Release date: 12/24/16.

This material is based upon work supported by the National Science Foundation and the Department of Energy under Grant No. NSF ACI 1339797, NSF-OCI-1032861, NSF-CCF-00444486, NSF-CNS 0325873, NSF-EIA 0122599, NSF-ACI-0090127, DOE-DE-FC02-01ER25478, DOE-DE-FC02-06ER25768.

LAPACK is a software package provided by Univ. of Tennessee, Univ. of California, Berkeley, Univ. of Colorado Denver and NAG Ltd..

1. Support and questions:

http://icl.cs.utk.edu/lapack-forum/

https://github.com/Reference-LAPACK/lapack/

2. LAPACK 3.7.0: What’s new

2.1. Linear Least Squares / Minimum Norm solution

A contribution from Syd Hashemi Ghermezi (UC Berkeley), Jim Demmel (UC Berkeley), with some help from Eugene Chereshnev (Intel) and Konstantin Arturov (Intel).

  • New TP (triangle on top of trapezoid kernels for LQ factorization

  • Short and Wide LQ (SWLQ) and Tall and Skinny QR (TSQR) factorization

  • New interface for QR and LQ factorization is GEQR and GELQ

  • Corresponding Linear Least Squares / Minimum Norm solution driver (GETSLS)

Added:

SRC/cgelq.f             SRC/dgelq.f             SRC/sgelq.f             SRC/zgelq.f
SRC/cgelqt.f            SRC/dgelqt.f            SRC/sgelqt.f            SRC/zgelqt.f
SRC/cgelqt3.f           SRC/dgelqt3.f           SRC/sgelqt3.f           SRC/zgelqt3.f
SRC/cgemlq.f            SRC/dgemlq.f            SRC/sgemlq.f            SRC/zgemlq.f
SRC/cgemlqt.f           SRC/dgemlqt.f           SRC/sgemlqt.f           SRC/zgemlqt.f
SRC/cgemqr.f            SRC/dgemqr.f            SRC/sgemqr.f            SRC/zgemqr.f
SRC/cgeqr.f             SRC/dgeqr.f             SRC/sgeqr.f             SRC/zgeqr.f
SRC/cgetsls.f           SRC/dgetsls.f           SRC/sgetsls.f           SRC/zgetsls.f
SRC/clamswlq.f          SRC/dlamswlq.f          SRC/slamswlq.f          SRC/zlamswlq.f
SRC/clamtsqr.f          SRC/dlamtsqr.f          SRC/slamtsqr.f          SRC/zlamtsqr.f
SRC/claswlq.f           SRC/dlaswlq.f           SRC/slaswlq.f           SRC/zlaswlq.f
SRC/clatsqr.f           SRC/dlatsqr.f           SRC/slatsqr.f           SRC/zlatsqr.f
SRC/ctplqt.f            SRC/dtplqt.f            SRC/stplqt.f            SRC/ztplqt.f
SRC/ctplqt2.f           SRC/dtplqt2.f           SRC/stplqt2.f           SRC/ztplqt2.f
SRC/ctpmlqt.f           SRC/dtpmlqt.f           SRC/stpmlqt.f           SRC/ztpmlqt.f

References:

  • Brian C. Gunter and Robert A. Van De Geijn, Parallel out-of-core computation and updating of the QR factorization, ACM Transactions on Mathematical Software, 31(1):60-78, 2005.

  • James Demmel, Laura Grigori, Mark Hoemmen, and Julien Langou. Communication-Optimal Parallel and Sequential QR and LU Factorizations. SIAM J. Scientific Computing, 34(1):A206—A239, 2012.

2.2. Symmetric-indefinite Factorization: Aasen’s tridiagonalization

A contribution from Ichitaro Yamazaki (University of Tennessee).

This is Aasen’s factorization for symmetric-indefinite factorization.

Added:

SRC/chesv_aa.f       SRC/dsysv_aa.f       SRC/ssysv_aa.f        SRC/zhesv_aa.f
SRC/chetrf_aa.f      SRC/dsytrf_aa.f      SRC/ssytrf_aa.f       SRC/zhetrf_aa.f
SRC/chetrs_aa.f      SRC/dsytrs_aa.f      SRC/ssytrs_aa.f       SRC/zhetrs_aa.f
SRC/clahef_aa.f      SRC/dlasyf_aa.f      SRC/slasyf_aa.f       SRC/zlahef_aa.f

References:

  • Miroslav Rozloznik, Gil Shklarski, and Sivan Toledo, Partitioned triangular tridiagonalization, ACM Transactions on Mathematical Software, 37(4), article 38, 16 pages, 2011

  • Jan Ole Aasen, On the reduction of a symmetric matrix to tridiagonal form, BIT, 11 (1971), pp. 233–242.

2.3. Symmetric-indefinite Factorization: New storage format for L factor in Rook Pivoting and Bunch Kaufman of LDLT

A contribution from Igor Kozachenko and Jim Demmel (UC Berkeley).

This storage format is akin to LU and enables Level 3 BLAS TRS and TRI. Added routines for new factorization code for symmetric indefinite ( or Hermitian indefinite ) matrices with bounded Bunch-Kaufman ( rook ) pivoting algorithm. New more efficient storage format for factors U (or L), block-diagonal matrix D, and pivoting information stored in IPIV: factor L is stored explicitly in lower triangle of A; diagonal of D is stored on the diagonal of A; subdiagonal elements of D are stored in array E; IPIV format is the same as in *_ROOK routines, but differs from SY Bunch-Kaufman routines (e.g. *SYTRF). The factorization output of these new rook _RK routines is not compatible with the existing _ROOK routines and vice versa. This new factorization format is designed in such a way, that there is a possibility in the future to write new Bunch-Kaufman routines that conform to this new factorization format. Then the future Bunch-Kaufman routines could share solver *TRS_3,inversion *TRI_3 and condition estimator *CON_3.

Added:

SRC/dsytf2_rk.f     SRC/ssytf2_rk.f      SRC/zsytf2_rk.f     SRC/zhetf2_rk.f      SRC/csytf2_rk.f  SRC/chetf2_rk.f
SRC/dlasyf_rk.f     SRC/slasyf_rk.f      SRC/zlasyf_rk.f     SRC/zlahef_rk.f      SRC/clasyf_rk.f  SRC/clahef_rk.f
SRC/dsytrf_rk.f     SRC/ssytrf_rk.f      SRC/zsytrf_rk.f     SRC/zhetrf_rk.f      SRC/csytrf_rk.f  SRC/chetrf_rk.f
SRC/dsytrs_3.f      SRC/ssytrs_3.f       SRC/zsytrs_3.f      SRC/zhetrs_3.f       SRC/csytrs_3.f   SRC/chetrs_3.f
SRC/dsycon_3.f      SRC/ssycon_3.f       SRC/zsycon_3.f      SRC/zhecon_3.f       SRC/csycon_3.f   SRC/checon_3.f
SRC/dsytri_3.f      SRC/ssytri_3.f       SRC/zsytri_3.f      SRC/zhetri_3.f       SRC/csytri_3.f   SRC/chetri_3.f
SRC/dsytri_3x.f     SRC/ssytri_3x.f      SRC/zsytri_3x.f     SRC/zhetri_3x.f      SRC/csytri_3x.f  SRC/chetri_3x.f
SRC/dsysv_rk.f      SRC/ssysv_rk.f       SRC/zsysv_rk.f      SRC/zhesv_rk.f       SRC/csysv_rk.f   SRC/chesv_rk.f

2.4. Symmetric eigenvalue problem: Two-stage algorithm for reduction to tridiagonal form

A contribution from Azzam Haidar (University of Tennessee).

This is the two-stage algorithm for reduction to tridiagonal form. Based on an algorithm from Lang.

Added:

SRC/chb2st_kernels.f    SRC/dsb2st_kernels.f    SRC/ssb2st_kernels.f    SRC/zhb2st_kernels.f
SRC/chbev_2stage.f      SRC/dsbev_2stage.f      SRC/ssbev_2stage.f      SRC/zhbev_2stage.f
SRC/chbevd_2stage.f     SRC/dsbevd_2stage.f     SRC/ssbevd_2stage.f     SRC/zhbevd_2stage.f
SRC/chbevx_2stage.f     SRC/dsbevx_2stage.f     SRC/ssbevx_2stage.f     SRC/zhbevx_2stage.f
SRC/cheev_2stage.f      SRC/dsyev_2stage.f      SRC/ssyev_2stage.f      SRC/zheev_2stage.f
SRC/cheevd_2stage.f     SRC/dsyevd_2stage.f     SRC/ssyevd_2stage.f     SRC/zheevd_2stage.f
SRC/cheevr_2stage.f     SRC/dsyevr_2stage.f     SRC/ssyevr_2stage.f     SRC/zheevr_2stage.f
SRC/cheevx_2stage.f     SRC/dsyevx_2stage.f     SRC/ssyevx_2stage.f     SRC/zheevx_2stage.f
SRC/chegv_2stage.f      SRC/dsygv_2stage.f      SRC/ssygv_2stage.f      SRC/zhegv_2stage.f
SRC/chetrd_2stage.f     SRC/dsytrd_2stage.f     SRC/ssytrd_2stage.f     SRC/zhetrd_2stage.f
SRC/chetrd_hb2st.F      SRC/dsytrd_sb2st.F      SRC/ssytrd_sb2st.F      SRC/zhetrd_hb2st.F
SRC/chetrd_he2hb.f      SRC/dsytrd_sy2sb.f      SRC/ssytrd_sy2sb.f      SRC/zhetrd_he2hb.f
SRC/clarfy.f            SRC/dlarfy.f            SRC/slarfy.f            SRC/zlarfy.f

References:

  • Christian H. Bischof, Bruno Lang, and Xiaobai Sun, A framework for symmetric band reduction, ACM Transactions on Mathematical Software, 26(4): 581-601, 2000.

2.5. Improved Complex Jacobi SVD

A contribution from Zlatko Drmac (University of Zagreb).

(1) LWORK query added; (2) few modifications in pure one sided Jacobi (XGESVJ) to remove possible error in the really extreme cases (sigma_max close to overflow and sigma_min close to underflow) - note that XGESVJ is designed to compute the singular values in the full range; it was used (double complex) to compute SVD of certain factored Hankel matrices with the condition number 1.0e616; (3) same modifications in the preconditioned Jacobi SVD (XGEJSV), the idea is also to extend the computational range, this brings assumptions on how other lapack routines behave under those extreme conditions.

Modified:

SRC/cgejsv.f    SRC/zgejsv.f
SRC/cgesvj.f    SRC/zgesvj.f
SRC/cgsvj0.f    SRC/zgsvj0.f
SRC/cgsvj1.f    SRC/zgsvj1.f

2.6. LAPACKE interfaces

A contribution from Julie Langou (University of Tennessee).

3. Developer list

External Contributors

  • Konstantin Arturov, Intel

  • Eugene Chereshnev, Intel

  • Zlatko Drmac, University of Zagreb

LAPACK developers involved in this release

  • Mark Gates (University of Tennessee)

  • Syd Hashemi Ghermezi (UC Berkeley)

  • Azzam Haidar (University of Tennessee)

  • Igor Kozachenko (University of California, Berkeley, USA)

  • Julie Langou (University of Tennessee, USA)

  • Osni Marques (University of California, Berkeley, USA)

  • Ichitaro Yamazaki (University of Tennessee)

Principal Investigators

  • Jim Demmel (University of California, Berkeley, USA)

  • Jack Dongarra (University of Tennessee and ORNL, USA)

  • Julien Langou (University of Colorado Denver, USA)

4. Thanks

  • MathWorks: Penny Anderson, Amanda Barry, Mary Ann Freeman, Bobby Cheng, Duncan Po, Pat Quillen, Christine Tobler.

  • Intel: Konstantin Arturov, Eugene Chereshnev

  • Gonum: Vladimír Chalupecký

  • ORACLE: Elena Ivanov.

  • IBM: Peng HongBo, Joan McComb, and Yi LB Peng.

  • Cygwin: Marco Atzeri

  • GitHub Users: turboencabulator@github, cmoha@github, banzaiman@github, advanpix@github, reeuwijk-altium@github, brandimarte@github, zerothi@github

  • Christoph Conrads

  • J. Kay Dewhurst (Max Planck Institute of Microstructure Physics)

  • Kyle Guinn

  • Berend Hasselman

  • Pavel Holoborodko

  • Hans Johnson (Univeristy of Iowa)

  • Nick Papior

  • Antonio Rojas

  • Julien Schueller (Phimeca)

5. Bug Fix