Vectorization of indexing of each row of a matrix by a corresponding row of another matrix?

I have a routine that creates a new matrix A from an old matrix M by using another matrix I as a source for indexing. More specifically, each row of A is obtained by indexing a row of M by the corresponding row from I (see code example below with small matrix sizes). I would like to accelerate/vectorize this routine for better performance if that's possible. I was thinking of somehow using a combination of linear and logical indexing for M and then reshaping back to A, but I don't immediately see how to generate appropriate index vectors.

I also have the analogous problem for 3D-matrices, where I have to loop through two indexes (I could merge both loops into a single one, but the problem with the size of the loop remains).

I_range = 10; % index range for the 2nd dimension of M
l = 5; % 1st dimension for I and M
w = 4; % 2nd dimension for A, and hence for I
M_range = 20; % sets value range for M

I = randi(I_range,l,w);
M = randi(M_range,l,I_range);

% need to accelerate the following routine:
A = zeros(l,w,'double'); % allocate

for j=1:l
    A(j,:) = M(j,I(j,:));
end

Answer 1

[KSSV]

I_range = 10; % index range for the 2nd dimension of M
l = 5; % 1st dimension for I and M
w = 4; % 2nd dimension for A, and hence for I
M_range = 20; % sets value range for M

I = randi(I_range,l,w);
M = randi(M_range,l,I_range);
% With loop 
% need to accelerate the following routine:
A = zeros(l,w,'double'); % allocate

for j=1:l
    A(j,:) = M(j,I(j,:));
end

% No loop 
row = repmat((1:size(I,1))',1,size(I,2)) ; 
row = row(:) ;
col = I(:) ;

idx = sub2ind(size(M),row,col) ;
A1 = reshape(M(idx),[],w) ; 
isequal(A,A1)

ans = logical
   1

[Marin Genov]

Many thanks! This is exactly what I was looking for!