I recently blogged about the upcoming Lang.NEXT 2012 conference in Redmond. And since the videos are not uploaded yet (and the talk about Julia should pretty much only soon start) I decided to use the time to do some early evaluation of the language with the beautiful suggestive name everyone seems to fall in love immediately. Since we all know how prone love is to projection, I felt I needed a more rational look on the language. And – as usual – as things get clearer you get to know each other more and more and butterflies turn into even more beautiful butterflies … or into something completely different ….

Lets start with some motivation. Julia wants to bridge the gap between established convenient mathematical (prototyping, desktop) systems and high performance computing (parallel) resources. So, basically, it wants to be comfortable and fast. “Huh?” – I hear you say, “this is what ILNumerics does as well!” – and of course you are right. But Julia originates from a very different motivation as ILNumerics. For us, the goal is to provide convenient numeric capabilities with high performance and a comfortable syntax – but to do it directly in a general purpose language. Basically, this brings a lot of advantages when it comes to deployment of your algorithm and it is much easier to utilize all those convenient development tools which are already there for C#. Furthermore, (frequent) transition from business logic to your numerical algorithms can become nasty and error prone.

Julia, on the other side, has to fight other enemies: dynamic language design. Things like dispatching schemes, type inference and – promotion, lexer and parser and certainly a lot more. I really bow to those guys! From a first view they did really succeed. And at the same time, I am glad, that Eric Lippert and his colleagues took away the hard stuff from us. But, of course: by going through all that pain of language design (ok, it sometimes might be fun as well) – you gain the opportunity to optimize your syntax to far less limits. A ‘plus’ of convenience.

Lets take a look at some code. Readers of this blog are already familiar with what turns out to become our favorite algorithm for comparing languages: the kmeans algorithm in its beauty and simplicity. Here comes the Julia version I managed to run on Windows:

function kmeansclust (X, k, maxIterations)

nan_ = 0.0 / 0.0;
n = size(X,2); 
classes = zeros(Int32,1,n); 
centers = rand(size(X,1),k); 
oldCenters = copy(centers); 
while (maxIterations > 0)
        println("iterations left: $maxIterations"); 
        maxIterations = maxIterations - 1;
        for i = 1:n
                Xexp = repmat(X[:,i],1,k);
            	dists = sum(abs(centers - Xexp),1); 
	        classes[i] = find(min(dists) == dists)[1];
        end
        for i = 1:k
            inClass = X[:,find(classes == i)];
            if (isempty(inClass))
                centers[:,i] = nan_;
            else
                centers[:,i] = mean(inClass,2);
            end
        end
        if (all(oldCenters == centers))
            break;
        end
        oldCenters = copy(centers);
 end
 (centers, classes)
end

Did you notice any differences to the Matlab version? They are subtle:

• Line 29 returns the result as tuple – a return keyword is not required. Moreover, what is returned does not need to be defined in the function definition.
• Julia implements reference semantics on arrays. This makes the copy() function necessary for assignments on full arrays (-> lines 7 and 27). For function calls this implies, that the function potentially alters its input! Julia states the convention to add a ! to the name of any function, which alters its input parameter.

Besides that, the syntax of Julia can be pretty much compatible to MATLAB^® – which is really impressive IMO. Under the hood, Julia even offers much more than MATLAB^® scripts are able to do: type inference and multiple dispatch, comprehensions, closures and nifty string features like variable expansion within string constants, as known from php. Julia utilizes the LLVM compiler suite for JIT compilation.

Julia is too young to judge, really. I personally find reference semantics for arrays somehow confusing. But numpy does it as well and nevertheless found a reasonable number of users.

While the above code run after some fine tuning, the current shape of the Windows prebuilt binaries somehow prevented a deeper look in terms of performance. It still needs some quirks and bugs removed. (The Windows version was provided only some hours earlier and it was the first publicly available version for Windows at all.) As soon as a more stable version comes out, I will provide some numbers – possibly with an optimized version (@bsxfun is not implemented yet which renders every comparison unfair). According to their own benchmarks, I would expect Julia to run around the speed of ILNumerics.