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Do more error checking on accumarray and accumdim input. * accumarray.m: Check that number indices matches number of values to accumulate. Document this change. * accumdim.m: Check that length of index vector equals length of array along given dimension. Also let the extension parameter be empty in addition to being zero. Document this change and reformat docstring. * data.cc (do_accumdim_sum): Check that number of indices matches number of values.
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Tue, 27 Dec 2011 13:45:30 -0500
parents 5b49cafe0599
children da67f032a712
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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)))
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124 error ("accumarray: dimension mismatch");
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125 endif
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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.
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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
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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))
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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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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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221 subs = sub2ind (sz, subs{:}); # creates index cache
10271
297996005012 1 more small fix in accumarray
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222 elseif (! isempty (sz) && length (sz) < 2)
10269
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223 error ("accumarray: needs at least 2 dimensions");
10274
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224 elseif (! isindex (subs)) # creates index cache
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225 error ("accumarray: indices must be positive integers");
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226 endif
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227
10268
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228
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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));
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237 ## set proper shape.
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238 A = reshape (A, sz);
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239 endif
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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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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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253 zero = false;
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254 elseif (fillval == 0 && all (vals(:) >= 0))
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255 ## This is a common case - fillval is zero, all numbers nonegative.
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256 zero = 0;
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257 else
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258 zero = NaN; # Neutral value.
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259 endif
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260
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261 if (isempty (sz))
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262 A = __accumarray_max__ (subs, vals, zero);
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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
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267
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268 if (fillval != zero && ! (isnan (fillval) || isnan (zero)))
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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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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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279 zero = true;
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280 elseif (fillval == 0 && all (vals(:) <= 0))
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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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286
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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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292 endif
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293
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294 if (fillval != zero && ! (isnan (fillval) || isnan (zero)))
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295 mask = true (size (A));
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296 mask(subs) = false;
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297 A(mask) = fillval;
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298 endif
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299 else
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300
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301 ## The general case. Reduce values.
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302 n = rows (subs);
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303 if (numel (vals) == 1)
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304 vals = vals(ones (1, n), 1);
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305 else
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306 vals = vals(:);
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307 endif
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308
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309 ## Sort indices.
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310 [subs, idx] = sort (subs);
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311 ## Identify runs.
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312 jdx = find (subs(1:n-1) != subs(2:n));
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313 jdx = [jdx; n];
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314 vals = mat2cell (vals(idx), diff ([0; jdx]));
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315 ## Optimize the case when function is @(x) {x}, i.e. we just want to
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316 ## collect the values to cells.
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317 persistent simple_cell_str = func2str (@(x) {x});
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318 if (! strcmp (func2str (func), simple_cell_str))
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319 vals = cellfun (func, vals);
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320 endif
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321 subs = subs(jdx);
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322
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323 ## Construct matrix of fillvals.
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324 if (iscell (vals))
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325 A = cell (sz);
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326 elseif (fillval == 0)
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327 A = zeros (sz, class (vals));
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328 else
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329 A = repmat (fillval, sz);
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330 endif
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331
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332 ## Set the reduced values.
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333 A(subs) = vals;
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334 endif
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
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335 endif
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
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336 endfunction
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
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diff changeset
337
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
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338 %!error (accumarray (1:5))
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339 %!error (accumarray ([1,2,3],1:2))
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
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340 %!assert (accumarray ([1;2;4;2;4],101:105), [101;206;0;208])
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
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341 %!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]
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diff changeset
342 %!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]
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343 %!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]
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344 %!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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345 %!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))
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346 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],1,[2,4]), [1,0,0,0;2,0,2,0])
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347 %!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])
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parents: 13787
diff changeset
348 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 0), [3; 4])
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diff changeset
349 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 1), sparse ([3; 4]))
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diff changeset
350 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 0), [3, 4])
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diff changeset
351 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 1), sparse ([3, 4]))
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352 %!test
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353 %! A = accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105,[2,4],@(x){x});
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354 %! assert (A{2},[102;104])
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diff changeset
355 %!test
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356 %! subs = ceil (rand (2000, 3)*10);
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357 %! vals = rand (2000, 1);
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358 %! assert (accumarray (subs, vals, [], @max), accumarray (subs, vals, [], @(x) max (x)));
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359 %!test
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360 %! subs = ceil (rand (2000, 1)*100);
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361 %! vals = rand (2000, 1);
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362 %! assert (accumarray (subs, vals, [100, 1], @min, NaN), accumarray (subs, vals, [100, 1], @(x) min (x), NaN));
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diff changeset
363 %!test
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diff changeset
364 %! subs = ceil (rand (2000, 2)*30);
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365 %! subsc = num2cell (subs, 1);
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366 %! vals = rand (2000, 1);
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367 %! assert (accumarray (subsc, vals, [], [], 0, true), accumarray (subs, vals, [], [], 0, true));
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368 %!test
9a16a61ed43d new optimizations for accumarray
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369 %! subs = ceil (rand (2000, 3)*10);
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370 %! subsc = num2cell (subs, 1);
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371 %! vals = rand (2000, 1);
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372 %! assert (accumarray (subsc, vals, [], @max), accumarray (subs, vals, [], @max));
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diff changeset
373
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
374