MATLAB: Matrix to Vector row-wise

Question

How to turn a matrix into a vector row-wise efficiently. Example:

>> a = [1 2; 3 4]

a =

     1     2
     3     4

the (:) notation gives me:

>> a(:)

ans =

     1
     3
     2
     4

but I want to get the result as this:

>> b = a'; b(:)

ans =

     1
     2
     3
     4

The transposition and the additional var-assignment makes it much slower. I could do it without the assignment via reshape like this:

>> reshape(a',4,1)

ans =

     1
     2
     3
     4

which is a very small bit faster then the previous one, see the bench:

runs = 1000;
num = 1000;
A = rand(num);

times = zeros(runs, 2);
for i = 1:runs
    tic
    x = A';
    x = x(:);
    t1 = toc;
    x = reshape(A',size(A,1)*size(A,2),1);
    t2 = toc-t1;
    times(i,:) = [t1 t2];    
end
format shortG
mt = mean(times)

mt =

    0.0037877    0.0037699

If I'm leaving away the transposition it would be very very much faster and the (:) syntax would be >100% faster:

runs = 100;
num = 5000;
A = rand(num);

times = zeros(runs, 2);
for i = 1:runs
    tic
    x = A(:);
    t1 = toc;
    x = reshape(A,size(A,1)*size(A,2),1);
    t2 = toc-t1;
    times(i,:) = [t1 t2];    
end
format shortG
mt = mean(times)

mt =

    3.307e-07   8.8382e-07

that's why I'm asking if there's such a nice syntax like (:) but to get it row-wise to a vector!? Thanks

Answer 1

Think about how the elements are organized in memory. Their "natural" order is column wise. Thus A(:) simply changes the header of the matrix but does not need to change enything in the memory storing the elements themselfs. However, when you transpose A, you need to re-arrange the elements in memory (copying and swapping) and this takes time.