matrex alternatives and similar packages
Based on the "Algorithms and Data structures" category

datastructures
A collection of protocols, implementations and wrappers to work with data structures. 
exconstructor
An Elixir library for generating struct constructors that handle external data with ease. 
exmatrix
ExMatrix is a small library for working with matrices, originally developed for testing matrix multiplication in parallel. 
parex
Parallel Execute (Parex) is an Elixir module for executing multiple (slow) processes in parallel. 
blocking_queue
BlockingQueue is a simple queue implemented as a GenServer. It has a fixed maximum length established when it is created. 
MapDiff
Calculates the difference between two (nested) maps, and returns a map representing the patch of changes. 
cuid
Collisionresistant ids optimized for horizontal scaling and sequential lookup performance, written in Elixir. 
paratize
Elixir library providing some handy parallel processing (execution) facilities that support configuring number of workers and timeout. 
ratio
Adds Rational Numbers and allows them to be used in common arithmatic operations. Also supports conversion between Floats and Rational Numbers. 
Mappable
Simple module that provides unified, simple interface for converting between different dictionarylike data types in Elixir. 
clope
Elixir implementation of CLOPE: A Fast and Effective Clustering Algorithm for Transactional Data.
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README
Matrex
Fast matrix manipulation library for Elixir implemented in C native code with highly optimized CBLAS sgemm() used for matrix multiplication.
For example, vectorized linear regression is about 13 times faster, than Octave single threaded implementation.
It's also memory efficient, so you can work with large matrices, about billion of elements in size.
Based on matrix code from https://github.com/sdwolfz/exlearn
Benchmarks
Comparison with NumPy
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
logistic_cost() 1000 1.23 ms/op
np.divide(A, B) 100 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
logistic_cost() 1000 1.23 ms/op (on par)
divide(A, B) 200 7.32 ms/op (~ 2× faster)
add(A, B) 200 7.71 ms/op (~ 2× faster)
sigmoid(A) 50 71.47 ms/op (23% faster)
dot(A, B) 10 213.31 ms/op (8% slower)
Comparison with pure Elixir libraries
Slaughter of the innocents, actually.
2015 MacBook Pro, 2.2 GHz Core i7, 16 GB RAM
Dot product of 500×500 matrices
Library  Ops/sec  Compared to Matrex 

Matrex  674.70  
Matrix  0.0923  7 312.62× slower 
Numexy  0.0173  38 906.14× slower 
ExMatrix  0.0129  52 327.40× slower 
Dot product of 3×3 matrices
Library  Ops/sec  Compared to Matrex 

Matrex  3624.36 K  
GraphMath  1310.16 K  2.77x slower 
Matrix  372.58 K  9.73x slower 
Numexy  89.72 K  40.40x slower 
ExMatrix  35.76 K  101.35x slower 
Transposing 1000x1000 matrix
Library  Ops/sec  Compared to Matrex 

Matrex  428.69  
ExMatrix  9.39  45.64× slower 
Matrix  8.54  50.17× slower 
Numexy  6.83  62.80× slower 
Example
Complete example of Matrex library at work: Linear regression on MNIST digits (Jupyter notebook)
Visualization
Matrex implements Inspect
protocol and looks nice in your console:
It can even draw a heatmap of your matrix in console! Here is an animation of logistic regression training with Matrex library and some matrix heatmaps:
Installation
The package can be installed
by adding matrex
to your list of dependencies in mix.exs
:
def deps do
[
{:matrex, "~> 0.6"}
]
end
MacOS
Everything works out of the box, thanks to Accelerate framework. If you encounter a compilation error
native/src/matrix_dot.c:5:10: fatal error: 'cblas.h' file not found
then make sure the XCode commandline tools are installed (xcodeselect install
).
If the error still not resolved, for MacOS Mojave, run
open /Library/Developer/CommandLineTools/Packages/macOS_SDK_headers_for_macOS_10.14.pkg
to restore /usr/include and /usr/lib.
On MacOS 10.15 this error can be solved with
export CPATH=/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/
or with
C_INCLUDE_PATH=/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/System/Library/Frameworks/Accelerate.framework/Frameworks/vecLib.framework/Headers mix compile
Ubuntu
You need to install scientific libraries for this package to compile:
> sudo aptget install buildessential erlangdev libatlasbasedev
Windows
It will definitely work on Windows, but we need a makefile and installation instruction. Please, contribute.
Choosing which BLAS to use
With the help of MATREX_BLAS
environment variable you can choose which BLAS library to link with.
It can take values blas
(the default), atlas
, openblas
or noblas
.
The last option means that you compile C code without any external dependencies, so, it should work anywhere with a C compiler place:
$ mix clean
$ MATREX_BLAS=noblas mix compile
Access behaviour
Access behaviour is partly implemented for Matrex, so you can do:
iex> m = Matrex.magic(3)
#Matrex[3×3]
┌ ┐
│ 8.0 1.0 6.0 │
│ 3.0 5.0 7.0 │
│ 4.0 9.0 2.0 │
└ ┘
iex> m[2][3]
7.0
Or even:
iex> m[1..2]
#Matrex[2×3]
┌ ┐
│ 8.0 1.0 6.0 │
│ 3.0 5.0 7.0 │
└ ┘
There are also several shortcuts for getting dimensions of matrix:
iex> m[:rows]
3
iex> m[:size]
{3, 3}
calculating maximum value of the whole matrix:
iex> m[:max]
9.0
or just one of it's rows:
iex> m[2][:max]
7.0
calculating onebased index of the maximum element for the whole matrix:
iex> m[:argmax]
8
and a row:
iex> m[2][:argmax]
3
Math operators overloading
Matrex.Operators
module redefines Kernel
math operators (+, , *, / <>) and
defines some convenience functions, so you can write calculations code in more natural way.
It should be used with great caution. We suggest using it only inside specific functions
and only for increased readability, because using Matrex
module functions, especially
ones which do two or more operations at one call, are 23 times faster.
Usage example
def lr_cost_fun_ops(%Matrex{} = theta, { %Matrex{} = x, %Matrex{} = y, lambda } = _params)
when is_number(lambda) do
# Turn off original operators
import Kernel, except: [: 1, +: 2, : 2, *: 2, /: 2, <>: 2]
import Matrex.Operators
import Matrex
m = y[:rows]
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
grad = (t(x) * (h  y) + (theta <> l) * lambda) / m
{scalar(j), grad}
end
The same function, coded with module methods calls (2.5 times faster):
def lr_cost_fun(%Matrex{} = theta, { %Matrex{} = x, %Matrex{} = y, lambda } = _params)
when is_number(lambda) do
m = y[:rows]
h = Matrex.dot_and_apply(x, theta, :sigmoid)
l = Matrex.ones(theta[:rows], theta[:cols]) > Matrex.set(1, 1, 0)
regularization =
Matrex.dot_tn(l, Matrex.square(theta))
> Matrex.scalar()
> Kernel.*(lambda / (2 * m))
j =
y
> Matrex.dot_tn(Matrex.apply(h, :log), 1)
> Matrex.subtract(
Matrex.dot_tn(
Matrex.subtract(1, y),
Matrex.apply(Matrex.subtract(1, h), :log)
)
)
> Matrex.scalar()
> (fn
:nan > :nan
x > x / m + regularization
end).()
grad =
x
> Matrex.dot_tn(Matrex.subtract(h, y))
> Matrex.add(Matrex.multiply(theta, l), 1.0, lambda)
> Matrex.divide(m)
{j, grad}
end
Enumerable protocol
Matrex implements Enumerable
, so, all kinds of Enum
functions are applicable:
iex> Enum.member?(m, 2.0)
true
iex> Enum.count(m)
9
iex> Enum.sum(m)
45
For functions, that exist both in Enum
and in Matrex
it's preferred to use Matrex
version, beacuse it's usually much, much faster. I.e., for 1 000 x 1 000 matrix Matrex.sum/1
and Matrex.to_list/1
are 438 and 41 times faster, respectively, than their Enum
counterparts.
Saving and loading matrix
You can save/load matrix with native binary file format (extra fast) and CSV (slow, especially on large matrices).
Matrex CSV format is compatible with GNU Octave CSV output, so you can use it to exchange data between two systems.
Example
iex> Matrex.random(5) > Matrex.save("rand.mtx")
:ok
iex> Matrex.load("rand.mtx")
#Matrex[5×5]
┌ ┐
│ 0.05624 0.78819 0.29995 0.25654 0.94082 │
│ 0.50225 0.22923 0.31941 0.3329 0.78058 │
│ 0.81769 0.66448 0.97414 0.08146 0.21654 │
│ 0.33411 0.59648 0.24786 0.27596 0.09082 │
│ 0.18673 0.18699 0.79753 0.08101 0.47516 │
└ ┘
iex> Matrex.magic(5) > Matrex.divide(Matrex.eye(5)) > Matrex.save("nan.csv")
:ok
iex> Matrex.load("nan.csv")
#Matrex[5×5]
┌ ┐
│ 16.0 ∞ ∞ ∞ ∞ │
│ ∞ 4.0 ∞ ∞ ∞ │
│ ∞ ∞ 12.0 ∞ ∞ │
│ ∞ ∞ ∞ 25.0 ∞ │
│ ∞ ∞ ∞ ∞ 8.0 │
└ ┘
NaN and Infinity
Float special values, like :nan
and :inf
live well inside matrices,
can be loaded from and saved to files.
But when getting them into Elixir they are transferred to :nan
,:inf
and :neg_inf
atoms,
because BEAM does not accept special values as valid floats.
iex> m = Matrex.eye(3)
#Matrex[3×3]
┌ ┐
│ 1.0 0.0 0.0 │
│ 0.0 1.0 0.0 │
│ 0.0 0.0 1.0 │
└ ┘
iex> n = Matrex.divide(m, Matrex.zeros(3))
#Matrex[3×3]
┌ ┐
│ ∞ NaN NaN │
│ NaN ∞ NaN │
│ NaN NaN ∞ │
└ ┘
iex> n[1][1]
:inf
iex> n[1][2]
:nan
Creating Matrex logo from MNIST letters
iex(166)> matrex_logo = \
...(166)> "../emnist/emnistletterstestimagesidx3ubyte" \
...(166)> > Matrex.load(:idx) \
...(166)> > Access.get(9601..10200) \
...(166)> > Matrex.list_of_rows() \
...(166)> > Enum.reduce(fn x, sum > add(x, sum) end) \
...(166)> > Matrex.reshape(28, 28) \
...(166)> > Matrex.transpose() \
...(166)> > Matrex.resize(2) \
...(166)> > Matrex.heatmap(:color24bit)