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- absolute error,
 ,
,  
- absolute gap,
 ,
,  
- accuracy,
 
- accuracy
- 
- high,
 , , , ,  
 
- Active Messages
- algorithmic
- 
- coherence
- reliability,
 , ,  
- repeatability
 
- algorithms, block-partitioned,
  
- alignment restrictions
- AM-II, see Active Messages
- angle between vectors and subspaces,
 , , , , , , , , , , , , , ,  
- arguments
- 
- BERR
- description conventions,
 , , , ,  
- descriptor,
 , , , , , , , ,  
- DIAG,
  
- dimensions
- FERR,
  
- global
- global column index,
 , , , ,  
- global input
- global output
- global row index,
 , , , ,  
- IA and JA,
  
- INFO,
 , ,  
- local
- local input
- local output
- LWORK
- options
- order of
- RCOND
- SIDE
- TRANS
- UPLO
- work space
 
- ARPACK
- array argument descriptions
- 
- block cyclic arrays
- block-column and block-row arrays
 
- array descriptor,
 , , , , , , , , , ,  
- array descriptor
- 
- block,
 , ,  
- block cyclic
- CTXT_
- definition of
- DLEN_
- DTYPE_,
  
- example
- LLD_
- M_ and N_,
  
- MB_ and NB_,
  
- out-of-core
- RSRC_ and CSRC_
 
- auxiliary routines,
  
- auxiliary routines, index of: see Appendix A
- avoiding poor performance
- backward error,
 , , , , , , , , , ,  
- backward stability,
 , ,  
- backward stability
- 
- componentwise
- normwise
 
- band matrix, distribution of
- bandwidth
- Berkeley NOW
- bidiagonal form,
 , ,  
- bidiagonal matrix, distribution of
- BLACS,
  
- BLACS
- 
- BLACS_ABORT,
  
- BLACS_BARRIER
- BLACS_EXIT
- BLACS_GRIDEXIT,
  
- BLACS_GRIDINFO
- BLACS_GRIDINIT
- BLACS_SET,
 , ,  
- C interface
- context
- context handle
- efficiency,
  
- Fortran 77 interface
- prebuilt libraries, availability of
- quick reference guide: see Appendix D
 
- BLAS,
 , , , ,  
- BLAS
- 
- Level 1
- Level 2
- Level 3
 
- block-column distribution,
 , ,  
- block-partitioned algorithms,
 , , , ,  
- block-row distribution,
 , ,  
- block cyclic distribution,
  
- blocking factor, see block size
- block size,
  
- block size
- 
- size of,
  
 
- bug reports
- bug reports
- 
- checklist
 
- bug
reports
- 
- mailing alias
 
- C 
- C 
- C 
- C 
- C 
- C 
- CAPSS
- checklist, high performance
- chordal distance
- cluster
- 
- eigenvalues
- singular values
 
- clusters of
workstations
- coefficient band matrix
- coefficient matrix,
 , , , , , ,  
- coefficient matrix
- 
- distribution of,
 , ,  
 
- coefficient tridiagonal matrix,
  
- coherence,
 , ,  
- column-major order
- column pivoting (QR)
- commercial use
- communication bandwidth
- communication deadlock
- communication latency
- communicator, MPI
- complete orthogonal factorization
- computational routines,
 , ,  
- Computational Routines, index of:  see Appendix A
- computers, see distributed memory computers
- condensed form, reduction to
- condition number,
 , , , , , , , , , , , , , , , , , ,  
- condition number
- 
- estimate,
  
 
- context, BLACS
- context handle
- coprocessor
- CoWs,
  
- CSRC_, see array descriptor
- CTXT_, see array descriptor
- data distribution
- data distribution
- 
- block
- block cyclic,
  
- block-column,
 , ,  
- block-row,
 , ,  
- general band matrix,
  
- general tridiagonal matrix,
  
- symmetric band matrix
- symmetric positive definite band matrix
- symmetric positive definite tridiagonal matrix
- symmetric tridiagonal matrix
 
- DDISNA,
  
- deadlock
- debugging
- 
- alignment restrictions
- errata.blacs,
  
- errata.scalapack,
  
- INFO > 0
- INFO < 0
- INFO < 0
- INFO > 0
- synchronization points
- TOOLS
- workspace requirements
 
- debugging hints
- 
- application
- installation
 
- debug level BLACS
- decomposition, see
data distribution
- DESC_, see array descriptor
- descriptor,
 , , , , , , , ,  
- descriptor, see array descriptor
- determining the size of local arrays,
 , ,  
- diagonally
dominant-like,
 , , , ,  
- distributed across process columns
- distributed across process rows
- distributed matrix
- distributed matrix, partitioning of
- distributed memory,
 , , , , , , , ,  
- distributed memory computers,
  
- distributed memory standards
- distributed vector
- distribution, see data distribution
- DLEN_, see array descriptor
- documentation
- documentation
- 
- installation guide,
  
 
- documentation, structure
- downloading instructions
- driver routine
- 
- generalized symmetric definite eigenvalue problem
- linear equations
- linear least squares
- SVD
 
- driver routine, symmetric eigenvalue
problem
- driver routines,
 , ,  
- driver routines
- 
- expert,
  
- simple,
  
 
- driver routines, index of: see 
Appendix A
- DSTEQR2
- DTYPE_, see array descriptor
- E(),
  
- effective rank
- efficiency
- efficiency
- 
- BLACS
- BLAS
- block-partitioned algorithms
 
- efficiency, transportable
- eigendecomposition
- 
- blocked form
- symmetric
 
- eigenvalue,
 , , , , , , , ,  
- eigenvalue
- 
- error bound,
 , , , , , , , ,  
- GSEP
- SEP
 
- eigenvalue problem
- 
- generalized symmetric
- generalized symmetric/Hermitian
 
- eigenvalue problem,symmetric/Hermitian
- eigenvalue problems
- 
- large scale
- large sparse
- nonsymmetric
 
- eigenvalue problems, symmetric/Hermitian
- eigenvector,
 , ,  
- eigenvector
- 
- error bound,
 , , , , , , , ,  
- GSEP,
  
- left
- right
- SEP
 
- elementary Householder matrix, see Householder matrix,
 , , , , , , , ,  
- elementary reflector, see Householder matrix,
 , , , , , ,  
- equilibration,
  
- errata
- 
- BLACS
- ScaLAPACK and PBLAS
 
- error
- 
- absolute,
 , ,  
- analysis
- backward,
 , , , , , , , , , ,  
- measurement of
- measurement of
- 
- matrix,
  
- scalar,
  
- subspace,
  
- vector,
  
 
- relative,
 , , , , , , , , , , , ,  
 
- error bounds
- 
- generalized symmetric definite eigenproblem,
  
- linear equations,
  
- linear least squares,
  
- singular value decomposition,
  
- symmetric eigenproblem,
  
 
- error handler, BLACS
- error handler, PBLAS,
  
- error handler, PXERBLA,
  
- example program
- 
- how to execute
- HPF
- output, using MPICH
- output, using PVM
- ScaLAPACK (PDGESV),
  
 
- expert driver
- expert driver, see driver routines, expert,
  
- External Data Representation (XDR)
- F 
- F 
- factorizations, see matrix factorizations
- failures
- failures
- 
- common causes
- error handling
- INFO
 
- FDDI
- Fiber Distributed Data
Interface (FDDI)
- floating-point arithmetic
- floating-point arithmetic
- 
 
- gradual underflow
- infinity
- NaN
- Not-a-Number
- overflow,
 , , , , , , , , , , , , , , , ,  
- relative machine precision,
  
- roundoff error
- subnormal numbers
- underflow,
 , , , ,  
 
- floating-point arithmetic, IEEE standard,
 , , , , , , , ,  
- flop counts, for ScaLAPACK drivers
- forward error
- forward stability,
  
- functionality
- gang scheduler,
- gap,
 , ,  
- generalized eigenproblem, symmetric definite
- generalized orthogonal factorization
- global
- global
- 
- matrix
- software components
- variables,
  
 
- global column
index (JA)
- global column index (JA),
  
- global input
- globally blocking receive
- global output
- global row index (IA),
 , ,  
- glossary
- GQR,
 , , , ,  
- granularity, of computation,
 , , , ,  
- grid, see process grid
- GRQ,
  
- GSEP
- guidelines, for high performance
- Hermitian eigenvalue problem, see eigenvalue problems
- Hessenberg form
- Hessenberg form
- 
- reduction to
- upper
 
- heterogeneity
- heterogeneous environment
- heterogeneous
network
- heterogeneous software issues
- 
- algorithmic integrity,
  
- machine parameters (PxLAMCH)
 
- hierarchical memory,
 , ,  
- homepage
- 
- BLACS
- MPI
- netlib
- PBLAS
- PVM
- ScaLAPACK,
  
 
- homogeneous network
- Householder matrix,
  
- Householder matrix
- 
- complex
 
- Householder transformation - blocked form
- Householder vector
- HPF
- 
- DISTRIBUTE,
 , , , , , , , , , , , , , , , ,  
- example program
- interface LA_GELS
- interface LA_GEMM
- interface LA_GESV
- interface LA_POSV
- interface to ScaLAPACK,
  
- LA_GELS
- LA_GEMM
- LA_GESV
- LA_POSV
- PROCESSORS
 
- ICTXT
- ICTXT, see BLACS
- ill-conditioned
- ill-posed
- incoherence
- infinity
- INFO
- input error
- installation
- installation
- 
- PxLAMCH
 
- insufficient workspace
- invariant subspaces
- 
- error bound
 
- inverse iteration
- inverting matrix, using factorization
- isoefficiency
- isogranularity
- iterative refinement
- LAPACK
- latency,
  
- layout, see data
distribution
- lcm(P ,P ,P ) )
- LDL factorization factorization
- leading dimension, see local array
- linear equations
- linear least
squares problem
- linear least squares
problem
- linear least squares problem,
 , ,  
- linear least squares problem
- 
- full rank
- overdetermined,
  
- rank-deficient,
 , ,  
- underdetermined
 
- linear systems, solution of,
  
- LLD_, see array descriptor
- LLS,
  
- load balance
- LOC () ()
- LOC () ()
- LOC () ()
- LOC () ()
- LOC () ()
- LOC () ()
- local
- local
- 
- software components
- variables,
  
 
- local array
- local array
- 
- determining the size of,
 , ,  
- local leading dimension
 
- local input
- locally blocking send
- local output
- LQ factorization
- LU factorization
- LU factorization
- 
- matrix types
 
- LWORK
- LWORK  WORK(1) WORK(1)
- LWORK query
- M_, see array descriptor
- machine precision,
  
- matrix factorizations
- 
- Cholesky,
  
- complete orthogonal
- generalized orthogonal
- generalized QR,
  
- generalized RQ
- LDL 
- LQ,
  
- LU
- orthogonal,
  
- QL
- QR,
 , ,  
- RQ
 
- matrix inversion,
  
- matrix of right-hand-side vectors
- matrix of solution vectors
- matrix partitioning
- matrix
sign function
- MB_, see array descriptor
- memory hierarchy,
 , ,  
- message-passing libraries
- 
- MPI,
  
- MPL,
  
- NX,
  
- PVM,
  
 
- message coprocessor
- message passing, see distributed memory
- MIMD,
  
- minimum norm
least squares solution
- minimum norm
solution
- minimum norm solution,
 , ,  
- MPI,
 , , , , , ,  
- MPI
- 
- communicator
- homepage
- reference implementation (MPICH)
 
- MPICH
- MPL,
  
- Multiple Instruction
Multiple Data (MIMD)
- Multiple Instruction Multiple Data (MIMD)
- MYCOL,
 , ,  
- MYROW,
 , ,  
- N_, see array descriptor
- naming scheme
- naming scheme
- 
- auxiliary
- driver and
computational
 
- NaN
- NB_, see array descriptor
- NBRHS
- netlib
- netlib
- 
- homepage
- mirror repositories
 
- networks of workstations
- nonrepeatability
- nonsymmetric eigenproblem
- norm
- 
- Frobenius norm
- matrix
- two norm
- vector
 
- Not-a-Number
- notation, table of
- NoWs,
  
- NPCOL, see P 
- NPROCS, see P
- NPROW, see P 
- NRHS
- numerical error, sources of
- numerical error, sources of
- 
- input error
- roundoff error,
  
 
- NX,
  
- optimal block
size, determination
of
- orthogonal (unitary) factorizations,
  
- orthogonal (unitary) transformation,
  
- orthogonal factorization, generalized
- orthogonal matrix,
  
- out-of-core linear solvers
- overdetermined system,
 , ,  
- overflow,
 , , , , , , , , , , , , , ,  
- P,
 , ,  
- P 
- P 
- P 
- P 
- P_ARPACK
- parallel efficiency,
  
- parallelizing BLAS-based programs: see Appendix B
- parallelizing LAPACK-based programs: see Appendix B
- ParPre
- partial pivoting
- partitioning unit, see block size,
  
- PBLAS,
  
- PBLAS
- 
- converting from the BLAS to: see Appendix B
- error handling
- PDGEMM
- PDGEMV
- PSGEMM
- PSGEMV
- quick reference guide: see Appendix D
 
- PCDBSV
- PCDBTRF,
 , ,  
- PCDBTRS,
  
- PCDTSV
- PCDTTRF,
 , ,  
- PCDTTRS,
  
- PCGBSV
- PCGBTRF,
 , ,  
- PCGBTRS,
  
- PCGEBRD
- PCGECON,
  
- PCGEEQU
- PCGEHRD
- PCGELQF,
  
- PCGELS,
 , ,  
- PCGEMR2D
- PCGEQLF
- PCGEQPF
- PCGEQRF,
 , ,  
- PCGERFS,
  
- PCGERQF
- PCGESVD,
 , , , ,  
- PCGESVX,
 , ,  
- PCGETRF
- PCGETRI
- PCGETRS
- PCGGQRF
- PCGGRQF
- PCHEEVX,
 , , , ,  
- PCHEGST
- PCHEGVX,
 , , , , , ,  
- PCHETRD
- PCHETRF
- PCHETRS
- PCPBSV
- PCPBTRF,
 , ,  
- PCPBTRS,
  
- PCPOCON,
 , ,  
- PCPOEQU
- PCPORFS,
  
- PCPOSV,
  
- PCPOSVX,
  
- PCPOTRF
- PCPOTRI
- PCPOTRS
- PCPTSV
- PCPTTRF
- PCPTTRS
- PCSTEIN,
  
- PCTRCON,
 , ,  
- PCTRMR2D
- PCTRRFS,
  
- PCTRTRI
- PCTRTRS,
 , ,  
- PCTZRZF
- PCUNGLQ
- PCUNGQR,
  
- PCUNMBR
- PCUNMHR
- PCUNMLQ
- PCUNMQR,
 , , , ,  
- PCUNMRZ
- PCUNMTR
- PDDBSV
- PDDBTRF,
 , ,  
- PDDBTRS,
  
- PDDTSV
- PDDTTRF,
 , ,  
- PDDTTRS,
  
- PDGBSV
- PDGBTRF,
 , ,  
- PDGBTRS,
  
- PDGEBRD,
  
- PDGECON,
  
- PDGEEQU
- PDGEHRD,
  
- PDGELQF,
  
- PDGELS,
 , , , ,  
- PDGEMR2D
- PDGEQLF
- PDGEQPF
- PDGEQRF,
 , ,  
- PDGERFS,
  
- PDGERQF
- PDGESV,
  
- PDGESVD,
 , , , , , , , , , ,  
- PDGESVX,
 , , , ,  
- PDGETRF
- PDGETRI
- PDGETRS
- PDGGQRF
- PDGGRQF
- PDLAHQR,
  
- PDLAMCH,
  
- PDORGLQ
- PDORGQR,
  
- PDORMBR,
  
- PDORMHR
- PDORMLQ,
  
- PDORMQR,
 , , , ,  
- PDORMRZ
- PDORMTR
- PDPBSV
- PDPBTRF,
 , ,  
- PDPBTRS,
  
- PDPOCON,
 , ,  
- PDPOEQU
- PDPORFS,
  
- PDPOSV,
 , ,  
- PDPOSVX,
  
- PDPOTRF
- PDPOTRI
- PDPOTRS
- PDPTSV
- PDPTTRF
- PDPTTRS
- PDSTEBZ,
  
- PDSTEIN,
  
- PDSYEV,
 , , , , , ,  
- PDSYEVX,
 , , , , , , , , , ,  
- PDSYGST
- PDSYGVX,
 , , , , , ,  
- PDSYR2K
- PDSYTRD,
  
- PDTRCON,
 , ,  
- PDTRMR2D
- PDTRRFS,
  
- PDTRTRI
- PDTRTRS,
 , ,  
- PDTZRZF
- peak performance
- performance,
 , ,  
- performance
- 
- diagnosing poor
- evaluation of
- improvement guidelines
- PDLAHQR
- PSGELS/PDGELS
- PSGEMM/PDGEMM
- PSGEMV/PDGEMV
- PSGESV/PDGESV
- PSGESVD/PDGESVD
- PSPOSV/PDPOSV
- PSSYEV/PDSYEV
- PSSYEVX/PDSYEVX
- recommendations
- tuning
 
- performance guidelines
- PETSc
- PIGEMR2D
- PITRMR2D
- pivoting
- 
- column (QR)
- partial
 
- poor performance
- PoPCs
- portability,
 , , , , , ,  
- prebuilt libraries
- 
- blacs
- scalapack
 
- process
- 
- column coordinate (MYCOL)
- row coordinate
(MYROW)
 
- process column
- process grid,
  
- process grid
- 
- initialization,
  
- mapping (column-major),
  
- mapping (row-major),
  
- mapping (user-defined),
  
- obtaining BLACS context
- P 
- P 
- shape,
  
 
- process mesh, see process grid
- processor
- process row
- prototype codes
- prototype
codes
- 
- HPF interface to ScaLAPACK
 
- prototype codes
- 
- matrix sign function,
  
- out-of-core linear solvers
- SuperLU
 
- PSDBSV
- PSDBTRF,
 , ,  
- PSDBTRS,
  
- PSDTSV
- PSDTTRF,
 , ,  
- PSDTTRS,
  
- PSGBSV
- PSGBTRF,
 , ,  
- PSGBTRS,
  
- PSGEBRD,
  
- PSGECON,
  
- PSGEEQU
- PSGEHRD,
  
- PSGELQF,
  
- PSGELS,
 , , , ,  
- PSGEMR2D
- PSGEQLF
- PSGEQPF
- PSGEQRF,
 , ,  
- PSGERFS,
  
- PSGERQF
- PSGESV,
 , ,  
- PSGESVD,
 , , , , , , , , , ,  
- PSGESVX,
 , , , , , , , ,  
- PSGETRF
- PSGETRI
- PSGETRS
- PSGGQRF
- PSGGRQF
- PSLAHQR,
  
- PSLAMCH,
  
- PSORGLQ
- PSORGQR,
  
- PSORMBR,
  
- PSORMHR
- PSORMLQ,
  
- PSORMQR,
 , , , ,  
- PSORMRZ
- PSORMTR
- PSPBSV
- PSPBTRF,
 , ,  
- PSPBTRS,
  
- PSPOCON,
 , ,  
- PSPOEQU
- PSPORFS,
  
- PSPOSV,
 , ,  
- PSPOSVX,
  
- PSPOTRF
- PSPOTRI
- PSPOTRS
- PSPTSV
- PSPTTRF
- PSPTTRS
- PSSTEBZ,
  
- PSSTEIN,
  
- PSSYEV,
 , , , , , ,  
- PSSYEVX,
 , , , , , , , , , ,  
- PSSYGST
- PSSYGVX,
 , , , , , ,  
- PSSYR2K
- PSSYTRD,
  
- PSTRCON,
 , ,  
- PSTRMR2D
- PSTRRFS,
  
- PSTRTRI
- PSTRTRS,
 , ,  
- PSTZRZF
- PVM,
 , , , ,  
- PVM
- 
- homepage
 
- PXERBLA,
 , ,  
- PZDBSV
- PZDBTRF,
 , ,  
- PZDBTRS,
  
- PZDTSV
- PZDTTRF,
 , ,  
- PZDTTRS,
  
- PZGBSV
- PZGBTRF,
 , ,  
- PZGBTRS,
  
- PZGEBRD
- PZGECON,
  
- PZGEEQU
- PZGEHRD
- PZGELQF,
  
- PZGELS,
 , ,  
- PZGEMR2D
- PZGEQLF
- PZGEQPF
- PZGEQRF,
 , ,  
- PZGERFS,
  
- PZGERQF
- PZGESVD,
 , , , ,  
- PZGESVX,
 , ,  
- PZGETRF
- PZGETRI
- PZGETRS
- PZGGQRF
- PZGGRQF
- PZHEEVX,
 , , , ,  
- PZHEGST
- PZHEGVX,
 , , , , , ,  
- PZHETRD
- PZHETRF
- PZHETRS
- PZPBSV
- PZPBTRF,
 , ,  
- PZPBTRS,
  
- PZPOCON,
 , ,  
- PZPOEQU
- PZPORFS,
  
- PZPOSV,
  
- PZPOSVX,
  
- PZPOTRF
- PZPOTRI
- PZPOTRS
- PZPTSV
- PZPTTRF
- PZPTTRS
- PZSTEIN,
  
- PZTRCON,
 , ,  
- PZTRMR2D
- PZTRRFS,
  
- PZTRTRI
- PZTRTRS,
 , ,  
- PZTZRZF
- PZUNGLQ
- PZUNGQR,
  
- PZUNMBR
- PZUNMHR
- PZUNMLQ
- PZUNMQR,
 , , , ,  
- PZUNMRZ
- PZUNMTR
- QL algorithm
- 
- implicit
 
- QL factorization
- QR algorithm
- 
- implicit
 
- QR factorization,
  
- QR factorization
- 
- blocked form
- generalized (GQR),
  
- with pivoting,
  
 
- query
- quick reference guides: see Appendix D
- rank
- rank-deficient, see linear least squares problem
- redistribution routines
- 
- PxGEMR2D
- PxTRMR2D
 
- reduction
- 
- bidiagonal
- standard form
- tridiagonal
- upper Hessenberg
 
- relative error,
 , , , , , , , , , , , ,  
- relative machine precision
- reliability, see test suites,
  
- repeatability,
  
- repeatability
- 
- enforcement of (BLACS_SET)
 
- replicated across process columns
- replicated across process rows
- replicated and distributed
- replicated vector,
  
- reporting bugs, see bug reports,
  
- right-hand-side matrix
- roundoff error,
  
- RQ factorization
- RQ factorization
- 
- generalized (GRQ),
  
 
- RSRC_, see array descriptor
- rule
of thumb
- scalability,
 , , , ,  
- ScaLAPACK
- 
- commercial use of
- converting from LAPACK to: see Appendix B
- prebuilt libraries, availability of
- quick reference guide: see Appendix D
 
- scaling
- Schur factorization
- Schur form
- Schur vectors
- scope,
  
- scope
- 
- groupings of processes
- in communication
- of a variable
- within a process grid
 
- scoped operation
- SDISNA,
  
- SEP,
  
- simple driver, see driver routines, simple,
  
- Single Program Multiple Data (SPMD)
- singular value
- singular value
decomposition (SVD)
- singular value decomposition (SVD)
- singular value
- 
- error bound,
  
 
- singular vector
- 
- error bound,
  
 
- singular vectors
- 
- left,
  
- right,
  
 
- software
hierarchy
- software standards
- software standards
- 
- distributed memory
 
- solution matrix
- spectral factorization
- SPMD
- SSTEQR2
- stability,
  
- stability
- 
- backward,
 , , , , , ,  
- forward
 
- standard form
- storage scheme
- 
- general tridiagonal
- Hermitian,
  
- orthogonal or unitary matrices
- symmetric
- symmetric tridiagonal
- triangular
 
- submatrix access
- subspaces
- 
- angle between
 
- subspaces, angle between,
 , , , , , , , , , , , ,  
- suggestions for reading
- SuperLU, see prototype codes
- support
- SVD
- Sylvester
equation
- symmetric eigenproblem
- T(),
  
- T () ()
- t 
- t 
- t 
- t 
- t 
- T 
- t 
- t , see latency , see latency
- t 
- t 
- t 
- terminology
- test suites,
 , , , , , , , , , , , , , , , ,  
- thread of execution, see process
- throughput, see bandwidth
- TOOLS
- 
- DESCINIT
- NUMROC
- PxLAPRNT
- SL_INIT
 
- transportable efficiency
- tridiagonal form,
 , , , , , , , ,  
- tridiagonal matrix, distribution of
- troubleshooting
- tuning
- underdetermined system,
 , ,  
- underflow,
 , , , ,  
- unitary matrix,
  
- upper Hessenberg form
- utility routines
- workspace query
- World Wide Web
- wrong results
- WWW
- XDR
 
Susan Blackford 
Tue May 13 09:21:01 EDT 1997