Mercurial > hg > octave-nkf
annotate scripts/linear-algebra/commutation_matrix.m @ 10509:ddbd812d09aa
properly compress sparse matrices after assembly
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Mon, 12 Apr 2010 12:57:44 +0200 |
| parents | f0c3d3fc4903 |
| children | 3140cb7a05a1 |
| rev | line source |
|---|---|
| 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 |
| 3321 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {} commutation_matrix (@var{m}, @var{n}) | |
| 22 ## Return the commutation matrix | |
| 23 ## @tex | |
| 24 ## $K_{m,n}$ | |
| 25 ## @end tex | |
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26 ## @ifnottex |
| 3321 | 27 ## K(m,n) |
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28 ## @end ifnottex |
| 3321 | 29 ## which is the unique |
| 30 ## @tex | |
| 31 ## $m n \times m n$ | |
| 32 ## @end tex | |
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33 ## @ifnottex |
| 3321 | 34 ## @var{m}*@var{n} by @var{m}*@var{n} |
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35 ## @end ifnottex |
| 3321 | 36 ## matrix such that |
| 37 ## @tex | |
| 38 ## $K_{m,n} \cdot {\rm vec} (A) = {\rm vec} (A^T)$ | |
| 39 ## @end tex | |
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40 ## @ifnottex |
| 3499 | 41 ## @math{K(m,n) * vec(A) = vec(A')} |
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42 ## @end ifnottex |
| 3321 | 43 ## for all |
| 44 ## @tex | |
| 45 ## $m\times n$ | |
| 46 ## @end tex | |
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47 ## @ifnottex |
| 3499 | 48 ## @math{m} by @math{n} |
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49 ## @end ifnottex |
| 3321 | 50 ## matrices |
| 51 ## @tex | |
| 52 ## $A$. | |
| 53 ## @end tex | |
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54 ## @ifnottex |
| 3499 | 55 ## @math{A}. |
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56 ## @end ifnottex |
| 3426 | 57 ## |
| 3321 | 58 ## If only one argument @var{m} is given, |
| 59 ## @tex | |
| 60 ## $K_{m,m}$ | |
| 61 ## @end tex | |
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62 ## @ifnottex |
| 3499 | 63 ## @math{K(m,m)} |
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64 ## @end ifnottex |
| 3321 | 65 ## is returned. |
| 3426 | 66 ## |
| 2540 | 67 ## See Magnus and Neudecker (1988), Matrix differential calculus with |
| 68 ## applications in statistics and econometrics. | |
| 3321 | 69 ## @end deftypefn |
| 2540 | 70 |
| 5428 | 71 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 2540 | 72 ## Created: 8 May 1995 |
| 73 ## Adapted-By: jwe | |
| 74 | |
| 75 function k = commutation_matrix (m, n) | |
| 3426 | 76 |
| 2540 | 77 if (nargin < 1 || nargin > 2) |
| 6046 | 78 print_usage (); |
| 2540 | 79 else |
| 4030 | 80 if (! (isscalar (m) && m == round (m) && m > 0)) |
| 2540 | 81 error ("commutation_matrix: m must be a positive integer"); |
| 82 endif | |
| 83 if (nargin == 1) | |
| 84 n = m; | |
| 4030 | 85 elseif (! (isscalar (n) && n == round (n) && n > 0)) |
| 2540 | 86 error ("commutation_matrix: n must be a positive integer"); |
| 87 endif | |
| 88 endif | |
| 3426 | 89 |
| 2540 | 90 ## It is clearly possible to make this a LOT faster! |
| 91 k = zeros (m * n, m * n); | |
| 92 for i = 1 : m | |
| 93 for j = 1 : n | |
| 94 k ((i - 1) * n + j, (j - 1) * m + i) = 1; | |
| 95 endfor | |
| 96 endfor | |
| 97 | |
| 98 endfunction |