Math Libraries at NERSC

The purpose of mathematical libraries is to provide users writing application codes with ready-to-use building blocks. The two major advantages that mathematical libraries offer are functionality and performance. Most of the libraries at NERSC exist primarily to offer functionality, but some, most notably the vendor supplied libraries, exist also to provide performance.

Consequently, when a certain functionality is provided by more than one library (with comparable quality), the user should pick the one that has the highest performance. A rule of thumb is therefore to always look for the functionality in the IBM supplied libraries before turning to other libraries.

Aztec

Aztec, which is included in the ACTS DOE Collection, is a library for solving large sparse linear systems arising in scientific and engineering applications. It is a stand-alone package comprising a set of iterative solvers, preconditioners and matrix-vector multiplication routines.

ESSL (IBM Engineering and Scientific Subroutine Library)

ESSL provides variety of optimized complex mathematical functions, for many different scientific and engineering applications such as Basic Linear Algebra Subroutines (BLAS), linear algebraic equation solvers (includes a few LAPACK routines), subset of LAPACK eigensystem analysis, Fourier Transforms. ESSL provides single and double precision versions for most routines. This library is not linked against automatically by the IBM compilers.

FFTW

FFTW is a portable, free, high performance DFT library which implements arbitrary radix, serial and multiple dimensional transforms in serial or parallel (MPI and POSIX threads models). One unique aspect of FFTW is its optional use of self-optimizing strategies, whereby subsequent calls become faster by building on previous timings. Wrapper functions provide a Fortran API to this native C library.

LAPACK

LAPACK provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems.

MASS (Mathematical Acceleration SubSystem)

MASS consists of libraries of tuned mathematical intrinsic scalar and vector functions.

NAG

NAG is collection of over 1000 user-callable routines for mathematical and statistical computation. Compared to the "other" general library, IMSL, NAG usually considered to be stronger in optimization.

NAG Parallel Library (MPI-based version)

NAG Parallel math and stat library provides routines for dedicated parallel machines and clusters of workstations or PCs. NAG parallel library and NAG Fortran library are two different products.

NAG SMP Library

NAG SMP Library is a library of Fortran 77 routines optimised for use on Symmetric Multi-processor (SMP) machines which are multi-processor platforms with a shared memory (such as a single node of the SP). It contains all the routines contained in the NAG Fortran library.

PARPACK

PARPACK is a parallel extension to the ARPACK (ARnoldi PACKage) software package collection of Fortran 77 subroutines designed to solve large-scale eigenvalue problems. Parallel ARPACK (PARPACK) extends ARPACK on distributed memory architectures. PARPACK message passing layer currently installed is MPI on the IBM SP.

PESSL (IBM Parallel Engineering and Scientific Subroutine Library)

PESSL is a parallel version of the ESSL library. It is used in conjunction with the serial version of ESSL. It contains number of Parallel BLAS (PBLAS) and ScaLAPACK routines.

PETSc (Portable, Extensible Toolkit for Scientific Computation)

PETSc, which is part of the ACTS DOE Collection, provides sets of tools for the parallel (as well as serial) numerical solution of PDEs that require solving large-scale, sparse nonlinear systems of equations.

ScaLAPACK

ScaLAPACK, also part of the ACTS DOE Collection, is a library of high-performance linear algebra routines for distributed-memory parallel computers.

SuperLU

SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. SuperLU package has three different versions: SuperLU for sequential machines, SuperLU_MT for shared memory parallel machines and SuperLU_DIST for distributed memory.

WSMP

WSMP The Watson Sparse Matrix Package, is a high-performance, robust, easy to use software package for solving large sparse systems of linear equations using a direct method on serial and multiprocessor workstations and on distributed-memory parallel computers with serial or multiprocessor nodes. WSMP is comprised of two parts. Part I of WSMP replaces the older software called WSSMP. Part II of WSMP library deals with the solution of general sparse system of linear equations.

Fast Fourier Transform software

Fast Fourier Transform software at NERSC.

Sparse Linear Equation Solvers

Sparse linear equation solvers at NERSC.

Random Number Generators

Available routines for generating and manipulating pseudo-random numbers. There is also a brief white paper offering general guidance on using random numbers in parallel programs, and brief descriptions of the classes of generators available.