Bode Plots using Python

I needed a quick way to plot some Bode plots for a second order system. I didn’t have access to Matlab, instead I searched for a solution using Python, and I found one. Documentation is a bit sparse  so this example might be helpful.

The signals packages supports the signal.bode method which turned out to be quite easy to use. Signal is part of the scipy package and is something we bundle with our Tellurium platform.

There a more comprehensive discussion of Python and Control Theory here.

import numpy as np
from scipy import signal
from matplotlib import pyplot as plt

# Coefficients in numerator of transfer function
num = [1]
# Coefficients in denominator of transfer function
# High order to low order, eg 1*s^2 + 0.1*s + 1
den = [1, 0.1, 1]

# Scan over zeta, a parameter for a second-order system
zetaRange = np.arange(0.1,1.1,0.1)

f1 = plt.figure()
for i in range(0,9):
    den = [1, 2*zetaRange[i], 1]
    print den
    s1 = signal.lti(num, den)
    % Specify our own frequency range: np.arange(0.1, 5, 0.01)
    w, mag, phase = signal.bode(s1, np.arange(0.1, 5, 0.01).tolist())
    plt.semilogx (w, mag, color="blue", linewidth="1")
plt.xlabel ("Frequency")
plt.ylabel ("Magnitude")
plt.savefig ("c:\\mag.png", dpi=300, format="png")


for i in range(0,9):
    den = [1, zetaRange[i], 1]
    s1 = signal.lti(num, den)
    w, mag, phase = signal.bode(s1, np.arange(0.1, 10, 0.02).tolist())
    plt.semilogx (w, phase, color="red", linewidth="1.1")
plt.xlabel ("Frequency")
plt.ylabel ("Amplitude")
plt.savefig ("c:\\phase.png", dpi=300, format="png")

Output from Python script:

Magnitude plot:mag

Phase plot:


Posted in General Science Interest, Modeling, Programming, Software, Systems Theory | 1 Comment

Disappointed with Drobo 5N

I got myself a Drobo 5N to serve as a backup of my data and other work. For those who don’t know the Drobo 5N is a 5 bay network attached storage (NAS) device. What is interesting about the Drobo is that any of the drives (and more than one) in one of the 5 bays can be removed without any effect to your stored data. This is because all data is redundantly spread across all drives. Not only that but the drives you can have in the 5 bays can be any size and any make.

The problem however is that the Drobo 5N is not truly a network attached storage device because you can only access directly from your computer on your local network, ie your office. So for example if you have a Drobo drive in your office you can’t access your data from home or anywhere else in the world. Most NAS system do allow access, for example by running an ftp server. It is possible to install an ftp server on a Drobo but the installation is buggy and trashes the firmware. So all in all the Drobo 5N is a bit of a disappointment.

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Programming Language Popularity

As programmers we sometimes like to play the game of what is the most popular programming language? There are various metrics online that try to measure this, most notably TIOBEPYPL and Trendy Skills. They are all flawed in someway and often diverge considerably in their rankings. For example PYPL ranks Swift at number 9 whereas its not even in the top  24 on TIOBE. C is ranked 8th on Trendy Skills but 1st in TIOBE and 6th on PYPL. Sometimes they correspond for example, Javascript is ranked 7th place on both TIOBE and PYPL,

Another ranking system, also flawed, is the #code20XX twitter based rank. This is where people vote for what programming languages they used in the specified year. On #code2104 this year, Javascript was the winner closely followed by Python, Java then Ruby. On TIOBE Ruby is ranked 15th, and Python 8th. The other language to show itself on code2014 was Object Pascal. I get a lot of criticism for programming in Object Pascal/Delphi but I like it because its easy to read, very flexible to use and through the various GUI frameworks is ideal for writing cross platform GUI applications. On #code2014 Object Pascal/Delphi came 9th (compared to 20th on TIOBE). Object Pascal/Delphi beat a couple of mainstream languages include C and C++. I think this says more about the enthusiasm of the community than anything else which is of course an important factor when considering a language to use. The downside of Object/Pascal/Delphi is the dollar expense of buying into the platform. Embarcardero who sell the compiler and IDE charge a significant amount to be a member of this group. It effectively excludes most students and hobbyists from the community which is a great shame. On the plus side we have of course freepascal and lazarus which are also excellent cross platform tools and largely Delphi compatible. They are still perhaps a little immature in places but they are developing quickly.



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Simple RK4 Code

Thought I’d start off the New Year with a simple freebie, a 4th Order Runge-Kutta class for Delphi, Windows and Mac OS. Should also work on Android and iOS mobile platforms and with Free Pascal. The code below shows how you’d use it. First declare the set of differential equations that need to be solved (TDoubleDynArray type can be found in Types):

Next, create a Runge-Kutta object:

The above code include the option to declare and initialize some parameters that are part of the differential equations. To actually integrate the system by one step use the line:

The y argument will contain the updated solution. Run the line again to do the next step etc. Note that the eval method takes three arguments, that current value for the independent variable (time), an array that contains the current values for the dependent variable, and the step size to use.

Download the code here. The download include a Windows exe that you can try right away.

Posted in Delphi, Modeling, Programming | 1 Comment

My First Mac OS Application

I finished my first Mac OS application. Two screenshots are shown below, I’ll be making it available download at the end of the week. This was a test application to see how easy it would be use write a portable application using Firemonkey. The application in question is a specialist tool that allows users to load systems biology models expressed in SBML models and simulate them. It also has some limited steady state functionality. It users libRoadRunner as the backend simulator ( Most of the underling UI business code is new but the graphing component is one I resurrected from an old Windows project I had. Took me a week or two to extract the code from the old VCL Delphi application and swap in Firemonkey canvas methods. The biggest issue I had was remembering that Firemonkey now uses single precision values to represent canvas coordinates (VCL uses integer values).

I developed the application first on Windows using XE6. Once it was working on Windows I compiled it for Mac OS. Other than a few very minor issues (eg forgetting to remove Windows in the uses clause) getting it running on the Mac was surprisingly uneventful. It took me about 20 mins to get it working on the Mac, I was impressed. Pserver, which is the conduit for moving a Delphi application to the Mac makes the process child’s play. It copies over the relevant files and metadata and creates the bundle on the Mac’s hard drive ready to be distributed.

Some gotchas to watch out for:

1. Scroll bars don’t show automatically on the Mac in scrollable controls, to make them show up include the following line in your main form OnCreate event:

where memo1 is the name of a memo control.

2. Use the Deployment option in the Project menu to specify any Mac OS dylibs you want to distribute. pserver will handle the copying and bundling of these automatically.

3. Loading dll and dylibs. Not really a gotcha but I thought it would be tricky. This was surprisingly easy and in fact no different from Windows.

DllHandle :=LoadLibrary(PWideChar (fullpath));

Obviously the path to the libraries will change because the files extensions are different.

but I need this code to deal with any errors in the loading:

errStr := string(dlerror());
errStr := SysErrorMessage(Winapi.Windows.GetLastError);

Use of GetProcAddress is identical in Windows and Mac OS.

4. I couldn’t find the equivalent of GetDeviceCaps on the Mac so assumed the same size for the Mac and Windows.

5. I didn’t realize the current version of Delphi (even XE7) generates 32-bit Mac OS binaries which means it can’t load any 64-bit libraries. This posed a bit of a problem initially as we only distribute libRoadRunner as a 64 bit library and the current guardian of libRoadrunner was unable to create a 32-bit version. Luckily one of my other students, (Kyle Medley) was savvy enough to compile a 32-bit version which saved the day.

6. Bugs in XE6:

a) Don’t use a separate stylebook for each form because closing and freeing a second form will corrupt the buttons or other visual element on the calling form.

b) TextHeight returns incorrect an value for an empty string

7. The Firemonkey TStringGrid is severely limited or at least it seems that way. It’s currently a poor cousin of this VCL partner. Not sure how to get round its limitations yet.

8. The trackar is a limited control, there is no way to alter the thumb size or shape, track width, etc.

9. Various visual artifacts on some of the styles, eg Auric has problems with thumbs in tack bars.

10. The online documentation on menu handling between Mac OS and Windows appears to be completely incorrect.

Screenshots from a Mac Pro:

Screen Shot 2014-10-21 at 1.06.17 PM


Screen Shot 2014-10-21 at 1.07.24 PM

Posted in Delphi, Programming, SBML, Software | Leave a comment

Windows 10: Finally a better console

The windows console (accessed via cmd) is the coelacanth of software, barely unchanged though millions of years of software evolution. But finally selection pressure has final created a new species. Today Microsoft announced the start of the Windows 10 build up, release date apparently early 2015. One thing that caught many people’s attention is an update, finally, to the ‘MSDOS’ console. Compared to consoles found on other platforms or windows third-party consoles, the Windows console is something that should be retired to the Smithsonian or the London British Museum. Finally however we are getting Ctrl-V for paste and Ctrl-C for copy. At last.

For the gory details read more at New experimental console features in Windows

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Roman Fort at Clunderwen?

About ten years ago, a roman road was discovered tracing a path west of Carmarthen. Currently the road is known to reach as far as Wiston where a roman fort was recently found in 2013. This was the first roman fort ever found in Pembrokeshire. Excavation at Whitland as a result of road improvements also confirmed the presence of the road (and witnessed by the writer).

While looking along the route of the roman road on Google maps I recently noticed a rectangular structure very close to the roman road as it passed south of Clunderwen. The image below was taken from Google Maps. The rectangular structure is shown inside the red square (SN12311893). The red line is the rough alignment for the roman road. North is at the top of the image. The houses to the left of the enclosure mark the southern part of Clunderwen with the railway line arcing just at the top of center of the image. The Royal Commission marks this site as a generic ‘ENCLOSURE;DEFENDED ENCLOSURE;HENGE’ but the rectangular dimensions do not match the usual shape for an iron age or post roman site. The site was only recorded in 2011 and even the Royal Commission is unsure how to interpret the site and suggests a possible roman origin. Of more interest is that the distance between Wiston where there is a confirmed roman fort and the one suggested here is between 9 and 10 miles which is a common roman distance between marching camps. The forts that extend from Edinburgh to the north of Scotland are roughly 10 miles apart. The size of the enclosure is roughly 1.3 acres. (94 meters by 54 meters). This is small for a marching camp but not unheard of. For example Knockcross in Cumbria is only 1.5 acres.  The Wiston camp is a little bigger at about 130 by 160 meters. 

The circumstantial evidence is therefore suggestive that the rectangular enclosure south of clunderwen is in fact another Pembrokeshire roman fort. Only excavation can confirm this hypothesis. 


Posted in General Interest | 1 Comment

Skynet Edges Closer

There is a fascinating article in science this week about the construction in hardware of a neural chip. This isn’t a new idea but scale and flexibility is novel. The chip is made by researchers from IBM and Cornell and can emulate 1,000,000 ‘neurons’. The developers claim that the approach is scalable, and efficient. Apparently chips can be cascaded to make even bigger networks.

I did a back of the envelope calculation to guestimate how many transistors it might take to emulate the brains from different organisms since we know how many transistors it took to make the chip.

This sentence was taken from Ars Technica: “The new processor, which the team is calling TrueNorth, takes a radically different approach. Its 5.4 billion transistors include over (1 million neurons) 4,000 individual cores” Assuming 100 billion neurons in a human brain that means it would take:

54 Trillion transistors to make a human brain, that is or roughly equivalent to 5,200 modern PCs, assuming 10 billion transistors per PC.

In other words not currently possible (In addition the fact that the chip only talks to 256 or neurons whereas the each brain neuron talks to about 7000). The IBM team would have to connect over 5000 chips to make a human brain, not that many it seems. Some other numbers:

Jelly Fish: ~ 4 Million transistors
Pond Snail Brain: ~ 60 Million transistors
Fruit Fly Brain: ~ 540 Million transistors
Honey Bee Brain: ~5.2 Billion transistors
Cockroach: ~5.3 Billion transistors 
Frog Brain: ~86 Billion transistors
Rat Brain: ~1 Trillion transistors
Human Brain: ~54 Trillion transistors

The single chip could just about simulate a Cockroach brain.

Brain data from … of_neurons1 and

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To Git or not to Git, that is the question

I’ve sort of reluctantly been pulled into the 21st century of Version Control to use GitHub. Originally an SVN user and many years before that CVS, I have found the Git world is so different that I still don’t trust myself is using it. I was therefore amused to find this web site “10 things I hate about Git’. What struck me most were the two information flow diagrams that describe the operation of SVN and Git, recreated below. I’ll let the reader draw their own conclusions.

SVN Concepts and commands for operating a remote Subversion repository

Git Concepts and commands for operating a remote GitHub repository

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What do 17 year old science students know (or not)?

This summer I had the opportunity to host five high school students at a UW science camp. I decided to give them a project where they could build circuits that could do addition and multiplication just using resistors.

I’ve been a high school teacher in the past so I though I knew the general level of education for 17 year olds. Let me remind everyone that we’re talking about students who are one year away from entering University. Let me say that again, they are one year away from entering University. This is what I found out:

1. They’ve never seen or used a multimeter before
2. They didn’t know what the symbol was for a battery or a resistor
3. They didn’t understand what the lines were between the circuit symbols (wires!)
4. They’d never heard of a capacitor
5. They’d never seen a breadboard before and had no idea what to with it.
6. They didn’t know the difference between DC and AC (or even what they were)

What is surprising was they did know about ohms law but didn’t know the symbol for an ohm. I am certain that if I asked them to wire up a battery and a light they would have been lost.

Is this the same country that landed men on the moon?

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