Parallel matrix transpose algorithms on distributed memory concurrent computers

This paper describes parallel matrix transpose algorithms on distributed memory concurrent processors. We assume that the matrix is distributed over a P × Q processor template with a block cyclic data distribution. P, Q, and the block size can be arbitrary, so the algorithms have wide applicability....

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Bibliographic Details
Published in:Parallel computing Vol. 21; no. 9; pp. 1387 - 1405
Main Authors: Choi, Jaeyoung, Dongarra, Jack J., Walker, David W.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.09.1995
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Distributed memory multiprocessors
Exact sciences and technology
Intel Touchstone Delta
Linear algebra
Matrix transpose algorithm
Memory and file management (including protection and security)
Memory organisation. Data processing
Point-to-point communication
Software
Theoretical computing
Distributed memory multiprocessors
Matrix transpose algorithm
Intel Touchstone Delta
Point-to-point communication
Linear algebra
Matrix diagonalization
Parallel algorithm
Distributed memory multiprocessor system
Matrix inversion
Distributed algorithm
Matrix calculus
Matrix product
Parallelism
Distributed system
Implementation
Point to point communication
ISSN:0167-8191, 1872-7336
Online Access:Get full text
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Summary:This paper describes parallel matrix transpose algorithms on distributed memory concurrent processors. We assume that the matrix is distributed over a P × Q processor template with a block cyclic data distribution. P, Q, and the block size can be arbitrary, so the algorithms have wide applicability. The communication schemes of the algorithms are determined by the greatest common divisor ( GCD) of P and Q. If P and Q are relatively prime, the matrix transpose algorithm involves complete exchange communication. If P and Q are not relatively prime, processors are divided into GCD groups and the communication operations are overlapped for different groups of processors. Processors transpose GCD wrapped diagonal blocks simultaneously, and the matrix can be transposed with LCM/GCD steps, where LCM is the least common multiple of P and Q. The algorithms make use of non-blocking, point-to-point communication between processors. The use of nonblocking communication allows a processor to overlap the messages that it sends to different processors, thereby avoiding unnecessary synchronization. Combined with the matrix multiplication routine, C = A · B, the algorithms are used to compute parallel multiplications of transposed matrices, C = A T · B T , in the PUMMA package [5]. Details of the parallel implementation of the algorithms are given, and results are presented for runs on the Intel Touchstone Delta computer.
ISSN:0167-8191
1872-7336
DOI:10.1016/0167-8191(95)00016-H