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# SwiftMatrix

SwiftMatrix is a Swift library that leverages Accelerate framework power to provide high-performance functions for matrix math. Its main purpose is to serve as vector calculation core for machine learning and deep learning projects.

SwiftMatrix has been developed trying to mimic syntax used in linear algebra as much as possible in order to simplify coding of complex operations

Credits go to Surge Library.

## Installation

Using XCode v.12 and upper add a package dependancy by selecting File > Swift Packages > Add Package Dependancy ... and entering following URL https://github.com/theolternative/SwiftMatrix

SwiftMatrix uses Swift 5 and Accelerate Framework

## Usage

import SwiftMatrix

let A = Matrix([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]) // 3x2 Matrix
let B = Matrix([[1.0, 2.0], [3.0, 4.0]]) // 2x2 Matrix
let dotProduct = A°B

SwiftMatrix supports following element-wise operations:

• comparison
• basic arithmetic: addition, subtraction, multiplication, division, power and square root
• logarithms and exponent
• trigonometric and hyperbolic functions
• statistics functions

Following matrix specific operations are also supported:

• Dot product
• Transpose
• Sum of rows or columns

Basic arithmetic operations can be performed on

• matrices of same sizes
• matrix and scalar (or scalar and matrix)
• matrix and vector of same column or row size (BROADCASTING)

All operations are performed in Double type

### Initialize

You can initialize a matrix by passing an array of array of Double, by repeating a value, a row or a column, by setting random numbers

let T = Matrix([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]])
let X = Matrix(rows: 3, columns: 4, repeatedValue: 0.0)
let Y = Matrix(columnVector: Matrix.random(rows: 4, columns: 1), columns: 5)
let Z = Matrix.random(rows: 4, columns: 5)

### Subscript

You can get or set a single element, a single row or a single column by using .all placeholder

var X = Matrix.diagonal(rows: 3, columns: 3, repeatedValue: 1.0)
X[1,1]=5.0
X[2,2]=X[1,1]
X[.all,0]=X[.all,1]
X[0,.all]=X[1,.all]

### Comparison

Equatable == is available and returns a boolean value <, <=, >, >= between matrices A and B of same sizes are supported and return a matrix C of same size where C[i,j] = 1.0 if A[i,j] op B[i,j] is true, 0.0 otherwise <, <=, >, >= between matrix A and scalar B are supported and return a matrix C of same size of B where C[i,j] = 1.0 if A[i,j] op B is true, 0.0 otherwise

let X = Matrix.random(rows: 3, columns: 3)
let Y = Matrix.random(rows: 3, columns: 3)
let V = X < Y
let Z = X < 1.0

### Arithmetic

+, -, *, /, ^ and √ are supported +=, -=, *=, /= compound assignments are supported Vector broadcasting is available for +, -, *, /

let X = Matrix.diagonal(rows: 5, columns: 5, repeatedValue: 1.0)
let Y = Matrix.diagonal(rows: 5, columns: 5, repeatedValue: 2.0)
var Z = X+Y
Z = Z + 1.0
Z = 1.0 + X
Z = X + X[.all, 1] // Broadcasting vector
Z = X * Y - Y / X
Z *= Z
Z = X^Y
Z = √Z

### Log and Exp

Natural log and exp, log base 2 and log base 10

• log(Matrix)
• log2(Matrix)
• log10(Matrix)
• exp(Matrix)
let X = Matrix.random(rows: 4, columns: 3)
let Y = log(X)
var Z = exp(Y)
Z = log10(Z)

### Trigonometry

Generic trig functions and hyperbolic versions are supoorted:

• sin(Matrix)
• cos(Matrix)
• tan(Matrix)
• arcsin(Matrix)
• arccos(Matrix)
• arctan(Matrix)
• sinh(Matrix)
• cosh(Matrix)
• tanh(Matrix)
• arcsinh(Matrix)
• arccosh(Matrix)
• arctanh(Matrix)
let X = Matrix.random(rows: 4, columns: 3)
let Y = sin(X)
let Z = arcsin(Y)

### Statistic functions

Some statistical functions are supported

• abs(Matrix) : returns a matrix with absolute values of elements
• min(Matrix) : returns minimum value across all elements
• max(Matrix) : returns maximm value across all elements
• maxel(z: Double, Matrix) : returns a matrix M where M[i,j]=max(z, M[i,j])
• minel(z: Double, Matrix) : returns a matrix M where M[i,j]=min(z, M[i,j])
• shuffle(Matrix, .row|.column) : returns a matrix M with rows or columns shuffled
let X = Matrix.random(rows: 4, columns: 3)
let Y = min(X)
let Z = maxel(1.0, Y)

### Matrix operators

Dot product, transpose and sum of rows/columns are supported

• Matrix ° Matrix : dot product
• Matrix′ : transpose
• Σ(Matrix, .row|.column|.both) : matrix containing sum of rows/columns/all elements
let X = Matrix.random(rows: 4, columns: 3)
let Y = X ° X′
let Z = Σ(Y, .row)

### Performance

Dot product uses cblas_dgemm BLAS library function Addition and subtraction between 2 matrices use cblas_daxpy BLAS library function which has been proved to be faster than vDSP counterpars vDSP_vaddD and vDSP_vsubD Division and multiplication between matrices use vDSP_vmulD and vDSP_vdivD Addition, subtraction, division and multiplication between matrix and scalar use vDSP.add, vDSP.subtract, vDSP.divide and vDSP.multiply which are faster than vDSP_vsaddD, vDSP_vssubD, vDSP_vsdivD and vDSP_vsmulD

## v1.1.4 - 2021-01-08T18:13:04

Corrected bug in addition and subtraction

## v1.1.2 - 2021-01-05T18:18:41

Added comparison between matrix and scalar Added tests for Σ function and comparison Added sum of all elements

## v1.1.1 - 2021-01-04T00:39:06

Arithmetic operations between matrix and scalar and between matrix and vector (broadcasting) have been completely rewritten in order to avoid allocation of container matrix for scalar or vector resulting in dramatic speed increase