Using Plapack,9780262720267

Using Plapack

by ; ; ; ; ; ;
ISBN13: 9780262720267
ISBN10: 0262720264
Format: Paperback
Pub. Date: 1997-03-15
Publisher(s): Mit Pr
List Price: $45.00

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Summary

PLAPACK is a library infrastructure for the parallel implementation of linear algebra algorithms and applications on distributed memory supercomputers such as the Intel Paragon, IBM SP2, Cray T3D/T3E, SGI PowerChallenge, and Convex Exemplar. This infrastructure allows library developers, scientists, and engineers to exploit a natural approach to encoding so-called blocked algorithms, which achieve high performance by operating on submatrices and subvectors. This feature, as well as the use of an alternative, more application-centric approach to data distribution, sets PLAPACK apart from other parallel linear algebra libraries, allowing for strong performance and significanltly less programming by the user. This book is a comprehensive introduction to all the components of a high-performance parallel linear algebra library, as well as a guide to the PLAPACK infrastructure. Scientific and Engineering Computation series

Table of Contents

Series Foreword xiii(2)
Preface xv
1 Introduction
1(18)
1.1 Why a New Infrastructure?
1(1)
1.2 Natural Description of Linear Algebra Algorithms
2(1)
1.3 Physically Based Matrix Distribution
3(5)
1.4 Redistributing and Duplicating Matrices and Vectors
8(4)
1.4.1 Redistributing vectors, matrix rows, and matrix columns
8(2)
1.4.2 Spreading vectors, matrix rows, and matrix columns
10(1)
1.4.3 Reducing vectors, matrix rows, and matrix columns
11(1)
1.4.4 Terminology
12(1)
1.5 Implementation of Basic Matrix-Vector Operations (Preview)
12(3)
1.5.1 Matrix-vector multiplication
12(1)
1.5.2 Rank-1 update
13(2)
1.6 Implementation of Basic Matrix-Matrix Operations (Preview)
15(1)
1.6.1 Matrix-matrix multiplication
15(1)
1.6.2 Attaining better performance
16(1)
1.7 Basic Linear Algebra Subprograms
16(1)
1.8 Message-Passing Interface
17(1)
1.9 Parallel Sparse Linear Algebra
17(1)
1.10 FORTRAN Interface
17(1)
1.11 Availability
18(1)
2 Templates and Linear Algebra Objects
19(24)
2.1 Initializing PLAPACK
19(1)
2.2 Distribution Templates
20(7)
2.2.1 Template creation
22(1)
2.2.2 Template destruction
23(2)
2.2.3 Template inquiry routines
25(2)
2.3 Linear Algebra Objects
27(12)
2.3.1 Linear algebra object creation
27(4)
2.3.2 Linear algebra object destruction
31(1)
2.3.3 Linear algebra object inquiry routines
31(6)
2.3.4 Extracting and setting local data
37(1)
2.3.5 Initializing object data
38(1)
2.4 Example
39(1)
2.5 Return Values
39(1)
2.6 More Operations and Information
39(4)
3 Advanced Linear Algebra Object Manipulation
43(16)
3.1 Creating Views into Objects
43(3)
3.2 Splitting of Linear Algebra Objects
46(4)
3.2.1 Splitting into four quadrants
46(2)
3.2.2 Splitting into two parts
48(2)
3.3 Shifting of Linear Algebra Objects
50(1)
3.4 Determining Where to Split
51(1)
3.5 Creating Objects "Conformal to" Other Objects
52(3)
3.6 Annotating Object Orientation
55(1)
3.7 Casting Object Types
56(1)
3.8 More Operations and Information
57(2)
4 Application Program Interface
59(16)
4.1 Introduction
59(1)
4.2 API-Activation
60(1)
4.3 Opening and Closing an Object
61(1)
4.4 Accessing a Vector
61(4)
4.5 Accessing a Matrix
65(2)
4.6 Completion and Synchronization
67(1)
4.7 Examples
67(6)
4.8 More Operations and Information
73(2)
5 Data Duplication and Consolidation
75(14)
5.1 Copy
75(3)
5.1.1 Copy involving vectors
75(1)
5.1.2 Copy involving multivectors
75(1)
5.1.3 Copy involving matrices
76(2)
5.1.4 Copy involving multiscalars
78(1)
5.1.5 Specialized copy
78(1)
5.2 Reduce
78(2)
5.3 Pipelining Computation and Communication
80(1)
5.4 A Building Block Approach to Implementing Copy and Reduce
81(5)
5.4.1 Collective communication operations
81(1)
5.4.2 Efficient implementation of collective communication
82(1)
5.4.3 Implementation of the copy
83(3)
5.4.4 Implementation of the reduce
86(1)
5.5 More Operations and Information
86(3)
6 Vector-Vector Operations
89(16)
6.1 Copy
89(3)
6.1.1 Standard FORTRAN call
89(1)
6.1.2 PLAPACK FORTRAN-C interface
89(1)
6.1.3 PLAPACK calls
90(2)
6.2 Swap
92(1)
6.2.1 Standard FORTRAN call
92(1)
6.2.2 PLAPACK FORTRAN-C interface
92(1)
6.2.3 PLAPACK calls
92(1)
6.3 Scaling a Vector (Object)
93(1)
6.3.1 Standard FORTRAN call
93(1)
6.3.2 PLAPACK FORTRAN-C interface
93(1)
6.3.3 PLAPACK calls
94(1)
6.4 Scaled Vector (Object) Addition
94(2)
6.4.1 Standard FORTRAN call
95(1)
6.4.2 PLAPACK FORTRAN-C interface
95(1)
6.4.3 PLAPACK calls
95(1)
6.5 Inner Product of Vectors
96(1)
6.5.1 Standard FORTRAN call
96(1)
6.5.2 PLAPACK FORTRAN-C interface
96(1)
6.5.3 PLAPACK calls
96(1)
6.6 Norms of Vectors
97(2)
6.6.1 Standard FORTRAN call
97(1)
6.6.2 PLAPACK FORTRAN-C interface
98(1)
6.6.3 PLAPACK calls
98(1)
6.7 Maximum Absolute Value in Vector
99(1)
6.7.1 Standard FORTRAN call
99(1)
6.7.2 PLAPACK FORTRAN-C interface
99(1)
6.7.3 PLAPACK calls
99(1)
6.8 Example: Parallelizing Inner Product
100(1)
6.9 Example: Parallelizing "axpy" for Vector Objects
101(2)
6.10 More Operations and Information
103(2)
7 Matrix-Vector Operations
105(20)
7.1 General Matrix-Vector Multiplication
105(3)
7.1.1 Standard FORTRAN call
105(1)
7.1.2 PLAPACK FORTRAN-C interface
105(1)
7.1.3 PLAPACK calls
106(2)
7.2 Symmetric Matrix-Vector Multiplication
108(2)
7.2.1 Standard FORTRAN call
108(1)
7.2.2 PLAPACK FORTRAN-C interface
109(1)
7.2.3 PLAPACK calls
109(1)
7.3 Triangular Matrix-Vector Multiplication
110(2)
7.3.1 Standard FORTRAN call
110(1)
7.3.2 PLAPACK FORTRAN-C interface
110(1)
7.3.3 PLAPACK calls
111(1)
7.4 Triangular Solve
112(1)
7.4.1 Standard FORTRAN call
112(1)
7.4.2 PLAPACK FORTRAN-C interface
112(1)
7.4.3 PLAPACK calls
113(1)
7.5 Rank-1 Update
113(2)
7.5.1 Standard FORTRAN call
113(1)
7.5.2 PLAPACK FORTRAN-C interface
114(1)
7.5.3 PLAPACK calls
114(1)
7.6 Symmetric Rank-1 Update
115(1)
7.6.1 Standard FORTRAN call
115(1)
7.6.2 PLAPACK FORTRAN-C interface
115(1)
7.6.3 PLAPACK calls
115(1)
7.7 Symmetric Rank-2 Update
116(2)
7.7.1 Standard FORTRAN call
116(1)
7.7.2 PLAPACK FORTRAN-C interface
117(1)
7.7.3 PLAPACK calls
117(1)
7.8 Example: Parallelizing Matrix-Vector Multiplication
118(3)
7.8.1 Simple implementation
118(1)
7.8.2 General implementation
119(2)
7.9 Example: Parallelizing Rank-1 Update
121(1)
7.9.1 Simple implementation
121(1)
7.9.2 General implementation
121(1)
7.10 More Operations and Information
122(3)
8 Matrix-Matrix Operations
125(36)
8.1 General Matrix-Matrix Multiplication
125(2)
8.1.1 Standard FORTRAN call
125(1)
8.1.2 PLAPACK FORTRAN-C interface
126(1)
8.1.3 PLAPACK calls
126(1)
8.2 Symmetric Matrix-Matrix Multiplication
127(4)
8.2.1 Standard FORTRAN call
129(1)
8.2.2 PLAPACK FORTRAN-C interface
129(1)
8.2.3 PLAPACK calls
129(2)
8.3 Symmetric Rank-k Update
131(1)
8.3.1 Standard FORTRAN call
131(1)
8.3.2 PLAPACK FORTRAN-C interface
131(1)
8.3.3 PLAPACK calls
131(1)
8.4 Symmetric Rank-2k Update
132(3)
8.4.1 Standard FORTRAN call
133(1)
8.4.2 PLAPACK FORTRAN-C interface
133(1)
8.4.3 PLAPACK calls
133(2)
8.5 Triangular Matrix-Matrix Multiplication
135(2)
8.5.1 Standard FORTRAN call
135(1)
8.5.2 PLAPACK FORTRAN-C interface
135(1)
8.5.3 PLAPACK calls
136(1)
8.6 Triangular Solve with Multiple Right-Hand-Sides
137(2)
8.6.1 Standard FORTRAN call
137(1)
8.6.2 PLAPACK FORTRAN-C interface
137(1)
8.6.3 PLAPACK calls
138(1)
8.7 Example: Parallelizing Matrix-Matrix Multiplication
139(19)
8.7.1 Forming C = AB + BC
139(3)
8.7.2 Forming C = ABT + BC
142(3)
8.7.3 Forming C = ATB + BC
145(2)
8.7.4 Forming C = ATBT + BC
147(1)
8.7.5 A more general approach
147(2)
8.7.6 Performance results
149(9)
8.8 Querying Algorithmic Blocking Size
158(1)
8.9 More Operations and Information
159(2)
9 Application of the Infrastructure
161(12)
9.1 Cholesky Factorization
161(1)
9.2 Right-Looking Variant
161(4)
9.2.1 Level-2 BLAS implementation
161(2)
9.2.2 Level-3 BLAS implementation
163(2)
9.3 Left-Looking Variant
165(7)
9.3.1 Level-2 BLAS implementation
165(1)
9.3.2 Level-3 BLAS implementation
166(2)
9.3.3 Towards further performance improvements
168(4)
9.4 More Operations and Information
172(1)
A Summary of PLAPACK Routines and Their Arguments 173(8)
B Summary of BLAS Related Routines 181(4)
Bibliography 185(2)
Index 187(4)
Constants Index 191(2)
Function Index 193

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