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update copyright notices
author John W. Eaton <jwe@octave.org>
date Fri, 14 Jan 2011 05:47:45 -0500
parents e151e23f73bc
children c792872f8942
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11523
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John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1995-2011 Kurt Hornik
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} cov (@var{x})
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21 ## @deftypefnx {Function File} {} cov (@var{x}, @var{opt})
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22 ## @deftypefnx {Function File} {} cov (@var{x}, @var{y})
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23 ## @deftypefnx {Function File} {} cov (@var{x}, @var{y}, @var{opt})
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24 ## Compute the covariance matrix.
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25 ##
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26 ## If each row of @var{x} and @var{y} is an observation, and each column is
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27 ## a variable, then the @w{(@var{i}, @var{j})-th} entry of
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28 ## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th
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29 ## variable in @var{x} and the @var{j}-th variable in @var{y}.
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30 ## @tex
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31 ## $$
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32 ## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y})
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33 ## $$
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34 ## where $\bar{x}$ and $\bar{y}$ are the mean values of $x$ and $y$.
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35 ## @end tex
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36 ## @ifnottex
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37 ##
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38 ## @example
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39 ## cov (x) = 1/N-1 * SUM_i (x(i) - mean(x)) * (y(i) - mean(y))
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40 ## @end example
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41 ##
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42 ## @end ifnottex
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43 ##
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44 ## If called with one argument, compute @code{cov (@var{x}, @var{x})}, the
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45 ## covariance between the columns of @var{x}.
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46 ##
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47 ## The argument @var{opt} determines the type of normalization to use.
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48 ## Valid values are
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49 ##
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50 ## @table @asis
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51 ## @item 0:
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52 ## normalize with @math{N-1}, provides the best unbiased estimator of the
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53 ## covariance [default]
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54 ##
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55 ## @item 1:
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56 ## normalize with @math{N}, this provides the second moment around the mean
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57 ## @end table
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58 ## @seealso{corrcoef, cor}
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59 ## @end deftypefn
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60
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61 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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62 ## Description: Compute covariances
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63
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64 function c = cov (x, y = [], opt = 0)
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65
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66 if (nargin < 1 || nargin > 3)
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67 print_usage ();
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68 endif
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69
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70 if (! (isnumeric (x) && isnumeric (y)))
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71 error ("cov: X and Y must be numeric matrices or vectors");
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72 endif
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73
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74 if (ndims (x) != 2 || ndims (y) != 2)
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75 error ("cov: X and Y must be 2-D matrices or vectors");
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76 endif
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77
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78 if (nargin == 2 && isscalar(y))
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79 opt = y;
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80 endif
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81
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82 if (opt != 0 && opt != 1)
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83 error ("cov: normalization OPT must be 0 or 1");
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84 endif
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85
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86 if (isscalar (x))
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87 c = 0;
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88 return;
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89 endif
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90
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91 if (rows (x) == 1)
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92 x = x';
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93 endif
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94 n = rows (x);
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95
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96 if (nargin == 1 || isscalar(y))
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97 x = center (x, 1);
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98 c = conj (x' * x / (n - 1 + opt));
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99 else
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100 if (rows (y) == 1)
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101 y = y';
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102 endif
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103 if (rows (y) != n)
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104 error ("cov: X and Y must have the same number of observations");
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105 endif
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106 x = center (x, 1);
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107 y = center (y, 1);
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108 c = conj (x' * y / (n - 1 + opt));
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109 endif
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110
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111 endfunction
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112
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113 %!test
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114 %! x = rand (10);
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115 %! cx1 = cov (x);
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116 %! cx2 = cov (x, x);
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117 %! assert(size (cx1) == [10, 10] && size (cx2) == [10, 10] && norm(cx1-cx2) < 1e1*eps);
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118
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119 %!test
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120 %! x = [1:5];
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121 %! c = cov (x);
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122 %! assert(isscalar (c));
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123 %! assert(c, 2.5);
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124
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125 %!test
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126 %! x = [1:5];
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127 %! c = cov (x, 0);
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128 %! assert(c, 2.5);
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129 %! c = cov (x, 1);
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130 %! assert(c, 2);
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131
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132 %!assert(cov (5), 0);
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133
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134 %% Test input validation
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135 %!error cov ();
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136 %!error cov (1, 2, 3, 4);
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137 %!error cov ([true, true]);
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138 %!error cov ([1, 2], [true, true]);
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139 %!error cov (ones (2,2,2));
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140 %!error cov (ones (2,2), ones (2,2,2));
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141 %!error cov (1, 3);
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 9245
diff changeset
142 %!error cov (ones (2,2), ones (3,2));
e151e23f73bc Overhaul base statistics functions and documentation of same.
Rik <octave@nomad.inbox5.com>
parents: 9245
diff changeset
143