Release date: 11/11/22.

This material is based upon work supported by the National Science Foundation and the Department of Energy.

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 3.11.0: What’s new

This is a major release and also addressing multiple bug fixes.

2.1. Normwise criterion for infinite eigenvalues in the QZ algorithm by @thijssteel

The normwise criterion is more robust at detecting infinite eigenvalues than the elementwise criterion (PR #698). See also https://arxiv.org/abs/2208.02057.

2.2 level-3 BLAS solvers for the triangular system and triangular Sylvester equations by @angsch

The triangular Sylvester equation has been recognized to be prone to overflow. For that purpose, *TRSYL utilizes a scaling factor to represent the solution as (s^{-1} X) and solve the scaled equation AX + XB = s C. Due to the scaling factor, there is some flexibility in the representation of the solution. The proposed level-3 BLAS version computes the scaling factors based on the upper bounds of blocks to enable level-3 BLAS. The scaling is typically slightly more aggressive so that an alternatively scaled final solution is computed. This is no problem as long as the scaling factor does not get flushed to zero (PR #651). The same upper bound calculation was used to write the level-3 BLAS solver for the triangular system, *LATRS3.

2.3 Givens rotations generated with less accumulation error by @weslleyspereira

New algorithms for computing Givens rotations in complex arithmetic that reduce the accumulation errors for computing each of the outputs, c, s, r. The new algorithms are, on average, more accurate than both the algorithms from LAPACK 3.9.1 and LAPACK 3.10.0 (PR #631). See also https://arxiv.org/abs/2211.04010.

2.4 Faster algorithms for Least Squares by @scr2016

The new algorithms, *GELST, are similar to *GELS. *GELST avoids computing triangular blocks twice as in *GELS, which means *GELST runs faster (PR #739).

2.5 Improvements on the building system and the Continuous Testing framework

2.6 Other improvements

  • Improves the computation of norms in {S,D}ORBDB6 and {C,Z}UNBDB6 by @Christoph Conrads in PR #647.

  • Uses a Newton step to compute the initial guess for ETA in {S,D}LAED4 to reduce the number of iterations by @weslleyspereira in PR #655.

  • Return immediately when scaling with one by @angsch in PR #674.

  • Rearrange the application of the Householder reflectors in *LAQR5, which lowers the instruction count when FMA is available by @angsch in PR #681.

  • Set SCALE early for robust triangular solvers by @angsch in PR #712.

  • Add {C,Z}ROTG, {CS,ZD}ROT, {S,D}CABS1 to CBLAS by @angsch in PR #721.

  • Add *LANGB to LAPACKE by @ACSimon33 in PR #725.

  • NaN check for trapezoidal matrices on LAPACKE by @ACSimon33 in PR #738 and PR #742.

2.7 Bug fixes

  • Fix LAPACKE_*tpmqrt_work for row-major matrices by @weslleyspereira in PR 540.

  • Fix leading dimension check in LAPACKE’s *geesv[x] and *gges[x] by @angsch in PR 665.

  • Fix the left-looking variant of GEQRF by @weslleyspereira in PR 690.

  • Fix workspace query for *SYEVD and *HEEVD routines by neil-lindquist@neil-lindquist in PR 691.

  • Fix behavior of SCALE in *LATBS and *LATRS, and avoids NaN generation if entries in CNORM exceed the overflow threshold by @angsch in PR 712.

Full Changelog

3. Developer list

LAPACK developers involved in this release

  • Weslley da Silva Pereira (University of Colorado Denver, USA)

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

  • Julie Langou (University of Tennessee, USA)

Principal Investigators

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

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

  • Julien Langou (University of Colorado Denver, USA)

3.1 New Contributors

4. Thanks again!

Github contribution details here

Thanks you all!

5. Bug Fix