swMATH ID: 503
Software Authors: LAPACK team: lapack@cs.utk.edu
Description: 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.
Homepage: http://www.netlib.org/lapack/
Programming Languages: FORTRAN
Keywords: orms; LAPACK software; library of FORTRAN 77 routines; nonsymmetric eigenproblem; linear least squares problems; singular value decomposition; QR and RQ factorizations; reduction of a band matrix
Related Software: BLAS; ScaLAPACK; Matlab; mctoolbox; LINPACK; ARPACK; EISPACK; CLAPACK; PETSc; SparseMatrix; JDQZ; ATLAS; JDQR; MUMPS; MPI; MKL; R; Algorithm 679; CUDA; FFTW
Cited in: 1,687 Documents
This software is also referenced in ORMS.
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Cited by 2,746 Authors

55 Dongarra, Jack J.
37 Demmel, James Weldon
32 Higham, Nicholas J.
32 Quintana-Ortí, Enrique S.
30 Benner, Peter
24 Drmač, Zlatko
24 van de Geijn, Robert Alexander
23 Quintana-Ortí, Gregorio
22 Mehrmann, Volker
18 Kågström, Bo
17 Bai, Zhaojun
15 Gu, Ming
15 Kressner, Daniel
15 Lang, Bruno
12 Bientinesi, Paolo
12 Hammarling, Sven J.
12 Lehoucq, Richard B.
12 Zlatev, Zahari
11 Duff, Iain S.
11 Gustavson, Fred G.
11 Toledo, Sivan
11 Vidal, Antonio Manuel
11 Waśniewski, Jerzy
10 Bischof, Christian H.
10 Li, Rencang
10 Parlett, Beresford Neill
10 Tomov, Stanimire Z.
10 Vömel, Christof
9 Byers, Ralph
9 Kurzak, Jakub
9 Ltaief, Hatem
9 Sorensen, Danny C.
8 Aishima, Kensuke
8 Alonso, Pedro
8 Hernández, Vicente G.
8 Ibáñez González, Jacinto Javier
8 Luszczek, Piotr
8 Manocha, Dinesh
8 Petkov, Petko Hr.
8 Walker, David W.
8 Watson, Layne Terry
7 Bangerth, Wolfgang
7 Bosner, Nela
7 Chu, Delin
7 Dhillon, Inderjit S.
7 Giraud, Luc
7 Haidar, Azzam
7 Keyes, David Elliot
7 Koev, Plamen
7 Konstantinov, Mikhail Mikhajlov
7 Paprzycki, Marcin
7 Petitet, Antoine
7 Sastre, Jorge
7 Sherwin, Spencer J.
7 Slapničar, Ivan
7 Tisseur, Françoise
7 Van Huffel, Sabine
7 Van Zee, Field Garritt
7 Ward, Michael J.
6 Arndt, Daniel
6 Barlow, Jesse L.
6 Berry, Michael W.
6 Buttari, Alfredo
6 Chandrasekaran, Shivkumar
6 Dopico, Froilán M.
6 Faragó, István
6 Foster, Leslie V.
6 Gates, Mark
6 Heister, Timo
6 Heltai, Luca
6 Henry, Greg M.
6 Jessup, Elizabeth R.
6 Kontoghiorghes, Erricos John
6 Kronbichler, Martin
6 Langou, Julien
6 Mach, Thomas
6 Maier, Matthias Sebastian
6 Marques, Osni A.
6 Pelteret, Jean-Paul
6 Rump, Siegfried Michael
6 Saad, Yousef
6 Song, Chongmin
6 Turcksin, Bruno
6 Van der Vorst, Henk Albertus
6 Watkins, David S.
6 Wei, Juncheng
6 Xia, Jianlin
6 Yamazaki, Ichitaro
6 Yang, Chao
5 Avron, Haim
5 Baboulin, Marc
5 Calvetti, Daniela
5 Choi, Jaeyoung
5 Corless, Robert Malcolm
5 di Serafino, Daniela
5 Eijkhout, Victor L.
5 Gansterer, Wilfried N.
5 Granat, Robert A.
5 Gunnels, John A.
5 Heroux, Michael A.
...and 2,646 more Authors
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Cited in 292 Serials

134 ACM Transactions on Mathematical Software
120 SIAM Journal on Scientific Computing
85 Journal of Computational Physics
77 SIAM Journal on Matrix Analysis and Applications
67 Computer Physics Communications
65 Journal of Computational and Applied Mathematics
64 Linear Algebra and its Applications
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37 Computer Methods in Applied Mechanics and Engineering
28 Numerical Algorithms
26 Computers & Mathematics with Applications
22 International Journal for Numerical Methods in Engineering
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17 Computers and Fluids
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15 Engineering Analysis with Boundary Elements
14 Journal of Scientific Computing
12 ETNA. Electronic Transactions on Numerical Analysis
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11 Journal of Fluid Mechanics
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9 Computing
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8 Mathematical Programming. Series A. Series B
7 Mathematics of Computation
7 Mathematics and Computers in Simulation
7 Physica D
7 Japan Journal of Industrial and Applied Mathematics
7 Advances in Computational Mathematics
7 Journal of Machine Learning Research (JMLR)
7 Acta Numerica
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6 European Journal of Operational Research
6 SIAM Review
6 Mathematical Programming Computation
5 Journal of Optimization Theory and Applications
5 Journal of Symbolic Computation
5 Journal of Parallel and Distributed Computing
5 Journal of Global Optimization
5 The Journal of Supercomputing
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5 Journal of Mathematical Chemistry
5 Concurrency and Computation: Practice & Experience
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4 Acta Mechanica
4 IMA Journal of Numerical Analysis
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4 International Journal of Parallel Programming
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3 International Journal of Computational Geometry & Applications
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3 JSIAM Letters
2 International Journal of Control
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2 Calcolo
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2 SIAM Journal on Control and Optimization
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Cited in 49 Fields

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179 Fluid mechanics (76-XX)
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103 Operations research, mathematical programming (90-XX)
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18 Information and communication theory, circuits (94-XX)
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12 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
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