Mercurial > octave
annotate scripts/statistics/base/cov.m @ 22226:9a0e30e24b9b
Calculate cov as Matlab does, not as its conjugate (bug #48315).
* NEWS: Announce change.
* cov.m: Remove "conj" from calculation of output. Update compatibility note
to explain what Matlab actually does.
author | Lachlan Andrew <lachlanbis@gmail.com> |
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date | Thu, 30 Jun 2016 18:30:26 +1000 |
parents | 516bb87ea72e |
children | 9fc91bb2aec3 |
rev | line source |
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19697
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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 |
3200 | 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 ## | |
3200 | 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 |
3367 | 19 ## -*- texinfo -*- |
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20 ## @deftypefn {} {} cov (@var{x}) |
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21 ## @deftypefnx {} {} cov (@var{x}, @var{opt}) |
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22 ## @deftypefnx {} {} cov (@var{x}, @var{y}) |
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23 ## @deftypefnx {} {} cov (@var{x}, @var{y}, @var{opt}) |
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24 ## Compute the covariance matrix. |
6754 | 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 |
3367 | 28 ## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th |
6754 | 29 ## variable in @var{x} and the @var{j}-th variable in @var{y}. |
30 ## @tex | |
31 ## $$ | |
32 ## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y}) | |
33 ## $$ | |
34 ## where $\bar{x}$ and $\bar{y}$ are the mean values of $x$ and $y$. | |
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 ## |
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59 ## Compatibility Note:: Octave always treats rows of @var{x} and @var{y} |
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60 ## as multivariate random variables. |
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61 ## For two inputs, however, @sc{matlab} treats @var{x} and @var{y} as two |
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62 ## univariate distributions regardless of their shapes, and will calculate |
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63 ## @code{cov ([@var{x}(:), @var{y}(:)])} whenever the number of elements in |
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64 ## @var{x} and @var{y} are equal. This will result in a 2x2 matrix. |
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65 ## Code relying on @sc{Matlab}'s definition will need to be |
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66 ## changed when running in Octave. |
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67 ## @seealso{corr} |
3367 | 68 ## @end deftypefn |
3200 | 69 |
5428 | 70 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
3456 | 71 ## Description: Compute covariances |
3200 | 72 |
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73 function c = cov (x, y = [], opt = 0) |
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74 |
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75 if (nargin < 1 || nargin > 3) |
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76 print_usage (); |
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77 endif |
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78 |
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79 if ( ! (isnumeric (x) || islogical (x)) |
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80 || ! (isnumeric (y) || islogical (y))) |
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81 error ("cov: X and Y must be numeric matrices or vectors"); |
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82 endif |
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84 if (ndims (x) != 2 || ndims (y) != 2) |
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85 error ("cov: X and Y must be 2-D matrices or vectors"); |
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86 endif |
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87 |
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88 if (nargin == 2 && isscalar (y)) |
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89 opt = y; |
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90 endif |
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91 |
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92 if (opt != 0 && opt != 1) |
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93 error ("cov: normalization OPT must be 0 or 1"); |
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94 endif |
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95 |
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96 ## Special case, scalar has zero covariance |
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97 if (isscalar (x)) |
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98 if (isa (x, "single")) |
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99 c = single (0); |
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100 else |
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101 c = 0; |
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102 endif |
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103 return; |
3200 | 104 endif |
105 | |
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106 if (isrow (x)) |
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107 x = x.'; |
3200 | 108 endif |
109 n = rows (x); | |
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110 |
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111 if (nargin == 1 || isscalar (y)) |
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112 x = center (x, 1); |
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113 c = x' * x / (n - 1 + opt); |
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114 else |
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115 if (isrow (y)) |
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116 y = y.'; |
3200 | 117 endif |
118 if (rows (y) != n) | |
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119 error ("cov: X and Y must have the same number of observations"); |
3200 | 120 endif |
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121 x = center (x, 1); |
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122 y = center (y, 1); |
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123 c = x' * y / (n - 1 + opt); |
3200 | 124 endif |
125 | |
126 endfunction | |
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128 |
7411 | 129 %!test |
130 %! x = rand (10); | |
131 %! cx1 = cov (x); | |
132 %! cx2 = cov (x, x); | |
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133 %! assert (size (cx1) == [10, 10] && size (cx2) == [10, 10]); |
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134 %! assert (cx1, cx2, 1e1*eps); |
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135 |
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136 %!test |
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137 %! x = [1:3]'; |
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138 %! y = [3:-1:1]'; |
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139 %! assert (cov (x, y), -1, 5*eps); |
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140 %! assert (cov (x, flipud (y)), 1, 5*eps); |
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141 %! assert (cov ([x, y]), [1 -1; -1 1], 5*eps); |
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142 |
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143 %!test |
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144 %! x = single ([1:3]'); |
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145 %! y = single ([3:-1:1]'); |
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146 %! assert (cov (x, y), single (-1), 5*eps); |
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147 %! assert (cov (x, flipud (y)), single (1), 5*eps); |
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148 %! assert (cov ([x, y]), single ([1 -1; -1 1]), 5*eps); |
7411 | 149 |
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150 %!test |
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151 %! x = [1:5]; |
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152 %! c = cov (x); |
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153 %! assert (isscalar (c)); |
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154 %! assert (c, 2.5); |
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155 |
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156 %!assert (cov (5), 0) |
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157 %!assert (cov (single (5)), single (0)) |
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158 |
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159 %!test |
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160 %! x = [1:5]; |
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161 %! c = cov (x, 0); |
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162 %! assert (c, 2.5); |
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163 %! c = cov (x, 1); |
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164 %! assert (c, 2); |
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166 ## Test input validation |
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167 %!error cov () |
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168 %!error cov (1, 2, 3, 4) |
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169 %!error cov ([1; 2], ["A", "B"]) |
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170 %!error cov (ones (2,2,2)) |
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171 %!error cov (ones (2,2), ones (2,2,2)) |
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172 %!error cov (1, 3) |
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173 %!error cov (ones (2,2), ones (3,2)) |
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174 |