LAPACK

LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008). The routines handle both real and complex matrices in both single and double precision.
LAPACK was designed as the successor to the linear equations and linear least-squares routines of LINPACK and the eigenvalue routines of EISPACK. LINPACK, written in the 1970s and 1980s, was designed to run on the then-modern vector computers with shared memory. LAPACK, in contrast, was designed to effectively exploit the caches on modern cache-based architectures, and thus can run orders of magnitude faster than LINPACK on such machines, given a well-tuned BLAS implementation. LAPACK has also been extended to run on distributed memory systems in later packages such as ScaLAPACK and PLAPACK.
Netlib LAPACK is licensed under a three-clause BSD style license, a permissive free software license with few restrictions.
Naming scheme.
Subroutines in LAPACK have a naming convention which makes the identifiers very compact. This was necessary as the first Fortran standards only supported identifiers up to six characters long, so the names had to be shortened to fit into this limit.
A LAPACK subroutine name is in the form codice_1, where:
For example, the subroutine to solve a linear system with a general (non-structured) matrix using real double-precision arithmetic is called codice_14.
Details on this scheme can be found in the Naming scheme section in LAPACK Users' Guide.
Use with other programming languages.
Many programming environments today support the use of libraries with C binding. The LAPACK routines can be used like C functions if a few restrictions are observed.
Several alternative language bindings are also available:
Implementations.
As with BLAS, LAPACK is frequently forked or rewritten to provide better performance on specific systems. Some of the implementations are:
Since LAPACK uses BLAS for the heavy-lifting, just linking to a better-tuned BLAS implementation usually improves the performance sufficiently. As a result, LAPACK is not reimplemented as often as BLAS is.
Similar projects.
These projects provide a similar functionality to LAPACK, but the main interface differs from that of LAPACK: 