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https://github.com/rugheid/Swift-MathEagle

A general math framework to make using math easy. Currently supports function solving and optimisation, matrix and vector algebra, complex numbers, big int, big frac, big rational, graphs and general handy extensions and functions.
https://github.com/rugheid/Swift-MathEagle

biginteger complex-numbers graph-algorithms mathematics matrix-math prime-numbers swift vector-math

Last synced: 7 days ago
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A general math framework to make using math easy. Currently supports function solving and optimisation, matrix and vector algebra, complex numbers, big int, big frac, big rational, graphs and general handy extensions and functions.

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README 

        
# Swift-MathEagle



![Travis](https://travis-ci.org/rugheid/Swift-MathEagle.svg?branch=master)



MathEagle is named after the golden eagle, since this is the fastest bird in the world (in horizontal flight).



This project is meant to make math easy in swift without losing performance. The syntax is designed to be as simple as

possible. Contributors are always welcome, the more the merrier!



## Warning!

MathEagle is still in its initial development phase so the syntax still changes frequently.



# Installation

The fastest way to add MathEagle to your project is to download it as a zip file and drag all files in the MathEagle/Source

folder to your project. Make sure to add them to your target. For Mac applications you can use the generated framework,

check the wiki for more information. I'm currently working on an iOS framework.



MathEagle requires gmp (GNU multiple precision arithmetic library) be installed.  Install gmp via

``brew install gmp`` assuming you have Homebrew installed.



# Supported Xcode Versions

MathEagle is fully compatible with:

- Xcode 9 and Swift 4



# Currently Supported

* Basic extensions, operators like power (** operator) and functions like sign and factorial

* Prime functions

* Complex numbers

* Single variable function root solving

* Single variable function optimization

* Matrix and Vector math

* Basic graph algorithms



MathEagle is fully generic, so almost all classes and functions work with any type (even types you define). MathEagle

vectors for example can also be of type Int, while the Float and Double type vectors use Accelerate in the background

for speed.



Take a look at the Wiki for documentation.



# Advantages

The biggest advantage of MathEagle is that it's totally generic. You can create matrices and vectors and use functions

like isPrime with all numeric types. You can even create your own type (let's say Quaternion), implement the protocols

and everything just works. Of course specific implementations are overloaded to maintain performance. Vector addition

for Float vectors for example is overloaded to use the Accelerate framework.



# Benchmarking

First benchmarking tests show that MathEagle is as fast as Python's famous numpy. You can check the "Benchmarking Files"

folder in MathEagle's tests. (These tests were conducted on an early 2013 15-inch Retina Macbook Pro with a

2.7 GHz Intel Core i7 and 16 GB of RAM.



Here are some plots for Vector addition:

![Vector Addition Float Benchmarking](/MathEagleTests/Benchmarking Files/Plot Images/VectorAdditionFloat.png)

![Vector Addition Double Benchmarking](/MathEagleTests/Benchmarking Files/Plot Images/VectorAdditionDouble.png)



# To Do

- [ ] Documentation

- [ ] Further General Development

- [ ] Incorporate Accelerate for all applications