Mercurial > hg > octave-nkf
annotate scripts/statistics/base/gls.m @ 20441:83792dd9bcc1
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> |
|---|---|
| date | Tue, 26 May 2015 21:07:42 -0700 |
| parents | b0f7ee81d974 |
| children |
| rev | line source |
|---|---|
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1 ## Copyright (C) 1996-2015 John W. Eaton |
| 3200 | 2 ## |
| 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. | |
| 3200 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 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/>. | |
| 3200 | 18 |
| 3381 | 19 ## -*- texinfo -*- |
| 3368 | 20 ## @deftypefn {Function File} {[@var{beta}, @var{v}, @var{r}] =} gls (@var{y}, @var{x}, @var{o}) |
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21 ## Generalized least squares model. |
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22 ## |
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23 ## Perform a generalized least squares estimation for the multivariate model |
| 3368 | 24 ## @tex |
| 25 ## $y = x b + e$ | |
| 26 ## with $\bar{e} = 0$ and cov(vec($e$)) = $(s^2)o$, | |
| 27 ## @end tex | |
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28 ## @ifnottex |
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29 ## @w{@math{y = x*b + e}} with @math{mean (e) = 0} and |
| 3499 | 30 ## @math{cov (vec (e)) = (s^2) o}, |
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31 ## @end ifnottex |
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32 ## where |
| 3426 | 33 ## @tex |
| 3368 | 34 ## $y$ is a $t \times p$ matrix, $x$ is a $t \times k$ matrix, $b$ is a $k |
| 35 ## \times p$ matrix, $e$ is a $t \times p$ matrix, and $o$ is a $tp \times | |
| 36 ## tp$ matrix. | |
| 37 ## @end tex | |
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38 ## @ifnottex |
| 3499 | 39 ## @math{y} is a @math{t} by @math{p} matrix, @math{x} is a @math{t} by |
| 40 ## @math{k} matrix, @math{b} is a @math{k} by @math{p} matrix, @math{e} | |
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41 ## is a @math{t} by @math{p} matrix, and @math{o} is a @math{t*p} by |
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42 ## @math{t*p} matrix. |
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43 ## @end ifnottex |
| 3426 | 44 ## |
| 3368 | 45 ## @noindent |
| 3499 | 46 ## Each row of @var{y} and @var{x} is an observation and each column a |
| 47 ## variable. The return values @var{beta}, @var{v}, and @var{r} are | |
| 48 ## defined as follows. | |
| 3426 | 49 ## |
| 3368 | 50 ## @table @var |
| 51 ## @item beta | |
| 3499 | 52 ## The GLS estimator for @math{b}. |
| 3426 | 53 ## |
| 3368 | 54 ## @item v |
| 3499 | 55 ## The GLS estimator for @math{s^2}. |
| 3426 | 56 ## |
| 3368 | 57 ## @item r |
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58 ## The matrix of GLS residuals, @math{r = y - x*beta}. |
| 3368 | 59 ## @end table |
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60 ## @seealso{ols} |
| 3368 | 61 ## @end deftypefn |
| 3200 | 62 |
| 63 ## Author: Teresa Twaroch <twaroch@ci.tuwien.ac.at> | |
| 64 ## Created: May 1993 | |
| 65 ## Adapted-By: jwe | |
| 66 | |
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67 function [beta, v, r] = gls (y, x, o) |
| 3200 | 68 |
| 69 if (nargin != 3) | |
| 6046 | 70 print_usage (); |
| 3200 | 71 endif |
| 72 | |
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73 if (! (isnumeric (x) && isnumeric (y) && isnumeric (o))) |
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74 error ("gls: X, Y, and O must be numeric matrices or vectors"); |
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75 endif |
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76 |
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77 if (ndims (x) != 2 || ndims (y) != 2 || ndims (o) != 2) |
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78 error ("gls: X, Y and O must be 2-D matrices or vectors"); |
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79 endif |
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80 |
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81 [rx, cx] = size (x); |
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82 [ry, cy] = size (y); |
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83 [ro, co] = size (o); |
| 3200 | 84 if (rx != ry) |
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85 error ("gls: number of rows of X and Y must be equal"); |
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86 endif |
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87 if (! issquare (o) || ro != ry*cy) |
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88 error ("gls: matrix O must be square matrix with rows = rows (Y) * cols (Y)"); |
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89 endif |
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90 |
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91 if (isinteger (x)) |
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92 x = double (x); |
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93 endif |
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94 if (isinteger (y)) |
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95 y = double (y); |
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96 endif |
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97 if (isinteger (o)) |
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98 o = double (o); |
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99 endif |
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100 |
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101 ## Start of algorithm |
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102 o ^= -1/2; |
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103 z = kron (eye (cy), x); |
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104 z = o * z; |
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105 y1 = o * reshape (y, ry*cy, 1); |
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106 u = z' * z; |
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107 r = rank (u); |
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108 |
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109 if (r == cx*cy) |
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110 b = inv (u) * z' * y1; |
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111 else |
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112 b = pinv (z) * y1; |
| 3200 | 113 endif |
| 114 | |
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115 beta = reshape (b, cx, cy); |
| 3200 | 116 |
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117 if (isargout (2) || isargout (3)) |
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118 r = y - x * beta; |
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119 if (isargout (2)) |
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120 v = (reshape (r, ry*cy, 1))' * (o^2) * reshape (r, ry*cy, 1) / (rx*cy - r); |
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121 endif |
| 3200 | 122 endif |
| 123 | |
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124 endfunction |
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125 |
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126 |
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127 %!test |
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128 %! x = [1:5]'; |
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129 %! y = 3*x + 2; |
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130 %! x = [x, ones(5,1)]; |
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131 %! o = diag (ones (5,1)); |
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132 %! assert (gls (y,x,o), [3; 2], 50*eps); |
| 3200 | 133 |
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134 ## Test input validation |
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135 %!error gls () |
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136 %!error gls (1) |
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137 %!error gls (1, 2) |
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138 %!error gls (1, 2, 3, 4) |
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139 %!error gls ([true, true], [1, 2], ones (2)) |
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140 %!error gls ([1, 2], [true, true], ones (2)) |
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141 %!error gls ([1, 2], [1, 2], true (2)) |
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142 %!error gls (ones (2,2,2), ones (2,2), ones (4,4)) |
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143 %!error gls (ones (2,2), ones (2,2,2), ones (4,4)) |
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144 %!error gls (ones (2,2), ones (2,2), ones (4,4,4)) |
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146 %!error gls (ones (2,2), ones (2,2), ones (2,2)) |
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147 |