The IMSL libraries, from Visual Numerics, are a comprehensive set of mathematical and statistical functions that programmers can embed into their software applications. IMSL provides high-performance computing software and expertise needed to develop and execute sophisticated numerical analysis applications. These libraries free you from developing your own internal code by providing pre-written mathematical and statistical algorithms that you can embed into your C, Java, and Fortran applications.
NAG has a longstanding worldwide reputation for the excellence of its numerical and statistical libraries which contain over a thousand mathematical and statistical functions. This includes routines for distributed and shared memory in C and Fortran as well as compilers.
The BLAS (Basic Linear Algebra Subprograms) are high quality "building block" routines for performing basic vector and matrix operations. Level 1 BLAS do vector-vector operations, Level 2 BLAS do matrix-vector operations, and Level 3 BLAS do matrix-matrix operations. Because the BLAS are efficient, portable, and widely available, they're commonly used in the development of high quality linear algebra software, LINPACK and LAPACK for example. Vendor supplied versions of these routines tuned to a particular architecture are usually available.
LAPACK is written in Fortran77 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. Vendor supplied versions of these routines tuned to a particular architecture are usually available.
The ScaLAPACK (or Scalable LAPACK) library includes a subset of LAPACK routines redesigned for distributed memory MIMD parallel computers. It is currently written in a Single-Program-Multiple-Data style using explicit message passing for interprocessor communication. It assumes matrices are laid out in a two-dimensional block cyclic decomposition. ScaLAPACK is designed for heterogeneous computing and is portable on any computer that supports MPI or PVM. Vendor supplied versions of these routines tuned to a particular architecture are usually available.
FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST). Authors of this (free) software claim to get very high, portable, performance, hence the name, "FFTW," which stands for the somewhat whimsical title of "Fastest Fourier Transform in the West."
Portable, Extensible Toolkit for Scientific Computation. PETSc is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations. It employs the MPI standard for all message-passing communication.
