Spring 2015 Dyalog Travelogue (The Saga Continues)

Continuing Morten and Gitte’s whistlestop tour round Europe before heading to the US for DYNA15

From left to right this time…

From left to right this time…

FH Bingen – must have good student parties?

FH Bingen – must have good student parties?

Day 3: Bramley-Bingen

Job interviews done by lunch-time, and we hopped in the car (without lunch) to Heathrow, flew to Frankfurt and finally arrived at Bingen at sunset, just in time for some Weissbier and Flammkücken with the other early arrivals. Bingen is located west of Frankfurt, where the Rhine leaves the plains and bends north through hills, heading for Köln, Düsseldorf and the North Sea. Separated from the river by a vineyard-covered hill lies Fachhochschule Bingen, where our, host Dieter Kilsch, uses APL with MatLab and other tools to teach students about quality control and other subjects.

Days 4 & 5: APL Germany Spring Meeting in Bingen

We spent the next two days in the company of about 25 German APL enthusiasts. This time we were first up with a 2.5 hour workshop on Futures and Isolates, and we were very pleased to see that all the delegates who had gone to the trouble of installing Dyalog APL were able to perform all the exercises. We’ll have to make them a little harder next time (Tuesday in Princeton) 🙂 . The afternoon was focused on IBM: News from the Z-series hardware front, and the IBM GSE requirements process, where APL2 users get together and vote on priorities for requests for enhancements. Wouldn’t it be great if our Dyalog users would gang up on us like that and help us to set priorities as a group?

The watch tower at the top of the hill south of Bingen

The watch tower at the top of the hill south of Bingen

The first session on Friday was an APL Germany “business session” which we were allowed to skip. Morten discovered that the Tourist Information office next to our hotel rented bikes. They were a little shocked that he was willing to spend €13 for on hour on a bike, but he felt that he really needed to burn some carbon off the spark plugs. Seems he can’t see a hill without feeling it is necessary to make an attempt to get to the top of it.

With Morten energised after an hour on the bike, it was time to return to the meeting. A couple of presentations were particularly interesting: before lunch, Jürgen Sauermann spoke about GNU APL, which is now 2 years old and up to version 1.5. It is very encouraging to see open source APL systems thriving and promoting the use of APL.



One of the presentations after lunch can only be described as mind-blowing! Jörg Hudelmaier presented a development environment for JavaScript applications, written in Dyalog APL. Jörg was able to prototype JavaScript applications in Dyalog APL, using the WinForms WebBrowser control to render the User Interface, processing callbacks in APL – using a set of APL functions that emulated enough JavaScript DOM support to make his application work. Once he had finished development, he wrote a translator that generated a stand-alone JavaScript application which could run in a browser.

We rounded the two days off with a presentation on our strategy and selected demos of features from versions 14.0 and 14.1: Key, the new experimental JSON parser/generator and the Compiler, threw ourselves in the rental car and headed to Denmark for 15 hours at home before we set off for JFK and Princeton. The story continues next week, on the other side of the Atlantic!

To be concluded…

Spring 2015 Dyalog Travelogue (Ferries, Trains, Planes and Automobiles)

The journey begins: Kronborg Castle, Helsingør

The journey begins: Kronborg Castle, Helsingør

Göteborg: Läppstiften and Barken

Göteborg: Läppstiften and Barken

One of my favourite times of the year is the period in March/April where we traditionally start with a visit to the FinnAPL Forest Seminar followed by the APL Germany Spring Meeting. This year there are two new stops to make: the Swedish APL Group has started holding meetings twice a year too – and we are running the first Dyalog North America meeting in Princeton.

The FinnAPL meeting was a few weeks ago; this week we are wrapping up the rest in a whirlwind tour of no less than five one-way trips to get us to Princeton late on Saturday.

Day 1: Helsingør to Göteborg

We were off to a beautifully easy start on Monday evening, with the 20-minute ferry ride from Helsingør, where Gitte Christensen and I live, to Helsingborg in Sweden. From here it was 1 hour and 45 minutes by snabbtåg (train) to Göteborg, where we arrived just in time for a run at sundown, over the bridge across the Göta river, from which the second image was taken. Our hotel, the beautiful ship Barken, is on the right, and the conference venue, Läppstiften (the Lipstick), a very short walk away to the left.

Day 2: Göteborg to London

Gitte catching some, er, fresh air outside the Hotel Barken

Gitte catching some, er, fresh air outside the Hotel Barken

After a good night’s rest we were welcomed on the 21st floor of the Lipstick by Lars Wenztel of Aplensia, our host for the day. Lars opened the meeting with a talk about the efficiency of using arrays to do product configuration and production planning at Volvo Car Corporation, which is also located just across the river from the meeting site. He mentioned how his team had been working to improve performance, and I would like to take that opportunity to remind you all to send us benchmarks that are representative of your most performance-critical application components so that we (Dyalog) can help you to speed things up.

I was up next with an updated Road Map presentation and demos of the new JSON parser and external workspaces (spoiler alert: Germans and North Americans will see something very similar later this week 🙂 ). The afternoon was full of interesting presentations on the use of APL, with Gert Møller from Genokey in Denmark as the last presenter. He brought the day to a close with his presentation of ongoing work on the application of array-based logic to the problem of reducing the cost, increasing the effectiveness of – and reducing the side-effects that patients are likely to experience when using – new drugs. And guess what…he mentioned that performance was important, too.

Front row: Gitte Christensen, Conrad Helgesson, Joakim Hårsman, Jens Andersson, Tina Leijding, Lars Wentzel. Second: Gilgamesh Athoraya, Ewa Svensson, Radha Jayabalan, Jonas Stensiö. Third: Peter Simonsson, Keerthi Thadikamalla, Per Ericsson, Erik Häggblom and feet of Ole Johansen. Off screen: Paul Grosvenor and Morten Kromberg

Tuesday was a wonderful day in the company of some very lively Swedish APL Users. It is wonderful to see how they have put APL to use in important production planning applications at some of Sweden’s largest manufacturing operations, and the rapidly-growing bio-informatics sector was also well represented. We ended the day deciding to meet again on November 11th, with a target focus of web servers and services. Nearly everyone present had either experience of or plans to implement web-based solutions in APL; there will be code reviews and perhaps even have some hands-on coding sessions next time!

spring2015pt1_6The original plan was to take the train and ferry again and have a night in our own beds, but an opportunity to interview two potential candidates for our current job opening had appeared and, since it would be 2-3 weeks before we were back in the UK, we decide to grasp it. One of the benefits of having a large collection of air miles is that you can spend them on last-minute one-way trips that would otherwise cost a fortune. So instead of hopping on the train, we found ourselves on the airport bus and then a BA flight to Heathrow.

To be continued…

Turning to a Heading with an MPU-9150

As the odour of fried electronics dissipates in the air, I’m unexpectedly afforded the opportunity to write this blog post a day or two earlier than planned. The on-board compass was exhibiting significant deviation, so I consulted my nephew Thorbjørn Christensen at DTU-Space. Thorbjørn makes a living designing magnetometers for space agencies around the world, and he suggested I use a ribbon cable to move the IMU away from the bot as a first step towards understanding the issue. He did warn me to be very careful when attaching it. I still don’t understand what I did wrong, but the evidence that I screwed up is pretty definitive: there are burn marks around every single connector and the IMU chip looks a bit soft in the middle. Most importantly, it no longer reports for duty on the Raspberry Pi’s I2C bus!

A fried IMU-9150

A fried IMU-9150 (click to enlarge)

The good news (apart from the fact that the Raspberry Pi, the Arduino and all other ‘bot components seem to have survived) is perhaps that, since I cannot play with the compass until I have a replacement, I found the time to write about where I am at the moment…and take some time out to work on my presentations for Dyalog ’14 (for those who managed to register before the user meeting in Eastbourne sold out, I still hope to do a ‘bot presentation on the evening of Tuesday September 23rd).

Introducing the MPU-9150

For the last few weeks, I have been using my “bot time” to play with the MPU-9150 breakout board that is attached to our ‘bot. The MPU-9150 is more or less identical to the 6050 that we were using earlier this summer to make gyro-controlled turns but also includes a magnetic compass, which will allow us to know the direction that we are heading in – making it a 9 degree of freedom inertial measurement unit, or “9-dof IMU” (9 = 3 gyro axes + 3 accelerometer axes + 3 compass axes).


I was extremely happy to discover that Richard Barnett had shared his RTIMULib on GitHub. RTIMULib is a Linux library that produces “Kalman-filtered quaternion or Euler angle pose data” based on data from a 9-dof IMU. Jay Foad at Dyalog was quickly able to provide me with a couple of additional C functions designed to be easy to call from Dyalog APL. Jay’s fork of RTIMULib is also available on GitHub. Since we can assume that we are driving on a flat surface, I have just been using two items from the wealth of information provided by this library: the current rate of rotation and the current compass direction – in both cases around the vertical (or “z”) axis.

My First Compass-Controlled Rotation

Due to the fried IMU, I am unable to post a video recording; fortunately, at the moment where I toasted the chip, the Dyalog session output still contained output data from the last run of the function I am working on, which aims to provide smooth rotation to a selected compass heading. In the chart below, the red line tracks the speed of rotation and shows that the “smooth” part still needs work – the speed oscillates quite violently between 60 and 150 degrees per second. The blue line shows the number of degrees that the ‘bot still needs to turn to reach the desired heading. The dotted red line is slightly mislabeled: rather than acceleration, it actually shows the power applied to the motors via a digital-to-analog converter that accepts values between 0 and 255, producing between 0 and 5v of voltage for the DC motors:

Rotating to a compass heading


  • From 0 to 0.4 seconds, we slowly increase power until we detect that rotation has started. We note the power setting required to start rotation.
  • 0.4 to 0.7 (ish), we detect acceleration and hold the throttle steady (increasing it very slightly a couple of times when acceleration appears to stop).
  • 0.7 to 1.1 seconds, cruise mode: whenever speed is above the target of 100 degrees/sec, we idle. When speed is below 100, we re-apply power at a level that was sufficient to start the rotation.
  • 1.1 to 1.4 seconds: We are less than 30 degrees from target, and the target velocity and thus power is reduced proportional to the remaining distance (at 15 degrees, we are down to 50 deg/sec)
  • 1.4 to 1.6 seconds: We detect that we rotated too far, and slam on the brakes, coming to a stop about 10 degrees from target.
  • 1.6 to 2.3 seconds: since we are less than 10 degrees from target, we enter “step” mode, giving very brief bursts of power at “start rotation” level, idling, and watching the heading until we reach the goal.
  • 2.4 seconds: We count the bursts and, after 10, we double the power setting to avoid getting bogged down (you cannot see the bursts in the chart, it only records the power level used for each one). A little more patience would have been good, this probably means we overshot by a bit.

The “Heading” Function

Achieving anything resembling smooth movement is still some way away, mostly due to the fact that motor response to a given input voltage varies enormously from motor to motor and between different applications to the same motor. The strategy described above is implemented by a function named “Heading”, which can be found in the file mpu9150.dyalog in the APLBot folder on GitHub. An obvious improvement would be to have the robot self-calibrate itself somehow and add a model of how fast rotation speeds up and slows down (based on, and constantly adjusted with, observed data), in order to dampen the oscillations. I intend to return to this when I have a new IMU (and my other user meeting presentations are under control).

This has turned out to be a lot harder than I imagined: suggestions are very welcome – please leave comments if you have a good idea!

Making Controlled Turns with the DyaBot

This blog originally started when I took delivery of the DyaBot, a Raspberry Pi and Arduino based variant of the C3Pi running Dyalog v13.2. The architecture of the ‘bot and instructions for building your own inexpensive robot can all be found in blog entries from April to July of last year.

The downside of only using inexpensive components is that some of them are not very precise. The worst problem we face is that the amount of wheel movement generated by the application of a particular power level varies from one motor to the next, and indeed from moment to moment. Trying to drive a specific distance in a straight line, or make an exact 90 degree turn regardless of the surface that the ‘bot is standing on, are impossible tasks with the original Dyabot. You can have a lot of fun, as I hope the early posts demonstrate, but we have higher ambitions!

Our next task is to add motion sensors to the DyaBot, with a goal of being able to measure actual motion with sufficient accuracy to maintain our heading while driving straight ahead – and to make exact turns to new headings, like the 90-degree turn made in this video (the ‘bot has been placed on a Persian carpet to provide a background containing right angles):

Introducing the MPU-6050

For some time we have had an MPU-6050, which has 3-axis rotation and acceleration sensors, attached to our I2C bus, but haven’t been able to use it. About ten days ago (sorry, I took a few days off last week), @RomillyC came to visit us in Bramley to help me read some Python code that was written for this device. The current acceleration or rotation on each axis is constantly available as a register and can be queried via I2C. Translated into APL, the code to read the current rate of rotation around the vertical axis is:

 ∇ r←z_gyro_reading ⍝ current z-axis rotation in degrees
   r←(read_word_2c 70)÷131 ⍝ Read register #70 and scale to deg/sec

 ∇ r←read_word_2c n;zz
   r←I2 256⊥read_byte_2c¨n+0 1               ⍝ Read 2 registers and make signed I2

 ∇ r←read_byte_2c n;z
   z←#.I2C.WriteArray i2c_address (1,n)0     ⍝ Write register address
   r←2 2⊃#.I2C.ReadArray i2c_address (1 0)1  ⍝ Read input

 I2←{⍵>32767:1-65535-⍵ ⋄ ⍵} ⍝ 16-bit 2's complement to signed

Integrating to Track Attitude

Reading the register directly gives us the instantaneous rate of rotation. If we want to track the attitude, we need to integrate the rates over time. The next layer of functions allows us to reset the attitude and perform very primitive integration by multiplying the current rotation with the elapsed time since the last measurement:

∇ r←z_gyro_reset            ⍝ Reset Gyro Integration
  z_gyro_time←now           ⍝ current time in ms
  z_gyro_posn←0             ⍝ current rotation is 0

∇ r←z_gyro;t;delta          ⍝ Integrated gyro rotation
  t←now                     ⍝ current time in ms
  delta←0.001×t-z_gyro_time ⍝ elapsed time in seconds
  z_gyro_time←t             ⍝ last time

We can now write a function to rotate through a given number of degrees (assuming that the gyro has just been reset): we set the wheels in motion, monitor the integrated angle until we are nearly there, then shut off the engines. We continue logging the angles for a brief moment to monitor the deceleration. The function returns a two-column matrix containing the “log” of rotation angles and timestamps:

    ∇ log←rotate angle;bot;i;t
      log←0 2⍴0 ⍝ Angle, time
      bot.Speed←3 ¯3 ⍝ Slow counter-clockwise rotation
      :Trap 1000 ⍝ Catch interrupts
          :Until t>angle-7 ⍝ Stop rotating 7 degrees before we are done    

      bot.Speed←0 ⍝ cut power to the motors
      :For i :In ⍳25 ⍝ Capture data as we slow down

The logged data from the rotation captured in the video at the top is charted below:

Controlled 90-Degree RotationEven with the primitive integration and rotation strategies, the results already look quite promising. I’ll be taking most of this week off – part of it without access to the internet(!), but once I am back, expect the next blog entry to explore writing functions that accelerate and slow down in a more controlled fashion as well as stop at the right spot rather than relying on a specific amount of friction to rotate through the last 7 degrees (note the very slight reverse rotation at the end, probably caused by the Persian carpet being a bit “springy”). I will also clean up the code and post the complete solution on GitHub – and perhaps even look at some better integration techniques.

If you would like to make sure you don’t miss the next installment, follow the RSS feed or Dyalog on Twitter.

Dancing with the Bots

Last week the ‘bots were busy preparing for the J Language Conference in Toronto, where they made their first public appearance together. Upon returning to Bramley they continued training and we are proud to present the first recording of their new dance:

The ‘bots are both running the same DyaBot class as last year. This class exposes a property called Speed, which is a 2-element vector representing the speed of the right and left wheels respectively. Valid values range from +100 (full speed ahead) to -100 (full reverse). The annotations displayed at the top left show the settings used for each step of the dance.

Controlling Two Robots at Once using Isolates

Isolates are a new feature included with Dyalog version 14.0, designed to make it easy to perform distributed processing. In addition to making it easy to used all the cores on your own laptop or workstation, isolates make it possible to harness the power of other machines. This requires the launching of an “isolate server” on each machine that wants to offer its services:

Starting an isolate server using PuTTY to run Dyalog on the robot.

Starting an isolate server on DyaBot00 using PuTTY.

Once we have an isolate server running on each robot we can take control of them from a remote session as follows:

      )load isolate
      #.isolate.AddServer 'dyabot00' (7052)      
      #.isolate.AddServer 'dyabot04' (7052)
      bots←isolate.New¨Bot Bot
 dyabot00  dyabot04

Above, we create two instances of the Bot namespace. The expression Bots.Init invokes the Init function, which returns the hostname, in each isolate:

:Namespace Bot

    ∇ r←Init;pwd
      pwd←∊⎕SH'pwd' ⍝ Find out where to copy from
      #.⎕CY botws←pwd,'/DyaBot/DyaBot.dws' ⍝ copy ws
      i←⎕NEW #.DyaBot ⍬ ⍝ Make DyaBot instance    
      r←⎕SH'hostname' ⍝ Return hostname


Next, we define a function “run” that will take a vector of dance steps as input. Each step is a character vector (because that makes editing slightly easier!) containing five numbers: The first two set the speed of one robot, the next two the speed of the other and the fifth defines the duration of the step. After each step we pause for a second, to give humans time to appreciate the spectacle:

    ∇ run cmds;data;i;cmd;z
[1]    ⎕DL 5
[2]    :For i :In ⍳≢cmds
[3]        :If ' '∨.≠cmd←i⊃cmds
[4]            data←1 0 1 0 1⊂2⊃⎕VFI cmd ⍝ Cut into 3 numeric pieces
[5]            z←bots.{i.Speed←⍵}2↑data ⋄ ⎕DL⊃¯1↑data ⋄ z←bots.(i.Speed←0)
[6]            ⎕DL 1
[7]        :EndIf
[8]    :EndFor

Now we are ready to roll: Call the run function with a suitable array and watch the robots dance (see the video at the top)!

50  50  0   0 1.5
 0   0 50  60 1.2
50 ¯50 50 ¯50 0.3
20  80 10  70 5  
50 ¯50 50 ¯50 0.3
50  50  0   0 1.5
 0   0 50  60 1.2

      dance choreography

Join us again next week to hear what happened when Romilly came to Bramley to help wire up the accelerometer and gyro!

Aligning Diff Output

‘Bots are off limits this week so here is a story from this year’s Iverson College – a fantastic week spent in the company of a wonderful mixture of array and functional language gurus and newbies, all learning from each other. One evening, Dhru Patel presented a problem that he was working on which involved displaying the results of a “diff” side by side with the matched rows aligned. For example, the input might be:

      OLD NEW
│This    │This    │
│is the  │original│
│original│is not  │
│text    │        │

Edited by Yoda, the text was. The selection of rows to be aligned requires finding the longest sequence of rows from the original data that matches rows in the edited data without ever skipping backwards through either sets of data. In this case, it is the original first and third row, matching the first two edited rows. We will return to how we might identify these rows in a future blog entry (meanwhile, try to grok John Scholes’ YouTube video on Depth First Searching and think about it). For now, we will provide this information as a left argument, a vector of Boolean vectors that marks the location of the matched rows:

      (1 0 1 0)(1 1 0) AlignMatched OLD NEW
│This    │This    │
│is the  │        │
│text    │        │
│        │is not  │

At Iverson College there was general agreement that “there should be a non-looping solution”, and Devon McCormick immediately stated that he would bet that it involved grade (). Let us explore:

      masks←(1 0 1 0)(1 1 0)
      ⎕←matched←∊masks ⍝ The two match masks catenated together
 1 0 1 0 1 1 0 
      ⎕←origin←(≢¨OLD NEW)/0 1 ⍝ 0 for items from the old array, 1 for new
 0 0 0 0 1 1 1 
      ⎕←block←∊+\¨masks ⍝ running count of matched rows
 1 1 2 2 1 2 2   
1 0 0 This    
1 1 0 is the  
2 0 0 original
2 1 0 text    
1 0 1 This    
2 0 1 original
2 1 1 is not  

Our goal is to create an expansion mask for each argument; this is going to insert blank lines at the points where a non-matched row from the other argument is included. The next step is to reorder everything by ascending block number, and within each block move the matched rows to the front (ascending by ~matched), as follows:

      ⎕←data←data[⍋data[;1 2];]
1 0 0 This    
1 0 1 This    
1 1 0 is the  
2 0 0 original
2 0 1 original
2 1 0 text    
2 1 1 is not 

This contains all the items from both texts in the order that they would need to appear in the final results. We can extract the reordered flag vectors:

       matched←~data[;2] ⋄ origin←data[;3]

Now, (origin=0) is an expansion mask that would expand OLD to match the above, and (origin=1) would do the same for NEW:

      0 1 {(origin=⍺)⍀⍵}¨OLD NEW
│This    │        │
│        │This    │
│is the  │        │
│original│        │
│        │original│
│text    │        │
│        │is not  │

To align the matched rows, we need to eliminate inserted blanks that correspond to matched rows from the other side:

      0 1{((~matched∧origin≠⍺)/origin=⍺)⍀⍵}¨OLD NEW
│This    │This    │
│is the  │        │
│text    │        │
│        │is not  │

In the final function, which collects the relevant lines of code from our experiments, we do not create the temporary “data” matrix, but reorder the origin and matched vectors individually – and instead of doing grade up on a two-column matrix, we compute an integer vector that will sort by descending matched within ascending block (because we know that grade up on a simple small-range integer vector will run like greased lightning):

 AlignMatched←{                ⍝ align matched rows of 1⊃⍵ and 2⊃⍵
     matched←∊⍺                ⍝ matches are marked by 1⊃⍺ and 2⊃⍺
     origin←(≢¨⍵)/0 1          ⍝ identify origin of items in matched (0=old. 1=new)
     block←∊+\¨⍺               ⍝ running count of matched rows
     order←⍋(2×block)-matched  ⍝ Order so matching rows are adjacent and order of
     (origin matched)←(⊂⊂order)⌷¨origin matched ⍝ items following matched row is preserved
     0 1{((~matched∧origin≠⍺)/origin=⍺)⍀⍵}¨⍵ ⍝ Expand exluding matched from "other" list


Reviving Lost Arts

The algorithm above makes use of techniques that were well-known in APL circles in the 1980s, but atrophied after nested arrays arrived on the scene and applications tended to keep parts of the data in separate leaves of an array rather than using simple data structures.

If you would like to read up on some of the old techniques, you might enjoy browsing the FinnAPL Idiom Library, and Bob Smith’s immortal Boolean Functions and Techniques. Although nested arrays might have made them a little less relevant in the 90s and 00s, the search for high-performance parallel solutions could bring them back, as explained in this session from Dyalog ’12, on Segmented Scans and Nested Data Parallelism by Andrzej Filinski.