Octave vs Scilab for PDEs in Finance

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:

Scilab 4.3s
Octave 4.1s

I then added the keyword sparse when I build the tridiagonal matrix and end up with:

Scilab 0.04s
Octave 0.02s
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.

Octave vs Scilab for PDEs in Finance

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:

Scilab 4.3s
Octave 4.1s

I then added the keyword sparse when I build the tridiagonal matrix and end up with:

Scilab 0.04s
Octave 0.02s
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.

Joda LocalDateTime vs DateTime

Joda has the concept of LocalDate/LocalDateTime and DateTime. The LocalDate is just a simple date, while DateTime is a date and a time zone.

Where I work we have a similar distinction, although not the same: a simple "absolute" date object without time vs a relative date (a timestamp) like the JDK Date.

The standard JDK Date class is a date without a time zone, but Sun deprecated in JDK 1.1 all methods allowing to use it like a LocalDate, forcing to use it through a Calendar (i.e. like a DateTime), that is, with a TimeZone.

I have found one explanation for a potential use case of LocalDateTime vs DateTime: when you take an appointment to the doctor for July 22nd at 10am, the future date is a fixed event. Some people say you just don't care about the TimeZone in this case, and therefore use LocalDateTime. I think it is a bit more subtle than that. One could think of using fixed arbitrary TimeZone, it could just easily be set to UTC or to the default Java time zone or even the correct one. While it's not typically what the user want to worry about, it could be a default setting (like in Google Calendar or in your OS). And that is exactly what the LocalDateTime does internally, it uses a fixed, non modifiable TimeZone.


If the future event is in a few years and you want to store it in a database, it can become more problematic because daylight saving might not be well determined yet. The number stored today might not mean the same thing in a few years. I am not sure if it can be a real issue, but I am not the only one to worry about that. As the LocalDateTime internally relies on UTC, it is not affected by this.

There is another more technical use case for LocalDateTime, if you have a list of dates in a contract, they are all according to the contract TimeZone, you then probably don't want to specify the TimeZone for each date. The question is then more is the DateTime concept a good idea?

Joda LocalDateTime vs DateTime

Joda has the concept of LocalDate/LocalDateTime and DateTime. The LocalDate is just a simple date, while DateTime is a date and a time zone.

Where I work we have a similar distinction, although not the same: a simple "absolute" date object without time vs a relative date (a timestamp) like the JDK Date.

The standard JDK Date class is a date without a time zone, but Sun deprecated in JDK 1.1 all methods allowing to use it like a LocalDate, forcing to use it through a Calendar (i.e. like a DateTime), that is, with a TimeZone.

I have found one explanation for a potential use case of LocalDateTime vs DateTime: when you take an appointment to the doctor for July 22nd at 10am, the future date is a fixed event. Some people say you just don't care about the TimeZone in this case, and therefore use LocalDateTime. I think it is a bit more subtle than that. One could think of using fixed arbitrary TimeZone, it could just easily be set to UTC or to the default Java time zone or even the correct one. While it's not typically what the user want to worry about, it could be a default setting (like in Google Calendar or in your OS). And that is exactly what the LocalDateTime does internally, it uses a fixed, non modifiable TimeZone.


If the future event is in a few years and you want to store it in a database, it can become more problematic because daylight saving might not be well determined yet. The number stored today might not mean the same thing in a few years. I am not sure if it can be a real issue, but I am not the only one to worry about that. As the LocalDateTime internally relies on UTC, it is not affected by this.

There is another more technical use case for LocalDateTime, if you have a list of dates in a contract, they are all according to the contract TimeZone, you then probably don't want to specify the TimeZone for each date. The question is then more is the DateTime concept a good idea?

The CUDA Performance Myth II

This is a kind of following to the CUDA performance myth. There is a recent news on the java concurrent mailing list about SplittableRandom class proposed for JDK8. It is a new parallel random number generator a priori usable for Monte-Carlo simulations.

It seems to rely on some very recent algorithm. There are some a bit older ones: the ancestor, L'Ecuyer MRG32k3a that can be parallelized through relatively costless skipTo methods, a Mersenne Twister variant MTGP, and even the less rigourous XorWow popularized by NVidia CUDA.

The book GPU Computing Gems provides some interesting stats as to GPU vs CPU performance for various generators (L'Ecuyer, Sobol, and Mersenne Twister)

A Quad core Xeon is only 4 times slower to generate normally distributed random numbers with Sobol. Fermi cards are faster now, but probably so are newer Xeons. I would have expected this kind of task to be the typical not too complex parallelizable task doable by a GPU, and yet the improvements are not very good (except if you look at raw random numbers, which is almost useless in applications). It confirms the idea that many real world algorithms are not so much faster with GPUs than with CPUs. I suppose what's interesting is that the GPU abstractions forces you to be relatively efficient, while the CPU flexibility might make you lazy.

The CUDA Performance Myth II

This is a kind of following to the CUDA performance myth. There is a recent news on the java concurrent mailing list about SplittableRandom class proposed for JDK8. It is a new parallel random number generator a priori usable for Monte-Carlo simulations.

It seems to rely on some very recent algorithm. There are some a bit older ones: the ancestor, L'Ecuyer MRG32k3a that can be parallelized through relatively costless skipTo methods, a Mersenne Twister variant MTGP, and even the less rigourous XorWow popularized by NVidia CUDA.

The book GPU Computing Gems provides some interesting stats as to GPU vs CPU performance for various generators (L'Ecuyer, Sobol, and Mersenne Twister)

A Quad core Xeon is only 4 times slower to generate normally distributed random numbers with Sobol. Fermi cards are faster now, but probably so are newer Xeons. I would have expected this kind of task to be the typical not too complex parallelizable task doable by a GPU, and yet the improvements are not very good (except if you look at raw random numbers, which is almost useless in applications). It confirms the idea that many real world algorithms are not so much faster with GPUs than with CPUs. I suppose what's interesting is that the GPU abstractions forces you to be relatively efficient, while the CPU flexibility might make you lazy.

Unity vs KDE in Virtualbox

The other day I installed the latest Ubuntu 13.04 under a VirtualBox virtual machine using Windows as host. To my surprise, unity failed to launch properly on the virtual machine reboot, with compiz complaining, something I have sometimes seen on my work laptop. It's more surprising in a VM since it is in a way much more standard (no strange graphic card, no strange driver, the same stuff for every VirtualBox user (maybe I'm wrong there?)). I therefore installed KDE as a way to bypass this issue. Not only it worked, but the UI was much faster: there was some very noticeable lag in Unity, slow fade in fade out effects, when it worked before the reboot.

I am no hater of Unity, it looks well polished, nice to the eye and I use it on a home computer. I find KDE looks a tiny bit less nice, although I prefer the standard scrollbars of KDE. I wonder if others have the same dreadful experience with Unity under VirtualBox.

Unity vs KDE in Virtualbox

The other day I installed the latest Ubuntu 13.04 under a VirtualBox virtual machine using Windows as host. To my surprise, unity failed to launch properly on the virtual machine reboot, with compiz complaining, something I have sometimes seen on my work laptop. It's more surprising in a VM since it is in a way much more standard (no strange graphic card, no strange driver, the same stuff for every VirtualBox user (maybe I'm wrong there?)). I therefore installed KDE as a way to bypass this issue. Not only it worked, but the UI was much faster: there was some very noticeable lag in Unity, slow fade in fade out effects, when it worked before the reboot.

I am no hater of Unity, it looks well polished, nice to the eye and I use it on a home computer. I find KDE looks a tiny bit less nice, although I prefer the standard scrollbars of KDE. I wonder if others have the same dreadful experience with Unity under VirtualBox.

Bessel and Harmonic Kinks in the Forward

As Bessel (sometimes called Hermite) spline interpolation is only C1, like the Harmonic spline from Fritsch-Butland, the forward presents small kinks compared to a standard cubic spline. Hyman filtering also creates a kink where it fixes the monotonicity. Those are especially visible with a log scale in time. Here is how it looks on the Hagan-West difficult curve.

Bessel and Harmonic Kinks in the Forward

As Bessel (sometimes called Hermite) spline interpolation is only C1, like the Harmonic spline from Fritsch-Butland, the forward presents small kinks compared to a standard cubic spline. Hyman filtering also creates a kink where it fixes the monotonicity. Those are especially visible with a log scale in time. Here is how it looks on the Hagan-West difficult curve.