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document accumarray complexity
author Jaroslav Hajek <highegg@gmail.com>
date Mon, 08 Feb 2010 13:22:09 +0100
parents db613bccd992
children 703038d648f1
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1 ## Copyright (C) 2007, 2008, 2009 David Bateman
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2 ## Copyright (C) 2009 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{csubs}, @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 row
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27 ## of @var{subs} corresponds to one of the values in @var{vals}.
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28 ##
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29 ## The size of the matrix will be determined by the subscripts themselves.
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30 ## However, if @var{sz} is defined it determines the matrix size. The length
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31 ## of @var{sz} must correspond to the number of columns in @var{subs}.
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32 ##
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33 ## The default action of @code{accumarray} is to sum the elements with the
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34 ## same subscripts. This behavior can be modified by defining the @var{func}
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35 ## function. This should be a function or function handle that accepts a
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36 ## column vector and returns a scalar. The result of the function should not
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37 ## depend on the order of the subscripts.
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38 ##
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39 ## The elements of the returned array that have no subscripts associated with
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40 ## them are set to zero. Defining @var{fillval} to some other value allows
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41 ## these values to be defined.
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42 ##
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43 ## By default @code{accumarray} returns a full matrix. If @var{issparse} is
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44 ## logically true, then a sparse matrix is returned instead.
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45 ##
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46 ## An example of the use of @code{accumarray} is:
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47 ##
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48 ## @example
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49 ## @group
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50 ## accumarray ([1,1,1;2,1,2;2,3,2;2,1,2;2,3,2], 101:105)
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51 ## @result{} ans(:,:,1) = [101, 0, 0; 0, 0, 0]
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52 ## ans(:,:,2) = [0, 0, 0; 206, 0, 208]
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53 ## @end group
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54 ## @end example
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55 ##
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56 ## The complexity in the non-sparse case is generally O(M+N), where N is the number of
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57 ## subscripts and M is the maximum subscript (linearized in multidimensional case).
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58 ## If @var{func} is one of @code{@@sum} (default), @code{@@max}, @code{@@min}
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59 ## or @code{@@(x) @{x@}}, an optimized code path is used.
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60 ## Note that for general reduction function the interpreter overhead can play a
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61 ## major part and it may be more efficient to do multiple accumarray calls and
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62 ## compute the results in a vectorized manner.
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63 ## @end deftypefn
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64
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65 function A = accumarray (subs, val, sz = [], func = [], fillval = [], isspar = [])
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66
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67 if (nargin < 2 || nargin > 6)
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68 print_usage ();
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69 endif
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70
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71 if (iscell (subs))
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72 subs = cellfun (@(x) x(:), subs, "UniformOutput", false);
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73 ndims = numel (subs);
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74 if (ndims == 1)
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75 subs = subs{1};
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76 endif
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77 else
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78 ndims = columns (subs);
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79 endif
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80
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81 if (isempty (fillval))
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82 fillval = 0;
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83 endif
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84
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85 if (isempty (isspar))
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86 isspar = false;
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87 endif
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88
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89 if (isspar)
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90
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91 ## Sparse case. Avoid linearizing the subscripts, because it could overflow.
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92
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93 if (fillval != 0)
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94 error ("accumarray: fillval must be zero in the sparse case");
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95 endif
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96
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97 ## Ensure subscripts are a two-column matrix.
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98 if (iscell (subs))
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99 subs = [subs{:}];
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100 endif
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101
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102 ## Validate dimensions.
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103 if (ndims == 1)
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104 subs(:,2) = 1;
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105 elseif (ndims != 2)
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106 error ("accumarray: in the sparse case, needs 1 or 2 subscripts");
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107 endif
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108
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109 if (isnumeric (val) || islogical (val))
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110 vals = double (val);
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111 else
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112 error ("accumarray: in the sparse case, values must be numeric or logical");
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113 endif
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114
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115 if (! (isempty (func) || func == @sum))
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116
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117 ## Reduce values. This is not needed if we're about to sum them, because
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118 ## "sparse" can do that.
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119
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120 ## Sort indices.
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121 [subs, idx] = sortrows (subs);
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122 n = rows (subs);
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123 ## Identify runs.
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124 jdx = find (any (diff (subs, 1, 1), 2));
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125 jdx = [jdx; n];
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126
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127 val = cellfun (func, mat2cell (val(:)(idx), diff ([0; jdx])));
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128 subs = subs(jdx, :);
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129 endif
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130
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131 ## Form the sparse matrix.
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132 if (isempty (sz))
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133 A = sparse (subs(:,1), subs(:,2), val);
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134 elseif (length (sz) == 2)
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135 A = sparse (subs(:,1), subs(:,2), val, sz(1), sz(2));
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136 else
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137 error ("accumarray: dimensions mismatch")
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138 endif
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139
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140 else
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141
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142 ## Linearize subscripts.
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143 if (ndims > 1)
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144 if (isempty (sz))
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145 if (iscell (subs))
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146 sz = cellfun (@max, subs);
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147 else
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148 sz = max (subs, [], 1);
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149 endif
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150 elseif (ndims != length (sz))
8934
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151 error ("accumarray: dimensions mismatch")
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152 endif
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153
10268
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154 ## Convert multidimensional subscripts.
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155 if (ismatrix (subs))
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156 subs = num2cell (subs, 1);
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157 endif
10274
db613bccd992 take advantage of new sort optimization in accumarray
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158 subs = sub2ind (sz, subs{:}); # creates index cache
10271
297996005012 1 more small fix in accumarray
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159 elseif (! isempty (sz) && length (sz) < 2)
10269
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160 error ("accumarray: needs at least 2 dimensions");
10274
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161 elseif (! isindex (subs)) # creates index cache
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162 error ("accumarray: indices must be positive integers");
10268
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163 endif
8934
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164
10268
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165
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166 ## Some built-in reductions handled efficiently.
8934
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167
10268
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168 if (isempty (func) || func == @sum)
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169 ## Fast summation.
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170 if (isempty (sz))
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171 A = __accumarray_sum__ (subs, val);
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172 else
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173 A = __accumarray_sum__ (subs, val, prod (sz));
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174 ## set proper shape.
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175 A = reshape (A, sz);
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176 endif
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177
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178 ## we fill in nonzero fill value.
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179 if (fillval != 0)
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180 mask = true (size (A));
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181 mask(subs) = false;
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182 A(mask) = fillval;
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183 endif
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184 elseif (func == @max)
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185 ## Fast maximization.
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186
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187 if (isinteger (val))
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188 zero = intmin (class (val));
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189 elseif (islogical (val))
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190 zero = false;
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191 elseif (fillval == 0 && all (val(:) >= 0))
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192 ## This is a common case - fillval is zero, all numbers nonegative.
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193 zero = 0;
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194 else
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195 zero = NaN; # Neutral value.
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196 endif
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197
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198 if (isempty (sz))
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199 A = __accumarray_max__ (subs, val, zero);
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200 else
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201 A = __accumarray_max__ (subs, val, zero, prod (sz));
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202 A = reshape (A, sz);
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203 endif
8934
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204
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205 if (fillval != zero && isnan (fillval) != isnan (zero))
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206 mask = true (size (A));
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207 mask(subs) = false;
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208 A(mask) = fillval;
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209 endif
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210 elseif (func == @min)
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211 ## Fast minimization.
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212
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213 if (isinteger (val))
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214 zero = intmax (class (val));
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215 elseif (islogical (val))
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diff changeset
216 zero = true;
10268
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217 else
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218 zero = NaN; # Neutral value.
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219 endif
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220
9a16a61ed43d new optimizations for accumarray
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221 if (isempty (sz))
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222 A = __accumarray_min__ (subs, val, zero);
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223 else
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224 A = __accumarray_min__ (subs, val, zero, prod (sz));
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225 A = reshape (A, sz);
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226 endif
8820
89b95972e178 fix previously introduced problem in octave_sort, improve design
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parents: 8507
diff changeset
227
10268
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228 if (fillval != zero && isnan (fillval) != isnan (zero))
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229 mask = true (size (A));
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230 mask(subs) = false;
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231 A(mask) = fillval;
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232 endif
9a16a61ed43d new optimizations for accumarray
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233 else
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234
9a16a61ed43d new optimizations for accumarray
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235 ## The general case. Reduce values.
9a16a61ed43d new optimizations for accumarray
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236 n = rows (subs);
9a16a61ed43d new optimizations for accumarray
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diff changeset
237 if (numel (val) == 1)
9a16a61ed43d new optimizations for accumarray
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diff changeset
238 val = val(ones (1, n), 1);
9a16a61ed43d new optimizations for accumarray
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239 else
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240 val = val(:);
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241 endif
9a16a61ed43d new optimizations for accumarray
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242
9a16a61ed43d new optimizations for accumarray
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diff changeset
243 ## Sort indices.
9a16a61ed43d new optimizations for accumarray
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244 [subs, idx] = sort (subs);
9a16a61ed43d new optimizations for accumarray
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diff changeset
245 ## Identify runs.
9a16a61ed43d new optimizations for accumarray
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diff changeset
246 jdx = find (diff (subs, 1, 1));
9a16a61ed43d new optimizations for accumarray
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diff changeset
247 jdx = [jdx; n];
9a16a61ed43d new optimizations for accumarray
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diff changeset
248 val = mat2cell (val(idx), diff ([0; jdx]));
9a16a61ed43d new optimizations for accumarray
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diff changeset
249 ## Optimize the case when function is @(x) {x}, i.e. we just want to
9a16a61ed43d new optimizations for accumarray
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250 ## collect the values to cells.
9a16a61ed43d new optimizations for accumarray
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diff changeset
251 persistent simple_cell_str = func2str (@(x) {x});
9a16a61ed43d new optimizations for accumarray
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diff changeset
252 if (! strcmp (func2str (func), simple_cell_str))
9a16a61ed43d new optimizations for accumarray
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diff changeset
253 val = cellfun (func, val);
9a16a61ed43d new optimizations for accumarray
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diff changeset
254 endif
9a16a61ed43d new optimizations for accumarray
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diff changeset
255 subs = subs(jdx);
9a16a61ed43d new optimizations for accumarray
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diff changeset
256
9a16a61ed43d new optimizations for accumarray
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diff changeset
257 ## Construct matrix of fillvals.
9a16a61ed43d new optimizations for accumarray
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diff changeset
258 if (iscell (val))
9a16a61ed43d new optimizations for accumarray
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diff changeset
259 A = cell (sz);
9a16a61ed43d new optimizations for accumarray
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diff changeset
260 elseif (fillval == 0)
9a16a61ed43d new optimizations for accumarray
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diff changeset
261 A = zeros (sz, class (val));
9a16a61ed43d new optimizations for accumarray
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diff changeset
262 else
9a16a61ed43d new optimizations for accumarray
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diff changeset
263 A = repmat (fillval, sz);
9a16a61ed43d new optimizations for accumarray
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diff changeset
264 endif
9a16a61ed43d new optimizations for accumarray
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parents: 9859
diff changeset
265
9a16a61ed43d new optimizations for accumarray
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diff changeset
266 ## Set the reduced values.
9a16a61ed43d new optimizations for accumarray
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diff changeset
267 A(subs) = val;
6770
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
268 endif
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
269 endif
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
270 endfunction
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
271
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
272 %!error (accumarray (1:5))
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
273 %!error (accumarray ([1,2,3],1:2))
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
parents:
diff changeset
274 %!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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275 %!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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parents:
diff changeset
276 %!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
277 %!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
278 %!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])
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
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parents:
diff changeset
279 %!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]
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diff changeset
280 %!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]
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diff changeset
281 %!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])
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
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diff changeset
282 %!test
babcbcc11ab6 [project @ 2007-07-06 08:44:04 by dbateman]
dbateman
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diff changeset
283 %! A = accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105,[2,4],@(x){x});
10268
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284 %! assert (A{2},[102;104])
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diff changeset
285 %!test
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286 %! subs = ceil (rand (2000, 3)*10);
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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287 %! val = rand (2000, 1);
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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288 %! assert (accumarray (subs, val, [], @max), accumarray (subs, val, [], @(x) max (x)));
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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289 %!test
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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290 %! subs = ceil (rand (2000, 1)*100);
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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291 %! val = rand (2000, 1);
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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292 %! assert (accumarray (subs, val, [100, 1], @min, NaN), accumarray (subs, val, [100, 1], @(x) min (x), NaN));
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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293 %!test
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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294 %! subs = ceil (rand (2000, 2)*30);
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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295 %! subsc = num2cell (subs, 1);
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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296 %! val = rand (2000, 1);
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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297 %! assert (accumarray (subsc, val, [], [], 0, true), accumarray (subs, val, [], [], 0, true));
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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298 %!test
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
diff changeset
299 %! subs = ceil (rand (2000, 3)*10);
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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300 %! subsc = num2cell (subs, 1);
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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301 %! val = rand (2000, 1);
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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302 %! assert (accumarray (subsc, val, [], @max), accumarray (subs, val, [], @max));
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
diff changeset
303
9a16a61ed43d new optimizations for accumarray
Jaroslav Hajek <highegg@gmail.com>
parents: 9859
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304