Sponsor

Since 2010, this material is based upon work supported by the National Science Foundation under Grant No. NSF-OCI-1032861. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF). Until 2006, this material was based upon work supported by the National Science Foundation under Grant No. ASC-9313958, NSF-0444486 and DOE Grant No. DE-FG03-94ER25219. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF) or the Department of Energy (DOE).

Contributing institutions

  • University of Rousse; Bulgaria

  • University of Zagreb; Croatia

  • Danish Computing Center for Research and Education; Denmark

  • Technical University of Denmark; Denmark

  • Fernuniversitaet Hagen; Germany

  • Technical University Aachen; Germany

  • IBM ECSEC; Italia

  • Universidad Jaime I; Spain

  • Umeå University; Sweden

  • ETH Zurich; Switzerland

  • Numerical Algorithms Group Ltd. (NAG); UK

  • University of Manchester; UK

  • Cray Research, Inc; US

  • Duke University; US

  • Georgia Institute of Technology; US

  • IBM Watson Research Center; US

  • Intel Corp., US

  • Kitware, US

  • Lawrence Berkeley National Laboratory; US

  • Oak Ridge National Laboratory; US

  • Randolph-Macon College; US

  • Rice University; US

  • University of California, Berkeley; US

  • University of California, Davis; US

  • University of Colorado Denver; US

  • University of Kansas; US

  • University of Kentucky; US

  • University of Tennessee; US

  • University of Washington; US

Contributor list

  • Ed Anderson (Cray Research Inc. and University of Tennessee; US),

  • Chuck Atkins (Kitware; US),

  • Zhaojun Bai (University of Kentucky and University of California, Davis; US),

  • V. A. Barker (Technical University of Denmark; Denmark),

  • Chris Bischof (Technical University Aachen; Germany),

  • Susan Blackford (University of Tennessee; US),

  • Zvonomir Bujanovic (University of Zagreb; Croatia),

  • Karen Braman (University of Kansas; US),

  • Ralph Byers (University of Kansas; US),

  • Jim Demmel (University of California, Berkeley; US),

  • Inderjit Dhillon (University of California, Berkeley; US),

  • Jack Dongarra (University of Tennessee and Oak Ridge National Laboratory; US),

  • Zlatko Drmac (University of Zagreb; Croatia),

  • Peng Du (University of Tennessee; US),

  • Jeremy Du Croz (Numerical Algorithms Group Ltd. (NAG); UK),

  • Mark Fahey (University of Kentucky; US),

  • Anne Greenbaum (University of Washington; US),

  • Ming Gu (University of California, Berkeley; US),

  • Fred Gustavson (IBM Watson Research Center; US),

  • Deaglan Halligan (University of California, Berkeley; US),

  • Sven Hammarling (Numerical Algorithms Group Ltd. (NAG); UK),

  • Yozo Hida (University of California, Berkeley; US),

  • Nick Higham (University of Manchester; UK),

  • Bill Hoffman (Kitware; US),

  • Intel MKL team (Intel Corp.; US),

  • Bo Kagström (Umeå University; Sweden),

  • Daniel Kressner (ETH Zurich; Switzerland),

  • William Kahan (University of California, Berkeley ; US),

  • Julie Langou, (University of Tennessee; US),

  • Julien Langou (University of Colorado Denver; US),

  • Craig Lucas, (University of Manchester and NAG Ltd., UK;),

  • Piotr Luszczek, (University of Tennessee; US),

  • Ren-Cang Li (University of California, Berkeley; US),

  • Xiaoye Li (Lawrence Berkeley National Laboratory; US),

  • M. Marinova (Danish Computing Center for Research and Education; Denmark),

  • Osni Marques (Lawrence Berkeley National Laboratory; US),

  • Peter Mayes (IBM ECSEC; Italia),

  • Alan McKenney (no affiliation),

  • Beresford Parlett (University of California, Berkeley; US),

  • Antoine Petitet (University of Tennessee; US),

  • Peter Poromaa (Umeå University; Sweden),

  • Enrique Quintana-Ortí (Universidad Jaime I; Spain),

  • Gregorio Quintana-Ortí (Universidad Jaime I; Spain),

  • Giuseppe Radicati (IBM ECSEC; Italia),

  • Huan Ren (University of California, Berkeley; US),

  • Jason Riedy (University of California, Berkeley; US; and Georgia Institute of Technology; US),

  • Jeff Rutter (University of California, Berkeley; US),

  • Edward Smyth (Numerical Algorithms Group Ltd. (NAG); UK),

  • Danny Sorensen (Rice University; US),

  • Ken Stanley (University of California, Berkeley; US),

  • Xiaobai Sun (Duke University; US)

  • Brian Sutton (Randolph-Macon College; US),

  • Françoise Tisseur (University of Tennessee; US),

  • Robert A. van de Geijn (University of Texas at Austin; US),

  • Kresimir Veselic (Fernuniversitaet Hagen; Germany)

  • Christof Voemel (University of California, Berkeley and Lawrence Berkeley National Laboratory; US).

  • Meghanath Vishvanath (University of California, Berkeley; US),

  • David Vu (University of California, Berkeley; US),

  • Jerzy Waśniewski (Technical University of Denmark, Denmark),

  • P. Yalamov (University of Rousse; Bulgaria).

Thanks for bug-report/patches/suggestions to:

  • LAPACK 3.3:

    Allin Cottrell (Wake Forest University),
    Mathew Cross (NAG),
    Zlatko Drmac (University of Zagreb, Croatia),
    Victor Liu, (Stanford University, Palo Alto),
    the Numpy team,
    Bart Oldeman, (Montreal, Quebec)
    Stephan Ripke (Broad Institute, Boston),
    Ake Sandgren (HPC2N, Umea University),
    Clint Whaley (University of Texas at San Antonio).
  • LAPACK 3.2.2:

    Marco Atzeri
    Guy Bencteux (CERMICS, France)
    Michael Chuvelev (Intel)
    Mathew Cross (NAG)
    William Gandler (NIH/CIT)
    Tim Hopkins
    "Jan"
    Ondra Kamenik
    Alexander V. Kobotov (Intel)
    Ashutosh Mahajan (Mathematics and Computer Science Division of Argonne National Labs)
    Lawrence Mulholland (NAG)
    Pat Quillen (MathWorks)
    Paul Roberts (NAG)
    Vasile Sima (National Institute for Research & Development in Informatics, Romania)
    Sergei Steshenko
    Kevin Wadleigh
    Zbigniew
  • LAPACK 3.2.1:

    Guy Bencteux (CERMICS, France)
    Edouard Canot (IRISA, France)
    Michael Chuvelev (Intel)
    "faber80"
    Bruno Pincon (ESIAL, France)
    Vasile Sima (National Institute for Research & Development in Informatics, Romania)
    Christof Voemel
    Daniel Waggoner
    Igor Zhuravlov
  • LAPACK 3.2:

    Patrick Alken (University of Colorado at Boulder, USA),
    Penny Anderson (MathWorks, MA, USA),
    Michael Baudin (Scilab, FR),
    Bobby Cheng (MathWorks, MA, USA),
    Michael Chuvelev (Intel, USA),
    Phil DeMier (IBM, USA),
    Michel Devel (UTINAM institute, University of Franche-Comte, UMR CNRSA, FR),
    Alan Edelmann (Massachusetts Institute of Technology, MA, USA),
    Carlo de Falco and all the Octave developers,
    Fernando Guevara (University of Utah, UT, USA),
    Christian Keil,
    Zbigniew Leyk (Wolfram, USA),
    Cleve Moler (MathWorks, MA, USA),
    Joao Moreira de Sa Coutinho,
    Lawrence Mulholland (NAG, UK),
    Duncan Po (MathWorks, MA, USA),
    Mick Pont (NAG, UK),
    Pat Quillen (MathWorks, MA, USA),
    Clint Whaley (University of Texas at San Antonio, TX, USA),
    Mikhail Wolfson (MIT, USA),
    Vittorio Zecca.
  • LAPACK 3.1.1:

    Tobias Burns
    Daniel Kressner
    Michael Wimmer
  • LAPACK 3.1:

    Eduardo Anglada (Universidad Autonoma de Madrid, Spain)
    David Barnes (University of Kent, England)
    Alberto Garcia (Universidad del Pais Vasco, Spain)
    Tim Hopkins (University of Kent, England)
    Javier Junquera (CITIMAC, Universidad de Cantabria, Spain)
    Mathworks: Penny Anderson, Bobby Cheng, Pat Quillen, Cleve Moler, Duncan Po, Bin Shi, Greg Wolodkin (MathWorks, USA)
    George McBane (Grand Valley State University, USA)
    Matyas Sustik (University of Texas at Austin, USA)
    Michael Wimmer (Universit├Ąt Regensburg, Germany)
    Simon Wood (University of Bath, UK) and in more generally all the R developers

Principal Investigators

  • Jim Demmel (University of California, Berkeley; US; Since 1992),

  • Jack Dongarra (University of Tennessee and Oak Ridge National Laboratory; US; Since 1992),

  • Julien Langou (University of Colorado Denver; US; Since 2006).

Contributors and their contributions

(single precision routine only for some fields)

CS Decomposition — SORCSD

  • Brian Sutton, Randolph-Macon College; US

    A cuncsd    A dorcsd    A sorcsd      A zuncsd
    A cunbdb    A dorbdb    A sorbdb      A zunbdb
    A cbbcsd    A dbbcsd    A sbbcsd      A zbbcsd
    A clapmr    A dlapmr    A slampr      A zlapmr
                A dlartgp   A slartgp
                A dlartgs   A slartgs

Secular Equation Solver (used in the Divide and Conquer Algorithm) — SLASD4

  • Ren-Cang Li, Computer Science Division, University of California at Berkeley, US

    SLASD4
    SLASD5

Pivoted Cholesky

  • Craig Lucas, (University of Manchester and NAG Ltd., UK)

    A SRC/cpstf2.f   A SRC/dpstf2.f   A SRC/spstf2.f   A SRC/zpstf2.f
    A SRC/cpstrf.f   A SRC/dpstrf.f   A SRC/spstrf.f   A SRC/zpstrf.f

Machine Parameter Routine — SLAMCH

  • Piotr Luszczek, (University of Tennessee; US),

  • Jason Riedy (Georgia Institute of Technology; US),

    M dlamch.f
    M slamch.f

Condition Number Estimate Subroutine — SLACN2

  • Nick Higham, University of Manchester

    SLACN2
    deprecated: SLACON (not thread safe)

General purpose auxiliary routines

  • Nick Higham, University of Manchester

    SCSUM1

Level-3 BLAS symmetric indefinite solve and symmetric indefinite inversion

  • Julie Langou, (University of Tennessee; US),

    M chesv.f        M dsysv.f         M ssysv.f       M zhesv.f
    A chetrs2.f      A dsytrs2.f       A ssytrs2.f     A zhetrs2.f
    A csyconv.f      A dsyconv.f       A ssyconv.f     A zsyconv.f
    A csyswapr.f     A dsyswapr.f      A ssyswapr.f    A zsyswapr.f
    A csytri2.f      A dsytri2.f       A ssytri2.f     A zsytri2.f
    A csytri2x.f     A dsytri2x.f      A ssytri2x.f    A zsytri2x.f

Mixed precision iterative refinement subroutines for exploiting fast single precision hardware

  • Julie Langou, (University of Tennessee; US),

  • Julien Langou (University of Colorado Denver; US; 2006-).

    A SRC/dsposv.f          A SRC/zcposv.f
    A SRC/dsgesv.f          A SRC/zcgesv.f

Jacobi SVD Algorithm — SGEJSV & SGESVJ

  • Zlatko Drmac of the University of Zagreb

  • Kresimir Veselic of the Fernuniversitaet Hagen

    SGEJSV
    SGESVJ
    SGSVJ0
    SGSVJ1

Divide & Conquer SVD Algorithm — SGESDD

Linear Least Squares solver based on Divide & Conquer SVD Algorithm — SGELSD

  • Ming Gu, Computer Science Division, University of California at Berkeley, US

  • Huan Ren, Computer Science Division, University of California at Berkeley, US

    SBDSDC
    SLASD0
    SLASD1
    SLASD2
    SLASD3
    SLASD6
    SLASD7
    SLASD8
    SLASDA
    SLASDQ
    SLASDT
    SGESDD
  • Ming Gu, Computer Science Division, University of California at Berkeley, US

  • Ren-Cang Li, Computer Science Division, University of California at Berkeley, US

  • Osni Marques, LBNL/NERSC, US

    SGELSD, SLALS0, SLALSA, SLALASD

QR factorization with column pivoting (Level 3 BLAS) — SGEQP3

  • G. Quintana Ortí, Depto. de Informatica, Universidad Jaime I, Spain

  • X. Sun, Computer Science Dept., Duke University, US

    SGEQP3
  • G. Quintana Ortí, Depto. de Informatica, Universidad Jaime I, Spain

  • X. Sun, Computer Science Dept., Duke University, US

  • Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.

    SGEQPF (deprecated), SLAQP2, SLAQPS

Linear Least Squares solver based on QR factorization with column pivoting — SGELSY

  • A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, US

  • E. Quintana Ortí, Depto. de Informatica, Universidad Jaime I, Spain

  • G. Quintana Ortí, Depto. de Informatica, Universidad Jaime I, Spain

    SGELSY
  • A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, US

    SLARZ
    SLARZB
    SLARZT
    SLATRZ
    SORMR3
    SORMRZ
    STZRZF

Nonsymmetric Eigenvalue Problem — NEP — SGEEV

Multishift QR algorithm with Aggressive Early Deflation — SHSEQR

  • Karen Braman (University of Kansas; US),

  • Ralph Byers (University of Kansas; US),

    SHSEQR, SLAQR0, SLAQR1, SLAQR2, SLAQR3, SLAQR4, SLAQR5

Generalized Schur Decomposition Reordering — STGSEN

Generalized Sylvester Equation Solver — STGSYL

  • Bo Kagström, Umeå University; Sweden

  • Peter Poromaa, Umeå University; Sweden

    SGESC2
    SLATDF
    STGEX2
    STGEXC
    STGSEN
    STGSNA
    STGSY2
    STGSYL
    SGETC2

Extra Precise Iterative Refinement Routines

  • James Demmel, Univ. of California, Berkeley, US

  • Deaglan Halligan, Univ. of California, Berkeley, US

  • Yozo Hida, Univ. of California, Berkeley, US

  • Jason Riedy, Univ. of California, Berkeley, US

    SGBEQUB
    SGBRFSX
    SGBSVXX
    SGEEQUB
    SGERFSX
    SGESVXX
    SLA_GBAMV
    SLA_GBRCOND
    SLA_GBRFSX_EXTENDED
    SLA_GBRPVGRW
    SLA_GEAMV
    SLA_GERCOND
    SLA_GERFSX_EXTENDED
    SLA_LIN_BERR
    SLA_PORCOND
    SLA_PORFSX_EXTENDED
    SLA_PORPVGRW
    SLA_RPVGRW
    SLA_SYAMV
    SLA_SYRCOND
    SLA_SYRFSX_EXTENDED
    SLA_SYRPVGRW
    SLA_WWADDW
    SLARSCL2
    SLASCL2
    SPOEQUB
    SPORFSX
    SPOSVXX
    SSYEQUB
    SSYRFSX
    SSYSVXX

Rectangular Full Packed Format

  • Fred Gustavson of the IBM Watson Research Center

    SLANSF
    STFSM
    STFTRI
    STFTTP
    STFTTR
    STPTTF
    SPFTRF
    SPFTRI
    SPFTRS
    STRTTF
  • Fred Gustavson of the IBM Watson Research Center

  • Julien Langou of the Univ. of Colorado Denver

    STRTTP
  • Julien Langou of the Univ. of Colorado Denver

    SSFRK
    STPTTR

Symmetric Eigenvalue Problem — SEP

Expert routines

  • Mark Fahey, Department of Mathematics, Univ. of Kentucky, US

    SLAGV2
    SSYGVD
    SSYGVX
    SSBGVD
    SSBGVX
    SSPGVD
    SSPGVX

Divide & Conquer Agorithm

  • Jeff Rutter, Computer Science Division, University of California at Berkeley, US

    SLAED0
    SLAED7
    SLAED8
    SLAED9
    SLAEDA
  • Jeff Rutter, Computer Science Division, University of California at Berkeley, US

  • Françoise Tisseur, University of Tennessee.

    SLAED1
    SLAED2
    SLAED3
    SSYEVD
    SSTEDC
  • Ren-Cang Li, Computer Science Division, University of California

    SLAED4
    SLAED5
    SLAED6

Multiple Relatively Robust Representations Algorithm — SYEVR

  • Beresford Parlett, University of California, Berkeley, US

  • Jim Demmel, University of California, Berkeley, US

  • Inderjit Dhillon, University of Texas, Austin, US

  • Osni Marques, LBNL/NERSC, US

  • Christof Voemel, University of California, Berkeley, US

    SLAR1V
    SLARRA
    SLARRB
    SLARRC
    SLARRE
    SLARRF
    SLARRJ
    SLARRR
    SLARRV
  • W. Kahan, University of California, Berkeley, US

  • Beresford Parlett, University of California, Berkeley, US

  • Jim Demmel, University of California, Berkeley, US

  • Inderjit Dhillon, University of Texas, Austin, US

  • Osni Marques, LBNL/NERSC, US

  • Christof Voemel, University of California, Berkeley, US

    SLARRD
  • Inderjit Dhillon, IBM Almaden, US

  • Osni Marques, LBNL/NERSC, US

  • Christof Voemel, LBNL/NERSC, US

    SSTEGR
  • Beresford Parlett, University of California, Berkeley, US

  • Jim Demmel, University of California, Berkeley, US

  • Inderjit Dhillon, University of Texas, Austin, US

  • Osni Marques, LBNL/NERSC, US

  • Christof Voemel, University of California, Berkeley, US

    SSTEMR
  • Osni Marques, LBNL/NERSC, US

  • Christof Voemel, University of California, Berkeley, US

  • Jason Riedy, University of California, Berkeley, US

    SLANEG
  • Inderjit Dhillon, IBM Almaden, US

  • Osni Marques, LBNL/NERSC, US

  • Ken Stanley, Computer Science Division, University of California at Berkeley, US

  • Jason Riedy, Computer Science Division, University of California at Berkeley, US

    SSTEVR
    SSYEVR

DQDS algorithm

  • Osni Marques of the Lawrence Berkeley National Laboratory

  • Beresford Parlett of the Univ. of California at Berkeley

    SLASQ1
    SLASQ2
    SLASQ3
    SLASQ4
    SLASQ5
    SLASQ6

Cholesky for banded matrices

  • Peter Mayes, IBM ECSEC, Rome, March 23, 1989

  • Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

    SPBTRF

CMAKE Build system

  • Chuck Atkins, Kitware, US

  • Bill Hoffman, Kitware, US

LAPACK 95

  • V. A. Barker (Technical University of Denmark; Denmark),

  • Susan Blackford (University of Tennessee; US),

  • Jack Dongarra (University of Tennessee and Oak Ridge National Laboratory; US),

  • Jeremy Du Croz (Numerical Algorithms Group Ltd. (NAG); UK),

  • Sven Hammarling (Numerical Algorithms Group Ltd. (NAG); UK),

  • M. Marinova (Danish Computing Center for Research and Education; Denmark),

  • Jerzy Waśniewski (Technical University of Denmark, Denmark),

  • P. Yalamov (University of Rousse; Bulgaria).

Variants for LU, QR and Cholesky

  • Peng Du (University of Tennsee, US)

C Interface to LAPACK

  • MKL team