annotate scripts/general/accumarray.m @ 21401:2f402f7c1a0b

accumarray: fix general case for empty list of subscripts (bug #47287) * accumarray.m: when SUBS is an empty array, accumarray was working only for the special cases of max, min, and sum. Fix that. Add tests.
author Carnë Draug <carandraug@octave.org>
date Sun, 28 Feb 2016 18:21:07 +0000
parents 00960129ebf4
children 8cfc50637511
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1 ## Copyright (C) 2007-2015 David Bateman
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2 ## Copyright (C) 2009-2010 VZLU Prague
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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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 (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {} {} accumarray (@var{subs}, @var{vals}, @var{sz}, @var{func}, @var{fillval}, @var{issparse})
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22 ## @deftypefnx {} {} accumarray (@var{subs}, @var{vals}, @dots{})
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23 ##
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24 ## Create an array by accumulating the elements of a vector into the
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25 ## positions defined by their subscripts.
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26 ##
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27 ## The subscripts are defined by the rows of the matrix @var{subs} and the
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28 ## values by @var{vals}. Each row of @var{subs} corresponds to one of the
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29 ## values in @var{vals}. If @var{vals} is a scalar, it will be used for each
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30 ## of the row of @var{subs}. If @var{subs} is a cell array of vectors, all
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31 ## vectors must be of the same length, and the subscripts in the @var{k}th
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32 ## vector must correspond to the @var{k}th dimension of the result.
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33 ##
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34 ## The size of the matrix will be determined by the subscripts
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35 ## themselves. However, if @var{sz} is defined it determines the matrix
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36 ## size. The length of @var{sz} must correspond to the number of columns
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37 ## in @var{subs}. An exception is if @var{subs} has only one column, in
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38 ## which case @var{sz} may be the dimensions of a vector and the
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39 ## subscripts of @var{subs} are taken as the indices into it.
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40 ##
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41 ## The default action of @code{accumarray} is to sum the elements with
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42 ## the same subscripts. This behavior can be modified by defining the
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43 ## @var{func} function. This should be a function or function handle
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44 ## that accepts a column vector and returns a scalar. The result of the
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45 ## function should not depend on the order of the subscripts.
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46 ##
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47 ## The elements of the returned array that have no subscripts associated
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48 ## with them are set to zero. Defining @var{fillval} to some other value
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49 ## allows these values to be defined. This behavior changes, however,
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50 ## for certain values of @var{func}. If @var{func} is @code{min}
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51 ## (respectively, @code{max}) then the result will be filled with the
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52 ## minimum (respectively, maximum) integer if @var{vals} is of integral
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53 ## type, logical false (respectively, logical true) if @var{vals} is of
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54 ## logical type, zero if @var{fillval} is zero and all values are
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55 ## non-positive (respectively, non-negative), and NaN otherwise.
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56 ##
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57 ## By default @code{accumarray} returns a full matrix. If
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58 ## @var{issparse} is logically true, then a sparse matrix is returned
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59 ## instead.
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60 ##
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61 ## The following @code{accumarray} example constructs a frequency table
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62 ## that in the first column counts how many occurrences each number in
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63 ## the second column has, taken from the vector @var{x}. Note the usage
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64 ## of @code{unique} for assigning to all repeated elements of @var{x}
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65 ## the same index (@pxref{XREFunique,,unique}).
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66 ##
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67 ## @example
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68 ## @group
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69 ## @var{x} = [91, 92, 90, 92, 90, 89, 91, 89, 90, 100, 100, 100];
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70 ## [@var{u}, ~, @var{j}] = unique (@var{x});
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71 ## [accumarray(@var{j}', 1), @var{u}']
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72 ## @result{} 2 89
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73 ## 3 90
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74 ## 2 91
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75 ## 2 92
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76 ## 3 100
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77 ## @end group
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78 ## @end example
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79 ##
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80 ## Another example, where the result is a multi-dimensional 3-D array and
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81 ## the default value (zero) appears in the output:
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82 ##
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83 ## @example
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84 ## @group
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85 ## accumarray ([1, 1, 1;
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86 ## 2, 1, 2;
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87 ## 2, 3, 2;
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88 ## 2, 1, 2;
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89 ## 2, 3, 2], 101:105)
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90 ## @result{} ans(:,:,1) = [101, 0, 0; 0, 0, 0]
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91 ## @result{} ans(:,:,2) = [0, 0, 0; 206, 0, 208]
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92 ## @end group
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93 ## @end example
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94 ##
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95 ## The sparse option can be used as an alternative to the @code{sparse}
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96 ## constructor (@pxref{XREFsparse,,sparse}). Thus
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97 ##
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98 ## @example
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99 ## sparse (@var{i}, @var{j}, @var{sv})
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100 ## @end example
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101 ##
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102 ## @noindent
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103 ## can be written with @code{accumarray} as
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104 ##
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105 ## @example
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106 ## accumarray ([@var{i}, @var{j}], @var{sv}', [], [], 0, true)
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107 ## @end example
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108 ##
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109 ## @noindent
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110 ## For repeated indices, @code{sparse} adds the corresponding value. To
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111 ## take the minimum instead, use @code{min} as an accumulator function:
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112 ##
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113 ## @example
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114 ## accumarray ([@var{i}, @var{j}], @var{sv}', [], @@min, 0, true)
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115 ## @end example
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116 ##
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117 ## The complexity of accumarray in general for the non-sparse case is
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118 ## generally O(M+N), where N is the number of subscripts and M is the
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119 ## maximum subscript (linearized in multi-dimensional case). If
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120 ## @var{func} is one of @code{@@sum} (default), @code{@@max},
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121 ## @code{@@min} or @code{@@(x) @{x@}}, an optimized code path is used.
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122 ## Note that for general reduction function the interpreter overhead can
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123 ## play a major part and it may be more efficient to do multiple
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124 ## accumarray calls and compute the results in a vectorized manner.
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125 ##
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126 ## @seealso{accumdim, unique, sparse}
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127 ## @end deftypefn
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128
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129 function A = accumarray (subs, vals, sz = [], func = [], fillval = [], issparse = [])
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130
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131 if (nargin < 2 || nargin > 6)
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132 print_usage ();
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133 endif
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134
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135 lenvals = length (vals);
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136
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137 if (iscell (subs))
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138 subs = cellfun (@vec, subs, "uniformoutput", false);
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139 ndims = numel (subs);
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140 if (ndims == 1)
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141 subs = subs{1};
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142 endif
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143
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144 lensubs = cellfun (@length, subs);
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145
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146 if (any (lensubs != lensubs(1)) || (lenvals > 1 && lenvals != lensubs(1)))
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147 error ("accumarray: dimension mismatch");
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148 endif
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149
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150 else
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151 ndims = columns (subs);
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152 if (lenvals > 1 && lenvals != rows (subs))
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153 error ("accumarray: dimension mismatch");
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154 endif
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155 endif
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156
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157 if (isempty (fillval))
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158 fillval = 0;
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159 endif
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160
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161 if (isempty (issparse))
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162 issparse = false;
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163 endif
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164
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165 if (issparse)
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166
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167 ## Sparse case. Avoid linearizing the subscripts, because it could
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168 ## overflow.
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169
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170 if (fillval != 0)
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171 error ("accumarray: FILLVAL must be zero in the sparse case");
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172 endif
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173
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174 ## Ensure subscripts are a two-column matrix.
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175 if (iscell (subs))
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176 subs = [subs{:}];
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177 endif
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178
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179 ## Validate dimensions.
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180 if (ndims == 1)
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181 subs(:,2) = 1;
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182 elseif (ndims != 2)
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183 error ("accumarray: in the sparse case, needs 1 or 2 subscripts");
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184 endif
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185
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186 if (isnumeric (vals) || islogical (vals))
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187 vals = double (vals);
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188 else
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189 error ("accumarray: in the sparse case, values must be numeric or logical");
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190 endif
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191
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192 if (! (isempty (func) || func == @sum))
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193
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194 ## Reduce values. This is not needed if we're about to sum them,
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195 ## because "sparse" can do that.
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196
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197 ## Sort indices.
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198 [subs, idx] = sortrows (subs);
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199 n = rows (subs);
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200 ## Identify runs.
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201 jdx = find (any (diff (subs, 1, 1), 2));
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202 jdx = [jdx; n];
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203
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204 vals = cellfun (func, mat2cell (vals(:)(idx), diff ([0; jdx])));
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205 subs = subs(jdx, :);
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206 mode = "unique";
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207 else
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208 mode = "sum";
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209 endif
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210
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211 ## Form the sparse matrix.
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212 if (isempty (sz))
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213 A = sparse (subs(:,1), subs(:,2), vals, mode);
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214 elseif (length (sz) == 2)
13788
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215
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216 ## Row vector case
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217 if (sz(1) == 1)
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218 [i, j] = deal (subs(:,2), subs(:,1));
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219 else
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220 [i, j] = deal (subs(:,1), subs(:,2));
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221 endif
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222 A = sparse (i, j, vals, sz(1), sz(2), mode);
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223 else
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224 error ("accumarray: dimensions mismatch");
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225 endif
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226
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227 else
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228
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229 ## Linearize subscripts.
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230 if (ndims > 1)
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231 if (isempty (sz))
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232 if (iscell (subs))
12931
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233 sz = cellfun ("max", subs);
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234 else
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235 sz = max (subs, [], 1);
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236 endif
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237 elseif (ndims != length (sz))
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238 error ("accumarray: dimensions mismatch");
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239 endif
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240
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241 ## Convert multidimensional subscripts.
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242 if (isnumeric (subs))
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243 subs = num2cell (subs, 1);
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244 endif
10274
db613bccd992 take advantage of new sort optimization in accumarray
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diff changeset
245 subs = sub2ind (sz, subs{:}); # creates index cache
10271
297996005012 1 more small fix in accumarray
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diff changeset
246 elseif (! isempty (sz) && length (sz) < 2)
10269
217d36560dfa small fixes to accumarray
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diff changeset
247 error ("accumarray: needs at least 2 dimensions");
10274
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diff changeset
248 elseif (! isindex (subs)) # creates index cache
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249 error ("accumarray: indices must be positive integers");
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250 endif
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251
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252
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253 ## Some built-in reductions handled efficiently.
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254
10268
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255 if (isempty (func) || func == @sum)
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256 ## Fast summation.
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257 if (isempty (sz))
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258 A = __accumarray_sum__ (subs, vals);
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259 else
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260 A = __accumarray_sum__ (subs, vals, prod (sz));
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261 ## set proper shape.
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262 A = reshape (A, sz);
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263 endif
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264
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265 ## we fill in nonzero fill value.
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266 if (fillval != 0)
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267 mask = true (size (A));
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268 mask(subs) = false;
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269 A(mask) = fillval;
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270 endif
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271 elseif (func == @max)
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272 ## Fast maximization.
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273
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274 if (isinteger (vals))
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275 zero = intmin (class (vals));
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276 elseif (islogical (vals))
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277 zero = false;
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278 elseif (fillval == 0 && all (vals(:) >= 0))
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279 ## This is a common case - fillval is zero, all numbers
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280 ## nonegative.
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281 zero = 0;
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282 else
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283 zero = NaN; # Neutral value.
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284 endif
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285
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286 if (isempty (sz))
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287 A = __accumarray_max__ (subs, vals, zero);
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288 else
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289 A = __accumarray_max__ (subs, vals, zero, prod (sz));
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290 A = reshape (A, sz);
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291 endif
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292
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293 if (fillval != zero && ! (isnan (fillval) || isnan (zero)))
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294 mask = true (size (A));
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295 mask(subs) = false;
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296 A(mask) = fillval;
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297 endif
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298 elseif (func == @min)
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299 ## Fast minimization.
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300
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301 if (isinteger (vals))
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302 zero = intmax (class (vals));
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303 elseif (islogical (vals))
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304 zero = true;
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305 elseif (fillval == 0 && all (vals(:) <= 0))
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306 ## This is a common case - fillval is zero, all numbers
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307 ## non-positive.
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308 zero = 0;
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309 else
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310 zero = NaN; # Neutral value.
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311 endif
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312
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313 if (isempty (sz))
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314 A = __accumarray_min__ (subs, vals, zero);
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315 else
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316 A = __accumarray_min__ (subs, vals, zero, prod (sz));
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317 A = reshape (A, sz);
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318 endif
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diff changeset
319
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320 if (fillval != zero && ! (isnan (fillval) || isnan (zero)))
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321 mask = true (size (A));
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322 mask(subs) = false;
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323 A(mask) = fillval;
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324 endif
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325 else
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diff changeset
326
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327 ## The general case. Reduce values.
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328 n = rows (subs);
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329 if (numel (vals) == 1)
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330 vals = vals(ones (1, n), 1);
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331 else
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332 vals = vals(:);
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333 endif
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parents: 11523
diff changeset
334
10268
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335 ## Sort indices.
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336 [subs, idx] = sort (subs);
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diff changeset
337 ## Identify runs.
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diff changeset
338 jdx = find (subs(1:n-1) != subs(2:n));
21401
2f402f7c1a0b accumarray: fix general case for empty list of subscripts (bug #47287)
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parents: 21400
diff changeset
339 if (n != 0) # bug #47287
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340 jdx = [jdx; n];
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diff changeset
341 endif
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342 vals = mat2cell (vals(idx), diff ([0; jdx]));
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343 ## Optimize the case when function is @(x) {x}, i.e. we just want
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344 ## to collect the values to cells.
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345 persistent simple_cell_str = func2str (@(x) {x});
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diff changeset
346 if (! strcmp (func2str (func), simple_cell_str))
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diff changeset
347 vals = cellfun (func, vals);
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348 endif
21401
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diff changeset
349
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diff changeset
350 subs = subs(jdx);
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diff changeset
351
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diff changeset
352 if (isempty (sz))
da67f032a712 accumarray.m: Handle the case of empty size argument for functions besides @sum
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diff changeset
353 sz = max (subs);
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diff changeset
354 if (length (sz) == 1)
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diff changeset
355 sz(2) = 1;
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diff changeset
356 endif
da67f032a712 accumarray.m: Handle the case of empty size argument for functions besides @sum
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 14113
diff changeset
357 endif
da67f032a712 accumarray.m: Handle the case of empty size argument for functions besides @sum
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 14113
diff changeset
358
10268
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diff changeset
359 ## Construct matrix of fillvals.
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diff changeset
360 if (iscell (vals))
10268
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diff changeset
361 A = cell (sz);
9a16a61ed43d new optimizations for accumarray
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diff changeset
362 elseif (fillval == 0)
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diff changeset
363 A = zeros (sz, class (vals));
10268
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diff changeset
364 else
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
365 A = repmat (fillval, sz);
9a16a61ed43d new optimizations for accumarray
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diff changeset
366 endif
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
367
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
368 ## Set the reduced values.
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diff changeset
369 A(subs) = vals;
6770
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
370 endif
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
371 endif
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
372 endfunction
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
373
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
374
21400
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diff changeset
375 %!assert (accumarray ([1; 2; 4; 2; 4], 101:105), [101; 206; 0; 208])
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
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diff changeset
376 %!assert (accumarray ([1 1 1; 2 1 2; 2 3 2; 2 1 2; 2 3 2], 101:105),
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
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diff changeset
377 %! cat (3, [101 0 0; 0 0 0], [0 0 0; 206 0 208]))
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parents: 20852
diff changeset
378
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
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diff changeset
379 %!assert (accumarray ([1 1 1; 2 1 2; 2 3 2; 2 1 2; 2 3 2], 101:105, [], @(x) sin (sum (x))),
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
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diff changeset
380 %! sin (cat (3, [101,0,0;0,0,0],[0,0,0;206,0,208])))
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diff changeset
381
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
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diff changeset
382 %!assert (accumarray ({[1 3 3 2 3 1 2 2 3 3 1 2], [3 4 2 1 4 3 4 2 2 4 3 4], [1 1 2 2 1 1 2 1 1 1 2 2]}, 101:112),
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
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diff changeset
383 %! cat (3, [0 0 207 0; 0 108 0 0; 0 109 0 317], [0 0 111 0; 104 0 0 219; 0 103 0 0]))
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
Carnë Draug <carandraug@octave.org>
parents: 20852
diff changeset
384
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
Carnë Draug <carandraug@octave.org>
parents: 20852
diff changeset
385 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 101:105, [2 4], @max, NaN),
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
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diff changeset
386 %! [101 NaN NaN NaN; 104 NaN 105 NaN])
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
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parents: 20852
diff changeset
387
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
Carnë Draug <carandraug@octave.org>
parents: 20852
diff changeset
388 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 101:105, [], @prod),
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
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parents: 20852
diff changeset
389 %! [101 0 0; 10608 0 10815])
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
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parents: 20852
diff changeset
390 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 101:105, [2 4], @prod, 0, true),
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
Carnë Draug <carandraug@octave.org>
parents: 20852
diff changeset
391 %! sparse ([1 2 2], [1 1 3], [101 10608 10815], 2, 4))
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
Carnë Draug <carandraug@octave.org>
parents: 20852
diff changeset
392 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 1, [2 4]), [1 0 0 0; 2 0 2 0])
00960129ebf4 accumarray.m: edit tests to follow coding guidelines.
Carnë Draug <carandraug@octave.org>
parents: 20852
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393 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 101:105, [2 4], @(x) length (x) > 1),
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394 %! [false false false false; true false true false])
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395
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396 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 0), [3; 4])
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397 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 1), sparse ([3; 4]))
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398 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 0), [3, 4])
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399 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 1), sparse ([3, 4]))
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400
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401 %!test
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402 %! A = accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 101:105, [2,4], @(x) {x});
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403 %! assert (A{2},[102; 104])
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404
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405 %!test
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406 %! subs = ceil (rand (2000, 3)*10);
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407 %! vals = rand (2000, 1);
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408 %! assert (accumarray (subs, vals, [], @max),
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409 %! accumarray (subs, vals, [], @(x) max (x)))
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410
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411 %!test
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412 %! subs = ceil (rand (2000, 1)*100);
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413 %! vals = rand (2000, 1);
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414 %! assert (accumarray (subs, vals, [100, 1], @min, NaN),
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415 %! accumarray (subs, vals, [100, 1], @(x) min (x), NaN))
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416
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417 %!test
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418 %! subs = ceil (rand (2000, 2)*30);
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419 %! subsc = num2cell (subs, 1);
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420 %! vals = rand (2000, 1);
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421 %! assert (accumarray (subsc, vals, [], [], 0, true),
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422 %! accumarray (subs, vals, [], [], 0, true))
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423
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424 %!test
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425 %! subs = ceil (rand (2000, 3)*10);
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426 %! subsc = num2cell (subs, 1);
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427 %! vals = rand (2000, 1);
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428 %! assert (accumarray (subsc, vals, [], @max),
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429 %! accumarray (subs, vals, [], @max));
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430
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431 %!error (accumarray (1:5))
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432 %!error (accumarray ([1,2,3],1:2))
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433
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434 ## Handle empty arrays (bug #47287)
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435 %!test
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436 %! ## min, max, and sum are special cases within accumarray so test them.
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437 %! funcs = {@(x) length (x) > 1, @min, @max, @sum};
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438 %! for idx = 1:numel (funcs)
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439 %! assert (accumarray (zeros (0, 1), [], [0 1] , funcs{idx}), zeros (0, 1))
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440 %! assert (accumarray (zeros (0, 1), [], [1 0] , funcs{idx}), zeros (1, 0))
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441 %! endfor
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Carnë Draug <carandraug@octave.org>
parents: 21400
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442
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Carnë Draug <carandraug@octave.org>
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443 ## Matlab returns an array of doubles even though FUNC returns cells. In
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444 ## Octave, we do not have that bug, at least for this case.
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445 %!assert (accumarray (zeros (0, 1), [], [0 1] , @(x) {x}), cell (0, 1))