6 Months of DifferentialEquations.jl: Where We Are and Where We Are Going

So around 6 months ago, DifferentialEquations.jl was first registered. It was at first made to be a library which can solve "some" types of differential equations, and that "some" didn't even include ordinary differential equations. The focus was mostly fast algorithms for stochastic differential equations and partial differential equations.

Needless to say, Julia makes you too productive. Ambitions grew. By the first release announcement, much had already changed. Not only were there ordinary differential equation solvers, there were many. But the key difference was a change in focus. Instead of just looking to give a production-quality library of fast methods, a major goal of DifferentialEquations.jl became to unify the various existing packages of Julia to give one user-friendly interface.

Since that release announcement, we have made enormous progress. At this point, I believe we have both the most expansive and flexible ... READ MORE

Modular Algorithms for Scientific Computing in Julia

December 7 2016 in Julia, Programming | Tags: | Author: Christopher Rackauckas

When most people think of the Julia programming language, they usually think about its speed. Sure, Julia is fast, but what I emphasized in a previous blog post is that what makes Julia tick is not just-in-time compilation, rather it's specialization. In that post, I talked a lot about how multiple dispatch allows for Julia to automatically specialize functions on the types of the arguments. That micro-specialization is what allows Julia to compile functions which are as fast as those from C/Fortran.

However, there is a form of "macro specialization" that Julia's design philosophy and multiple dispatch allows one to build libraries for. It allows you to design an algorithm in a very generic form, essentially writing your full package with inputs saying "insert scientific computing package here", allowing users to specialize the entire overarching algorithm to the specific problem. ... READ MORE

7 Julia Gotchas and How to Handle Them

October 4 2016 in Julia, Programming | Tags: | Author: Christopher Rackauckas

Let me start by saying Julia is a great language. I love the language, it is what I find to be the most powerful and intuitive language that I have ever used. It's undoubtedly my favorite language. That said, there are some "gotchas", tricky little things you need to know about. Every language has them, and one of the first things you have to do in order to master a language is to find out what they are and how to avoid them. The point of this blog post is to help accelerate this process for you by exposing some of the most common "gotchas" offering alternative programming practices.

Julia is a good language for understanding what's going on because there's no magic. The Julia developers like to have clearly defined rules for how things act. This means that all behavior ... READ MORE

Introducing DifferentialEquations.jl

Edit: This post is very old. See this post for more up-to-date information.

Differential equations are ubiquitous throughout mathematics and the sciences. In fact, I myself have studied various forms of differential equations stemming from fields including biology, chemistry, economics, and climatology. What was interesting is that, although many different people are using differential equations for many different things, pretty much everyone wants the same thing: to quickly solve differential equations in their various forms, and make some pretty plots to describe what happened.

The goal of DifferentialEquations.jl is to do exactly that: to make it easy solve differential equations with the latest and greatest algorithms, and put out a pretty plot. The core idea behind DifferentialEquations.jl is that, while it is easy to describe a differential equation, they have such diverse behavior that experts have spent over a century compiling ... READ MORE

Using Julia's Type System For Hidden Performance Gains

What I want to share today is how you can use Julia's type system to hide performance gains in your code. What I mean is this: in many cases you may find out that the optimal way to do some calculation is not a "clean" solution. What do you do? What I want to do is show how you can define special arrays which are wrappers such that these special "speedups" are performed in the background, while having not having to keep all of that muck in your main algorithms. This is easiest to show by example.

The examples I will be building towards are useful for solving ODEs and SDEs. Indeed, these tricks have all been implemented as part of DifferentialEquations.jl and so these examples come from a real use case! They really highlight a main feature of Julia: ... READ MORE

Finalizing Your Julia Package: Documentation, Testing, Coverage, and Publishing

In this tutorial we will go through the steps to finalizing a Julia package. At this point you have some functionality you wish to share with the world... what do you do? You want to have documentation, code testing each time you commit (on all the major OSs), a nice badge which shows how much of the code is tested, and put it into metadata so that people could install your package just by typing Pkg.add("Pkgname"). How do you do all of this?

Note: At anytime feel free to checkout my package repository DifferentialEquations.jl which should be a working example.

Generate the Package and Get it on Github

First you will want to generate your package and get it on Github repository. Make sure you have a Github account, and then setup the environment variables in the git shell:


Optimal Number of Workers for Parallel Julia

How many workers do you choose when running a parallel job in Julia? The answer is easy right? The number of physical cores. We always default to that number. For my Core i7 4770K, that means it's 4, not 8 since that would include the hyperthreads. On my FX8350, there are 8 cores, but only 4 floating-point units (FPUs) which do the math, so in mathematical projects, I should use 4, right? I want to demonstrate that it's not that simple.

Where the Intuition Comes From

Most of the time when doing scientific computing you are doing parallel programming without even knowing it. This is because a lot of vectorized operations are "implicitly paralleled", meaning that they are multi-threaded behind the scenes to make everything faster. In other languages like Python, MATLAB, and R, this is also the case. Fire up MATLAB ... READ MORE

Benchmarks of Multidimensional Stack Implementations in Julia

Datastructures.jl claims it's fast. How does it do? I wrote some quick codes to check it out. What I wanted to do is find out which algorithm does best for implementing a stack where each element is three integers. I tried filling a pre-allocated array, pushing into three separate vectors, and different implementations of the stack from the DataStructures.jl package.

function baseline()
stack = Array{Int64,2}(1000000,3)
for i=1:1000000,j=1:3
function baseline2()
stack = Array{Int64,2}(1000000,3)
for j=1:3,i=1:1000000
function f0()
stack = Array{Int64}(1000000,3)
for i = 1:1000000
stack[i,:] = [i,i,i]
function f02()
stack = Array{Int64}(3,1000000)
for i = 1:1000000
stack[:,i] = [i;i;i]
function f1()
stack1 = Vector{Int64}(1)
stack2 ... READ MORE

Interfacing with a Xeon Phi via Julia

(Disclaimer: This is not a full-Julia solution for using the Phi, and instead is a tutorial on how to link OpenMP/C code for the Xeon Phi to Julia. There may be a future update where some of these functions are specified in Julia, and Intel's compilertools.jl looks like a viable solution, but for now it's not possible.)

Intel's Xeon Phi has a lot of appeal. It's an instant cluster in your computer, right? It turns out it's not quite that easy. For one, the installation process itself is quite tricky, and the device has stringent requirements for motherboard choices. Also, making out at over a taraflop is good, but not quite as high as NVIDIA's GPU acceleration cards.

However, there are a few big reasons why I think our interest in the Xeon Phi should be renewed. For one, Intel ... READ MORE

Multiple-GPU Parallelism on the HPC with Julia

February 28 2016 in CUDA, HPC, Julia, Programming | Tags: , , , | Author: Christopher Rackauckas

This is the exciting Part 3 to using Julia on an HPC. First I got you started with using Julia on multiple nodes. Second, I showed you how to get the code running on the GPU. That gets you pretty far. However, if you got a trial allocation on Cometand started running jobs, you may have noticed when looking at the architecture that you're not getting to use the full GPU. In the job script I showed you, I asked for 2 GPUs. Why? Well, that's because the flagship NVIDIA GPU, the Tesla K80, is actually a duel GPU and you have to control the two parts separately. You may have been following along on your own computer and have been wondering how you use the multiple GPUs in your setup as well. This tutorial will ... READ MORE