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 webpages to obtain background information on this project:

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.

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.