repmat vs simple matrix multiplication in MATLAB

Question

Let v be a row vector of length n. The goal is to create a matrix A with m rows that are all equal to v.

MATLAB has a function for this that is

Answer 1

Lets compare them!

When testing algorithms 2 metrics are important: time, and memory.

Lets start with time:

Clearly repmat wins!

Memory:

profile -memory on
for m=1000:1000:50000
f1=@()(repmat(v,[m 1]));
f2=@()(ones(m,1)*v);
ii=ii+1;
t1(ii)=timeit(f1);
t2(ii)=timeit(f2);
end
profreport

It seems that both take the same amount of memory. However, the profiler is known for not showing all the memory, so we can not fully trust it.

Still, it is clear that repmat is better

Answer 2

You should use repmat().

Matrix Multiplication is O(n ^ 3) operation which is much slower then replicating data in memory.
On top of that, the second option allocate more data in memory of the size of the output.

In the case above you create a vector which the outer multiplication is faster yet still not as memory operation.

MATLAB doesn't use the knowledge all vector elements are 1, hence you multiply each element of x by 1 m times.

Both operations will be mainly memory bounded, yet more efficient, fast and direct method would be going with repmat().

The question is, what you do afterwards?
Because you may not need repmat().