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| Deletions are marked like this. | Additions are marked like this. |
| Line 3: | Line 3: |
| * Michael Abshoff * Martin Albrecht |
* Michael Abshoff -> LinBox debianization * Martin Albrecht -> GF(2), M4RI |
| Line 6: | Line 6: |
| * Gregory Bard | * Gregory Bard -> M4RI |
| Line 11: | Line 11: |
| * Robert Miller (especially sparse GF(2)) * David Roe (p-adic linear algebra?) * Arne Storjohann * William Stein * Ralf-Philipp Weinmann |
* Robert Miller (especially sparse GF(2)) -> sparse GF(2) * David Roe (p-adic linear algebra?) -> cyclotomic linear algebra * Arne Storjohann -> * William Stein -> Cyclotomic linear algebra, HNF * Ralf-Philipp Weinmann -> Sparse Elimination, Nullspace |
| Line 17: | Line 17: |
| == GF(2) == | == Dense GF(2) == |
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== Sparse GF(2) (and other small finite fields) == * 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 == * Nullspace computation (Burcin) == Cyclotomic linear algebra == == p-adic linear algebra == == LinBox debianization and 1.1.6 spkgization == * mabshoff, Clément |
Dev Days 1: Exact Linear Algebra
Michael Abshoff -> LinBox debianization
Martin Albrecht -> GF(2), M4RI
- Nick Alexander
Gregory Bard -> M4RI
- Rob Beezer
- Tom Boothby
- Craig Citro
- Burcin Erocal
Robert Miller (especially sparse GF(2)) -> sparse GF(2)
David Roe (p-adic linear algebra?) -> cyclotomic linear algebra
Arne Storjohann ->
William Stein -> Cyclotomic linear algebra, HNF
Ralf-Philipp Weinmann -> Sparse Elimination, Nullspace
Dense GF(2)
- implement LQUP decomposition [Clement, Martin]
- implement LQUP routine [Clement]
- implement TRSM routine [Clement]
- implement efficient column swaps/rotations [Martin]
- SSE2 might help a lot here
- 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 [Martin]
- 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
- try to fit three matrices rather than two into L2 or understand why it works so good for two
- detect L1/L2 cache sizes at runtime and choose optimal parameters for them
- implement Bill's half table idea and benchmark it
Sparse GF(2) (and other small finite fields)
- Sparse Reduced Echelon form (RPW)
- Sparse Elimination:
improve LinBox gauss-domain
- eclib sparse elimination
- ....
- 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
- Nullspace computation (Burcin)
Cyclotomic linear algebra
== p-adic linear algebra ==
LinBox debianization and 1.1.6 spkgization
- mabshoff, Clément