Mercurial > hg > octave-nkf
annotate scripts/general/accumarray.m @ 14138:72c96de7a403 stable
maint: update copyright notices for 2012
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 02 Jan 2012 14:25:41 -0500 |
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1 ## Copyright (C) 2007-2012 David Bateman |
11523 | 2 ## Copyright (C) 2009-2010 VZLU Prague |
6770 | 3 ## |
7016 | 4 ## This file is part of Octave. |
6770 | 5 ## |
7016 | 6 ## Octave is free software; you can redistribute it and/or modify it |
7 ## under the terms of the GNU General Public License as published by | |
8 ## the Free Software Foundation; either version 3 of the License, or (at | |
9 ## your option) any later version. | |
10 ## | |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
6770 | 15 ## |
16 ## You should have received a copy of the GNU General Public License | |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
6770 | 19 |
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{}) |
6770 | 23 ## |
7186 | 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. |
6770 | 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 |
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38 ## subscripts of @var{subs} are taken as the indices into it. |
6770 | 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. |
6770 | 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. |
6770 | 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}). |
6770 | 65 ## |
66 ## @example | |
67 ## @group | |
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68 ## @var{x} = [91, 92, 90, 92, 90, 89, 91, 89, 90, 100, 100, 100]; |
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69 ## [@var{u}, ~, @var{j}] = unique (@var{x}); |
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70 ## [accumarray(@var{j}', 1), @var{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) |
6770 | 89 ## @result{} ans(:,:,1) = [101, 0, 0; 0, 0, 0] |
90 ## ans(:,:,2) = [0, 0, 0; 206, 0, 208] | |
91 ## @end group | |
92 ## @end example | |
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93 ## |
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94 ## The sparse option can be used as an alternative to the @code{sparse} |
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95 ## constructor (@pxref{doc-sparse}). Thus |
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96 ## |
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97 ## @example |
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98 ## sparse (@var{i}, @var{j}, @var{sv}) |
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99 ## @end example |
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100 ## |
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101 ## @noindent |
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102 ## can be written with @code{accumarray} as |
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103 ## |
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104 ## @example |
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105 ## accumarray ([@var{i}, @var{j}], @var{sv}', [], [], 0, true) |
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106 ## @end example |
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107 ## |
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108 ## @noindent |
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109 ## For repeated indices, @code{sparse} adds the corresponding value. To |
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110 ## take the minimum instead, use @code{min} as an accumulator function: |
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111 ## |
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112 ## @example |
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113 ## accumarray ([@var{i}, @var{j}], @var{sv}', [], @@min, 0, true) |
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114 ## @end example |
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115 ## |
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116 ## The complexity of accumarray in general for the non-sparse case is |
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117 ## generally O(M+N), where N is the number of subscripts and M is the |
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118 ## maximum subscript (linearized in multi-dimensional case). If |
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119 ## @var{func} is one of @code{@@sum} (default), @code{@@max}, |
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120 ## @code{@@min} or @code{@@(x) @{x@}}, an optimized code path is used. |
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121 ## Note that for general reduction function the interpreter overhead can |
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122 ## play a major part and it may be more efficient to do multiple |
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123 ## accumarray calls and compute the results in a vectorized manner. |
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124 ## |
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125 ## @seealso{accumdim, unique, sparse} |
6770 | 126 ## @end deftypefn |
127 | |
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128 function A = accumarray (subs, vals, sz = [], func = [], fillval = [], issparse = []) |
6770 | 129 |
130 if (nargin < 2 || nargin > 6) | |
131 print_usage (); | |
132 endif | |
133 | |
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134 lenvals = length (vals); |
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135 |
7186 | 136 if (iscell (subs)) |
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137 subs = cellfun (@vec, subs, "uniformoutput", false); |
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138 ndims = numel (subs); |
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139 if (ndims == 1) |
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140 subs = subs{1}; |
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141 endif |
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142 |
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143 lensubs = cellfun (@length, subs); |
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144 |
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145 if (any (lensubs != lensubs(1)) || |
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146 (lenvals > 1 && lenvals != lensubs(1))) |
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147 error ("accumarray: dimension mismatch"); |
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148 endif |
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149 |
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150 else |
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151 ndims = columns (subs); |
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152 if (lenvals > 1 && lenvals != rows (subs)) |
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153 error ("accumarray: dimension mismatch") |
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154 endif |
6770 | 155 endif |
156 | |
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157 if (isempty (fillval)) |
6770 | 158 fillval = 0; |
159 endif | |
160 | |
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161 if (isempty (issparse)) |
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162 issparse = false; |
6770 | 163 endif |
7186 | 164 |
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165 if (issparse) |
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166 |
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167 ## Sparse case. Avoid linearizing the subscripts, because it could |
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168 ## overflow. |
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169 |
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170 if (fillval != 0) |
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171 error ("accumarray: FILLVAL must be zero in the sparse case"); |
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172 endif |
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173 |
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174 ## Ensure subscripts are a two-column matrix. |
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175 if (iscell (subs)) |
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176 subs = [subs{:}]; |
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177 endif |
6770 | 178 |
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179 ## Validate dimensions. |
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180 if (ndims == 1) |
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181 subs(:,2) = 1; |
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182 elseif (ndims != 2) |
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183 error ("accumarray: in the sparse case, needs 1 or 2 subscripts"); |
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184 endif |
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185 |
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186 if (isnumeric (vals) || islogical (vals)) |
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187 vals = double (vals); |
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188 else |
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189 error ("accumarray: in the sparse case, values must be numeric or logical"); |
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190 endif |
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191 |
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192 if (! (isempty (func) || func == @sum)) |
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193 |
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194 ## Reduce values. This is not needed if we're about to sum them, |
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195 ## because "sparse" can do that. |
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196 |
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197 ## Sort indices. |
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198 [subs, idx] = sortrows (subs); |
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199 n = rows (subs); |
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200 ## Identify runs. |
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201 jdx = find (any (diff (subs, 1, 1), 2)); |
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202 jdx = [jdx; n]; |
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203 |
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204 vals = cellfun (func, mat2cell (vals(:)(idx), diff ([0; jdx]))); |
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205 subs = subs(jdx, :); |
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206 mode = "unique"; |
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207 else |
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208 mode = "sum"; |
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209 endif |
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210 |
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211 ## Form the sparse matrix. |
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212 if (isempty (sz)) |
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213 A = sparse (subs(:,1), subs(:,2), vals, mode); |
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214 elseif (length (sz) == 2) |
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215 |
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216 ## Row vector case |
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217 if (sz(1) == 1) |
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218 [i, j] = deal (subs(:,2), subs(:,1)); |
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219 else |
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220 [i, j] = deal (subs(:,1), subs(:,2)); |
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221 endif |
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222 A = sparse (i, j, vals, sz(1), sz(2), mode); |
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223 else |
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224 error ("accumarray: dimensions mismatch"); |
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225 endif |
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226 |
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227 else |
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228 |
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229 ## Linearize subscripts. |
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230 if (ndims > 1) |
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231 if (isempty (sz)) |
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232 if (iscell (subs)) |
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233 sz = cellfun ("max", subs); |
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234 else |
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235 sz = max (subs, [], 1); |
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236 endif |
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237 elseif (ndims != length (sz)) |
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238 error ("accumarray: dimensions mismatch"); |
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239 endif |
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240 |
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241 ## Convert multidimensional subscripts. |
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242 if (ismatrix (subs)) |
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243 subs = num2cell (subs, 1); |
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244 endif |
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245 subs = sub2ind (sz, subs{:}); # creates index cache |
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246 elseif (! isempty (sz) && length (sz) < 2) |
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247 error ("accumarray: needs at least 2 dimensions"); |
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248 elseif (! isindex (subs)) # creates index cache |
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249 error ("accumarray: indices must be positive integers"); |
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250 endif |
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251 |
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252 |
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253 ## Some built-in reductions handled efficiently. |
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254 |
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255 if (isempty (func) || func == @sum) |
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256 ## Fast summation. |
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257 if (isempty (sz)) |
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258 A = __accumarray_sum__ (subs, vals); |
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259 else |
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260 A = __accumarray_sum__ (subs, vals, prod (sz)); |
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261 ## set proper shape. |
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262 A = reshape (A, sz); |
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263 endif |
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264 |
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265 ## we fill in nonzero fill value. |
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266 if (fillval != 0) |
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267 mask = true (size (A)); |
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268 mask(subs) = false; |
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269 A(mask) = fillval; |
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270 endif |
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271 elseif (func == @max) |
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272 ## Fast maximization. |
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273 |
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274 if (isinteger (vals)) |
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275 zero = intmin (class (vals)); |
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276 elseif (islogical (vals)) |
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277 zero = false; |
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278 elseif (fillval == 0 && all (vals(:) >= 0)) |
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279 ## This is a common case - fillval is zero, all numbers |
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280 ## nonegative. |
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281 zero = 0; |
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282 else |
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283 zero = NaN; # Neutral value. |
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284 endif |
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285 |
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286 if (isempty (sz)) |
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287 A = __accumarray_max__ (subs, vals, zero); |
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288 else |
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289 A = __accumarray_max__ (subs, vals, zero, prod (sz)); |
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290 A = reshape (A, sz); |
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291 endif |
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292 |
10775 | 293 if (fillval != zero && ! (isnan (fillval) || isnan (zero))) |
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294 mask = true (size (A)); |
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295 mask(subs) = false; |
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296 A(mask) = fillval; |
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297 endif |
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298 elseif (func == @min) |
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299 ## Fast minimization. |
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300 |
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301 if (isinteger (vals)) |
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302 zero = intmax (class (vals)); |
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303 elseif (islogical (vals)) |
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304 zero = true; |
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305 elseif (fillval == 0 && all (vals(:) <= 0)) |
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306 ## This is a common case - fillval is zero, all numbers |
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307 ## non-positive. |
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308 zero = 0; |
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309 else |
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310 zero = NaN; # Neutral value. |
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311 endif |
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312 |
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313 if (isempty (sz)) |
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314 A = __accumarray_min__ (subs, vals, zero); |
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315 else |
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316 A = __accumarray_min__ (subs, vals, zero, prod (sz)); |
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317 A = reshape (A, sz); |
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318 endif |
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319 |
10775 | 320 if (fillval != zero && ! (isnan (fillval) || isnan (zero))) |
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321 mask = true (size (A)); |
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322 mask(subs) = false; |
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323 A(mask) = fillval; |
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324 endif |
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325 else |
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326 |
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327 ## The general case. Reduce values. |
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328 n = rows (subs); |
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329 if (numel (vals) == 1) |
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330 vals = vals(ones (1, n), 1); |
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331 else |
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332 vals = vals(:); |
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333 endif |
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334 |
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335 ## Sort indices. |
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336 [subs, idx] = sort (subs); |
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337 ## Identify runs. |
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338 jdx = find (subs(1:n-1) != subs(2:n)); |
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339 jdx = [jdx; n]; |
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340 vals = mat2cell (vals(idx), diff ([0; jdx])); |
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341 ## Optimize the case when function is @(x) {x}, i.e. we just want |
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342 ## to collect the values to cells. |
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343 persistent simple_cell_str = func2str (@(x) {x}); |
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344 if (! strcmp (func2str (func), simple_cell_str)) |
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345 vals = cellfun (func, vals); |
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346 endif |
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347 subs = subs(jdx); |
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348 |
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349 if (isempty (sz)) |
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350 sz = max (subs); |
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351 if (length (sz) == 1) |
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352 sz(2) = 1; |
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353 endif |
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354 endif |
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355 |
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356 ## Construct matrix of fillvals. |
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357 if (iscell (vals)) |
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358 A = cell (sz); |
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359 elseif (fillval == 0) |
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360 A = zeros (sz, class (vals)); |
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361 else |
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362 A = repmat (fillval, sz); |
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363 endif |
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364 |
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365 ## Set the reduced values. |
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366 A(subs) = vals; |
6770 | 367 endif |
368 endif | |
369 endfunction | |
370 | |
371 %!error (accumarray (1:5)) | |
372 %!error (accumarray ([1,2,3],1:2)) | |
373 %!assert (accumarray ([1;2;4;2;4],101:105), [101;206;0;208]) | |
374 %!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])) | |
375 %!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]))) | |
376 %!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])) | |
377 %!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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378 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105, [], @prod), [101, 0, 0; 10608, 0, 10815]) |
6770 | 379 %!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)) |
380 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],1,[2,4]), [1,0,0,0;2,0,2,0]) | |
381 %!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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382 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 0), [3; 4]) |
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383 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 1), sparse ([3; 4])) |
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384 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 0), [3, 4]) |
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385 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 1), sparse ([3, 4])) |
6770 | 386 %!test |
387 %! A = accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105,[2,4],@(x){x}); | |
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388 %! assert (A{2},[102;104]) |
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389 %!test |
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390 %! subs = ceil (rand (2000, 3)*10); |
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391 %! vals = rand (2000, 1); |
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392 %! assert (accumarray (subs, vals, [], @max), accumarray (subs, vals, [], @(x) max (x))); |
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393 %!test |
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394 %! subs = ceil (rand (2000, 1)*100); |
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395 %! vals = rand (2000, 1); |
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396 %! assert (accumarray (subs, vals, [100, 1], @min, NaN), accumarray (subs, vals, [100, 1], @(x) min (x), NaN)); |
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397 %!test |
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398 %! subs = ceil (rand (2000, 2)*30); |
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399 %! subsc = num2cell (subs, 1); |
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400 %! vals = rand (2000, 1); |
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401 %! assert (accumarray (subsc, vals, [], [], 0, true), accumarray (subs, vals, [], [], 0, true)); |
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402 %!test |
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403 %! subs = ceil (rand (2000, 3)*10); |
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404 %! subsc = num2cell (subs, 1); |
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405 %! vals = rand (2000, 1); |
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406 %! assert (accumarray (subsc, vals, [], @max), accumarray (subs, vals, [], @max)); |
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407 |
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408 |