Multi-dimensional Swift math

What's New

Swift 4.0


Conversion to Swift 4.0


Upsurge is a math utilities library. It provides support for linear operations on vectors and matrices, and slicing of higher-dimensional tensors. It relies on Accelerate, which is a framework that provides high-performance functions for matrix math, digital signal processing, and image manipulation by harnessing SIMD instructions available in modern CPUs.

Upsurge is a fork of Surge which was abandoned for a while. Upsurge supports tensors and has better support for matrices and arrays. It provides a custom ValueArray class as an alternative to Swift's built-in Array. It being a class instead of a struct means that you can manage when and if it gets copied, making memory management more explicit. This also allows defining the += operator to mean addition instead of concatenation.


  • Tensor and tensor slicing: tensor.asMatrix(1, 1, 0...4, 0...4)
  • Matrix and matrix operations: let result = A * B′
  • ValueArrays with explicit copying and numeric operators: let result = A • B
  • Accelerate functions: let conv = convolution(signal: signal, kernel: kernel)


Upsurge supports both CocoaPods (pod 'Upsurge') and Carthage (github "aleph7/Upsurge"). For macOS apps you can use the Swift Package Manager to install Upsurge by adding the proper description to your Package.swift file:

import PackageDescription

let package = Package(
    name: "YOUR_PROJECT_NAME",
    targets: [],
    dependencies: [
        .Package(url: "", Version(0,8,.max)),


Arrays and vector operations

All of Upsurge's linear (1-dimensional) operations can be performed on anything that conforms to LinearType. Swift's built-in arrays and array slices conform to LinearType, of course. But Upsurge also defines the ValueArray class to store a one-dimensional collection of values. ValueArray is very similar to Swift's Array but it is optimized to reduce unnecessary memory allocation. These are the most important differences:

  • Its instances have a fixed size defined on creation. When you create a ValueArray you can define a capacity var a = ValueArray<Double>(capacity: 100) and then append elements up to that capacity. Or you can create it with specific elements var a: ValueArray = [1.0, 2.0, 3.0] but then you can't add any more elements after.
  • It is a class. That means that creating a new variable will only create a reference and modifying the reference will also modify the original. For instance doing var a: ValueArray = [1, 2, 3]; var b = a and then b[0] = 5 will result in a being [5, 2, 3]. If you want to create a copy you need to do var b = ValueArray(a) or var b = a.copy().
  • You can create an uninitialized ValueArray by doing var a = ValueArray<Double>(capacity: n) or var a = ValueArray<Doube>(count: n). This is good for when you are going to fill up the array yourself. But you can also use var a = ValueArray(count: n, repeatedValue: 0.0) if you do want to initialize all the values.

Creating arrays

Create a ValueArray with specific literal elements when you know ahead of time what the contents are, and you don't need to add more elements at a later time:

let a: ValueArray = [1.0, 3.0, 5.0, 7.0]

Create a ValueArray with a capacity and then fill it in when you are loading the contents from an external source or have a very large array:

let a = ValueArray<Double>(capacity: 100)
for v in intputSource {

Finally there is a way of initializing both the capacity and the count of a ValueArray. You should rarely need this but it's there for when you are doing operations on existing arrays using low-level APIs that take pointers:

func operation(a: ValueArray<Double>) {
    let N = a.count
    let b = ValueArray<Double>(count: N)
    // ...

Vector arithmetic

You can perform operations on ValueArray in an intuitive manner:

let a: ValueArray = [1.0, 3.0, 5.0, 7.0]
let b: ValueArray = [2.0, 4.0, 6.0, 8.0]
let addition = a + b // [3.0, 7.0, 11.0, 15.0]
let product  = a  b // 100.0

Matrix operations

import Upsurge

let A = Matrix<Double>([
    [1,  1],
    [1, -1]
let C = Matrix<Double>([

// find B such that A*B=C
let B = inv(A) * C // [2.0, 1.0]′

// Verify result
let r = A*B - C    // zero   


A block Matrix can be formed by repeating a 1-D ValueArray or 2-D Matrix mxn times.

import Upsurge

let a = ValueArray = [1.0, 2.0]
// Tile source array 2 times in each directon,
// returning a 2X4 block matrix
let A = a.tile(2, 2)

let B = Matrix<Double>([
    [1.0,  2.0],
    [3.0,  4.0]
// Tile source matrix 2 times in each directon,
// returning a 4x4 block matrix
let r = B.tile(2, 2)


The Tensor class makes it easy to manipulate multi-dimensional data. You can easily slice or flatten a tensor to get matrices and vectors that you can operate on.


Upsurge is available under the MIT license. See the LICENSE file for more info.


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Last updated: Thu May 30 2024 01:33:56 GMT-0900 (Hawaii-Aleutian Daylight Time)