I was used to Scilab for small experiments involving linear algebra. I also like some of Scilab choices in algorithms: for example it provides PCHIM monotonic spline algorithm, and uses Cody for the cumulative normal distribution.
Matlab like software is particularly well suited to express PDE solvers in a relatively concise manner. To illustrate some of my experiments, I started to write a Scilab script for the Arbitrage Free SABR problem. It worked nicely and is a bit nicer to read than my equivalent Scala program. But I was a bit surprised by the low performance.
Then I heard about Octave, which is even closer to Matlab syntax than Scilab and started wondering if it was better or faster. Here are my results for 1000 points and 10 time-steps:
I then added the keyword sparse when I build the tridiagonal matrix and end up with:
Scala 0.034s (first run)
Scala 0.004s (once Hotpot has kicked in)
So Octave looks a bit better than Scilab in terms of performance. However I could not figure out from the documentation what algorithm was used for the cumulative normal distribution and if there was a monotonic spline interpolation in Octave.
In general I find it impressive that Octave is faster than the first run of Scala or Java, and impressive as well that the Hotspot makes gain of x10.