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Blackford L.S., Choi J., Geary A. — ScaLAPACK User's Guide
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Название: ScaLAPACK User's GuideАвторы: Blackford L.S., Choi J., Geary A.Аннотация: ScaLAPACK is an acronym for Scalable Linear Algebra Package or Scalable LAPACK. It is a library of high-performance linear algebra routines for distributed memory message-passing MIMD computers and networks of workstations supporting parallel virtual machine (PVM) and/or message passing interface (MPI). It is a continuation of the LAPACK project, which designed and produced analogous software for workstations, vector supercomputers, and shared memory parallel computers. Both libraries contain routines for solving systems of linear equations, least squares problems, and eigenvalue problems. The goals of both projects are efficiency, scalability, reliability, portability, flexibility, and ease of use. Each Users' Guide includes a CD-ROM containing the HTML version of the ScaLAPACK Users' Guide, the source code for the package, testing and timing programs, prebuilt versions of the library for a number of computers, example programs, and the full set of LAPACK Working Notes
Язык: Рубрика: Руководства по программному обеспечению /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 325Добавлена в каталог: 11.04.2010Операции: Положить на полку |
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xxv 93 97 xxv 94 97 xxv 94 97 xxvi 215 xxvi 215 xxvi 96 97 xxvi 97 100 xxvi xxvi xxvi 95 97 xxvi 96 97 100 Absolute error 126 127 Absolute gap 140 143 146 Accuracy 120 135 Accuracy, high 133 140 141 143 Active Messages 98 Algorithmic, coherence 124 Algorithmic, reliability 3 124 125 Algorithmic, repeatability 124 Algorithms, block-partitioned 93 94 Alignment restrictions 89 AM — II, see Active Messages 98 Angle between vectors and subspaces 128—130 138 141 144 147 Arguments, BERR 136 Arguments, description conventions 67 81—83 Arguments, descriptor 26 57 67 81 Arguments, DIAG 69 87 Arguments, dimensions 88 Arguments, FERR 134 136 Arguments, global 214 Arguments, global column index 22 67 81 Arguments, global input 86 Arguments, global output 86 Arguments, global row index 22 67 81 Arguments, IA and JA 22 67 Arguments, INFO 89 153 Arguments, local 214 Arguments, local input 86 Arguments, local output 86 Arguments, LWORK 88 Arguments, options 86 Arguments, order of 86 Arguments, RCOND 127 Arguments, SIDE 86 Arguments, TRANS 87 Arguments, UPLO 87 Arguments, work space 88 ARPACK 11 Array argument descriptions, block cyclic arrays 67 Array argument descriptions, block-column and block-row arrays 79 Array descriptor 26 57 67 81 213 Array descriptor, block 78 84 Array descriptor, block cyclic 65 Array descriptor, CTXT xxv Array descriptor, definition of 57 Array descriptor, DLEN_ 57 Array descriptor, DTYPE_ xxv 58 Array descriptor, example 26 Array descriptor, LLD_ 66 Array descriptor, MB_ and NB_ 63 66 Array descriptor, M_ and N_ 63 66 Array descriptor, out-of-core 84 Array descriptor, RSRC. and CSRC 22 Auxiliary routines 4 29 Auxiliary routines, index of (see Appendix A) Avoiding poor performance 157 Backward error 131 135 136 138 141 Backward stability 131 142 147 Backward stability, componentwise 132 Backward stability, normwise 131 Band matrix, distribution of 74 Bandwidth 97 Berkeley NOW 98 Bidiagonal form 50 52 108 Bidiagonal matrix, distribution of 77 BLACS 95 213 BLACS, BLACS — G RID INFO 25 BLACS, BLACS — GRIDEXIT 27 57 BLACS, BLACS — GRIDINIT 55 BLACS, BLACS — SET 125 BLACS, BLACS.ABORT 89 153 BLACS, BLACS.BARRIER 151 BLACS, BLACS.EXIT 57 BLACS, C interface 206 BLACS, context 56 BLACS, context handle 56 BLACS, efficiency 7 95 BLACS, Fortran 77 BLACS, interface 206 BLACS, prebuilt libraries, availability of 7 BLAS 6 93 157 213 BLAS, level 1 93 BLAS, Level 2 93 BLAS, Level 3 93 Block cyclic distribution 58 63 Block size 104 213 Block size, size of 92 113 Block-column distribution 70 72 Block-partitioned algorithms 4 55 93 94 Block-row distribution 71—73 Blocking factor, see block size 213 bug reports 10 Bug reports, checklist 149 Bug reports, mailing alias 149 CAPSS 11 Checklist, high performance 91 Chordal distance 147 Cluster, eigenvalues 140 Cluster, singular values 143 Clusters of workstations 91 Coefficient band matrix 74 Coefficient matrix 36 74 76 77 153 Coefficient matrix, distribution of 69 78 Coefficient tridiagonal matrix 76 77 Coherence 124 125 Column pivoting (QR) 43 Column-major order 73 Commercial use 8 Communication bandwidth 97 Communication deadlock 124 Communication latency 97 Communicator, MPI 6 Complete orthogonal factorization 44 Computational routines 4 29 36 Computational Routines, index of (see Appendix A) Computers 91 Condensed form, reduction to 108 Condition number 127 131 133—137 145 146 148 Condition number, estimate 132 135 Context handle 56 Context, BLACS 6 Coprocessor 96 Cows 91 93 CSRC_ (see Array descriptor xxv) CTXT_ (see Array descriptor xxv) Data distribution 214 Data distribution, block 70 Data distribution, block cyclic 58 94 Data distribution, block-column 70 72 Data distribution, block-row 71—73 Data distribution, general band matrix 70 79 Data distribution, general tridiagonal matrix 70 79 Data distribution, symmetric band matrix 79 Data distribution, symmetric positive definite band matrix 70 Data distribution, symmetric positive definite tridiagonal matrix 70 Data distribution, symmetric tridiagonal matrix 79 DDISNA 140 143 Deadlock 124 Debug level BLACS 151 Debugging hints, application 151 Debugging hints, installation 150 Debugging, alignment restrictions 89 Debugging, errata, scalapack 150 152 Debugging, errata.blacs 150 152 Debugging, synchronization points 151 Debugging, TOOLS 151 Debugging, workspace requirements 151 Decomposition (see Data distribution) Descriptor 26 57 67 81 DESC_ (see Array descriptor xxv) Determining the size of local arrays 64 66 73 Diagonally dominant-like 31 37 38 Distributed across process columns 69 Distributed across process rows 69 Distributed matrix 66 Distributed matrix, partitioning of 66 Distributed memory xix xxi 3 4 6 55 Distributed memory computers 91 Distributed memory standards 5 Distributed vector 69 Distribution, see data distribution 214 DLEN_ (see Array descriptor xxv) Documentation 9 Documentation, installation guide 8 149 Documentation, structure 85 Downloading instructions 7 Driver routine, generalized symmetric definite eigenvalue problem 36 Driver routine, linear equations 32 Driver routine, linear least squares 34 Driver routine, SVD 35 Driver routine, symmetric eigenvalue problem 35 Driver routines 4 29 32 Driver routines, expert 32 35 Driver routines, index of (see Appendix A) Driver routines, simple 32 35 DSTEQR 2 47 48 DTYPE_ see Array descriptor xxv) E() xxv 95 97 Effective rank 43 Efficiency 99 Efficiency, BLACS 6 Efficiency, BLAS 6 Efficiency, block-partitioned algorithms 6 Efficiency, transportable 93 Eigendecomposition, blocked form 108 Eigendecomposition, symmetric 138 Eigenvalue 34 47—49 138 Eigenvalue problem, generalized symmetric 51 Eigenvalue problem, generalized symmetric/Hermitian 36 Eigenvalue problem, symmetric/Hermitian 34 Eigenvalue problems, large scale 11 Eigenvalue problems, large sparse 11 Eigenvalue problems, nonsymmetric 48 Eigenvalue problems, symmetric/Hermitian 47 Eigenvector 34 47 138 Elementary Householder matrix (see Householder) Elementary Householder matrix, matrix 41 42 44 50 52 Elementary reflector (see Householder matrix) Equilibration 32 39 Errata, BLACS 10 Errata, ScaLAPACK and PBLAS 10 Error bound 138 140 144 145 147 Error bound, GSEP 36 Error bound, left 48 Error bound, right 48 Error bound, SEP 47 Error bounds, generalized symmetric definite eigenproblem 144 146 Error bounds, linear equations 133 135 Error bounds, linear least squares 136 138 Error bounds, singular value decomposition 141 142 Error bounds, symmetric eigenproblem 138 139 Error handler, BLACS 155 Error handler, PBLAS 154 Error handler, PXERBLA 89 153 Error, absolute 126 127 Error, analysis 131 Error, backward 131 135 136 138 141 Error, matrix 126 127 Error, measurement of 126 Error, relative 121 122 126 127 129 131 135 Error, scalar 126 Error, subspace 126 127 Error, vector 126 Example program, how to execute 13 Example program, HPF 197 Example program, output, using MPICH 23 Example program, output, using PVM 24 Example program, ScaLAPACK (PDGESV) 19 181 Expert driver (see Driver routines expert) eXternal Data Representation (XDR) 125 Factorizations (see Matrix factorizations) failures 152 Failures, common causes 152 Failures, error handling 89 Failures, FDDI 92 Failures, INFO 89 Fiber distributed data interface (FDDI) 92 Floating-point arithmetic 121 Floating-point arithmetic, 121 Floating-point arithmetic, gradual underflow 123 Floating-point arithmetic, IEEE standard 120— 125 Floating-point arithmetic, infinity 123 Floating-point arithmetic, NaN 123 Floating-point arithmetic, Not-a-Number 123 Floating-point arithmetic, overflow 121—123 127 135 138 140 143 Floating-point arithmetic, relative machine precision 121 122 Floating-point arithmetic, roundoff error 122 Floating-point arithmetic, subnormal numbers 123 Floating-point arithmetic, underflow 121—123 Flop counts, for ScaLAPACK drivers 103 Fmm 5 xxv 97 100 Forward error 39 Forward stability 132 Functionality 3 Gang scheduler 91 Gap 140 143 146 Generalized (GRQ) 46 Generalized eigenproblem, symmetric definite 51 Generalized orthogonal factorization 44 global 214 Global column index (JA) xxv 22 67 Global input 86 Global output 86 Global row index (IA) xxv 22 67 Global, matrix 214 Global, software components 4 Global, variables 214 216 Globally blocking receive 95 Glossary 213 GQR 44—46 Granularity, of computation 4 6 29 32 grid (see Process grid 215) GRQ 46 GSEP 36 Guidelines, for high performance 91 Hermitian eigenvalue problem (see Eigenvalue) Hermitian eigenvalue problem, problems 34 Hessenberg form 108 Hessenberg form, reduction to 108 Hessenberg form, upper 49 Heterogeneity 124 Heterogeneous environment 6 Heterogeneous network 125 Heterogeneous software issues, algorithmic integrity 140 143 Heterogeneous software issues, machine parameters (PxLAMCH) 121 Hierarchical memory 4 5 54 Homepage, BLACS 25 Homepage, MPI 9 Homepage, netlib 7 Homepage, PBLAS 202
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