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annotate scripts/linear-algebra/duplication_matrix.m @ 8920:eb63fbe60fab
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| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Sat, 07 Mar 2009 10:41:27 -0500 |
| parents | 81d6ab3ac93c |
| children | f0c3d3fc4903 |
| rev | line source |
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| 8920 | 1 ## Copyright (C) 1995, 1996, 1999, 2000, 2002, 2005, 2006, 2007, 2009 |
| 7017 | 2 ## Kurt Hornik |
| 3426 | 3 ## |
| 3922 | 4 ## This file is part of Octave. |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 3426 | 10 ## |
| 3922 | 11 ## Octave is distributed in the hope that it will be useful, but |
| 2540 | 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 14 ## General Public License for more details. |
| 15 ## | |
| 2540 | 16 ## You should have received a copy of the GNU General Public License |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 2540 | 19 |
| 3426 | 20 ## -*- texinfo -*- |
| 3321 | 21 ## @deftypefn {Function File} {} duplication_matrix (@var{n}) |
| 22 ## Return the duplication matrix | |
| 23 ## @iftex | |
| 24 ## @tex | |
| 25 ## $D_n$ | |
| 26 ## @end tex | |
| 27 ## @end iftex | |
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28 ## @ifnottex |
| 3499 | 29 ## @math{Dn} |
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30 ## @end ifnottex |
| 3321 | 31 ## which is the unique |
| 32 ## @iftex | |
| 33 ## @tex | |
| 34 ## $n^2 \times n(n+1)/2$ | |
| 35 ## @end tex | |
| 36 ## @end iftex | |
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37 ## @ifnottex |
| 3499 | 38 ## @math{n^2} by @math{n*(n+1)/2} |
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39 ## @end ifnottex |
| 3321 | 40 ## matrix such that |
| 41 ## @iftex | |
| 42 ## @tex | |
| 43 ## $D_n * {\rm vech} (A) = {\rm vec} (A)$ | |
| 44 ## @end tex | |
| 45 ## @end iftex | |
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46 ## @ifnottex |
| 3499 | 47 ## @math{Dn vech (A) = vec (A)} |
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48 ## @end ifnottex |
| 3321 | 49 ## for all symmetric |
| 50 ## @iftex | |
| 51 ## @tex | |
| 52 ## $n \times n$ | |
| 53 ## @end tex | |
| 54 ## @end iftex | |
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55 ## @ifnottex |
| 3499 | 56 ## @math{n} by @math{n} |
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57 ## @end ifnottex |
| 3321 | 58 ## matrices |
| 59 ## @iftex | |
| 60 ## @tex | |
| 61 ## $A$. | |
| 62 ## @end tex | |
| 63 ## @end iftex | |
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64 ## @ifnottex |
| 3499 | 65 ## @math{A}. |
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66 ## @end ifnottex |
| 3426 | 67 ## |
| 2540 | 68 ## See Magnus and Neudecker (1988), Matrix differential calculus with |
| 69 ## applications in statistics and econometrics. | |
| 3321 | 70 ## @end deftypefn |
| 2540 | 71 |
| 5428 | 72 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 2540 | 73 ## Created: 8 May 1995 |
| 74 ## Adapged-By: jwe | |
| 75 | |
| 76 function d = duplication_matrix (n) | |
| 77 | |
| 78 if (nargin != 1) | |
| 6046 | 79 print_usage (); |
| 2540 | 80 endif |
| 81 | |
| 4030 | 82 if (! (isscalar (n) && n == round (n) && n > 0)) |
| 2540 | 83 error ("duplication_matrix: n must be a positive integer"); |
| 84 endif | |
| 85 | |
| 86 d = zeros (n * n, n * (n + 1) / 2); | |
| 87 | |
| 88 ## It is clearly possible to make this a LOT faster! | |
| 89 count = 0; | |
| 90 for j = 1 : n | |
| 91 d ((j - 1) * n + j, count + j) = 1; | |
| 92 for i = (j + 1) : n | |
| 93 d ((j - 1) * n + i, count + i) = 1; | |
| 94 d ((i - 1) * n + j, count + i) = 1; | |
| 95 endfor | |
| 96 count = count + n - j; | |
| 97 endfor | |
| 98 | |
| 99 endfunction |