矩阵乘法的并行化实验报告全解.docx

1、矩阵乘法的并行化实验报告全解北京科技大学 计算机与通信工程学院实 验 报 告实验名称： 学生姓名： 专 业： 班 级： 学 号： 指导教师： 实验成绩：_实验地点： 实验时间：2015年05月一、实验目的与实验要求1、实验目的1对比矩阵乘法的串行和并行算法，查看运行时间，得出相应的结论；2观察并行算法不同进程数运行结果，分析得出结论；2、实验要求1编写矩阵乘法的串行程序，多次运行得到结果汇总；2编写基于MPI，分别实现矩阵乘法的并行化。对实现的并行程序进行正确性测试和性能测试，并对测试结果进行分析。二、实验设备（环境）及要求VS2013C+语言MPICH2三、实验内容与步骤实验1，矩阵乘法的串

2、行实验（1）实验内容编写串行程序，运行汇总结果。（2）主要步骤按照正常的矩阵乘法计算方法，在VS2013上编写矩阵乘法的串行程序，编译后多次运行，得到结果汇总。实验2矩阵乘法的并行化实验3个总进程5个总进程7个总进程9个进程16个进程四：实验结果与分析（一）矩阵乘法并行化矩阵并行化算法分析：并行策略：1间隔行带划分法算法描述：将C=A*B中的A矩阵按行划分，从进程分得其中的几行后同时进行计算，最后通信将从进程的结果合并的主进程的C矩阵中对于矩阵A*B如图：进程1：矩阵A第一行 进程2：矩阵A第二行 进程3：矩阵A第三行 进程1：矩阵A第四行时间复杂度分析：f(n) =6+2+8+k*n+k*n

3、+k*n+3+10+n+k*n+k*n+n+2(k为从进程分到的行数)因此O(n)=(n)；空间复杂度分析：从进程的存储空间不共用，f(n)=n;因此O(n)=(n);2间隔行带划分法算法描述：将C=A*B中的A矩阵按行划分，从进程分得其中的几行后同时进行计算，最后通信将从进程的结果合并的主进程的C矩阵中对于矩阵A*B如图：进程1：矩阵A第一行 进程2：矩阵A第二行 进程3：矩阵A第三行 进程3：矩阵A第四行时间复杂度分析：f(n) =6+2+8+k*n+k*n+k*n+3+10+n+k*n+k*n+n+2(k为从进程分到的行数)因此O(n)=(n)；空间复杂度分析：从进程的存储空间不共用，f

4、(n)=n;因此T(n)=O(n);测试环境简介：VS2013Win7旗舰版正确性测试结果：并行结果：串行结果：通过比较发现两者相同，因此可以确定运算结果正确。性能测试结果：串行125ms107ms108ms98ms109ms110ms3进程0.009647ms0.009936ms0.010825ms0.009207ms0.008811ms0.009831ms5进程0.007795ms0.007648ms0.008588ms0.008334ms0.007686ms0.007731ms7进程0.010729ms0.011336ms0.011606ms0.011403ms0.011621ms0.0

5、14563ms9进程0.016547ms0.014439ms0.016300ms0.015455ms0.015187ms0.011240ms16进程0.024964ms0.027917ms0.024721ms0.028152ms0.022296ms0.021321ms通过对比分析得出，并行算法能够有效提高矩阵乘法的运算效率；（二）串行算法分析时间复杂度：f(n)=2+n2+2*n+3*n+7+n+n+7;因此T(n)=O(n2)空间复杂度：T（n）=O(1)五：结论（讨论）1、 实验结论(1) 根据前面实验结果，可以证明并行算法比串行算法更能有效地运算矩阵乘法，可以提高效率数十倍(2) 如下图

6、，根据结果可以得出并行程序并不是进程数越多，程序运行时间越短，程序运行还受计算机运算器数的限制2、讨论1由于矩阵乘法的运算并不是很复杂，因此运算时间很短，达到了毫秒级，因此准确度有一定的影响；2因为时间紧迫，未能进一步分析代码，同时只用了一种并行算法。六：代码附录串行算法：#include #include #include #include #define N 30#define M 30void juzhen_mul(int m, int n, int *p1M, int m1, int n1, int *p2M) int i, j, x = 0; int cNM = 0 ; 2 for

7、(i = 0; im;) for (j = 0; jm1; j+) cix += *(p1i + j)*(p2j + x); 30*30 m1*m printf(%d, cix); printf( ); 2*30 2*m x+; if (x = n1) x = 0; i+; printf(n); 2*30 3*m void main() double start, finish; start = (double)clock(); char H; int i, j; int *paM, *pbM; int m = 30, n = 30; int aMN = 90, 6, 55, 1, 81, 1

8、8, 40, 57, 43, 23, 51, 73, 97, 3, 89, 57, 98, 58, 7, 12, 72, 2, 35, 74, 60, 59, 23, 30, 67, 53, 46, 35, 12, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 7

9、9, 8, 90, 75, 8, 85, 49, 68, 15, 38, 50, 39, 91, 22, 47, 97, 45, 82, 96, 66, 81, 40, 58, 75, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12, 90, 6, 55, 1, 81, 18, 40, 57, 43,

10、23, 51, 73, 97, 3, 89, 57, 98, 58, 7, 12, 72, 2, 35, 74, 60, 59, 23, 30, 67, 53, 46, 35, 12, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8

11、, 85, 49, 68, 15, 38, 50, 39, 91, 22, 47, 97, 45, 82, 96, 66, 81, 40, 58, 75, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12, 90, 6, 55, 1, 81, 18, 40, 57, 43, 23, 51, 73, 97,

12、 3, 89, 57, 98, 58, 7, 12, 72, 2, 35, 74, 60, 59, 23, 30, 67, 53, 46, 35, 12, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8, 85, 49, 68, 1

13、5, 38, 50, 39, 91, 22, 47, 97, 45, 82, 96, 66, 81, 40, 58, 75, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12, 90, 6, 55, 1, 81, 18, 40, 57, 43, 23, 51, 73, 97, 3, 89, 57, 98,

14、 58, 7, 12, 72, 2, 35, 74, 60, 59, 23, 30, 67, 53, 46, 35, 12, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8, 85, 49, 68, 15, 38, 50, 39,

15、91, 22, 47, 97, 45, 82, 96, 66, 81, 40, 58, 75, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12, 90, 6, 55, 1, 81, 18, 40, 57, 43, 23, 51, 73, 97, 3, 89, 57, 98, 58, 7, 12, 72,

16、 2, 35, 74, 60, 59, 23, 30, 67, 53, 46, 35, 12, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8, 85, 49, 68, 15, 38, 50, 39, 91, 22, 47, 97,

17、 45, 82, 96, 66, 81, 40, 58, 75, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12, 90, 6, 55, 1, 81, 18, 40, 57, 43, 23, 51, 73, 97, 3, 89, 57, 98, 58, 7, 12, 72, 2, 35, 74, 60,

18、 59, 23, 30, 67, 53, 46, 35, 12, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8, 85, 49, 68, 15, 38, 50, 39, 91, 22, 47, 97, 45, 82, 96, 66

19、, 81, 40, 58, 75, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12; 7 for (i = 0; im; i+) pai = ai; m int bMN = 90, 6, 55, 1, 81, 18, 40, 57, 43, 23, 51, 73, 97, 3, 89, 57, 98,

20、58, 7, 12, 72, 2, 35, 74, 60, 59, 23, 30, 67, 53, 46, 35, 12, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8, 85, 49, 68, 15, 38, 50, 39, 9

21、1, 22, 47, 97, 45, 82, 96, 66, 81, 40, 58, 75, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12, 90, 6, 55, 1, 81, 18, 40, 57, 43, 23, 51, 73, 97, 3, 89, 57, 98, 58, 7, 12, 72,

22、2, 35, 74, 60, 59, 23, 30, 67, 53, 46, 35, 12, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8, 85, 49, 68, 15, 38, 50, 39, 91, 22, 47, 97,

23、45, 82, 96, 66, 81, 40, 58, 75, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12, 90, 6, 55, 1, 81, 18, 40, 57, 43, 23, 51, 73, 97, 3, 89, 57, 98, 58, 7, 12, 72, 2, 35, 74, 60,

24、59, 23, 30, 67, 53, 46, 35, 12, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8, 85, 49, 68, 15, 38, 50, 39, 91, 22, 47, 97, 45, 82, 96, 66,

25、 81, 40, 58, 75, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12, 90, 6, 55, 1, 81, 18, 40, 57, 43, 23, 51, 73, 97, 3, 89, 57, 98, 58, 7, 12, 72, 2, 35, 74, 60, 59, 23, 30, 67,

26、 53, 46, 35, 12, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8, 85, 49, 68, 15, 38, 50, 39, 91, 22, 47, 97, 45, 82, 96, 66, 81, 40, 58, 75

27、, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12, 90, 6, 55, 1, 81, 18, 40, 57, 43, 23, 51, 73, 97, 3, 89, 57, 98, 58, 7, 12, 72, 2, 35, 74, 60, 59, 23, 30, 67, 53, 46, 35, 12

28、, 64, 97, 21, 69, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8, 85, 49, 68, 15, 38, 50, 39, 91, 22, 47, 97, 45, 82, 96, 66, 81, 40, 58, 75, 75, 26, 61, 5

29、9, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12, 90, 6, 55, 1, 81, 18, 40, 57, 43, 23, 51, 73, 97, 3, 89, 57, 98, 58, 7, 12, 72, 2, 35, 74, 60, 59, 23, 30, 67, 53, 46, 35, 12, 64, 97, 21, 6

30、9, 31, 21, 77, 14, 64, 71, 97, 5, 46, 100, 57, 64, 34, 20, 3, 4, 5, 67, 20, 5, 41, 99, 53, 63, 90, 70, 73, 34, 55, 42, 27, 1, 85, 32, 85, 26, 69, 91, 43, 31, 73, 32, 49, 15, 74, 79, 8, 90, 75, 8, 85, 49, 68, 15, 38, 50, 39, 91, 22, 47, 97, 45, 82, 96, 66, 81, 40, 58, 75, 75, 26, 61, 59, 51, 17, 66, 56, 20, 39, 62, 29, 57, 94, 81, 34, 9, 54, 58, 33, 96, 2, 55, 7, 38, 43, 87, 19, 72, 91, 16, 28, 53, 12, 76, 39, 50, 99, 63, 28, 89, 43, 19, 12 ; for (i = 0; im; i+) pbi = bi; m int m1 = 30, n1 = 30; printf(矩阵A*B= n