Matrex - A blazing fast matrix library for Elixir/Erlang with C implementation using CBLAS (Machine Learning)

[versilov]

Could not wait for the missing Elixir ML libraries to appear, so, I wrote one myself, taking https://github.com/sdwolfz/exlearn as a foundation.

The name is Matrex and it’s super-fast (compared to pure Elixir implementations) matrix manipulation lib.

Critical code is written in C using CBLAS subroutines and linked as Erlang NIFs.
It’s about 50-5000 times faster, than pure Elixir.

In the repo you will find MathLab fmincg() ported to Elixir with the help of the library
and logistic regression MNIST digits recognition exercise from Andrew Ng’s ML course implemented in Elixir (15 times faster, than Octave implentation).

It can be used like this:

y = Matrex.load("y.mtx")

j =
      y
      |> Matrex.dot_tn(Matrex.apply(h, :log), -1)
      |> Matrex.substract(
        Matrex.dot_tn(
          Matrex.substract(1, y),
          Matrex.apply(Matrex.substract(1, h), :log)
        )
      )
      |> Matrex.scalar()
      |> (fn
            NaN -> NaN
            x -> x / m + regularization
          end).()

Or like this:

    import Matrex.Operators
   
    h = sigmoid(x * theta)
    l = ones(size(theta)) |> set(1, 1, 0.0)

    j = (-t(y) * log(h) - t(1 - y) * log(1 - h) + lambda / 2 * t(l) * pow2(theta)) / m

I’ve also created a Jupyter notebook with logistic regression algorithm in Elixir built with the help of this library.

Please, check Matrex on GitHub,
take a look at Matrex hex docs,
and tell me what you think of it.

[chrismcg]

This is great to see, nice work!

[grych]

Man, this is so great!

[michalmuskala]

This looks really good!

I wonder about the decision of keeping everything in a binary with sizes in front vs having a C struct and a nif resource. Wouldn’t the later be easier to handle and possibly also slightly faster on some operations?

[versilov]

Michal,

I considered using NIF resource, but decided to stay with explicit binary for 3 reasons:

1. I don’t want to add unnecessary NIFs, when Elixir gives the same speed or operation is not time-critical.
2. Pattern matching for simple operations, like getting the size of the matirx.
3. There is an idea to implement Elixir versions of all the NIFs, so they would
   work as fallback functions that work everywhere. E.g., when NIFs would fail to compile for some reasons. I don’t know if it’s worth the effort, but don’t want to cut off such possibilities.

And NIF resource leaves us only with , AFAIK?

%Matrex{} struct now works mostly for the purpose of implementing protocols and behaviours (Inspect, Enum and Access). It gives the opportunity to add more fields later, to distinguish matrices with
different element types and sizes, different matrix shapes and so on.

So, I believe, the current setup gives greater flexibility in future development.
But I did not dig deep into NIF resources, so, maybe I am missing something.

[michalmuskala]

I guess you’re right.

Another approach I could see would be to have columns and rows directly in the struct. What do you think? This could allow users to do matrix.rows and matrix.cols or similar. You could possibly unpack those in the elixir layer and call the NIFs with 3 arguments instead of one.
I could imagine then the “data” field could be either a binary or a NIF resource depending on what’s more useful and the Elixir code would treat it as completely opaque.

[versilov]

Yeah, thought about it also, but postponed for two reasons:

1. Did not want to hinder library release by rewriting the codebase I inherited from exlearn.
2. It gives only more clean access to some properties (matrix.rows instead of matrix[:rows]),
   not the highest priority feature for now.

I definitely plan to experiment with this approach in the future to see how it would work in real life.

Thanks for the thorough feedback, I am amazed with the Elixir community:)

[OvermindDL1]

This does look very awesome!

Have you thought about adding a kernel builder interface? I.E. you’d build up a command queue then ‘submit’ it to the BLAS backend to perform it all as quickly as possible (some have JIT-style engines that can take such a command queue and run it as optimized assembly over the dataset, potentially even to other hardware optimized for the purpose).

[versilov]

Thank you!

Yes, I think what you’ve described is the second library we desperately need in Elixir to make it shine in machine learning.

Have a look at these two repos, cuda and neuro: https://github.com/sirin-tech
They use kernels, defined in PTX ISA internal assembly language, to feed them into NVIDIA CUDA interface.
The only drawback is that they have zero documentation, as far as I know.

I plan to contact these guys and may be visit them in person to unite development efforts. I hope, these libs
need only good docs and some polishing, so we can get the next piece of Elixir ML puzzle faster:)

[PragTob]

This looks great, thank you very much for your work!

[versilov]

Thanks for all your praise!

As we move towards version 1.0, here come new features:

• Heatmap of the matrix with Matrex.heatmap/3
  This one is the coolest. Now you can monitor learning process and get insights from your matrices right inside terminal. Just have a look:
   
   
   
   

• reshape/3 and concat/2. Fast and convenient matrix creation from enumerable of elements or other matrices.
  Here’s how you can load MNIST digits dataset and show a subset of the data with one line of code:
  

  

• Other minor additions: normalize/1, resize/2, min_finite/1, max_finite/1, to_row/1, to_columns/1, list_of_rows/2.

Would be glad to hear your feedback, bug reports and ideas.

[OvermindDL1]

Hah, that looks exceptionally cool!

/me needs to find time to play with it soon…

[chrismcg]

I definitely want to play with this now I just tried installing it on macOS 10.12.6 and am getting:

% mix compile
==> matrex
Compiling: native/src/matrix.c
In file included from native/src/matrix.c:1:
native/src/../include/matrix.h:4:10: fatal error: 'cblas.h' file not found
#include <cblas.h>
         ^~~~~~~~~

Is there something else I need to do to have it find the headers from the Accelerate framework?

[chrismcg]

So I had to add:

	CFLAGS += -I/System/Library/Frameworks/Accelerate.framework/Versions/Current/Frameworks/vecLib.framework/Versions/Current/Headers/

To the ifeq (BLAS, blas) section of the Makefile in deps/matrex to get it to compile.

[OvermindDL1]

Or could just use cmake and hunter or so to always acquire and use clblas or openblas or whatever as well?

[versilov]

Thanks for the bug report. I’ve added include path to the Makefile.

Please, check if it works on your systems.

[chrismcg]

master branch compiles now here. Thanks for the quick update.

[versilov]

Compared Matrex performance to NumPy. Looks like we are going more or less on par, with Matrex being two times faster on element-wise operations and a bit slower on dot product.

2015 MacBook Pro, 2.2 GHz Core i7, 16 GB RAM

Operations are performed on 3000×3000 matrices filled with random numbers.

You can run benchmarks from the /bench folder with python numpy_bench.py and MIX_ENV=bench mix bench commands.

NumPy

benchmark         iterations	average time
np.divide(A, B)   30            15.43 ms/op
np.add(A, B)      100           14.62 ms/op
sigmoid(A)        50            93.28 ms/op
np.dot(A, B)      10            196.57 ms/op

Matrex

benchmark     iterations   average time
divide(A, B)         200   7.32 ms/op (~ 2× faster)
add(A, B)            200   7.71 ms/op (~ 2× faster)
sigmoid(A)            20   71.47 ms/op (23% faster)
dot(A, B)             10   213.31 ms/op (8% slower)

[sym_num]

I am creating a framework for Deep Learning. Matrex is very useful. Thank you.

[sym_num]

Mr. Versilov, your Matrex is very helpful. Thank you so much. Thanks to you, I can easily use CBLAS from Elixir.
By the way, I have a request. Could you make a library that uses CuBLAS（NVIDIA) from Elixir? Or please tell me how to use CuBLAS from Elixir.

Kenichi Sasagawa