中国料学火计算机科学与波术系 niversity of Science and Technolo ogy of China DEAT三 NT OF C口 MPUTER SCIENGE AND TECHNOLOr 棋盘划分的矩阵转置 情形2:p<n2 划分:An划分成D个大小如×1子块 P 算法:①桉me连接进行块转置(不同处理器)∥2yp(4+4n2/p)-通讯 ②进行块内转置(同一处理器内) 计算 Tn=nn+2、P+21,n2/√P…运行时间 2p 2 o)(0.|02(3)0.4(05)06(07 0)x(01)(20,(21)(40x(41)(60x(61 P P P P3 PI P2 (1.o)(.1)(.2)(1,3)(a,4)(15a,6)a1, (1,0)(,1)(3,0)*(3,1)(5,0)x(5,1)(7,0)(7,1) (2,0)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(2, 0n2),(0.3)(22)x(2,3)(42)x(4,3)(6,2)x(63) P4 P P4 P (3,0)1(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(3,7) (1,2)(,3)(3,2)*(3,3)(5,2)x(5,3)(7,2)“(7,3) (4,0)(4,1)(4,2)(4,3)(434)(4,5)(4,6)(,7) 4)x(.5)(2,4)x(2,5)(4,4)x(4,5)(6,4)x(6,5) P10 lI P P (5,0)(5,1)(5,2)(5,3)|(5,4)(5,5)(5,6)( (1,4)“(1,5)(3,4)“(3,5)(5,4)“(5,5)(7,4)“(7,5) (6,0)(6,1)(6,2)(6,3)(6,4)(6,5)(616)|(6, (06)x(0,7(2.6),(2.7)(4,6)x(,7)(6.6)x(6,7 P P P (7,0)(7,1)(7,2)(7,3)(7,4)(7,5)(7,6)(, (1,6)“(1,7)(3,6)“(3,7)(5,6)*(5,7)(7,6)“(7,7 通讯步 转置后 国家高性能计算中心(合肥 2021/2/19 图9.4国家高性能计算中心（合肥） 13 2021/2/19 棋盘划分的矩阵转置 ▪ 情形2: p<n2 。 - 划分: - 算法: ①按mesh连接进行块转置(不同处理器间) ②进行块内转置(同一处理器内) 通讯步 转置后 P P P P P P P P P P P P ( b ) ( a ) 图9.4 P P P P P P P P P P P P P P P P 0 4 8 12 1 5 9 13 2 6 10 14 3 7 11 15 (0,0) (1,0) (0,2) (1,2) (1,4) (0,4) (1,6) (0,6) (0,1) (1,1) (0,3) (1,3) (1,5) (0,5) (1,7) (0,7) (2,0) (3,0) (2,2) (3,2) (3,4) (2,4) (3,6) (2.6) (2,1) (3,1) (2,3) (3,3) (3,5) (2,5) (3,7) (2,7) (4,0) (5,0) (4,2) (5,2) (5,4) (4,4) (5,6) (4,6) (4,1) (5,1) (4,3) (5,3) (5,5) (4,5) (5,7) (4,7) (6,0) (7,0) (6,2) (7,2) (7,4) (6,4) (7,6) (6,6) (6,1) (7,1) (6,3) (7,3) (7,5) (6,5) (7,7) (6,7) 4 8 12 P0 P 1 5 9 13 P 2 6 10 14 P 3 7 11 15 (1,0) (2,0) (3,0) (5,0) (4,0) (7,0) (6,0) (0,0) (0,1) (1,1) (2,1) (3,1) (5,1) (4,1) (7,1) (6,1) (0,2) (1,2) (2,2) (3,2) (5,2) (4,2) (7,2) (6,2) (0,3) (1,3) (2,3) (3,3) (5,3) (4,3) (7,3) (6,3) (0,4) (1,4) (2,4) (3,4) (5,4) (4,4) (7,4) (6,4) (0,5) (1,5) (2,5) (3,5) (5,5) (4,5) (7,5) (6,5) (0,6) (1,6) (2,6) (3,6) (5,6) (4,6) (7,6) (6,6) (0,7) (1,7) (2,7) (3,7) (5,7) (4,7) (7,7) (6,7) Ann划分成p个大小为n p  n p 子块 // 2 p(t s +t w n 2 / p)通讯 计算 p n 2 // 2 t p t n p运行时间 p n Tp s w 2 2 / 2 2 2 = + +