Mercurial > octave
annotate scripts/general/accumarray.m @ 28959:5394d688d456
doc: Use @code{} within alternate text for @xref,@pxref macros for better Info display.
* accumarray.m, structfun.m, slash.m, csvread.m, csvwrite.m, edit.m,
setfield.m, lsqnonneg.m, pqpnonneg.m, camlookat.m, camorbit.m, camup.m, barh.m,
camlight.m, isocaps.m, isosurface.m, loglogerr.m, polar.m, reducepatch.m,
reducevolume.m, semilogxerr.m, semilogyerr.m, findall.m, findobj.m, beta.m,
movmad.m, movmax.m, movmean.m, movmedian.m, movmin.m, movprod.m, movstd.m,
movsum.m, movvar.m, test.m, datenum.m:
Place alternate text in @code{} macro so it displays better in plaintext Info.
author | Rik <rik@octave.org> |
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date | Mon, 19 Oct 2020 09:33:28 -0700 |
parents | 2883b3d08b7e |
children | 7854d5752dd2 |
rev | line source |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2007-2020 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
6770 | 7 ## |
7016 | 8 ## This file is part of Octave. |
6770 | 9 ## |
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10 ## Octave is free software: you can redistribute it and/or modify it |
7016 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
7016 | 14 ## |
15 ## Octave is distributed in the hope that it will be useful, but | |
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
6770 | 19 ## |
20 ## You should have received a copy of the GNU General Public License | |
7016 | 21 ## along with Octave; see the file COPYING. If not, see |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
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26 ## -*- texinfo -*- | |
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27 ## @deftypefn {} {} accumarray (@var{subs}, @var{vals}, @var{sz}, @var{func}, @var{fillval}, @var{issparse}) |
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28 ## @deftypefnx {} {} accumarray (@var{subs}, @var{vals}, @dots{}) |
6770 | 29 ## |
7186 | 30 ## Create an array by accumulating the elements of a vector into the |
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31 ## positions defined by their subscripts. |
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32 ## |
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33 ## The subscripts are defined by the rows of the matrix @var{subs} and the |
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34 ## values by @var{vals}. Each row of @var{subs} corresponds to one of the |
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35 ## values in @var{vals}. If @var{vals} is a scalar, it will be used for each |
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36 ## of the row of @var{subs}. If @var{subs} is a cell array of vectors, all |
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37 ## vectors must be of the same length, and the subscripts in the @var{k}th |
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38 ## vector must correspond to the @var{k}th dimension of the result. |
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40 ## The size of the matrix will be determined by the subscripts |
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41 ## themselves. However, if @var{sz} is defined it determines the matrix |
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42 ## size. The length of @var{sz} must correspond to the number of columns |
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43 ## in @var{subs}. An exception is if @var{subs} has only one column, in |
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44 ## which case @var{sz} may be the dimensions of a vector and the |
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45 ## subscripts of @var{subs} are taken as the indices into it. |
6770 | 46 ## |
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47 ## The default action of @code{accumarray} is to sum the elements with |
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48 ## the same subscripts. This behavior can be modified by defining the |
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49 ## @var{func} function. This should be a function or function handle |
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50 ## that accepts a column vector and returns a scalar. The result of the |
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51 ## function should not depend on the order of the subscripts. |
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52 ## |
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53 ## The elements of the returned array that have no subscripts associated |
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54 ## with them are set to zero. Defining @var{fillval} to some other value |
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55 ## allows these values to be defined. This behavior changes, however, |
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56 ## for certain values of @var{func}. If @var{func} is @code{@@min} |
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57 ## (respectively, @code{@@max}) then the result will be filled with the |
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58 ## minimum (respectively, maximum) integer if @var{vals} is of integral |
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59 ## type, logical false (respectively, logical true) if @var{vals} is of |
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60 ## logical type, zero if @var{fillval} is zero and all values are |
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61 ## non-positive (respectively, non-negative), and NaN otherwise. |
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63 ## By default @code{accumarray} returns a full matrix. If |
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64 ## @var{issparse} is logically true, then a sparse matrix is returned |
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65 ## instead. |
6770 | 66 ## |
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67 ## The following @code{accumarray} example constructs a frequency table |
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68 ## that in the first column counts how many occurrences each number in |
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69 ## the second column has, taken from the vector @var{x}. Note the usage |
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70 ## of @code{unique} for assigning to all repeated elements of @var{x} |
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71 ## the same index (@pxref{XREFunique,,@code{unique}}). |
6770 | 72 ## |
73 ## @example | |
74 ## @group | |
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75 ## @var{x} = [91, 92, 90, 92, 90, 89, 91, 89, 90, 100, 100, 100]; |
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76 ## [@var{u}, ~, @var{j}] = unique (@var{x}); |
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77 ## [accumarray(@var{j}', 1), @var{u}'] |
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78 ## @result{} 2 89 |
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79 ## 3 90 |
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80 ## 2 91 |
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81 ## 2 92 |
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82 ## 3 100 |
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83 ## @end group |
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84 ## @end example |
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85 ## |
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86 ## Another example, where the result is a multi-dimensional 3-D array and |
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87 ## the default value (zero) appears in the output: |
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88 ## |
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89 ## @example |
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90 ## @group |
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91 ## accumarray ([1, 1, 1; |
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92 ## 2, 1, 2; |
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93 ## 2, 3, 2; |
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94 ## 2, 1, 2; |
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95 ## 2, 3, 2], 101:105) |
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97 ## @result{} ans(:,:,2) = [0, 0, 0; 206, 0, 208] |
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99 ## @end example | |
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100 ## |
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101 ## The sparse option can be used as an alternative to the @code{sparse} |
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102 ## constructor (@pxref{XREFsparse,,@code{sparse}}). Thus |
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103 ## |
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104 ## @example |
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105 ## sparse (@var{i}, @var{j}, @var{sv}) |
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106 ## @end example |
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107 ## |
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108 ## @noindent |
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109 ## can be written with @code{accumarray} as |
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110 ## |
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111 ## @example |
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112 ## accumarray ([@var{i}, @var{j}], @var{sv}', [], [], 0, true) |
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113 ## @end example |
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114 ## |
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115 ## @noindent |
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116 ## For repeated indices, @code{sparse} adds the corresponding value. To |
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117 ## take the minimum instead, use @code{min} as an accumulator function: |
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118 ## |
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119 ## @example |
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120 ## accumarray ([@var{i}, @var{j}], @var{sv}', [], @@min, 0, true) |
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121 ## @end example |
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122 ## |
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123 ## The complexity of accumarray in general for the non-sparse case is |
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124 ## generally O(M+N), where N is the number of subscripts and M is the |
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125 ## maximum subscript (linearized in multi-dimensional case). If |
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126 ## @var{func} is one of @code{@@sum} (default), @code{@@max}, |
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127 ## @code{@@min} or @code{@@(x) @{x@}}, an optimized code path is used. |
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128 ## Note that for general reduction function the interpreter overhead can |
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129 ## play a major part and it may be more efficient to do multiple |
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130 ## accumarray calls and compute the results in a vectorized manner. |
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131 ## |
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132 ## @seealso{accumdim, unique, sparse} |
6770 | 133 ## @end deftypefn |
134 | |
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135 function A = accumarray (subs, vals, sz = [], func = [], fillval = [], issparse = []) |
6770 | 136 |
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137 if (nargin < 2) |
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139 endif | |
140 | |
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141 lenvals = length (vals); |
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142 |
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144 subs = cellfun (@vec, subs, "uniformoutput", false); |
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145 ndims = numel (subs); |
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146 if (ndims == 1) |
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147 subs = subs{1}; |
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148 endif |
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149 |
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150 lensubs = cellfun (@length, subs); |
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151 |
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152 if (any (lensubs != lensubs(1)) || (lenvals > 1 && lenvals != lensubs(1))) |
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153 error ("accumarray: dimension mismatch"); |
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154 endif |
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155 |
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156 else |
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157 ndims = columns (subs); |
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158 if (lenvals > 1 && lenvals != rows (subs)) |
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159 error ("accumarray: dimension mismatch"); |
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160 endif |
6770 | 161 endif |
162 | |
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163 if (isempty (func)) |
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164 func = @sum; |
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165 elseif (! is_function_handle (func)) |
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166 error ("accumarray: FUNC must be a function handle"); |
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167 endif |
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168 |
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169 if (isempty (fillval)) |
6770 | 170 fillval = 0; |
171 endif | |
172 | |
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173 if (isempty (issparse)) |
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174 issparse = false; |
6770 | 175 endif |
7186 | 176 |
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177 if (issparse) |
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178 |
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179 ## Sparse case. |
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180 ## Avoid linearizing the subscripts, because it could overflow. |
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181 |
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182 if (fillval != 0) |
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183 error ("accumarray: FILLVAL must be zero in the sparse case"); |
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184 endif |
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185 |
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186 ## Ensure subscripts are a two-column matrix. |
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187 if (iscell (subs)) |
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188 subs = [subs{:}]; |
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189 endif |
6770 | 190 |
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191 ## Validate dimensions. |
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192 if (ndims == 1) |
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193 subs(:,2) = 1; |
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194 elseif (ndims != 2) |
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195 error ("accumarray: in the sparse case, needs 1 or 2 subscripts"); |
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196 endif |
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197 |
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198 if (isnumeric (vals) || islogical (vals)) |
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199 vals = double (vals); |
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200 else |
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201 error ("accumarray: in the sparse case, values must be numeric or logical"); |
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202 endif |
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203 |
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204 if (func != @sum) |
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205 |
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206 ## Reduce values. This is not needed if we're about to sum them, |
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207 ## because "sparse" can do that. |
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208 |
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209 ## Sort indices. |
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210 [subs, idx] = sortrows (subs); |
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211 n = rows (subs); |
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212 ## Identify runs. |
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213 jdx = find (any (diff (subs, 1, 1), 2)); |
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214 jdx = [jdx; n]; |
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215 |
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216 vals = cellfun (func, mat2cell (vals(:)(idx), diff ([0; jdx]))); |
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217 subs = subs(jdx, :); |
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218 mode = "unique"; |
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219 else |
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220 mode = "sum"; |
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221 endif |
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222 |
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223 ## Form the sparse matrix. |
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224 if (isempty (sz)) |
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225 A = sparse (subs(:,1), subs(:,2), vals, mode); |
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226 elseif (length (sz) == 2) |
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227 |
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228 ## Row vector case |
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229 if (sz(1) == 1) |
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230 [i, j] = deal (subs(:,2), subs(:,1)); |
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231 else |
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232 [i, j] = deal (subs(:,1), subs(:,2)); |
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233 endif |
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234 A = sparse (i, j, vals, sz(1), sz(2), mode); |
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235 else |
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236 error ("accumarray: dimensions mismatch"); |
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237 endif |
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238 |
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239 else |
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240 |
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241 ## Linearize subscripts. |
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242 if (ndims > 1) |
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243 if (isempty (sz)) |
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244 if (iscell (subs)) |
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245 sz = cellfun ("max", subs); |
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246 else |
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247 sz = max (subs, [], 1); |
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248 endif |
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249 elseif (ndims != length (sz)) |
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250 error ("accumarray: dimensions mismatch"); |
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251 endif |
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252 |
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253 ## Convert multidimensional subscripts. |
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254 if (isnumeric (subs)) |
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255 subs = num2cell (subs, 1); |
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256 endif |
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257 subs = sub2ind (sz, subs{:}); # creates index cache |
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258 elseif (! isempty (sz) && length (sz) < 2) |
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259 error ("accumarray: needs at least 2 dimensions"); |
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260 elseif (! isindex (subs)) # creates index cache |
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261 error ("accumarray: indices must be positive integers"); |
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262 endif |
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263 |
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264 |
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265 ## Some built-in reductions handled efficiently. |
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266 |
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267 if (func == @sum) |
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268 ## Fast summation. |
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269 if (isempty (sz)) |
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270 A = __accumarray_sum__ (subs, vals); |
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271 else |
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272 A = __accumarray_sum__ (subs, vals, prod (sz)); |
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273 ## set proper shape. |
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274 A = reshape (A, sz); |
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275 endif |
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276 |
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277 ## we fill in nonzero fill value. |
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278 if (fillval != 0) |
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279 mask = true (size (A)); |
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280 mask(subs) = false; |
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281 A(mask) = fillval; |
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282 endif |
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283 elseif (func == @max) |
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284 ## Fast maximization. |
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285 |
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286 if (isinteger (vals)) |
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287 zero = intmin (vals); |
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288 elseif (islogical (vals)) |
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289 zero = false; |
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290 elseif (fillval == 0 && all (vals(:) >= 0)) |
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291 ## This is a common case - fillval is zero, all numbers |
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292 ## nonegative. |
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293 zero = 0; |
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294 else |
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295 zero = NaN; # Neutral value. |
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296 endif |
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297 |
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298 if (isempty (sz)) |
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299 A = __accumarray_max__ (subs, vals, zero); |
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300 else |
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301 A = __accumarray_max__ (subs, vals, zero, prod (sz)); |
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302 A = reshape (A, sz); |
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303 endif |
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304 |
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306 mask = true (size (A)); |
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307 mask(subs) = false; |
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308 A(mask) = fillval; |
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309 endif |
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310 elseif (func == @min) |
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311 ## Fast minimization. |
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312 |
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313 if (isinteger (vals)) |
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314 zero = intmax (vals); |
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315 elseif (islogical (vals)) |
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316 zero = true; |
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317 elseif (fillval == 0 && all (vals(:) <= 0)) |
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318 ## This is a common case - fillval is zero, all numbers |
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319 ## non-positive. |
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320 zero = 0; |
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321 else |
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322 zero = NaN; # Neutral value. |
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323 endif |
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324 |
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325 if (isempty (sz)) |
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326 A = __accumarray_min__ (subs, vals, zero); |
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327 else |
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328 A = __accumarray_min__ (subs, vals, zero, prod (sz)); |
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329 A = reshape (A, sz); |
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330 endif |
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331 |
10775 | 332 if (fillval != zero && ! (isnan (fillval) || isnan (zero))) |
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333 mask = true (size (A)); |
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334 mask(subs) = false; |
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335 A(mask) = fillval; |
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336 endif |
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337 else |
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338 |
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339 ## The general case. Reduce values. |
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340 n = rows (subs); |
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341 if (numel (vals) == 1) |
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342 vals = vals(ones (1, n), 1); |
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343 else |
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344 vals = vals(:); |
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345 endif |
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346 |
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347 ## Sort indices. |
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348 [subs, idx] = sort (subs); |
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349 ## Identify runs. |
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350 jdx = find (subs(1:n-1) != subs(2:n)); |
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351 if (n != 0) # bug #47287 |
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352 jdx = [jdx; n]; |
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353 endif |
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354 vals = mat2cell (vals(idx), diff ([0; jdx])); |
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355 ## Optimize the case when function is @(x) {x}, i.e., we just want |
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356 ## to collect the values to cells. |
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357 persistent simple_cell_str = func2str (@(x) {x}); |
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358 if (! strcmp (func2str (func), simple_cell_str)) |
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359 vals = cellfun (func, vals); |
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360 endif |
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361 |
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362 subs = subs(jdx); |
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363 |
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364 if (isempty (sz)) |
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365 sz = max (subs); |
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366 ## If subs is empty, sz will be too, and length will be 0, hence "<= 1" |
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367 if (length (sz) <= 1) |
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368 sz(2) = 1; |
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369 endif |
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370 endif |
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371 |
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372 ## Construct matrix of fillvals. |
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373 if (iscell (vals)) |
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374 A = cell (sz); |
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375 elseif (fillval == 0) |
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376 A = zeros (sz, class (vals)); |
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377 else |
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378 A = repmat (fillval, sz); |
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379 endif |
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380 |
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381 ## Set the reduced values. |
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382 A(subs) = vals; |
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384 endif | |
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385 |
6770 | 386 endfunction |
387 | |
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388 |
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389 %!assert (accumarray ([1; 2; 4; 2; 4], 101:105), [101; 206; 0; 208]) |
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390 %!assert (accumarray ([1 1 1; 2 1 2; 2 3 2; 2 1 2; 2 3 2], 101:105), |
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391 %! cat (3, [101 0 0; 0 0 0], [0 0 0; 206 0 208])) |
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392 |
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393 %!assert (accumarray ([1 1 1; 2 1 2; 2 3 2; 2 1 2; 2 3 2], 101:105, [], @(x) sin (sum (x))), |
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394 %! sin (cat (3, [101,0,0;0,0,0],[0,0,0;206,0,208]))) |
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395 |
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396 %!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), |
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397 %! 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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398 |
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399 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 101:105, [2 4], @max, NaN), |
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400 %! [101 NaN NaN NaN; 104 NaN 105 NaN]) |
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401 |
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402 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 101:105, [], @prod), |
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403 %! [101 0 0; 10608 0 10815]) |
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404 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 101:105, [2 4], @prod, 0, true), |
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405 %! sparse ([1 2 2], [1 1 3], [101 10608 10815], 2, 4)) |
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406 %!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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407 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 101:105, [2 4], @(x) length (x) > 1), |
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408 %! [false false false false; true false true false]) |
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409 |
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410 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 0), [3; 4]) |
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411 %!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 1), sparse ([3; 4])) |
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412 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 0), [3, 4]) |
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413 %!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 1), sparse ([3, 4])) |
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414 |
6770 | 415 %!test |
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416 %! A = accumarray ([1 1; 2 1; 2 3; 2 1; 2 3], 101:105, [2,4], @(x) {x}); |
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417 %! assert (A{2},[102; 104]); |
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418 |
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419 %!test |
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420 %! subs = ceil (rand (2000, 3)*10); |
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421 %! vals = rand (2000, 1); |
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422 %! assert (accumarray (subs, vals, [], @max), |
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423 %! accumarray (subs, vals, [], @(x) max (x))); |
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424 |
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425 %!test |
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426 %! subs = ceil (rand (2000, 1)*100); |
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427 %! vals = rand (2000, 1); |
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428 %! assert (accumarray (subs, vals, [100, 1], @min, NaN), |
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429 %! accumarray (subs, vals, [100, 1], @(x) min (x), NaN)); |
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430 |
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431 %!test |
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432 %! subs = ceil (rand (2000, 2)*30); |
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433 %! subsc = num2cell (subs, 1); |
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434 %! vals = rand (2000, 1); |
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435 %! assert (accumarray (subsc, vals, [], [], 0, true), |
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436 %! accumarray (subs, vals, [], [], 0, true)); |
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437 |
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438 %!test |
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439 %! subs = ceil (rand (2000, 3)*10); |
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440 %! subsc = num2cell (subs, 1); |
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441 %! vals = rand (2000, 1); |
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442 %! assert (accumarray (subsc, vals, [], @max), |
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443 %! accumarray (subs, vals, [], @max)); |
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444 |
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445 %!error accumarray (1:5) |
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446 %!error accumarray ([1,2,3],1:2) |
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447 |
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448 ## Handle empty arrays |
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449 %!test <*47287> |
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450 %! ## min, max, and sum are special cases within accumarray so test them. |
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451 %! funcs = {@(x) length (x) > 1, @min, @max, @sum}; |
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452 %! for idx = 1:numel (funcs) |
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453 %! assert (accumarray (zeros (0, 1), [], [0 1] , funcs{idx}), zeros (0, 1)); |
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454 %! assert (accumarray (zeros (0, 1), [], [1 0] , funcs{idx}), zeros (1, 0)); |
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455 %! assert (accumarray (zeros (0, 1), [], [] , funcs{idx}), zeros (0, 1)); |
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456 %! endfor |
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457 |
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458 ## Matlab returns an array of doubles even though FUNC returns cells. In |
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459 ## Octave, we do not have that bug, at least for this case. |
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460 %!assert (accumarray (zeros (0, 1), [], [0 1] , @(x) {x}), cell (0, 1)) |
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461 |
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462 %!error <FUNC must be a function handle> |
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463 %! accumarray ([1; 2; 3], [1; 2; 3], [3 1], '@(x) {x}') |