Can I vectorize this matrix task in MATLAB? - matlab

Question

I have a square matrix A which I would like to manipulate using a matrix D. The result will be the matrix B. The entry B(i, j) will be a sum of a number of elements from A(:, j), as determined by D.
Let me show what I have in codes -
A = magic(3); % initial matrix
D = [1, 2, 3; 2, 2, 3; 1, 3, 1]; % map matrix
B = zeros(3); % resultant matrix
for i = 1:3
for j = 1:3
B(D(i, j), j) = B(D(i, j), j) + A(i, j);
end
end
Now, to explain we have D as :
D = [1, 2, 3;
2, 2, 3;
1, 3, 1];
These D values basically act as the row indices to accumulate into output array B, while column indices would be iterating numbers themselves -
col = [1 2 3;
1 2 3;
1 2 3];
Thus, the summations are :
B(1,1) += A(1,1) % Indices from first row from D to select B
B(2,2) += A(1,2)
B(3,3) += A(1,3)
B(2,1) += A(2,1) % Indices from second row from D to select B
B(2,2) += A(2,2)
B(3,3) += A(2,3)
B(1,1) += A(3,1) % Indices from third row from D to select B
B(3,2) += A(3,2)
B(1,3) += A(3,3)
Thus, at B(1,1) we would accumulate two values from A : A(1,1) and A(3,1) and so on.
When the matrices are large, this process takes a long time. Is there a way to vectorize this computation?

Answer 1

Here's one approach using accumarray and bsxfun -
[m,n] = size(A);
% Generate all linear indices corresponding to D
idx = bsxfun(#plus,D,m*(0:n-1))
% Use accumarray to accumulate values for each of those indices.
% We need some reshaping to get a final 2D output after feeding in column
% vectors for using accumarray
Bout = reshape(accumarray(idx(:),A(:),[m*n,1]),[m,n])
Sample run -
>> % Setup inputs and run loopy version
A = randi(9,4,6);
D = randi(size(A,1),4,6);
B = zeros(size(A));
for i = 1:size(A,1)
for j = 1:size(A,2)
B(D(i, j), j) = B(D(i, j), j) + A(i, j);
end
end
% Proposed vectorized method
>> [m,n] = size(A);
>> idx = bsxfun(#plus,D,m*(0:n-1));
>> Bout = reshape(accumarray(idx(:),A(:),[m*n,1]),[m,n]);
% Verify results
>> max(abs(Bout(:)-B(:)))
ans =
0