Basic Comparison of Various Computing Languages

Python, Julia, Matlab, IDL, R, Java, Scala, C, Fortran

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Authors:

• Jules Kouatchou ([email protected])
• Alexander Medema

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We use simple test cases to compare various high level programming languages (Python, Julia, Matlab, IDL, R, Java, Scala, C, Fortran). We implement the test cases from an angle of a novice programmer who is not familiar with the optimization techniques available in the languages. The goal is to highlight the strengths and weaknesses of each language but not to claim that one language is better than the others.

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Background Information

Check the following docyments to obtain background information on this project:

• 2017
• 2018
• 2019

List of Test Cases

The test cases are listed in categories that include:

• Loops and Vectorization
• String Manipulations
• Numerical Calculations
• Input/Output

Each test is "simple" enough to be quickly written in any of the languages and is meant to address issues such as:

• Access of non-contiguous memory locations
• Use of recursive functions,
• Utilization of loops or vectorization,
• Opening of a large number of files,
• Manipulation of strings of arbitrary lengths,
• Multiplication of matrices,
• Use of iterative solvers
• etc.

The source files are contain in the directories:

  C\    Fortran\  IDL\  Java\  Julia\  Matlab\  Python\  R\  Scala\

There is also a directory Data that contains a Python script that generates the NetCDF4 files needed for the test case on reading a large collection of files. It also has sample text files for the Count Unique Words in a File test case.

Loops and Vectorization

• Copy Multidimensional Arrays

   Given an aribitraty n x n x 3 matrix A we perform the operations:
    
        A(i,j,1) = A(i,j,2)
        A(i,j,3) = A(i,j,1)
        A(i,j,2) = A(i,j,3)
   
   using loops and vectorization.
  

String Manipulations

• Look and Say Sequence

   The look and say sequence reads a single integer. In each subsequent entry,
   the number of appearances of each integer in the previous entry is
   concatenated to the front of that integer. For example, an entry of 1223
   would be followed by 112213, or "one 1, two 2's, one 3."
   Here, we start with the number 1223334444 and determine the look and say
   sequence of order n (as n varies).
  

• Count Unique Words in a File

   We open an arbitrary file and count the number of unique words in it
   with the assumption that words such as:
   
           ab   Ab   aB    a&*(-b:    17;A#~!b
           
   are the same.
   
   For our tests, we use the four files: 
   
          world192.txt, plrabn12.txt, bible.txt, and book1
          
   taken from the website (The Canterbury Corpus):
   
         http://corpus.canterbury.ac.nz/descriptions/
  

Numerical Computations

• Fibonacci Sequence

   The Fibonacci Sequence is a sequence of numbers where each successive number
   is the sum of the two that precede it:
  
           F_n = F_n-1 + F_n-2 .
  
   Its first entries are
  
           F_0 = 0 ,  F_1 = F_2 = 1 .
  
   We measure the elapsed time when calculating an nth Fibonacci number.
   The calculation times are taken for both iterative and recursive calculation
   methods.
  

• Matrix Multiplication

   Two randomly generated n x n matrices A and B are multiplied.
   The time to perform the multiplication is measured. This test highlights the
   importance of using the language's built-in libraries.
  

• Belief Propagation Algorithm

   Belief propagation is an algorithm used for inference, often in the fields of
   artificial intelligence, speech recognition, computer vision, image processing,
   medical diagnostics, parity check codes, and others. The algorithm requires
   repeated matrix multiplication and then a normalization of the matrix.
   This test measures the elapsed time when performing n iterations of the
   algorithm.
  

• Metropolis-Hastings Algorithm

   The Metropolis-Hastings algorithm is a an algorithm used to determine random
   samples from a probability distribution. This implementation uses a
   two-dimensional distribution (Domke 2012), and measures the elapsed time to
   iterate n times.
  

• Compute the FFTs

   We create a n x n matrix M that randomn random complex values.
   We the compute the Fast Fourier Transform (FFT) of M and the absolute
   value of the result.
  

• Iterative Solver

    We use the Jacobi iterative solver to numerically approximate the solution
    of the two-dimensional Laplace equation (that was discretized with a
    fouth order compact schems) to a differential equation. we record the
    elapsed time as the number of grid point varies.
  

• Square Root of a Matrix

   Given an n x n matrix A, we are looking for the matrix B such that:
   
           B * B = A
           
   In our calculations, we consider A with 6s on the diagonal and 1s elsewhere.
  

• Gauss-Legendre quadrature

   Gauss-Legendre quadrature is a numerical method for approximating definite
   integrals. It uses a weighted sum of n values of the integrand function.
   The result is exact if the integrand function is a polynomial of degree 0
   to 2n - 1. Here we consier an exponential function over the interval [-3,3]
   and record the time to perform the integral when n varies.
  

• Function evaluations

   We iteratively calculate trigonometric functions on an n-element list of
   values, and then compute inverse trigonometric functions on the same list.
   The time to complete the full operations is measured as n varies.
  

• Munchausen Numbers

   A Munchausen number is a natural number that is equal to the sum of its digits
   raised to each digit's power. In base 10, there are four such numbers: 
   0, 1, 3435 and 438579088. We determine how much time it takes to find them.
  

• Pernicious Numbers

   A pernicious number is a positive integer which has prime number of ones in 
   its binary representation. The first pernicious number is 3 since 
   3 = (11)(in binary representation) and 1 + 1 = 2, which is a prime. 
   The first 10 pernicious numbers are:
       
       3, 5, 6, 7, 9, 10, 11, 12, 13, 14
       
   We determine the 100000th pernicious number, i.e., the integer 323410.
  

Input/Output

• Reading a Large Collection of Files

  We have a set of daily NetCDF files (7305) covering a period of 20 years.
  The files for a given year are in a sub-directory labeled YYYY
  (for instance Y1990, Y1991, Y1992, etc.). We want to write a script that
  opens each file, reads a three-dimensional variable (longitude/latitude/level),
  and manipulates it. A pseudo code for the script reads:
  
      Loop over the years
           Obtain the list of NetCDF files
           Loop over the files
                Read the variable (longitude/latitude/level)
                Compute the zonal mean average (new array of latitude/level)
                Extract the column array at latitude 86 degree South
                Append the column array to a "master" array (or matrix)
  
  The goal is to be able to do a generate the three-diemsional arrays
  (year/level/value) and carry out a contour plot.
  

Results

September 2019

Language	Version
Python	3.7
Julia	0.6.2
Java	10.0.2
Scala	2.13.0
IDL	8.5
R	3.6.1
Matlab	R2017b
GNU Compilers	9.1

May 2020

Language	Version
Python	3.7
Numba	0.45.1
Julia	1.2
Java	13.0.1
Scala	2.13.2
IDL	8.5
R	3.6.3
Matlab	R2020a
GNU Compilers	9.3.0

August 2021

Language	Version
Python	3.9
Numba	0.53.1
Julia	1.6.2
Java	15
Scala
IDL	8.5
R	4.1.0
Matlab	R2020a
GNU Compilers	11.1.0

• The pernicious number test case was added.
• All the calculations were done in an Intel Xeon Skylake node (40 cores, 2.4 Ghz per core, 4 Gb of memory per core).