ifinfo |
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39 ## matrix such that |
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40 ## @iftex |
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41 ## @tex |
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42 ## $K_{m,n} \cdot {\rm vec} (A) = {\rm vec} (A^T)$ |
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43 ## @end tex |
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44 ## @end iftex |
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45 ## @ifinfo |
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46 ## @math{K(m,n) * vec(A) = vec(A')} |
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47 ## @end ifinfo |
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48 ## for all |
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49 ## @iftex |
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50 ## @tex |
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51 ## $m\times n$ |
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52 ## @end tex |
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53 ## @end iftex |
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54 ## @ifinfo |
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55 ## @math{m} by @math{n} |
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56 ## @end ifinfo |
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57 ## matrices |
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58 ## @iftex |
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59 ## @tex |
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60 ## $A$. |
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61 ## @end tex |
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62 ## @end iftex |
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63 ## @ifinfo |
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64 ## @math{A}. |
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65 ## @end ifinfo |
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66 ## |
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67 ## If only one argument @var{m} is given, |
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68 ## @iftex |
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69 ## @tex |
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70 ## $K_{m,m}$ |
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71 ## @end tex |
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72 ## @end iftex |
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73 ## @ifinfo |
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74 ## @math{K(m,m)} |
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75 ## @end ifinfo |
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76 ## is returned. |
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77 ## |
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78 ## See Magnus and Neudecker (1988), Matrix differential calculus with |
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79 ## applications in statistics and econometrics. |
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80 ## @end deftypefn |
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81 |
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82 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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83 ## Created: 8 May 1995 |
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84 ## Adapted-By: jwe |
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85 |
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86 function k = commutation_matrix (m, n) |
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87 |
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88 if (nargin < 1 || nargin > 2) |
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89 print_usage (); |
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90 else |
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91 if (! (isscalar (m) && m == round (m) && m > 0)) |
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92 error ("commutation_matrix: m must be a positive integer"); |
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93 endif |
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94 if (nargin == 1) |
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95 n = m; |
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96 elseif (! (isscalar (n) && n == round (n) && n > 0)) |
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97 error ("commutation_matrix: n must be a positive integer"); |
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98 endif |
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99 endif |
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100 |
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101 ## It is clearly possible to make this a LOT faster! |
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102 k = zeros (m * n, m * n); |
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103 for i = 1 : m |
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104 for j = 1 : n |
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105 k ((i - 1) * n + j, (j - 1) * m + i) = 1; |
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106 endfor |
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107 endfor |
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108 |
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109 endfunction |
