Matlab is no longer slow at for loops

Here, I discuss the most widespread piece of knowledge on Matlab : its inherent slowness with for loop. I am sure many of you will be surprised to know that it is no longer the case (at least to the extent people used to refer it to). I demonstrate this statement, explain why, and discuss some of the consequences of this fact.

It is friday night, you are invited to a cocktail party with some of your colleagues. At some point during the evening, a discussion is randomly started about programming languages. You mention that you use Matlab for your data analysis and one of your colleague looks down on you with disdain :

• Him : “Really? What a terrible language! It’s so terrible at for loops. How can you stand it?”
• You : “I am used to vectorize my code now. It’s not so bad when you get at it.
• Someone picking up the conversation : “Actually, now, Matlab is not so bad at for loops anymore.
• You and Him : “What are you talking about?”
• Someone : “Yes, it’s because of the JIT.

Who is right? As usually in these cocktails, everyone.

As an interpreted language, Matlab is supposedly slow at for loops as it has to read each line of code including all the lines generated by the for loop. But this was true many years ago. Matlab is not a pure interpreted language anymore and incorporate some JIT (for Just In Time) compilation routines. Before we go into the details of what this is, let me demonstrate.

I need a very strong case for this as the slowness of Matlab at for loops is really a strong and established knowledge that is still being taught in universities. I am going to take the best exemple of all : Matlab documentation itself.

To demonstrate the power of vectorizing over for loops, Mathworks uses the following example in both their online page and the documentation that is provided to all Matlab installations:

% For loop form
i = 0;
for t = 0:.01:10
    i = i + 1;
    y(i) = sin(t);
end

% Vectorized form
t = 0:.01:10;
y = sin(t);

Nothing fancy here.

To demonstrate my case, I am going to make some very slight modifications to this code. One will be to separate memory allocation from the for loop itself. I am going to encapsulate each calculation in a different function to clearly separate both memory space AND I will add TIC/TOC statements to measure the actual time spent, exactly as it is advised on the documentation:

The second example executes much faster than the first and is the way MATLAB is meant to be used. Test this on your system by creating scripts that contain the code shown, and then using the tic and toc functions to measure the performance.

So the new code is :

function vecto
TestVec
TestFor

function TestVec
y=zeros(1,1001);
tic;
% Vectorized form
t = 0:.01:10;
y = sin(t);
toc;

function TestFor
y=zeros(1,1001);
tic;
% For loop form
i = 0;
for t = 0:.01:10
i = i + 1;
y(i) = sin(t);
end
toc;

Here is what I get :

>> vecto
Elapsed time is 0.000044 seconds.
Elapsed time is 0.000063 seconds.

The for loop version takes about 63 us, i.e. 21 us more than the vectorized version. One would say. Q.E.D. , Matlab is BAD at for loop. Yes, BUT it used to be worse, much much much much worse. I don’t personaly consider this slow (and I am known to be demanding on calculating speed).

As I said, Matlab is not purely an interpreted language anymore. Some form of pre-compilation is ran each time you start a M-file now. This is the infamous JIT for Just-In-Time compilation.  Mathworks decided not to document this part of their program as they don’t want you to rely on the JIT. So it is very difficult to know exactly how it works. Apparently it is a fast moving target in the source code. You can discuss this choice (I personaly dislike it very much) but a clear consequence of this is that few people really know about it and Matlab extreme slowness with For loops is still being taught (and discuss in cocktail parties).

This being said, how bad was Matlab in the past with for loop?

You can get a clue at this using another undocumented command :

feature accel off

Once you have executed this, the JIT is deactivated. The new result of our little ‘vecto’ function is :

>> vecto
Elapsed time is 0.000066 seconds.
Elapsed time is 0.001755 seconds.

Yes, without the JIT, the for loop is 30 times slower. I told you it used to much much much much worse! I don’t personally consider for loop to be so bad nowadays.

Then, if even the one example from Mathworks is not convincing anymore, why vectorizing?

For two important reasons :

• It is a much more elegant way to do mathematic and is usually easier to maintain and read.
• The whole computer industry is going to multi-core and most of Matlab routines are now inherently multi-core. The for loop will not be using your multiple cores while the vectorized code will.

Indeed, if you push our previous code a little to much more elements like this :

function vecto
TestVec
TestFor

function TestVec
y=zeros(1,1000001);
tic;
% Vectorized form
t = 0:.00001:10;
y = sin(t);
toc;

function TestFor
y=zeros(1,1000001);
tic;
% For loop form
i = 0;
for t = 0:.00001:10
i = i + 1;
y(i) = sin(t);
end
toc;

You should get something like :

>> vecto
Elapsed time is 0.014492 seconds.
Elapsed time is 0.062195 seconds.

The difference between the for loop version and vectorized version is increasing a lot. What’s happening?

I have a dual core and the vectorized version is making use of it nicely whereas the for loop version not. Luckily you can also deactivate the multi-core by re-launching matlab in single core mode using :

matlab -singleCompThread

And this time, you will get :

>> vecto
Elapsed time is 0.032697 seconds.
Elapsed time is 0.059152 seconds.

Nice, isn’t it? The vectorized version is now two times slower and the difference between the two codes is now similar to our previous run with fewer elements.

The first conclusion to all this is that Matlab is not really slow at for loop anymore. So make use of them.

The second conclusion is that you should still vectorize to make use of multiple cores.

And the last conclusion is that you have a lot to say at your next cocktail party!