并行MATLAB：多核与多节点计算机的实战指南（2009）

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《并行MATLAB for Multicore and Multinode Computers》（2009）是一本专门针对多核和多节点计算机的并行MATLAB编程的开创性著作。该书旨在为专业科学家和工程师，以及使用MATLAB的本科生和研究生提供实用的指导，帮助他们设计、编写高效并行程序。该系列书籍——“软件、环境与工具”——关注于计算方法的实践实现，特别是强调对高性能科学计算的需求，通过介绍当前的软件技术状态、应用、算法、数学软件、工具、语言和编译器，以及计算环境和可视化等关键领域。本书由杰克·J·唐拉雅担任编辑，他在田纳西大学和橡树岭国家实验室有着丰富的经验。编辑委员会成员包括来自加州大学伯克利分校的詹姆斯·W·邓梅尔、印第安纳大学的丹尼斯·甘农、AT&T贝尔实验室的埃里克·格罗斯和阿贡国家实验室的乔治·J·莫雷。这个系列还包括其他作品，如《并行计算科学中的并行处理》（由帕尔马·拉格万、迈克尔·A·霍洛克斯和霍斯特·D·西蒙共同编辑）、《 Lanczos和共轭梯度算法：从理论到有限精度计算》（作者：热拉尔·莫尔坦）。本书的核心内容深入探讨了如何在MATLAB环境中充分利用多核处理器和分布式系统，包括但不限于并行算法的设计原则，如何编写和优化并行代码，以及如何有效地进行调试和测试。此外，书中还可能涵盖了如何处理数据并行、任务并行、消息传递模式以及如何利用MATLAB的并行计算工具箱，如parfor循环、并行矩阵运算和并行函数调用等。对于那些希望提升MATLAB程序性能的专业人员和学生来说，这本书提供了宝贵的资源，帮助他们跨越单线程限制，进入高效的并行计算世界，从而解决更大规模的复杂问题。通过阅读这本书，读者将不仅掌握并行编程的基本原理，还能学习如何在实际项目中实施和优化这些技术，提高工作效率和科学计算的质量。

List of Tables

2.1 Mandelbrot parallel mapping. . . . . . . . . . . . . . . . . . . . . . 15

2.2 Debugging steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Multicore and multinode Mandelbrot performance. . . . . . . . . . 20

2.4 ZoomImage parallel mapping. . . . . . . . . . . . . . . . . . . . . . 24

2.5 Multicore and multinode ZoomImage performance. . . . . . . . . . 28

2.6 Multicore and multinode ParallelIO performance. . . . . . . . . . 36

3.1 Beamformer parallel mapping. . . . . . . . . . . . . . . . . . . . . 43

3.2 Multicore and multinode Beamformer performance. . . . . . . . . 50

3.3 Beamformer parallel pipeline mapping. . . . . . . . . . . . . . . . 50

4.1 Taxonomy of parallel applications. . . . . . . . . . . . . . . . . . . 60

4.2 Multicore and multinode Blurimage performance. . . . . . . . . . 73

5.1 Distributed array design goals. . . . . . . . . . . . . . . . . . . . . 81

5.2 Distributed array parallel support functions. . . . . . . . . . . . . 84

5.3 Distributed array distributions. . . . . . . . . . . . . . . . . . . . . 85

5.4 Mandelbrot load imbalance. . . . . . . . . . . . . . . . . . . . . . . 87

5.5 Implementation levels. . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.6 MPI functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.7 Selected user application results. . . . . . . . . . . . . . . . . . . . 103

6.1 Parallel algorithm characteristics. . . . . . . . . . . . . . . . . . . 111

6.2 Software implementation eﬃciency estimates. . . . . . . . . . . . . 135

6.3 Software coding rate estimates. . . . . . . . . . . . . . . . . . . . . 137

6.4 Approximate relative productivity. . . . . . . . . . . . . . . . . . . 139

7.1 HPC Challenge parallel algorithm characteristics. . . . . . . . . . 153

7.2 Memory hierarchy parameters. . . . . . . . . . . . . . . . . . . . . 157

7.3 HPC Challenge implementation results. . . . . . . . . . . . . . . . 164

8.1 Multicore and multinode Stream triadd performance. . . . . . . . 178

9.1 Multicore RandomAccess performance. . . . . . . . . . . . . . . . 197

9.2 Multinode RandomAccess performance. . . . . . . . . . . . . . . . 199

List of Algorithms

Algorithm 1.1 Add one serial . . . . . . . . . . . . . . . . . . . . . . . . . 4

Algorithm 1.2 Add one parallel . . . . . . . . . . . . . . . . . . . . . . . 5

Algorithm 2.1 Mandelbrot serial . . . . . . . . . . . . . . . . . . . . . . . 14

Algorithm 2.2 Mandelbrot parallel . . . . . . . . . . . . . . . . . . . . . . 15

Algorithm 2.3 ZoomImage serial . . . . . . . . . . . . . . . . . . . . . . . 23

Algorithm 2.4 ZoomImage parallel . . . . . . . . . . . . . . . . . . . . . . 24

Algorithm 2.5 Serial IO . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Algorithm 2.6 ParallelIO . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Algorithm 3.1 Beamformer serial . . . . . . . . . . . . . . . . . . . . . . 41

Algorithm 3.2 Beamformer parallel . . . . . . . . . . . . . . . . . . . . . 42

Algorithm 3.3 Beamformer pipeline . . . . . . . . . . . . . . . . . . . . . 51

Algorithm 4.1 Blurimage serial . . . . . . . . . . . . . . . . . . . . . . . . 57

Algorithm 4.2 Blurimage manager/worker . . . . . . . . . . . . . . . . . 65

Algorithm 4.3 Blurimage message passing . . . . . . . . . . . . . . . . . 66

Algorithm 4.4 Blurimage distributed array . . . . . . . . . . . . . . . . . 66

Algorithm 5.1 Network speedtest . . . . . . . . . . . . . . . . . . . . . . 96

Algorithm 8.1 Serial Stream . . . . . . . . . . . . . . . . . . . . . . . . . 171

Algorithm 8.2 Parallel Stream . . . . . . . . . . . . . . . . . . . . . . . . 173

Algorithm 9.1 Serial RandomAccess . . . . . . . . . . . . . . . . . . . . . 183

Algorithm 9.2 Parallel RandomAccess spray . . . . . . . . . . . . . . . . 185

Algorithm 9.3 Parallel RandomAccess tree . . . . . . . . . . . . . . . . . 188

Algorithm 10.1 Parallel FFT . . . . . . . . . . . . . . . . . . . . . . . . . 204

Algorithm 11.1 Serial LU . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

Algorithm 11.2 Parallel LU . . . . . . . . . . . . . . . . . . . . . . . . . . 220

Algorithm A.1 Serial 2D ﬁlter . . . . . . . . . . . . . . . . . . . . . . . . 235

Algorithm A.2 Parallel 2D ﬁlter . . . . . . . . . . . . . . . . . . . . . . . 237

Algorithm A.3 Block parallel 2D ﬁlter . . . . . . . . . . . . . . . . . . . . 239

Algorithm A.4 Hierarchical parallel 2D ﬁlter . . . . . . . . . . . . . . . . 240

Algorithm A.5 Hierarchical block parallel 2D ﬁlter . . . . . . . . . . . . . 242

Algorithm A.6 Implicit pipeline 2D ﬁlter . . . . . . . . . . . . . . . . . . 243

Algorithm A.7 Task parallel 2D ﬁlter . . . . . . . . . . . . . . . . . . . . 245

Algorithm A.8 Fine-grained task parallel 2D ﬁlter . . . . . . . . . . . . . 247

Algorithm A.9 Generic hierarchical block parallel 2D ﬁlter . . . . . . . . 248

Algorithm A.10 Hierarchical helper functions . . . . . . . . . . . . . . . . . 249

xvii

Preface

MATLAB



is currently the dominant language of technical computing with

approximately one million users worldwide, many of whom can beneﬁt from the

increased power oﬀered by widely available multicore processors and multinode

computing clusters. MATLAB is also an ideal environment for learning about par-

allel computing, allowing the user to focus on parallel algorithms instead of the

details of the implementation. The succinctness of MATLAB allows many speciﬁc

examples to be presented to illustrate parallel programming concepts.

The subject of this book is parallel programming in MATLAB and is hopefully

the ﬁrst of many books on this topic, as there are now a wide variety of parallel

MATLAB libraries [Choy 2004] for users to choose from. I am fortunate to have been

involved in the development of two of these libraries [Kepner 2004, Kepner 2003].

The most widely used of these libraries include pMatlab (developed by MIT Lincoln

Laboratory), the Parallel Computing Toolbox (developed by The MathWorks, Inc.),

and StarP (developed at MIT, UCSB, and Interactive Supercomputing, Inc.). All

of these libraries provide direct support for parallel computing using distributed

arrays and other parallel programming models. The speciﬁc examples in this book

are written using the freely available pMatlab library. pMatlab has the advantage

of running either standalone or on top of the aforementioned parallel MATLAB

libraries. So all the examples in the book can be run in any of the parallel MATLAB

environments. Fortunately, the concepts illustrated in the book are independent of

the underlying implementation and valid for any particular parallel programming

syntax the user may prefer to use. The software along with installation instructions

can be found at the book website:

http://www.siam.org/KepnerBook

The expressive power of MATLAB allows us to concentrate on the techniques

for creating parallel programs that run well (as opposed to the syntactic mechanics

of writing parallel programs). Our primary focus is on the designing, coding, de-

bugging, and testing techniques required to quickly produce well-performing parallel

programs in a matter of hours instead of weeks or months (see Figure 1). These

techniques have been developed over the years through thousands of one-on-one

interactions with hundreds of parallel MATLAB users.

A general familiarity with MATLAB is assumed (see [Higham & Higham 2005]

and [Moler 2004] for an introduction to MATLAB). The target audience of the book

xix

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