PC??????? ??????????????

1
PC?????????????????????

• ????,?? ??(?????)

2
??

• ????????(PC????)???? ???????????????????
• ???????????????ScaLAPACK????
• ??????(???????1???)????????????????
• ??????????????

3
????
?????
???????
?????
???
???
??????????????
PC LAPACK(BLAS, ATLAS) ?????? LAPACK,
ScaLAPACK PC???? ScaLAPACK(MPI, PVM)
4
ScaLAPACK???
ScaLAPACK
PBLAS
Global
Local
LAPACK
BLACS
BLAS
MPI, PVM
ATLAS
5
????????????(1)
????????????
???
???
6
????????????(2)
1 S. Oishi and S. Rump (2000) 2 T. Ogita, S.
Oishi and Y. Ushiro (2001)
7
LU???????????
???,
???
LU?????????? ?? ??????
????????
8
????

• ??
• ????(PDGEMM)?????
• ????????????????
• ????????
• PC (Pentium III 800MHz,
• Memory 256MB)
• ??64?,LAN??(Gigabit ether)

9
????(PDGEMM)
1000010000 ???????

• ???
• PDGEMM(PBLAS)???
• DGEMM(BLAS)?ATLAS????

10
????(PDGEMM)???
11
????????????

• ???????? 10010000
• ?????? PDGESV(ScaLAPACK)
• ????????
• LU?????????????

12
????????????????
????? ???? ???? ?????????? ??????
100 0.76 0.34 1.5E-12
500 3.89 0.76 1.4E-10
1000 8.29 1.90 1.9E-09
5000 55.14 34.80 1.3E-07
10000 182.53 169.70
13
LU?????? ??? ???
????? ??????
100 1.3E-08 1.5E-12
500 2.6E-05 1.4E-10
1000 1.2E-03 1.9E-09
5000 0.5 1.3E-07
10000 12.6 (gt1)
14
????

• 1) S. Oishi, S. Rump Fast Verification of
  Solutions of Matrix Equations, Numer. Math., to
  appear (2001)
• 2) ScaLAPACK HomePage
• http//www.netlib.org/scalapack/
• 3) ScaLAPACK Tutorial(????)
• http//phase.etl.go.jp/phase/lapack-j/ScaLAPAC
  K/