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Chapter 7-Matrix multiplication slides from Book of Parallel Computing Theory and practices by Michael J. Quinn

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Chapter 7-Matrix multiplication slides from Book of Parallel Computing Theory and practices by Michael J. Quinn
MATRIX MULTIPLICATION
(Part b)
By:
Shahrzad Abedi
Professor: Dr. Haj Seyed Javadi

MATRIX Multiplication
• SIMD
• MIMD
– Multiprocessors
– Multicomputers

Chapter 7: Matrix Multiplication , Parallel Computing :Theory and Practice, Michael J. Quinn

2

Matrix Multiplication Algorithms for Multiprocessors p1 p2 p3 p4 p1 p2

Chapter 7: Matrix Multiplication , Parallel Computing :Theory and Practice, Michael J. Quinn

p3

p4

3

Matrix Multiplication Algorithm for a UMA Multiprocessor

p1 p2 p3 p4 Chapter 7: Matrix Multiplication , Parallel Computing :Theory and Practice, Michael J. Quinn

4

Matrix Multiplication Algorithm for a UMA Multiprocessor
Example:
n= 8 , P=2
C

 n/p= 4

A

B

p1

p2

n/p times 
We must read n/p rows of A and we must read every element of B, n/p times
Chapter 7: Matrix Multiplication , Parallel Computing :Theory and Practice, Michael J. Quinn

5

Matrix Multiplication Algorithms for Multiprocessors
• Question : Which Loop should be made parallel in the sequential Matrix multiplication algorithm? • Grain Size :
– Amount of work performed between processor interactions – Ratio of Computation time to Communication
Time : Computation time / Communication time
Chapter 7: Matrix Multiplication , Parallel Computing :Theory and Practice, Michael J. Quinn

6

Sequential Matrix Multiplication
Algorithm

Chapter 7: Matrix Multiplication , Parallel Computing :Theory and Practice, Michael J. Quinn

7

Matrix Multiplication Algorithms for Multiprocessors
• Design Strategy If load balancing is not a problem maximize grain size
• Question : Which Loop should be made parallel ? i or j or k ?
• K has data dependency X
• If j  Grain-size = O(n3/np)= O(n2/p)
• If i  Grain-size = O(n3/p)
Chapter 7: Matrix Multiplication , Parallel Computing :Theory and Practice, Michael J. Quinn

8

Matrix Multiplication Algorithm for a UMA Multiprocessor
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