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## Index

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)
LDL 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)
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
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