Fully Documented Routines

Fundamental Support Routines

Chapter A00: Library Identification

• A00AAFP Prints details of the PINEAPL Library implementation

Chapter C06: Summation of Series

• C06GXFP Factorizes an interger n as n = n1 x n2. This routine may be used in conjuction with C06MCFP .
• C06MCFP Computes the direct or the inverse 1-d FFT of a complex sequence
• C06FUFP Computes the direct or the inverse 2-d FFT of a complex sequence
• C06MXFP Computes the direct or the inverse 3-d FFT of a complex sequence

Chapter D03: Partial Differential Equations

• D03EFFP Computes solution of 2-d Helmholtz equation in Cartesian coordinates
• D03FBFP Computes solution of 3-d Helmholtz equation

Chapter E04: Minimising or Maximising a Function

• E04JAFP Minimizes a general nonlinear objective function (subject to simple bound) using the quasi-Newton algorithm
• E04JCF Minimizes a general function (subject to linear constraints) using a multidirectional search method of Dennis and Torczon - sequential version
• E04JCFP Minimizes a general function (subject to linear constraints) using a multidirectional search method of Dennis and Torczon - parallel version
• E04UCFP Minimizes a general nonlinear objective function (subject to general constraints) using a sequential quadratic programming algorithm
• E04UDFP Manages options-files for E04UCFP
• E04UEFP Manages options-files for E04UCFP

Chapter F01: Matrix Operations and Distribution

• F01CPFP finds the element-wise absolute maximum or minimum of a group of integer matrices over the Library Grid.
• F01CRFP Computes the transpose of a matrix which is distributed in row-block form
• F01XAFP Distributes a real square sparse matrix, represented in coordinate storage format, in cyclic row block form
• F01XBFP Distributes a real square sparse matrix, represented in coordinate storage format, in general row block form
• F01XEFP Distributes a real dense vector conformally to a sparse matrix
• F01XFFP Gathers a real dense vector, distributed conformally to a sparse matrix, to one or more processors
• F01XGFP Distributes an integer dense vector conformally to sparse matrix
• F01XHFP Gathers an integer dense vector, distributed conformally to a sparse matrix, to one or more processors
• F01XPFP Distributes a complex square sparse matrix, represented in coordinate storage format, in cyclic row block form
• F01XQFP Distributes a complex square sparse matrix, represented in coordinate storage format, in general row block form
• F01XTFP Distributes a complex dense vector conformally to a sparse matrix
• F01XUFP Gathers a complex dense vector, distributed conformally to a sparse matrix, to one or more processors
• F01YAFP Generates a real square sparse matrix, represented in coordinate storage format, in-place according to a cyclic row block distribution
• F01YBFP Generates a real square sparse matrix, represented in coordinate storage format, in-place according to a cyclic row block distribution, optionally generating the numerical values of non-zero elements only
• F01YCFP Generates a real square sparse matrix, represented in coordinate storage format, in-place according to a general row block distribution, optionally generating the numerical values of non-zero elements only
• F01YEFP Generates a real dense vector in-place such that its elements are distributed conformally to a sparse matrix
• F01YPFP Generates a complex square sparse matrix, represented in coordinate storage format, in-place according to a cyclic row block distribution
• F01YQFP Generates a complex square sparse matrix, represented in coordinate storage format, in-place according to a cyclic row block distribution, optionally generating the numerical values of non-zero elements only
• F01YRFP Generates a complex square sparse matrix, represented in coordinate storage format, in-place according to a general row block distribution, optionally generating the numerical values of non-zero elements only
• F01YTFP Generates a complex dense vector in-place such that its elements are distributed conformally to a sparse matrix
• F01YXFP Generates/distributes a real banded symmetric matrix in column block fashion
• F01YYFP Generates/distributes a real matrix using the Row Block Distribution, used with F07JEFP or F07HEFP
• F01ZFFP Performs a 3-d ik-global transpose of 3-d (l x m x n) real array of data A(i,j,k) distributed in i-block form
• F01ZHFP Generates/distribute an l by m by n real array on a grid of logical processors in i-block form
• F01ZKFP Generates a distributed l by m by n real matrix on a grid of logical processors in jk-block form
• F01ZMFP Generates/distruntes a matrix in row block form
• F01ZZFP Generates/distributes a real vector - used with F07JDFP

Chapter F04: Simultaneous Linear Equations

• F04HBFP Solves a real symmetric positive-definite banded simultaneous linear equations with multiple right-hand sides (Black Box)
• F04JBFP Solves a real symmetric positive-definite tridiagonal simultaneous linear equations with multiple right-hand sides (Black Box)

Chapter F07: Linear Equations (ScaLAPACK)

• F07HDFP Performs the Cholesky factorization of a real banded symmetric positive-definite matrix (PDPBTRF)
• F07HEFP Solves a real banded symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07HDFP (PDPBTRF)
• F07JDFP Performs the Cholesky factorization of a real tridiagonal symmetric positive-definite matrix (PDPTTRF)
• F07JEFP Solves a real tridiagonal symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already

factorized by F07JDFP (PDPTTRF)

Chapter F11: Sparse Linear Algebra

• Chapter Introduction
• F11BAFP Sets up parameters for F11BBFP and F11BCFP
• F11BBFP Solves a real general (unsymmetric) system of simultaneous linear equations using a Restarted Generalised Minimal RESidual (RGMRES), a Conjugate Gradient Squared (CGS), a BI-Conjugate Gradient STABilized (BI-CGSTAB), or a Transpose-Free Quasi-Minimal Residual (TFQMR) iterative method
• F11BCFP Provides information about the computations carried out by F11BBFP
• F11BPFP Sets up parameters for F11BQFP and F11BRFP
• F11BQFP Solves a complex general (non-Hermitian) system of simultaneous linear equations using a Restarted Generalised Minimal RESidual (RGMRES), a Conjugate Gradient Squared (CGS), a BI-Conjugate Gradient STABilized (BI-CGSTAB), or a Transpose-Free Quasi-Minimal Residual (TFQMR) iterative method
• F11BRFP Provides information about the computations carried out by F11BQFP
• F11DAFP Computes incomplete LU factorizations of overlapping or non-overlapping diagonal blocks of a real square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11DBFP Implements an overlapping or non-overlapping additive Schwarz preconditioner based on the incomplete LU factorizations computed by F11DAFP
• F11DCFP Solves a real general (unsymmetric) system of simultaneous linear equations using a Restarted Generalised Minimal RESidual (RGMRES), a Conjugate Gradient Squared (CGS), a BI-Conjugate Gradient STABilized (BI-CGSTAB), or a Transpose-Free Quasi-Minimal Residual (TFQMR) iterative method in conjunction with an overlapping or non-overlapping additive Schwarz preconditioner (Black Box)
• F11DDFP Performs a multi-color SOR or SSOR iterative method for a real square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11DEFP Solves a real general (unsymmetric) system of simultaneous linear equations using a Restarted Generalised Minimal RESidual (RGMRES), a Conjugate Gradient Squared (CGS), a BI-Conjugate Gradient STABilized (BI-CGSTAB), or a Transpose-Free Quasi-Minimal Residual (TFQMR) iterative method in conjunction with a Jacobi, SOR or SSOR preconditioner (Black Box)
• F11DFFP Performs a Jacobi iterative method for a real square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11DPFP Computes incomplete LU factorizations of overlapping or non-overlapping diagonal blocks of a complex square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11DQFP Implements an overlapping or non-overlapping additive Schwarz preconditioner based on the incomplete LU factorizations computed by F11DPFP
• F11DRFP Solves a complex general (non-Hermitian) system of simultaneous linear equations using a Restarted Generalised Minimal RESidual (RGMRES), a Conjugate Gradient Squared (CGS), a BI-Conjugate Gradient STABilized (BI-CGSTAB), or a Transpose-Free Quasi-Minimal Residual (TFQMR) iterative method in conjunction with an overlapping or non-overlapping additive Schwarz preconditioner (Black Box)
• F11DSFP Performs a multi-color SOR or SSOR iterative method for a complex square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11DTFP Solves a complex general (non-Hermitian) system of simultaneous linear equations using a Restarted Generalised Minimal RESidual (RGMRES), a Conjugate Gradient Squared (CGS), a BI-Conjugate Gradient STABilized (BI-CGSTAB), or a Transpose-Free Quasi-Minimal Residual (TFQMR) iterative method in conjunction with a Jacobi, SOR or SSOR preconditioner (Black Box)
• F11DUFP Performs a Jacobi iterative method for a complex square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11GAFP Sets up parameters for F11GBFP and F11GCFP
• F11GBFP Solves a real symmetric system of simultaneous linear equations using a Conjugate Gradient (CG) or a Lanczos-based (SYMMLQ) iterative method
• F11GCFP Provides information about the computations carried out by F11GBFP
• F11JCFP Solves a real symmetric system of simultaneous linear equations using a Conjugate Gradient (CG) or a Lanczos-based (SYMMLQ) iterative method in conjunction with an overlapping or non-overlapping additive Schwarz preconditioner (Black Box)
• F11JEFP Solves a real symmetric system of simultaneous linear equations using a Conjugate Gradient (CG) or a Lanczos-based (SYMMLQ) iterative method in conjunction with a Jacobi or SSOR preconditioner (Black Box)
• F11XBFP Computes a matrix-vector or transposed matrix-vector product involving a real square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11XCFP Exchanges the interface part of a real dense vector, distributed conformally to a sparse matrix, between processors
• F11XQFP Computes a matrix-vector, transposed matrix-vector or conjugate transposed matrix-vector product involving a complex square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11XRFP Exchanges the interface part of a complex dense vector, distributed conformally to a sparse matrix, between processors
• F11YAFP Permutes the non-zero elements of a real square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form, into the order previously determined by F11ZBFP or F11ZCFP
• F11YBFP Permutes the local part of a real dense vector, distributed conformally to a sparse matrix, from distribution-based order into matrix-based order
• F11YCFP Permutes the local part of a real dense vector, distributed conformally to a sparse matrix, from matrix-based order into distribution-based order
• F11YPFP Permutes the non-zero elements of a complex square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form, into the order previously determined by F11ZQFP or F11ZRFP
• F11YQFP Permutes the local part of a complex dense vector, distributed conformally to a sparse matrix, from distribution-based order into matrix-based order
• F11YRFP Permutes the local part of a complex dense vector, distributed conformally to a sparse matrix, from matrix-based order into distribution-based order
• F11ZAF Reorders the non-zero elements of a real square matrix, represented in coordinate storage format, by increasing row index and by increasing column index within each row
• F11ZBFP Pre-processes a real square sparse matrix, represented in coordinate storage format, distributed in cyclic row block form, such that subsequent matrix operations can be performed efficiently
• F11ZCFP Pre-processes a real square sparse matrix, represented in coordinate storage format, distributed in general row block form, such that subsequent matrix operations can be performed efficiently
• F11ZFFP Generates overlap areas of specified size for the local diagonal blocks of a real square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11ZGFP Generates a multi-color ordering of a real square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11ZQFP Pre-processes a complex square sparse matrix, represented in coordinate storage format, distributed in cyclic row block form, such that subsequent matrix operations can be performed efficiently
• F11ZRFP Pre-processes a complex square sparse matrix, represented in coordinate storage format, distributed in general row block form, such that subsequent matrix operations can be performed efficiently
• F11ZUFP Generates overlap areas of specified size for the local diagonal blocks of a complex square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11ZVFP Generates a multi-color ordering of a complex square sparse matrix, represented in coordinate storage format, distributed in cyclic or general row block form
• F11ZZFP Release of memory allocated internally for auxiliary information

Chapter G05: Random Number Generators

• Chapter Introduction
• G05AAFP Genrates a pseudo-random real numbers from a uniform distribution over (0,1), Wichmann--Hill generator
• G05ABFP Selects a random number generator and initialise seeds to give repeatable sequence

Chapter X04: Input/Output Utilities

• X04BFFP Outputs a set of real general matrices distributed on a 2-d logical processor grid, used with the F02 routines
• X04XBFP Outputs a square matrix distributed in the row block fashion
• X04YAFP Outputs a real dense vector distributed conformally to a sparse matrix
• X04YPFP Outputs a complex dense vector distributed conformally to a sparse matrix

Chapter Y01: Load Distribution and Balancing

• Chapter Introduction
• Y01ABF Partitions a weighted or unweighted symmetric graph into equally sized subgraphs such that the edge-cut between different subgraphs is small
• Y01BAFP Transforms a partitioning vector into a general row block distribution

Chapter Z01: Library Utilities

• Chapter Introduction
• 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 Identifies the root processor
• Z01ADFP May be used in creating processes outside the default library mechanism, allows multigridding, used in more advanced applications (PVM-based version only)
• Z01AEFP May be used in creating processes outside the default library mechanism, allows multigridding, used in more advanced applications (MPI-based version only)
• Z01BAFP Returns the 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 Returns information about PVM tasks (PVM-based version only)
• Z01BEFP Returns the topology to be used by BLACS for broadcasting and global operations
• Z01BFFP Enables debugging (PVM-based version only)
• Z01BGFP Returns information about MPI tasks (MPI-based version only)
• Z01CAFP Returns the 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)
• Z01CDFP Returns the process coordinate which possesses the entry of a distributed matrix specified by a global index (INDXG2P)
• Z01CFFP Computes the number of rows of a row block distributed matrix
• Z02EAFP Modifies the error checking level used by PINEAPL Library routines

Chapter X01: Mathematical Constants

• Chapter Introduction
• X01AAF pi
• X01ABF Euler's constant, gamma

Chapter X02: Machine Constants

• Chapter Introduction
• 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