Editing LAPACK (section)

{{Short description|Software library for numerical linear algebra}}
{{Infobox software
| name                   = LAPACK (Netlib reference implementation)
| logo                   = LAPACK logo.svg
| logo size              = 120px
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| author                 =
| developer              =
| released               = {{Start date and age|1992}}
| latest release version = {{Wikidata|property|reference|edit|P348}}
| latest release date    = {{Start date and age|{{wikidata|qualifier|P348|P577}}|df=yes}}
| latest preview version =
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| programming language   = [[Fortran 90]]
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| genre                  = [[Software library]]
| license                = [[BSD-new]]
| website                = <!-- Wikidata -->
}}

'''LAPACK''' ("Linear Algebra Package") is a standard [[software library]] for [[numerical linear algebra]]. It provides [[subroutine|routines]] for solving [[systems of linear equations]] and [[numerical methods for linear least squares|linear least squares]], [[eigendecomposition of a matrix|eigenvalue problems]], and [[singular value decomposition]]. It also includes routines to implement the associated [[matrix factorization]]s such as [[LU decomposition|LU]], [[QR decomposition|QR]], [[Cholesky decomposition|Cholesky]] and [[Schur decomposition]].<ref name="LAPACK User Manual">{{cite book|last1=Anderson|first1=E.|last2=Bai|first2=Z.|last3=Bischof|first3=C.|last4=Blackford|first4=S.|last5=Demmel|first5=J.|author-link5=James Demmel|last6=Dongarra|first6=J.|author-link6=Jack Dongarra|last7=Du Croz|first7=J.|last8=Greenbaum|first8=A.|author-link8=Anne Greenbaum|last9=Hammarling|first9=S.|last10=McKenney|first10=A.|last11=Sorensen|first11=D.
| title =LAPACK Users' Guide
| edition = Third
| publisher = Society for Industrial and Applied Mathematics
| year = 1999
| location = Philadelphia, PA
| isbn = 0-89871-447-8
| url = https://www.netlib.org/lapack/lug/
| access-date=28 May 2022
}}</ref> LAPACK was originally written in [[FORTRAN 77]], but moved to [[Fortran 90]] in version 3.2 (2008).<ref>{{cite web|url=https://www.netlib.org/lapack/lapack-3.2.html|title=LAPACK 3.2 Release Notes|date=16 November 2008}}</ref> The routines handle both [[real number|real]] and [[complex number|complex]] matrices in both [[single precision|single]] and [[double precision]]. LAPACK relies on an underlying [[Basic Linear Algebra Subprograms|BLAS]] implementation to provide efficient and portable computational building blocks for its routines.<ref name="LAPACK User Manual" />{{rp|at=[https://www.netlib.org/lapack/lug/node65.html "The BLAS as the Key to Portability"]}}

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 processor|vector computer]]s with shared memory.  LAPACK, in contrast, was designed to effectively exploit the [[CPU cache|cache]]s on modern cache-based architectures and the [[instruction-level parallelism]] of modern [[superscalar processor]]s,<ref name="LAPACK User Manual" />{{rp|at=[https://www.netlib.org/lapack/lug/node61.html "Factors that Affect Performance"]}} and thus can run orders of magnitude faster than LINPACK on such machines, given a well-tuned [[Basic Linear Algebra Subprograms|BLAS]] implementation.<ref name="LAPACK User Manual" />{{rp|at=[https://www.netlib.org/lapack/lug/node65.html "The BLAS as the Key to Portability"]}} LAPACK has also been extended to run on [[distributed memory]] systems in later packages such as [[ScaLAPACK]] and PLAPACK.<ref>{{cite web|access-date=20 April 2017| date=12 June 2007| title=PLAPACK: Parallel Linear Algebra Package| url=https://www.cs.utexas.edu/users/plapack/| website=www.cs.utexas.edu| publisher=[[University of Texas at Austin]]}}</ref>

Netlib LAPACK is licensed under a three-clause [[BSD licenses|BSD style]] license, a [[permissive free software license]] with few restrictions.<ref>{{cite web |title=LICENSE.txt |url=https://www.netlib.org/lapack/LICENSE.txt |website=Netlib |access-date=28 May 2022}}</ref>