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Grammarcheck of documentation before 3.6.0 release. * accumarray.m, blkdiag.m, nargoutchk.m, nthargout.m, profexplore.m, profile.m, computer.m, orderfields.m, recycle.m, version.m, sqp.m, matlabroot.m, __plt_get_axis_arg__.m, isonormals.m, isosurface.m, __fltk_file_filter__.m, __is_function__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m, __uiobject_split_args__.m, __uiputfile_fltk__.m, uicontextmenu.m, uiresume.m, uiwait.m, mkpp.m, ppder.m, residue.m, addpref.m, getpref.m, ispref.m, loadprefs.m, prefsfile.m, saveprefs.m, rmpref.m, setpref.m, fftshift.m, bicg.m, bicgstab.m, cgs.m, gmres.m, __sprand_impl__.m, quantile.m, deblank.m, strsplit.m, addtodate.m, bsxfun.cc, kron.cc, regexp.cc, data.cc, file-io.cc, graphics.cc, load-save.cc, mappers.cc: Grammarcheck of documentation before 3.6.0 release.
author Rik <octave@nomad.inbox5.com>
date Wed, 23 Nov 2011 08:38:19 -0800
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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}.
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30 ##
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31 ## The size of the matrix will be determined by the subscripts
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32 ## themselves. However, if @var{sz} is defined it determines the matrix
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33 ## size. The length of @var{sz} must correspond to the number of columns
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34 ## in @var{subs}. An exception is if @var{subs} has only one column, in
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35 ## which case @var{sz} may be the dimensions of a vector and the subscripts
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36 ## of @var{subs} are taken as the indices into it.
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37 ##
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38 ## The default action of @code{accumarray} is to sum the elements with
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39 ## the same subscripts. This behavior can be modified by defining the
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40 ## @var{func} function. This should be a function or function handle
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41 ## that accepts a column vector and returns a scalar. The result of the
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42 ## function should not depend on the order of the subscripts.
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43 ##
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44 ## The elements of the returned array that have no subscripts associated
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45 ## with them are set to zero. Defining @var{fillval} to some other value
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46 ## allows these values to be defined. This behaviour changes, however,
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47 ## for certain values of @var{func}. If @var{func} is @code{min}
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48 ## (respectively, @code{max}) then the result will be filled with the
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49 ## minimum (respectively, maximum) integer if @var{vals} is of integral
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50 ## type, logical false (respectively, logical true) if @var{vals} is of
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51 ## logical type, zero if @var{fillval} is zero and all values are
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52 ## nonpositive (respectively, non-negative), and NaN otherwise.
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53 ##
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54 ## By default @code{accumarray} returns a full matrix. If
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55 ## @var{issparse} is logically true, then a sparse matrix is returned
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56 ## instead.
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57 ##
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58 ## The following @code{accumarray} example constructs a frequency table
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59 ## that in the first column counts how many occurrences each number in
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60 ## the second column has, taken from the vector @var{x}. Note the usage
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61 ## of @code{unique} for assigning to all repeated elements of @var{x}
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62 ## the same index (@pxref{doc-unique}).
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63 ##
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64 ## @example
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65 ## @group
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66 ## x = [91, 92, 90, 92, 90, 89, 91, 89, 90, 100, 100, 100];
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67 ## [u, ~, j] = unique (x);
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68 ## [accumarray(j', 1), u']
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69 ## @result{} 2 89
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70 ## 3 90
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71 ## 2 91
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72 ## 2 92
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73 ## 3 100
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74 ## @end group
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75 ## @end example
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76 ##
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77 ## Another example, where the result is a multi-dimensional 3-D array and
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78 ## the default value (zero) appears in the output:
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79 ##
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80 ## @example
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81 ## @group
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82 ## accumarray ([1, 1, 1;
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83 ## 2, 1, 2;
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84 ## 2, 3, 2;
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85 ## 2, 1, 2;
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86 ## 2, 3, 2], 101:105)
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87 ## @result{} ans(:,:,1) = [101, 0, 0; 0, 0, 0]
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88 ## ans(:,:,2) = [0, 0, 0; 206, 0, 208]
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89 ## @end group
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90 ## @end example
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91 ##
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92 ## The complexity in the non-sparse case is generally O(M+N), where N is
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93 ## the number of subscripts and M is the maximum subscript (linearized
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94 ## in multi-dimensional case). If @var{func} is one of @code{@@sum}
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95 ## (default), @code{@@max}, @code{@@min} or @code{@@(x) @{x@}}, an
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96 ## optimized code path is used. Note that for general reduction function
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97 ## the interpreter overhead can play a major part and it may be more
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98 ## efficient to do multiple accumarray calls and compute the results in
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99 ## a vectorized manner.
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100 ##
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101 ## @seealso{accumdim, unique}
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102 ## @end deftypefn
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103
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104 function A = accumarray (subs, vals, sz = [], func = [], fillval = [], issparse = [])
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105
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106 if (nargin < 2 || nargin > 6)
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107 print_usage ();
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108 endif
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109
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110 if (iscell (subs))
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111 subs = cellfun ("vec", subs, "uniformoutput", false);
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112 ndims = numel (subs);
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113 if (ndims == 1)
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114 subs = subs{1};
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115 endif
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116 else
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117 ndims = columns (subs);
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118 endif
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119
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120 if (isempty (fillval))
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121 fillval = 0;
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122 endif
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123
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124 if (isempty (issparse))
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125 issparse = false;
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126 endif
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127
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128 if (issparse)
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129
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130 ## Sparse case. Avoid linearizing the subscripts, because it could overflow.
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131
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132 if (fillval != 0)
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133 error ("accumarray: FILLVAL must be zero in the sparse case");
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134 endif
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135
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136 ## Ensure subscripts are a two-column matrix.
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137 if (iscell (subs))
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138 subs = [subs{:}];
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139 endif
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140
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141 ## Validate dimensions.
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142 if (ndims == 1)
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143 subs(:,2) = 1;
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144 elseif (ndims != 2)
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145 error ("accumarray: in the sparse case, needs 1 or 2 subscripts");
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146 endif
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147
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148 if (isnumeric (vals) || islogical (vals))
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149 vals = double (vals);
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150 else
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151 error ("accumarray: in the sparse case, values must be numeric or logical");
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152 endif
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153
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154 if (! (isempty (func) || func == @sum))
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155
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156 ## Reduce values. This is not needed if we're about to sum them, because
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157 ## "sparse" can do that.
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158
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159 ## Sort indices.
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160 [subs, idx] = sortrows (subs);
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161 n = rows (subs);
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162 ## Identify runs.
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163 jdx = find (any (diff (subs, 1, 1), 2));
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164 jdx = [jdx; n];
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165
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166 vals = cellfun (func, mat2cell (vals(:)(idx), diff ([0; jdx])));
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167 subs = subs(jdx, :);
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168 mode = "unique";
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169 else
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170 mode = "sum";
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171 endif
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172
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173 ## Form the sparse matrix.
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174 if (isempty (sz))
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175 A = sparse (subs(:,1), subs(:,2), vals, mode);
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176 elseif (length (sz) == 2)
13788
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177
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178 ## Row vector case
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179 if (sz(1) == 1)
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180 [i, j] = deal (subs(:,2), subs(:,1));
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181 else
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182 [i, j] = deal (subs(:,1), subs(:,2));
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183 endif
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184 A = sparse (i, j, vals, sz(1), sz(2), mode);
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185 else
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186 error ("accumarray: dimensions mismatch");
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187 endif
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188
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189 else
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190
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191 ## Linearize subscripts.
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192 if (ndims > 1)
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193 if (isempty (sz))
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194 if (iscell (subs))
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195 sz = cellfun ("max", subs);
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196 else
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197 sz = max (subs, [], 1);
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198 endif
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199 elseif (ndims != length (sz))
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200 error ("accumarray: dimensions mismatch");
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201 endif
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202
10268
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203 ## Convert multidimensional subscripts.
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204 if (ismatrix (subs))
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205 subs = num2cell (subs, 1);
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206 endif
10274
db613bccd992 take advantage of new sort optimization in accumarray
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207 subs = sub2ind (sz, subs{:}); # creates index cache
10271
297996005012 1 more small fix in accumarray
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208 elseif (! isempty (sz) && length (sz) < 2)
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209 error ("accumarray: needs at least 2 dimensions");
10274
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210 elseif (! isindex (subs)) # creates index cache
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211 error ("accumarray: indices must be positive integers");
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212 endif
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213
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214
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215 ## Some built-in reductions handled efficiently.
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216
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217 if (isempty (func) || func == @sum)
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218 ## Fast summation.
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219 if (isempty (sz))
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220 A = __accumarray_sum__ (subs, vals);
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221 else
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222 A = __accumarray_sum__ (subs, vals, prod (sz));
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223 ## set proper shape.
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224 A = reshape (A, sz);
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225 endif
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226
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227 ## we fill in nonzero fill value.
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228 if (fillval != 0)
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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
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233 elseif (func == @max)
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234 ## Fast maximization.
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235
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236 if (isinteger (vals))
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237 zero = intmin (class (vals));
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238 elseif (islogical (vals))
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239 zero = false;
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240 elseif (fillval == 0 && all (vals(:) >= 0))
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241 ## This is a common case - fillval is zero, all numbers nonegative.
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242 zero = 0;
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243 else
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244 zero = NaN; # Neutral value.
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245 endif
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246
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247 if (isempty (sz))
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248 A = __accumarray_max__ (subs, vals, zero);
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249 else
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250 A = __accumarray_max__ (subs, vals, zero, prod (sz));
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251 A = reshape (A, sz);
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252 endif
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253
10775
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254 if (fillval != zero && ! (isnan (fillval) || isnan (zero)))
10268
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255 mask = true (size (A));
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256 mask(subs) = false;
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257 A(mask) = fillval;
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258 endif
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259 elseif (func == @min)
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260 ## Fast minimization.
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261
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262 if (isinteger (vals))
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263 zero = intmax (class (vals));
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264 elseif (islogical (vals))
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265 zero = true;
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266 elseif (fillval == 0 && all (vals(:) <= 0))
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267 ## This is a common case - fillval is zero, all numbers nonpositive.
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268 zero = 0;
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269 else
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270 zero = NaN; # Neutral value.
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271 endif
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272
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273 if (isempty (sz))
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274 A = __accumarray_min__ (subs, vals, zero);
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275 else
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276 A = __accumarray_min__ (subs, vals, zero, prod (sz));
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277 A = reshape (A, sz);
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278 endif
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279
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280 if (fillval != zero && ! (isnan (fillval) || isnan (zero)))
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281 mask = true (size (A));
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282 mask(subs) = false;
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283 A(mask) = fillval;
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284 endif
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285 else
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286
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287 ## The general case. Reduce values.
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288 n = rows (subs);
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289 if (numel (vals) == 1)
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290 vals = vals(ones (1, n), 1);
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291 else
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292 vals = vals(:);
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293 endif
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294
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295 ## Sort indices.
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296 [subs, idx] = sort (subs);
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297 ## Identify runs.
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298 jdx = find (subs(1:n-1) != subs(2:n));
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299 jdx = [jdx; n];
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300 vals = mat2cell (vals(idx), diff ([0; jdx]));
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301 ## Optimize the case when function is @(x) {x}, i.e. we just want to
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302 ## collect the values to cells.
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303 persistent simple_cell_str = func2str (@(x) {x});
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304 if (! strcmp (func2str (func), simple_cell_str))
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305 vals = cellfun (func, vals);
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306 endif
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307 subs = subs(jdx);
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308
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309 ## Construct matrix of fillvals.
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310 if (iscell (vals))
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311 A = cell (sz);
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312 elseif (fillval == 0)
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313 A = zeros (sz, class (vals));
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314 else
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315 A = repmat (fillval, sz);
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316 endif
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317
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318 ## Set the reduced values.
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319 A(subs) = vals;
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320 endif
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321 endif
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322 endfunction
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323
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324 %!error (accumarray (1:5))
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325 %!error (accumarray ([1,2,3],1:2))
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326 %!assert (accumarray ([1;2;4;2;4],101:105), [101;206;0;208])
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327 %!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]))
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328 %!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])))
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329 %!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]))
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330 %!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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331 %!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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332 %!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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333 %!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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334 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 0), [3; 4])
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335 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 1), sparse ([3; 4]))
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336 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 0), [3, 4])
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337 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 1), sparse ([3, 4]))
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338 %!test
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339 %! A = accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105,[2,4],@(x){x});
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340 %! assert (A{2},[102;104])
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341 %!test
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342 %! subs = ceil (rand (2000, 3)*10);
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343 %! vals = rand (2000, 1);
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344 %! assert (accumarray (subs, vals, [], @max), accumarray (subs, vals, [], @(x) max (x)));
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345 %!test
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346 %! subs = ceil (rand (2000, 1)*100);
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347 %! vals = rand (2000, 1);
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348 %! assert (accumarray (subs, vals, [100, 1], @min, NaN), accumarray (subs, vals, [100, 1], @(x) min (x), NaN));
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349 %!test
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350 %! subs = ceil (rand (2000, 2)*30);
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351 %! subsc = num2cell (subs, 1);
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352 %! vals = rand (2000, 1);
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353 %! assert (accumarray (subsc, vals, [], [], 0, true), accumarray (subs, vals, [], [], 0, true));
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354 %!test
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355 %! subs = ceil (rand (2000, 3)*10);
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356 %! subsc = num2cell (subs, 1);
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357 %! vals = rand (2000, 1);
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358 %! assert (accumarray (subsc, vals, [], @max), accumarray (subs, vals, [], @max));
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359
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360