Parallel Library Contents

Chapter A00: Library Identification

A00AAFP

Prints details of the NAG Parallel Library implementation

Chapter D01: Quadrature

D01ATFP

1-d quadrature, adaptive, finite interval, allowing for badly behaved integrands

D01AUFP

1-d quadrature, adaptive, finite interval, suitable for oscillating functions

D01AXFP

1-d quadrature, adaptive, finite interval, weight functions cos(omega x) or sin(omega x)

D01DAFP

2-d quadrature, finite region

D01FAFP

Multi-dimensional quadrature, hyper-rectangle, adaptive

D01GCFP

Multi-dimensional quadrature, general product region, number-theoretic method

Chapter E04: Minimising or Maximising a Function

E04FDFP

Unconstrained minimum of a sum of squares, Gauss--Newton algorithm using function values only (easy-to-use)

E04JBFP

Minimum of a general nonlinear function with unconstrained, Gauss--Newton algorithm using function values only (easy-to-use)

Chapter F01: Matrix Operations and Distribution

F01YAFP

Cyclic row block distribution routine for real sparse matrices stored in coordinate storage format

F01YEFP

Distribution routine for real dense vectors distributed conformally to sparse matrices

F01ZPFP

Gathering of a block distributed real vector used for F07 and F08 ScaLAPACK routines

F01ZQFP

Real matrix generation and distribution in cyclic 2-d block fashion, used for F07 and F08 ScaLAPACK routines

F01ZRFP

Real matrix generation and distribution in block column fashion, used for F02 routines

F01ZSFP

Real matrix generation and distribution in cyclic 2-d block fashion, used for F04 (Black Box) routines

F01ZVFP

Complex matrix generation and distribution in cyclic 2-d block fashion, used for F07 and F08 ScaLAPACK routines

F01ZWFP

Complex matrix generation and distribution in block column fashion, used for F02 routines

F01ZXFP

Complex matrix generation and distribution in cyclic 2-d block fashion, used for F04 (Black Box) routines

Chapter F02: Eigenvalues and Eigenvectors

F02FQFP

Eigenvalues and eigenvectors of a real symmetric matrix, one-sided Jacobi method

F02FRFP

Eigenvalues and eigenvectors of a complex Hermitian matrix, one-sided Jacobi method

F02WQFP

Singular Value Decomposition (SVD) of a real matrix, one-sided Jacobi method

F02WRFP

Singular Value Decomposition (SVD) of a complex matrix, one-sided Jacobi method

Chapter F04: Simultaneous Linear Equations

F04EBFP

Solution of real simultaneous linear equations with multiple right-hand sides (Black Box)

F04ECFP

Solution of complex simultaneous linear equations with multiple right-hand sides (Black Box)

F04FBFP

Solution of real symmetric positive-definite simultaneous linear equations with multiple right-hand sides (Black Box)

F04FCFP

Solution of complex Hermitian positive-definite simultaneous linear equations with multiple right-hand sides (Black Box)

F04GBFP

Solution of a real linear least-squares problem multiple right-hand sides (Black Box)

Chapter F07: Linear Equations (ScaLAPACK)

F07ADFP

LU factorization of a real general matrix (PDGETRF)

F07AEFP

Solution of a real system of linear equations, right-hand sides, matrix already factorized by F07ADFP (PDGETRF)

F07ARFP

LU factorization of a complex general matrix (PZGETRF)

F07ASFP

Solution of a complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARFP (PZGETRF)

F07FDFP

Cholesky factorization of a real symmetric positive- matrix (PDPOTRF)

F07FEFP

Solution of a real symmetric positive-definite system of equations, multiple right-hand sides, matrix already factorized by F07FDFP (PDPOTRF)

F07FRFP

Cholesky factorization of a complex Hermitian positive-definite matrix (PZPOTRF)

F07FSFP

Solution of a complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRFP (PZPOTRF)

F07TGFP

Estimate the condition number of a real triangular matrix (PDTRCON)

Chapter F08: Least-squares Problems (ScaLAPACK)

F08AEFP

QR factorization of a real general rectangular matrix (PDGEQRF)

F08AFFP

Form all or part of an orthogonal Q from QR factorization determined by F08AEFP (PDGEQRF)

F08AGFP

Apply the orthogonal transformation determined by F08AEFP (PDORMQR)

F08ASFP

QR factorization of a complex general rectangular matrix (PZGEQRF)

F08ATFP

Form all or part of a unitary Q from QR factorization determined by F08ASFP (PZGEQRF)

F08AUFP

Apply the unitary transformation determined by F08ASFP (PZUNMQR)

F08FEFP

Orthogonal reduction of a real symmetric matrix to form (PDSYTRD)

F08JJFP

All or selected eigenvalues of a real symmetric tridiagonal matrix by bisection (PDSTEBZ)

Chapter F11: Sparse Linear Algebra

F11BAFP

Set-up for F11BBFP and F11BCFP, iterative solution of real (unsymmetric) system of simultaneous linear equations, Restarted Generalised Minimal Residual method (RGMRES)

F11BBFP

Main solver, iterative solution of a general (unsymmetric) system of simultaneous linear equations, Restarted Generalised Minimal Residual method (RGMRES)

F11BCFP

Information about the computations carried out by F11BBFP, iterative solution of a general (unsymmetric) system of simultaneous linear equations, Restarted Generalised Minimal Residual method (RGMRES)

F11DAFP

Incomplete LU factorization of the local diagonal blocks of a real sparse matrix, represented in coordinate storage format, distributed on a logical grid of processors in cyclic row block form

F11DBFP

Solution of real system of linear equations, involving a real block diagonal sparse matrix, represented in coordinate storage format, distributed on a logical grid of processors in cyclic row block form

F11DCFP

Black-box routine for sparse system of linear equations

F11GAFP

Set-up for F11GBFP and F11GCFP, iterative solution of a symmetric system of simultaneous linear equations, Conjugate Gradient method or a Lanczos method based on SYMMLQ

F11GBFP

Main solver, iterative solution of a symmetric system of simultaneous linear equations, Conjugate Gradient method or a Lanczos method based on SYMMLQ

F11GCFP

Information about the computations carried out by F11GBFP, iterative solution of a symmetric system of simultaneous linear equations, Conjugate Gradient method or a Lanczos method based on SYMMLQ

F11XAFP

Set-up for F11XBFP, matrix-vector or transposed matrix-vector product involving a real sparse matrix, represented in coordinate storage format, distributed on a logical grid of processors in cyclic row block form

F11XBFP

Computes a matrix-vector or transposed matrix-vector product involving a real sparse matrix, represented in coordinate storage format, distributed on a logical grid of processors in cyclic row block form

F11ZAFP

General set-up routine for real sparse matrices, represented in coordinate storage format, distributed on a logical grid of processors in cyclic row block form

Chapter G05: Random Number Generators

G05AAFP

Pseudo-random real numbers, uniform distribution over (0,1), Wichmann--Hill generator

G05ABFP

Select a random number generator and initialise seeds to give repeatable sequence

Chapter X04: Input/Output Utilities

X04AAF

Returns or sets a unit number for error message

X04ABF

Returns or sets a unit number for advisory messages

X04BCFP

Reads a real general matrix from an external file (stored in its natural, non-distributed form) into an array in a cyclic 2-d block distribution on 2-d logical processor grid, used for the F07 and F08 ScaLAPACK routines

X04BDFP

Outputs a real general matrix stored in a cyclic 2-d block distribution on a 2-d logical processor grid to an external file (in its natural, non-distributed form), used with the F07 and F08 ScaLAPACK routines

X04BFFP

Outputs a set of real general matrices distributed on a 2-d logical processor grid, used with the F02 routines

X04BGFP

Reads a general real matrix from an external file (stored in its natural, non-distributed form) into an array in a cyclic 2-d block distribution on a 2-d logical processor grid, used for the F04 (Black Box) routines

X04BHFP

Outputs a general real matrix stored in a cyclic 2-d block distribution on a 2-d logical processor grid to an external file (in its natural, non-distributed form), used with the F04 (Black Box) routines

X04BRFP

Reads a complex general matrix from an external file (stored in its natural, non-distributed form) into an array in a cyclic 2-d block distribution on 2-d logical processor grid, used for the F07 and F08 ScaLAPACK routines

X04BSFP

Outputs a complex general matrix stored in a cyclic 2-d block distribution on a 2-d logical processor grid to an external file (in its natural, non-distributed form), used with the F07 and F08 ScaLAPACK routines

X04BUFP

Outputs a set of complex general matrices distributed on a 2-d logical processor grid, used with the F02 routines

X04BVFP

Reads a general complex matrix from an external file (stored in its natural, non-distributed form) into an array in a cyclic 2-d block distribution on a 2-d logical processor grid, used for the F04 (Black Box) routines

X04BWFP

Outputs a general complex matrix stored in a cyclic 2-d block distribution on a 2-d logical processor grid to an external file (in its natural, non-distributed form), used with the F04 (Black Box) routines

X04YAFP

Outputs a real dense vector, distributed conformally to a sparse matrix on a logical grid of processors, to an external file

Chapter Z01: Library Utilities

Z01AAFP

Defines a 2-d logical processor grid (Library Grid) and returns the BLACS context

Z01ABFP

Undefines the logical processor grid and invalidates the BLACS context initialised by Z01AAFP

Z01ACFP

Root processor identifier

Z01ADFP

Used in creating processes outside the default library mechanism, allows multigridding, used in more advanced applications (PVM-based version only)

Z01AEFP

Used in creating processes outside the default library mechanism, allows multigridding, used in more advanced applications (MPI-based version only)

Z01BAFP

Row and column indices of the root processor within the logical grid

Z01BBFP

Identifies logical processors in context in the 2-d grid declared by Z01AAFP

Z01BDFP

Information about PVM tasks (PVM-based version only)

Z01BEFP

Topology to be used by BLACS for broadcasting and global operations

Z01BFFP

Enables debugging (PVM-based version only)

Z01BGFP

Information about MPI tasks (MPI-based version only)

Z01CAFP

Number of rows or columns of a matrix held locally on a given processor when the matrix is distributed in the cyclic 2-d block fashion (NUMROC)

Z01CBFP

Length of the workspace for F08AEFP and F08AFFP

Z01CCFP

Length of the workspace for F08AGFP

Z01CDFP

Process coordinate which possesses the entry of a distributed matrix specified by a global index (INDXG2P)

Z01CEFP

Length of the workspace for F08FEFP (PDSYTRD) Fundamental Support Routines

Chapter X01: Mathematical Constants

X01AAF

pi

X01ABF

Euler's constant, gamma

Chapter X02: Machine Constants

X02AHF

Largest permissible argument for sin and cos

X02AJF

Machine precision

X02AKF

Smallest positive model number

X02ALF

Largest positive model number

X02AMF

Safe range of real floating-point arithmetic

X02ANF

Safe range of complex floating-point arithmetic

X02BBF

Largest representable integer

X02BEF

Maximum number of decimal digits that can be represented

X02BHF

Parameter of floating-point arithmetic model, b

X02BJF

Parameter of floating-point arithmetic model, p

X02BKF

Parameter of floating-point arithmetic model, e_{min}

X02BLF

Parameter of floating-point arithmetic model, e_{max}

X02DJF

Parameter of floating-point arithmetic model, ROUNDS