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Julia-Matlab-Benchmark

This repository is a place for accurate benchmarks between Julia and MATLAB and comparing the two.

Various commonly used operations for Matrix operations, Mathematical calculations, Data Processing, Image processing, Signal processing, and different algorithms are tested.

#Julia vs Matlab

#Julia openBLAS vs Julia MKL

#Julia SIMD vs Julia openBLAS

#Everything

Development and Future

This repository will be extended as more functions are added to the JuliaMatlab repository, which is meant to map all the Matlab functions to Julia native functions.

Other Features

  • Latest Julia language is used (compatible with 1.0.4 and higher).
  • Julia + Intel MKL is also tested. (https://github.com/JuliaComputing/MKL.jl)
  • Different number of BLAS threads are tested (BLAS.set_num_threads(n))
  • For some of the functions, Julia's SIMD is tested instead of built-in functions.
  • Accurate benchmarking tools are used both in Julia and MATLAB to get an reliable result

Julia-openBLAS-vs-Julia-MKL

Results

Matrix Generation

Generation of a Square Matrix using the randn() function and rand().

  • MATLAB Code - mA = randn(matrixSize, matrixSize), mB = randn(matrixSize, matrixSize).
  • Julia Code - mA = randn(matrixSize, matrixSize), mB = randn(matrixSize, matrixSize).

Matrix Generation

Matrix Addition

Addition of 2 square matrices where each is multiplied by a scalar.

  • MATLAB Code - mA = (scalarA .* mX) + (scalarB .* mY).
  • Julia Code - mA = (scalarA .* mX) .+ (scalarB .* mY) (Using the dot for Loop Fusion).

Matrix Addition

Matrix Multiplication

Multiplication of 2 square matrices after a scalar is added to each.

  • MATLAB Code - mA = (scalarA + mX) * (scalarB + mY).
  • Julia Code - mA = (scalarA .+ mX) * (scalarB .+ mY) (Using the dot for Loop Fusion).

Matrix Multiplication

Matrix Quadratic Form

Calculation of Matrix / Vector Quadratic Form.

  • MATLAB Code - mA = ((mX * vX).' * (mX * vX)) + (vB.' * vX) + sacalrC;.
  • Julia Code - mA = (transpose(mX * vX) * (mX * vX)) .+ (transpose(vB) * vX) .+ scalarC; (Using the dot for Loop Fusion).

Matrix Quadratic Form

Matrix Reductions

Set of operations which reduce the matrix dimension (Works along one dimension). The operation is done on 2 different matrices on along different dimensions. The result is summed with broadcasting to generate a new matrix.

  • MATLAB Code - mA = sum(mX, 1) + min(mY, [], 2);.
  • Julia Code - mA = sum(mX, dims=1) .+ minimum(mY, dims=2); (Using the dot for Loop Fusion).

Matrix Reductions

Element Wise Operations

Set of operations which are element wise.

  • MATLAB Code - mD = abs(mA) + sin(mB);, mE = exp(-(mA .^ 2)); and mF = (-mB + sqrt((mB .^ 2) - (4 .* mA .* mC))) ./ (2 .* mA);.
  • Julia Code - mD = abs.(mA) .+ sin.(mB);, mE = exp.(-(mA .^ 2)); and mF = (-mB .+ sqrt.((mB .^ 2) .- (4 .* mA .* mC))) ./ (2 .* mA); (Using the dot for Loop Fusion).

Element Wise Operations

Matrix Exponent

Calculation of Matrix Exponent.

  • MATLAB Code - mA = expm(mX);.
  • Julia Code - mA = exp(mX);.

Matrix Exponent

Matrix Square Root

Calculation of Matrix Square Root.

  • MATLAB Code - mA = sqrtm(mY);.
  • Julia Code - mA = sqrt(mY);.

Matrix Square Root

SVD

Calculation of all 3 SVD Matrices.

  • MATLAB Code - [mU, mS, mV] = svd(mX).
  • Julia Code - F = svd(mX, full = false); # F is SVD object, mU, mS, mV = F;.

SVD

Eigen Decomposition

Calculation of 2 Eigen Decomposition Matrices.

  • MATLAB Code - [mD, mV] = eig(mX).
  • Julia Code - F = eigen(mX); # F is eigen object, mD, mV = F;.

Eigen Decomposition

Cholesky Decomposition

Calculation of Cholseky Decomposition.

  • MATLAB Code - mA = cholesky(mY).
  • Julia Code - mA = cholesky(mY).

Cholseky Decomposition

Matrix Inversion

Calculation of the Inverse and Pseudo Inverse of a matrix.

  • MATLAB Code - mA = inv(mY) and mB = pinv(mX).
  • Julia Code - mA = inv(mY) and mB = pinv(mX).

Matrix Inversion

Linear System Solution

Solving a Vector Linear System and a Matrix Linear System.

  • MATLAB Code - vX = mA \ vB and mX = mA \ mB.
  • Julia Code - vX = mA \ vB and mX = mA \ mB.

Linear System Solution

Linear Least Squares

Solving a Vector Least Squares and a Matrix Least Squares. This is combines Matrix Transpose, Matrix Multiplication, Matrix Inversion (Positive Definite) and Matrix Vector / Matrix Multiplication.

  • MATLAB Code - vX = (mA.' * mA) \ (mA.' * vB) and mX = (mA.' * mA) \ (mA.' * mB).
  • Julia Code - mXT=transpose(mX); vA = ( mXT * mX) \ ( mXT * vB); mA = ( mXT * mX) \ ( mXT * mB);.

Linear Least Squares

Squared Distance Matrix

Calculation of the Squared Distance Matrix between 2 sets of Vectors. Namely, each element in the matrix is the squared distance between 2 vectors. This is calculation is needed for instance in the K-Means algorithm. It is composed of Matrix Reduction operation, Matrix Multiplication and Broadcasting.

  • MATLAB Code - mA = sum(mX .^ 2, 1).' - (2 .* mX.' * mY) + sum(mY .^ 2, 1).
  • Julia Code - mA = transpose( sum(mX .^ 2, dims=1) ) .- (2 .* transpose(mX) * mY) .+ sum(mY .^ 2, dims=1); (Using the dot for Loop Fusion).

Squared Distance Matrix

K-Means Algorithm

Running 10 iterations of the K-Means Algorithm.

  • MATLAB Code - See MatlabBench.m at KMeans().
  • Julia Code - See JuliaBench.jl at KMeans().

K-Means Algorithm

How to Run

Download repository. Or add the package in Julia:

] add https://github.com/juliamatlab/Julia-Matlab-Benchmark

Run the Benchmark - Julia

  • From console:

    include("JuliaMain.jl");

Run the Benchmark - MATLAB

  • From MATLAB command line :

    MatlabMain

Run The Analysis In MATLAB

  • From MATLAB command line

MatlabAnalysisMain.

  • Images of the performance test will be created and displayed.

Run The Analysis In Julia

  • From Julia command line

include("JuliaAnalysisMain.jl");.

  • Images of the performance test will be created and displayed.

To Do:

Discourse Discussion Forum:

coming soon

System Configuration

  • System Model - Dell Latitude 5590 https://www.dell.com/en-ca/work/shop/dell-tablets/latitude-5590/spd/latitude-15-5590-laptop

  • CPU - Intel(R) Core(TM) i5-8250U @ 1.6 [GHz] 1800 Mhz, 4 Cores, 8 Logical Processors.

  • Memory - 1x8GB DDR4 2400MHz Non-ECC

  • Windows 10 Professional 64 Bit

  • WORD_SIZE: 64

  • MATLAB R2018b.

    • BLAS Version (version -blas) - Intel(R) Math Kernel Library Version 2018.0.1 Product Build 20171007 for Intel(R) 64 architecture applications, CNR branch AVX2
    • LAPACK Version (version -lapack) - Intel(R) Math Kernel Library Version 2018.0.1 Product Build 20171007 for Intel(R) 64 architecture applications CNR branch AVX2 Linear Algebra Package Version 3.7.0

Two version of Julia was used:

  • JuliaMKL: Julia 1.4.0 + MKL.

    • Julia Version (versioninfo()) - Julia VersionVersion 1.4.0-DEV.233 Commit 32e3c9ea36 (2019-10-02 12:28 UTC);
    • BLAS Version - LinearAlgebra.BLAS.vendor(): Intel MKL . For tutorial to install https://github.com/JuliaComputing/MKL.jl
    • LAPACK Version - libopenblas64_.
    • LIBM Version - libopenlibm.
    • LLVM Version - libLLVM-6.0.1 (ORCJIT, skylake).
    • JULIA_NUM_THREADS = 1. This number of threads is different from BLAS threads. BLAS threads is changed in the code by BLAS.set_num_threads(1) and BLAS.set_num_threads(4)

  • Julia: Julia 1.4.0

    • Julia Version (versioninfo()) - Julia VersionVersion 1.4.0-DEV.233 Commit 32e3c9ea36 (2019-10-02 12:28 UTC);
    • BLAS Version - LinearAlgebra.BLAS.vendor(): openBlas64 .
    • LAPACK Version - libopenblas64_.
    • LIBM Version - libopenlibm.
    • LLVM Version - libLLVM-6.0.1 (ORCJIT, skylake).
    • JULIA_NUM_THREADS = 1. This number of threads is different from BLAS threads. BLAS threads is changed in the code by BLAS.set_num_threads(1) and BLAS.set_num_threads(4)

The idea for this repository is taken from https://github.com/aminya/MatlabJuliaMatrixOperationsBenchmark which was a fork from https://github.com/RoyiAvital/MatlabJuliaMatrixOperationsBenchmark

By Amin Yahyaabadi