tr ts r - - PDF document
tr ts r srs trt sr rt t
✶
✷
✸
✹
✺
✻
3 5 4 2 1 1 2 3 4 5 3 5 4 2 1 1 2 3 4 5
Fill−in Non Zero
A=
Fill−in L+U−I
Zero
Factors Active matrix Stack memory Active memory
3 2 4 5 1
1 5 4 2 3 3 4 4 5 5
Factor Contribution block
P0 P1 P0 P0 P1 P3 P2 P1 P3 P2 P0 P1 P3 P0 P1 P0 P0 P3 P0 P2 P2 P0 P2 P2 P3 P0 P0 P0 P1 P3 P2 P3 SUBTREES TIME P0 P3 P2 P3 and P0 chosen at runtime 1D pipelined factorization 2D static decomposition : STATIC : DYNAMIC
200 400 600 800 1000 1200 1400 1600 10 20 30 40 50 60 Memory peak Nb processors Active memory Factors zone Total memory
▼❊❚■❙
200 400 600 800 1000 1200 1400 1600 10 20 30 40 50 60 Memory peak Nb processors Active memory Factors zone Total memory
P❖❘❉
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 10 20 30 40 50 60 70 Maximum peak of active memory / maximum peak of total memory (ratio) Number of processors AUDIKW_1 CONESHL_MOD CONESHL2 CONV3D ULTRASOUND80
200 400 600 800 1000 1200 10 20 30 40 50 60 70 Elapsed time for factorization (seconds) Number of processors IC Synchronous OOC Asynchronous OOC
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 10 20 30 40 50 60 70 Elapsed time for factorization (ratio) Number of processors Synchronous OOC / IC Asynchronous OOC / IC
❆❯❉■❑❲ ✶
1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 10 20 30 40 50 60 70 Elapsed time for factorization (ratio) Number of processors Synchronous OOC / IC Asynchronous OOC / IC
❈❖◆❊❙❍▲ ▼❖❉
0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 20 40 60 80 100 120 140 Elapsed time for factorization (ratio) Number of processors Synchronous OOC / IC Asynchronous OOC / IC
❈❖◆❊❙❍▲✷
1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 30 40 50 60 70 80 90 100 110 120 130 Elapsed time for factorization (ratio) Number of processors Synchronous OOC / IC Asynchronous OOC / IC
❈❖◆❱✸❉✻✹
0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 10 20 30 40 50 60 70 Elapsed time for factorization (ratio) Number of processors Synchronous OOC / IC Asynchronous OOC / IC
❯▲❚❘❆❙❖❯◆❉✽✵
t✐♠❡ ✐♥✲❝♦r❡
t✐♠❡ ✐♥✲❝♦r❡
20 40 60 80 100 120 140 20 40 60 80 100 120 140 Elapsed time for solve step (ratio OOC / IC) Number of processors AUDIKW_1 CONESHL_MOD CONESHL2 CONV3D64 ULTRASOUND80
❛s②♥❝❤r♦♥♦✉s ■✴❖ ✭t❤r❡❛❞✮ ♠♦r❡ ❝♦♠♣❧❡① ♠❡♠♦r② ♠❛♥❛❣❡♠❡♥t ✭♠✉❧t✐♣❧❡ ♦r ❝②❝❧✐❝ ✇♦r❦s♣❛❝❡s✮
Memory peak
❲♦rst ❝❛s❡✳
Memory peak
❇❡st ❝❛s❡✳
n 2 1
cb cb
1 n 2
cb
...
stack memory area written to disk allocation of a frontal matrix active frontal matrix Active memory Physical memory Active memory Physical memory Active memory Physical memory Allocation of a new frontal matrix After I/O
❋ ✰
♥
❳
❥❂✶
❝❜❥
▼❥ ✰
❥✶
❳
❦❂✶
❝❜❦
▼♣❛r❡♥t ❂ ♠❛① ✏ ♠❛①
❥❂✶❀♥✭▼❥ ✰ ❥✶
❳
❦❂✶
❝❜❦✮❀ ❋ ✰
♥
❳
❥❂✶
❝❜❥ ✑
♠❛①✭✵❀ ❋ ✰
♥
❳
❥❂✶
❝❜❥ ▼✵✮
♠❛①✭✵❀ ▼❥ ✰
❥✶
❳
❦❂✶
❝❜❦ ▼✵✮
❱ ■✴❖ ❂ ♠❛① ✏ ♠❛①
❥❂✶❀♥✭▼❥ ✰ ❥✶
❳
❦❂✶
❝❜❦✮❀ ❋ ✰
♥
❳
❥❂✶
❝❜❥ ✑ ▼✵
✶
t❤❡ ❛♠♦✉♥t ♦❢ ■✴❖ ❱ ■❂❖
✐
✐s ✐♥❞❡♣❡♥❞❡♥t ❢r♦♠ t❤❡ ♣♦s✐t✐♦♥ ♦❢ ❝❤✐❧❞ ✐ ✐♥ t❤❡ s❝❤❡❞✉❧❡
✷
❛❧❧ ❝♦♥tr✐❜✉t✐♦♥ ❜❧♦❝❦s t❤❛t ✇❡r❡ ✐♥ ♠❡♠♦r② ❤❛✈❡ t♦ ❜❡ ✇r✐tt❡♥ t♦ ❞✐s❦ ✇❤❡♥ ✐ ✐s ♣r♦❝❡ss❡❞
✏ ♠❛①
❥❂✶❀♥✭♠✐♥✭▼❥❀ ▼✵✮ ✰ ❥✶
❳
❦❂✶
❝❜❦✮❀ ❋ ✰
♥
❳
❥❂✶
❝❜❥ ✑ ▼✵ ✰
♥
❳
✐❂✶
❱ ■❂❖
✐
♠❛①
❥❂✶❀♥
✏ ♠✐♥✭▼❥❀ ▼✵✮ ✰
❥✶
❳
❦❂✶
❝❜❦ ✑
✐❂✶ ②❥✮ ✐s ♦❜t❛✐♥❡❞ ✇❤❡♥ t❤❡ s❡q✉❡♥❝❡
❖r❞❡r ♥♥③ ♥♥③✭▲❥❯✮ ✂ ✶✵✻ ❖♣s✂✶✵✾
❆❯❉■❑❲ ✶ ✾✹✸✻✾✺ ✸✾✷✾✼✼✼✶ ✶✸✻✽✳✻ ✺✻✽✷ ❈❖◆❊❙❍▲ ▼❖❉ ✶✷✻✷✷✶✷ ✹✸✵✵✼✼✽✷ ✼✾✵✳✽ ✶✻✹✵ ❈❖◆❊❙❍▲✷ ✽✸✼✾✻✼ ✷✷✸✷✽✻✾✼ ✷✻✻✳✻ ✷✶✽✳✺
❈❖◆❱✸❉✻✹ ✽✸✻✺✺✵ ✶✷✺✹✽✷✺✵ ✷✻✾✸✳✾ ✷✸✽✽✵ ❯▲❚❘❆❙❖❯◆❉✽✵ ✺✸✶✹✹✶ ✸✸✵✼✻✶✻✶ ✾✽✶✳✹ ✸✾✶✺