Mercurial > octave-nkf
annotate scripts/linear-algebra/duplication_matrix.m @ 20266:83792dd9bcc1
Use in-place operators in m-files where possible.
* scripts/audio/@audioplayer/set.m, scripts/audio/@audiorecorder/set.m,
scripts/audio/mu2lin.m, scripts/elfun/cosd.m, scripts/general/del2.m,
scripts/general/profexplore.m, scripts/general/quadl.m, scripts/general/rat.m,
scripts/general/rotdim.m, scripts/help/get_first_help_sentence.m,
scripts/help/private/__strip_html_tags__.m, scripts/image/cubehelix.m,
scripts/io/textread.m, scripts/linear-algebra/duplication_matrix.m,
scripts/linear-algebra/housh.m, scripts/linear-algebra/krylov.m,
scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m,
scripts/linear-algebra/onenormest.m, scripts/optimization/fminsearch.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/qp.m,
scripts/plot/appearance/annotation.m, scripts/plot/appearance/axis.m,
scripts/plot/appearance/legend.m, scripts/plot/appearance/specular.m,
scripts/plot/draw/colorbar.m, scripts/plot/draw/hist.m,
scripts/plot/draw/plotmatrix.m, scripts/plot/draw/private/__stem__.m,
scripts/plot/util/__actual_axis_position__.m,
scripts/plot/util/__gnuplot_drawnow__.m, scripts/plot/util/findobj.m,
scripts/plot/util/print.m, scripts/plot/util/private/__go_draw_axes__.m,
scripts/plot/util/private/__print_parse_opts__.m, scripts/plot/util/rotate.m,
scripts/polynomial/pchip.m, scripts/polynomial/polyaffine.m,
scripts/polynomial/polyder.m, scripts/polynomial/private/__splinefit__.m,
scripts/polynomial/residue.m, scripts/signal/arch_fit.m,
scripts/signal/arch_rnd.m, scripts/signal/bartlett.m,
scripts/signal/blackman.m, scripts/signal/freqz.m, scripts/signal/hamming.m,
scripts/signal/hanning.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/signal/stft.m,
scripts/sparse/bicgstab.m, scripts/sparse/cgs.m,
scripts/sparse/private/__sprand_impl__.m, scripts/sparse/qmr.m,
scripts/sparse/sprandsym.m, scripts/sparse/svds.m, scripts/specfun/legendre.m,
scripts/special-matrix/gallery.m, scripts/statistics/base/gls.m,
scripts/statistics/models/logistic_regression.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/wilcoxon_test.m,
scripts/time/datevec.m:
Use in-place operators in m-files where possible.
author | Rik <rik@octave.org> |
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date | Tue, 26 May 2015 21:07:42 -0700 |
parents | 03b9d17a2d95 |
children |
rev | line source |
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maint: Update copyright notices for 2015.
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1995-2015 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 |
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26 ## @nospell{@math{Dn}} |
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27 ## @end ifnottex |
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28 ## which is the unique |
3321 | 29 ## @tex |
30 ## $n^2 \times n(n+1)/2$ | |
31 ## @end tex | |
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32 ## @ifnottex |
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33 ## @math{n^2} by @math{n*(n+1)/2} |
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34 ## @end ifnottex |
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35 ## matrix such that |
3321 | 36 ## @tex |
37 ## $D_n * {\rm vech} (A) = {\rm vec} (A)$ | |
38 ## @end tex | |
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39 ## @ifnottex |
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40 ## @nospell{@math{Dn vech (A) = vec (A)}} |
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41 ## @end ifnottex |
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42 ## for all symmetric |
3321 | 43 ## @tex |
44 ## $n \times n$ | |
45 ## @end tex | |
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46 ## @ifnottex |
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47 ## @math{n} by @math{n} |
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48 ## @end ifnottex |
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49 ## matrices |
3321 | 50 ## @tex |
51 ## $A$. | |
52 ## @end tex | |
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53 ## @ifnottex |
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54 ## @math{A}. |
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55 ## @end ifnottex |
3426 | 56 ## |
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57 ## See @nospell{Magnus and Neudecker} (1988), @cite{Matrix Differential |
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58 ## Calculus with 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 | |
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71 if (! (isscalar (n) && n > 0 && n == fix (n))) |
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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 | |
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80 d((j - 1) * n + j, count + j) = 1; |
2540 | 81 for i = (j + 1) : n |
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82 d((j - 1) * n + i, count + i) = 1; |
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83 d((i - 1) * n + j, count + i) = 1; |
2540 | 84 endfor |
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85 count += n - j; |
2540 | 86 endfor |
87 | |
88 endfunction | |
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89 |
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90 |
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91 %!test |
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92 %! N = 2; |
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93 %! A = rand (N); |
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94 %! B = A * A'; |
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95 %! C = A + A'; |
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96 %! D = duplication_matrix (N); |
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97 %! assert (D * vech (B), vec (B), 1e-6); |
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98 %! assert (D * vech (C), vec (C), 1e-6); |
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99 |
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100 %!test |
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101 %! N = 3; |
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102 %! A = rand (N); |
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103 %! B = A * A'; |
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104 %! C = A + A'; |
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105 %! D = duplication_matrix (N); |
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106 %! assert (D * vech (B), vec (B), 1e-6); |
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107 %! assert (D * vech (C), vec (C), 1e-6); |
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108 |
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109 %!test |
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110 %! N = 4; |
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111 %! A = rand (N); |
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112 %! B = A * A'; |
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113 %! C = A + A'; |
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114 %! D = duplication_matrix (N); |
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115 %! assert (D * vech (B), vec (B), 1e-6); |
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116 %! assert (D * vech (C), vec (C), 1e-6); |
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117 |
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118 %!error duplication_matrix () |
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119 %!error duplication_matrix (0.5) |
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120 %!error duplication_matrix (-1) |
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121 %!error duplication_matrix (ones (1,4)) |
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122 |