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lapack-3.12.0.txt

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LAPACK 3.12.0

Release date: 11/24/23.

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..

Support and questions:

LAPACK 3.12.0: What’s new

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

Dynamic Mode Decomposition (DMD)

  • xGEDMD computes the Dynamic Mode Decomposition (DMD) for a pair of data snapshot matrices. For the input matrices X and Y such that Y = A*X with an inaccessible matrix A, xGEDMD computes a certain number of Ritz pairs of A using the standard Rayleigh-Ritz extraction from a subspace of range(X) that is determined using the leading left singular vectors of X. Optionally, xGEDMD returns the residuals of the computed Ritz pairs, the information needed for a refinement of the Ritz vectors, or the eigenvectors of the Exact DMD.

  • xGEDMDQ does the same as xGEDMD but uses a QR factorization based compression of the data.

  • See: Z. Drmac: A LAPACK implementation of the Dynamic Mode Decomposition I. Technical report. AIMDyn Inc. and LAPACK Working Note 298.

  • Developed and coded by Zlatko Drmac, Faculty of Science, University of Zagreb. In cooperation with AIMdyn Inc., Santa Barbara, CA. And supported by (1) DARPA SBIR project "Koopman Operator-Based Forecasting for Nonstationary Processes from Near-Term, Limited Observational Data", Contract No: W31P4Q-21-C-0007; (2) DARPA PAI project "Physics-Informed Machine Learning Methodologies", Contract No: HR0011-18-9-0033; (3) DARPA MoDyL project "A Data-Driven, Operator-Theoretic Framework for Space-Time Analysis of Process Dynamics", Contract No: HR0011-16-C-0116. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the DARPA SBIR Program Office. Distribution Statement A: Approved for Public Release, Distribution Unlimited. Cleared by DARPA on September 29, 2022

  • Adding Dynamic Mode Decomposition (DMD) into LAPACK by @dbielich in PR 736

  • Update C prototypes and LAPACKE interfaces for ?GEDMD/?GEDMDQ by @martin-frbg in PR 880

Truncated QR with Column Pivoting

  • The routine computes a truncated (rank K) or full rank Householder QR factorization with column pivoting of a real M-by-N matrix A using Level 3 BLAS.

  • The truncation criteria (i.e. when to stop the factorization) can be any of the following: (1) The input parameter KMAX, the maximum number of columns KMAX to factorize; (2) The input parameter ABSTOL, the absolute tolerance for the maximum column 2-norm of the residual matrix R22(K); (3) The input parameter RELTOL, the tolerance for the maximum column 2-norm matrix of the residual matrix R22(K) divided by the maximum column 2-norm of the original matrix A, which is equal to abs(R(1,1)). The algorithm stops when any of these conditions is first satisfied, otherwise the whole matrix A is factorized.

  • Truncated QR with Column Pivoting by @scr2016 in PR 891

Reciprocal Scaling of complex vectors

  • [C/Z]RSCL multiplies an n-element complex vector x by the complex scalar 1/a. This is done without overflow or underflow as long as the final result x/a does not overflow or underflow.

  • See: "An algorithm for scaling vectors by the reciprocal of a complex number", Weslley da Silva Pereira, [arXiv:2311.05736](https://arxiv.org/abs/2311.05736)

  • Adds CRSCL by @weslleyspereira in PR 839

Improvements in the 64-bit API

Bug fixes and other changes

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)

New Contributors

Thanks to all our contributors!

  • Special Thanks to the Mathworks team: Penny Anderson, Mary Ann Freeman, Bobby Cheng, Pat Quillen, Christine Tobler, Heiko Weichelt.

  • Special Thanks to the AIMdyn Inc. team Igor Mezic and Maria Fonoberova.

The LAPACK team

Thanks you all!

Bug Fix