Help extracting data from 3D matrices

Given a matrix A, such that size(A) = {m,n,l}, and a vector v: mx1,

I would like to obtain a 2D matrix F: mxn, in which:

each row of F is given by [i, : , v(i)].

And I would like to do this parametrically, with 1 line. An example to play with below.

m = 2;
n = 2;
l = 3;

A = [];
A(:,:,1) = [1 0;
            0 0];
A(:,:,2) = [ 0 2;
            0 0];
A(:,:,3) = [0 0;
            3 0];

v = [2;3];

% I would like to obtain something like below, but parametrically and
%   without for/if/etc.
F = [];
F(1, :) = squeeze(A(1, : , v(1)));
F(2, :) = squeeze(A(2, : , v(2)));

A

A = 
A(:,:,1) =

     1     0
     0     0


A(:,:,2) =

     0     2
     0     0


A(:,:,3) =

     0     0
     3     0

F

F = 2×2

0 2 3 0

Thanks everyone,

E.

[Dyuman Joshi]

Just asking, why do you not want to use loops?

[Giovanni Bambini]

for loops and if logics break code execution and increase computation time considerably. In a really long code,I tried converting all ifs and for (when possible) to vectorial code. Even tho the number of computations increased a lot, I managed to obtain a really huge speedup (didn't measure it, but it felt something like 2.5x).

[Dyuman Joshi]

"for loops and if logics break code execution and increase computation time considerably."

Do you have a source for this?

Yes, vectorization is faster than using loops, but that does not mean loops are slow.

Let's compare Voss's answer below to a for loop approach -

%Taking a big sample for proper testing
A = rand(2500,500,100);
v = randi(size(A,3),size(A,1),1);

fun1 = @() forloop(A,v);
fun2 = @() vectorization(A,v);

z1 = fun1();
z2 = fun2();

%Check for equality
isequal(z1,z2)

ans = logical
   1

fprintf('Time taken by the for loop is %f secs', timeit(fun1))

Time taken by the for loop is 0.021966 secs

fprintf('Time taken by the vectorized method is %f secs', timeit(fun2))

Time taken by the vectorized method is 0.026751 secs

function F = forloop(A,v)
[m,n,l] = size(A);
F = zeros(m,n);
for k=1:m
    F(k,:) = A(k,:,v(k));
end
end


function F = vectorization(A,v)
[m,n,l] = size(A);
idx = sub2ind([m,n,l],repelem(1:m,1,n),repmat(1:n,1,m),repelem(v(:).',1,n));
F = reshape(A(idx),[],m).';
end

As you can see from the above results, the for loop is the faster method here.

Though one can argue that there might be a better method utilizing vectorization, but the point I am trying to convey, is that vectorization being faster does not mean for loops are considerably slower (unless not used properly)

[Giovanni Bambini]

Your analysis is really interesting, but I don't know if it considers all possible scenarios. Discarding the fact that for() are way faster than IFs when implemented properly and thus the difference may not be noticible, cpu and computers are nowadays very complex structures (several level of caches, multicores and NoCs, different types of cores (i.e. Intel P,E), vectorized instructions and accelerators (AVX, etc.), Out of order execution, ...) and thus a simple code with a not-huge memory footprint, even if bigger than the original, may not incapsulate all scenarios.

Saying that, it is highly possible that in the above case, as well as in several other cases, for() loops may be faster than other implementations, but as a personal rule (and also for ease of reading the code) I prefer to use vectorized commands possibly already implemented by Matlab like the aforementioned sub2ind() and reshape(), because I assume they are already implemented in the best way possible and highly scalable.

Anyway your insight was really helpful, and in the future I will not restrain from for() loops as strictly as before.

E.

Answer 1

[Voss]

Here's one way:

A = cat(3,[1 0; 0 0],[0 2; 0 0],[0 0; 3 0]);
v = [2;3];
[m,n,l] = size(A);

idx = sub2ind([m,n,l],repelem(1:m,1,n),repmat(1:n,1,m),repelem(v(:).',1,n));
F = reshape(A(idx),[],m).';

disp(F);

     0     2
     3     0

[Giovanni Bambini]

Thanks, this is the kind of magic I was looking for. Didn't know about the sub2ind function.

[Voss]

You're welcome!