logical indexing from matrix to vector

How to extract nonzero columns from rows (in a matrix whose each rows have only one column as 1 and others 0) and put them into a vector rows?

A=rand(4,5);
B=rand(4,5);
C=rand(4,5);
D=logical([1 0 0 0 0; 0 0 0 0 1; 0 1 0 0 0; 0 0 1 0 0]);% each row has 1 nonzero column
E=zeros(4,3);
%get first column of E, E(:,1) to be all rows of A at the nonzero column of A. For instance, 
% F=zeros(4,5), then F(D)=A(D) will put those nonzero columns of A into matching positions in F. But I want those to go to E(:,1).
% Then, E(:,2) contains all elements B(D), and E(:,3) contains all elements
% C(D).

Answer 1

[Voss]

Here is one way:

A=rand(4,5);
B=rand(4,5);
C=rand(4,5);

display(A);

A = 4×5

0.4104 0.9407 0.5917 0.6464 0.7284 0.6918 0.8538 0.6330 0.5557 0.5605 0.1275 0.8258 0.1423 0.8855 0.3392 0.2219 0.1713 0.1226 0.2026 0.0638

display(B);

B = 4×5

0.1526 0.9030 0.3792 0.0172 0.4932 0.0312 0.8822 0.1125 0.2305 0.6067 0.3733 0.2005 0.6237 0.5705 0.0556 0.3156 0.5108 0.7459 0.5075 0.5017

display(C);

C = 4×5

0.4056 0.3240 0.5035 0.9342 0.7651 0.3437 0.9692 0.8953 0.2602 0.0158 0.9978 0.0599 0.1278 0.8558 0.4685 0.9000 0.4657 0.6759 0.1337 0.0315

D=logical([1 0 0 0 0; 0 0 0 0 1; 0 1 0 0 0; 0 0 1 0 0]);% each row has 1 nonzero column
display(D);

D = 4×5 logical array
   1   0   0   0   0
   0   0   0   0   1
   0   1   0   0   0
   0   0   1   0   0

E=zeros(4,3);
[r,c] = find(D);
for i = 1:numel(r)
    E(r(i),:) = [A(r(i),c(i)) B(r(i),c(i)) C(r(i),c(i))];
end

display(E);

E = 4×3

0.4104 0.1526 0.4056 0.5605 0.6067 0.0158 0.8258 0.2005 0.0599 0.1226 0.7459 0.6759