--- /dev/null
+## Copyright (C) 2007-2012 David Bateman
+## Copyright (C) 2009-2010 VZLU Prague
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING. If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} accumarray (@var{subs}, @var{vals}, @var{sz}, @var{func}, @var{fillval}, @var{issparse})
+## @deftypefnx {Function File} {} accumarray (@var{subs}, @var{vals}, @dots{})
+##
+## Create an array by accumulating the elements of a vector into the
+## positions defined by their subscripts. The subscripts are defined by
+## the rows of the matrix @var{subs} and the values by @var{vals}. Each
+## row of @var{subs} corresponds to one of the values in @var{vals}. If
+## @var{vals} is a scalar, it will be used for each of the row of
+## @var{subs}. If @var{subs} is a cell array of vectors, all vectors
+## must be of the same length, and the subscripts in the @var{k}th
+## vector must correspond to the @var{k}th dimension of the result.
+##
+## The size of the matrix will be determined by the subscripts
+## themselves. However, if @var{sz} is defined it determines the matrix
+## size. The length of @var{sz} must correspond to the number of columns
+## in @var{subs}. An exception is if @var{subs} has only one column, in
+## which case @var{sz} may be the dimensions of a vector and the
+## subscripts of @var{subs} are taken as the indices into it.
+##
+## The default action of @code{accumarray} is to sum the elements with
+## the same subscripts. This behavior can be modified by defining the
+## @var{func} function. This should be a function or function handle
+## that accepts a column vector and returns a scalar. The result of the
+## function should not depend on the order of the subscripts.
+##
+## The elements of the returned array that have no subscripts associated
+## with them are set to zero. Defining @var{fillval} to some other value
+## allows these values to be defined. This behavior changes, however,
+## for certain values of @var{func}. If @var{func} is @code{min}
+## (respectively, @code{max}) then the result will be filled with the
+## minimum (respectively, maximum) integer if @var{vals} is of integral
+## type, logical false (respectively, logical true) if @var{vals} is of
+## logical type, zero if @var{fillval} is zero and all values are
+## non-positive (respectively, non-negative), and NaN otherwise.
+##
+## By default @code{accumarray} returns a full matrix. If
+## @var{issparse} is logically true, then a sparse matrix is returned
+## instead.
+##
+## The following @code{accumarray} example constructs a frequency table
+## that in the first column counts how many occurrences each number in
+## the second column has, taken from the vector @var{x}. Note the usage
+## of @code{unique} for assigning to all repeated elements of @var{x}
+## the same index (@pxref{doc-unique}).
+##
+## @example
+## @group
+## @var{x} = [91, 92, 90, 92, 90, 89, 91, 89, 90, 100, 100, 100];
+## [@var{u}, ~, @var{j}] = unique (@var{x});
+## [accumarray(@var{j}', 1), @var{u}']
+## @result{} 2 89
+## 3 90
+## 2 91
+## 2 92
+## 3 100
+## @end group
+## @end example
+##
+## Another example, where the result is a multi-dimensional 3-D array and
+## the default value (zero) appears in the output:
+##
+## @example
+## @group
+## accumarray ([1, 1, 1;
+## 2, 1, 2;
+## 2, 3, 2;
+## 2, 1, 2;
+## 2, 3, 2], 101:105)
+## @result{} ans(:,:,1) = [101, 0, 0; 0, 0, 0]
+## @result{} ans(:,:,2) = [0, 0, 0; 206, 0, 208]
+## @end group
+## @end example
+##
+## The sparse option can be used as an alternative to the @code{sparse}
+## constructor (@pxref{doc-sparse}). Thus
+##
+## @example
+## sparse (@var{i}, @var{j}, @var{sv})
+## @end example
+##
+## @noindent
+## can be written with @code{accumarray} as
+##
+## @example
+## accumarray ([@var{i}, @var{j}], @var{sv}', [], [], 0, true)
+## @end example
+##
+## @noindent
+## For repeated indices, @code{sparse} adds the corresponding value. To
+## take the minimum instead, use @code{min} as an accumulator function:
+##
+## @example
+## accumarray ([@var{i}, @var{j}], @var{sv}', [], @@min, 0, true)
+## @end example
+##
+## The complexity of accumarray in general for the non-sparse case is
+## generally O(M+N), where N is the number of subscripts and M is the
+## maximum subscript (linearized in multi-dimensional case). If
+## @var{func} is one of @code{@@sum} (default), @code{@@max},
+## @code{@@min} or @code{@@(x) @{x@}}, an optimized code path is used.
+## Note that for general reduction function the interpreter overhead can
+## play a major part and it may be more efficient to do multiple
+## accumarray calls and compute the results in a vectorized manner.
+##
+## @seealso{accumdim, unique, sparse}
+## @end deftypefn
+
+function A = accumarray (subs, vals, sz = [], func = [], fillval = [], issparse = [])
+
+ if (nargin < 2 || nargin > 6)
+ print_usage ();
+ endif
+
+ lenvals = length (vals);
+
+ if (iscell (subs))
+ subs = cellfun (@vec, subs, "uniformoutput", false);
+ ndims = numel (subs);
+ if (ndims == 1)
+ subs = subs{1};
+ endif
+
+ lensubs = cellfun (@length, subs);
+
+ if (any (lensubs != lensubs(1)) ||
+ (lenvals > 1 && lenvals != lensubs(1)))
+ error ("accumarray: dimension mismatch");
+ endif
+
+ else
+ ndims = columns (subs);
+ if (lenvals > 1 && lenvals != rows (subs))
+ error ("accumarray: dimension mismatch")
+ endif
+ endif
+
+ if (isempty (fillval))
+ fillval = 0;
+ endif
+
+ if (isempty (issparse))
+ issparse = false;
+ endif
+
+ if (issparse)
+
+ ## Sparse case. Avoid linearizing the subscripts, because it could
+ ## overflow.
+
+ if (fillval != 0)
+ error ("accumarray: FILLVAL must be zero in the sparse case");
+ endif
+
+ ## Ensure subscripts are a two-column matrix.
+ if (iscell (subs))
+ subs = [subs{:}];
+ endif
+
+ ## Validate dimensions.
+ if (ndims == 1)
+ subs(:,2) = 1;
+ elseif (ndims != 2)
+ error ("accumarray: in the sparse case, needs 1 or 2 subscripts");
+ endif
+
+ if (isnumeric (vals) || islogical (vals))
+ vals = double (vals);
+ else
+ error ("accumarray: in the sparse case, values must be numeric or logical");
+ endif
+
+ if (! (isempty (func) || func == @sum))
+
+ ## Reduce values. This is not needed if we're about to sum them,
+ ## because "sparse" can do that.
+
+ ## Sort indices.
+ [subs, idx] = sortrows (subs);
+ n = rows (subs);
+ ## Identify runs.
+ jdx = find (any (diff (subs, 1, 1), 2));
+ jdx = [jdx; n];
+
+ vals = cellfun (func, mat2cell (vals(:)(idx), diff ([0; jdx])));
+ subs = subs(jdx, :);
+ mode = "unique";
+ else
+ mode = "sum";
+ endif
+
+ ## Form the sparse matrix.
+ if (isempty (sz))
+ A = sparse (subs(:,1), subs(:,2), vals, mode);
+ elseif (length (sz) == 2)
+
+ ## Row vector case
+ if (sz(1) == 1)
+ [i, j] = deal (subs(:,2), subs(:,1));
+ else
+ [i, j] = deal (subs(:,1), subs(:,2));
+ endif
+ A = sparse (i, j, vals, sz(1), sz(2), mode);
+ else
+ error ("accumarray: dimensions mismatch");
+ endif
+
+ else
+
+ ## Linearize subscripts.
+ if (ndims > 1)
+ if (isempty (sz))
+ if (iscell (subs))
+ sz = cellfun ("max", subs);
+ else
+ sz = max (subs, [], 1);
+ endif
+ elseif (ndims != length (sz))
+ error ("accumarray: dimensions mismatch");
+ endif
+
+ ## Convert multidimensional subscripts.
+ if (ismatrix (subs))
+ subs = num2cell (subs, 1);
+ endif
+ subs = sub2ind (sz, subs{:}); # creates index cache
+ elseif (! isempty (sz) && length (sz) < 2)
+ error ("accumarray: needs at least 2 dimensions");
+ elseif (! isindex (subs)) # creates index cache
+ error ("accumarray: indices must be positive integers");
+ endif
+
+
+ ## Some built-in reductions handled efficiently.
+
+ if (isempty (func) || func == @sum)
+ ## Fast summation.
+ if (isempty (sz))
+ A = __accumarray_sum__ (subs, vals);
+ else
+ A = __accumarray_sum__ (subs, vals, prod (sz));
+ ## set proper shape.
+ A = reshape (A, sz);
+ endif
+
+ ## we fill in nonzero fill value.
+ if (fillval != 0)
+ mask = true (size (A));
+ mask(subs) = false;
+ A(mask) = fillval;
+ endif
+ elseif (func == @max)
+ ## Fast maximization.
+
+ if (isinteger (vals))
+ zero = intmin (class (vals));
+ elseif (islogical (vals))
+ zero = false;
+ elseif (fillval == 0 && all (vals(:) >= 0))
+ ## This is a common case - fillval is zero, all numbers
+ ## nonegative.
+ zero = 0;
+ else
+ zero = NaN; # Neutral value.
+ endif
+
+ if (isempty (sz))
+ A = __accumarray_max__ (subs, vals, zero);
+ else
+ A = __accumarray_max__ (subs, vals, zero, prod (sz));
+ A = reshape (A, sz);
+ endif
+
+ if (fillval != zero && ! (isnan (fillval) || isnan (zero)))
+ mask = true (size (A));
+ mask(subs) = false;
+ A(mask) = fillval;
+ endif
+ elseif (func == @min)
+ ## Fast minimization.
+
+ if (isinteger (vals))
+ zero = intmax (class (vals));
+ elseif (islogical (vals))
+ zero = true;
+ elseif (fillval == 0 && all (vals(:) <= 0))
+ ## This is a common case - fillval is zero, all numbers
+ ## non-positive.
+ zero = 0;
+ else
+ zero = NaN; # Neutral value.
+ endif
+
+ if (isempty (sz))
+ A = __accumarray_min__ (subs, vals, zero);
+ else
+ A = __accumarray_min__ (subs, vals, zero, prod (sz));
+ A = reshape (A, sz);
+ endif
+
+ if (fillval != zero && ! (isnan (fillval) || isnan (zero)))
+ mask = true (size (A));
+ mask(subs) = false;
+ A(mask) = fillval;
+ endif
+ else
+
+ ## The general case. Reduce values.
+ n = rows (subs);
+ if (numel (vals) == 1)
+ vals = vals(ones (1, n), 1);
+ else
+ vals = vals(:);
+ endif
+
+ ## Sort indices.
+ [subs, idx] = sort (subs);
+ ## Identify runs.
+ jdx = find (subs(1:n-1) != subs(2:n));
+ jdx = [jdx; n];
+ vals = mat2cell (vals(idx), diff ([0; jdx]));
+ ## Optimize the case when function is @(x) {x}, i.e. we just want
+ ## to collect the values to cells.
+ persistent simple_cell_str = func2str (@(x) {x});
+ if (! strcmp (func2str (func), simple_cell_str))
+ vals = cellfun (func, vals);
+ endif
+ subs = subs(jdx);
+
+ if (isempty (sz))
+ sz = max (subs);
+ if (length (sz) == 1)
+ sz(2) = 1;
+ endif
+ endif
+
+ ## Construct matrix of fillvals.
+ if (iscell (vals))
+ A = cell (sz);
+ elseif (fillval == 0)
+ A = zeros (sz, class (vals));
+ else
+ A = repmat (fillval, sz);
+ endif
+
+ ## Set the reduced values.
+ A(subs) = vals;
+ endif
+ endif
+endfunction
+
+%!error (accumarray (1:5))
+%!error (accumarray ([1,2,3],1:2))
+%!assert (accumarray ([1;2;4;2;4],101:105), [101;206;0;208])
+%!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]))
+%!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])))
+%!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]))
+%!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])
+%!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105, [], @prod), [101, 0, 0; 10608, 0, 10815])
+%!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))
+%!assert (accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],1,[2,4]), [1,0,0,0;2,0,2,0])
+%!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])
+%!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 0), [3; 4])
+%!assert (accumarray ([1; 2], [3; 4], [2, 1], @min, [], 1), sparse ([3; 4]))
+%!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 0), [3, 4])
+%!assert (accumarray ([1; 2], [3; 4], [1, 2], @min, [], 1), sparse ([3, 4]))
+%!test
+%! A = accumarray ([1 1; 2 1; 2 3; 2 1; 2 3],101:105,[2,4],@(x){x});
+%! assert (A{2},[102;104])
+%!test
+%! subs = ceil (rand (2000, 3)*10);
+%! vals = rand (2000, 1);
+%! assert (accumarray (subs, vals, [], @max), accumarray (subs, vals, [], @(x) max (x)));
+%!test
+%! subs = ceil (rand (2000, 1)*100);
+%! vals = rand (2000, 1);
+%! assert (accumarray (subs, vals, [100, 1], @min, NaN), accumarray (subs, vals, [100, 1], @(x) min (x), NaN));
+%!test
+%! subs = ceil (rand (2000, 2)*30);
+%! subsc = num2cell (subs, 1);
+%! vals = rand (2000, 1);
+%! assert (accumarray (subsc, vals, [], [], 0, true), accumarray (subs, vals, [], [], 0, true));
+%!test
+%! subs = ceil (rand (2000, 3)*10);
+%! subsc = num2cell (subs, 1);
+%! vals = rand (2000, 1);
+%! assert (accumarray (subsc, vals, [], @max), accumarray (subs, vals, [], @max));
+
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff