Mercurial > octave
annotate scripts/statistics/ranks.m @ 31551:fd29c7a50a78 stable
maint: use commas, semicolons consistently with Octave conventions.
* makeValidName.m: Remove %!test and move BIST %!asserts to column 1.
* base64decode.m, base64encode.m, which.m, logm.m, uniquetol.m, perms.m:
Delete semicolon (';') at end of %!assert BIST.
* lin2mu.m, interp2.m, interpn.m, lsqnonneg.m, pqpnonneg.m, uniquetol.m,
betainc.m, normalize.m: Add semicolon (';') to end of assert statement within
%!test BIST.
* __memoize__.m, tar_is_bsd.m, publish.m: Add semicolon (';') to line with
keyword "persistent".
* stft.m: Use comma (',') after "case" keyword when code immediately follows.
* gallery.m: Align commas used in case statements in massive switch block.
Remove unnecessary parentheses around a numeric case argument.
* ranks.m: Remove semicolon (';') from case statemnt argument.
author | Rik <rik@octave.org> |
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date | Sat, 26 Nov 2022 06:32:08 -0800 |
parents | 5d3faba0342e |
children | 597f3ee61a48 |
rev | line source |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 1995-2022 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
3426 | 7 ## |
3922 | 8 ## This file is part of Octave. |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
3922 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
3426 | 14 ## |
3922 | 15 ## Octave is distributed in the hope that it will be useful, but |
3200 | 16 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
3426 | 19 ## |
3200 | 20 ## You should have received a copy of the GNU General Public License |
7016 | 21 ## along with Octave; see the file COPYING. If not, see |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
3200 | 25 |
3453 | 26 ## -*- texinfo -*- |
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27 ## @deftypefn {} {@var{y} =} ranks (@var{x}) |
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28 ## @deftypefnx {} {@var{y} =} ranks (@var{x}, @var{dim}) |
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29 ## @deftypefnx {} {@var{y} =} ranks (@var{x}, @var{dim}, @var{rtype}) |
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30 ## Return the ranks (in the sense of order statistics) of @var{x} along the |
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31 ## first non-singleton dimension adjusted for ties. |
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32 ## |
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33 ## If the optional @var{dim} argument is given, operate along this dimension. |
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34 ## |
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35 ## The optional parameter @var{rtype} determines how ties are handled. All |
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36 ## examples below assume an input of @code{[ 1, 2, 2, 4 ]}. |
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37 ## |
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38 ## @table @asis |
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39 ## @item 0 or @qcode{"fractional"} (default) for fractional ranking (1, 2.5, |
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40 ## 2.5, 4); |
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41 ## |
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42 ## @item 1 or @qcode{"competition"} for competition ranking (1, 2, 2, 4); |
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43 ## |
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44 ## @item 2 or @qcode{"modified"} for modified competition ranking (1, 3, 3, 4); |
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45 ## |
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46 ## @item 3 or @qcode{"ordinal"} for ordinal ranking (1, 2, 3, 4); |
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47 ## |
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48 ## @item 4 or @qcode{"dense"} for dense ranking (1, 2, 2, 3). |
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49 ## @end table |
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50 ## |
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51 ## @seealso{spearman, kendall} |
3453 | 52 ## @end deftypefn |
3426 | 53 |
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54 function y = ranks (x, dim, rtype = 0) |
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56 if (nargin < 1) |
6046 | 57 print_usage (); |
4885 | 58 endif |
3426 | 59 |
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60 if (! (isnumeric (x) || islogical (x))) |
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61 error ("ranks: X must be a numeric vector or matrix"); |
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62 endif |
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63 |
4885 | 64 nd = ndims (x); |
65 sz = size (x); | |
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66 |
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67 if (nargin < 2 || isempty (dim)) |
4886 | 68 ## Find the first non-singleton dimension. |
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69 (dim = find (sz > 1, 1)) || (dim = 1); |
4885 | 70 else |
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71 if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) |
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72 error ("ranks: DIM must be an integer and a valid dimension"); |
4885 | 73 endif |
3200 | 74 endif |
3426 | 75 |
4886 | 76 if (sz(dim) == 1) |
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77 y = ones (sz); # dimension DIM is singleton, so all are ranked first. |
4885 | 78 else |
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79 ## The algorithm works only on dim = 1, so permute if necessary. |
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80 ## FIXME: Most all functions now accept a dim argument. |
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81 ## Would it be faster not to permute and use the dim argument |
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82 ## to sort, find, cumsum, etc.? |
4885 | 83 if (dim != 1) |
84 perm = [1 : nd]; | |
4886 | 85 perm(1) = dim; |
86 perm(dim) = 1; | |
4885 | 87 x = permute (x, perm); |
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88 sz = size (x); |
4885 | 89 endif |
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90 |
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91 [sx, ids] = sort (x); # sx is sorted x. |
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92 lin = repmat ((1:rows (x))', [1, sz(2:end)]); # linearly increasing array. |
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93 |
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94 switch (rtype) |
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95 case {0, "fractional"} |
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96 lin = (_competition (lin, sx, sz) + _modified (lin, sx, sz)) / 2; |
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97 case {1, "competition"} |
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98 lin = _competition (lin, sx, sz); |
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99 case {2, "modified"} |
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100 lin = _modified (lin, sx, sz); |
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101 case {3, "ordinal"} |
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102 ## no processing needed here. |
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103 case {4, "dense"} |
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104 lin = _dense (lin, sx, sz); |
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105 otherwise |
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106 if (! ischar (rtype)) |
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107 rtype = num2str (rtype); |
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108 endif |
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109 error ("ranks: unknown RTYPE '%s'", rtype); |
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110 endswitch |
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111 |
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112 y = NaN (size (lin)); |
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113 |
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114 ## Offsets to map indices into each column to indices into the linear array. |
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115 ## FIXME: Would sub2ind be faster here? |
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116 idf = zeros (sz); |
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117 idf(1, :) = 0 : sz(1) : (numel (ids)-1); |
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118 idf(:, :) = repmat (idf(1, :), [sz(1), ones(1,length(sz)-1)]); |
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119 y(ids + idf) = lin; |
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120 |
4885 | 121 if (dim != 1) |
122 y = permute (y, perm); | |
123 endif | |
3200 | 124 endif |
3426 | 125 |
3200 | 126 endfunction |
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127 |
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128 function linnew = _dense (lin, sx, sz) |
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129 infvec = -Inf ([1, sz(2:end)]); |
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130 fnewp = logical (diff ([infvec; sx])); |
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131 linnew = cumsum (fnewp, 1); |
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132 endfunction |
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133 |
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134 function linnew = _competition (lin, sx, sz) |
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135 |
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136 ## Stop increasing lin when sx does not increase. Otherwise, same as before. |
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137 infvec = -Inf ([1, sz(2:end)]); |
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138 fnewp = find (diff ([infvec; sx])); |
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139 linnew = zeros (size (lin)); |
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140 linnew(fnewp) = lin(fnewp); |
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141 linnew = cummax (linnew, 1); |
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142 |
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143 endfunction |
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144 |
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145 function linnew = _modified (lin, sx, sz) |
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146 |
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147 ## Traverse lin backwards. Stop decreasing it when sx doesn't decrease. |
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148 infvec = Inf ([1, sz(2:end)]); |
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149 fnewp = find (diff ([sx; infvec])); |
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150 linnew = Inf (size (lin)); |
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151 linnew(fnewp) = lin(fnewp); |
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152 linnew = flip (cummin (flip (linnew, 1)), 1); |
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153 |
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154 endfunction |
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155 |
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156 |
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157 %!assert (ranks (1:2:10), 1:5) |
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158 %!assert (ranks (10:-2:1), 5:-1:1) |
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159 %!assert (ranks ([2, 1, 2, 4]), [2.5, 1, 2.5, 4]) |
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160 %!assert (ranks (ones (1, 5)), 3*ones (1, 5)) |
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161 %!assert (ranks (1e6*ones (1, 5)), 3*ones (1, 5)) |
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162 %!assert (ranks (rand (1, 5), 1), ones (1, 5)) |
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163 |
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164 %!assert (ranks ([1, 2, 2, 4], [], "fractional"), [1, 2.5, 2.5, 4]) |
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165 %!assert (ranks ([1, 2, 2, 4], [], "competition"), [1, 2, 2, 4]) |
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166 %!assert (ranks ([1, 2, 2, 4], [], "modified"), [1, 3, 3, 4]) |
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167 %!assert (ranks ([1, 2, 2, 4], [], "ordinal"), [1, 2, 3, 4]) |
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168 %!assert (ranks ([1, 2, 2, 4], [], "dense"), [1, 2, 2, 3]) |
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169 |
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170 ## Test input validation |
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171 %!error <Invalid call> ranks () |
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172 %!error <X must be a numeric vector or matrix> ranks ({1, 2}) |
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173 %!error <X must be a numeric vector or matrix> ranks (['A'; 'B']) |
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174 %!error <DIM must be an integer> ranks (1, 1.5) |
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175 %!error <DIM must be .* a valid dimension> ranks (1, 0) |
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176 %!error <unknown RTYPE 'foobar'> ranks (ones (2), 1, "foobar") |