MATLAB 2016a Release Summary for Scientific Computing
March 15 2016 in MATLAB, Programming | Tags: 2016a, MATLAB, optimization, parallel | Author: Christopher Rackauckas
There is a lot to read every time MATLAB releases a new version. Here is a summary of what has changed in 2016a from the eyes of someone doing HPC/Scientific Computing/Numerical Analysis. This means I will leave off a lot, and you should check it out yourself but if you’re using MATLAB for science then this may cover most of the things you care about.
- Support for sparse matrices on the GPU. A nice addition is sprand and pcg (Preconditioned Conjugate Gradient solvers) for sprase GPU matrices.
- One other big change in the parallel computing toolbox is you can now set nonlinear solvers to estimate gradients and Jacobians in parallel. This should be a nice boost to the MATLAB optimization toolbox.
- In the statistics and machine learning toolbox, they added some algorithms for high dimensional data and now let you run kmeans … READ MORE
Simple Parallel Optimization in Mathematica
February 2 2016 in Mathematica | Tags: optimization, parallel | Author: Christopher Rackauckas
A quick search on Google did not get hits for a standard method of parallelizing NMaximize and NMinimize, so I wanted to share how I did it.
My implementation is a simple use of a Map-Reduce type of parallelism. What this means is that we map the same problem out to N many processes, and when they finish they each give one result, and we apply a reduction function to reduce the N results to 1. So what we will do is map the NMaximize function to each of N cores, where they will each solve it on a random seed. From there, each process will return what it found as the minimum, and we will take the minimum of these minimums as our best estimate of the global minimums.
Notice that this is not optimal in all cases: for … READ MORE
Julia iFEM 2: Optimizing Stiffness Matrix Assembly
January 23 2016 in FEM, Julia, MATLAB, Programming | Tags: julia, optimization, sparse, vectorization | Author: Christopher Rackauckas
This is the second post looking at building a finite element method solver in Julia. The first post was about mesh generation and language bindings. In this post we are going to focus on performance. We start with the command from the previous post:
node,elem = squaremesh([0 1 0 1],.01)
which generates an array elem where each row holds the reference indices to the 3 points which form a triangle (element). The actual locations of these points are in the array node, and so node(1) gives the points in the (x,y)-plane for the $$i$$th point. What the call is saying is that these are generated for the unit square with mesh-size .01, meaning we have 10201 triangles.
The approach to building the stiffness matrix for the … READ MORE