matrixmultiplicationparallel.ppsx
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The document evaluates the performance of parallelizing a naive matrix multiplication algorithm using OpenMP on a multicore processor. It implements sequential and parallel versions of square matrix multiplication and measures execution time. Results show that as the number of threads and matrix size increase, execution time decreases and speedup and efficiency increase, demonstrating that the parallel implementation outperforms the serial version, especially for larger datasets.
![PARALLEL_SQUARE_NAIVE_MATRIX-MULTIPLY (A, B, C)
#pragma omp parallel for schedule(dynamic, chunk)
collapse(2) private(i, j, k) shared(A, B, C)
for(i=0;i<n;i++)
for( j=0;j<n;j++)
for(k=0;k<n;k++)
C[i][j]+=A[i][k]*B[k][j];
Return C;
Pseudo Code for Parallel version](https://image.slidesharecdn.com/matrixmultiplicationparallel-220622022301-fe71ca50/85/matrixmultiplicationparallel-ppsx-6-320.jpg)
matrixmultiplicationparallel.ppsx
- 1. A Diagnostic research on the effect of Matrix Multiplication Parallelism on Multicore 30.06.2020
- 2. • Matrix multiplication is an important core computation in many areas of scientific computing • Normally for small multiplication we lean towards to use naive matrix multiplication algorithm which has rich data parallelism. • To obtain more performance through that algorithm we parallelized them using OpenMP. • Implementation of this system is done in Intel Core i9-7900X having 3.30 GHz x 20 CPU with 31.1 GB RAM. • The operating System used is Fedora 27 and the software is Geanv Version 2 IDE, GCC Linux Compiler. Objective
- 3. • Parallel computing has been the fast evolving research area in the last few decades. • Parallel computing means dividing the same task into subtasks and all the subtasks execute simultaneous on multiple processors to yield the output. • This paper shows the effect of Square Naive Matrix Multiplication algorithm on sequential as well as parallel implementation. • Performances were evaluated in a multicore on the basis of its run time • Chip Microprocessors - As we increase the capacity of chip placing multiple processors on a single chip became practical. • OpenMP is an API that uses multithreaded and shared memory parallelism. Parallel Computing
- 4. Square Naive Matrix Multiplication • Executing Matrix multiplication using Naive algorithm is referred as Square Naïve Matrix multiplication. • Each entry is calculated as sum of products. • The product of two Square Matrices A and B obtaining C Square matrix. • each entry of the product is computed as a sum of n pairwise products where n represents number of rows/columns.
- 5. SQUARE_NAÏVE_MATRIX-MULTIPLY (A, B, C) N = A.rows for i = 1 to N for j = 1 to N Cij = 0 for k = 1 to N Cij = Cij + Aik * Bkj Return C Pseudo Code for Serial version
- 6. PARALLEL_SQUARE_NAIVE_MATRIX-MULTIPLY (A, B, C) #pragma omp parallel for schedule(dynamic, chunk) collapse(2) private(i, j, k) shared(A, B, C) for(i=0;i<n;i++) for( j=0;j<n;j++) for(k=0;k<n;k++) C[i][j]+=A[i][k]*B[k][j]; Return C; Pseudo Code for Parallel version
- 7. OpenMP Clause • num_thread(integer) • Schedule(type_of_schedule, Chunk size) • Collapse(number_of_nested_for_loop) • Private(list_of_variables) • Shared(list_of_variables)
- 8. Design
- 9. Implementation – Sequential Version • A sequential Square Naive Matrix Multiplication algorithm was implemented in C++ GCC Compiler without using OpenMP. • the parallel codes have been written in C++ GCC Compiler with using OpenMP. • C=A×B given A is n*n matrix with the element aij, B is n*n matrix with element bij and the product C is n*n matrix with elements cij. • The performances of the sequential matrix multiplication are mostly affected by the inefficiency of accessing the memory especially when implemented in C++.
- 10. Implementation – Parallel Version • major design issues implementing using OpenMP can be determined. • Square Naive matrix multiplication algorithm parallelism can be accomplished through the use of OpenMP components such as compiler directives, runtime library routines and environment variables. • Both codes are executed in Fedora 27 Linux Operating System on Intel Core i9-7900 Multicore system. • The running time and performance (speed up, efficiency) of the serial and parallel square Naive matrix multiplication algorithms has been done.
- 11. • Speed up • Efficiency Efficiency = Speedup and Efficiency time execution Parallel time execution Sequential Speedup 11 Dr.D.Christopher Durairaj & Mrs.A.Bharathi Lakshmi
- 12. Result – Time Taken Cores 1000 x 1000 2000 x 2000 3000 x 3000 4000 x 4000 5000 x 5000 1 4.1621 54.4683 233.9659 639.1539 1282.2257 2 2.1539 25.9129 118.3784 316.9857 641.8125 4 1.0993 17.0027 64.2888 172.9639 329.7763 8 0.5822 8.5168 34.0960 81.1930 163.0773 12 0.5074 5.8074 22.6845 62.6338 135.0753 16 0.5061 4.7371 19.4545 57.1035 126.0156 18 0.4708 4.6368 18.6277 52.2070 120.5529 20 0.4487 0.5695 0.6275 0.5502 0.5177
- 14. Result - Speedup Cores 1000× 1000 2000× 2000 3000× 3000 4000× 4000 5000× 5000 2 1.9323 2.1020 1.9764 2.0163 1.9978 4 3.7861 3.2035 3.6393 3.6953 3.8882 8 7.1488 6.3954 6.8620 7.8720 7.8627 12 8.2022 9.3791 10.3139 10.2046 9.4927 16 8.2241 11.4983 12.0263 11.1929 10.1751 18 8.8407 11.7469 12.5601 12.2427 10.6362 20 11.3795 14.6478 15.6904 15.2592 13.7029
- 16. Result - Efficiency Cores 1000× 1000 2000× 2000 3000× 3000 4000× 4000 5000× 5000 2 0.9662 1.0510 0.9882 1.0082 0.9989 4 0.9465 0.8009 0.9098 0.9238 0.9720 8 0.8936 0.7994 0.8577 0.9840 0.9828 12 0.6835 0.7816 0.8595 0.8504 0.7911 16 0.5140 0.7186 0.7516 0.6996 0.6359 18 0.4912 0.6526 0.6978 0.6801 0.5909 20 0.4002 0.5826 0.6621 0.6423 0.5482
- 18. Summary • number of threads assignment in per core and matrix sizes increases. • the performance (Speedup and Efficiency) also increases in square Naive matrix multiplication algorithm parallel implementation. • the execution time of parallel computing with OpenMP got the best achievement than the serial computing. • When handled with larger datasets.