LAPACK

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.{{rp|at=[https://www.netlib.org/lapack/lug/node24.html "Naming Scheme"]}}

A LAPACK subroutine name is in the form pmmaaa, where:

• p is a one-letter code denoting the type of numerical constants used. S, D stand for real floating-point arithmetic respectively in single and double precision, while C and Z stand for complex arithmetic with respectively single and double precision. The newer version, LAPACK95, uses generic subroutines in order to overcome the need to explicitly specify the data type.
• mm is a two-letter code denoting the kind of matrix expected by the algorithm. The codes for the different kind of matrices are reported below; the actual data are stored in a different format depending on the specific kind; e.g., when the code DI is given, the subroutine expects a vector of length n containing the elements on the diagonal, while when the code GE is given, the subroutine expects an {{math|n×n}} array containing the entries of the matrix.
• aaa is a one- to three-letter code describing the actual algorithm implemented in the subroutine, e.g. SV denotes a subroutine to solve linear system, while R denotes a rank-1 update.

For example, the subroutine to solve a linear system with a general (non-structured) matrix using real double-precision arithmetic is called DGESV.{{Rp|at=[https://www.netlib.org/lapack/lug/node26.html "Linear Equations"]}}

Many programming environments today support the use of libraries with C binding (LAPACKE, a standardised C interface,{{cite web |title=The LAPACKE C Interface to LAPACK |url=https://netlib.org/lapack/lapacke.html |website=LAPACK — Linear Algebra PACKage |access-date=2024-09-22 }} has been part of LAPACK since version 3.4.0{{cite web |title=LAPACK 3.4.0 |url=https://netlib.org/lapack/lapack-3.4.0.html |website=LAPACK — Linear Algebra PACKage |access-date=2024-09-22 }}), allowing LAPACK routines to be used directly so long as a few restrictions are observed. Additionally, many other software libraries and tools for scientific and numerical computing are built on top of LAPACK, such as R,{{Cite web |title=R: LAPACK Library |url=https://stat.ethz.ch/R-manual/R-patched/library/base/html/La_library.html |access-date=2022-03-19 |website=stat.ethz.ch }} MATLAB,{{cite web |title=LAPACK in MATLAB |url=https://www.mathworks.com/help/matlab/math/lapack-in-matlab.html |website=Mathworks Help Center |access-date=28 May 2022 }} and SciPy.{{cite web |title=Low-level LAPACK functions |url=https://docs.scipy.org/doc/scipy/reference/linalg.lapack.html |website=SciPy v1.8.1 Manual |access-date=28 May 2022 }}

Several alternative language bindings are also available:

• Armadillo for C++
• IT++ for C++
• LAPACK++ for C++
• Lacaml for OCaml
• SciPy for Python
• Gonum for Go
• [https://metacpan.org/pod/PDL::LinearAlgebra PDL::LinearAlgebra] for Perl Data Language
• [https://metacpan.org/pod/Math::Lapack Math::Lapack] for Perl
• [https://github.com/2xmax/NLapack NLapack] for .NET
• [https://github.com/DanielMartensson/CControl CControl] for C in embedded systems
• [https://docs.rs/lapack/latest/lapack/ lapack] for rust

As with BLAS, LAPACK is sometimes forked or rewritten to provide better performance on specific systems. Some of the implementations are:

; Accelerate: Apple's framework for macOS and iOS, which includes tuned versions of BLAS and LAPACK.{{Cite web|url=https://developer.apple.com/library/mac/#releasenotes/Performance/RN-vecLib/|title=Guides and Sample Code|website=developer.apple.com|access-date=2017-07-07}}{{Cite web|url=https://developer.apple.com/library/ios/#documentation/Accelerate/Reference/AccelerateFWRef/|title=Guides and Sample Code|website=developer.apple.com|access-date=2017-07-07}}

; Netlib LAPACK: The official LAPACK.

; Netlib ScaLAPACK: Scalable (multicore) LAPACK, built on top of PBLAS.

; Intel MKL: Intel's Math routines for their x86 CPUs.

; OpenBLAS: Open-source reimplementation of BLAS and LAPACK.

; Gonum LAPACK: A partial native Go implementation.

Since LAPACK typically calls underlying BLAS routines to perform the bulk of its computations, simply linking to a better-tuned BLAS implementation can be enough to significantly improve performance. As a result, LAPACK is not reimplemented as often as BLAS is.

These projects provide a similar functionality to LAPACK, but with a main interface differing from that of LAPACK:

; Libflame: A dense linear algebra library. Has a LAPACK-compatible wrapper. Can be used with any BLAS, although BLIS is the preferred implementation.{{cite web |title=amd/libflame: High-performance object-based library for DLA computations |url=https://github.com/amd/libflame |website=GitHub |publisher=AMD |date=25 August 2020}}

; Eigen: A header library for linear algebra. Has a BLAS and a partial LAPACK implementation for compatibility.

; MAGMA: Matrix Algebra on GPU and Multicore Architectures (MAGMA) project develops a dense linear algebra library similar to LAPACK but for heterogeneous and hybrid architectures including multicore systems accelerated with GPGPUs.

; PLASMA: The Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) project is a modern replacement of LAPACK for multi-core architectures. PLASMA is a software framework for development of asynchronous operations and features out of order scheduling with a runtime scheduler called QUARK that may be used for any code that expresses its dependencies with a directed acyclic graph.{{Cite web |url=http://icl.eecs.utk.edu/ |title=ICL |website=icl.eecs.utk.edu |access-date=2017-07-07 }}

{{See also|Basic Linear Algebra Subprograms#Similar libraries (not compatible with BLAS)}}

{{Portal|Free and open-source software}}

• List of numerical libraries
• Math Kernel Library (MKL)
• NAG Numerical Library
• SLATEC, a FORTRAN 77 library of mathematical and statistical routines
• QUADPACK, a FORTRAN 77 library for numerical integration

{{Reflist}}

{{Numerical linear algebra}}

Category:Fortran libraries

Category:Free software programmed in Fortran

Category:Numerical linear algebra

Category:Numerical software

Category:Software using the BSD license