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I started learning Julia not a long time ago and I decided to do a simple comparison between Julia and Matlab on a simple code for computing Euclidean distance matrices from a set of high dimensional points.

The task is simple and can be divided into two cases:

Case 1: Given two datasets in the form of n x d matrices, say X1 and X2, compute the pair wise Euclidean distance between each point in X1 and all the points in X2. If X1 is of size n1 x d, and X2 is of size n2 x d, then the resulting Euclidean distance matrix D will be of size n1 x n2. In the general setting, matrix D is not symmetric, and diagonal elements are not equal to zero.

Case 2: Given one dataset in the form of n x d matrix X, compute the pair wise Euclidean distance between all the n points in X. The resulting Euclidean distance matrix D will be of size n x n, symmetric, with zero elements on the main diagonal.

My implementation of these functions in Matlab and in Julia is given below. Note that none of the implementations rely on loops of any sort, but rather simple linear algebra operations. Also, note that the implementation using both languages is very similar.

My expectations before running any tests for these implementations is that the Julia code will be much faster than the Matlab code, and by a significant margin. To my surprise, this was not the case!

The parameters for my experiments are given below with the code. My machine is a MacBook Pro. (15" Mid 2015) with 2.8 GHz Intel Core i7 (Quad Core), and 16 GB 1600 MHz DDR3.

Matlab version: R2018a

Julia version: 0.6.3
BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Haswell)
LAPACK: libopenblas64_
LIBM: libopenlibm
LLVM: libLLVM-3.9.1 (ORCJIT, haswell)

The results are given in Table (1) below.

Table 1: Average time in seconds (with standard deviation) over 30 trials for computing Euclidean distance matrices between two different datasets (Col. 1), and between all pairwise points in one dataset (Col. 2).

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