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annotate scripts/linear-algebra/duplication_matrix.m @ 11523:fd0a3ac60b0e
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| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 14 Jan 2011 05:47:45 -0500 |
| parents | 1740012184f9 |
| children | 60bd7ebb12fc |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 1995-2011 Kurt Hornik |
| 3426 | 2 ## |
| 3922 | 3 ## This file is part of Octave. |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 3426 | 9 ## |
| 3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
| 2540 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 13 ## General Public License for more details. |
| 14 ## | |
| 2540 | 15 ## You should have received a copy of the GNU General Public License |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 2540 | 18 |
| 3426 | 19 ## -*- texinfo -*- |
| 3321 | 20 ## @deftypefn {Function File} {} duplication_matrix (@var{n}) |
| 21 ## Return the duplication matrix | |
| 22 ## @tex | |
| 23 ## $D_n$ | |
| 24 ## @end tex | |
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25 ## @ifnottex |
| 3499 | 26 ## @math{Dn} |
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27 ## @end ifnottex |
| 3321 | 28 ## which is the unique |
| 29 ## @tex | |
| 30 ## $n^2 \times n(n+1)/2$ | |
| 31 ## @end tex | |
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32 ## @ifnottex |
| 3499 | 33 ## @math{n^2} by @math{n*(n+1)/2} |
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34 ## @end ifnottex |
| 3321 | 35 ## matrix such that |
| 36 ## @tex | |
| 37 ## $D_n * {\rm vech} (A) = {\rm vec} (A)$ | |
| 38 ## @end tex | |
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39 ## @ifnottex |
| 3499 | 40 ## @math{Dn vech (A) = vec (A)} |
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41 ## @end ifnottex |
| 3321 | 42 ## for all symmetric |
| 43 ## @tex | |
| 44 ## $n \times n$ | |
| 45 ## @end tex | |
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46 ## @ifnottex |
| 3499 | 47 ## @math{n} by @math{n} |
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48 ## @end ifnottex |
| 3321 | 49 ## matrices |
| 50 ## @tex | |
| 51 ## $A$. | |
| 52 ## @end tex | |
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53 ## @ifnottex |
| 3499 | 54 ## @math{A}. |
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55 ## @end ifnottex |
| 3426 | 56 ## |
| 2540 | 57 ## See Magnus and Neudecker (1988), Matrix differential calculus with |
| 58 ## applications in statistics and econometrics. | |
| 3321 | 59 ## @end deftypefn |
| 2540 | 60 |
| 5428 | 61 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 2540 | 62 ## Created: 8 May 1995 |
| 63 ## Adapged-By: jwe | |
| 64 | |
| 65 function d = duplication_matrix (n) | |
| 66 | |
| 67 if (nargin != 1) | |
| 6046 | 68 print_usage (); |
| 2540 | 69 endif |
| 70 | |
| 4030 | 71 if (! (isscalar (n) && n == round (n) && n > 0)) |
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72 error ("duplication_matrix: N must be a positive integer"); |
| 2540 | 73 endif |
| 74 | |
| 75 d = zeros (n * n, n * (n + 1) / 2); | |
| 76 | |
| 77 ## It is clearly possible to make this a LOT faster! | |
| 78 count = 0; | |
| 79 for j = 1 : n | |
| 80 d ((j - 1) * n + j, count + j) = 1; | |
| 81 for i = (j + 1) : n | |
| 82 d ((j - 1) * n + i, count + i) = 1; | |
| 83 d ((i - 1) * n + j, count + i) = 1; | |
| 84 endfor | |
| 85 count = count + n - j; | |
| 86 endfor | |
| 87 | |
| 88 endfunction |