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annotate scripts/linear-algebra/commutation_matrix.m @ 14363:f3d52523cde1
Use Octave coding conventions in all m-file %!test blocks
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get_first_help_sentence.m, help.m, type.m, unimplemented.m, which.m, imread.m,
imwrite.m, dlmwrite.m, fileread.m, is_valid_file_id.m, strread.m, textread.m,
textscan.m, commutation_matrix.m, cond.m, condest.m, cross.m,
duplication_matrix.m, expm.m, housh.m, isdefinite.m, ishermitian.m,
issymmetric.m, logm.m, normest.m, null.m, onenormest.m, orth.m, planerot.m,
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fullfile.m, getfield.m, gzip.m, info.m, inputname.m, isappdata.m, isdeployed.m,
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warning_ids.m, xor.m, fminbnd.m, fsolve.m, fzero.m, lsqnonneg.m, optimset.m,
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fftshift.m, freqz.m, hamming.m, hanning.m, ifftshift.m, sinc.m, sinetone.m,
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statistics.m, std.m, table.m, var.m, zscore.m, betacdf.m, betainv.m, betapdf.m,
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expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m,
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hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m,
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tcdf.m, tinv.m, tpdf.m, trnd.m, unidcdf.m, unidinv.m, unidpdf.m, unidrnd.m,
unifcdf.m, unifinv.m, unifpdf.m, unifrnd.m, wblcdf.m, wblinv.m, wblpdf.m,
wblrnd.m, kolmogorov_smirnov_test.m, kruskal_wallis_test.m, base2dec.m,
bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m,
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strcat.m, strjust.m, strmatch.m, strsplit.m, strtok.m, strtrim.m, strtrunc.m,
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Use Octave coding conventions in all m-file %!test blocks
author | Rik <octave@nomad.inbox5.com> |
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date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 72c96de7a403 |
children | d63878346099 |
rev | line source |
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1 ## Copyright (C) 1995-2012 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 | |
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25 ## @ifnottex |
3321 | 26 ## K(m,n) |
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27 ## @end ifnottex |
3321 | 28 ## which is the unique |
29 ## @tex | |
30 ## $m n \times m n$ | |
31 ## @end tex | |
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32 ## @ifnottex |
3321 | 33 ## @var{m}*@var{n} by @var{m}*@var{n} |
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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 | |
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39 ## @ifnottex |
3499 | 40 ## @math{K(m,n) * vec(A) = vec(A')} |
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41 ## @end ifnottex |
3321 | 42 ## for all |
43 ## @tex | |
44 ## $m\times n$ | |
45 ## @end tex | |
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46 ## @ifnottex |
3499 | 47 ## @math{m} 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 ## |
3321 | 57 ## If only one argument @var{m} is given, |
58 ## @tex | |
59 ## $K_{m,m}$ | |
60 ## @end tex | |
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61 ## @ifnottex |
3499 | 62 ## @math{K(m,m)} |
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63 ## @end ifnottex |
3321 | 64 ## is returned. |
3426 | 65 ## |
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66 ## See Magnus and Neudecker (1988), @cite{Matrix Differential Calculus with |
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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 |
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79 if (! (isscalar (m) && m == fix (m) && m > 0)) |
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80 error ("commutation_matrix: M must be a positive integer"); |
2540 | 81 endif |
82 if (nargin == 1) | |
83 n = m; | |
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84 elseif (! (isscalar (n) && n == fix (n) && n > 0)) |
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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 | |
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98 |
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99 |
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100 %!test |
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101 %! c = commutation_matrix (1,1); |
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102 %! assert (c,1); |
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103 |
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104 %!test |
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105 %! A = rand (3,5); |
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106 %! vc = vec (A); |
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107 %! vr = vec (A'); |
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108 %! c = commutation_matrix (3,5); |
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109 %! assert (c*vc, vr); |
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110 |
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111 %!test |
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112 %! A = rand (4,6); |
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113 %! vc = vec (A); |
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114 %! vr = vec (A'); |
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115 %! c = commutation_matrix (4,6); |
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116 %! assert (c*vc, vr); |
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117 |
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118 %!error <M must be a positive integer> commutation_matrix (0,0) |
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119 %!error <N must be a positive integer> commutation_matrix (1,0) |
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120 %!error <M must be a positive integer> commutation_matrix (0,1) |
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121 |