ODEs with Java using the Apache Commons Math library

It drives me nuts when I struggle to get my head around something just to, when I eventually do, discover that it is not really as complicated as the documentation makes it out to be. Simple examples are what I need. Here is an example of how to implement the Lorenz System. Not that I really know much about the Lorenz System but it is always a simple system to use when you want to try out a new way of solving differential equations. More information about the Lorenz System can be found in Wikipedia.

The first thing to do is to create a class containing the equations. The Lorenz system consists of the following three equations:

Doing this using the Apache Commons Math library means that we have to create a class that implements the FirstOrderDifferentialEquations interface. This interface requires two methods to be implemented, which are computeDerivatives and getDimension:

01 import org.apache.commons.math3.exception.DimensionMismatchException; 02 import org.apache.commons.math3.exception.MaxCountExceededException; 03 import org.apache.commons.math3.ode.FirstOrderDifferentialEquations; 04  05 public class Lorenz implements FirstOrderDifferentialEquations { 06  07         double sigma = 10.0; 08         double beta = 8 / 3; 09         double rho = 28.0; 10         double X, Y, Z; 11  12         @Override 13         public void computeDerivatives(double t, double[] y, double[] yDot) 14                         throws MaxCountExceededException,                             DimensionMismatchException { 15                 X = y[0]; 16                 Y = y[1]; 17                 Z = y[2]; 18                 yDot[0] = sigma * (Y - X); 19                 yDot[1] = X * (rho - Z) - Y; 20                 yDot[2] = (X * Y) - (beta * Z); 21         } 22  23         @Override 24         public int getDimension() { 25                 // TODO Auto-generated method stub 26                 return 3; 27         } 28 }

Java2html

The next step is to write the code that will call the integrator. There are various integrators. For this application we'll use the ClassicalRungeKuttaIntegrator. You will also need a step handler to capture each step of the integration:

01 import org.apache.commons.math3.ode.FirstOrderDifferentialEquations; 02 import org.apache.commons.math3.ode.nonstiff.ClassicalRungeKuttaIntegrator; 03 import org.apache.commons.math3.ode.sampling.StepHandler; 04  05 public class LorenzMain { 06  07         public static void main(String[] args) { 08  09                 ClassicalRungeKuttaIntegrator rk4 =                             new ClassicalRungeKuttaIntegrator(0.01); 10                 FirstOrderDifferentialEquations ode = new Lorenz(); 11                 double[] y = new double[] { 10.0, -2.0, 50 }; // initial state 12                 StepHandler stepHandler = new                             WriteToFileStepHandler("lorenz.csv"); 13                 rk4.addStepHandler(stepHandler); 14                 rk4.integrate(ode, // equations 15                                 0.0, // start time 16                                 y, // initial conditions 17                                 100.0, // end time 18                                 y); // result 19                 for (int i = 0; i < y.length; i++) { 20                         System.out.println(y[i]); 21                 } 22         } 23 }

Java2html

The step handler has to implement the StepHandler class. For the step handler below I created a constructor that takes a filename so that the results can be written to a csv file. Obviously you can do whatever you want with this data:

01 import java.io.File; 02 import java.io.PrintWriter; 03 import java.util.ArrayList; 04  05 import org.apache.commons.math3.exception.MaxCountExceededException; 06 import org.apache.commons.math3.ode.sampling.StepHandler; 07 import org.apache.commons.math3.ode.sampling.StepInterpolator; 08  09  10 public class WriteToFileStepHandler implements StepHandler { 11         ArrayList<String> steps = new ArrayList<String>(); 12         String filename; 13          14         public WriteToFileStepHandler(String filename) { 15                 this.filename = filename; 16         } 17         @Override 18         public void handleStep(StepInterpolator interpolator, boolean isLast) 19                         throws MaxCountExceededException { 20                 double t = interpolator.getCurrentTime(); 21                 double[] y = interpolator.getInterpolatedState(); 22                         String onestep = "" + t; 23                         for (int i = 0; i < y.length; i++) { 24                                 onestep += ", " + y[i]; 25                         } 26                         steps.add(onestep); 27                 if (isLast) { 28                         try { 29                                 PrintWriter writer =  30                                 new PrintWriter(new File(filename),                                     "UTF-8");                                     31                                 for (String step : steps) { 32                                         writer.println(step); 33                                 } 34                                 writer.close(); 35                         } catch (Exception e) { 36                         } 37                         ; 38                 } 39         } 40  41         @Override 42         public void init(double t0, double[] y0, double t) { 43                 // TODO Auto-generated method stub 44  45         } 46  47 }

Java2html

Last but not the least I read the file with R and created the graph:

Motorcyclist having to cope with ignorant idiots on the road.

A message to the bloke in the big black Seat that had a blonde lady next to him in the passenger seat and was driving past St James' Park at about 16.30 on Saturday 28 September 2013.

The reason you wouldn't let me into the traffic stream is not, as you so gracefully tried to sign to me, because I am a wanker. It is because you are a very rude, immature, ignorant and dumb old fart.

Rude, because if you had any sense of decency you would not have tried to push me out of the lane by driving up my left. Considering the traffic at that time, it would have been kind to let me in even if I was, which I wasn't by the way, in the wrong.

You see this is why you are ignorant because if you knew anything, you would have known that motorcycles are allowed to filter up the right of traffic and then merge in again. Mostly, the reason it becomes difficult to merge into traffic, is because immature people like you, apparently, are afraid that some body part is going to shrink or fall off if you let a motorcyclist get in front of you. I can assure you this is not the case. You can ask your doctor if you don't believe me. 

You must be dumb or else you would have done something by now to improve you knowledge of driving skills and traffic. You seemed to be about my age, give or take 5 years which means you have had more than enough time to do this.

Lastly you are an old fart just because of all of the above and "old fart" pretty much sums up the whole lot.

Suzuki Burgman UH200

In June 2009 I bought myself a brand new Sym Symply 125cc scooter for about £1500 to get myself to and from University. 15000 miles later I sold the Symply back to the agent for £200 because it would just cost too much to keep it on the road. However, I still needed something to get to uni and back. So I put the £200 towards buying a second hand Suzuki Burgman. I have been riding the Burgman that last two weeks and it really is such a delight. Despite the horrible weather we have had up here in the north of England I find myself  enjoying every minute of the trip.

One of the major advantages of the Burgman is that it has a massive luggage space under the seat. Unlike the Symply my helmet actually fits in there. Apparently it can take two helmets. I haven't tried two helmets but I'm pretty sure it will do it easily. I'm one of those people that are forever carrying myself to death with my backpack that I cart along with me wherever I go. The backpack fits under the seat with all my other goods and gadgets with ease.

The second thing that makes the actual ride such a joy is the seat. It is really comfortable. The seat is nice and wide and it has a little bit of a support behind your back. With more leg space you can stretch your legs out a bit making it much more relaxing. The Burgman is also much lower and I can put both my feet down flat when I stop, again making for a much more relaxed ride (or stop if you please).

The Symply had a little hook onto which one could hang a bag by your feet. When you hung a bag in the footwell though you had to swing your leg over the seat to get onto the scooter. Although, I guess, this kept me supple it was a bit of a drag and a couple of times the hooks on my boot nipped a tear in the seat which was  very annoying. With the big luggage compartment on the Burgman this problem does not arise.

I have only filled up the tank twice so I haven't worked out the fuel consumption yet, but the fuel tank on the Burgman is at least double the size of the Symply's. I did at least 120 miles after the first fill-up and the tank wasn't empty yet.

So both thumbs up for the Burgman!

The Suzuki Burgman UH200

The Sym Symply 125 when it was new.

Lack-of-service-BT continues ...

So, about 3 weeks ago someone from BT calls me and offers to put me through to their disputes team. Being in the middle of the day on a Friday while I'm in the lab, I couldn't take the call, so I was told to call back and ask for disputes. Today, after about 3 weeks it was the first time I was home during the day so that I could make the call. As usual I had to venture through an endless maze of menu options before someone answered the phone. Between being put on hold and arguing the fact that I actually want to talk to disputes and not pay extra to get out of a contract that was mis-sold to me, I was cut off after 19 minutes and 55 seconds. Then the first amazing thing happened. I was called back within seconds and offered an apology for being cut off. I was then transfered to someone whom I believe must be in disputes. I had to explain the whole static IP address again and was then transferred to someone to me that they just have to tell me that they are going to investigate the issue and have to inform me that they will be retrieving and listening to the original calls. Amazing! This is what I've been wanting from the beginning. So, hopefully in the next 5 working days I'll hear from them and get this resolved.

Lack-of-service-BT

It is probably not news to anybody that BT is totally incapable of providing decent support for their own services. Or even that they use illegal means such as lying and/or misselling to catch you as a customer.

However, like an idiot, I managed to get myself caught by them once again. Probably because of a naive believe that people can't be that bad all the time.

In January this year BT called me about switching to them for broadband. I used to be with Zen, who are very good, but they don't provide support after hours and over weekends which are the only times I have to resolve any issues. So when the BT guy called and confirmed SEVERAL TIMES that he can indeed provide me with 20MB broadband, 40Gb download, some other things AND A STATIC IP address, I decided to change.

Well, it is now June and my IP address has changed 4 times. When it changed the first time, in February, I submitted a complaint via the BT website. After a few days I received the normal confirmation with an incident number. To this day, I have not had a response. When it changed for the second time, I called (like an idiot) and merely was passed from one poor sod in India to another to get nothing resolved. This week, the IP changed again on 08.06.2011. Before I could even complain, it changed again today (10.06.2011). So I spent another hour being transferred between India and England and back to India just to be promised about an hour an a half (that, Mr BT translates to 90 minutes) ago that someone from customer services will call me back in 20 minutes. I have also submitted another online complaint and this time actually received an automated confirmation within a few minutes.

So, dear reader, if you have any idea who one is suppose to call to get BT issues resolved, please leave a comment. Or, just to show that you have read this, please leave a comment. I would like for as many people as possible to read this and not be caught in BT's dishonesty/incompetence. Tell your friends to read this and leave a comment. Maybe eventually some BT person with enough savvy, knowledge, influence and will to live, will read it, contact me and resolve the issue.

Another dissertation

So I'm almost at the end of my second MSc and hard at work with the writing of my dissertation. This time it is a MSc in Bioinformatics and Computational Systems Biology. So still very computery, but with a lot of Biology. Specifically molecular and synthetic biology.

I have decided to start writing this just to take a break from the dissertation every now and then. It has been difficult to get my thoughts organised and I hope thinking about something else every now and then will help.

Like last year I decided to use LaTeX. Unlike last year, I don't have to write a 10 to 15 thousand word document, but rather a 16 page write up of my research in the style of the Bioinformatics Journal. For this purpose I had to download a template provided by the Bioinformatics Journal.

I have selected applications again that will run on both Linux and Windows because my computer at uni runs Windows and all my computers at home run Linux. Off course the main requirement is that the software has to be open source.

Firstly there is Mendeley for managing references. It is quite good and I have been using it all year. It has a plug-in for OpenOffice and it works well with LaTeX too. Mendeley also keeps itself synchronised with a web account so when I work on a different computer I can synchronise that too with my references.

Then off course there is Texmaker that I used last year. I managed to set it up to run my own make script from one of the customizable menu items.

I managed to create a nice E-R diagram with DBDesigner4 for the mySQL database that I had to design and the rest of my graphics I have been making with Inkscape. As usual it is a bit of a faff to the graphics in the right place, but I found some nice tips here http://andrewjpage.com/index.php?/archives/48-Figure-spanning-2-columns-in-Latex.html.

I have had quite a bit of success this year running Windows applications on Linux using Wine. My favourite photo manipulation program is still Irfanview. It is not open source and you should really register it (which I have done). For £6 it is more than worth it though. I really don't mind supporting software like this little gem.

PDF-XChange Viewer is another application that I have really become attached too. I run it on both Windows and Linux. On Linux it runs quite successfully with Wine. It allows one to mark-up PDF documents, so unlike last year I don't have two files full of printed papers.

I also started using Dropbox this year. And boy, has that made my life easier! I now know my stuff is backed up and it is usually in at least three places, my PC at uni, my PC at home and my laptop. I only need to log on to the Internet and my computer is synchronised with the Dropbox website. If off course I am on somebody else's computer or a computer in one of the clusters at uni I only need to log onto the Dropbox website and download the document I need. Amazing.

Well, I should probably get back to the dissertation - or to bed, if I can convince myself to fall asleep ...

Categorical imperative

Act only according to that maxim whereby you can at the same time will that it should become a universal law.

Immanuel Kant (translated by James W. Ellington)

Reference: Wikipedia