Ytukyg

I have $2$ matrices of different sizes: $8 times 3$ matrix $A$ and $2 times 3$ matrix $B$. I need to subtract from each row of $B$, a particular row of $A$ and sum these values. This I need to do for all the rows for $A$ and store the result in another matrix $C$. Is there a way to do this avoiding both for loops?

I can avoid one using bsxfun but seems like I need to use one for loop for iterating over the elements of $A$.

If I understand correctly, you want to (1) subtract every row of A from every row of B, and then (2) sum all values within each resulting row.

1. 
   

   For step (1) you can use a single bsxfun, but you need to permute dimensions:

   
   
   

   subtractedRows = bsxfun(@minus, B, permute(A,[3 2 1]));
   
   

   
   
   

   For any m, n, subtractedRows(m,:,n) gives B(m,:)-A(n,:).

   
   


2. 
   

   For step (2) you only need to sum along second dimension:

   
   
   

   result = squeeze(sum(subtractedRows,2));
   
   

   
   

It sounds like you can sum across the columns of A and B before subtracting and simplify the computation.

If broadcasting is available (newest versions of Matlab and Octave):

C = sum(B, 2) - sum(A, 2)'

If not:

C = repmat(sum(B, 2), [1 rows(A)]) - repmat(sum(A, 2)', [rows(B) 1])