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annotate scripts/statistics/base/cov.m @ 20818:9d2023d1a63c

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binoinv.m: Implement binary search algorithm for 28X performance increase (bug #34363). * binoinv.m: Call new functions scalar_binoinv or vector_binoinv to calculate binoinv. If there are still uncalculated values then call bin_search_binoinv to perform binary search for remaining values. Add more BIST tests. * binoinv.m (scalar_binoinv): New subfunction to calculate binoinv for scalar x. Stops when x > 1000. * binoinv.m (vector_binoinv): New subfunction to calculate binoinv for scalar x. Stops when x > 1000.
author Lachlan Andrew <lachlanbis@gmail.com>
date Sun, 11 Oct 2015 19:49:40 -0700
parents d9341b422488
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 ## Copyright (C) 1995-2015 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 ##
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59 ## Compatibility Note:: Octave always computes the covariance matrix.
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60 ## For two inputs, however, @sc{matlab} will calculate
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61 ## @code{cov (@var{x}(:), @var{y}(:))} whenever the number of elements in
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62 ## @var{x} and @var{y} are equal. This will result in a scalar rather than
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63 ## a matrix output. Code relying on this odd definition will need to be
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64 ## changed when running in Octave.
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65 ## @seealso{corr}
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66 ## @end deftypefn
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67
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68 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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69 ## Description: Compute covariances
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70
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71 function c = cov (x, y = [], opt = 0)
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72
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73 if (nargin < 1 || nargin > 3)
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74 print_usage ();
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75 endif
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76
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77 if ( ! (isnumeric (x) || islogical (x))
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78 || ! (isnumeric (y) || islogical (y)))
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79 error ("cov: X and Y must be numeric matrices or vectors");
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80 endif
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81
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82 if (ndims (x) != 2 || ndims (y) != 2)
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83 error ("cov: X and Y must be 2-D matrices or vectors");
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84 endif
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85
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86 if (nargin == 2 && isscalar (y))
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87 opt = y;
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88 endif
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89
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90 if (opt != 0 && opt != 1)
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91 error ("cov: normalization OPT must be 0 or 1");
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92 endif
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93
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94 ## Special case, scalar has zero covariance
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95 if (isscalar (x))
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96 if (isa (x, "single"))
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97 c = single (0);
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98 else
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99 c = 0;
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100 endif
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101 return;
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102 endif
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103
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104 if (isrow (x))
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105 x = x.';
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106 endif
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107 n = rows (x);
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108
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109 if (nargin == 1 || isscalar (y))
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110 x = center (x, 1);
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111 c = conj (x' * x / (n - 1 + opt));
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112 else
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113 if (isrow (y))
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114 y = y.';
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115 endif
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116 if (rows (y) != n)
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117 error ("cov: X and Y must have the same number of observations");
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118 endif
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119 x = center (x, 1);
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120 y = center (y, 1);
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121 c = conj (x' * y / (n - 1 + opt));
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122 endif
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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 = rand (10);
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129 %! cx1 = cov (x);
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130 %! cx2 = cov (x, x);
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131 %! assert (size (cx1) == [10, 10] && size (cx2) == [10, 10]);
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132 %! assert (cx1, cx2, 1e1*eps);
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133
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134 %!test
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135 %! x = [1:3]';
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136 %! y = [3:-1:1]';
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137 %! assert (cov (x, y), -1, 5*eps);
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138 %! assert (cov (x, flipud (y)), 1, 5*eps);
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139 %! assert (cov ([x, y]), [1 -1; -1 1], 5*eps);
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140
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141 %!test
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142 %! x = single ([1:3]');
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143 %! y = single ([3:-1:1]');
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144 %! assert (cov (x, y), single (-1), 5*eps);
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145 %! assert (cov (x, flipud (y)), single (1), 5*eps);
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146 %! assert (cov ([x, y]), single ([1 -1; -1 1]), 5*eps);
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147
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148 %!test
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149 %! x = [1:5];
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150 %! c = cov (x);
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151 %! assert (isscalar (c));
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152 %! assert (c, 2.5);
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153
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154 %!assert (cov (5), 0)
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155 %!assert (cov (single (5)), single (0))
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156
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157 %!test
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158 %! x = [1:5];
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159 %! c = cov (x, 0);
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160 %! assert (c, 2.5);
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161 %! c = cov (x, 1);
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162 %! assert (c, 2);
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163
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164 ## Test input validation
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165 %!error cov ()
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166 %!error cov (1, 2, 3, 4)
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167 %!error cov ([1; 2], ["A", "B"])
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168 %!error cov (ones (2,2,2))
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169 %!error cov (ones (2,2), ones (2,2,2))
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170 %!error cov (1, 3)
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171 %!error cov (ones (2,2), ones (3,2))
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172