Download: lapack-3.12.0.tar.gz

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

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

[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

Fix CBLAS tests with 64-bit indexing by @svillemot in PR 767

Add Index-64 API as extended API with _64 suffix for CBLAS by @mkrainiuk in PR 846

Revert "Add Index-64 API as extended API with _64 suffix for CBLAS" by @langou in PR 856

Add Index-64 API as extended API with _64 suffix for CBLAS by @mkrainiuk in PR 867

Create DOCS/CBLAS.md by @mkrainiuk in PR 863

Reduce number of macros in fortran compilation line for BLAS _64 API by @mkrainiuk in PR 861

Windows build fix by @ACSimon33 in PR 760

Added option to enable flat namespace on macOS by @ACSimon33 in PR 762

Fix bug in new test case for LAPACK 3.11 SLATRS3 by @dklyuchinskiy in PR 755

Check for NaNs in *GECON by @weslleyspereira in PR 765

Fixed bug in array bounds in complex syl01 test by @dklyuchinskiyin PR 758

Fix uninitialized M when quick return in DLARRD and SLARRD by @akobotov in PR 769

In LAPACKE tgsen, allocate iwork when ijob = 0. Fixes #772. by @mgates3 in PR 773

Fix SLATRS3 and CLATRS3 tests by @bartoldeman in PR 764

Fix uninitialized out variables in LARR functions by @echeresh in PR 775

Warnings supression in some LAPACKE functions by @jgpallero in PR 780

Revert "Warnings supression in some LAPACKE functions" by @langou in PR 781

Warnings supression and deletion of unnecessary check in some LAPACKE xLARFB functions by @jgpallero in PR 782

remove redundant space from xerbla call sbgv/hbgv by @dklyuchinskiy in PR 792

don’t subtract N_DEFLATED from istop twice by @thijssteel in PR 794

fix rfp test for DIAG = U by @dklyuchinskiy in PR 796

fix bug in complex precision tests (c|z)het21 by @EduardFedorenkov in PR 798

CMake: Disable TEST_FORTRAN_COMPILER by @jschueller in PR 761

Fix typos in documentation by @angsch in PR 750

Add minimum permissions to workflows by @gabibguti in PR 804

Add numerical tests for trevc3 by @angsch in PR 682

Remove legacy function LABAD by @angsch in PR 805

Refactor xGEBAL by @eprovst in PR 808

Fix typos and errors in comments by @jip in PR 809

cmake: allow setting a prefix for the library names by @joseeroman in PR 810

Fix typos in comments by @jip in PR 811

fix #813 by @langou in PR 814

Replace the (partially defined) constant index variable INDIBL in ?SBGVX and related by @martin-frbg in PR 807

CTGEVC, ZTGEVC: fix typo in description of VR argument by @svillemot in PR 812

Add Security Policy by @gabibguti in PR 819

typos by @musvaage in PR 820

extend tests for error exit sysv sytd2 gehd2 by @dklyuchinskiy in PR 795

CMake: avoid "make" in blas++ and lapack++ by @nim65s in PR 821

appveyor: output test failures by @nim65s in PR 822

Reference actions by commit SHA by @gabibguti in PR 829

LAPACKE interfaces for [cz]unhr_col and [sd]orhr_col by @sknepper in PR 827

fix segfault problem when executing LAPACKE_*geqrt on row major #766 by @sbite0138 in PR 768

Adds comment related to zero-sized matrix B in GELSY by @weslleyspereira in PR 833

update brief descriptions of function purpose, Closes #230 by @weslleyspereira in PR 831

Fix scaling in (S/D)TGSNA, fix #103, thanks to @elivanova by @weslleyspereira in PR 830

Exits xLARUV when N < 1 by @weslleyspereira in PR 837

Create GitHub action to test CMake build system on Windows by @weslleyspereira in PR 524

Fix bug in lapacke_[s,d]geesx by @weslleyspereira in PR 836

Removes unused SMIN from bdsqr by @weslleyspereira in PR 832

Use a better (more informative) message when we say the compiler intr… by @weslleyspereira in PR 845

Improve variants of Cholesky and QR by @angsch in PR 847

fixes #848 by @jaganmn in PR 849

Attempt to fix Appveyor on Windows by @angsch in PR 854

fix dlasd0 / slasd0 documentation issue by @mtowara in PR 855

Remove legacy warning for non IEEE 754 compliant machines by @angsch in PR 852

Add verbose build to CI by @mkrainiuk in PR 858

[cz]hetrd_hb2st.F, [sd]sytrd_sb2st.F OpenMP fixes by @chrwarm in PR 860

new doxygen group structure by @mgates3 in PR 802

Correct the order of returned eigenvalue and eigenvectors for 2x2 matrices with IL=IU in C/D/S/Z/STEMR by @aravindh-krishnamoorthy in PR 867

fix nrhs=0 case in ?gelss by @eaberendeev in PR 876

Fix computation of uplo in LAPACKE_xlarfb by @vladimir-ch in PR 878

Fix workspace query corner cases by @angsch in PR 883

Fix actual arguments in some procedure calls by @mjacobse in PR 885

Improve Cholesky variants by @angsch in PR 889

Removes usage of Experimental (interactive) mode in ctest by @weslleyspereira in PR 892

Updates the documentation of xGEMV and xGBMV related to when M=0 and N=0 by @weslleyspereira in PR 843

Add Scorecard by @gabibguti in PR 895

Remove auxiliary GEQRS, GELQS by @angsch in PR 900

CMake config for IntelLLVM (ifx) and NVIDIA HPC SDK (nvfortran) by @ACSimon33 in PR 898

Fix build for CMake >= 3.27 by @scivision in PR 910

allow absolute GNU install dirs by @chayleaf in PR 893

dtgex2: add 2 to iwork length to prevent OOB interaction in Dtgsy2 by @soypat in PR 907

Adds OpenSSF Scorecard badge by @weslleyspereira in PR 896

Fix issue #908 related to accumulation in xLASSQ by @weslleyspereira in PR 909

Apply ROUNDUP_LWORK function in lapack by @kleineLi in PR 904

Compilation of LAPACKE possibly independent from Fortran by @weslleyspereira in PR 834

Always use C as linker language for CBLAS by @weslleyspereira in PR 920

Uses Valgrind for ExperimentalMemCheck in ctest by @weslleyspereira in PR 844

Adding in quotes in cmake for Intel ifx and linux build by @colleeneb in PR 922

Fix complex BDSQR maxit by @pleshkovvli in PR 927

xORBDB6/xUNBDB6: fix a constant by @christoph-conrads in PR 928

Fixed Fortran preprocessor flag for NAG Fortran compiler by @ACSimon33 in PR 939

Fixed void main() for AppleClang by @ACSimon33 in PR 940

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

Igor Kozachenko (University of California, Berkeley, USA)

Julie Langou (University of Tennessee, USA)

Jim Demmel (University of California, Berkeley, USA)

Jack Dongarra (University of Tennessee and ORNL, USA)

Julien Langou (University of Colorado Denver, USA)

@dklyuchinskiy made their first contribution in PR 755

@akobotov made their first contribution in PR 769

@bartoldeman made their first contribution in PR 764

@jgpallero made their first contribution in PR 780

@EduardFedorenkov made their first contribution in PR 798

@gabibguti made their first contribution in PR 804

@eprovst made their first contribution in PR 808

@joseeroman made their first contribution in PR 810

@musvaage made their first contribution in PR 820

@nim65s made their first contribution in PR 821

@sknepper made their first contribution in PR 827

@sbite0138 made their first contribution in PR 768

@dbielich made their first contribution in PR 736

@jaganmn made their first contribution in PR 849

@mkrainiuk made their first contribution in PR 846

@chrwarm made their first contribution in PR 860

@aravindh-krishnamoorthy made their first contribution in PR 867

@eaberendeev made their first contribution in PR 876

@chayleaf made their first contribution in PR 893

@soypat made their first contribution in PR 907

@kleineLi made their first contribution in PR 904

@colleeneb made their first contribution in PR 922

@pleshkovvli made their first contribution in PR 927

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.

Closed bugs

Open bugs

All open issues