Hacker News Reader

Comment by ericlavigne | Hacker News Reader

The instructor emphasized the performance benefit of Octave's optimized matrix operations. Did you use Colt's matrix operations, or were you able to match the performance of vectorized Octave code with non-vectorized Clojure code?

View on HN

I think the real magic comes from understanding the algorithms as matrix operations, and then implementing them by more or less just writing down the algebra.

Can you give a source for learning about "algorithms as matrix operations"? I tried searching on that phrase in Google Scholar but didn't get anything useful.

If you can express the code using the functions and operators of linear algebra, you can simply write the math and get fast, elegant code. May even run on a GPU.

Fortran is frequently used for physics simulation. We used Mathematica, Maple and Matlab even in non-computing classes.

See http://www.netlib.org/lapack/

Also http://en.wikipedia.org/wiki/Array_programming

Your first phrase captures what I assumed he meant, I was wondering if there is anything available that could help me recognize algorithms that could or should be expressed that way, and how to do it. Your Wikipedia link was helpful.

I am working on a calculus refresher right now (I really need it) and am planning on working through an elementary linear algebra text once that is done, which is why I particularly noticed the comment. I have found that having an idea of applications helps retention, which is one reason I am trying to track down something more concrete.

Most of the textbooks on machine learning present things in that way (it's really the only way). For example, check out Elements of Statistical Learning (http://www-stat.stanford.edu/~tibs/ElemStatLearn/).

If, like me, you thought "linear algebra" meant "stuff without exponents", you should start here:

http://www-math.mit.edu/~gs/papers/starting2matrices.pdf

It's the most accessible starter I've found to date. There is also a linear algebra group-learning thread somewhere on HN.

I also implemented some of the exercises in clojure, and my naive implementation without colt or incanter ran orders of magnitude slower than my octave code.

Then again i did not code it with performance in mind. I overloaded algo.generic for matrix operations, so the fixnum math was probably not inlined.

I used Colt. I'd be interested to see if Clojure parallelization and under-the-hood optimizations could match vectorization performance. Note, I haven't run official benchmarks yet. My comparisons have been more like "back propagation and gradient checking took about the same length of time in both".

I believe Incanter uses Colt/Parallel Colt under the hood

Reply on news.ycombinator.com