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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 zero-filled 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 number-crunching 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] (http://en.kioskea.net/faq/616-multicore-cpu-how-to-disable-a-core#procedure-when-using-windows-vista-7-and-xp)

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 Matrix

100x100 Matrix

200x200

400x400

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/LICENSE-2.0

   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.