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| Linear Algebra PACKage | |
|---|---|
| Name | Linear Algebra PACKage |
| Developer | Netlib contributors, Jack Dongarra, Olaf Schenk, Andreas M. Bruaset |
| Released | 1970s |
| Latest release version | varies (Fortran, C, LAPACK++) |
| Programming language | Fortran, C, C++ |
| Operating system | UNIX, Linux, Microsoft Windows, macOS |
| Genre | Numerical linear algebra library |
| License | Permissive, BSD-style, LGPL variants |
Linear Algebra PACKage is a standard collection of numerical routines for solving systems of linear equations, eigenvalue problems, and singular value decomposition. It originated as a collaboration among researchers associated with University of Tennessee, Oak Ridge National Laboratory, Argonne National Laboratory, and the broader Netlib community to provide reliable, high-performance building blocks for scientific computing. The package underpins many scientific and engineering codes developed at institutions like Lawrence Berkeley National Laboratory, CERN, NASA, US Department of Energy, and industrial laboratories including IBM and Intel.
The package supplies routines for dense and banded matrix problems used in projects at Los Alamos National Laboratory, Sandia National Laboratories, Rutgers University, University of California, Berkeley, and Princeton University. It interfaces with standards and tools originating from BLAS implementations like GotoBLAS, OpenBLAS, Intel Math Kernel Library, and vendor libraries from Cray Research and Fujitsu. The project is historically linked to numerical analysis work by figures such as James Wilkinson, Alan Turing, John von Neumann, and contemporary developers including Jack Dongarra and François Tisseur.
Development traces to algorithmic advances reported at conferences like the International Congress of Mathematicians and workshops at Argonne National Laboratory and Oak Ridge National Laboratory. Early Fortran implementations grew from research at University of Manchester, Cambridge University, and collaboration among researchers like Cleve Moler and Gene Golub. Successive versions incorporated techniques from publications in journals such as SIAM Journal on Numerical Analysis and conferences including the International Conference on Numerical Linear Algebra and the ACM/IEEE Supercomputing Conference. Funding and stewardship involved agencies including the National Science Foundation and the U.S. Department of Energy.
Routines cover LU, Cholesky, and QR factorizations, eigenvalue solvers for symmetric and nonsymmetric matrices, and singular value decomposition, used in projects at Los Alamos National Laboratory, CERN, NASA Jet Propulsion Laboratory, and European Space Agency. The package integrates pivoting strategies influenced by work from Alan K. Cline and stability analyses reminiscent of James Wilkinson. It provides interfaces for dense linear systems used in codes developed at General Electric, Siemens, Philips, and computational groups at Massachusetts Institute of Technology, Stanford University, and California Institute of Technology.
Implemented primarily in Fortran, the codebase is layered atop optimized BLAS kernels and can be linked with vendor-tuned implementations from Intel Corporation, AMD, and NVIDIA. It supports parallelization via MPI stacks used at Oak Ridge National Laboratory and Lawrence Livermore National Laboratory and interacts with scalable frameworks like ScaLAPACK, PLASMA, and MAGMA. Build and distribution routes historically used Netlib mirrors, package managers at Debian, Red Hat, and repositories maintained by GitHub and Bitbucket.
Benchmark suites from TOP500 and performance studies at Euro-Par and ACM/IEEE Supercomputing Conference compare implementations linked against OpenBLAS, Intel Math Kernel Library, and Cray libraries. Performance tuning leverages cache-blocking, vectorization for SSE, AVX, and NEON instruction sets developed by Intel Corporation, ARM Limited, and AMD. Comparative analyses published in SIAM Review and at ISC High Performance quantify throughput on systems from IBM POWER, Cray XC series, and commodity clusters used in research at Max Planck Society and CERN.
Bindings and front-ends connect the package to ecosystems including MATLAB, GNU Octave, Python (via NumPy, SciPy), R, Julia, and domain packages used at Stanford University and ETH Zurich. High-level frameworks such as TensorFlow, PyTorch, and scientific stacks developed by Google and Facebook leverage routines through vendor libraries from NVIDIA and Intel. Educational courses at Massachusetts Institute of Technology, Harvard University, University of Cambridge, and Oxford University reference the package for reproducible numerical experiments.
The package underlies computations in computational fluid dynamics used by NASA, electromagnetic simulations at CERN, structural analysis in firms like Arup, and signal processing research at Bell Labs and Bell Telephone Laboratories. It enabled advances in climate modeling at NOAA and Met Office and data analysis in projects at Stanford University and University of California, Berkeley. Its algorithms contributed to standards employed in high-performance computing centers such as Argonne National Laboratory and Lawrence Berkeley National Laboratory and have been recognized in awards to contributors like Jack Dongarra by institutions including the Association for Computing Machinery.
Category:Numerical linear algebra libraries