3.12.0[1]
/ 24 November 2023; 5 months ago (24 November 2023)
Repository
github.com/Reference-LAPACK/lapack
Written in
Fortran 90
Type
Software library
License
BSD-new
Website
netlib.org/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.[2] LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008).[3] The routines handle both real and complex matrices in both single and double precision. LAPACK relies on an underlying BLAS implementation to provide efficient and portable computational building blocks for its routines.[2]: "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 computers with shared memory. LAPACK, in contrast, was designed to effectively exploit the caches on modern cache-based architectures and the instruction-level parallelism of modern superscalar processors,[2]: "Factors that Affect Performance" and thus can run orders of magnitude faster than LINPACK on such machines, given a well-tuned BLAS implementation.[2]: "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.[4]
Netlib LAPACK is licensed under a three-clause BSD style license, a permissive free software license with few restrictions.[5]
^"Release 3.12.0". 24 November 2023. Retrieved 19 December 2023.
^ abcdAnderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D. (1999). LAPACK Users' Guide (Third ed.). Philadelphia, PA: Society for Industrial and Applied Mathematics. ISBN 0-89871-447-8. Retrieved 28 May 2022.
^"LAPACK 3.2 Release Notes". 16 November 2008.
^"PLAPACK: Parallel Linear Algebra Package". www.cs.utexas.edu. University of Texas at Austin. 12 June 2007. Retrieved 20 April 2017.
LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations...
The ScaLAPACK (or Scalable LAPACK) library includes a subset of LAPACK routines redesigned for distributed memory MIMD parallel computers. It is currently...
is written in C/C++ and Fortran. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math. Intel IPP...
floating-point formats. According to formal definition — used by Prof. Demmel, LAPACK and Scilab. It represents the largest relative rounding error in round-to-nearest...
NET written in C# and F#. It features functionality similar to BLAS and LAPACK. The software library provides facilities for: Linear algebra classes with...
which stores all the elements for a given row contiguously in memory. LAPACK defines various matrix representations in memory. There is also Sparse matrix...
engineering, and financial applications. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math. The library...
LAPACK Users' guide. SIAM. Anderson, E., Bai, Z., Dongarra, J., Greenbaum, A., McKenney, A., Du Croz, J., ... & Sorensen, D. (1990, November). LAPACK:...
trailing-edge.com. Archived from the original on 2020-08-03. Retrieved 2020-05-06. "lapack (l) - Linux Man Pages". www.systutorials.com. Archived from the original...
belongs to R n {\displaystyle \mathbb {R} ^{n}} . Here are some of the LAPACK routines that apply to block reflectors "*larft" forms the triangular vector...
open-source implementation of the BLAS (Basic Linear Algebra Subprograms) and LAPACK APIs with many hand-crafted optimizations for specific processor types....
supercomputers in the 1970s and early 1980s. It has been largely superseded by LAPACK, which runs more efficiently on modern architectures. LINPACK makes use...
than a general matrix by using a special storage scheme. For instance, the LAPACK Fortran package stores an unsymmetric tridiagonal matrix of order n in three...
implementation of the BLAS APIs as well as some additional functions from LAPACK, a higher-level library built on top of BLAS. In BLAS, functionality is...
scipy.sparse library. Internally, both MATLAB and NumPy rely on BLAS and LAPACK for efficient linear algebra computations. Python bindings of the widely...
ISBN 978-0-521-88068-8 Online Matrix Calculator Performs QR decomposition of matrices. LAPACK users manual gives details of subroutines to calculate the QR decomposition...
end if return end Furthermore, as Edward Anderson discovered in improving LAPACK, a previously overlooked numerical consideration is continuity. To achieve...
{O}}(n^{3})} operations. See the Nonsymmetric Eigenproblems section in LAPACK Users' Guide. Lie theory applications include: Every invertible operator...
algorithms and utilizes the functionality of software interfaces such as BLAS, LAPACK, and MPI. In 2004, Trilinos received an R&D100 Award. Several supercomputing...
partial port of the LAPACK to C++, C#, Delphi, Visual Basic, etc. (spdmatrixcholesky, hpdmatrixcholesky) libflame is a C library with LAPACK functionality....
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/ 24 November 2023