sum of matrix omitting one dimension
4 visualizaciones (últimos 30 días)
Mostrar comentarios más antiguos
Rafael Schwarzenegger
el 2 de Nov. de 2017
Comentada: Stephen23
el 2 de Nov. de 2017
Hi, I would like to ask how I could sum over a n dimensional matrix except one dimension, so the output is a vector. The ndims are not known in forehand. The summation is giving always a vector. (In my case a marginal pdf in statistics). Something like sum(K(:) except i-th dimension)
The best in a cyclus ( ndims not known).
For example having matrix K, the sums would be [6 22], [12 16], [10 18]
K(:,:,1) =
0 1
2 3
K(:,:,2) =
4 5
6 7
3 comentarios
Cedric
el 2 de Nov. de 2017
There may be a mistake in your example. Isn't the first 12 supposed to be 22?
Respuesta aceptada
Stephen23
el 2 de Nov. de 2017
Editada: Stephen23
el 2 de Nov. de 2017
Here is one very simple way:
>> d = 3; % dimension
>> v = 1:ndims(K);
>> v([1,d]) = v([d,1]);
>> s = sum(reshape(permute(K,v),size(K,d),[]),2)
s =
6
22
It works by swapping the first and the desired dimension, then reshaping so that all trailing dimensions are reduced to one. The sum is then trivially along each row.
Note that the method I show here also has the significant advantage that it does not create any variables with copies of the data from the input array: this will be important for scaling to larger input arrays. Also note that slow and complex arrayfun or cellfun are not required for this task!
4 comentarios
Stephen23
el 2 de Nov. de 2017
@Rafael Schwarzenegger: the dimensions of the input array are automatically measured using ndims(K).
Más respuestas (1)
Cedric
el 2 de Nov. de 2017
Here is one way, but there is probably a simpler approach:
buffer = arrayfun(@(k) permute(KL, circshift(1:ndims(KL), k-1)), 1:ndims(KL), 'UniformOutput', false) ;
s = cellfun(@(M) sum(reshape(M, [], size(M,2))), buffer, 'UniformOutput', false) ;
where s is a cell array of sum vectors.
EDIT : I won't have time, but maybe you can see how dimensions work with SHIFTDIM and understand how to have the outputs ordered as needed:
buffer = arrayfun(@(k) shiftdim(KL, k-1), 1:ndims(KL), 'UniformOutput', false) ;
s = cellfun(@(M) sum(reshape(M, [], size(M,2))), buffer, 'UniformOutput', false) ;
PS : you'll have to test whether it really does what you need. The approach is based on the fact that MATLAB reads memory column first
4 comentarios
Cedric
el 2 de Nov. de 2017
As mentioned by Stephen, arrayfun and cellfun are not necessary. They are hidden loops and I used them for conciseness. You can build a FOR loop if you prefer, and again, as Stephen mentions it would have the advantage not to require storing copies of your data (if you are dealing with large arrays).
Ver también
Categorías
Más información sobre Creating and Concatenating Matrices en Help Center y File Exchange.
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!