[Paper Review] A Basic Introduction on Math-Link in Mathematica

Sonam Maiti|ArXiv.org|Mar 1, 2006

Polynomial and algebraic computation2 references3 citations

TL;DR

This paper presents a foundational guide to using MathLink in Mathematica for integrating external programs, particularly XL Fortran-90 code, to accelerate complex numerical computations. It demonstrates how to compile, link, and execute external Fortran programs from within Mathematica notebooks using commands like SetDirectory, Export, ReadList, and Eigenvalues, enabling efficient data exchange and high-performance computing workflows.

ABSTRACT

Starting from the basic ideas of mathematica, we give a detailed description about the way of linking of external programs with mathematica through proper mathlink commands. This article may be quite helpful for the beginners to start with and write programs in mathematica. In the first part, we illustrate how to use a mathemtica notebook and write a complete program in the notebook. Following with this, we also mention elaborately about the utility of the local and global variables those are very essential for writing a program in mathematica. All the commands needed for doing different mathematical operations can be found with some proper examples in the mathematica book written by Stephen Wolfram \cite{wolfram}. In the rest of this article, we concentrate our study on the most significant issue which is the process of linking of {\em external programs} with mathematica, so-called the mathlink operation. By using proper mathlink commands one can run very tedious jobs efficiently and the operations become extremely fast.

Motivation & Objective

• To provide beginners with a comprehensive introduction to Mathematica notebook usage and program development.
• To explain the role and distinction between local and global variables in Mathematica programming.
• To demonstrate the integration of external Fortran programs (especially XL Fortran-90) into Mathematica using MathLink for enhanced computational performance.
• To illustrate practical techniques for file I/O, directory management, and matrix operations across Mathematica and external programs.
• To enable researchers to offload computationally intensive tasks to compiled external code while maintaining seamless data flow within Mathematica.

Proposed method

• Use Mathematica notebooks to write and execute programs, with input processed in cells and results displayed in output cells after pressing Shift+Enter.
• Define functions using the Block construct to encapsulate local variables and modularize code, such as in the sample[time_] function.
• Compile external Fortran-90 programs into executable files (e.g., 'mat') using XL Fortran compilers like xlf or xlf95 with optimization flags.
• Use SetDirectory[] to navigate to the directory containing the external executable, ensuring correct path resolution for file operations.
• Employ Export["mat3.dat", output] to write matrix data from Mathematica to a file for use by the external program.
• Utilize ReadList["!mat < mat3.dat", Number, RecordLists -> True] to invoke the external program via MathLink and read its output back into Mathematica for further processing.

Experimental results

Research questions

• RQ1 How can external Fortran programs be effectively linked to Mathematica for high-performance numerical computation?
• RQ2 What are the correct procedures for compiling and optimizing XL Fortran-90 source files for use with Mathematica via MathLink?
• RQ3 How can data be exchanged between Mathematica and external programs using file-based I/O and MathLink commands?
• RQ4 What role do local and global variables play in structuring robust Mathematica programs for integration with external code?
• RQ5 How can matrix operations and eigenvalue computations be performed after retrieving data from an external Fortran program?

Key findings

• MathLink enables seamless execution of external Fortran programs from within Mathematica notebooks, significantly improving performance for computationally intensive tasks.
• The use of Export and ReadList with the '!program < file' syntax allows Mathematica to invoke and retrieve results from compiled external programs reliably.
• Proper directory management via SetDirectory[] and ResetDirectory[] ensures correct file path resolution during program execution.
• Matrix operations such as Eigenvalues can be computed in Mathematica after reading data from external programs, demonstrating end-to-end data flow.
• The integration of XL Fortran-90, F77, and F95 programs via MathLink is feasible and efficient, provided correct compilation and linking commands are used.
• The method supports complex workflows involving dynamic matrix generation, file I/O, and symbolic computation, enabling scalable numerical research.