LAPACK 3.5.0

Release date: 11/13.

This material is based upon work supported by the National Science Foundation and the Department of Energy under Grant No. 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/

2. Thanks

Thanks for bug-report/patches/suggestions to:

Alexander Kobotov (INTEL) - r1350
Bo Kagstrom
Brian Sutton (Randolph-Macon College) - r1414
Duncan Po (Mathworks) - r1349
Elena Ivanov (ORACLE) - r1416
Hong Bo Peng (IBM) - r1425
Lawrence Mulholland (NAG) - r1439
Mathieu Faverge (INRIA) - r1447 and r1449
Michael Baudin (SciLAB)
Sergey Kuznetsov (INTEL) - r1384
Tyrone Rees (STFC Rutherford Appleton Laboratory, UK) - r1385
Victor Liu (Stanford University) - r1372

Forum users: * bmoloney (OHSU) * eem2314

3. LAPACK 3.5.0: What’s new

[Igor Kozachenko] added Symmetric/Hermitian LDLT factorization routines with rook pivoting algorithm

A ./SRC/checon_rook.f   A ./SRC/csytrf_rook.f   A ./SRC/ssycon_rook.f    A ./SRC/zhetrs_rook.f
A ./SRC/chesv_rook.f    A ./SRC/csytri_rook.f   A ./SRC/ssysv_rook.f     A ./SRC/zlahef_rook.f
A ./SRC/chetf2_rook.f   A ./SRC/csytrs_rook.f   A ./SRC/ssytf2_rook.f    A ./SRC/zlasyf_rook.f
A ./SRC/chetrf_rook.f   A ./SRC/dlasyf_rook.f   A ./SRC/ssytrf_rook.f    A ./SRC/zsycon_rook.f
A ./SRC/chetri_rook.f   A ./SRC/dsycon_rook.f   A ./SRC/ssytri_rook.f    A ./SRC/zsysv_rook.f
A ./SRC/chetrs_rook.f   A ./SRC/dsysv_rook.f    A ./SRC/ssytrs_rook.f    A ./SRC/zsytf2_rook.f
A ./SRC/clahef_rook.f   A ./SRC/dsytf2_rook.f   A ./SRC/zhecon_rook.f    A ./SRC/zsytrf_rook.f
A ./SRC/clasyf_rook.f   A ./SRC/dsytrf_rook.f   A ./SRC/zhesv_rook.f     A ./SRC/zsytri_rook.f
A ./SRC/csycon_rook.f   A ./SRC/dsytri_rook.f   A ./SRC/zhetf2_rook.f    A ./SRC/zsytrs_rook.f
A ./SRC/csysv_rook.f    A ./SRC/dsytrs_rook.f   A ./SRC/zhetrf_rook.f
A ./SRC/csytf2_rook.f   A ./SRC/slasyf_rook.f   A ./SRC/zhetri_rook.f

A ./lapacke/src/lapacke_csysv_rook.c
A ./lapacke/src/lapacke_csysv_rook_work.c
A ./lapacke/src/lapacke_dsysv_rook.c
A ./lapacke/src/lapacke_dsysv_rook_work.c
A ./lapacke/src/lapacke_ssysv_rook.c
A ./lapacke/src/lapacke_ssysv_rook_work.c
A ./lapacke/src/lapacke_zsysv_rook.c
A ./lapacke/src/lapacke_zsysv_rook_work.c

A ./TESTING/LIN/cchkhe_rook.f   A ./TESTING/LIN/schksy_rook.f
A ./TESTING/LIN/cchksy_rook.f   A ./TESTING/LIN/sdrvsy_rook.f
A ./TESTING/LIN/cdrvhe_rook.f   A ./TESTING/LIN/slavsy_rook.f
A ./TESTING/LIN/cdrvsy_rook.f   A ./TESTING/LIN/ssyt01_rook.f
A ./TESTING/LIN/chet01_rook.f   A ./TESTING/LIN/zchkhe_rook.f
A ./TESTING/LIN/clavhe_rook.f   A ./TESTING/LIN/zchksy_rook.f
A ./TESTING/LIN/clavsy_rook.f   A ./TESTING/LIN/zdrvhe_rook.f
A ./TESTING/LIN/csyt01_rook.f   A ./TESTING/LIN/zdrvsy_rook.f
A ./TESTING/LIN/dchksy_rook.f   A ./TESTING/LIN/zhet01_rook.f
A ./TESTING/LIN/ddrvsy_rook.f   A ./TESTING/LIN/zlavhe_rook.f
A ./TESTING/LIN/dlavsy_rook.f   A ./TESTING/LIN/zlavsy_rook.f
A ./TESTING/LIN/dsyt01_rook.f   A ./TESTING/LIN/zsyt01_rook.f

[Brian Sutton] 2-by-1 CSD to be used for tall and skinny matrix with orthonormal columns

(in LAPCK 3.4.0, we already integrated CSD of a full square orthogonal matrix)

More info here:

Stable computation of the CS decomposition: simultaneous bidiagonalization
The fundamental CS decomposition
Computing the complete CS decomposition
[Bradley Lowery, Julien Langou and Rodney James, r1413] New stopping criteria for balancing.

Fix from Bradley Lowery, Julien Langou and Rodney James: http://arxiv.org/abs/1401.5766

This fix the problem described in: http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=13&t=4270

M ./SRC/cgebal.f        M ./SRC/dgebal.f        M ./SRC/sgebal.f        M ./SRC/zgebal.f

[Victor Liu, r1372] New complex division algorithm.

Following the algorithm of Michael Baudin, Robert L. Smith (see arxiv.1210.4539 )

M ./SRC/dladiv.f        M ./SRC/sladiv.f

improvements: * slasyf.f, clasyf.f, clahef.f, dlasyf.f, zlahef.f, zlasyf.f :: various improvements by Igor Kozachenko * dhgeqz.f, shgeqz.f :: improvements by Duncan Po (MathWorks), committed by Rodney James * dlasd4.f, slasd4.f :: improvements by Sergey Kuznetsov (Intel), committed by Rodney James * clarfb.f, dlarfb.f, slarfb.f, zlarfb.f :: improvements by Rodney James

3. External Contributors

5. Developer list

Principal Investigators

Jim Demmel (University of California, Berkeley, USA)
Jack Dongarra (University of Tennessee and ORNL, USA)
Julien Langou (University of Colorado Denver, USA)

LAPACK developers involved in this release

Igor Kozachenko (University of California, Berkeley, USA)
Julie Langou (University of Tennessee, USA)
Rodney James (University of Colorado Denver, USA)

6. More details

 *xSYSV_ROOK: LDL^T^ with rook pivoting.* Contribution by Craig Lucas (University
of Manchester and NAG) and Sven Hammarling (NAG).  These subroutines enable
better stability than the Bunch-Kaufman pivoting scheme currently used in
LAPACK xSYSV solvers; also, the elements of L are bounded, which is important
in some applications.  The computational time of xSYSV_ROOK is slightly higher than
the one of xSYSV.

New stopping criteria for balancing.
more robust complex division routine [DLADIV]- suggested by Victor Liu <[email protected]> contributed by Michael Baudin, Robert L. Smith Source: http://arxiv.org/abs/1210.4539 Robert L. Smith is actually the original inventor of the current algorithm in Lapack. I have attached my modified DLADIV routine, which passes all the tests in the build process.

7. Bug Fix

see here