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annotate scripts/linear-algebra/duplication_matrix.m @ 2540:c3d634d49ce4

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[project @ 1996-11-20 00:20:12 by jwe]
author jwe
date Wed, 20 Nov 1996 00:21:25 +0000
parents
children 6923abb04e16
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2540
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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 ## usage: duplication_matrix (n)
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18 ##
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19 ## Returns the duplication matrix D_n which is the unique n^2 by
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20 ## n*(n+1)/2 matrix such that D_n * vech (A) = vec (A) for all
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21 ## symmetric n by n matrices A.
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22 ##
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23 ## See Magnus and Neudecker (1988), Matrix differential calculus with
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24 ## applications in statistics and econometrics.
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25
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26 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
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27 ## Created: 8 May 1995
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28 ## Adapged-By: jwe
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29
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30 function d = duplication_matrix (n)
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31
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32 if (nargin != 1)
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33 usage ("duplication_matrix (n)");
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34 endif
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35
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36 if (! (is_scalar (n) && n == round (n) && n > 0))
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37 error ("duplication_matrix: n must be a positive integer");
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38 endif
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39
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40 d = zeros (n * n, n * (n + 1) / 2);
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41
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42 ## It is clearly possible to make this a LOT faster!
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43 count = 0;
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44 for j = 1 : n
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45 d ((j - 1) * n + j, count + j) = 1;
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46 for i = (j + 1) : n
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47 d ((j - 1) * n + i, count + i) = 1;
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48 d ((i - 1) * n + j, count + i) = 1;
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49 endfor
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50 count = count + n - j;
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51 endfor
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52
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53 endfunction