N-D matrix accumarray

23 次查看（过去 30 天）
Daniele Rocchetta
Daniele Rocchetta 2017-3-30
评论： Daniele Rocchetta 2017-3-30
Hi,
I'm working with (large) N-D matrices and need to sum elements along their dimensions, according to grouping index vectors. To exemplify
A is a 4-D matrix with dimensions (3,4,2,7), and
x1 = (2 1 2 3) <- same length as 2nd dimension in A
x2 = (3 3 2 1 3 2 4) <- same length as 4th dimension in A
I would like to find a formula f to sum the matrix along dimension 2 using the grouping variable x1 and along dimension 4 using the grouping variable x2. In the case of x2, for instance, the first, second and fifth 3x4x2 hyperplanes (group "3") should be summed together, as should the third and sixth (group "2"), while groups "1" and "4" should not change. Whether through a one-liner or a loop through the two dimensions involved, the final result should be a matrix of dimension (3,3,2,4).
I've seen similar cases using accumarray and/or arrayfun, but only applied to special (and straightforward) 2-D or 3-D (<- flattened to 2-D in the solutions proposed) matrices.
Is there a generalized (matrix of any dimension) and efficient way, through those or other functions, to obtain the result above?
Greateful in advance for any solution or lead you could provide.
Kind regards
Dan

请先登录，再回答此问题。

采纳的回答

Guillaume
Guillaume 2017-3-30
编辑：Guillaume 2017-3-30
Yes, accumarray will do it easily. You just need to generate the correct subscripts for it, which is the cartesian product of all the indices in all the dimension, replacing the appropriate dimensions with your grouping variables:
A = randi(100, [3 4 2 7]); %demo data
%generate indices in all the dimension, and replace appropriate one with grouping variables:
indices = arrayfun(@(s) 1:s, size(A), 'UniformOutput', false); %vector of indices in each dimension
indices{2} = [2 1 2 3]; %grouping in 2nd dimension
indices{4} = [3 3 2 1 3 2 4]; %grouping in 4th dimension
%calculate cartesian product of indices
[indices{:}] = ndgrid(indices{:});
indices = cell2mat(cellfun(@(v) v(:), indices, 'UniformOutput', false));
%apply accumarray with default sum function
B = accumarray(indices, A(:));
Edit: note that the above will work with arrays of any dimension (within reason, ndgrid will run out of memory for too many dimensions).
  3 个评论
显示 1更早的评论
Guillaume
Guillaume 2017-3-30
With regards to the ordering, yes, that's how accumarray works. To have the result you want:
[~, ~, newgrouping] = unique(grouping, 'stable');
Daniele Rocchetta
Daniele Rocchetta 2017-3-30
That's great thanks! You didn't even leave the last mile for me... Kudos Dan

请先登录，再进行评论。

更多回答（1 个）

Andrei Bobrov
Andrei Bobrov 2017-3-30
A = randi(10,3,4,2,7);
x1 = [2 1 2 3];
x2 = [3 3 2 1 3 2 4];
s = size(A);
[a,b,c,d] = ndgrid(1:s(1),x1,1:s(3),x2);
out = accumarray([a(:),b(:),c(:),d(:)], A(:));
  1 个评论
Daniele Rocchetta
Daniele Rocchetta 2017-3-30
Hi Andrei and thanks for you help. Unfortunately your algorithm does not have the degree of generality I need, while correct for the exemplified case above. The matrices I work with can have a different number of dimensions, and the dimensions along which to sum are also unknown at the outset. All the best Dan

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Numeric Types 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by