Swift Matrix and Machine Learning Library

Apple’s Swift is a high level language that’s asking for some numerical library to perform computation fast or at the very least easily. A way to have iOS run high-level code similar to Python or Matlab is something I’ve been waiting for, and am incredibly excited to see the results. This will make porting complex signal processing algorithms to C much easier. Porting from Python/MATLAB to C was (and is) a pain in the butt, and this library aims to make the conversion between a Python/Matlab algorithm and a mobile app simple.

Currently, the Swift Matrix Library or swix gives you

  • operators (+, etc) and various functions (sin, etc) that operate on entire arrays
  • easy initializers for 1D and 2D arrays
  • dot product, matrix inversion, eigenvalues, etc
  • machine learning algorithms (SVM, kNN, SVD/PCA, more to come)
  • speed optimizations
  • one dimensional Fourier transforms

In most cases, this library calls the Accelerate framework or OpenCV. I optimized what I needed to, meaning all operators and select mathematical functions are fast while the functions I didn’t need are slow. If you want to speed up some function or add add another feature in those libraries, feel free to submit a pull request on Github (preferred!) or contact me at @stsievert or sieve121@umn.edu. Oh, and if you use this project I’d love to hear about it!

When I was crafting this library, I primarily followed the footsteps and example set by NumPy. For the more complex mathematical functions (e.g., SVD) I tested it against NumPy. Matlab, at least for the SVD, returns slightly different output.

Additionally, I followed NumPy’s syntax whenever possible. For example, NumPy and Matlab differ in their initializer called ones by ones((M,N)) and ones(M,N) respectively. If in doubt or getting weird compiler bugs, look at NumPy for Matlab users or the section on possible bugs.

As an example, here’s some Objective-C sample code that integrates the Accelerate framework:

void copy(double* x, double* y, int N){
    cblas_dcopy(N, x, 1, y, 1);
void add_two_vectors(double * x, double * y, double * result, int N){
    copy(y, result, N);
    cblas_daxpy(N, 1.0, x, 1, result, 1);
void add_scalar(double x, double * y, double * result, int N){
    vDSP_vsaddD(y, 1, &x, result, 1, N)
void multiply_two_vectors(double * x, double * y, double * result, int N){
    vDSP_vmulD(x, 1, y, 1, result, 1, N);
void set_value(double value, double * x, int N){
    catlas_dset(N, value, x, 1);
void main(){
    int N = 10;
    double * x = (double *)malloc(sizeof(double) * N);
    double * y = (double *)malloc(sizeof(double) * N);
    double * temp = (double *)malloc(sizeof(double) * N);
    double * result = (double *)malloc(sizeof(double) * N);

    set_value(3.142, x, N);
    set_value(1.618, y, N);
    add_two_vectors(x, y, temp, N);
    add_scalar(4, temp, temp, N);
    multiply_two_vectors(x, temp, result, N);

The equivalent Swift syntax with this library?

var N = 10
var x = ones(N) * pi
var y = ones(N) * phi
var result = (x+y+4)*x

Looking at the speed results in Speed we find that Swift is roughly equal with Python/Matlab with this library.


If you would like to run all of Python’s NumPy on iOS, look at kivy-ios or the beeware tools. More details can be found on the Installation page.


These docs look like Python functions as they use Python’s autodocs. However, these docs describe Swift functions.


These docs call files classes. ie, when you see matrix.complex_math.<function>, it’s in the file swix/matrix/complex-math.swift. The only exceptions are the classes vector and matrix.


If a variable has the same name as a function included in swix you will get compile errors. I’ll wait to resolve this until Swift has good package handling.