Release date: 11/21/19.

This material is based upon work supported by the National Science Foundation and the Department of Energy under Grant No. NSF ACI 1339797, NSF-OCI-1032861, NSF-CCF-00444486, NSF-CNS 0325873, NSF-EIA 0122599, NSF-ACI-0090127, DOE-DE-FC02-01ER25478, DOE-DE-FC02-06ER25768.

LAPACK is a software package provided by Univ. of Tennessee, Univ. of California, Berkeley, Univ. of Colorado Denver and NAG Ltd..

1. Support and questions:

2. LAPACK 3.9.0: What’s new

2.1. LAPACK QR-preconditioned QR SVD method

LAPACK QR-preconditioned QR SVD method for computing the SVD with high accuracy 􏰒􏰑􏰐􏰏􏰎􏰍􏰌􏰋􏰏􏰍􏰑􏰐 􏰌􏰉 by Zlatko Drmac 􏰋􏰥􏰘􏰫􏰡􏰝􏰠􏰘􏰟􏰩 􏰞􏰜 􏰵􏰦􏰪􏰝􏰡􏰖

NEW: xGESVDQ routines

See Zlatko Drmac, Algorithm 977: A QR-Preconditioned QR SVD Method for Computing the SVD with High Accuracy. ACM Trans. Math. Softw. 44(1): 11:1-11:30 (2017)

2.2 LAPACK Householder Reconstruction

NEW: cunhr_col.f
NEW: dorhr_col.f
NEW: sorhr_col.f
NEW: zunhr_col.f

DORHR_COL takes an M-by-N real matrix Q_in with orthonormal columns as input, stored in A, and performs Householder Reconstruction (HR), i.e. reconstructs Householder vectors V(i) implicitly representing another M-by-N matrix Q_out, with the property that Q_in = Q_out*S, where S is an N-by-N diagonal matrix with diagonal entries equal to +1 or -1. The Householder vectors (columns V(i) of V) are stored in A on output, and the diagonal entries of S are stored in D. Block reflectors are also returned in T (same output format as DGEQRT).


DOGTSQR reconstructs a matrix with orthonormal columns from the output of DLATSQR.

Contributors: Igor Kozachenko and Jim Demmel 􏰋􏰒 􏰌􏰡􏰝􏱄􏰡􏰗􏰡􏰩

3. Developer list

External Contributors
  • Zlatko Drmac, University of Zagreb

LAPACK developers involved in this release
  • Julie Langou (University of Tennessee, USA)

  • Igor Kozachenko (University of California, Berkeley, 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)

4. Thanks

  • MathWorks: Penny Anderson, Amanda Barry, Mary Ann Freeman, Bobby Cheng, Duncan Po, Pat Quillen, Christine Tobler.

  • Intel: Eugene Chereshnev

  • GitHub Users: Andreas Noack, Isuru Fernando, Kirana Bergstrom, Kyle Guinn Martin Kroeker, Nick Papior, Rao Garimella, Reinhold Gschweicher.Sébastien Villemo guozhong.zhuang

5. Bug Fix