Mercurial > hg > octave-nkf
annotate scripts/linear-algebra/commutation_matrix.m @ 12297:175127b734a4 release-3-4-x
ChangeLog fixes
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Sun, 30 Jan 2011 01:57:40 -0500 |
| parents | fd0a3ac60b0e |
| children | 8dd680993088 |
| 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 |
| 3321 | 19 ## -*- texinfo -*- |
| 20 ## @deftypefn {Function File} {} commutation_matrix (@var{m}, @var{n}) | |
| 21 ## Return the commutation matrix | |
| 22 ## @tex | |
| 23 ## $K_{m,n}$ | |
| 24 ## @end tex | |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
25 ## @ifnottex |
| 3321 | 26 ## K(m,n) |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
27 ## @end ifnottex |
| 3321 | 28 ## which is the unique |
| 29 ## @tex | |
| 30 ## $m n \times m n$ | |
| 31 ## @end tex | |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
32 ## @ifnottex |
| 3321 | 33 ## @var{m}*@var{n} by @var{m}*@var{n} |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
34 ## @end ifnottex |
| 3321 | 35 ## matrix such that |
| 36 ## @tex | |
| 37 ## $K_{m,n} \cdot {\rm vec} (A) = {\rm vec} (A^T)$ | |
| 38 ## @end tex | |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
39 ## @ifnottex |
| 3499 | 40 ## @math{K(m,n) * vec(A) = vec(A')} |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
41 ## @end ifnottex |
| 3321 | 42 ## for all |
| 43 ## @tex | |
| 44 ## $m\times n$ | |
| 45 ## @end tex | |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
46 ## @ifnottex |
| 3499 | 47 ## @math{m} by @math{n} |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
48 ## @end ifnottex |
| 3321 | 49 ## matrices |
| 50 ## @tex | |
| 51 ## $A$. | |
| 52 ## @end tex | |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
53 ## @ifnottex |
| 3499 | 54 ## @math{A}. |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
55 ## @end ifnottex |
| 3426 | 56 ## |
| 3321 | 57 ## If only one argument @var{m} is given, |
| 58 ## @tex | |
| 59 ## $K_{m,m}$ | |
| 60 ## @end tex | |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
61 ## @ifnottex |
| 3499 | 62 ## @math{K(m,m)} |
|
8517
81d6ab3ac93c
Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents:
7017
diff
changeset
|
63 ## @end ifnottex |
| 3321 | 64 ## is returned. |
| 3426 | 65 ## |
|
10791
3140cb7a05a1
Add spellchecker scripts for Octave and run spellcheck of documentation
Rik <octave@nomad.inbox5.com>
parents:
9211
diff
changeset
|
66 ## See Magnus and Neudecker (1988), @cite{Matrix Differential Calculus with |
|
3140cb7a05a1
Add spellchecker scripts for Octave and run spellcheck of documentation
Rik <octave@nomad.inbox5.com>
parents:
9211
diff
changeset
|
67 ## Applications in Statistics and Econometrics.} |
| 3321 | 68 ## @end deftypefn |
| 2540 | 69 |
| 5428 | 70 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 2540 | 71 ## Created: 8 May 1995 |
| 72 ## Adapted-By: jwe | |
| 73 | |
| 74 function k = commutation_matrix (m, n) | |
| 3426 | 75 |
| 2540 | 76 if (nargin < 1 || nargin > 2) |
| 6046 | 77 print_usage (); |
| 2540 | 78 else |
| 4030 | 79 if (! (isscalar (m) && m == round (m) && m > 0)) |
|
11472
1740012184f9
Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
Rik <octave@nomad.inbox5.com>
parents:
10791
diff
changeset
|
80 error ("commutation_matrix: M must be a positive integer"); |
| 2540 | 81 endif |
| 82 if (nargin == 1) | |
| 83 n = m; | |
| 4030 | 84 elseif (! (isscalar (n) && n == round (n) && n > 0)) |
|
11472
1740012184f9
Use uppercase for variable names in error() strings to match Info documentation. Only m-files done.
Rik <octave@nomad.inbox5.com>
parents:
10791
diff
changeset
|
85 error ("commutation_matrix: N must be a positive integer"); |
| 2540 | 86 endif |
| 87 endif | |
| 3426 | 88 |
| 2540 | 89 ## It is clearly possible to make this a LOT faster! |
| 90 k = zeros (m * n, m * n); | |
| 91 for i = 1 : m | |
| 92 for j = 1 : n | |
| 93 k ((i - 1) * n + j, (j - 1) * m + i) = 1; | |
| 94 endfor | |
| 95 endfor | |
| 96 | |
| 97 endfunction |