Mercurial > octave
annotate scripts/statistics/ranks.m @ 26077:31b443b5a6c1
ranks.m: Overhaul function for performance (25X) and addition of tie-breaking (bug #36372).
* NEWS: Announce overhaul of ranks function and tie-breaking.
* contributors.in: Add Dave Goel to list of contributors.
* ranks.m: Rewrite docstring to include new options. Redo input validation to
support three arguments. Use switch statement on RTYPE to call appropriate
subfunction for ranking with possible tie values. Add new BIST tests for
tie-breaking functionality. Redo input validation BIST tests.
* ranks.m (_competition, _modified, _dense): Three new subfunctions to break
ties according to different algorithms.
author | Dave Goel <deego3@gmail.com> |
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date | Thu, 15 Nov 2018 11:35:54 -0800 |
parents | 6652d3823428 |
children | 00f796120a6d |
rev | line source |
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1 ## Copyright (C) 1995-2018 Kurt Hornik |
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2 ## Copyright (C) 2012 Dave Goel |
3426 | 3 ## |
3922 | 4 ## This file is part of Octave. |
5 ## | |
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6 ## Octave is free software: you can redistribute it and/or modify it |
3922 | 7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation, either version 3 of the License, or |
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9 ## (at your option) any later version. |
3426 | 10 ## |
3922 | 11 ## Octave is distributed in the hope that it will be useful, but |
3200 | 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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14 ## GNU General Public License for more details. |
3426 | 15 ## |
3200 | 16 ## You should have received a copy of the GNU General Public License |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <https://www.gnu.org/licenses/>. |
3200 | 19 |
3453 | 20 ## -*- texinfo -*- |
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21 ## @deftypefn {} {} ranks (@var{x}) |
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22 ## @deftypefnx {} {} ranks (@var{x}, @var{dim}) |
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23 ## @deftypefnx {} {} ranks (@var{x}, @var{dim}, @var{rtype}) |
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24 ## Return the ranks (in the sense of order statistics) of @var{x} along the |
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25 ## first non-singleton dimension adjusted for ties. |
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26 ## |
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27 ## If the optional @var{dim} argument is given, operate along this dimension. |
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28 ## |
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29 ## The optional parameter @var{rtype} determines how ties are handled. All |
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30 ## examples below assume an input of @code{[ 1, 2, 2, 4 ]}. |
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31 ## |
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32 ## @table @asis |
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33 ## @item 0 or @qcode{"fractional"} (default) for fractional ranking (1, 2.5, |
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34 ## 2.5, 4); |
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35 ## |
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36 ## @item 1 or @qcode{"competition"} for competition ranking (1, 2, 2, 4); |
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37 ## |
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38 ## @item 2 or @qcode{"modified"} for modified competition ranking (1, 3, 3, 4); |
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39 ## |
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40 ## @item 3 or @qcode{"ordinal"} for ordinal ranking (1, 2, 3, 4); |
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41 ## |
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42 ## @item 4 or @qcode{"dense"} for dense ranking (1, 2, 2, 3). |
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43 ## @end table |
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44 ## |
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45 ## @seealso{spearman, kendall} |
3453 | 46 ## @end deftypefn |
3426 | 47 |
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48 function y = ranks (x, dim, rtype = 0) |
3200 | 49 |
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50 if (nargin < 1 || nargin > 3) |
6046 | 51 print_usage (); |
4885 | 52 endif |
3426 | 53 |
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54 if (! (isnumeric (x) || islogical (x))) |
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55 error ("ranks: X must be a numeric vector or matrix"); |
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56 endif |
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57 |
4885 | 58 nd = ndims (x); |
59 sz = size (x); | |
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60 |
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61 if (nargin < 2 || isempty (dim)) |
4886 | 62 ## Find the first non-singleton dimension. |
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63 (dim = find (sz > 1, 1)) || (dim = 1); |
4885 | 64 else |
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65 if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) |
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66 error ("ranks: DIM must be an integer and a valid dimension"); |
4885 | 67 endif |
3200 | 68 endif |
3426 | 69 |
4886 | 70 if (sz(dim) == 1) |
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71 y = ones (sz); # dimension DIM is singleton, so all are ranked first. |
4885 | 72 else |
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73 ## The algorithm works only on dim = 1, so permute if necessary. |
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74 ## FIXME: Most all functions now accept a dim argument. |
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75 ## Would it be faster not to permute and use the dim argument |
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76 ## to sort, find, cumsum, etc.? |
4885 | 77 if (dim != 1) |
78 perm = [1 : nd]; | |
4886 | 79 perm(1) = dim; |
80 perm(dim) = 1; | |
4885 | 81 x = permute (x, perm); |
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82 sz = size (x); |
4885 | 83 endif |
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84 |
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85 [sx, ids] = sort (x); # sx is sorted x. |
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86 lin = repmat ((1:rows (x))', [1, sz(2:end)]); # linearly increasing array. |
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87 |
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88 switch (rtype) |
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89 case {0, "fractional"}; |
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90 lin = (_competition (lin, sx, sz) + _modified (lin, sx, sz)) / 2; |
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91 case {1, "competition"}; |
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92 lin = _competition (lin, sx, sz); |
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93 case {2, "modified"}; |
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94 lin = _modified (lin, sx, sz); |
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95 case {3, "ordinal"}; |
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96 ## no processing needed here. |
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97 case {4, "dense"}; |
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98 lin = _dense (lin, sx, sz); |
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99 otherwise |
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100 if (! ischar (rtype)) |
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101 rtype = num2str (rtype); |
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102 end |
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103 error ("ranks: unknown RTYPE '%s'", rtype); |
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104 endswitch |
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105 |
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106 y = NaN (size (lin)); |
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107 |
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108 ## Offsets to map indices into each column to indices into the linear array. |
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109 ## FIXME: Would sub2ind be faster here? |
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110 idf = zeros (sz); |
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111 idf(1, :) = 0 : sz(1) : (numel (ids)-1); |
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112 idf(:, :) = repmat (idf(1, :), [sz(1), ones(1,length(sz)-1)]); |
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113 y(ids + idf) = lin; |
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114 |
4885 | 115 if (dim != 1) |
116 y = permute (y, perm); | |
117 endif | |
3200 | 118 endif |
3426 | 119 |
3200 | 120 endfunction |
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121 |
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122 function linnew = _dense (lin, sx, sz) |
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123 infvec = -Inf ([1, sz(2:end)]); |
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124 fnewp = logical (diff ([infvec; sx])); |
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125 linnew = cumsum (fnewp, 1); |
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126 endfunction |
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127 |
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128 function linnew = _competition (lin, sx, sz) |
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129 ## Stop increasing lin when sx does not increase. Otherwise, same as before. |
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130 infvec = -Inf ([1, sz(2:end)]); |
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131 fnewp = find (diff ([infvec; sx])); |
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132 linnew = zeros (size (lin)); |
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133 linnew(fnewp) = lin(fnewp); |
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134 linnew = cummax (linnew, 1); |
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135 endfunction |
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136 |
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137 function linnew = _modified (lin, sx, sz) |
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138 ## Traverse lin backwards. Stop decreasing it when sx doesn't decrease. |
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139 infvec = Inf ([1, sz(2:end)]); |
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140 fnewp = find (diff ([sx; infvec])); |
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141 linnew = Inf (size (lin)); |
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142 linnew(fnewp) = lin(fnewp); |
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143 linnew = flip (cummin (flip (linnew, 1)), 1); |
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144 endfunction |
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145 |
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146 |
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147 %!assert (ranks (1:2:10), 1:5) |
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148 %!assert (ranks (10:-2:1), 5:-1:1) |
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149 %!assert (ranks ([2, 1, 2, 4]), [2.5, 1, 2.5, 4]) |
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150 %!assert (ranks (ones (1, 5)), 3*ones (1, 5)) |
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151 %!assert (ranks (1e6*ones (1, 5)), 3*ones (1, 5)) |
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152 %!assert (ranks (rand (1, 5), 1), ones (1, 5)) |
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153 |
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154 %!assert (ranks ([1, 2, 2, 4], [], "fractional"), [1, 2.5, 2.5, 4]) |
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155 %!assert (ranks ([1, 2, 2, 4], [], "competition"), [1, 2, 2, 4]) |
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156 %!assert (ranks ([1, 2, 2, 4], [], "modified"), [1, 3, 3, 4]) |
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157 %!assert (ranks ([1, 2, 2, 4], [], "ordinal"), [1, 2, 3, 4]) |
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158 %!assert (ranks ([1, 2, 2, 4], [], "dense"), [1, 2, 2, 3]) |
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159 |
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160 ## Test input validation |
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161 %!error ranks () |
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162 %!error ranks (1, 2, 3, 4) |
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163 %!error <X must be a numeric vector or matrix> ranks ({1, 2}) |
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164 %!error <X must be a numeric vector or matrix> ranks (['A'; 'B']) |
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165 %!error <DIM must be an integer> ranks (1, 1.5) |
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166 %!error <DIM must be .* a valid dimension> ranks (1, 0) |
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167 %!error <unknown RTYPE 'foobar'> ranks (ones (2), 1, "foobar") |