Quote of the day: You can’t learn too much linear algebra

Benedict Gross, Professor of Mathematics at Harvard said in his E-222 lecture: ‘You can’t learn too much linear algebra’.

If you read my WordPress pages in Signals and Systems, I’m trying a new approach to explain the materials done under the classical approach in a much more compact way using basic ideas in linear algebra.

Linear algebra is fun and easy to learn (at intro levels), once you get used to the fact that it’s a carefully picked set of restrictions that most physical problems boils down to. In high school algebra, it’s disguised as ‘method of detached coefficients’ when you solve systems of simultaneous equations.

Once you model your problem into linear equations (the hardest part), you will see the equivalence (or mathematically equivalent analogs) of different problems ranging from economics to circuits and mechanics. The beauty of the ‘detached coefficients’ approach separates the context of the problem from its mathematical structure as the application specific variables are often grouped as a vector (or matrix) that you deal with as a unit. In fact, most problem boils down to this:

    \[ \bf{Ax = b} \]

It’s your job to construct \bf{A}, \bf{x} and \bf{b} and tell people what they mean.

I agree with Gilbert Strang, Professor of Mathematics at MIT that it’s time to make linear algebra the standard curriculum over calculus. Digital control used to be a very advanced graduate class, but after a few decades, it’s undergraduate material. Linear algebra has very few knowledge dependencies (hard pre-requisites), so it’s great material to teach at any level.

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Agilent Infiniium (Motorola VP22) Motherboard USB Pinouts for DOM SSD

The Motorola VP22 motherboard used in a variety of modern Agilent’s Infiniium series oscilloscope (the ones with Megazoom) and logic analyzers has a 5-pin USB port that’s not quite the same as the standard headers on most motherboards.

The reason I needed the pinouts of the USB port is because I have a 40-pin DOM SSD to replace the old clunky mechanical hard drive, which needs 5V for power.

I don’t want to modify/resolder the original wire harness (for the LS-120 and CD-ROM drive) nor I have the molex connectors to make a power splitter. Luckily, I found somewhere that I can safely tap a 5V for low power devices: the internal USB header. Here’s a picture with the DOM SSD module wired:

VP22 USB Power Tap

This post serves as a reminder to myself that the ground is the second pin to the left and 5V is the rightmost pin. The pinout diagram as follow:

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(Front-end) Attenuator Autopsy of HP 54616B Digital Oscilloscope

One day I got a call from a friend saying that he accidentally fed high voltage signal (line voltage) and broke one of the channels.

My hunch is that since he didn’t feed kilo-volts into it, the damage is limited to the (front-end) attenuator (an expensive part). I had an extra unit lying around so I just swapped it for him so he can get it up and running.

Once I got the time, I opened it up the broken unit to see the damage. My hunch was correct:

Fried 1NB7-8303 54616B Attenuator Block

The 500Mhz attenuator used in 5461XB, 54505B/54506B/54510B/54512B (has to be version ‘B’), 54520/54540 series, and early Infiniiums 54810 series, E1428A (VXI board), 166XCS/166XES (MSO), 167XG-003, etc. are all the same: 1NB7-8303 (or 1NB7-8458). For 5461XB, it’s tucked inside 54616-68401*, which is a big metal case that covers 2 attenuators and an external trigger PCB (see the picture on the right hand side). Everything else is tucked individually inside 54512-63402 metal shield.

In this autopsy, the resistive trace of 1NB7-8303 was blown open-circuit (charred), so bad that it spot-welded the metal casing.

I took a good attenuator and measured resistance that the blown open ‘trace’ should have been. Turns out it’s a little less than 1Ω so I used 4-lead Kelvin sensing from my Agilent 34401A multimeter. I calibrated that meter using my Data Precision 8200 reference and agreed with my Fluke DMM, so hopefully I wasn’t way off.

I could have put a small SMD resistor matching the resistance of the blown trace, but since I have a few back up attenuators lying around, I’d rather not risk the signal integrity by doing so, since I cannot guarantee the temperature specification if I just replaced it with a resistor. The scope was up and running in perfect condition after replacing the attenuator.

Now you know what happens when you feed line voltage to a scope. The damage is usually limited, but the front-end (attenuator) is the most expensive RF part that makes a scope truly a scope (see Dave’s rant on EEVblog). The ADC hybrid can get just as expensive, but usually the attenuator takes the hit before your input gets to fry the ADC.


* Be very careful about a similar looking block with similar number 54503-63401 or 54503-63402. It has the same metal housing, but inside the attenuator chip 1NB7-8116 or 1NB7-8288, which is NOT compatible with first generation Infiniiums, later 54500 series or 5461XB series. They are used in 54502A, 54503A, 54504A, 54510A.

54501A never showed up in the discussion because 100Mhz scopes does not need the individually shielded metal block. The attenuator was directly soldered to the main assembly.

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Agilent 54641D (Mixed Signal) 54642A (Digital) Oscilloscope Fan Mod

Agilent 54641D has a ADC hybrid (1NB7-8394) converter that runs very hot. The heatsink does a very good job extracting the heat from the chip, but there’s nothing to carry the heat away from the heatsink. The heatsink is actually hand-burning hot when passively cooled. Even with the case, the bottom of the unit gets so hot that it actually warms up the instrument below it.

For longetivity, I decided to give it a tiny fan. But given the tight space at the bottom, how can I squeeze a standard 5mm fan? A squirrel cage fan (preferably 5mm side, 15mm thick) might do the trick, but where am I supposed to secure it? Turns out there’s a screw hole for the fan and there’s only one place I can screw it down:

Fan for 54642D's ADC

I padded the fan with 3 plastic washers to create a surface level with the two ASIC chips the fan is sitting on.

Where should I get the power for the fan? It’s not a low-end 100Mhz scope, so I took extra precaution to not have a DC power line flying all over the circuit board to generate noise. I twisted the power wires together just to lower the EMI and follow the same holes Agilent designed to let the power cable go through.

It’s a little risky to steal power from the circuit board directly when I don’t have the schematics, but luckily I found a printer power port which nowadays nobody uses which I can steal the power from.

I could have tapped the 12V fan power from the power module for the power supply fan, but I noticed the printer power port is even better: it’s around 7~9V:  I don’t want the noise from running it at full speed (squirrel cage fan are typically noisier).

54642D Printer Power

 

Finally I made an internal terminal for the printer power so the fan can be easily detached. Weakly wrapped it in a clear heat shrink tube so it won’t get accidentally disconnected yet reminds myself that a connector was built instead of directly soldered on.

At last I tie-wrapped the power wire to the other power wires Agilent already secured so they won’t dangle during transportation.

54642D Tie-wrapped

Self-calibration expects the temperature to be stable, so the oscilloscope needs to be warmed up before a cal would register. That means before the fan, it’d take a long while for the ADC to heat up to a guaranteed temperature.

With the new fan, the calibration needs to be done again because it’s much cooler now. Even better, it takes nearly no time to warm the oscilloscope up for calibration because the steady temperature isn’t high anymore.

Of course this mod works for 54641A, 54641D, 54642A, 54642D as well. Technically you can put it in any 5462X oscilloscope, but since they are 100Mhz, you don’t need to cool the ADC down that much.


I recently tried it on a 54642A, which has only one stream instead of two, so one chip with glued heatsink and one ASIC (1821-5733) is gone. Looks like I can use the screw hole on the top left (the one with a red condom over it). Unfortunately, since the only way to use that screw hole is to flip the fan over, it became an inferior choice because

  • The suction part came from the bottom of the case instead of the board. That means I’m blocking ventilation for some components.
  • The fan’s power line is now close to the board, creating potential signal integrity issues (might not be material, but why mess with EMI issues when there’s no real advantage anyway?)

In other words, even if it looks tempting to deviate from my original solution for the non-MSOs, there’s no good reason doing so.


Now that I have a seek thermal camera module, here’s the thermal picture after the fan has been installed (accompanied with the picture of the board):

You can see from the thermal picture how effective the heatsink is. It took only a very weak breeze to carry the majority of the heat away. The 12V squirrel cage fan running at ~7V is pretty quiet, yet it cools the ADC hybrid down to near room temperature.


The real reason why I did this fan mod is because I had some units (like 54641A) bought from the used market that after powering it up for 30 minutes, the signal displayed just went nuts and jumped all over the place. I opened up the ADC and the metal bracket holding it down had a lot of heat stress pattern on it (the golden bracket looked purple-rainbowish). The unit was fixed after swapping the ADC hybrid from a donor unit, but now I know the ADC hybrid really needs to be kept cool to ensure longevity.

By the way, if you need a replacement ADC hybrid (1NB7-8394), I have 2 pcs at $660/ea.

First come first served. Call me at 650-804-5024 if you suspect it’s the ADC hybrid that needs to be replaced. The fan mod is complimentary with any repair/service I do for 54640 series oscilloscope that exceeds $800 after parts and labor.


Since I’m now selling 54640-series oscilloscopes with this as a value-added service, I’d ask my kind readers NOT TO use the technique learned here to offer products and services that might compete with my offerings. Feel free to apply it to units that you’ll keep for yourself. I’ll trust you 🙂

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MATLAB Techniques: Resuming loops in a script

If you have a time-consuming for-loop in a script and you want to terminate it for some reason (like checking partial results, debugging, etc) but you don’t want to start over again. What would you do if you want minimal typing each time you stop?

Here’s how I do it:

if( exist('k', 'var') ) k0=k; else k0=1; end
for k=k0:1000
  % Your code here
end

If you want to restart the loop, simply enter k=1 in the command prompt and you’re good to go. Otherwise it will pick up where you left off.

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MATLAB Fundamentals: Vectorization

A coworker whose background is in embedded systems (with a C background and no MATLAB at all), after hearing my rants that people are coding MATLAB like C using way more for-loops than necessary, asked me if he has two vectors,

a = 0:32767;
b = 0:32767;

and he want all combinations of the elements in a and b so that for each index pair (i, j), he will get

    \[ 167\left(\frac{a_j+42}{b_j+17} \right)\]

There are 32768^2 combinations out there. At first, I showed him the typical method shown in the MATLAB’s introduction materials:

% Should have used ndgrid() for a more natural (column first) layout
[B, A] = meshgrid(a, b);

C = 167*(A+42)./(B+17)

Then he asked, ‘This way I have to store the matrices A and B. Wouldn’t it be memory intensive? Is there a better way to do it like with functional programming?’ Now I have to show him a more advanced trick that requires some mental leaps (the ones necessary to get sophisticated at the MATLAB language):

C = 167*bsxfun(@rdivide, a'+42, b+17)

This one liner does not save intermediate input values, so it’s memory efficient as well.

bsxfun() is a function that takes two inputs (we call it a binary function) which any of them can be a matrix, vector or scalar. It will conceptually expand the dimensions so the function handle (e.g. @rdivide) get to apply to all combinations as if the inputs are expanded (repeated) to the longer of each dimension supplied. I bet under the hood it’s just a pair of for-loops with the loop increments managed so it doesn’t waste memory storing the intermediaries.

In the example above, I have a column a^T+42 and a row b+17. The output C is arranged as if a^T+42 is copied right to meet the length of b+17, and b+17 is copied down to meet the length of a^T+42.

This involves two major concepts one needs to program the MATLAB way : vectorization and anonymous functions. Not something you’d tell a day-zero beginner (probably scare them off), but showing them a Ninja trick after they understand the beginner’s method might motivate them to learn the true power of MATLAB.


Rik has pointed out in the comments below that TMW introduced implicit expansion that makes the bsxfun() obsolete. This is an excellent move (readability), despite it won’t police matrix crimes anymore so educators should teach about implicit expansion as the first thing as it’d be hard to debug is the user is not aware of the behavior. Thanks Rik!

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Structuring your MATLAB code base

When your MATLAB project gets large, or when you have a lot of projects, it’s time to consider restructuring your code and libraries so you can focus on what matters the most instead of plowing through the mess you just created.

For my projects, I usually create a file called ‘managedPathAndFiles_{myProjectName}.m’ at the top-level folder. The comments in the demo code below highlight the techniques used:

function [file, folder] = managedPathAndFile_myProject(isRegenerated)
% isRegenerated: set to 'false' to skip addpath() (which is slow)

 % Optional default input arguments by name instead of couting nargin
 if( ~exist('isRegenerated', 'var') )
   isRegenerated = true;
 end

 % Note the use of nested structures (like replacing _ with .)
 % You can use the hierarchy to group folders/files in a way you can 
 % operate on them in one-shot

 % Use the location of this file as anchor 
 % 'pwd' is unreliable because you can call this from other folders if
 % it's in MATLAB's path
 folder.root = fileparts( mfilename('fullpath') );
 
 % Include your project specific subroutines in the MATLAB path
 % Use fullfile() to generate platform independent folder structures
 folder.core.root = fullfile(folder.root, 'core');
 folder.core.helper = fullfile(folder.core.root, 'helper'); 
 % Add all the paths under the folder in one shot
 if( isRegenerated )
   % '-end' avoids name conflict by yielding to the incumbent paths 
   addpath( genpath(folder.core.root), '-end' );
 end
 
 % Automatically create data storage folder
 folder.data.root = fullfile(folder.root, 'data');
 folder.data.cache = fullfile(folder.data.cache, 'data');
 if( isRegenerated )
   % Outputting something will absorb the error if the path alreayd
   % exist. I made a mkdir_silent() in my libraries, but used the
   % native call here for demo.
   [~, ~] = structfun(@mkdir, folder.data);
 end
 
 % Sometimes you might have config or external files to load
 file.data.statistics = fullfile(folder.data.root, 'statistics.mat');
 
end

Many people don’t know about the function genpath() so they ended up lumping all their dependencies in one folder which makes my eyes bleed. Organize your files into a tree that makes sense now!

I’d recommend any serious MATLAB developer build their own library folder with a consistent naming and a sensible tree hierarchy. After looking into FEX and what’s natively available in MATLAB and you still need to roll out your own code, you’re likely to rediscover what you’ve already built just by establishing a new .m file/function you are about to write in the folder you’d most naturally put it in (like people with like mind: self, tend to pick the same names).

Sometimes you have to whip up some ‘crappy’ code that doesn’t generalize (or can be reused) in other contexts. Consider putting them in a /private folder under the caller so it won’t be visible to everybody else. Of course, I encourage people spend a little more time to write the code properly so it can be put in your own MATLAB library.

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How I learned MATLAB inside out

Back when I was a struggling graduate student working 3 university jobs to stay afloat, one of the job was to build a multi-center data collection system that take cares of remote data upload, store it in a database and visualize the waveforms and records.

I surveyed other platforms and languages for a couple of months and finally settled on MATLAB because at the time MATLAB had the most convenient data types (cells), data loading/saving (‘.mat’ files so I don’t have to manage the datatypes/format), external interfaces, and most importantly MATLAB FileExchange (FEX) pretty much cover every generic idea I can think of. With MATLAB, my work is pretty much down to coding the high level ‘business’ logic.

And no, I wasn’t biased towards MATLAB at the time because I have a signal processing background. I didn’t know much about MATLAB’s programming support back then other than number crunching (just like the 90% of the public who misundestood the power of the language), so I wouldn’t choose it for a software project at that level of complexity without much research.

Learning the guts of MATLAB, architecturing and coding the entire system took me only 3 months (well, it included a 1 month non-stop 16 hours a day, 7-days a week shut-in programming). Not a shabby platform for a project that is supposed to take 4 years. In fact, the rest of the time was spent

  1. reading the last owners *#@&ed up perl code and fighting to get the fragile linux setup to work on other machines, then reverse the entire project requirements from the source code because there wasn’t any documentation and the previous owners graduated.
  2. reconstruct Guidant’s half-finished (done by a 3rd party then abandoned) binary data reader by finishing the hardest part of the incomplete XSLT code.

The rest that has to do with MATLAB was relatively easy once I learned the main ideas through their documentation, newsgroups, Loren’s blog and the official support.

To understand and appreciate the beauty of MATLAB and use it effectively, you have to get past the following hurdles:

  1. Basic data structures: cell, struct and language features.
  2. Vectorization: use for-loops only in limited cases
  3. Anonymous function (Lambdas), cellfun(), arrayfun(), bsxfun(), structfun()
  4. Overloading and OOP
  5. Tables (Heterogeneous data structures) and Categorical objects (Nominal, Ordinal)

or else you are coding it like a C programmer: a complete waste of MATLAB’s license fees. If you know these 5 aspects of MATLAB well and would say there are strictly superior options out there, please let me know in the comments section and I’ll look into it.

 

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MATLAB Quirks: cellfun() high-performance trap

cellfun() is a powerful function in MATLAB which mirrors the idea of applying a ‘map’ operation (as in functional programming) to monads (cells: a datatype that holds any arbitrary data type, including itself).

One common use is to identify which cells are empty so you can ignore them. Typically, you can do

index.emptyCells = cellfun(@isempty, C);

According to the help (H1) page, there is a limited set of strings that you can use in place of the function handle (functor) for backward compatibility:

 
A = CELLFUN('fun', C), where 'fun' is one of the following strings,
returns a logical or double array A the elements of which are computed 
from those of C as follows:
 
   'isreal'     -- true for cells containing a real array, false
                   otherwise 
   'isempty'    -- true for cells containing an empty array, false 
                   otherwise 
   'islogical'  -- true for cells containing a logical array, false 
                   otherwise 
   'length'     -- the length of the contents of each cell 
   'ndims'      -- the number of dimensions of the contents of each cell
   'prodofsize' -- the number of elements of the contents of each cell
 
A = CELLFUN('size', C, K) returns the size along the K-th dimension of
the contents of each cell of C.
 
A = CELLFUN('isclass', C, CLASSNAME) returns true for each cell of C
that contains an array of class CLASSNAME.  Unlike the ISA function, 
'isclass' of a subclass of CLASSNAME returns false.

Turns out these functions have their native implementation and runs super-fast. But I got burned once when I tried to use this on cells containing table() objects:

index.emptyCells = cellfun('isempty', cellsOfTables);

I meant to find out if I have zero-row or zero-column (empty) table objects with that. It gave me all false even when my cells have these 0-by-0 tables. What a Terrible Failure?! Turns out these ‘backward compatibility’ native implementations (I guess they already have cellfun() before having function handles) looks at the raw data stream like PODs (Plain Old Datatypes) as a C program would do.

A table() object has lots of stuff stored in it like variable (column) names, so there’s no way a program looking at an arbitrary binary stream without accounting for such data type will consider that object empty. It’s up to the overloaded isempty() or numel() of the class to tell what is empty and what’s not, but it needs to be called by the function handle to establish which method to call.

Lesson learned: don’t use those special string based functor in cellfun() unless you know for sure it’s a POD. Otherwise it will get you the wrong answer at the speed of light.

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