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README
ExMatrix
ExMatrix is an Elixir library implementing a parallel matrix multiplication algorithm with other utilities for working with matrices.
Installation
The latest version is 0.0.1
and requires Elixir ~> 1.0
.
Releases are published through hex.pm. Add as a dependency in your mix.exs
file:
defp deps do
[ { :exmatrix, "~> 0.0.1" } ]
end
Matrices
Matrices are expected to be lists of lists of numbers, so for example, a simple 2x2 matrix might look like
iex> matrix = [[0, 0], [1,1]]
[[0, 0], [1,1]]
To get an empty matrix you can use new_matrix
to generate a zerofilled matrix
iex> ExMatrix.new_matrix(2,2)
[[0, 0], [0,0]]
To test out the library, you can generate a random matrix using random_cells
by passing the number of rows, columns and a maximum value to be contained in each cell.
iex> random_cells(2, 2, 10)
[[3, 4], [9, 0]]
Multiplication
To multiply two matrices together you can call either multiply
or pmultiply
if you wish to do the multiplication in parallel.
iex> matrix_a = [[2,3], [3,5]]
[[2,3], [3,5]]
iex> matrix_b = [[1,2], [5,1]]
[[1,2], [5,1]]
iex> ExMatrix.multiply(matrix_a, matrix_b)
[[17, 1], [28, 1]]
Addition
Addition of matrices happens as you might expect, with the add
function
iex> matrix_a = [[0, 1, 2], [9, 8, 7]]
[[0, 1, 2], [9, 8, 7]]
iex> matrix_b = [[6, 5, 4], [3, 4, 5]]
[[6, 5, 4], [3, 4, 5]]
iex> ExMatrix.add(matrix_a, matrix_b)
[[6, 6, 6], [12, 12, 12]]
If you provide two matrices where the number of rows or columns differs, then an ArgumentError
is raised.
Subtraction
Subtraction is performed on two matrices (which must have the same dimentions) by using the subtract
function
iex> matrix_a = [[0, 1, 2], [9, 8, 7]]
[[0, 1, 2], [9, 8, 7]]
iex> from_matrix = [[6, 5, 4], [3, 4, 5]]
[[6, 5, 4], [3, 4, 5]]
iex> ExMatrix.subtract(matrix_a, from_matrix)
[[6, 4, 2], [6, 4, 2]]
If you provide two matrices where the number of rows or columns differs, then an ArgumentError
is raised.
Utility functions
Size
The size
function will return the number of rows and columns in your matrix.
iex> {rows, cols} = ExMatrix.size([[1,2,3], [4, 5, 6], [7, 8, 9]])
{3, 3}
iex> rows
3
Transpose
You can transpose a matrix so that the columns become rows (rotating the matrix by 90 degrees).
iex> ExMatrix.transpose([[1,2,3], [4, 5, 6], [7, 8, 9]])
[[1, 4, 7], [2, 5, 8], [3, 6, 9]]
Benchmarks
The initial aim of ExMatrix was to benchmark how well it performed when scaled across a differing number of CPU cores. Rather than measure the numbercrunching ability of Elixir, the benchmarks included measure how well it performs when large matrices are multiplied on 1, 2, 4 and 8 cores.
You can run the benchmarks yourself using the mix bench command.
MIX_ENV=prod mix bench
To try the benchmark with differing numbers of cores, depends on your operating system.
 OSX  Use Instruments.app where in the Preferences pane you can change the number of active cores.
 Linux  This page on stackexchange describes how to turn off individual cores on linux.
 Windows  You can turn off individual cores using the steps described here
OSX  8 cores, 16Gb RAM
The following results show the outcome of running the benchmarks on the author's machine (OSX, 8cores, 16Gb) using 1, 2, 4 and 8 cores. The matrix sizes used were 50x50, 100x100, 200x200, 400x400. There is a threshold (to be determined) below which the size of the computation on the matrix is apparently outweighed by the time taken to spawn and wait for the processes. The charts below show for the 50x50 and 100x100 matrices no better performance between 1 and 2 cores, and it maybe that the threshold is around this point.
Total times
The table below shows the times (in ms) as reported by benchfella.
50x50  100x100  200x200  400x400  

1 core  101  817  7881  74524 
2 cores  105  795  6028  51493 
4 cores  54  404  3340  27339 
8 cores  31  240  1858  15179 
50x50 Matrix
[](doc/img/50x50.png)
100x100 Matrix
[](doc/img/100x100.png)
200x200
[](doc/img/200x200.png)
400x400
[](doc/img/400x400.png)
License
Copyright 2015 A115 Ltd
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*Note that all licence references and agreements mentioned in the exmatrix README section above
are relevant to that project's source code only.