Java 2D arrays
I had to find a bit of code to solve a set of simultaneous equations for some prototype code i'm working on.
Having to do this gives me the willies really because linear algebra was never much fun for me ...
I only have to solve a pretty simple system - 6x6 - and I settled on using Jama, mostly because it's a small and simple library. The code is also fairly clean and I need to eventually port this to OpenCL too.
The code uses 2-D arrays to store it's matrices, but I know 2-D matrices in Java aren't particularly efficient - they are implemented much the way you would do it in C. That is an array of pointers which point to the rows of the array. Thus every 2D access requires 2 array dereferences. Anyway as I need to port it to OpenCL eventually anyway I tried converting the Matrix and LUDecomposition classes to use linear arrays. Then I just use simple arithmetic to map 2-D indices onto this linear array (i.e. i*n + j).
I got pretty much exactly a 2x performance boost from this simple change. Which is in-line with what I expected but I didn't quite expect it to be so close to 2x. The memory accesses far out-weigh any arithmetic on a modern CPU, and since 2-D arrays require 2x as many memory accesses (and 2x the range checks i presume), halving the memory accesses required lead to a 2x speed up. Even though the twin-array access was replaced by the more complex multiply and an addition as the index calculation.
Jama is wildly out of date, and I didn't look at the alternatives which might focus more on performance, but it shows that at least in this case 2-D arrays come at quite a cost.
Not really looking forward to getting it working in OpenCL either, trying to parallelise it is going to be a bit of a hassle. Then again maybe the challenge will be refreshing - I need something to spark me up at the moment.
This whole chunk of work is getting me down a bit - I have a big pile of hard to decipher ('matlabotomised') code to convert before I even get something to test, and then I have to try to remove some of the matlabisms that don't make sense in a real language, or require unnecessary excess memory. Then I have to get it working. And once that's done I have to re-do it all again from Java to OpenCL and get that working ... but i'm just not into it these last few weeks. Lack of sleep mostly (I keep waking at sun-up, I really must exercise), but also some other distractions - a few days of nice weather, family visiting, and so on.
This is also why I haven't had time to work on any of the other projects - I just don't have the energy. Lawn is looking good though.