Mercurial > octave
annotate scripts/set/uniquetol.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 8afdeac24ba4 |
children | df030ac26390 |
rev | line source |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2020-2022 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/>. |
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7 ## |
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8 ## This file is part of Octave. |
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9 ## |
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10 ## Octave is free software: you can redistribute it and/or modify it |
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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. |
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14 ## |
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15 ## Octave is distributed in the hope that it will be useful, but |
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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. |
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19 ## |
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20 ## You should have received a copy of the GNU General Public License |
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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 ######################################################################## |
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25 |
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26 ## -*- texinfo -*- |
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27 ## @deftypefn {} {@var{c} =} uniquetol (@var{A}) |
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28 ## @deftypefnx {} {@var{c} =} uniquetol (@var{A}, @var{tol}) |
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29 ## @deftypefnx {} {@var{c} =} uniquetol (@dots{}, @var{property}, @var{value}) |
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30 ## @deftypefnx {} {[@var{c}, @var{ia}, @var{ic}] =} uniquetol (@dots{}) |
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31 ## Return the unique elements of @var{A} within tolerance @var{tol}. |
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32 ## |
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33 ## Two values, @var{x} and @var{y}, are within relative tolerance if |
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34 ## @code{abs (@var{x} - @var{y}) <= @var{tol} * max (abs (@var{A}(:)))}. |
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35 ## |
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36 ## The input @var{A} must be a floating point type (double or single). |
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37 ## |
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38 ## If @var{tol} is unspecified, the default tolerance is 1e-12 for double |
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39 ## precision input or 1e-6 for single precision input. |
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40 ## |
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41 ## The function may also be called with the following optional property/value |
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42 ## pairs. Property/value pairs must be passed after other input arguments: |
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43 ## |
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44 ## @table @asis |
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45 ## @item @qcode{"ByRows"} (default: @code{false}) |
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46 ## When true, return the unique rows of @var{A}. @var{A} must be a 2-D array |
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47 ## to use this option. For rows, the criteria for uniqueness is changed to |
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48 ## @code{all (abs (@var{x} - @var{y}) <= @var{tol}*max (abs (@var{A}),[],1))} |
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49 ## which compares each column component of a row against a column-specific |
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50 ## tolerance. |
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51 ## |
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52 ## @item @qcode{"DataScale"} |
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53 ## The tolerance test is changed to |
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54 ## @code{abs (@var{x} - @var{y}) <= @var{tol}*@var{DS}} where @var{DS} is a |
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55 ## scalar unless the property @qcode{"ByRows"} is true. In that case, @var{DS} |
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56 ## can either be a scalar or a vector with a length equal to the number of |
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57 ## columns in @var{A}. Using a value of @code{1.0} for @var{DS} will change |
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58 ## the tolerance from a relative one to an absolute tolerance. Using a value |
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59 ## of @code{Inf} will disable testing. |
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60 ## |
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61 ## @item @qcode{"OutputAllIndices"} (default: @code{false}) |
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62 ## When true, @var{ia} is a cell array (not a vector) that contains the indices |
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63 ## for @emph{all} elements in @var{A} that are within tolerance of a value in |
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64 ## @var{C}. That is, each cell in @var{ia} corresponds to a single unique |
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65 ## value in @var{C}, and the values in each cell correspond to locations in |
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66 ## @var{A}. |
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67 ## @end table |
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68 ## |
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69 ## The output @var{c} is a row vector if the input @var{A} is a row vector. |
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70 ## For all other cases, a column vector is returned. |
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71 ## |
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72 ## The optional output @var{ia} is a column index vector such that |
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73 ## @code{@var{c} = @var{A}(@var{ia})}. If the @qcode{"ByRows"} property is |
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74 ## true, the condition is @code{@var{c} = @var{A}(@var{ia}, :)}. If the |
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75 ## @qcode{"OutputAllIndices"} property is true, then the values |
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76 ## @code{@var{A}(@var{ia}@{@var{i}@})} are all within tolerance of the unique |
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77 ## value @code{@var{c}(@var{i})}. |
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78 ## |
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79 ## The optional output @var{ic} is a column index vector such that |
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80 ## @code{@var{A} = @var{c}(@var{ic})} when @var{A} is a vector. When @var{A} |
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81 ## is a matrix, @code{@var{A}(:) = @var{c}(@var{ic})}. If the @qcode{"ByRows"} |
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82 ## property is true then @code{@var{A} = @var{c}(@var{ic},:)}. |
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83 ## |
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84 ## Example: small round-off errors require @code{uniquetol}, not @code{unique} |
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85 ## |
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86 ## @example |
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87 ## @group |
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88 ## x = [1:5]; |
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89 ## ## Inverse_Function (Function (x)) should return exactly x |
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90 ## y = exp (log (x)); |
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91 ## D = unique ([x, y]) |
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92 ## @result{} [1.0000 2.0000 3.0000 3.0000 4.0000 5.0000 5.0000] |
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93 ## C = uniquetol ([x, y]) |
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94 ## @result{} [1 2 3 4 5] |
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95 ## @end group |
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96 ## @end example |
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97 ## |
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98 ## @seealso{unique, union, intersect, setdiff, setxor, ismember} |
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99 ## @end deftypefn |
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100 |
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101 |
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102 function [c, ia, ic] = uniquetol (A, varargin) |
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103 |
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104 if (nargin < 1) |
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105 print_usage (); |
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106 endif |
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107 |
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108 if (isempty (A)) |
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109 c = A; |
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110 ia = []; |
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111 ic = []; |
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112 return; |
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113 endif |
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114 |
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115 if (! isfloat (A) || iscomplex (A)) |
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116 error ("Octave:uniquetol:unsupported-type", |
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117 "uniquetol: A must be a double or single precision non-complex array"); |
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118 endif |
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119 |
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120 if (nargin == 1 || ischar (varargin{1})) |
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121 tol = ifelse (isa (A, "double"), 1e-12, 1e-6); |
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122 elseif (! (isfloat (varargin{1}) && isscalar (varargin{1})) |
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123 || iscomplex (varargin{1})) |
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124 error ("Octave:uniquetol:unsupported-type", |
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125 "uniquetol: TOL must be a double or single precision non-complex scalar"); |
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126 else |
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127 tol = varargin{1}; |
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128 varargin(1) = []; |
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129 endif |
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130 |
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131 if (mod (numel (varargin), 2)) |
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132 error ("uniquetol: PROPERTY/VALUE arguments must be passed in pairs"); |
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133 endif |
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134 |
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135 by_rows = false; |
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136 output_all_indices = false; |
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137 data_scale = []; |
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138 |
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139 for k = 1:2:numel (varargin) |
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140 if (! ischar (varargin{k})) |
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141 error ("uniquetol: PROPERTY must be a string"); |
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142 endif |
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143 |
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144 if (strcmpi (varargin{k}, "ByRows")) |
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145 by_rows = logical (varargin{k+1}); |
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146 if (by_rows && ndims (A) > 2) |
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147 error ('uniquetol: A must be a 2-D array when "ByRows" is true'); |
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148 endif |
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149 elseif (strcmpi (varargin{k}, "OutputAllIndices")) |
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150 output_all_indices = logical (varargin{k+1}); |
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151 elseif (strcmpi (varargin{k}, "DataScale")) |
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152 data_scale = varargin{k+1}(:).'; |
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153 if (! isfloat (data_scale) || iscomplex (data_scale) |
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154 || any (data_scale(:) < 0) || any (isnan (data_scale(:)))) |
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155 error ("uniquetol: DataScale must be a non-NaN, positive floating point scalar or vector"); |
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156 endif |
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157 cols_data_scale = columns (data_scale); |
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158 if (cols_data_scale != 1 && cols_data_scale != columns (A)) |
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159 error ("uniquetol: invalid DataScale size"); |
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160 endif |
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161 else |
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162 error ("uniquetol: unknown property '%s'", varargin{k}); |
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163 endif |
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164 endfor |
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165 |
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166 if (isempty (data_scale)) |
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167 data_scale = max (abs (A(! isinf (A))(:))); |
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168 endif |
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169 |
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170 tol *= data_scale; |
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171 |
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172 if (by_rows) |
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173 |
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174 nr = rows (A); |
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175 nc = columns (A); |
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176 Iall = zeros (nr, 1); |
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177 I = NaN (nc, 1); |
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178 ia = {}; |
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179 J = NaN (nc, 1); |
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180 j = 1; |
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181 ii = 0; |
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182 |
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183 for i = 1:nr |
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184 if (any (Iall == i)) |
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185 continue; |
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186 else |
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187 equ = all (abs (A - A(i,:)) <= tol, 2); |
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188 equ(i,1) = equ(i,1) || any (! isfinite (A(i,:)), 2); |
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189 sumeq = sum (equ); |
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190 ia_tmp = find (equ); |
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191 if (output_all_indices) |
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192 ia{end+1} = ia_tmp; |
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193 endif |
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194 Iall(ii+(1:sumeq)) = ia_tmp; |
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195 I(j) = ia_tmp(1); |
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196 J(equ) = j; |
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197 ii += sumeq; |
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198 j += 1; |
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199 endif |
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200 endfor |
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201 |
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202 I(isnan (I)) = []; |
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203 J(isnan (J)) = []; |
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204 c = A(I,:); |
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205 |
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206 if (! output_all_indices) |
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207 ia = I(1:j-1); |
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208 endif |
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209 ic = J; |
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210 |
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211 else |
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212 isrowvec = isrow (A); |
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213 A = A(:); |
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214 nr = rows (A); |
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215 isnanA = isnan (A); |
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216 anyisnanA = any (isnanA); |
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217 [sortA, sAi] = sort (A); |
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218 diffsortA = diff (sortA); |
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219 isinfsortA = isinf (sortA); |
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220 isnansortA = isnan (sortA); |
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221 numnan = sum (isnansortA); |
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222 if (any (isinfsortA)) |
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223 sAnin = sortA(! (isinfsortA | isnansortA)); |
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224 diffsortA(isinf (diffsortA)) = abs (sAnin(end) - sAnin(1)) + 10; |
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225 endif |
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226 csdx = cumsum (diffsortA); |
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227 ue = [true; diff([0; csdx-mod(csdx,tol)]) > eps(max(csdx))]; |
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228 ueold = NaN; |
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229 while (any (ueold != ue)) |
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230 ueold = ue; |
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231 belowtol = [false; diff(sortA(ue)) < tol]; |
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232 if (any (belowtol)) |
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233 needstomove = find (ue)(belowtol); |
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234 ue(needstomove) = false; |
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235 needstomove(needstomove >= nr-numnan) = []; |
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236 ue(needstomove+1) = true; |
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237 endif |
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238 endwhile |
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239 c = sortA(ue); |
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240 [~, sortsAi] = sort (sAi); |
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241 cumsumue = cumsum (ue); |
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242 ic = cumsumue(sortsAi); |
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243 if (anyisnanA) |
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244 findisnanA = find (isnanA); |
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245 else |
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246 findisnanA = []; |
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247 endif |
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248 if (output_all_indices) |
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249 nu = cumsumue(end); |
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250 ia = cell (1, nu); |
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251 for k = 1:nu |
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252 ia{k} = setdiff (sAi(cumsumue==k), findisnanA); |
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253 endfor |
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254 else |
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255 ia = sAi(ue); |
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256 endif |
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257 |
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258 if (anyisnanA) |
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259 rowsc1 = rows (c) + (1:sum (isnanA)); |
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260 c(rowsc1) = NaN; |
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261 ia(rowsc1) = findisnanA; |
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262 ic(isnanA) = rowsc1; |
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263 endif |
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264 |
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265 ## FIXME: Matlab-compatible orientation of output |
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266 ## Actually, Matlab prefers row vectors (2021/03/24), but this is different |
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267 ## from all the other set functions which prefer column vectors. Assume |
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268 ## that this is a bug in Matlab's implementation and prefer column vectors. |
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269 if (isrowvec) |
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270 c = c.'; |
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271 endif |
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272 |
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273 endif |
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274 |
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275 endfunction |
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276 |
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277 |
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278 %!assert (uniquetol ([1 1 2; 1 2 1; 1 1 2+10*eps]), [1;2]) |
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279 %!assert (uniquetol ([1 1 2; 1 0 1; 1 1 2+10*eps], "byrows", true), |
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280 %! [1 1 2; 1 0 1]) |
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281 %!assert (uniquetol ([]), []) |
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282 %!assert (uniquetol ([1]), [1]) |
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283 %!assert (uniquetol ([2, 1]), [1, 2]); |
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284 %!assert (uniquetol ([1; 2]), [1; 2]) |
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285 %!assert (uniquetol ([-Inf, 1, NaN, Inf, NaN, Inf]), [-Inf, 1, Inf, NaN, NaN]); |
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286 %!assert (uniquetol (zeros (1, 0)), zeros (1, 0)); |
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287 %!assert (uniquetol (zeros (1, 0), "byrows", true), zeros (1, 0)) |
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288 %!assert (uniquetol ([1,2,2,3,2,4], "byrows", true), [1,2,2,3,2,4]) |
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289 %!assert (uniquetol ([1,2,2,3,2,4]), [1,2,3,4]) |
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290 %!assert (uniquetol ([1,2,2,3,2,4].', "byrows", true), [1;2;3;4]) |
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291 %!assert (uniquetol (sparse ([2,0;2,0])), sparse ([0;2])) |
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292 %!assert (uniquetol (sparse ([1,2;2,3])), sparse ([1;2;3])) |
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293 %!assert (uniquetol (single ([1,2,2,3,2,4]), "byrows", true), |
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294 %! single ([1,2,2,3,2,4])) |
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295 %!assert (uniquetol (single ([1,2,2,3,2,4])), single ([1,2,3,4])) |
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296 %!assert (uniquetol (single ([1,2,2,3,2,4].'), "byrows", true), |
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297 %! single ([1;2;3;4])) |
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298 |
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299 ## Matlab compatibility of output |
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300 %!test |
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301 %! x = 1:0.045:3; |
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302 %! y = uniquetol (x, 0.1, "datascale", 1); |
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303 %! assert (y(1:4), [1, 1.135, 1.27, 1.405]); |
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304 |
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305 ## Test index vector return arguments |
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306 %!test |
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307 %! [c, ia, ic] = uniquetol ([1,1,2,3,3,3,4]); |
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308 %! assert (c, [1,2,3,4]); |
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309 %! assert (ia, [1;3;4;7]); |
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310 %! assert (ic, [1;1;2;3;3;3;4]); |
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311 |
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312 ## Test index vector return arguments with "ByRows" |
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313 %!test |
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314 %! A = [2, 3, 4; 2, 3, 4]; |
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315 %! [c, ia, ic] = uniquetol (A, "byrows", true); |
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316 %! assert (c, [2, 3, 4]); |
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317 %! assert (A(ia,:), c); |
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318 %! assert (c(ic,:), A); |
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319 |
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320 %!test |
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321 %! x = (2:7)'*pi; |
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322 %! y = exp (log (x)); |
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323 %! C = uniquetol ([x; y]); |
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324 %! assert (C, x, 1e-12); |
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325 |
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326 ## Test "ByRows" Property |
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327 %!test |
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328 %! A = [0.06, 0.21, 0.38; 0.38, 0.21, 0.39; 0.54, 0.56, 0.41; 0.46, 0.52, 0.95]; |
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329 %! B = log (exp (A)); |
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330 %! C = uniquetol ([A; B], "ByRows", true); |
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331 %! assert (C, A); |
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332 |
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333 ## Test "DataScale" Property |
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334 %!test |
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335 %! x = 10^11; |
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336 %! C = uniquetol ([x, exp(log(x))], 1e-6, "DataScale", 1); |
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337 %! assert (C, [x, exp(log(x))]); |
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338 |
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339 ## Test "OutputAllIndices" Property |
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340 %!test |
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341 %! A = [.1 .2 .3 10]; |
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342 %! [C, ia, ic] = uniquetol (A, .1, "OutputAllIndices", true); |
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343 %! assert (C, [.1, 10]); |
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344 %! assert (ia, {(1:3)', 4}); |
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345 %! assert (ic, [1; 1; 1; 2]); |
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346 |
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347 ## Test input validation |
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348 %!error <Invalid call> uniquetol () |
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349 %!error <A must be a double or single precision> uniquetol (int8 (1)) |
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350 %!error <A must be .* non-complex> uniquetol (1i) |
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351 %!error <TOL must be a double .* precision> uniquetol (1, int8 (1)) |
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352 %!error <TOL must be a .* scalar> uniquetol (1, [1, 2]) |
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353 %!error <TOL must be .* non-complex> uniquetol (1, 1i) |
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354 %!error <arguments must be passed in pairs> uniquetol (1, 2, "byrows") |
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355 %!error <PROPERTY must be a string> uniquetol (1, 2, 3, "bar") |
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356 %!error <A must be a 2-D array> uniquetol (ones (2,2,2), "byrows", true) |
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357 %!error <DataScale must be a .* floating point> uniquetol (1, "DataScale", '1') |
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358 %!error <DataScale must be .* positive> uniquetol (1, "DataScale", -1) |
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359 %!error <DataScale must be .* positive> uniquetol (1, "DataScale", 1i) |
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360 %!error <DataScale must be a non-NaN> uniquetol (1, "DataScale", NaN) |
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361 %!error <invalid DataScale size> uniquetol (1, "DataScale", [1 2]) |
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362 %!error <unknown property 'foo'> uniquetol (1, "foo", "bar") |
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363 %!error <unknown property 'foo'> uniquetol (1, 2, "foo", "bar") |