LAPACK swMATH ID: 503 Software Authors: LAPACK 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; MKL; R; CUDA; MPI; Algorithm 679; GitHub Cited in: 1,815 Documents This software is also referenced in ORMS. Standard Articles 4 Publications describing the Software, including 4 Publications in zbMATH Year Improving test coverage of LAPACK. Zbl 1122.68745Barnes, David J.; Hopkins, Tim R. 2007 LAPACK user’s guide. This work is dedicated to Jim Wilkinson. 3rd ed. Zbl 0934.65030Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D. 1999 LAPACK user’s guide. 2nd ed. Zbl 0843.65018Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrouchov, S.; Sorensen, D. 1995 LAPACK users’ guide. Zbl 0755.65028Anderson, E.; Bai, Z.; Bischof, C. 1992 all top 5 Cited by 3,018 Authors 55 Dongarra, Jack J. 37 Demmel, James Weldon 34 Higham, Nicholas John 33 Benner, Peter 33 Quintana-Ortí, Enrique S. 25 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 13 Bientinesi, Paolo 12 Hammarling, Sven J. 12 Lehoucq, Richard B. 12 Toledo, Sivan 12 Zlatev, Zahari 11 Duff, Iain S. 11 Gustavson, Fred G. 11 Li, Rencang 11 Vidal, Antonio Manuel 11 Waśniewski, Jerzy 10 Bischof, Christian H. 10 Ltaief, Hatem 10 Parlett, Beresford Neill 10 Tomov, Stanimire Z. 10 Vömel, Christof 9 Alonso, Pedro 9 Byers, Ralph 9 Kurzak, Jakub 9 Sorensen, Danny C. 8 Aishima, Kensuke 8 Bangerth, Wolfgang 8 Hernández, Vicente G. 8 Ibáñez González, Jacinto Javier 8 Keyes, David Elliot 8 Koev, Plamen 8 Luszczek, Piotr 8 Manocha, Dinesh 8 Petkov, Petko Hr. 8 Walker, David W. 8 Watson, Layne Terry 8 Yang, Chao 7 Arndt, Daniel 7 Baboulin, Marc 7 Bosner, Nela 7 Chu, Delin 7 Dhillon, Inderjit S. 7 Giraud, Luc 7 Haidar, Azzam 7 Heister, Timo 7 Heltai, Luca 7 Konstantinov, Mikhail Mikhajlov 7 Kronbichler, Martin 7 Langou, Julien 7 Maier, Matthias Sebastian 7 Paprzycki, Marcin 7 Pelteret, Jean-Paul 7 Petitet, Antoine 7 Saad, Yousef 7 Sastre, Jorge 7 Sherwin, Spencer J. 7 Slapničar, Ivan 7 Tisseur, Françoise 7 Turcksin, Bruno 7 Van Huffel, Sabine 7 Van Zee, Field Garritt 7 Ward, Michael J. 7 Xia, Jianlin 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 Henry, Greg M. 6 Jessup, Elizabeth R. 6 Kontoghiorghes, Erricos John 6 Mach, Thomas 6 Marques, Osni A. 6 Novaković, Vedran 6 Rump, Siegfried Michael 6 Song, Chongmin 6 Van der Vorst, Henk Albertus 6 Vandebril, Raf 6 Watkins, David S. 6 Wei, Juncheng 6 Yamazaki, Ichitaro 5 Amestoy, Patrick R. 5 Avron, Haim 5 Calvetti, Daniela 5 Choi, Jaeyoung 5 Corless, Robert Malcolm 5 Darve, Eric 5 di Serafino, Daniela 5 Eijkhout, Victor L. ...and 2,918 more Authors all top 5 Cited in 304 Serials 141 ACM Transactions on Mathematical Software 129 SIAM Journal on Scientific Computing 92 Computer Physics Communications 91 Journal of Computational Physics 80 SIAM Journal on Matrix Analysis and Applications 70 Journal of Computational and Applied Mathematics 64 Linear Algebra and its Applications 43 Numerical Linear Algebra with Applications 40 Computer Methods in Applied Mechanics and Engineering 30 Numerical Algorithms 26 International Journal for Numerical Methods in Engineering 25 Computers & Mathematics with Applications 21 Applied Mathematics and Computation 21 Parallel Computing 17 Computers and Fluids 16 BIT 16 Numerische Mathematik 16 Applied Numerical Mathematics 16 Journal of Scientific Computing 16 Engineering Analysis with Boundary Elements 12 Computational Optimization and Applications 12 ETNA. 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The Electronic Journal of Linear Algebra 4 Parallel Algorithms and Applications 4 Computing and Visualization in Science 4 Chaos 4 Communications in Nonlinear Science and Numerical Simulation 4 Parallel Processing Letters 4 Communications in Computational Physics 3 Classical and Quantum Gravity 3 Computers and Structures 3 International Journal of Solids and Structures 3 Journal of Mathematical Physics 3 Programming and Computer Software 3 SIAM Journal on Numerical Analysis 3 Theoretical Computer Science 3 SIAM Journal on Scientific and Statistical Computing 3 Computer Aided Geometric Design 3 COMPEL 3 Numerical Methods for Partial Differential Equations 3 Annals of Operations Research 3 International Journal of Computational Geometry & Applications 3 International Journal of Computer Mathematics 3 SIAM Journal on Applied Mathematics 3 Journal of Nonlinear Science 3 Advances in Engineering Software 3 Communications in Numerical Methods in Engineering 3 Journal of Geodesy 3 Mathematical Communications 3 Computational Geosciences 3 Combustion Theory and Modelling 3 Archives of Computational Methods in Engineering 3 International Journal of Parallel, Emergent and Distributed Systems 3 Lecture Notes in Computational Science and Engineering 3 JSIAM Letters 3 Springer Texts in Statistics 2 International Journal of Control 2 International Journal of Heat and Mass Transfer ...and 204 more Serials all top 5 Cited in 51 Fields 1,291 Numerical analysis (65-XX) 254 Linear and multilinear algebra; matrix theory (15-XX) 232 Computer science (68-XX) 192 Fluid mechanics (76-XX) 132 Partial differential equations (35-XX) 112 Operations research, mathematical programming (90-XX) 95 Mechanics of deformable solids (74-XX) 91 Quantum theory (81-XX) 81 Statistics (62-XX) 72 Statistical mechanics, structure of matter (82-XX) 71 Systems theory; control (93-XX) 51 Ordinary differential equations (34-XX) 44 Biology and other natural sciences (92-XX) 42 Optics, electromagnetic theory (78-XX) 26 Calculus of variations and optimal control; optimization (49-XX) 22 General and overarching topics; collections (00-XX) 22 Dynamical systems and ergodic theory (37-XX) 21 Mechanics of particles and systems (70-XX) 21 Geophysics (86-XX) 19 Classical thermodynamics, heat transfer (80-XX) 18 Information and communication theory, circuits (94-XX) 17 Combinatorics (05-XX) 17 Approximations and expansions (41-XX) 15 Probability theory and stochastic processes (60-XX) 14 Field theory and polynomials (12-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Operator theory (47-XX) 12 Functions of a complex variable (30-XX) 11 Real functions (26-XX) 10 Integral equations (45-XX) 10 Astronomy and astrophysics (85-XX) 9 Commutative algebra (13-XX) 9 Relativity and gravitational theory (83-XX) 7 Algebraic geometry (14-XX) 5 History and biography (01-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 3 Special functions (33-XX) 3 Difference and functional equations (39-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mathematics education (97-XX) 2 Number theory (11-XX) 2 Potential theory (31-XX) 2 Integral transforms, operational calculus (44-XX) 2 Functional analysis (46-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 1 Mathematical logic and foundations (03-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) Citations by Year