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accumarray.m: Handle the case of empty size argument for functions besides @sum
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Tue, 27 Dec 2011 13:51:35 -0500
parents dac62c415e8b
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1 ## Copyright (C) 2007-2011 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 {Function File} {} accumarray (@var{subs}, @var{vals}, @var{sz}, @var{func}, @var{fillval}, @var{issparse})
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22 ## @deftypefnx {Function File} {} 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. The subscripts are defined by
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26 ## the rows of the matrix @var{subs} and the values by @var{vals}. Each
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27 ## row of @var{subs} corresponds to one of the values in @var{vals}. If
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28 ## @var{vals} is a scalar, it will be used for each of the row of
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29 ## @var{subs}. If @var{subs} is a cell array of vectors, all vectors
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30 ## must be of the same length, and the subscripts in the @var{k}th
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31 ## vector must correspond to the @var{k}th dimension of the result.
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32 ##
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33 ## The size of the matrix will be determined by the subscripts
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34 ## themselves. However, if @var{sz} is defined it determines the matrix
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35 ## size. The length of @var{sz} must correspond to the number of columns
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36 ## in @var{subs}. An exception is if @var{subs} has only one column, in
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37 ## which case @var{sz} may be the dimensions of a vector and the subscripts
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38 ## of @var{subs} are taken as the indices into it.
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39 ##
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40 ## The default action of @code{accumarray} is to sum the elements with
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41 ## the same subscripts. This behavior can be modified by defining the
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42 ## @var{func} function. This should be a function or function handle
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43 ## that accepts a column vector and returns a scalar. The result of the
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44 ## function should not depend on the order of the subscripts.
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45 ##
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46 ## The elements of the returned array that have no subscripts associated
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47 ## with them are set to zero. Defining @var{fillval} to some other value
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48 ## allows these values to be defined. This behavior changes, however,
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49 ## for certain values of @var{func}. If @var{func} is @code{min}
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50 ## (respectively, @code{max}) then the result will be filled with the
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51 ## minimum (respectively, maximum) integer if @var{vals} is of integral
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52 ## type, logical false (respectively, logical true) if @var{vals} is of
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53 ## logical type, zero if @var{fillval} is zero and all values are
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54 ## non-positive (respectively, non-negative), and NaN otherwise.
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55 ##
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56 ## By default @code{accumarray} returns a full matrix. If
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57 ## @var{issparse} is logically true, then a sparse matrix is returned
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58 ## instead.
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59 ##
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60 ## The following @code{accumarray} example constructs a frequency table
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61 ## that in the first column counts how many occurrences each number in
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62 ## the second column has, taken from the vector @var{x}. Note the usage
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63 ## of @code{unique} for assigning to all repeated elements of @var{x}
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64 ## the same index (@pxref{doc-unique}).
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65 ##
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66 ## @example
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67 ## @group
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68 ## x = [91, 92, 90, 92, 90, 89, 91, 89, 90, 100, 100, 100];
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69 ## [u, ~, j] = unique (x);
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70 ## [accumarray(j', 1), u']
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71 ## @result{} 2 89
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72 ## 3 90
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73 ## 2 91
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74 ## 2 92
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75 ## 3 100
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76 ## @end group
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77 ## @end example
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78 ##
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79 ## Another example, where the result is a multi-dimensional 3-D array and
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80 ## the default value (zero) appears in the output:
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81 ##
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82 ## @example
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83 ## @group
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84 ## accumarray ([1, 1, 1;
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85 ## 2, 1, 2;
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86 ## 2, 3, 2;
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87 ## 2, 1, 2;
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88 ## 2, 3, 2], 101:105)
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89 ## @result{} ans(:,:,1) = [101, 0, 0; 0, 0, 0]
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90 ## ans(:,:,2) = [0, 0, 0; 206, 0, 208]
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91 ## @end group
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92 ## @end example
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93 ##
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94 ## The complexity in the non-sparse case is generally O(M+N), where N is
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95 ## the number of subscripts and M is the maximum subscript (linearized
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96 ## in multi-dimensional case). If @var{func} is one of @code{@@sum}
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97 ## (default), @code{@@max}, @code{@@min} or @code{@@(x) @{x@}}, an
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98 ## optimized code path is used. Note that for general reduction function
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99 ## the interpreter overhead can play a major part and it may be more
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100 ## efficient to do multiple accumarray calls and compute the results in
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101 ## a vectorized manner.
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102 ##
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103 ## @seealso{accumdim, unique}
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104 ## @end deftypefn
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105
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106 function A = accumarray (subs, vals, sz = [], func = [], fillval = [], issparse = [])
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107
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108 if (nargin < 2 || nargin > 6)
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109 print_usage ();
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110 endif
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111
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112 lenvals = length (vals);
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113
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114 if (iscell (subs))
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115 subs = cellfun (@vec, subs, "uniformoutput", false);
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116 ndims = numel (subs);
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117 if (ndims == 1)
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118 subs = subs{1};
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119 endif
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120
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121 lensubs = cellfun (@length, subs);
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122
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123 if (any (lensubs != lensubs(1)) || (lenvals > 1 && lenvals != lensubs(1)))
dac62c415e8b Do more error checking on accumarray and accumdim input.
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124 error ("accumarray: dimension mismatch");
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diff changeset
125 endif
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diff changeset
126
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127 else
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128 ndims = columns (subs);
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129 if (lenvals > 1 && lenvals != rows (subs))
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130 error ("accumarray: dimension mismatch")
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131 endif
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132 endif
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133
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134 if (isempty (fillval))
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135 fillval = 0;
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136 endif
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137
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138 if (isempty (issparse))
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139 issparse = false;
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140 endif
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141
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142 if (issparse)
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143
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144 ## Sparse case. Avoid linearizing the subscripts, because it could overflow.
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145
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146 if (fillval != 0)
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147 error ("accumarray: FILLVAL must be zero in the sparse case");
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148 endif
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149
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150 ## Ensure subscripts are a two-column matrix.
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151 if (iscell (subs))
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152 subs = [subs{:}];
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153 endif
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154
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155 ## Validate dimensions.
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156 if (ndims == 1)
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157 subs(:,2) = 1;
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158 elseif (ndims != 2)
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159 error ("accumarray: in the sparse case, needs 1 or 2 subscripts");
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160 endif
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161
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162 if (isnumeric (vals) || islogical (vals))
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163 vals = double (vals);
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164 else
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165 error ("accumarray: in the sparse case, values must be numeric or logical");
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166 endif
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167
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168 if (! (isempty (func) || func == @sum))
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169
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170 ## Reduce values. This is not needed if we're about to sum them, because
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171 ## "sparse" can do that.
11587
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diff changeset
172
10268
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173 ## Sort indices.
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174 [subs, idx] = sortrows (subs);
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175 n = rows (subs);
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176 ## Identify runs.
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177 jdx = find (any (diff (subs, 1, 1), 2));
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178 jdx = [jdx; n];
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179
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180 vals = cellfun (func, mat2cell (vals(:)(idx), diff ([0; jdx])));
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181 subs = subs(jdx, :);
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182 mode = "unique";
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183 else
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184 mode = "sum";
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185 endif
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186
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187 ## Form the sparse matrix.
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188 if (isempty (sz))
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189 A = sparse (subs(:,1), subs(:,2), vals, mode);
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190 elseif (length (sz) == 2)
13788
9ab64f063c96 Consistently allow creation of sparse vectors in accumarray
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191
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192 ## Row vector case
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193 if (sz(1) == 1)
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194 [i, j] = deal (subs(:,2), subs(:,1));
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195 else
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196 [i, j] = deal (subs(:,1), subs(:,2));
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197 endif
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198 A = sparse (i, j, vals, sz(1), sz(2), mode);
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199 else
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200 error ("accumarray: dimensions mismatch");
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201 endif
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202
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203 else
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204
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205 ## Linearize subscripts.
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206 if (ndims > 1)
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207 if (isempty (sz))
9a16a61ed43d new optimizations for accumarray
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208 if (iscell (subs))
12931
cefd568ea073 Replace function handles with function names in cellfun calls for 15% speedup.
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diff changeset
209 sz = cellfun ("max", subs);
10268
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210 else
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211 sz = max (subs, [], 1);
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212 endif
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213 elseif (ndims != length (sz))
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214 error ("accumarray: dimensions mismatch");
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215 endif
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216
10268
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217 ## Convert multidimensional subscripts.
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218 if (ismatrix (subs))
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219 subs = num2cell (subs, 1);
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220 endif
10274
db613bccd992 take advantage of new sort optimization in accumarray
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diff changeset
221 subs = sub2ind (sz, subs{:}); # creates index cache
10271
297996005012 1 more small fix in accumarray
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diff changeset
222 elseif (! isempty (sz) && length (sz) < 2)
10269
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diff changeset
223 error ("accumarray: needs at least 2 dimensions");
10274
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diff changeset
224 elseif (! isindex (subs)) # creates index cache
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225 error ("accumarray: indices must be positive integers");
10268
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226 endif
8934
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227
10268
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228
9a16a61ed43d new optimizations for accumarray
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229 ## Some built-in reductions handled efficiently.
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diff changeset
230
10268
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231 if (isempty (func) || func == @sum)
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232 ## Fast summation.
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233 if (isempty (sz))
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234 A = __accumarray_sum__ (subs, vals);
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235 else
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236 A = __accumarray_sum__ (subs, vals, prod (sz));
8934
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diff changeset
237 ## set proper shape.
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238 A = reshape (A, sz);
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239 endif
c2099a4d12ea partially optimize accumarray
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diff changeset
240
c2099a4d12ea partially optimize accumarray
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diff changeset
241 ## we fill in nonzero fill value.
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242 if (fillval != 0)
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243 mask = true (size (A));
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244 mask(subs) = false;
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diff changeset
245 A(mask) = fillval;
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246 endif
10268
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247 elseif (func == @max)
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248 ## Fast maximization.
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249
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250 if (isinteger (vals))
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251 zero = intmin (class (vals));
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252 elseif (islogical (vals))
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diff changeset
253 zero = false;
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254 elseif (fillval == 0 && all (vals(:) >= 0))
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diff changeset
255 ## This is a common case - fillval is zero, all numbers nonegative.
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256 zero = 0;
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diff changeset
257 else
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258 zero = NaN; # Neutral value.
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259 endif
9a16a61ed43d new optimizations for accumarray
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260
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261 if (isempty (sz))
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262 A = __accumarray_max__ (subs, vals, zero);
10268
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263 else
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264 A = __accumarray_max__ (subs, vals, zero, prod (sz));
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265 A = reshape (A, sz);
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266 endif
8934
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parents: 8920
diff changeset
267
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diff changeset
268 if (fillval != zero && ! (isnan (fillval) || isnan (zero)))
10268
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269 mask = true (size (A));
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270 mask(subs) = false;
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271 A(mask) = fillval;
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272 endif
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273 elseif (func == @min)
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274 ## Fast minimization.
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275
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diff changeset
276 if (isinteger (vals))
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277 zero = intmax (class (vals));
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278 elseif (islogical (vals))
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diff changeset
279 zero = true;
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parents: 13175
diff changeset
280 elseif (fillval == 0 && all (vals(:) <= 0))
14062
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parents: 13931
diff changeset
281 ## This is a common case - fillval is zero, all numbers non-positive.
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282 zero = 0;
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283 else
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284 zero = NaN; # Neutral value.
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285 endif
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parents: 9859
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286
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parents: 9859
diff changeset
287 if (isempty (sz))
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288 A = __accumarray_min__ (subs, vals, zero);
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289 else
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290 A = __accumarray_min__ (subs, vals, zero, prod (sz));
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291 A = reshape (A, sz);
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parents: 9859
diff changeset
292 endif
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89b95972e178 fix previously introduced problem in octave_sort, improve design
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parents: 8507
diff changeset
293
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diff changeset
294 if (fillval != zero && ! (isnan (fillval) || isnan (zero)))
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diff changeset
295 mask = true (size (A));
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parents: 9859
diff changeset
296 mask(subs) = false;
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297 A(mask) = fillval;
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parents: 9859
diff changeset
298 endif
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
299 else
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parents: 9859
diff changeset
300
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parents: 11523
diff changeset
301 ## The general case. Reduce values.
10268
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diff changeset
302 n = rows (subs);
11469
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diff changeset
303 if (numel (vals) == 1)
c776f063fefe Overhaul m-script files to use common variable name between code and documentation.
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diff changeset
304 vals = vals(ones (1, n), 1);
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diff changeset
305 else
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diff changeset
306 vals = vals(:);
10268
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diff changeset
307 endif
11587
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parents: 11523
diff changeset
308
10268
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diff changeset
309 ## Sort indices.
9a16a61ed43d new optimizations for accumarray
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diff changeset
310 [subs, idx] = sort (subs);
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
311 ## Identify runs.
10283
b178769f31ca more small improvements in accumarray
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parents: 10277
diff changeset
312 jdx = find (subs(1:n-1) != subs(2:n));
10268
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diff changeset
313 jdx = [jdx; n];
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diff changeset
314 vals = mat2cell (vals(idx), diff ([0; jdx]));
10268
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parents: 9859
diff changeset
315 ## Optimize the case when function is @(x) {x}, i.e. we just want to
9a16a61ed43d new optimizations for accumarray
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diff changeset
316 ## collect the values to cells.
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
317 persistent simple_cell_str = func2str (@(x) {x});
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
318 if (! strcmp (func2str (func), simple_cell_str))
11469
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diff changeset
319 vals = cellfun (func, vals);
10268
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diff changeset
320 endif
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
321 subs = subs(jdx);
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
322
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da67f032a712 accumarray.m: Handle the case of empty size argument for functions besides @sum
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 14113
diff changeset
323 if (isempty (sz))
da67f032a712 accumarray.m: Handle the case of empty size argument for functions besides @sum
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 14113
diff changeset
324 sz = max (subs);
da67f032a712 accumarray.m: Handle the case of empty size argument for functions besides @sum
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 14113
diff changeset
325 if (length (sz) == 1)
da67f032a712 accumarray.m: Handle the case of empty size argument for functions besides @sum
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parents: 14113
diff changeset
326 sz(2) = 1;
da67f032a712 accumarray.m: Handle the case of empty size argument for functions besides @sum
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 14113
diff changeset
327 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
328 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
329
10268
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diff changeset
330 ## Construct matrix of fillvals.
11469
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diff changeset
331 if (iscell (vals))
10268
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diff changeset
332 A = cell (sz);
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
333 elseif (fillval == 0)
11469
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diff changeset
334 A = zeros (sz, class (vals));
10268
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diff changeset
335 else
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parents: 9859
diff changeset
336 A = repmat (fillval, sz);
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
337 endif
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
338
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
339 ## Set the reduced values.
11469
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diff changeset
340 A(subs) = vals;
6770
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dbateman
parents:
diff changeset
341 endif
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
342 endif
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
343 endfunction
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
344
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
345 %!error (accumarray (1:5))
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
346 %!error (accumarray ([1,2,3],1:2))
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
347 %!assert (accumarray ([1;2;4;2;4],101:105), [101;206;0;208])
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
348 %!assert (accumarray ([1,1,1;2,1,2;2,3,2;2,1,2;2,3,2],101:105),cat(3, [101,0,0;0,0,0],[0,0,0;206,0,208]))
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
349 %!assert (accumarray ([1,1,1;2,1,2;2,3,2;2,1,2;2,3,2],101:105,[],@(x)sin(sum(x))),sin(cat(3, [101,0,0;0,0,0],[0,0,0;206,0,208])))
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
350 %!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),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]))
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
351 %!assert (accumarray ([1,1;2,1;2,3;2,1;2,3],101:105,[2,4],@max,NaN),[101,NaN,NaN,NaN;104,NaN,105,NaN])
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diff changeset
352 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105, [], @prod), [101, 0, 0; 10608, 0, 10815])
6770
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dbateman
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diff changeset
353 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105,[2 4],@prod,0,true),sparse([1,2,2],[1,1,3],[101,10608,10815],2,4))
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
354 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],1,[2,4]), [1,0,0,0;2,0,2,0])
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
355 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105,[2,4],@(x)length(x)>1),[false,false,false,false;true,false,true,false])
13788
9ab64f063c96 Consistently allow creation of sparse vectors in accumarray
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 13787
diff changeset
356 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 0), [3; 4])
9ab64f063c96 Consistently allow creation of sparse vectors in accumarray
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 13787
diff changeset
357 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 1), sparse ([3; 4]))
9ab64f063c96 Consistently allow creation of sparse vectors in accumarray
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 13787
diff changeset
358 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 0), [3, 4])
9ab64f063c96 Consistently allow creation of sparse vectors in accumarray
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 13787
diff changeset
359 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 1), sparse ([3, 4]))
6770
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parents:
diff changeset
360 %!test
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
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diff changeset
361 %! A = accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105,[2,4],@(x){x});
10268
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diff changeset
362 %! assert (A{2},[102;104])
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
363 %!test
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
diff changeset
364 %! subs = ceil (rand (2000, 3)*10);
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diff changeset
365 %! vals = rand (2000, 1);
c776f063fefe Overhaul m-script files to use common variable name between code and documentation.
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diff changeset
366 %! assert (accumarray (subs, vals, [], @max), accumarray (subs, vals, [], @(x) max (x)));
10268
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diff changeset
367 %!test
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
368 %! subs = ceil (rand (2000, 1)*100);
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diff changeset
369 %! vals = rand (2000, 1);
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parents: 11191
diff changeset
370 %! assert (accumarray (subs, vals, [100, 1], @min, NaN), accumarray (subs, vals, [100, 1], @(x) min (x), NaN));
10268
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diff changeset
371 %!test
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
372 %! subs = ceil (rand (2000, 2)*30);
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
373 %! subsc = num2cell (subs, 1);
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diff changeset
374 %! vals = rand (2000, 1);
c776f063fefe Overhaul m-script files to use common variable name between code and documentation.
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parents: 11191
diff changeset
375 %! assert (accumarray (subsc, vals, [], [], 0, true), accumarray (subs, vals, [], [], 0, true));
10268
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diff changeset
376 %!test
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
377 %! subs = ceil (rand (2000, 3)*10);
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
378 %! subsc = num2cell (subs, 1);
11469
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parents: 11191
diff changeset
379 %! vals = rand (2000, 1);
c776f063fefe Overhaul m-script files to use common variable name between code and documentation.
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parents: 11191
diff changeset
380 %! assert (accumarray (subsc, vals, [], @max), accumarray (subs, vals, [], @max));
10268
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parents: 9859
diff changeset
381
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
diff changeset
382