Basic Comparison of Various Computing Languages

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

Authors:

• Jules Kouatchou (Jules.Kouatchou@nasa.gov)
• Alexander Medema

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.

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

May 2020

August 2021

• 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).