chore(deps): update dependency lapack to v3.11.0

[renovate]

This PR contains the following updates:

Package	Type	Update	Change
lapack	http_archive	minor	v3.10.1 -> v3.11.0

---

Release Notes

Reference-LAPACK/lapack

v3.11.0: Official Release for LAPACK 3.11.0

Compare Source

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..

The following notes are also at http://netlib.org/lapack/lapack-3.11.0.html

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 solvers for the triangular system and triangular Sylvester equation 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, *TRSYL3, 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.

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

Other improvements

• Improves the computation of norms in {S,D}ORBDB6 and {C,Z}UNBDB6 by @​christoph-conrads in https://github.com/Reference-LAPACK/lapack/pull/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 https://github.com/Reference-LAPACK/lapack/pull/655.
• Return immediately when scaling with one by @​angsch in https://github.com/Reference-LAPACK/lapack/pull/674.
• Rearrange the application of the Householder reflectors in *LAQR5, which lowers the instruction count when FMA is available by @​angsch in https://github.com/Reference-LAPACK/lapack/pull/681.
• Add {C,Z}ROTG, {CS,ZD}ROT, {S,D}CABS1 to CBLAS by @​angsch in https://github.com/Reference-LAPACK/lapack/pull/721.
• Add *LANGB to LAPACKE by @​ACSimon33 in https://github.com/Reference-LAPACK/lapack/pull/725.
• NaN check for trapezoidal matrices on LAPACKE by @​ACSimon33 in https://github.com/Reference-LAPACK/lapack/pull/738 and https://github.com/Reference-LAPACK/lapack/pull/742.

Bug fixes

• Fix LAPACKE_*tpmqrt_work for row-major matrices by @​weslleyspereira in https://github.com/Reference-LAPACK/lapack/pull/540.
• Fix leading dimension check in LAPACKE's *geesv[x] and *gges[x] by @​angsch in https://github.com/Reference-LAPACK/lapack/pull/665.
• Fix the left-looking variant of GEQRF by @​weslleyspereira in https://github.com/Reference-LAPACK/lapack/pull/690.
• Fix workspace query for *SYEVD and *HEEVD routines by @​neil-lindquist in https://github.com/Reference-LAPACK/lapack/pull/691.
• Fix behavior of SCALE in *LATBS and *LATRS, and avoids NaN generation if entries in CNORM exceed the overflow threshold by @​angsch in https://github.com/Reference-LAPACK/lapack/pull/712.

New Contributors

• @​PhillHS made their first contribution in https://github.com/Reference-LAPACK/lapack/pull/601
• @​mtowara made their first contribution in https://github.com/Reference-LAPACK/lapack/pull/663
• @​dbakshee made their first contribution in https://github.com/Reference-LAPACK/lapack/pull/671
• @​ACSimon33 made their first contribution in https://github.com/Reference-LAPACK/lapack/pull/686
• @​friedc made their first contribution in https://github.com/Reference-LAPACK/lapack/pull/677
• @​neil-lindquist made their first contribution in https://github.com/Reference-LAPACK/lapack/pull/691
• @​ivan-pi made their first contribution in https://github.com/Reference-LAPACK/lapack/pull/699
• @​mjacobse made their first contribution in https://github.com/Reference-LAPACK/lapack/pull/702
• @​MonicaLiu0311 made their first contribution in https://github.com/Reference-LAPACK/lapack/pull/720
• @​eltociear made their first contribution in https://github.com/Reference-LAPACK/lapack/pull/735

Full Changelog: Reference-LAPACK/lapack@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

---

Configuration

📅 Schedule: Branch creation - At any time (no schedule defined), Automerge - At any time (no schedule defined).

🚦 Automerge: Disabled by config. Please merge this manually once you are satisfied.

♻ Rebasing: Whenever PR becomes conflicted, or you tick the rebase/retry checkbox.

🔕 Ignore: Close this PR and you won't be reminded about this update again.

---

• If you want to rebase/retry this PR, check this box

---

This PR has been generated by Mend Renovate. View repository job log here.