Parallel Matrix Multiplication in Java

In this post I would like to discuss my experiment today on parallelising matrix multiplication. First off, I would like to give credit to the following stackoverflow thread, to all the authors of the questions, answers, and the codes.
http://stackoverflow.com/questions/5484204/parallel-matrix-multiplication-in-java-6

The fascination on parallelised matrix multiplication started when I was implementing an RBM in Java. On that particular implementation, the training phase was very slow, where some training instances may last for half a day. In comparison, a library called Medal https://github.com/dustinstansbury/medal which is written on top of MATLAB only took less than 5 minutes for the same computation! As it turns out, that godly speed was possible because matrix operations in MATLAB is highly optimised and parallelised. That makes me wonder how to parallelise matrix operations, and in particular, matrix multiplication.

So today I decided to investigate further and this post will serve as the highlight of the day.