IMSL Fortran Numerical Library

The IMSL™ Fortran Numerical Library is the gold standard mathematical and statistical code library for Fortran programmers developing high performance computing applications. The IMSL Fortran Numerical Library contains highly accurate and reliable Fortran algorithms with full coverage of mathematics and statistics and complete backward compatibility.

The IMSL Fortran Numerical Library is a comprehensive library of mathematical and statistical algorithms available in one cohesive package. It combines the powerful and flexible interface features of the Fortran language with the performance benefits of both distributed memory and shared memory multiprocessing architectures.

The IMSL Fortran Numerical Library is also available in a 100% thread safe edition, the new IMSL Thread Safe Fortran Numerical Library, making it unique in its class. It is the only library of its kind, with highly comprehensive algorithm coverage, full backward compatibility and complete thread safety. In addition, it delivers all of the algorithms, expertise, benefits and convenience contained in the IMSL Fortran Numerical Library.

The strength and precision of the IMSL Numerical Libraries have been evolving steadily for over three decades. Each subroutine and algorithm has undergone rigorous testing and quality assurance, providing IMSL users with more time to focus on their application.

One Cohesive Package of Advanced Numerical Algorithms
At the heart of the IMSL Numerical Libraries lies the comprehensive and trusted IMSL mathematical and statistical numerical algorithms. The IMSL Fortran Numerical Library includes all of the algorithms from the IMSL family of Fortran libraries over the years, including the IMSL F90 Library, the IMSL FORTRAN 77 Library, and the IMSL parallel processing features. Utilities are included to simplify large-scale computing with the ScaLAPACK library. The IMSL Libraries are the gold standard for comprehensive libraries of numerical computing algorithms that software developers can embed into their applications.

Powerful Interface Modules
The IMSL Fortran Numerical Library includes new powerful and flexible interface modules for all applicable routines, which accomplish the following:

• Allows users to utilize the fast, convenient optional arguments of the modern Fortran syntax for 100% of the relevant algorithms in the library, allowing for greater control and faster, simpler code development
• Only require a short list of required arguments for each algorithm to facilitate development of simpler Fortran applications
• Provide full depth and control via optional arguments for experienced programmers
• Reduce development effort by checking data-type matches and array sizing at compile time
• With operators and function modules, provide faster and more natural programming through an object-oriented approach
• A simple and flexible interface to the library routines speeds programming and simplifies documentation

Complete Backward Compatibility
For over two decades, the IMSL Fortran Numerical Library has maintained full backward compatibility with all previous versions of the Library. No code modifications are required for existing applications that rely on previous versions of the IMSL Fortran Numerical Library. Calls to routines from the IMSL FORTRAN 77 Library with the F77 syntax continue to function.

Fully Tested
Visual Numerics has developed over three decades of experience in testing IMSL numerical algorithms for quality and performance across an extensive range of the latest compilers and environments. Visual Numerics works with compiler partners and hardware partners to ensure a high degree of reliability and performance optimization. This experience has allowed Visual Numerics to refine its test methods with painstaking detail. The result of this effort is a robust, sophisticated suite of test methods that allow the IMSL user to rely on the numerical analysis functionality and focus their bandwidth on their application development and testing.

SMP/OpenMP Support
The IMSL Fortran Numerical Library offers expanded SMP support for a number of parallel processing environments. Computationally intensive algorithms in the areas of linear systems and matrix manipulation, eigensystem analysis, and fast Fourier transforms (FFTs) leverage SMP capabilities on a variety of systems.

MPI Enabled
IMSL Fortran Numerical Library provides a dynamic interface for computing mathematical solutions over a distributed system via Message Passing Interface (MPI). MPI enabled routines offer a simple, reliable user interface.

The IMSL Fortran library provides a number of MPI-enabled routines with an MPI-enhanced interface that provides:

• Computational control of the server node
• Scalability of computational resources
• Automatic processor prioritization
• Self-scheduling algorithm to keep processors continuously active
• Box data type application
• Computational integrity
• Dynamic error processing
• Homogeneous and heterogeneous network functionality
• Use of descriptive names and generic interfaces
• A suite of testing and benchmark software

More Robust Non-linear Optimization
New nonlinearly constrained optimization routine

Time-series Algorithms
These algorithms are part of the TIMe Series Analysis and Control (TIMSAC) package developed by the Institute of Statistical Mathematics (ISM) in Japan. Time series analysis is heavily used in many fields, including economics, financial engineering, climate analysis, data mining, and many more.

• MAX_ARMA Exact maximum likelihood estimation of the parameters in a univariate Autoregressive Moving Average (ARMA) time series model
• Useful in developing predictive models for complex time series data
• Automatic Model Selection Fitting
• These routines enables model fitting of time series data, such as stock prices or process data, to be fitted automatically. This automatic fitting feature thus allows model fitting to be embedded in other processes
• Univariate and multi-variate versions available
• Akaike's Information Criterion or Final Prediction Error methodologies available
• Bayesian Seasonal adjustment for time series data
• Used in areas such as economics, financial engineering, climate studies, retail sales data mining and forecasting, to name just a few

Quasi Monte-Carlo Routine for High-dimensional Integration

• Allows numerical approximation of integrals over a very high dimensional cube
• Can be used by financial engineers to evaluate the risk of pools of mortgages requiring integration over a 360-degree cube, for example

New Faure Sequence Routine
Computes a low-discrepancy sequence, which is used in Quasi Monte-Carlo analysis

New GARCH Routine
Used to model time series data, such as the price of oil or interest rates

New 100% Thread Safe Edition
The IMSL Fortran Numerical Library is also available in a 100% thread safe edition, the new IMSL Thread Safe Fortran Numerical Library, making it unique in its class. It is the only library of its kind, with highly comprehensive algorithm coverage, full backward compatibility and complete thread safety. In addition, it delivers all of the algorithms, expertise, benefits and convenience contained in the IMSL Fortran Numerical Library.

What's new in 6.0?

• Dense Linear Programming Optimizer — for state-of-the-art constrained dense linear programming optimization. This version of the IMSL Fortran Numerical Library offers the world’s fastest optimizer of its kind in a general-purpose mathematical library, and data format readers to facilitate usage with existing users of Linear Programming. In recent benchmarks, the IMSL Fortran Library averaged 10 times faster than a leading Linear Programming Optimizer product on Netlib tests, and is the only broad-based numerical library containing a dense solver with performance of this caliber. 
   
• ScaLAPACK (Linear Algebra PACKage) Integration – gives users easy access to MPI-enabled algorithms, and allows them to write parallel code without needing to know parallel programming. In addition, a new “SCALAPACK_SETUP” function automatically configures MPI and ScaLAPACK and combines with other convenience routines to allow non-expert users to solve large problems on distributed systems while avoiding many of the messy details. 
   
• LAPACK Integration - provides easy access to SMP-enabled algorithms and allows users to write parallel code without needing to know parallel programming. 
   
• Intel® Math Kernel Library (Intel MKL) Integration - provides a substantial performance increase for IMSL Fortran Library users developing high performance computing applications, and improves installation and support for IMSL library customers running on Intel processor-based platforms. 
   
• Mersenne Twister random number generator technique – algorithm featuring fast generation of very high quality pseudorandom numbers, predominantly used within financial applications. 
   
• SuperLU for Sparse Linear Algebra – a direct solver for large sparse systems of linear equations.