Wednesday, April 23, 2014

A Weekend With Julia: An R User's Reflections

 The Famous Julia

First off, I am not going to talk much about Julia's speed. Everybody has seen the tables and graphs showing how in this benchmark or another, Julia is tens times or a hundred times faster than R.  Most blog posts talking about Julia test the generality of these results (Bogumił Kamiński 2013, Randy Zwitch 2013, and  Wes McKinney 2012).

Enough said about machine speed!  Let's talk more about intuitive appeal, compactness of notation, and aesthetics.

Julia has some very thoughtful design features that make it an extremely enjoyable language to program in despite being in a nascent state.

1. Julia has some great ways of handling string expressions.  In Julia all strings are subsettable.  Thus:

julia> a = "Hello world"; a[3:7]
"llo w"

In R:
R>a <- "Hello world"; substr(a, 3, 7)

Also, "Julia allows interpolation into string literals using $, as in Perl:"(doc) julia>user = "Bob" julia>"Hello$user. How are you?"
"Hello Bob. How are you?"

2. Julia implements comprehension syntax for defining arrays which is an incredibly powerful method. Formally it looks something like this: A = [ F(x,y,...) for x=rx, y=ry, ... ]

Imagine we would like to define an area equivalent to the number line:

julia> A = [ x*y for x=1:12, y=1:12]; A
12x12 Array{Int64,2}:
1   2   3   4   5   6   7   8    9   10   11   12
2   4   6   8  10  12  14  16   18   20   22   24
3   6   9  12  15  18  21  24   27   30   33   36
4   8  12  16  20  24  28  32   36   40   44   48
5  10  15  20  25  30  35  40   45   50   55   60
6  12  18  24  30  36  42  48   54   60   66   72
7  14  21  28  35  42  49  56   63   70   77   84
8  16  24  32  40  48  56  64   72   80   88   96
9  18  27  36  45  54  63  72   81   90   99  108
10  20  30  40  50  60  70  80   90  100  110  120
11  22  33  44  55  66  77  88   99  110  121  132
12  24  36  48  60  72  84  96  108  120  132  144

Let's see how we might do this in R.
R><-matrix(nrow=12,ncol=12); A <-col(A)*row(A); A
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,]    1    2    3    4    5    6    7    8    9    10    11    12
[2,]    2    4    6    8   10   12   14   16   18    20    22    24
[3,]    3    6    9   12   15   18   21   24   27    30    33    36
[4,]    4    8   12   16   20   24   28   32   36    40    44    48
[5,]    5   10   15   20   25   30   35   40   45    50    55    60
[6,]    6   12   18   24   30   36   42   48   54    60    66    72
[7,]    7   14   21   28   35   42   49   56   63    70    77    84
[8,]    8   16   24   32   40   48   56   64   72    80    88    96
[9,]    9   18   27   36   45   54   63   72   81    90    99   108
[10,]   10   20   30   40   50   60   70   80   90   100   110   120
[11,]   11   22   33   44   55   66   77   88   99   110   121   132
[12,]   12   24   36   48   60   72   84   96  108   120   132   144

3. Functions can be written in a mathematically intuitive form.
julia> f(x,y)=x^3-y+x*y; f(3,2)
31

4. Numerical constants leading functions are automatically interpreted
julia> x=13; 3x
39

julia> (12+4)x
208

R> x<-13; 3*x
39

R> (12+4)*x
208

5. Julia does not worry about deep nesting of functions. Imagine a very silly function that adds up all of the integers between 1 and n.
julia> f(n)=(n>1 ? f(n-1)+n: n); f(100)
5050

R> f <-function(n) ifelse(n>1, f(n-1)+n, n); f(100)
[1] 5050

Both R and Julia seem to work fine.  But what happens when we go a little deeper?
R> f(10^3)
Fails while

julia> f(10^5)

Does not even cause a hiccup! Now I have never been in the situation of needing this many recursions but this result reflects the general power of the language.

6. Julia has no problem with many Unicode characters. Thus if you want θ(μ,σ,φ)=μ^σ/φ
julia> θ(μ,σ,φ)=μ^σ/φ; θ(1,2,3)
0.3333333333333333

Personally I find this notation extremely appealing as it succinctly communicates the equation for which the researcher is actually dealing with as opposed to what typically happens when I code R.

R> theta <function(mu, sigma, phi) = mu^sigma/phi; theta(1,2,3)

Besides being more compact, Julia's notation requires less mental juggling in order to translate from mathematical concepts to direct implementation.

7. Tuple fast assignment.

I am not sure if I am referring to this properly. Perhaps one of the omniscient badasses working on Julia can correct me if I am not describing this feature correctly.

I will just show you how it works:
julia> a, b, c, d = 1, 22, 33, 444
julia> b,d
(22, 444)

This might seem very trivial but check out how easy it is to pass parameters into a function. Item response theory probability of a 4PL model defined with ability parameter θ and item parameters a,b,c,d.

function ppi(θ=0, ipar=(1, 0, 0, 1), D=1.7)
  a, b, c, d = ipar
  # Define exponential factor appearing in
  # numerator and denominator.
  ε = e^(D * a * (θ - b))
  # Define final probability being returned.
  c + ((d-c)*ε)/(1+ε)
end

julia> ppi()
0.5

8. The Readability of programming in Julia.

What I mean by this is that when programming in Julia, so long as you follow basic rules regarding programming efficiency your program is likely to run at a comparable speed in Julia as it would be if it were programmed in C. For me this is a big deal. It means that I do not have to think about figuring out how to program the same task in two different languages if I am programming a new library or feature.

Likewise, when reading functions and libraries written in Julia, I hopefully will have to worry less about working with other languages. This should make it possible for the source code for functions to be more accessible for the purposes of learning and improving my understanding of programming.

Some Critiques
It is at this time that I want to mention a few critiques.  As I see it, these critiques are entirely based on the novelty of the Julia environment which is completely addressed by the creators listing the current version of the language in 0.2 and testing 0.3.  As far as how the language actually performs, I have no complaints.  It does not have as many libraries as R but they are in development.

1. The documentation is surprisingly very readable and surprisingly enjoyable.  I found that reading through documentation not only enhanced my understanding of Julia but significantly enhanced my understanding of programming languages in general.  That said, the documentation seems to be written from programming polyglots to other programming polyglots.  I think it would be very difficult for someone without programming experience to read the documentation and be able to do much with Julia.

2. The documentation is sparse on examples and the examples tend to be at a high level of complexity.  I personally think that the best way to learn to program is through examples (though this might explain my spotting understanding of abstract concepts like scope).  The documentation of Julia has a fair number of examples but I would think that doubling the number of examples would be very helpful.  In addition, there are quite a number of functions written for Julia which do not have any documentation at all.  Obviously it would be helpful to have documentation for such functions.

3. Finally, as a windows users (I know, poor form) it is not very easy to use Julia.  I have been using Forio's Julia Studio (since I do not like working with Window's command line) but don't find it that great to work with plus it is proprietary (though free).  It would be nice if there was a very basic windows IDE like R's for which I could write code in Nopepad++ and send it to Julia.  But once again this is a minor issue.  I am resolved to get a Linux build running on my machine once I make my way back to a country with decent internet.

1. "6. Julia has no problem with many Unicode characters" has great potential to lead to code that's difficult to read, type, diff, search-replace etc.

6. Julia has no problem with many Unicode characters

1. I remember that back in the 1980s when ASCII was the only thing going, there were people who claimed that Germans would stop using umlauts and even that the Chinese and Japanese would stop using their characters because they were too hard to use in computers. But instead of everyone going to the lowest common denominator, computers got better. Why is math any different? Isn't it nicer to call something θ instead of theta?

2. yeah, it's nicer. But "θ" isn't on a standard US-EN keyboard, and each and every letter of "theta" is.

3. Well put. I almost bought that idea.

4. yes but you have the choice either way... there might be times for demonstration purposes where using special characters is superior

2. Good post! You can try LightTable with Julia plugin as IDE. You can evaluate your code in-place while editing.

1. Great suggestion! I am checking this out right now.

3. Great post! Thank you for sharing.

The one Windows user at our Julia users group likes IJulia as a dev environment.
http://nbviewer.ipython.org/url/jdj.mit.edu/~stevenj/IJulia%20Preview.ipynb

The implementation is basically IPython with a Julia profile. If you don't have a Python install on your Windows machine, it may take some time to set up. (Yes, on a Mac it's easy, but you probably heard that.)

4. Great but this R code is really cumbersome:
A <-matrix(nrow=12,ncol=12); A <-col(A)*row(A); A

- Nobody would ever consider anything as cumbersome as this instead of a simpler and more efficient way:

outer(1:12, 1:12)
# one could argue (function(x) outer(x,x))(1:12) sounds nicer but this is a matter of taste

5. Good article! Do you have any experience with the R-integration (with the R - interface)?

6. Note: Julia Studio is discontinued (and tbh when you wrote this it should've been too), from their website: "As a replacement for Julia Studio, Forio recommends Juno" http://junolab.org/

7. Francis, you should consider writing code in sublime text :)