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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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Performance 6 91 Performance guidelines 91 Performance, diagnosing poor 115 Performance, evaluation of 113 Performance, improvement guidelines 116 Performance, PDLAHQR 109 Performance, PSGELS/PDGELS 104 Performance, PSGEMM/PDGEMM 101 Performance, PSGEMV/PDGEMV 101 Performance, PSGESV/PDGESV 104 Performance, PSGESVD/PDGESVD 109 Performance, PSPOSV/PDPOS V 104 Performance, PSSYEV/PDSYEV 108 Performance, PSSYEVX/PDSYEVX 108 Performance, recommendations 157 performance, tuning 117 PETSc 11 PIGEMR 2 PITRMR 2 Pivoting, column (QR) 43 Pivoting, partial 37 poor performance 115 PoPCs 93 Portability 3 6 93 122 Prebuilt libraries, blacs 7 Prebuilt libraries, scalapack 7 Process column 215 Process grid 55 215 Process grid, 216 Process grid, 216 Process grid, initialization 25 56 Process grid, mapping (column-major) 55 56 Process grid, mapping (row-major) 55 56 Process grid, mapping (user-defined) 56 Process grid, obtaining BLACS context 25 Process grid, shape 92 113 Process mesh (see Process grid 55) Process row 216 Process, column coordinate (MYCOL) 25 Process, row coordinate (MYROW) 25 Processor 215 Prototype codes 11 Prototype codes, HPF interface to ScaLAPACK 11 Prototype codes, matrix sign function 11 109 Prototype codes, out-of-core linear solvers 11 Prototype codes, Super LU 11 PSDBSV 33 135 160 221 PSDBTRF 38 40 74 78 160 222 PSDBTRS 38 40 76 160 222 PSDTSV 33 135 160 223 PSDTTRF 38 40 77 78 160 225 PSDTTRS 38 40 78 160 226 PSGBSV 33 134 160 227 PSGBTRF 38 40 74 78 160 228 PSGBTRS 38 40 76 160 229 PSGEBRD 50 108 160 161 230 PSGECON 38 40 135 160 231 PSGEEQU 39 40 160 166 232 PSGEHRD 49 108 160 161 233 PSGELQF 42 45 50 160 161 167 168 234 PSGELS 34 104 136 138 160 235 PSGEMR 2 PSGEQLF 44 45 160 161 167 168 236 PSGEQPF 43 45 160 237 PSGEQRF 41 43 45 50 161 162 167 168 238 PSGERFS 38 40 136 161 239 PSGERQF 44 45 161 162 168 240 PSGESV 33 104 133 153 161 241 PSGESVD 35 50 109 125 138 141 144 161 242 PSGESVX 33 125 131 134 136 153 154 161 244 PSGETRF 38 40 160 161 247 PSGETRI 38 40 161 248 PSGETRS 38 40 161 248 PSGGQRF 45 161 249 PSGGRQF 46 161 251 PSLAHQR 49 109 252 253 PSLAMCH 121 122 166 PSORGLQ 42 45 161 253 PSORGQL 45 161 254 PSORGQR 41 43 45 161 255 PSORGRQ 45 161 256 PSORMBR 50 161 257 PSORMHR 49 161 258 PSORMLQ 42 45 161 260 PSORMQL 45 161 261 PSORMQR 41—43 45 162 262 PSORMRQ 45 162 264 PSORMRZ 44 45 162 265 PSORMTR 47 48 162 266 PSPBSV 33 134 162 268 PSPBTRF 38 40 75 78 162 269 PSPBTRS 38 40 76 162 270 PSPOCON 38 40 134 135 162 271 PSPOEQU 39 40 162 166 272 PSPORFS 38 40 136 162 273 PSPOSV 33 104 134 162 274 PSPOSVX 33 125 136 162 275 PSPOTRF 38 40 162 163 168 278 PSPOTRI 38 40 162 278 PSPOTRS 38 40 162 279 PSPTSV 33 134 163 280 PSPTTRF 40 77 163 281 PSPTTRS 40 78 163 282 PSSTEBZ 47 48 141 163 283 PSSTEIN 47 48 163 284 PSSYEV 35 108 125 138 139 163 286 PSSYEVX 35 108 115 121 125 138 140 163 287 PSSYGST 51 163 291 PSSYGVX 36 121 125 132 144 146 163 292 PSSYR 2 PSSYTRD 47 48 108 162 163 295 PSTRCON 38 40 135 138 163 296 PSTRMR 2 PSTRRFS 38 40 136 163 298 PSTRTRI 38 40 163 299 PSTRTRS 38 40 42 163 300 PSTZRZF 43 45 162 163 301 PVM 3 6 7 95 PVM, homepage 9 PXERBLA 89 153 168 PZDBSV 33 135 221 PZDBTRF 38 40 74 78 222 PZDBTRS 38 40 76 222 PZDTSV 33 135 223 PZDTTRF 38 40 77 78 225 PZDTTRS 38 40 78 226 PZGBSV 33 134 227 PZGBTRF 38 40 74 78 228 PZGBTRS 38 40 76 229 PZGEBRD 50 230 PZGECON 38 40 135 231 PZGEEQU 39 40 232 PZGEHRD 49 233 PZGELQF 42 45 50 234 PZGELS 34 136 138 235 PZGEMR 2 PZGEQLF 44 45 236 PZGEQPF 43 45 237 PZGEQRF 41 43 45 50 238 PZGERFS 38 40 136 239 PZGERQF 44 45 240 PZGESV 33 241 PZGESVD 50 138 141 144 PZGESVX 33 125 131 136 244 PZGETRF 38 40 247 PZGETRI 38 40 248 PZGETRS 38 40 248 PZGGQRF 45 249 PZGGRQF 46 251 PZHEEVX 35 121 125 138 140 287 PZHEGST 51 291 PZHEGVX 36 121 125 132 144 146 292 PZHETRD 47 48 295 PZHETRF 38 PZHETRS 38 PZPBSV 33 134 268 PZPBTRF 38 40 75 78 269 PZPBTRS 38 40 76 270 PZPOCON 38 40 134 135 271 PZPOEQU 39 40 272 PZPORFS 38 40 136 273 PZPOSV 33 134 274 PZPOSVX 33 125 136 275 PZPOTRF 38 40 278 PZPOTRI 38 40 278 PZPOTRS 38 40 279 PZPTSV 33 134 280 PZPTTRF 40 77 281 PZPTTRS 40 78 282 PZSTEIN 47 48 284 PZTRCON 38 40 135 138 296 PZTRMR 2 PZTRRFS 38 40 136 298 PZTRTRI 38 40 299 PZTRTRS 38 40 42 300 PZTZRZF 43 45 301 PZUNGLQ 42 45 253 PZUNGQL 45 254 PZUNGQR 41 43 45 255 PZUNGRQ 45 256 PZUNMBR 50 257 PZUNMHR 49 258 PZUNMLQ 42 45 260 PZUNMQL 45 261 PZUNMQR 41—43 45 262 PZUNMRQ 45 264 PZUNMRZ 44 45 265 PZUNMTR 47 48 266 QL algorithm, implicit 47 QL factorization 44 QR algorithm, implicit 47 QR factorization 41 QR factorization, blocked form 104 QR factorization, generalized (GQR) 44 QR factorization, with pivoting 43 Query 88 Rank 43 Redistribution routines, PxGEMR2D 170 Redistribution routines, PxTRMR2D 170 Reduction, bidiagonal 50 Reduction, standard form 51 Reduction, tridiagonal 47 Reduction, upper Hessenberg 49 Relative error 121 122 126 127 129 131 135 Relative machine precision 121 Reliability (see Test suites 9 149) Repeatability 124 125 Repeatability, enforcement of (BLACS — SET) 125 Replicated across process columns 69 Replicated across process rows 69 Replicated and distributed 69 Replicated vector 90 Reporting bugs, see bug reports 10 149 Right-hand-side matrix 36 Roundoff error 121 122 RQ factorization 44 RSRC_ (see Array descriptor xxvi) rule of thumb 91 Scalability 3 54 94 95 ScaLAPACK, commercial use of 8 ScaLAPACK, prebuilt libraries, availability of 7 Scaling 39 Schur factorization 48 Schur form 49 Schur vectors 48 Scope 57 216 Scope in communication 216 Scope of a variable 216 Scope, groupings of processes 57 Scope, within a process grid 216 Scoped operation 57 SDISNA 140 143 SEP 34 47 Simple driver (see Driver routines simple 32 35) Single Program Multiple Data (SPMD) 3 Singular value 49 Singular value decomposition (SVD) 35 49 Singular value, error bound 142 143 Singular vector, error bound 142 143 Singular vectors, left 35 49 Singular vectors, right 35 49 Software hierarchy 4 Software standards 3 Software standards, distributed memory 5 Solution matrix 36 Spectral factorization 34 SPMD 3 SSTEQR 2 47 48 Stability 41 120 Stability, backward 131 132 142 147 Stability, forward 132 Standard form 51 Storage scheme, general tridiagonal 84 Storage scheme, Hermitian 69 Storage scheme, orthogonal or unitary matrices 52 Submatrix access 67 Subspaces, angle between 128—130 138 144 147 Suggestions for reading xxiii SuperLU (see Prototype codes 11) Support 10 SVD 35 Sylvester equation 132 symmetric 69 Symmetric eigenproblem 47 Symmetric tridiagonal 84 Symmetric tridiagonal, triangular 69 T() xxvi 95 97 Terminology xxv test suites 9 149 thread of execution (see Process 215) Throughput (see Bandwidth 97) TOOLS, DESCINIT 26 TOOLS, NUMROC xxvi TOOLS, PxLAPRNT 151 TOOLS, SLJNIT 26 Transportable efficiency 93 Tridiagonal form 47 52 108 141 Tridiagonal matrix, distribution of 76 troubleshooting 149 tuning 117 Underdetermined system 34 42 Underflow 121—123 Unitary matrix 41 Upper Hessenberg form 49 Utility routines 151 Workspace query 88 World Wide Web 9 Wrong results 154 WWW 9 XDR 125
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