Julia, while being "a scripting language", it is far more complex than other scripting languages. The goal for these slides is to give a proper mental model for approaching Julia
Higham: An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
%BPATH1 Brownian path simulation function [t,W]=BPATH1(T,N) randn('state',100) dt = T/N; dW = zeros(10,N); W = zeros(10,N); dW(:,1) = sqrt(dt)*randn(1,10); W(:,1) = dW(:,1); for j = 2:N dW(:,j) = sqrt(dt)*randn(1,10); W(:,j) = W(:,j-1) + dW(:,j); end t = [0:dt:T-dt]; end % In Another File... f = @() BPATH1(1,10000); timeit(f,2) [t,W] = BPATH1(1,10000); plot(t,W,'r-') xlabel('t','FontSize',16) ylabel('W(t)','FontSize',16,'Rotation',0)
function bpath(T,N) srand(100) dt = T/N dW = zeros(10,N) W = zeros(10,N) dW[:,1] = sqrt(dt)*randn(10) W[:,1] = dW[:,1] for j = 2:N dW[:,j] .= sqrt(dt)*randn(10) W[:,j] .= W[:,j-1] .+ dW[:,j] end [0:dt:T-dt],W end # Translation took < 1 minute @time t,W = bpath(1,100000) # Timing is slower in Jupyter! @time t,W = bpath(1,100000) # Timing is slower in Jupyter! # 10x speedup over MATLAB using Plots plot(t,W',color=:red,xlabel="t",ylabel="W(t)")
0.312249 seconds (1.58 M allocations: 123.550 MB, 5.14% gc time) 0.051225 seconds (1.30 M allocations: 111.374 MB, 16.63% gc time)
Julia combines the interests, features, and libraries of all of these groups. To which group(s) do you belong?
We want a language that’s open source, with a liberal license. We want the speed of C with the dynamism of Ruby. We want a language that’s homoiconic, with true macros like Lisp, but with obvious, familiar mathematical notation like Matlab. We want something as usable for general programming as Python, as easy for statistics as R, as natural for string processing as Perl, as powerful for linear algebra as Matlab, as good at gluing programs together as the shell. Something that is dirt simple to learn, yet keeps the most serious hackers happy. We want it interactive and we want it compiled.
(Did we mention it should be as fast as C?)
While we’re being demanding, we want something that provides the distributed power of Hadoop — without the kilobytes of boilerplate Java and XML; without being forced to sift through gigabytes of log files on hundreds of machines to find our bugs. We want the power without the layers of impenetrable complexity. We want to write simple scalar loops that compile down to tight machine code using just the registers on a single CPU. We want to write A*B and launch a thousand computations on a thousand machines, calculating a vast matrix product together.
Julia's syntax is pulled from places considered "best-in-class":
No matter who you are, some of the terminology will be familiar, while other parts will be pulled from a domain you may have never heard of.
Conclusion: While Julia looks at the surface like R/Python/MATLAB, what's actually happening under the hood is very different. It is this design difference which is essential to getting the full performance out of Julia while not sacrificing readability. The goal of the workshop is to show you how this works, and how to make it work to your advantage.
Since Julia has so many different influences meshed together, there is a "rabbit hole" of features to explore, designs to investigate, and performance tricks to exploit. We will be peaking into the rabbit hole. Here's a good snippet of a podcast that addresses some misconceptions.
Karpinski: The syntax is superficially similar to MATLAB, so you can often translate MATLAB code to Julia just by changing a few parenthesis to square brackets for indexing into arrays and not really changing too much else. But the symantics are closest probably to Python: it's [a] very straightforward dynamic language to write use. But then there's sort of this rabbit hole of advanced features that you can go down that you don't need to know about right away to write useful programs, but which can help you as you find yourself doing harder and harder things.
Edelman: What happens when you start to go down this rabbit hole is you become programmer, something for when you used these other languages you never knew you were missing, and never knew you wanted to be. But then when you do it, you wonder how you lived without it.
Listen to 5:50 - 17:00