LAPACK 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. 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 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 all top 5 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 39 Numerical Linear Algebra with Applications 37 Computer Methods in Applied Mechanics and Engineering 28 Numerical Algorithms 26 Computers & Mathematics with Applications 22 International Journal for Numerical Methods in Engineering 21 Parallel Computing 20 Applied Mathematics and Computation 17 Computers and Fluids 16 BIT 16 Numerische Mathematik 16 Applied Numerical Mathematics 15 Engineering Analysis with Boundary Elements 14 Journal of Scientific Computing 12 ETNA. 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A 2 Calcolo 2 Information Sciences 2 Programming and Computer Software 2 SIAM Journal on Control and Optimization ...and 192 more Serials all top 5 Cited in 49 Fields 1,213 Numerical analysis (65-XX) 234 Linear and multilinear algebra; matrix theory (15-XX) 220 Computer science (68-XX) 179 Fluid mechanics (76-XX) 128 Partial differential equations (35-XX) 103 Operations research, mathematical programming (90-XX) 87 Mechanics of deformable solids (74-XX) 74 Quantum theory (81-XX) 67 Systems theory; control (93-XX) 64 Statistics (62-XX) 53 Statistical mechanics, structure of matter (82-XX) 51 Ordinary differential equations (34-XX) 43 Biology and other natural sciences (92-XX) 33 Optics, electromagnetic theory (78-XX) 23 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) 20 Geophysics (86-XX) 18 Classical thermodynamics, heat transfer (80-XX) 18 Information and communication theory, circuits (94-XX) 16 Approximations and expansions (41-XX) 15 Mechanics of particles and systems (70-XX) 14 Field theory and polynomials (12-XX) 13 Combinatorics (05-XX) 12 Probability theory and stochastic processes (60-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Real functions (26-XX) 11 Functions of a complex variable (30-XX) 11 Operator theory (47-XX) 11 Astronomy and astrophysics (85-XX) 10 Integral equations (45-XX) 8 Commutative algebra (13-XX) 8 Relativity and gravitational theory (83-XX) 6 Algebraic geometry (14-XX) 5 History and biography (01-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Number theory (11-XX) 2 Potential theory (31-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Integral transforms, operational calculus (44-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 2 Mathematics education (97-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) Citations by Year