Generalized Matrix Product

问题:

I'm fairly new to MATLAB. Normal matrix multiplication of a M x K matrix by an K x N matrix -- C = A * B -- has c_ij = sum(a_ik * b_kj, k = 1:K). What if I want this to be instead c_ij = sum(op(a_ik, b_kj), k = 1:K) for some simple binary operation op? Is there any nice way to vectorize this in MATLAB (or maybe even a built-in function)?

EDIT: This is currently the best I can do.

% A is M x K, B is K x N
% op is min
C = zeros(M, N);
for i = 1:M:
    C(i, :) = sum(bsxfun(@min, A(i, :)', B));
end

回答1:

Listed in this post is a vectorized approach that persists with bsxfun by using permute to create singleton dimensions as needed by bsxfun to let the singleton-expansion do its work and thus essentially replacing the loop in the original post. Please be reminded that bsxfun is a memory hungry implementation, so expect speedup with it only until it is stretched too far. Here's the final solution code -

op = @min;   %// Edit this with your own function/ operation
C = sum(bsxfun(op, permute(A,[1 3 2]),permute(B,[3 2 1])),3)

NB - The above solution was inspired by Removing four nested loops in Matlab.

回答2:

if the operator can operate element-by-element (like .*):

if(size(A,2)~=size(B,1))
    error(blah, blah, blah...);
end

C = zeros(size(A,1),size(B,2));
for i = 1:size(A,1)
    for j = 1:size(B,2)
        C(i,j) = sum(binaryOp(A(i,:)',B(:,j)));
    end
end

回答3:

You can always write the loops yourself:

A = rand(2,3);
B = rand(3,4);

op = @times;            %# use your own function here
C = zeros(size(A,1),size(B,2));
for i=1:size(A,1)
    for j=1:size(B,2)
        for k=1:size(A,2)
            C(i,j) = C(i,j) + op(A(i,k),B(k,j));
        end
    end
end

isequal(C,A*B)

回答4:

Depending on your specific needs, you may be able to use bsxfun in 3D to trick the binary operator. See this answer for more infos: https://stackoverflow.com/a/23808285/1121352 Another alternative would be to use cellfun with a custom function: http://matlabgeeks.com/tips-tutorials/computation-using-cellfun/