Optimal Number of Workers for Parallel Julia
April 16 2016 in HPC, Julia, Programming, Stochastics | Tags: BLAS, hyperthreading, julia, parallel computing, workers | Author: Christopher Rackauckas
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
Interfacing with a Xeon Phi via Julia
March 4 2016 in C, HPC, Julia, Programming, Stochastics, Xeon Phi | Tags: C, julia, MIC, OpenMP, parallel, Xeon Phi | Author: Christopher Rackauckas
(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
What Exactly is Brownian Motion and Why Does it Matter?
January 19 2016 in Stochastics | Tags: biology, brownian motion, nonstandard analysis, stochastic differential equations, Wiener process | Author: Christopher Rackauckas
When you talk about randomness, stochastics, and noise, everything always seems to be going back to “Brownian motion” and “white noise”. But what exactly are these things?
The problem is that if you ask someone who researches the subject, you most likely get many different definitions at the same time. The reason is because, although there are many equivalent definitions (and terms), every single one only seems to be a small part of the intuition of what this thing actually is. So I am going to state without proof equivalent formulations of $$B(t)$$, which is the same as $$B_{t}$$, which is the same as $$W_{t}$$… READ MORE