insert singelton dimension for broadcasting

18 views (last 30 days)
Alexander
Alexander on 23 Mar 2023
Edited: DGM on 29 Mar 2023
Let A be of size (M x N x P) and B be of size (M x N x K). What's the most conveniant way to broadcast C = A.*B such that C is of size (M x N x P x K) ?
In python it's
C = A[:,:,np.newaxis,:]*B[:,:,:,np.newaxis]
I can get it working by using reshape so that A is of (M x N x 1 X P), but it's a bit annoying because

Answers (3)

Catalytic
Catalytic on 23 Mar 2023
You could also create your own specialized function that does it -
[M,N,P,K]=deal(2,3,4,5);
A=rand(M,N,P);
B=rand(M,N,K);
C=tensortimes(A,B);
size(C)
ans = 1×4
2 3 4 5
function C=tensortimes(A,B)
[m,n,p]=size(A);
[mm,nn,k]=size(B);
assert(mm==m && nn==n, 'First 2 dimensions don''t match');
C=A.*reshape(B,m,n,1,k);
end

Catalytic
Catalytic on 23 Mar 2023
Edited: Catalytic on 23 Mar 2023
Inserting dimensions seems like as much a pain as reshape, but if you must do it that way, here's an approach closer to the Python style -
[M,N,P,K]=deal(2,3,4,5);
A=rand(M,N,P);
B=rand(M,N,K);
C=A.*newdim(B,3); size(C)
ans = 1×4
2 3 4 5
function A=newdim(A,n)
%insert a singleton dimension at one or more locations in size(A),
%designated by vector n.
n0=ndims(A);
n=unique(n);
N=max(n0+numel(n),max(n));
dims=nan(1,N);
dims(n)=1;
nanlocs=find(isnan(dims));
dims(nanlocs(1:n0))=size(A);
dims(isnan(dims))=1;
A=reshape(A,dims);
end
  4 Comments
Alexander
Alexander on 27 Mar 2023
the beauty is in python, you don't need to know the size of the dimension you are re-arranging, just the location or index. At minimum it saves 1 line of code, and reduces dummy temp variables.
If MATLAB by default had the newdim.m functionality you proposed, that'd be I think very intuitive, or if they implemented a A(:,:,newaxis) slice tool even better
Catalytic
Catalytic on 27 Mar 2023
If MATLAB by default had the newdim.m functionality you proposed, that'd be I think very intuitive
This seems to imply that the newdim function does what you want. If so, I wonder if you'd consider clicking Accept. From the standpoint of your convenience, it shouldn't matter whether the function is provided by MathWorks or by me.

Sign in to comment.


Catalytic
Catalytic on 23 Mar 2023
Edited: Catalytic on 23 Mar 2023
You didn't complete your description of why reshape() is "a bit annoying". If you're going to be doing the same operation repeatedly, this can cut down on the syntax somewhat (by reusing I) -
[M,N,P,K]=deal(2,3,4,5);
A=rand(M,N,P);
B=rand(M,N,K);
I=reshape(1:M*N*K, M,N,1,K);
C=A.*B(I);
size(C)
ans = 1×4
2 3 4 5
  5 Comments
Catalytic
Catalytic on 29 Mar 2023
Yes, but for this you need to keep track of the total number of dimensions, whereas with newdim, you do not.
DGM
DGM on 29 Mar 2023
Edited: DGM on 29 Mar 2023
You are correct. What's frustrating to automation is that despite MATLAB arrays implicitly having infinite trailing singleton dimensions, you can't borrow arbitrarily from them in a call to permute(). The permutation vector must contain no gaps or repetition, so you can effectively only borrow from the dims(X)+1 dimension.
Still, it's important to the novice to get familiar with both reshape() and permute(), especially if they're starting to learn how to use one without realizing the power of using both.

Sign in to comment.

Categories

Find more on Matrices and Arrays in Help Center and File Exchange

Community Treasure Hunt

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

Start Hunting!