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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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Homepage, PVM 9 Homepage, ScaLAPACK 7 9 Homogeneous network 124 Householder matrix 52 105 Householder matrix, complex 52 Householder transformation - blocked form 104 Householder vector 52 HPF, DISTRIBUTE 61—64 72 73 197 HPF, example program 197 HPF, interface LA — GELS 197 HPF, interface LAJPOSV 197 HPF, interface LA_GEMM 197 HPF, interface LA_GESV 197 HPF, interface to ScaLAPACK 11 197 HPF, LA.GELS 197 HPF, LAJPOSV 197 HPF, LA_GEMM 197 HPF, LA_GESV 197 HPF, PROCESSORS 197 ICTXT (see BLACS 56) Ill-conditioned 131 Ill-posed 131 Incoherence 124 infinity 123 Info 89 Input error 121 Installation 8 Installation, PxLAMCH 122 Insufficient workspace 151 Invariant subspaces, error bound 140 Inverse iteration 47 Inverting matrix, using factorization 38 Isoefficiency 96 Isogranularity 96 Iterative refinement 39 LAPACK 93 latency 55 97 layout (see Data distribution 214) Lcm(Pr,Pc) xxv LDLT factorization 38 Leading dimension (see Local array 214) Linear equations 36 Linear least squares problem 33 41—43 Linear least squares problem, full rank 42 Linear least squares problem, overdetermined 34 136 Linear least squares problem, rank-deficient 43 50 Linear least squares problem, underdetermined 42 Linear systems, solution of 33 36 LLD_ (see Array descriptor xxv) LLS 33 34 Load balance 94 local 214 Local input 86 Local leading dimension 214 Local output 86 Local, determining the size of 64 66 73 Local, local array 214 Local, software components 4 local, variables 214 216 Locally blocking send 95 LOCc() xxv 64 214 LOCr() xxvi 64 214 LQ factorization 42 LU factorization 37 LU factorization, matrix types 37 LWORK 88 LWORK 88 LWORK query 88 Machine precision 121 122 Matrix factorizations, 38 Matrix factorizations, Cholesky 37 38 Matrix factorizations, complete orthogonal 44 Matrix factorizations, generalized orthogonal 44 Matrix factorizations, generalized QR 44 Matrix factorizations, generalized RQ 46 Matrix factorizations, LQ 34 42 Matrix factorizations, LU 37 Matrix factorizations, orthogonal 41 Matrix factorizations, QL 44 Matrix factorizations, QR 34 41 Matrix factorizations, RQ 44 Matrix inversion 33 38 Matrix of right-hand-side vectors 36 Matrix of solution vectors 36 Matrix partitioning 66 Matrix sign function 11 MB_ (see Array descriptor xxvi) Memory hierarchy 4 5 54 Message coprocessor 96 Message passing (see Distributed memory 3) Message-passing libraries, MIMD 3 6 Message-passing libraries, MPI 7 95 Message-passing libraries, MPL 7 95 Message-passing libraries, NX 7 95 Message-passing libraries, PVM 7 95 Minimum norm least squares solution 34 Minimum norm solution 34 42 44 50 MPI 3 6 7 56 95 MPI, communicator 56 MPI, homepage 9 MPI, reference implementation (MPICH) 13 MPICH 13 MPL 7 95 Multiple instruction multiple data (MIMD) 3 6 MYCOL xxvi 25 215 MYROW xxvi 25 215 M_, see array descriptor xxvi Naming scheme 30 Naming scheme, auxiliary 32 Naming scheme, driver and computational 31 NaN 123 NBRHS xxvi NEL (see Array descriptor xxvi) NETLIB 7 Netlib, homepage 7 Netlib, mirror repositories 7 Networks of workstations 91 Nonrepeatability 124 Nonsymmetric eigenproblem 48 Norm, Frobenius norm 126 129 Norm, infinity norm 126 Norm, matrix 126 127 Norm, one norm 126 Norm, two norm 126 129 Norm, vector 126 Not-a-number 123 Notation, table of xxv NoWs 91 93 NPCOL, see xxvi NPROCS, see P xxvi NPROW, see xxvi NRHS xxvi Numerical error, sources of 121 Numerical error, sources of input error 121 Numerical error, sources of roundoff error 121 122 NX 7 95 N_ (see Array descriptor xxvi) Optimal block size, determination of 118 Orthogonal (unitary) factorizations 41 Orthogonal (unitary) transformation 43 108 Orthogonal factorization, generalized 44 Orthogonal matrix 41 Out-of-core linear solvers 11 Over deter mined system 33 34 138 Overflow 121—123 127 135 138 140 143 P xxvi 55 215 P.ARPACK 11 Parallel efficiency 95 97 Parallelizing BLAS-based programs (see Appendix B 176) Parallelizing LAPACK-based programs (see Appendix B 176) PARPRE 11 Partial pivoting 37 Partitioning unit (see Block size 104 213) PBLAS 94 215 PBLAS, converting from the BLAS to (see Appendix B 176) PBLAS, error handling 154 PBLAS, PDGEMM 101 PBLAS, PDGEMV 101 PBLAS, peak performance 93 PBLAS, PSGEMM 101 PBLAS, PSGEMV 101 PCDBSV 33 135 160 221 PCDBTRF 38 40 74 78 160 222 PCDBTRS 38 40 76 160 222 PCDTSV 33 135 160 223 PCDTTRF 38 40 77 78 160 225 PCDTTRS 38 40 78 160 226 PCGBSV 33 134 160 227 PCGBTRF 38 40 74 78 160 228 PCGBTRS 38 40 76 160 229 PCGEBRD 50 160 161 230 PCGECON 38 40 135 160 231 PCGEEQU 39 40 160 166 232 PCGEHRD 49 160 161 233 PCGELQF 42 45 50 160 161 167 168 234 PCGELS 34 136 138 160 235 PCGEMR 2 PCGEQLF 44 45 160 161 167 168 236 PCGEQPF 43 45 160 237 PCGEQRF 41 43 45 50 161 162 167 168 238 PCGERFS 38 40 136 161 239 PCGERQF 44 45 161 162 168 240 PCGESV 33 161 241 PCGESVD 50 138 141 144 PCGESVX 33 125 131 136 161 244 PCGETRF 38 40 160 161 247 PCGETRI 38 40 161 248 PCGETRS 38 40 161 248 PCGGQRF 45 161 249 PCGGRQF 46 161 251 PCHEEVX 35 121 125 138 140 163 287 PCHEGST 51 163 291 PCHEGVX 36 121 125 132 144 146 163 292 PCHETRD 47 48 162 163 295 PCHETRF 38 PCHETRS 38 PCPBSV 33 134 162 268 PCPBTRF 38 40 75 78 162 269 PCPBTRS 38 40 76 162 270 PCPOCON 38 40 134 135 162 271 PCPOEQU 39 40 162 166 272 PCPORFS 38 40 136 162 273 PCPOSV 33 134 162 274 PCPOSVX 33 125 136 162 275 PCPOTRF 38 40 162 163 168 278 PCPOTRI 38 40 162 278 PCPOTRS 38 40 162 279 PCPTSV 33 134 163 280 PCPTTRF 40 77 163 281 PCPTTRS 40 78 163 282 PCSTEIN 47 48 163 284 PCTRCON 38 40 135 138 163 296 PCTRMR 2 PCTRRFS 38 40 136 163 298 PCTRTRI 38 40 163 299 PCTRTRS 38 40 42 163 300 PCTZRZF 43 45 162 163 301 PCUNGLQ 42 45 161 253 PCUNGQL 45 161 254 PCUNGQR 41 43 45 161 255 PCUNGRQ 45 161 256 PCUNMBR 50 161 257 PCUNMHR 49 161 258 PCUNMLQ 42 45 161 260 PCUNMQL 45 161 261 PCUNMQR 41—43 45 162 262 PCUNMRQ 45 162 264 PCUNMRZ 44 45 162 265 PCUNMTR 47 48 162 266 PDDBSV 33 135 221 PDDBTRF 38 40 74 78 222 PDDBTRS 38 40 76 222 PDDTSV 33 135 223 PDDTTRF 38 40 77 78 225 PDDTTRS 38 40 78 226 PDGBSV 33 134 227 PDGBTRF 38 40 74 78 228 PDGBTRS 38 40 76 229 PDGEBRD 50 108 230 PDGECON 38 40 135 231 PDGEEQU 39 40 232 PDGEHRD 49 108 233 PDGELQF 42 45 50 234 PDGELS 34 104 136 138 235 PDGEMR 2 PDGEQLF 44 45 236 PDGEQPF 43 45 237 PDGEQRF 41 43 45 50 238 PDGERFS 38 40 136 239 PDGERQF 44 45 240 PDGESV 33 104 133 241 PDGESVD 35 50 109 125 138 141 144 242 PDGESVX 33 125 131 134 136 244 PDGETRF 38 40 247 PDGETRI 38 40 248 PDGETRS 38 40 248 PDGGQRF 45 249 PDGGRQF 46 251 PDLAHQR 49 109 252 253 PDLAMCH 121 122 166 PDORGLQ 42 45 253 PDORGQL 45 254 PDORGQR 41 43 45 255 PDORGRQ 45 256 PDORMBR 50 257 PDORMHR 49 258 PDORMLQ 42 45 260 PDORMQL 45 261 PDORMQR 41—43 45 262 PDORMRQ 45 264 PDORMRZ 44 45 265 PDORMTR 47 48 266 PDPBSV 33 134 268 PDPBTRF 38 40 75 78 269 PDPBTRS 38 40 76 270 PDPOCON 38 40 134 135 271 PDPOEQU 39 40 272 PDPORFS 38 40 136 273 PDPOSV 33 104 134 274 PDPOSVX 33 125 136 275 PDPOTRF 38 40 278 PDPOTRI 38 40 278 PDPOTRS 38 40 279 PDPTSV 33 134 280 PDPTTRF 40 77 281 PDPTTRS 40 78 282 PDSTEBZ 47 48 141 283 PDSTEIN 47 48 284 PDSYEV 35 108 125 138 139 286 PDSYEVX 35 108 115 121 125 138 140 287 PDSYGST 51 291 PDSYGVX 36 121 125 132 144 146 292 PDSYR 2 PDSYTRD 47 48 108 295 PDTRCON 38 40 135 138 296 PDTRMR 2 PDTRRFS 38 40 136 298 PDTRTRI 38 40 299 PDTRTRS 38 40 42 300 PDTZRZF 43 45 301
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