Mercurial > hg > octave-lyh
annotate scripts/general/accumarray.m @ 12931:cefd568ea073
Replace function handles with function names in cellfun calls for 15% speedup.
* accumarray.m arrayfun.m, blkdiag.m, cell2mat.m, common_size.m, interp3.m,
interpn.m, __isequal__.m, structfun.m, voronoi.m, strread.m, fullfile.m,
getfield.m, __xzip__.m, setfield.m, what.m, pkg.m, axis.m, pareto.m,
__ghostscript__.m, __go_draw_axes__.m, __patch__.m, refreshdata.m, whitebg.m,
lcm.m, index.m, strcat.m, strmatch.m, validatestring.m: Replace function
handles in calls to cellfun with double quoted function names.
author | Rik <octave@nomad.inbox5.com> |
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date | Sat, 06 Aug 2011 18:03:18 -0700 |
parents | 0ce4a9cd6a7f |
children | 25effffba9b0 |
rev | line source |
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11523 | 1 ## Copyright (C) 2007-2011 David Bateman |
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}) |
6770 | 22 ## @deftypefnx {Function File} {} accumarray (@var{csubs}, @var{vals}, @dots{}) |
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 row |
6770 | 27 ## of @var{subs} corresponds to one of the values in @var{vals}. |
28 ## | |
29 ## The size of the matrix will be determined by the subscripts themselves. | |
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30 ## However, if @var{sz} is defined it determines the matrix size. The length |
6770 | 31 ## of @var{sz} must correspond to the number of columns in @var{subs}. |
32 ## | |
33 ## The default action of @code{accumarray} is to sum the elements with the | |
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34 ## same subscripts. This behavior can be modified by defining the @var{func} |
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35 ## function. This should be a function or function handle that accepts a |
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36 ## column vector and returns a scalar. The result of the function should not |
6770 | 37 ## depend on the order of the subscripts. |
38 ## | |
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39 ## The elements of the returned array that have no subscripts associated with |
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40 ## them are set to zero. Defining @var{fillval} to some other value allows |
6770 | 41 ## these values to be defined. |
42 ## | |
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43 ## By default @code{accumarray} returns a full matrix. If @var{issparse} is |
6770 | 44 ## logically true, then a sparse matrix is returned instead. |
45 ## | |
46 ## An example of the use of @code{accumarray} is: | |
47 ## | |
48 ## @example | |
49 ## @group | |
7186 | 50 ## accumarray ([1,1,1;2,1,2;2,3,2;2,1,2;2,3,2], 101:105) |
6770 | 51 ## @result{} ans(:,:,1) = [101, 0, 0; 0, 0, 0] |
52 ## ans(:,:,2) = [0, 0, 0; 206, 0, 208] | |
53 ## @end group | |
54 ## @end example | |
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55 ## |
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56 ## The complexity in the non-sparse case is generally O(M+N), where N is the |
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57 ## number of |
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58 ## subscripts and M is the maximum subscript (linearized in multi-dimensional |
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59 ## case). |
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60 ## If @var{func} is one of @code{@@sum} (default), @code{@@max}, @code{@@min} |
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61 ## or @code{@@(x) @{x@}}, an optimized code path is used. |
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62 ## Note that for general reduction function the interpreter overhead can play a |
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63 ## major part and it may be more efficient to do multiple accumarray calls and |
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64 ## compute the results in a vectorized manner. |
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65 ## @seealso{accumdim} |
6770 | 66 ## @end deftypefn |
67 | |
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68 function A = accumarray (subs, vals, sz = [], func = [], fillval = [], issparse = []) |
6770 | 69 |
70 if (nargin < 2 || nargin > 6) | |
71 print_usage (); | |
72 endif | |
73 | |
7186 | 74 if (iscell (subs)) |
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75 subs = cellfun ("vec", subs, "uniformoutput", false); |
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76 ndims = numel (subs); |
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77 if (ndims == 1) |
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78 subs = subs{1}; |
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79 endif |
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80 else |
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81 ndims = columns (subs); |
6770 | 82 endif |
83 | |
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84 if (isempty (fillval)) |
6770 | 85 fillval = 0; |
86 endif | |
87 | |
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88 if (isempty (issparse)) |
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89 issparse = false; |
6770 | 90 endif |
7186 | 91 |
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92 if (issparse) |
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93 |
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94 ## Sparse case. Avoid linearizing the subscripts, because it could overflow. |
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95 |
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96 if (fillval != 0) |
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97 error ("accumarray: FILLVAL must be zero in the sparse case"); |
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98 endif |
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99 |
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100 ## Ensure subscripts are a two-column matrix. |
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101 if (iscell (subs)) |
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102 subs = [subs{:}]; |
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103 endif |
6770 | 104 |
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105 ## Validate dimensions. |
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106 if (ndims == 1) |
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107 subs(:,2) = 1; |
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108 elseif (ndims != 2) |
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109 error ("accumarray: in the sparse case, needs 1 or 2 subscripts"); |
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110 endif |
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111 |
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112 if (isnumeric (vals) || islogical (vals)) |
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113 vals = double (vals); |
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114 else |
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115 error ("accumarray: in the sparse case, values must be numeric or logical"); |
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116 endif |
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117 |
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118 if (! (isempty (func) || func == @sum)) |
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119 |
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120 ## Reduce values. This is not needed if we're about to sum them, because |
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121 ## "sparse" can do that. |
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122 |
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123 ## Sort indices. |
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124 [subs, idx] = sortrows (subs); |
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125 n = rows (subs); |
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126 ## Identify runs. |
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127 jdx = find (any (diff (subs, 1, 1), 2)); |
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128 jdx = [jdx; n]; |
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129 |
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130 vals = cellfun (func, mat2cell (vals(:)(idx), diff ([0; jdx]))); |
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131 subs = subs(jdx, :); |
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132 mode = "unique"; |
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133 else |
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134 mode = "sum"; |
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135 endif |
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136 |
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137 ## Form the sparse matrix. |
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138 if (isempty (sz)) |
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139 A = sparse (subs(:,1), subs(:,2), vals, mode); |
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140 elseif (length (sz) == 2) |
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141 A = sparse (subs(:,1), subs(:,2), vals, sz(1), sz(2), mode); |
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142 else |
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143 error ("accumarray: dimensions mismatch"); |
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144 endif |
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145 |
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146 else |
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147 |
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148 ## Linearize subscripts. |
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149 if (ndims > 1) |
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150 if (isempty (sz)) |
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151 if (iscell (subs)) |
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152 sz = cellfun ("max", subs); |
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153 else |
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154 sz = max (subs, [], 1); |
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155 endif |
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156 elseif (ndims != length (sz)) |
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157 error ("accumarray: dimensions mismatch"); |
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158 endif |
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159 |
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160 ## Convert multidimensional subscripts. |
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161 if (ismatrix (subs)) |
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162 subs = num2cell (subs, 1); |
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163 endif |
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164 subs = sub2ind (sz, subs{:}); # creates index cache |
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165 elseif (! isempty (sz) && length (sz) < 2) |
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166 error ("accumarray: needs at least 2 dimensions"); |
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167 elseif (! isindex (subs)) # creates index cache |
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168 error ("accumarray: indices must be positive integers"); |
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169 endif |
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170 |
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171 |
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172 ## Some built-in reductions handled efficiently. |
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173 |
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174 if (isempty (func) || func == @sum) |
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175 ## Fast summation. |
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176 if (isempty (sz)) |
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177 A = __accumarray_sum__ (subs, vals); |
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178 else |
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179 A = __accumarray_sum__ (subs, vals, prod (sz)); |
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180 ## set proper shape. |
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181 A = reshape (A, sz); |
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182 endif |
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183 |
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184 ## we fill in nonzero fill value. |
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185 if (fillval != 0) |
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186 mask = true (size (A)); |
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187 mask(subs) = false; |
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188 A(mask) = fillval; |
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189 endif |
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190 elseif (func == @max) |
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191 ## Fast maximization. |
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192 |
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193 if (isinteger (vals)) |
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194 zero = intmin (class (vals)); |
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195 elseif (islogical (vals)) |
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196 zero = false; |
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197 elseif (fillval == 0 && all (vals(:) >= 0)) |
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198 ## This is a common case - fillval is zero, all numbers nonegative. |
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199 zero = 0; |
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200 else |
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201 zero = NaN; # Neutral value. |
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202 endif |
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203 |
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204 if (isempty (sz)) |
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205 A = __accumarray_max__ (subs, vals, zero); |
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206 else |
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207 A = __accumarray_max__ (subs, vals, zero, prod (sz)); |
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208 A = reshape (A, sz); |
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209 endif |
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210 |
10775 | 211 if (fillval != zero && ! (isnan (fillval) || isnan (zero))) |
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212 mask = true (size (A)); |
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213 mask(subs) = false; |
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214 A(mask) = fillval; |
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215 endif |
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216 elseif (func == @min) |
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217 ## Fast minimization. |
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218 |
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219 if (isinteger (vals)) |
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220 zero = intmax (class (vals)); |
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221 elseif (islogical (vals)) |
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222 zero = true; |
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223 else |
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224 zero = NaN; # Neutral value. |
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225 endif |
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226 |
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227 if (isempty (sz)) |
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228 A = __accumarray_min__ (subs, vals, zero); |
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229 else |
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230 A = __accumarray_min__ (subs, vals, zero, prod (sz)); |
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231 A = reshape (A, sz); |
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232 endif |
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233 |
10775 | 234 if (fillval != zero && ! (isnan (fillval) || isnan (zero))) |
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235 mask = true (size (A)); |
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236 mask(subs) = false; |
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237 A(mask) = fillval; |
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238 endif |
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239 else |
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240 |
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241 ## The general case. Reduce values. |
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242 n = rows (subs); |
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243 if (numel (vals) == 1) |
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244 vals = vals(ones (1, n), 1); |
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245 else |
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246 vals = vals(:); |
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247 endif |
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248 |
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249 ## Sort indices. |
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250 [subs, idx] = sort (subs); |
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251 ## Identify runs. |
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252 jdx = find (subs(1:n-1) != subs(2:n)); |
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253 jdx = [jdx; n]; |
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254 vals = mat2cell (vals(idx), diff ([0; jdx])); |
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255 ## Optimize the case when function is @(x) {x}, i.e. we just want to |
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256 ## collect the values to cells. |
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257 persistent simple_cell_str = func2str (@(x) {x}); |
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258 if (! strcmp (func2str (func), simple_cell_str)) |
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259 vals = cellfun (func, vals); |
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260 endif |
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261 subs = subs(jdx); |
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262 |
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263 ## Construct matrix of fillvals. |
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264 if (iscell (vals)) |
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265 A = cell (sz); |
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266 elseif (fillval == 0) |
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267 A = zeros (sz, class (vals)); |
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268 else |
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269 A = repmat (fillval, sz); |
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270 endif |
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271 |
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272 ## Set the reduced values. |
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273 A(subs) = vals; |
6770 | 274 endif |
275 endif | |
276 endfunction | |
277 | |
278 %!error (accumarray (1:5)) | |
279 %!error (accumarray ([1,2,3],1:2)) | |
280 %!assert (accumarray ([1;2;4;2;4],101:105), [101;206;0;208]) | |
281 %!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])) | |
282 %!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]))) | |
283 %!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])) | |
284 %!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]) | |
285 %!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)) | |
286 %!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],1,[2,4]), [1,0,0,0;2,0,2,0]) | |
287 %!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]) | |
288 %!test | |
289 %! A = accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105,[2,4],@(x){x}); | |
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290 %! assert (A{2},[102;104]) |
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291 %!test |
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292 %! subs = ceil (rand (2000, 3)*10); |
11469
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Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
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293 %! vals = rand (2000, 1); |
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294 %! assert (accumarray (subs, vals, [], @max), accumarray (subs, vals, [], @(x) max (x))); |
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295 %!test |
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296 %! subs = ceil (rand (2000, 1)*100); |
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297 %! vals = rand (2000, 1); |
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parents:
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298 %! assert (accumarray (subs, vals, [100, 1], @min, NaN), accumarray (subs, vals, [100, 1], @(x) min (x), NaN)); |
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299 %!test |
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300 %! subs = ceil (rand (2000, 2)*30); |
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301 %! subsc = num2cell (subs, 1); |
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302 %! vals = rand (2000, 1); |
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303 %! assert (accumarray (subsc, vals, [], [], 0, true), accumarray (subs, vals, [], [], 0, true)); |
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304 %!test |
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parents:
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305 %! subs = ceil (rand (2000, 3)*10); |
9a16a61ed43d
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Jaroslav Hajek <highegg@gmail.com>
parents:
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306 %! subsc = num2cell (subs, 1); |
11469
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Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
11191
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307 %! vals = rand (2000, 1); |
c776f063fefe
Overhaul m-script files to use common variable name between code and documentation.
Rik <octave@nomad.inbox5.com>
parents:
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308 %! assert (accumarray (subsc, vals, [], @max), accumarray (subs, vals, [], @max)); |
10268
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parents:
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309 |
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parents:
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310 |