- almost defeated mine
- It is pronounced "MARI" now.
PLUQ Factorisation of Dense GF(2) Matrices
learned a lot from Clement
- still work in progress, some initial code is written
- nothing to be shown yet, but will keep working
- work-in-progress, alpha, not working code will be released in a few days with the standard M4RI library
- autodetection of L1 and L2 cache
- switch over to Strassen-Winograd Multiplication by default in Sage
- learned a potential further improvement to multiplication from Bill Hart (needs to be implemented)
Performance on Core2Duo improved:
1 sage: A = random_matrix(GF(2),3.2*10^4,3.2*10^4) 2 sage: B = random_matrix(GF(2),3.2*10^4,3.2*10^4) 3 sage: time C = A._multiply_strassen(B,cutoff=4092) #Old 4 CPU times: user 51.32 s, sys: 0.14 s, total: 51.46 s 5 Wall time: 51.86 6 7 sage: time C = A._multiply_strassen(B,cutoff=8192) #New 8 CPU times: user 44.93 s, sys: 0.15 s, total: 45.08 s 9 Wall time: 45.32
1 sage: A = random_matrix(GF(2),3.2*10^4,3.2*10^4) 2 sage: time A.echelonize() #Old 3 CPU times: user 53.67 s, sys: 0.05 s, total: 53.71 s 4 Wall time: 53.99 5 6 sage: A = random_matrix(GF(2),3.2*10^4,3.2*10^4) 7 sage: time A.echelonize() #New 8 CPU times: user 44.25 s, sys: 0.03 s, total: 44.29 s 9 Wall time: 44.50
- RAM consumption for elimination seems lower than Magma, since we don't use any temporaries due to the lack of asymptotically fast elimination. (after you substract the static Sage RAM).
Magma: Total time: 340.579 seconds, Total memory usage: 1934.02MB (for 640002 / 8 / 1024.02 = 488.281MB)
- newest benchmarks:
> A:=RandomMatrix(GF(2),64*10^3, 64*10^3); > time E:=EchelonForm(A); Time: 336.350
- Tried to implement parallel elimination and failed
If it worked however it would enable in the only parallel Gröbner basis engine (PolyBoRi) in commutative polynomial rings I'm aware of.
- Editor Meetings
- found out that the mention of "mark**ing" is not allowed on this wiki