Mathias Brandewinder on .NET, F#, VSTO and Excel development, and quantitative analysis / machine learning.
22. March 2015 17:27

I will admit it, I got a bit upset by James McCaffrey’s column in MSDN magazine this month, “Gradient Descent Training Using C#”. While the algorithm explanations are quite good, I was disappointed by the C# sample code, and kept thinking to myself “why oh why isn’t this written in F#”. This is by no means intended as a criticism of C#; it’s a great language, but some problems are just better suited for different languages, and in this case, I couldn’t fathom why F# wasn’t used.

Long story short, I just couldn’t let it go, and thought it would be interesting to take that C# code, and do a commented rewrite in F#. I won’t even go into why the code does what it does – the article explains it quite well – but will instead purely focus on the implementation, and will try to keep it reasonably close to the original, at the expense of some additional nifty things that could be done.

The general outline of the code follows two parts:

• Create a synthetic dataset, creating random input examples, and computing the expected result using a known function,
• Use gradient descent to learn the model parameters, and compare them to the true value to check whether the method is working.

You can download the original C# code here. Today we’ll focus only on the first part, which is mainly contained in two methods, MakeAllData and MakeTrainTest:

static double[][] MakeAllData(int numFeatures, int numRows, int seed)
{
Random rnd = new Random(seed);
double[] weights = new double[numFeatures + 1]; // inc. b0
for (int i = 0; i < weights.Length; ++i)
weights[i] = 20.0 * rnd.NextDouble() - 10.0; // [-10.0 to +10.0]

double[][] result = new double[numRows][]; // allocate matrix
for (int i = 0; i < numRows; ++i)
result[i] = new double[numFeatures + 1]; // Y in last column

for (int i = 0; i < numRows; ++i) // for each row
{
double z = weights[0]; // the b0
for (int j = 0; j < numFeatures; ++j) // each feature / column except last
{
double x = 20.0 * rnd.NextDouble() - 10.0; // random X in [10.0, +10.0]
result[i][j] = x; // store x
double wx = x * weights[j + 1]; // weight * x
z += wx; // accumulate to get Y
}
double y = 1.0 / (1.0 + Math.Exp(-z));
if (y > 0.55)  // slight bias towards 0
result[i][numFeatures] = 1.0; // store y in last column
else
result[i][numFeatures] = 0.0;
}
Console.WriteLine("Data generation weights:");
ShowVector(weights, 4, true);

return result;
}

MakeAllData takes a number of features and rows, and a seed for the random number generator so that we can replicate the same dataset repeatedly. The dataset is represented as an array of array of doubles. The first columns, from 0 to numFeatures – 1, contain random numbers between –10 and 10. The last column contains a 0 or a 1. What we are after here is a classification model: each row can take two states (1 or 0), and we are trying to predict them from observing the features. In our case, that value is computed using a logistic model: we have a set of weights (which we also generate randomly), corresponding to each feature, and the output is

logistic [ x1; x2; … xn ] = 1.0 / (1.0 + exp ( - (w0 * 1.0 + w1 * x1 + w2 * x2 + … + wn * xn))

Note that w0 plays the role of a constant term in the equation, and is multiplied by 1.0 all the time. This is adding some complications to a code where indices are already flying left and right, because now elements in the weights array are mis-aligned by one element with the elements in the features array. Personally, I also don’t like adding another column to contain the predicted value, because that’s another implicit piece of information we have to remember.

In that frame, I will make two minor changes here, just to keep my sanity. First, as is often done, we will insert a column containing just 1.0 in each observation, so that the weights and features are now aligned. Then, we will move the 0s and 1s outside of the features array, to avoid any ambiguity.

Good. Instead of creating a Console application, I’ll simply go for a script. That way, I can just edit my code and check live whether it does what I want, rather than recompile and run every time.

Let’s start with the weights. What we are doing here is simply creating an array of numFeatures + 1 elements, populated by random values between –10.0 and 10.0. We’ll go a bit fancy here: given that we are also generating random numbers the same way a bit further down, let’s extract a function that generates numbers uniformly between a low and high value:

let rnd = Random(seed)
let generate (low,high) = low + (high-low) * rnd.NextDouble()
let weights = Array.init (numFeatures + 1) (fun _ -> generate(-10.0,10.0))

The next section is where things get a bit thornier. The C# code creates an array, then populates it row by row, first filling in the columns with random numbers, and then applying the logistic function to compute the value that goes in the last column. We can make that much clearer, by extracting that function out. The logistic function is really doing 2 things:

• first, the sumproduct of 2 arrays,
• and then, 1.0/(1.0 + exp ( – z ).

That is easy enough to implement:

let sumprod (v1:float[]) (v2:float[]) =
Seq.zip v1 v2 |> Seq.sumBy (fun (x,y) -> x * y)

let sigmoid z = 1.0 / (1.0 + exp (- z))

let logistic (weights:float[]) (features:float[]) =
sumprod weights features |> sigmoid

We can now use all this, and generate a dataset by simply first creating rows of random values (with a 1.0 in the first column for the constant term), applying the logistic function to compute the value for that row, and return them as a tuple:

open System

let sumprod (v1:float[]) (v2:float[]) =
Seq.zip v1 v2 |> Seq.sumBy (fun (x,y) -> x * y)

let sigmoid z = 1.0 / (1.0 + exp (- z))

let logistic (weights:float[]) (features:float[]) =
sumprod weights features |> sigmoid

let makeAllData (numFeatures, numRows, seed) =

let rnd = Random(seed)
let generate (low,high) = low + (high-low) * rnd.NextDouble()
let weights = Array.init (numFeatures + 1) (fun _ -> generate(-10.0,10.0))

let dataset =
[| for row in 1 .. numRows ->
let features =
[|
yield 1.0
for feat in 1 .. numFeatures -> generate(-10.0,10.0)
|]
let value =
if logistic weights features > 0.55
then 1.0
else 0.0
(features, value)
|]

weights, dataset

Done. Let’s move to the second part of the data generation, with the MakeTrainTest method. Basically, what this does is take a dataset, shuffle it, and split it in two parts, 80% which we will use for training, and 20% we leave out for validation.

static void MakeTrainTest(double[][] allData, int seed,
out double[][] trainData, out double[][] testData)
{
Random rnd = new Random(seed);
int totRows = allData.Length;
int numTrainRows = (int)(totRows * 0.80); // 80% hard-coded
int numTestRows = totRows - numTrainRows;
trainData = new double[numTrainRows][];
testData = new double[numTestRows][];

double[][] copy = new double[allData.Length][]; // ref copy of all data
for (int i = 0; i < copy.Length; ++i)
copy[i] = allData[i];

for (int i = 0; i < copy.Length; ++i) // scramble order
{
int r = rnd.Next(i, copy.Length); // use Fisher-Yates
double[] tmp = copy[r];
copy[r] = copy[i];
copy[i] = tmp;
}
for (int i = 0; i < numTrainRows; ++i)
trainData[i] = copy[i];

for (int i = 0; i < numTestRows; ++i)
testData[i] = copy[i + numTrainRows];
}

Again, there is a ton of indexing going on, which in my old age I find very hard to follow. Upon closer inspection, really, the only thing complicated here is the Fischer-Yates shuffle, which takes an array and randomly shuffles the order. The rest is pretty simply – we just want to shuffle, and then split into two arrays. Let’s extract the shuffle code (which happens to also be used and re-implemented later on):

let shuffle (rng:Random) (data:_[]) =
let copy = Array.copy data
for i in 0 .. (copy.Length - 1) do
let r = rng.Next(i, copy.Length)
let tmp = copy.[r]
copy.[r] <- copy.[i]
copy.[i] <- tmp
copy

We went a tiny bit fancy again here, and made the shuffle work on generic arrays; we also pass in the Random instance we want to use, so that we can control / repeat shuffles if we want, by passing a seeded Random. Does this work? Let’s check in FSI:

> [| 1 .. 10 |] |> shuffle (Random ());;
val it : int [] = [|6; 7; 2; 10; 8; 5; 4; 9; 3; 1|]

Looks reasonable. Let’s move on – we can now implement the makeTrainTest function.

let makeTrainTest (allData:_[], seed) =

let rnd = Random(seed)
let totRows = allData.Length
let numTrainRows = int (float totRows * 0.80) // 80% hard-coded

let copy = shuffle rnd allData
copy.[.. numTrainRows-1], copy.[numTrainRows ..]

Done. A couple of remarks here. First, F# is a bit less lenient than C# around types, so we have to be explicit when converting the number of rows to 80%, first to float, then back to int. As an aside, this used to annoy me a bit in the beginning, but I have come to really like having F# as this slightly psycho-rigid friend who nags me when I am taking a dangerous path (for instance, dividing two integers and hoping for a percentage).

Besides that, I think the code is markedly clearer. The complexity of the shuffle has been nicely contained, and we just have to slice the array to get a training and test sets. As an added bonus, we got rid of the out parameters, and that always feels nice and fuzzy.

I’ll leave it at for today; next time we’ll look at the second part, the learning algorithm itself. Before closing shop, let me make a couple of comments. First, the code is a tad shorter, but not by much. I haven’t really tried, and deliberately made only the changes I thought were needed. What I like about it, though, is that all the indexes are gone, except for the shuffle. In my opinion, this is a good thing. I find it difficult to keep it all in my head when more than one index is involved; when I need to also remember what columns contain special values, I get worried – and just find it hard to figure out what is going on. By contrast, I think makeTrainTest, for instance, conveys pretty directly what it does. makeAllData, in spite of some complexity, also maps closely the way I think about my goal: “I want to generate rows of inputs” – this is precisely what the code does. There is probably an element of culture to it, though; looping over arrays has a long history, and is familiar to every developer, and what looks readable to me might look entirely weird to some.

Easier, or more complicated than before? Anything you like or don’t like – or find unclear? Always interested to hear your opinion! Ping me on Twitter if you have comments.

22. March 2014 13:11

A couple of days ago, I got into the following Twitter exchange:

So why do I think FsCheck + XUnit = The Bomb?

I have a long history with Test-Driven Development; to this day, I consider Kent Beck’s “Test-Driven Development by Example” one of the biggest influences in the way I write code (any terrible code I might have written is, of course, to be blamed entirely on me, and not on the book).

In classic TDD style, you typically proceed by writing incremental test cases which match your requirements, and progressively write the code that will satisfy the requirements. Let’s illustrate on an example, a password strength validator. Suppose that my requirements are “a password must be at least 8 characters long to be valid”. Using XUnit, I would probably write something along these lines:

namespace FSharpTests

open Xunit
open CSharpCode

module Password validator tests =

[<Fact>]
let length above 8 should be valid () =
let validator = Validator ()


… and in the CSharpCode project, I would then write the dumbest minimal implementation that could passes that requirement, that is:

public class Validator
{
{
return true;
}
}


Next, I would write a second test, to verify the obvious negative:

namespace FSharpTests

open Xunit
open CSharpCode

module Password validator tests =

[<Fact>]
let length above 8 should be valid () =
let validator = Validator ()

[<Fact>]
let length under 8 should not be valid () =
let validator = Validator ()


This fails, producing the following output in Visual Studio:

… which forces me to fix my implementation, for instance like this:

public class Validator
{
{
{
return false;
}

return true;
}
}


Let’s pause here for a couple of remarks. First, note that while my tests are written in F#, the code base I am testing against is in C#. Mixing the two languages in one solution is a non-issue. Then, after years of writing C# test cases with names like Length_Above_8 _Should_Be_Valid, and arguing whether this was better or worse than LengthAbove8 ShouldBeValid, I find that having the ability to simply write “length above 8 should be valid”, in plain old English (and seeing my tests show that way in the test runner as well), is pleasantly refreshing. For that reason alone, I would encourage F#-curious C# developers to try out writing tests in F#; it’s a nice way to get your toes in the water, and has neat advantages.

But that’s not the main point I am interested here. While this process works, it is not without issues. From a single requirement, “a password must be at least 8 characters long to be valid”, we ended up writing 2 test cases. First, the cases we ended up are somewhat arbitrary, and don’t fully reflect what they say. I only tested two instances, one 7 characters long, one 8 characters long. This is really relying on my ability as a developer to identify “interesting cases” in a vast universe of possible passwords, hoping that I happened to cover sufficient ground.

This is where FsCheck comes in. FsCheck is a port of Haskell’s QuickCheck, a property-based testing framework. The term “property” is somewhat overloaded, so let’s clarify: what “Property” means in that context is a property of our program that should be true, in the same sense as mathematically, a property of any number x is “x * x is positive”. It should always be true, for any input x.

Install FsCheck via Nuget, as well as the FsCheck XUnit extension; you can now write tests that verify properties by marking them with the attribute [<Property>], instead of [<Fact>], and the XUnit test runner will pick them up as normal tests. For instance, taking our example from right above, we can write:

namespace FSharpTests

open Xunit
open FsCheck
open FsCheck.Xunit
open CSharpCode

module Specification =

[<Property>]
let square should be positive (x:float) =
x * x > 0.


Let’s run that – fail. If you click on the test results, here is what you’ll see:

FsCheck found a counter-example, 0.0. Ooops! Our specification is incorrect here, the square value doesn’t have to be strictly positive, and could be zero. This is an obvious mistake, let’s fix the test, and get on with our lives:

[<Property>]
let square should be positive (x:float) =
x * x >= 0.


More...

3. March 2013 11:01

Recently, I had a few interesting discussions on F# code readability. One argument I often hear about F# is that by virtue of its succinctness, it increases the signal-to-noise ratio. I certainly found this to be true: when the entire code fits on your screen, and you don’t have to scroll around to figure out what is going on, navigating a code base becomes significantly simpler.

Relatedly, because the F# syntax is so much lighter than C#, some of my coding habits evolved. I stick to the “one public type per file” guideline in C#, and initially did the same in F#. That didn’t last long: declaring a Record Type in F# is a one-liner, and dedicating an entire file to it seems… overkill:

type Person = { FirstName: string; LastName: string; BornOn: DateTime }


As a result, my F# solutions tend to contain less files, and each file is more “self-contained”, usually declaring a couple of types and implementing some operations involving these types in a module. Again, less navigation required: open one file, and the truth, the whole truth, and nothing but the truth is right there on your screen.

In my experience, this also makes refactoring tools much less important in F# than C#. The lack of refactoring tools in F# used to be one of my main gripes with using the language. At that point, I don’t really care that much any more, because I don’t really need them that badly. Sure, it would be nice to propagate a rename automatically – but lots of the refactoring tools I commonly use with C# deal with navigating around or moving pieces of code from file to file (extract class, method, etc…), all problems that are minor when your code sits in just a couple of files, and the “what class owns what responsibility” issue vanishes because your functions are at a module level.

Conversely, I have found myself annoyed a few times looking at F# code where succinctness erred on the side of obfuscation. This tendency for terse naming conventions seems to be a cultural heritage from other functional languages, and makes sense to an extent – functional code tends to focus on applying generic transformations to “things”, and not that much on what the “thing” might be.

As an illustration, I have seen often code along these lines:

match list with
| x::xs -> ...


No need to go full on Java on your code, but a bit of naming effort goes a long way in making code intelligible:

match list with


That being said, extreme terseness can be fun, at times – I don’t think I’ll see a C# Game of Life implementation that fits in a Tweet any time soon .

Another readability aspect I found interesting with F# code is that the order of declarations matters, and the order of the files in the project matters as well. This seemingly odd constraint has a good reason – it makes the awesome F# type inference work.

Over time, I actually began to appreciate this not as a constraint, but almost as a feature. One problem I keep running into when I look into a C# code base I am not familiar with is “damn! where should I start?”. There is no clear way to proceed through the code, and I have ended up countless times navigating haphazardly from class to class, hoping to stumble upon a solid starting point.

I don’t really have that problem with F# code bases – essentially, I either start from the first line of the first file, and read forward, or the last line of the last file, working my way back. Either way works; the first one reads like a constructive proof, walking you every step to the ineluctable conclusion, the second one starts with the “high point” of the code base, digging progressively into the nitty-gritty and assumptions that were made to get there.

Someone reacted by saying that I was “just rationalizing”. There is probably some truth in that – but I believe there is something to be said for having a natural reading order in a code base. As a side-note, this is also one of my minor annoyances with GitHub: in the browser, the files from an F# repository are displayed in alphabetical order, which loses the logical project organization.

I might also change my tune when I have to deal with a truly large F# code base, which hasn’t happened to me yet. At that point, I may long for more freedom in organizing my code, and, say, arrange it by topical folders. For the moment, though, this hasn’t been an issue for me!

26. January 2013 19:08

Phil Trelford recently released Foq, a small F# mocking library (with a very daring name). If most of your code is in F#, this is probably not a big deal for you, because the technique of mocking isn’t very useful in F# (at least in my experience). On the other hand, if your goal is to unit test some C# code in F#, then Foq comes in very handy.

So why would you want to write your unit tests in F# in the first place?

namespace CodeBase
{
using System;

public class Translator
{
public const string ErrorMessage = "Translation failure";

public Translator(ILogger logger, IService service)
{
this.logger = logger;
this.service = service;
}

public string Translate(string input)
{
try
{
return this.service.Translate(input);
}
catch (Exception exception)
{
this.logger.Log(exception);
return ErrorMessage;
}
}
}

public interface ILogger
{
void Log(Exception exception);
}

public interface IService
{
string Translate(string input);
}
}
We have a class, Translator, which takes 2 dependencies, a logger and a service. The main purpose of the class is to Translate a string, by calling the service. If the call succeeds, we return the translation, otherwise we log the exception and return an arbitrary error message.

This piece of code is very simplistic, but illustrates well the need for Mocking. If I want to unit test that class, there are 3 things I need to verify:

• when the translation service succeeds, I should receive whatever the service says is right,
• when the translation service fails, I should receive the error message,
• when the translation service fails, the exception should be logged.

In standard C#, I would typically resort to a Mocking framework like Moq or NSubstitute to test this. What the framework buys me is the ability to create cheaply a fake implementation for the interfaces, setup their behavior to whatever my scenario is (“stubbing”), and in the case of the logger, where I can’t observe through state whether the exception has been logged, verify that the proper call has been made (“mocking”).

This is how my test suite would look:

namespace MoqTests
{
using System;
using CodeBase;
using Moq;
using NUnit.Framework;

[TestFixture]
public class TestsTranslator
{
[Test]
public void Translate_Should_Return_Successful_Service_Response()
{
var input = "Hello";
var output = "Kitty";

var service = new Mock<IService>();
service.Setup(s => s.Translate(input)).Returns(output);

var logger = new Mock<ILogger>();

var translator = new Translator(logger.Object, service.Object);

var result = translator.Translate(input);

Assert.That(result, Is.EqualTo(output));
}

[Test]
public void When_Service_Fails_Translate_Should_Return_ErrorMessage()
{
var service = new Mock<IService>();
service.Setup(s => s.Translate(It.IsAny<string>())).Throws<Exception>();

var logger = new Mock<ILogger>();

var translator = new Translator(logger.Object, service.Object);

var result = translator.Translate("Hello");

Assert.That(result, Is.EqualTo(Translator.ErrorMessage));
}

[Test]
public void When_Service_Fails_Exception_Should_Be_Logged()
{
var error = new Exception();
var service = new Mock<IService>();
service.Setup(s => s.Translate(It.IsAny<string>())).Throws(error);

var logger = new Mock<ILogger>();

var translator = new Translator(logger.Object, service.Object);

translator.Translate("Hello");

logger.Verify(l => l.Log(error));
}
}
}


More...

1. December 2012 13:55

I have been obsessing about the following idea lately – what if I could run a FSI session from within Excel? The motivation behind this is double. First, one thing Excel is good at is creating and formatting charts. If I could use F# for data manipulation, and Excel for data visualization, I would be a happy camper. Then, I think F# via FSI could provide an interesting alternative for Excel automation. I’d much rather leverage existing .NET libraries to, say, grab data from the internet, than write some VBA to do that – and the ability to write live code in FSI would be less heavy handed that VSTO automation, and closer to what people typically do in Excel, that is, explore data. Having the ability to execute F# scripts would be, at least for me, very useful.

Seeing Tim Robinson’s awesome job with FsNotebook.net kicked me out of procrastination. Even though FsNotebook is still in early development, it provides a very nice user experience – on the web. If something that nice can be done on the web, it should be feasible on a local machine.

As an aside, Tim is looking for feedback and input on FsNotebook – go try it out, it’s really fun:

Anyways – this is the grand plan, now we need to start with baby steps. If I want to embed FSI in Excel (presumably via a VSTO add-in), I need a way to talk to FSI from .NET, so that I can create a Session and send arbitrary strings of code to be evaluated.

As usual, StackOverflow provided two good starting points (this answer, and this answer) – so I set out to look into the Process class, which I didn’t know much about, and attempted to spawn a FSI.EXE process, redirecting input and output. Turns out it’s not overly complicated – here are the 34 lines of code I ended up with so far (see it on GitHub):

namespace ClearLines.FsiRunner

open System.Diagnostics

type public FsiSession(fsiPath: string) =

let info = new ProcessStartInfo()
let fsiProcess = new Process()

do
info.RedirectStandardInput <- true
info.RedirectStandardOutput <- true
info.UseShellExecute <- false
info.CreateNoWindow <- true
info.FileName <- fsiPath

fsiProcess.StartInfo <- info

[<CLIEvent>]

[<CLIEvent>]

member this.Start() =
fsiProcess.Start()