Reference-LAPACK/lapack v3.11 on GitHub

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..

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.

level-3 BLAS solver for 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).

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.

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).

Improvements on the building system and the Continuous Testing framework

Regression test for illegal modification of Y in *GEMV by @matcross in #622.
Test the Fortran intrinsic ABS and complex divisions and report failures during build by @weslleyspereira in #623.
Appveyor is working in the Continuous Testing once more by @martin-frbg in #627.
More tests and fixes for type mismatches by @angsch in #675.
Solve build issues with IBM XLF by @friedc in #677.
Explicit type casts to INT by @angsch in #684.
Fix an out-of-bounds write in the tests by @angsch in #685.
Adding support for NAG Fortran compiler (nagfor) by @ACSimon33 in #686.
Fix time check flag propagation and default value by @ACSimon33 in #696.
Fixed format warnings in 64 bit integer builds by @ACSimon33 in #700.
Explicit type casts and more rigorous CI by @weslleyspereira in #703.
Fix type mismatches in function calls of testing code by @mjacobse in #706.
Fix lower triangular band matrix generation by @angsch in #728.

Other improvements

Improves the computation of norms in {S,D}ORBDB6 and {C,Z}UNBDB6 by @christoph-conrads in #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 #655.
Return immediately when scaling with one by @angsch in #674.
Improve FMA usage in *LAQR5 by @angsch in #681.
Set SCALE early for robust triangular solvers by @angsch in #712.
Add {C,Z}ROTG, {CS,ZD}ROT, {S,D}CABS1 to CBLAS by @angsch in #721.
Add *LANGB to LAPACKE by @ACSimon33 in #725.
NaN check for trapezoidal matrices on LAPACKE by @ACSimon33 in #738 and #742.

Bug fixes

Fix LAPACKE_*tpmqrt_work for row-major matrices by @weslleyspereira in #540.
Fix leading dimension check in LAPACKE's *geesv[x] and *gges[x] by @angsch in #665.
Fix the left-looking variant of GEQRF by @weslleyspereira in #690.
Fix workspace query for *SYEVD and *HEEVD routines by @neil-lindquist in #691.

New Contributors

@PhillHS made their first contribution in #601
@mtowara made their first contribution in #663
@dbakshee made their first contribution in #671
@ACSimon33 made their first contribution in #686
@friedc made their first contribution in #677
@neil-lindquist made their first contribution in #691
@ivan-pi made their first contribution in #699
@mjacobse made their first contribution in #702
@MonicaLiu0311 made their first contribution in #720
@eltociear made their first contribution in #735

Full Changelog: v3.10.1...v3.11

Thanks to all our contributors!
Thanks to the Mathworks team: Penny Anderson, Mary Ann Freeman, Bobby Cheng, Pat Quillen, Christine Tobler, Heiko Weichelt.

The LAPACK team

Reference-LAPACK/lapack v3.11 Official Release for LAPACK 3.11.0 on GitHub