## Fractals from iterating sines

August 23rd, 2013

In a recent blog-post, John Cook, considered when series such as the following converged for a given complex number z

z1 = sin(z)
z2 = sin(sin(z))
z3 = sin(sin(sin(z)))

John’s article discussed a theorem that answered the question for a few special cases and this got me thinking: What would the complete set of solutions look like? Since I was halfway through my commute to work and had nothing better to do, I thought I’d find out.

The following Mathematica code considers points in the square portion of the complex plane where both real and imaginary parts range from -8 to 8. If the sequence converges for a particular point, I colour it black.

LaunchKernels[4]; (*Set up for 4 core parallel compute*)
ParallelEvaluate[SetSystemOptions["CatchMachineUnderflow" -> False]];
convTest[z_, tol_, max_] := Module[{list},
list = Quiet[
NestWhileList[Sin[#] &, z, (Abs[#1 - #2] > tol &), 2, max]];
If[
Length[list] < max && NumericQ[list[[-1]]]
, 1, 0]
]
step = 0.005;
extent = 8;
AbsoluteTiming[
data = ParallelMap[convTest[#, 10*10^-4, 1000] &,
Table[x + I y, {y, -extent, extent, step}, {x, -extent, extent,
step}]
, {2}];]
ArrayPlot[data]

I quickly emailed John to tell him of my discovery but on actually getting to work I discovered that the above fractal is actually very well known. There’s even a colour version on Wolfram’s MathWorld site.  Still, it was a fun discovery while it lasted

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## Dear Software Vendors: Your network licensing causes me pain.

August 12th, 2013

Right now it’s packaging season (not the official term!) at my university–a time of year when IT staff have to battle with silent installers, SCCM, MSI creation and Adminstudio in order to create the student desktop image for the next academic year.  Packaging season makes me grouchy, it makes me work late and it makes me massively over-react to every minor installation issue caused by software vendors. Right now, however, I am not grouchy because of packaging season..I am grouchy because of concurrent network licensing (or floating licensing if you are Wikipedia).

I like network licenses…they make many aspects of my job easier but they the way they are implemented by some software vendors causes them to be a pain.  Over the years, I’ve bothered many a support-desk with my network license tails of woe and thought that I would collate them all together in one blog post.

The more of these things your software does, the more pain you cause me and my colleagues.

1. You don’t use standard FlexLM/FlexNet.

Like it or loathe it, FlexLM is used by the vast majority of software vendors out there. We run license servers that host dozens of FlexLM based applications and we have got the administration of these down to a fine art.  In fact, we’ve replaced the vast majority of the process with a script. If an application uses FlexLM, system administration and license monitoring is bordering on the trivial for us now.  The further you stray away from FlexLM, the more difficult our job becomes.

One thing guaranteed to ruin my day is a call from a vendor I’ve worked with for years who says ‘Great news Mike, we’re ditching FlexLM for our own, in house license system.’  Fabulous! Rather than use our lovely, generic, one-size fits all scripts, we are going to have to do a load of extra work and testing just for you.  I look forward to all the new and interesting bugs your system will generate.

2. You don’t support redundant license servers.

The idea behind redundant license servers is this:  Instead of your application relying on just one machine, it relies on three; only two of which have to be operational at any one time.  This gives us resiliency and resiliency is a good thing when you are teaching a lab with 120 students in it.

I’ll keep this simple.  If you don’t support redundant license servers, it means that you don’t believe that your software is important. It tells me that you are just playing at being a big, grown up piece of software but you don’t really think anyone will take you seriously.

3. You support redundant license servers but can’t select them via the installer.

At install time, there is no option to give three severs. The user can only give one. You then expect the user to copy a pre-prepared license file that has details of all three servers as a post-installation step.

What usually happens here is that users give the primary license server, find that the application will launch and stop reading the installation instructions.  At some point in the future, we take down the primary license server for maintenance and the vast majority of self-serve installations break!

4. You use the LM_LICENSE_FILE environment variable

The problem is, so does everyone else. We end up with a situation where the LM_LICENSE_FILE variable is pointing at several license servers and some client applications really don’t like that. Be a good FlexLM citizen and use a vendor specific environment variable.  For example, MATLAB uses MLM_LICENSE_FILE and I could give them a big hug just for that!

5. You ‘helpfully’ tell the user when the license is about to expire.

I’ve moaned about this before. 1000 users panicking and emailing the helpdesk…lovely!  Bonus points are awarded if you don’t allow any supported way of switching these warnings off.

6. Your new license doesn’t support old clients.

This should speak for itself and happens more than I’d like.  We can’t upgrade the entire estate instantaneously and even if we could, we probably wouldn’t want to.  Some users, for one reason or another, cling to old versions of your software like grim death. They don’t care that there is a new shiny version available, all they know is that I broke their application and they hate me for it.

When we discover that old versions of your application will stop working, it also delays roll out of the new version since we have to do a lot of user-communications and ensure that nothing mission-critical will stop working.  This makes power-users of your application hate me because they want the new shiny version.

7. You don’t have a silent installer.

Strictly speaking not a network license moan but closely related.  We use network licensing because we deploy your software to lots of machines.  When I say ‘lots’ I mean thousands.  It turns out, however, that you don’t support scripted installation (sometimes called ‘silent installation’ or ‘unattended installation’).  This means that your software is a lot more difficult to deploy than your competitor!  I’m now a big fan of your competitor!

8. You have a silent installer but it’s a bad one.

If I install manually, via point and click, I can configure every aspect of your application.  Your silent installer, on the other hand, is just a /S switch that does a default install…no configuration possible.  Bonus points for ‘silent’ installers that include pop-up dialogue boxes that can’t be switched off.

While on the topic of silent installation, can I just ask that you directly support deployment by SCCM on Windows please?  It will help with next year’s packaging season big time!

Cheers,

Mike

## KryPy – A Python module for Krylov subspace methods for the solution of linear algebraic systems.

August 6th, 2013

The first stable version of KryPy was released in late July.  KryPy is “a Python  module for Krylov subspace methods for the solution of linear algebraic systems. This includes enhanced versions of CG, MINRES and GMRES as well as methods for the efficient solution of sequences of linear systems.”

Here’s a toy example taken from KryPy’s website that shows how easy it is to use.

from numpy import ones
from scipy.sparse import spdiags
from krypy.linsys import gmres

N = 10
A = spdiags(range(1,N+1), [0], N, N)
b = ones((N,1))

sol = gmres(A, b)
print (sol['relresvec'])

Thanks to KryPy’s author, André Gaul, for the news.

## Generate a vector of powers more quickly using cumprod in MATLAB

August 5th, 2013

While working on someone’s MATLAB code today there came a point when it was necessary to generate a vector of powers.  For example, [a a^2 a^3….a^10000] where a=0.999

a=0.9999;
y=a.^(1:10000);

This isn’t the only way one could form such a vector and I was curious whether or not an alternative method might be faster. On my current machine we have:

>> tic;y=a.^(1:10000);toc
Elapsed time is 0.001526 seconds.
>> tic;y=a.^(1:10000);toc
Elapsed time is 0.001529 seconds.
>> tic;y=a.^(1:10000);toc
Elapsed time is 0.001716 seconds.

Let’s look at the last result in the vector y

>> y(end)
ans =
0.367861046432970

So, 0.0015-ish seconds to beat.

>> tic;y1=cumprod(ones(1,10000)*a);toc
Elapsed time is 0.000075 seconds.
>> tic;y1=cumprod(ones(1,10000)*a);toc
Elapsed time is 0.000075 seconds.
>> tic;y1=cumprod(ones(1,10000)*a);toc
Elapsed time is 0.000075 seconds.

soundly beaten! More than a factor of 20 in fact. Let’s check out that last result

>> y1(end)
ans =
0.367861046432969

Only a difference in the 15th decimal place–I’m happy with that. What I’m wondering now, however, is will my faster method ever cause me grief?

This is only an academic exercise since this is not exactly a hot spot in the code!

## Numerate degree subjects should include exposure to a variety of computational software

August 2nd, 2013

In common with many higher educational establishments, the University I work for has site licenses for a wide variety of scientific software applications such as Labview, MATLAB, Mathematica, NAG, Maple and Mathcad— a great boon to students and researcher who study and work there.   The computational education of a typical STEM undergraduate will include exposure to at least some of these systems along with traditional programming languages such as Java, C or Fortran and maybe even a little Excel when times are particularly bad!

Some argue that such exposure to multiple computational systems is a good thing while others argue that it leads to confusion and a ‘jack of all trades and master of none situation.’  Those who take the latter viewpoint tend to want to standardize on one system or other depending on personal preferences and expertise.

MATLAB, Python, Fortran and Mathematica are a few systems I’ve seen put forward over the years with the idea being that students will learn the basics of one system in their first few weeks and then the entire subject curriculum will be interwoven with these computational skills.  In this way, students can use their computational skills as an aid to deeper subject understanding without getting bogged down with the technical details of several different computational systems.  As you might expect, software vendors are extremely keen on this idea and will happily parachute in a few experts to help universities with curriculum development for free since this will possibly lead to their system being adopted.

Maybe we’ll end up with electrical engineers who’ve only ever seen Labview, mathematicians who’ve only ever used Maple, mechanical engineers who’ve only ever used MATLAB and economists who can only use Excel.  While the computational framework(s) used to teach these subjects are less important than the teaching of the subject itself, I firmly believe that part of a well-rounded, numerate education should include exposure to several computational systems and such software mono-cultures should be avoided at all costs.

Part of the reason for writing this post is to ask what you think so comments are very welcome.

## Which Ultrabook for 2013?

August 1st, 2013

I am currently in the market for a new thin and light laptop; the things that everyone seems to be calling ultrabooks these days.  Here’s what I’ve considered so far and the major good/bad points from my point of view.

• 2013 Macbook Air: Good: Fantastic hardware specs including Haswell and Intel HD 5000. I’ll get an educational discount. Bad: No touchscreen, I’m not interested in OS X. No tablet mode.
• Lenovo Yoga 11sGood: Both a tablet and a laptop but it’s a laptop first and a tablet second.  Bad: Only 3rd generation Intel.  Weird to hold in laptop mode because your fingers are mashing the keyboard.
• Haswell based Dell XPS 12Good:Haswell. Beautiful mechanism for switching between tablet/laptop. Bad: Only Intel HD 4400 graphics compared to the Air’s Intel HD 5000.  I’ve heard that the connection between computer and screen is unencrypted WiDi. Possibly just FUD but its putting me off right now.
• Samsung Ativ Book 9 Plus Good: Haswell. Amazing display resolution. Bad: Much higher resolution than the Macbook Air but with weaker GPU (Intel HD 4400)–that surely can’t be a good combination? No tablet mode. Win 8 doesn’t handle such high  resolution screens well but should be fixed in 8.1.
• Samsung Ativ Q: Good: Haswell. Amazing display resolution. Tablet mode.Win 8+Android.  Bad: No trackpad. Looks horrible in laptop mode–seems to be a tablet first and laptop second.  Like the Book 9 plus, it has a relatively weak GPU (Intel HD 4400) to drive all those pixels.

I think that at the moment, what I want is the form factor and weight of the Dell XPS12 with the resolution of the Samsung and the hardware specs of the Air.  I’m open to suggestions though.