How to efficiently sum values in matrix using indices from a logical statement of a different matrix

I have two 2D matrices, A and B which are of the same size. The values of A are my output values, and the values of B are the probabilities of each value in A. So, prob(A(i,j)) = B(i,j). I expect there to be many repetitions in A (not each output is unique) so I want to find two vectors, one which tells me the unique values of A and the other which tells me the probability of each of those unique values.

I know I can use the unique() function to find the unique values of A. But currently, my approach to finding the probability of each unique value (looping and summing - see example below) is by far the slowest part of my code. Is there a faster way to do this?

%Set up matrix of values
A = [0 1 2 3;
    1 2 3 4;
    2 3 4 5];

%Set up matrix of probabilities
B = [0.05 0.02 0.03 0.10;
     0.10 0.30 0.10 0.05;
     0.10 0.05 0.05 0.05];

%Find vector of unique values of A
uniA = unique(A);

%Find probabilities of each value of A (This is what I want to make more
%efficient)
prob_uniA = zeros(size(uniA));
for i = 1:length(uniA)
    prob_uniA(i) = sum(B(A == uniA(i)));
end

Notes: In reality, my A and B matrices are approximately 1000x1000. I am looking to improve the speed because this process is implemented within a for loop with ~15 iterations (and will be applied to 200 different datasets in the future, so small gains in size here make a big difference in overall time). I am running a 2020 Mac Mini with M1 chip, 16GB memory.

Thanks!

Answer 1

[the cyclist]

%Set up matrix of values
A = [0 1 2 3;
    1 2 3 4;
    2 3 4 5];

%Set up matrix of probabilities
B = [0.05 0.02 0.03 0.10;
     0.10 0.30 0.10 0.05;
     0.10 0.05 0.05 0.05];

% Find the unique values of A, and the indices that map each original value
% to the unique ones
[uniA,~,k] = unique(A);

% Sum the probabilities via the mapping created
prob_uniA = accumarray(k,B(:))

prob_uniA = 6×1

0.0500 0.1200 0.4300 0.2500 0.1000 0.0500