MathSwift

MathSwift is an iOS Dynamic Framework written in Swift which supports complex mathmatical operations. Currently it mainly support matrix and some advanced linear algrbra operations such as singular value decomposition. It may also serve as a demostration of good practice for developing iOS/OSX dynamic frameworks in pure Swift, including a complete set of unit tests.

Installation

MathSwift supports installation using Carthage. You can integrate MathSwift with your project by adding the following line in your Cartfile:

github "huangenyan/MathSwift"

To use MathSwift in your code, just remember to import it in your source code files:

import MathSwift

Usage

The full documentation of MathSwift isn't available yet. However, each public method is well commented in the code so you may refer to it. Here I just show some examples.

Create a matrix

There are several ways for initializing a matrix:

// Create with dimension
let m1 = Matrix(rows:3, columns:3)

// Create with 2D-array
let m2 = Matrix(elements:[[11,12,13],[21,22,23],[31,32,33]])

Access elements

You can access the element(s) in the matrix by using the subscript syntax with the format m[row(s), column(s)]:

var m = Matrix(elements:[[11,12,13],[21,22,23],[31,32,33]])

// Index is an integer. subscript syntax will always return a Matrix so we need to convert it to double manually.
// Get
let a11: Double = m[0,0].toDouble()!
// Set
m[0,0] = a11.toMatrix()
m[0,0] = 0.0 // Double literal will be automatically converted to Matrix

// Index is an array.
// Get
let firstCol = m[[0,1,2],0] // == [[11],[21],[31]]
let firstLastCol = m[[0,1,2],[0,2]] // == [[11,13],[21,23],[31,33]]
// Set
m[[0,1,2],0] = firstCol

// Index is a range.
// Get
let firstTwoCol = m[[0,1,2],0..<2]
let upperLeft4 = m[0...1,0...1]
// Set
m[0...1,0...1] = upperLeft4

// Index is `ALL`
// Get
let firstRow = m[0,ALL] // equals to m[0,[0,1,2]]
// Set
m[0,ALL] = firstRow

Operations on matrix

I hope the code below will explain everything about operators :]. Please note this is not Swift code but just some intuitive expressions, which is similar to the matrix expression in Matlab.

// Addition and subtraction
[1 2; 3 4] + [1 1; 1 1] = [2 3; 4 5]
[1 2; 3 4] - [1 1; 1 1] = [0 1; 2 3]
[1 2; 3 4] + 1 = [2 3; 4 5]
1 + [1 2; 3 4] = [2 3; 4 5]
[1 2; 3 4] - 1 = [0 1; 2 3]
-[1 2; 3 4] = [-1 -2; -3 -4]
1 - [1 2; 3 4] = [0 -1; -2 -3]

// Element-wise multiplication/division
[1 2; 3 4] *~ [2 2; 2 2] = [2 4; 6 8]
[2 4; 6 8] /~ [2 2; 2 2] = [2 4; 6 8]

// Scalar multiplication/division
[1 2; 3 4] * 2 = [2 4; 6 8]
2 * [1 2; 3 4] = [2 4; 6 8]
[2 4; 6 8] / 2 = [1 2; 3 4]
12 / [1 2; 3 4] = [12 6; 4 3]

// Element-wise exponentiation
[1 2; 3 4] ^~ 2 = [1 4; 9 16]

// Matrix exponentiation
[1 2; 3 4] ^ 2 = [1 2; 3 4] * [1 2; 3 4] = [7 10; 15 22]

// Production of two matrices
[1 2; 3 4] * [1 2; 3 4] = [7 10; 15 22]

// Horizontal concantenation
[1 2; 3 4] +++ [5; 6] = [1 2 5; 3 4 6]

// Vertical concantenation
[1 2; 3 4] --- [5 6] = [1 2; 3 4; 5 6]

The transpose, inverse and some other properties of a matrix is available as well. For example, you can get the transpose of a matrix by m.transpose.

huangenyan / MathSwift