LAPACK — Linear Algebra PACKage

LAPACK is written in Fortran 90 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision.

The original goal of the LAPACK project was to make the widely used EISPACK and LINPACK libraries run efficiently on shared-memory vector and parallel processors. On these machines, LINPACK and EISPACK are inefficient because their memory access patterns disregard the multi-layered memory hierarchies of the machines, thereby spending too much time moving data instead of doing useful floating-point operations. LAPACK addresses this problem by reorganizing the algorithms to use block matrix operations, such as matrix multiplication, in the innermost loops. These block operations can be optimized for each architecture to account for the memory hierarchy, and so provide a transportable way to achieve high efficiency on diverse modern machines. We use the term "transportable" instead of "portable" because, for fastest possible performance, LAPACK requires that highly optimized block matrix operations be already implemented on each machine.

LAPACK routines are written so that as much as possible of the computation is performed by calls to the Basic Linear Algebra Subprograms (BLAS). LAPACK is designed at the outset to exploit the Level 3 BLAS — a set of specifications for Fortran subprograms that do various types of matrix multiplication and the solution of triangular systems with multiple right-hand sides. Because of the coarse granularity of the Level 3 BLAS operations, their use promotes high efficiency on many high-performance computers, particularly if specially coded implementations are provided by the manufacturer.

Highly efficient machine-specific implementations of the BLAS are available for many modern high-performance computers. For details of known vendor- or ISV-provided BLAS, consult the BLAS FAQ. Alternatively, the user can download ATLAS to automatically generate an optimized BLAS library for the architecture. A Fortran 77 reference implementation of the BLAS is available from netlib; however, its use is discouraged as it will not perform as well as a specifically tuned implementation.

This material is based upon work supported by the National Science Foundation and the Department of Energy (DOE). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF) or the Department of Energy (DOE).

The LAPACK project is also sponsored in part by MathWorks and Intel since many years.

Do not forget to check our GitHub repository for Current and Fixed issues and Improvements

LAPACK is a community-wide effort.LAPACK relies on many contributors, and we would like to acknowledge their outstanding work. Here is the list of LAPACK contributors since 1992.

If you are wishing to contribute, please have a look at the LAPACK Program Style. This document has been written to facilitate contributions to LAPACK by documenting their design and implementation guidelines.

LAPACK Project Software Grant and Corporate Contributor License Agreement (“Agreement”) [Download]

Contributions are always welcome and can be sent to the LAPACK team.

Version 1.0 : February 29, 1992

Version 2.0: September 30, 1994

Version 3.0: June 30, 1999

Version 3.1.0: November 12, 2006

Version 3.2: November 18, 2008

Version 3.3.0: November 14, 2010

Version 3.4.0: November 11, 2011

Version 3.5.0: November 19, 2013

Version 3.6.0: November 15, 2015

Version 3.7.0: December 24, 2016

Version 3.8.0: November 17, 2017

Version 3.9.0: November 21, 2019

Version 3.10.0: June 28, 2021

Version 3.11.0: November 11, 2022

Version 3.12.0: November 24, 2023

Please report to our FAQ to know the list of the current vendors implementations.

LAPACK 95 by Jerzy Waśniewski

JLAPACK

LAPACK extensions for high performance linear algebra computations. This version includes support for solving linear systems using LU, Cholesky, and QR matrix factorizations. lapack++ by Roldan Pozo

Subdirectory containing CCI (Call Conversion Interface) for LAPACK/ESSL. See lawn82 for more information.