LAPACK development repository
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-3.12.0.html
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 unaccessible 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.
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.
[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.
void main() for AppleClang by @ACSimon33 in https://github.com/Reference-LAPACK/lapack/pull/940
Full Changelog: https://github.com/Reference-LAPACK/lapack/compare/v3.11.0...v3.12.0
Thanks to all our contributors! Thanks to the Mathworks team: Penny Anderson, Mary Ann Freeman, Bobby Cheng, Pat Quillen, Christine Tobler, Heiko Weichelt. Thanks to the AIMdyn Inc. team: Igor Mezic and Maria Fonoberova.
The LAPACK team
This contains releases/versions of LAPACK previous to the Git history, only for purposes of historical reference or comparison.
[!WARNING] Be aware that known bugs exist in these tar files, and have been fixed in subsequent versions! As a result, these tar files should never be used for a current LAPACK installation! You can find the latest release of LAPACK at https://github.com/Reference-LAPACK/lapack/releases
Releases attached:
[!NOTE] The assets named "Source code" relate to the first commit in the Git history of LAPACK.
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
The normwise criterion is more robust at detecting infinite eigenvalues than the elementwise criterion (PR #698). See also https://arxiv.org/abs/2208.02057.
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.
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.
The new algorithms, *GELST, are similar to *GELS. *GELST avoids computing triangular blocks twice as in *GELS, which means *GELST runs faster (PR #739).
*GEMV by @matcross in https://github.com/Reference-LAPACK/lapack/pull/622.{S,D}ORBDB6 and {C,Z}UNBDB6 by @christoph-conrads in https://github.com/Reference-LAPACK/lapack/pull/647.ETA in {S,D}LAED4 to reduce the number of iterations by @weslleyspereira in https://github.com/Reference-LAPACK/lapack/pull/655.*LAQR5, which lowers the instruction count when FMA is available by @angsch in https://github.com/Reference-LAPACK/lapack/pull/681.{C,Z}ROTG, {CS,ZD}ROT, {S,D}CABS1 to CBLAS by @angsch in https://github.com/Reference-LAPACK/lapack/pull/721.*LANGB to LAPACKE by @ACSimon33 in https://github.com/Reference-LAPACK/lapack/pull/725.LAPACKE_*tpmqrt_work for row-major matrices by @weslleyspereira in https://github.com/Reference-LAPACK/lapack/pull/540.*geesv[x] and *gges[x] by @angsch in https://github.com/Reference-LAPACK/lapack/pull/665.*SYEVD and *HEEVD routines by @neil-lindquist in https://github.com/Reference-LAPACK/lapack/pull/691.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.Full Changelog: https://github.com/Reference-LAPACK/lapack/compare/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
Release notes on http://netlib.org/lapack/lapack-3.10.1.html
Thank you to all our contributors The LAPACK team
Release notes on http://netlib.org/lapack/lapack-3.10.0.html
Thank you to all our contributors The LAPACK team
Release notes on http://netlib.org/lapack/lapack-3.9.1.html
Thank you to all our contributors The LAPACK team
Release notes on http://netlib.org/lapack/lapack-3.9.0.html
Thank you to all our contributors The LAPACK team
Official Release for LAPACK 3.7.1
Please see release notes at: http://www.netlib.org/lapack/lapack-3.7.0.html