Dev Days 1: Exact Linear Algebra

• Michael Abshoff -> LinBox debianization

• MartinAlbrecht -> M4RI GF(2)

• Nick Alexander -> cylcotomic linalg

• Gregory Bard -> M4RI

• Rob Beezer
• Tom Boothby

• Craig Citro -> cyclotomic linalg, p-adic linalg

• Burcin Erocal -> nullspace of polynomial matrices

• Robert Miller (especially sparse GF(2)) -> sparse GF(2)

• David Roe (p-adic linear algebra?) -> cyclotomic linear algebra

• Arne Storjohann -> HNF, Sparse GF(2) Linalg

• William Stein -> Cyclotomic linear algebra, HNF (LLL)

• Ralf-Philipp Weinmann -> Sparse Elimination, Nullspace

Dense GF(2)

• implement LQUP decomposition [ClementPernet, MartinAlbrecht]

  • implement LQUP routine [Clement]

  • implement _mzd_addmul_weird [Clement]

  • implement LQUP basecase routine based on M4RI mzd_lqup_m4ri [MartinAlbrecht]

    • dont' zero out in _mzd_gauss_submatrix

    • don't zero out below

    • remember rowswaps => P

    • remember Q[r] = c (translate to Lapack style later )

  • implement TRSM routine [Clement]

  • implement inplace triangular matrix inversion mzd_trtri [Clement]

  • implement triangular triangular matrix multiplication mzd_trtrm [Clement]

  • implement column swaps [MartinAlbrecht]

  • implement column rotations [MartinAlbrecht]

  • implement memory efficient mzd_addmul_strassen [Martin]

    • See Clement's et al. paper on memory efficient Strassen-Winograd

• implement Arne's asymptotically fast elimination algorithm [MartinAlbrecht]

  • It was agreed that this is not what we want for M4RI, a toy implementation is available at: http://www.informatik.uni-bremen.de/cgi-bin/cgiwrap/malb/blosxom.pl/2008/06/13#gauss-jordan-storjohann

• implement multi-core multiplication with optimal speed-up
  • OpenMP seems to be nice and easy
  • 2 cores probably main target, but think about 4 cores too
• improve efficiency of M4RM

  • try 7 instead of 8 Gray code tables to leave room for the actual matrix in L1 [MartinAlbrecht]

    • It seems slower to be slower to use 7 tables rather than 8

  • try say 16 tables instead of 8 on the Core2Duo [MartinAlbrecht]

  • try Bill Hart's idea for L1 cache efficiency on the Core2Duo [MartinAlbrecht]

    • The idea is: construct 8 gray code tables but use one once it is in L1 a lot to reduce before using the second

  • try to fit three matrices rather than two into L2 or understand why it works so good for two [MartinAlbrecht]

    • it works since once we've written the date we can go on computing and let a cache handle the rest
    • a cache miss for reading on the other hand really prevents us from computing

  • detect L1/L2 cache sizes at runtime and choose optimal parameters for them [MartinAlbrecht]

  • Implement memory management s.t. the sys time on Opterons decreases.

  • implement Bill's [http://groups.google.com/group/sage-devel/msg/6279228095b3d9f7 half table idea] and benchmark it

Sparse GF(2) (and other small finite fields)

• [Arne, Ralph, Clément, Rob Miller]
• Sparse Reduced Echelon form (RPW)
  • Sparse Elimination:

    • improve LinBox gauss-domain

    • eclib sparse elimination
    • ....
• ....

Hermite Normal Form

• [Arne, Clément, William]

• new algorithm, based on system solving (Arne Storjohann) -> already an implementation

  • integrate it in IML
  • benchmark it against Sage
• generalization: block vector system solving
  • implementation
  • benchmark

• LLL trick for the existing implementation in Sage (William & Clément)

Polynomial Matrix computations

• [Burcin]
• Nullspace computation (Burcin)

Cyclotomic linear algebra

• [Rob Bradshaw, Craig, William]

P-adic linear algebra

• [David Roe, Craig, David Cohet]

LinBox debianization and 1.1.6 spkgization

• [mabshoff, Clément]
• get rid of gmp++
• generate and test linbox-1.1.6rc0.spkg