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A Proposal for a Heterogeneous Cluster ScaLAPACK (Dense Linear Solvers)

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(1)A Proposal for a Heterogeneous Cluster ScaLAPACK (Dense Linear Solvers) Vincent Boudet, Fabrice Rastello, Yves Robert. To cite this version: Vincent Boudet, Fabrice Rastello, Yves Robert. A Proposal for a Heterogeneous Cluster ScaLAPACK (Dense Linear Solvers). [Research Report] LIP RR-1999-17, Laboratoire de l’informatique du parallélisme. 1999, 2+16p. �hal-02101810�. HAL Id: hal-02101810 https://hal-lara.archives-ouvertes.fr/hal-02101810 Submitted on 17 Apr 2019. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) Laboratoire de l’Informatique du Parall´elisme. SPI. ´ Ecole Normale Sup´erieure de Lyon Unit´e Mixte de Recherche CNRS-INRIA-ENS LYON no 5668.    . 

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(757) J    .    M #   

(758)     . 1      

(759)      

(760)       

(761)    

(762) ,  

(763) 

(764)  ?/           

(765) 

(766) 

(767)

(768) ! 1   . 1   

(769)     ?     . 

(770)          

(771)   .   

(772) 

(773) 

(774)

(775) F 

(776)  . . . %$  

(777) 

(778)  #31 4 1      

(779)   

(780) 

(781)  .   :  

(782)  :   

(783)  " #$%$&'O%;<  . 

(784)  :   .     *  .     

(785)     ,  

(786)    

(787)  

(788)     

(789)  " #$%$&'O%;<   

(790)    B9    

(791)    . .   :    

(792)     1    

(793)     .    

(794)       ,  . . (  . $   1       

(795)    <  

(796)   

(797)  H

(798)   =    .   

(799)    

(800)  

(801)  @ A 

(802)   M.

(803) LU decomposition. Execution time on a Network (myrinet/IP) of 3 processors. 1500. Execution time (seconds). cyclic distribution (+). 1000. 500. heterogeneous distribution (x). "optimal" algorithm (d). 0. 0. 500. 1000. 1500 2000 2500 3000 Squarred matrix of size NxN. Value of N.. 3500. 4000. 4500.  J:  #3       1 

(804)  ,   

(805)   . 

(806) ,    : 

(807) :MJM1 

(808) :CBM1 

(809) :BMM ! 1 

(810)    

(811)     

(812) .  

(813) 11111111 

(814)   

(815) 

(816) 

(817)

(818)  ,    9B   

(819) 

(820) F 9B  . LU decomposition. Execution time on a Network (ethernet/IP) of 6 workstations. 1000. 900. 800. cyclic distribution (+). Execution time (seconds). 700. 600. 500. 400. 300 heterogeneous distribution (x) 200. 100 "optimal" algorithm (d) 0 500. 1000. 1500 2000 2500 Squarred matrix of size NxN. Value of N.. 3000. 3500.  :  #3      1 

(821)  ,   

(822)   . 

(823)     :  :M1 *: C1 . :M1  :91 + :DM1 :B ! 1 

(824)    

(825)      1 + 1 *1 1  1 . 1 1 + 1  

(826) .  

(827)  

(828) 

(829) 

(830)

(831) ,    J   

(832) 

(833) F D  . .

(834) QR decomposition. Execution time on a Network (myrinet/IP) of 3 processors. 1800. 1600 cyclic distribution (+). Execution time (seconds). 1400. 1200. 1000. 800. "optimal" algorithm (d). 600. 400. 200. 0. heterogeneous distribution (x). 0. 500. 1000. 1500 2000 2500 3000 Squarred matrix of size NxN. Value of N.. 3500. 4000.  I:  4       1 

(835)  ,   

(836)   . 

(837)     : 

(838) :JM1 

(839) :91 

(840) :D ! 1 

(841)    

(842)     

(843) 11111111.  

(844) 

(845)   

(846) 

(847) 

(848)

(849) ,       

(850) 

(851) F C  . QR decomposition. Execution time on a Network (ethernet/IP) of 6 workstations. 1800. 1600. Execution time (seconds). 1400. cyclic distribution (+). 1200. 1000. 800. heterogeneous distribution (x). 600. 400. "optimal" algorithm (d). 200. 0 500. 1000. 1500 2000 2500 Squarred matrix of size NxN. Value of N.. 3000. 3500.  :  4      1 

(852)  ,   

(853)   . 

(854)     :  :9MM1 *:M1 . :JD1  :J1 + :M1 :9 ! 1 

(855)    

(856)     1+ 1 1 *1. 1 11+ 1 

(857)  .  

(858) 

(859) 

(860) 

(861)

(862) ,    D   

(863) 

(864) F C  . 9.

(865)   

(866)    

(867)    ! 1    

(868)   1  .   ,  

(869)   1 

(870)         

(871)      

(872)     

(873)  *   

(874)  21   

(875)  ,     

(876)    

(877)  

(878)  

(879)    .    =  

(880)  

(881)   

(882) * .      ,  

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