Guide and Reference

Parallel Engineering and Scientific
Subroutine Library for AIX
Guide and Reference

SA22-7273-00

5765-C41

Notes!

Special notices are included in "Special Notices".

For a summary of changes for Parallel ESSL Version 2, see page "What's New For Parallel ESSL".

First Edition (December 1997)

This edition applies to Version 2 of the IBM* Parallel Engineering and Scientific Subroutine Library (Parallel ESSL) for Advanced Interactive Executive (AIX*) licensed program, program number 5765-C41.

Changes are periodically made to the information herein.

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Table of Contents

Looking for a Subroutine?

Special Notices

Programming Interfaces

About This Book

How to Use This Book

How to Find a Subroutine Description

Where to Find Related Publications

How to Look Up a Bibliography Reference

How to Interpret Product Names Used in This Document

Abbreviated Names

Scalar Data Notations

Special Characters, Symbols, Expressions, and Abbreviations

Interpreting the Subroutine Descriptions

Notes and Coding Rules

Error Conditions

What's New For Parallel ESSL

What's New for Parallel ESSL Version 2.1

Changes for Parallel ESSL Release 2.1 for AIX

Changes for Parallel ESSL Release 2.0 for AIX

Changes for Parallel ESSL Release 1 for AIX

In Brief--What's Provided in Parallel ESSL

Guide Information

Overview, Requirements, and List of Subroutines

Overview of Parallel ESSL

How Parallel ESSL Works under the Parallel Environment (PE)

Accuracy of the Computations

The Fortran Language Interface to the Message Passing Subroutines

Hardware and Software Products That Can Be Used with Parallel ESSL

Parallel ESSL--Hardware

Parallel ESSL--System Software

Parallel ESSL--Software Products

Installation and Customization

Software Products for Displaying Parallel ESSL Online Information

Parallel ESSL--PostScript File

ESSL Internet Resources

Obtaining Documentation

Accessing ESSL's Home Pages

Getting on the ESSL Mailing List

BLACS--Usage in Parallel ESSL for Communication

List of Parallel ESSL Subroutines (Message Passing and HPF)

Linear Algebraic Equations

Eigensystem Analysis and Singular Value Analysis

Fourier Transforms

Random Number Generation

Distributing Your Data

About Global Data Structures

About Process Grids

What to Do in Your Program

Block, Cyclic, and Block-Cyclic Data Distributions

Specifying and Distributing Data in a Message Passing Program

Specifying Block-Cyclically-Distributed Vectors and Matrices

Specifying Block-Cyclically-Distributed Matrices for the Banded Linear Algebraic Equations

Distributing Data Structures

Specifying Sparse Matrices for the Fortran 90 and Fortran 77 Sparse Linear Algebraic Equations

Specifying Sequences for the Fourier Transforms

Distributing Data in an HPF Program

Sequences (Fourier Transform)

Coding and Running Your Program

Coding Tips for Optimizing Parallel Performance

Avoiding Conflicts with Parallel ESSL and ESSL for AIX Routine Names

Coding Your Message Passing Program

Initializing the BLACS

Using Extrinsic Procedures--The Fortran 90 Sparse Linear Algebraic Equation Subroutines

Setting Up the Parallel ESSL Header File for C and C++

Application Program Outline

Application Program Outline for the Fortran 90 Sparse Linear Algebraic Equations and Their Utilities

Application Program Outline for the Fortran 77 Sparse Linear Algebraic Equations and Their Utilities

Running Your Message Passing Program

Dynamic Linking Versus Static Linking

Fortran Program Procedures

C Program Procedures

C++ Program Procedures

Coding Your HPF Program

Coding the Calling Sequences

Coding the Directives for Distributing Your Data

Sample HPF Programs

Running Your HPF Program

Dynamic Linking Versus Static Linking

HPF Program Procedures

Migrating Your Program

Migrating to Parallel ESSL Version 2.1

Array Descriptor Considerations

Type-1 Array Descriptor

Type-501 and -502 Array Descriptors

Future Migration Considerations for Array Descriptors

Migrating from ScaLAPACK 1.5 to Parallel ESSL Version 2.1

Using Error Handling

Where to Find More Information About Errors

Getting Help from IBM Support

National Language Support

PESSL_ERROR_SYNC Environment Variable

Dealing with Errors

Program Exceptions

Input-Argument Errors

Computational Errors

Resource Errors

Communication Errors

Informational and Attention Messages

Miscellaneous Errors

ESSL for AIX Error Messages

MPI Error Messages

Message Conventions

Input-Argument Error Messages (001-299)

Computational Error Messages (300-399)

Resource Error Messages (400-499)

Communication Error Messages (500-599)

Informational and Attention Messages (600-699)

Miscellaneous Error Messages (700-799)

Input-Argument Error Messages (800-999)

Reference Information (Message Passing)

Level 2 PBLAS (Message Passing)

Overview of the Level 2 PBLAS Subroutines

Level 2 PBLAS Subroutines

PDGEMV--Matrix-Vector Product for a General Matrix or Its Transpose

PDSYMV--Matrix-Vector Product for a Real Symmetric Matrix

PDGER--Rank-One Update of a General Matrix

PDSYR--Rank-One Update of a Real Symmetric Matrix

PDSYR2--Rank-Two Update of a Real Symmetric Matrix

PDTRMV--Matrix-Vector Product for a Triangular Matrix or Its Transpose

PDTRSV--Solution of Triangular System of Equations with a Single Right-Hand Side

Level 3 PBLAS (Message Passing)

Overview of the Level 3 PBLAS Subroutines

Level 3 PBLAS Subroutines

PDGEMM and PZGEMM--Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose

PDSYMM--Matrix-Matrix Product Where One Matrix is Real Symmetric

PDTRMM--Triangular Matrix-Matrix Product

PDTRSM--Solution of Triangular System of Equations with Multiple Right-Hand Sides

PDSYRK--Rank-K Update of a Real Symmetric Matrix

PDSYR2K--Rank-2K Update of a Real Symmetric Matrix

PDTRAN--Matrix Transpose for a General Matrix

Linear Algebraic Equations (Message Passing)

Overview of the Dense Linear Algebraic Equation Subroutines

Overview of the Banded Linear Algebraic Equation Subroutines

Overview of the Fortran 90 Sparse Linear Algebraic Equation Subroutines

Overview of the Fortran 77 Sparse Linear Algebraic Equation Subroutines

Dense Linear Algebraic Equation Subroutines

PDGETRF and PZGETRF--General Matrix Factorization

PDGETRS and PZGETRS--General Matrix Solve

PDPOTRF and PZPOTRF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization

PDPOTRS and PZPOTRS--Positive Definite Real Symmetric or Complex Hermitian Matrix Solve

Banded Linear Algebraic Equation Subroutines

PDPBSV--Positive Definite Symmetric Band Matrix Factorization and Solve

PDPBTRF--Positive Definite Symmetric Band Matrix Factorization

PDPBTRS--Positive Definite Symmetric Band Matrix Solve

PDGTSV and PDDTSV--General Tridiagonal Matrix Factorization and Solve

PDGTTRF and PDDTTRF--General Tridiagonal Matrix Factorization

PDGTTRS and PDDTTRS--General Tridiagonal Matrix Solve

PDPTSV--Positive Definite Symmetric Tridiagonal Matrix Factorization and Solve

PDPTTRF--Positive Definite Symmetric Tridiagonal Matrix Factorization

PDPTTRS--Positive Definite Symmetric Tridiagonal Matrix Solve

Fortran 90 Sparse Linear Algebraic Equation Subroutines and Their Utility Subroutines

PADALL--Allocates Space for an Array Descriptor for a General Sparse Matrix

PSPALL--Allocates Space for a General Sparse Matrix

PGEALL--Allocates Space for a Dense Vector

PSPINS--Inserts Local Data into a General Sparse Matrix

PGEINS--Inserts Local Data into a Dense Vector

PSPASB--Assembles a General Sparse Matrix

PGEASB--Assembles a Dense Vector

PSPGPR--Preconditioner for a General Sparse Matrix

PSPGIS--Iterative Linear System Solver for a General Sparse Matrix

PGEFREE--Deallocates Space for a Dense Vector

PSPFREE--Deallocates Space for a General Sparse Matrix

PADFREE--Deallocates Space for an Array Descriptor for a General Sparse Matrix

Example--Using the Fortran 90 Sparse Subroutines

Fortran 77 Sparse Linear Algebraic Equation Subroutines and Their Utility Subroutines

PADINIT--Initializes an Array Descriptor for a General Sparse Matrix

PDSPINIT--Initializes a General Sparse Matrix

PDSPINS--Inserts Local Data into a General Sparse Matrix

PDGEINS--Inserts Local Data into a Dense Vector

PDSPASB--Assembles a General Sparse Matrix

PDGEASB--Assembles a Dense Vector

PDSPGPR--Preconditioner for a General Sparse Matrix

PDSPGIS--Iterative Linear System Solver for a General Sparse Matrix

Example--Using the Fortran 77 Sparse Subroutines

Eigensystem Analysis and Singular Value Analysis (Message Passing)

Overview of the Eigensystem Analysis and Singular Value Analysis Subroutines

Eigensystem Analysis and Singular Value Analysis Subroutines

PDSYEVX--Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix

PDSYTRD--Reduce a Real Symmetric Matrix to Tridiagonal Form

PDGEHRD--Reduce a General Matrix to Upper Hessenberg Form

PDGEBRD--Reduce a General Matrix to Bidiagonal Form

Fourier Transforms (Message Passing)

Overview of the Fourier Transforms Subroutines

Acceptable Lengths for the Transforms

Fourier Transforms Subroutines

PSCFT2 and PDCFT2--Complex Fourier Transforms in Two Dimensions

PSRCFT2 and PDRCFT2--Real-to-Complex Fourier Transforms in Two Dimensions

PSCRFT2 and PDCRFT2--Complex-to-Real Fourier Transforms in Two Dimensions

PSCFT3 and PDCFT3--Complex Fourier Transforms in Three Dimensions

PSRCFT3 and PDRCFT3--Real-to-Complex Fourier Transforms in Three Dimensions

PSCRFT3 and PDCRFT3--Complex-to-Real Fourier Transforms in Three Dimensions

Random Number Generation (Message Passing)

Overview of the Random Number Generation Subroutines

Random Number Generation Subroutines

PDURNG--Uniform Random Number Generator

Utilities (Message Passing)

Overview of the Utility Subroutines

Utility Subroutines

IPESSL--Determine the Level of Parallel ESSL Installed on Your System

NUMROC--Compute the Number of Rows or Columns of a Block-Cyclically Distributed Matrix Contained in a Process

Reference Information (HPF)

PBLAS (HPF)

Overview of the PBLAS Subroutines

PBLAS Subroutines

GEMM--Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose

SYMM--Matrix-Matrix Product Where One Matrix is Real Symmetric

TRMM--Triangular Matrix-Matrix Product

TRSM--Solution of Triangular System of Equations with Multiple Right-Hand Sides

SYRK--Rank-K Update of a Real Symmetric Matrix

SYR2K--Rank-2K Update of a Real Symmetric Matrix

TRAN--Matrix Transpose for a General Matrix

Linear Algebraic Equations (HPF)

Overview of the Dense Linear Algebraic Equation Subroutines

Overview of the Banded Linear Algebraic Equation Subroutines

Dense Linear Algebraic Equation Subroutines

GETRF--General Matrix Factorization

GETRS--General Matrix Solve

POTRF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization

POTRS--Positive Definite Real Symmetric or Complex Hermitian Matrix Solve

Banded Linear Algebraic Equation Subroutines

PBSV--Positive Definite Symmetric Band Matrix Factorization and Solve

PBTRF--Positive Definite Symmetric Band Matrix Factorization

PBTRS--Positive Definite Symmetric Band Matrix Solve

GTSV and DTSV--General Tridiagonal Matrix Factorization and Solve

GTTRF and DTTRF--General Tridiagonal Matrix Factorization

GTTRS and DTTRS--General Tridiagonal Matrix Solve

PTSV--Positive Definite Symmetric Tridiagonal Matrix Factorization and Solve

PTTRF--Positive Definite Symmetric Tridiagonal Matrix Factorization

PTTRS--Positive Definite Symmetric Tridiagonal Matrix Solve

Eigensystem Analysis and Singular Value Analysis (HPF)

Overview of the Eigensystem Analysis and Singular Value Analysis Subroutines

Eigensystem Analysis and Singular Value Analysis Subroutines

SYEVX--Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix

SYTRD--Reduce a Real Symmetric Matrix to Tridiagonal Form

GEHRD--Reduce a General Matrix to Upper Hessenberg Form

GEBRD--Reduce a General Matrix to Bidiagonal Form

Fourier Transforms (HPF)

Overview of the Fourier Transforms Subroutines

Acceptable Lengths for the Transforms

Fourier Transforms Subroutines

FFT--Fourier Transforms in Two Dimensions

FFT--Fourier Transforms in Three Dimensions

Random Number Generation (HPF)

Overview of the Random Number Generation Subroutine

Random Number Generation Subroutine

URNG--Uniform Random Number Generator

Appendix A. BLACS Quick Reference Guide

BLACS Initialization Subroutines

BLACS Deallocating Resources Subroutines

BLACS Sending Subroutines

BLACS Receiving Subroutines

BLACS Global Operation Subroutines

BLACS Informational and Miscellaneous Subroutines

Argument Options

Appendix B. Sample Programs

Sample Programs and Utilities Provided with Parallel ESSL

Sample Thermal Diffusion Programs

Thermal Diffusion Discussion Paper

Program Main (Message Passing)

Module Parameters (Message Passing)

Module Diffusion (Message Passing)

Module Fourier (Message Passing)

Module Scale (Message Passing)

Program Main (HPF)

Module Parameters (HPF)

Module Diffusion (HPF)

Module Fourier (HPF)

Sample Sparse Linear Algebraic Equations Programs

Fortran 90 Sample Sparse Program

Fortran 77 Sample Sparse Program

Fortran 90 Sample Sparse Program (using the Harwell-Boeing exchange format)

Sample PARTS Subroutine

The READ_MAT Subroutine

The MAT_DIST Subroutine

The DESYM Subroutine

Sample Makefiles and Run Script

Makefile (Message Passing)

Appendix C. Glossary

Appendix D. Bibliography

Parallel ESSL Publications

Evaluation and Planning

Related Publications

Index

Looking for a Subroutine?

DTSV...
GTSV and DTSV--General Tridiagonal Matrix Factorization and Solve
DTTRF...
GTTRF and DTTRF--General Tridiagonal Matrix Factorization
DTTRS...
GTTRS and DTTRS--General Tridiagonal Matrix Solve
FFT...
FFT--Fourier Transforms in Two Dimensions,
FFT--Fourier Transforms in Three Dimensions
GEBRD...
GEBRD--Reduce a General Matrix to Bidiagonal Form
GEHRD...
GEHRD--Reduce a General Matrix to Upper Hessenberg Form
GEMM...
GEMM--Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
GETRF...
GETRF--General Matrix Factorization
GETRS...
GETRS--General Matrix Solve
GTSV...
GTSV and DTSV--General Tridiagonal Matrix Factorization and Solve
GTTRF...
GTTRF and DTTRF--General Tridiagonal Matrix Factorization
GTTRS...
GTTRS and DTTRS--General Tridiagonal Matrix Solve
IPESSL...
IPESSL--Determine the Level of Parallel ESSL Installed on Your System
NUMROC...
NUMROC--Compute the Number of Rows or Columns of a Block-Cyclically Distributed Matrix Contained in a Process
PADALL
PADALL--Allocates Space for an Array Descriptor for a General Sparse Matrix
PADFREE
PADFREE--Deallocates Space for an Array Descriptor for a General Sparse Matrix
PADINIT
PADINIT--Initializes an Array Descriptor for a General Sparse Matrix
PBSV...
PBSV--Positive Definite Symmetric Band Matrix Factorization and Solve
PBTRF...
PBTRF--Positive Definite Symmetric Band Matrix Factorization
PBTRS...
PBTRS--Positive Definite Symmetric Band Matrix Solve
PDCFT2...
PSCFT2 and PDCFT2--Complex Fourier Transforms in Two Dimensions
PDCFT3...
PSCFT3 and PDCFT3--Complex Fourier Transforms in Three Dimensions
PDCRFT2...
PSCRFT2 and PDCRFT2--Complex-to-Real Fourier Transforms in Two Dimensions
PDCRFT3...
PSCRFT3 and PDCRFT3--Complex-to-Real Fourier Transforms in Three Dimensions
PDDTSV...
PDGTSV and PDDTSV--General Tridiagonal Matrix Factorization and Solve
PDDTTRF...
PDGTTRF and PDDTTRF--General Tridiagonal Matrix Factorization
PDDTTRS...
PDGTTRS and PDDTTRS--General Tridiagonal Matrix Solve
PDGEASB
PDGEASB--Assembles a Dense Vector
PDGEBRD...
PDGEBRD--Reduce a General Matrix to Bidiagonal Form
PDGEHRD...
PDGEHRD--Reduce a General Matrix to Upper Hessenberg Form
PDGEINS
PDGEINS--Inserts Local Data into a Dense Vector
PDGEMM...
PDGEMM and PZGEMM--Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
PDGEMV...
PDGEMV--Matrix-Vector Product for a General Matrix or Its Transpose
PDGER...
PDGER--Rank-One Update of a General Matrix
PDGETRF...
PDGETRF and PZGETRF--General Matrix Factorization
PDGETRS...
PDGETRS and PZGETRS--General Matrix Solve
PDGTSV...
PDGTSV and PDDTSV--General Tridiagonal Matrix Factorization and Solve
PDGTTRF...
PDGTTRF and PDDTTRF--General Tridiagonal Matrix Factorization
PDGTTRS...
PDGTTRS and PDDTTRS--General Tridiagonal Matrix Solve
PDPBSV...
PDPBSV--Positive Definite Symmetric Band Matrix Factorization and Solve
PDPBTRF...
PDPBTRF--Positive Definite Symmetric Band Matrix Factorization
PDPBTRS...
PDPBTRS--Positive Definite Symmetric Band Matrix Solve

PDPOTRF...
PDPOTRF and PZPOTRF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
PDPOTRS...
PDPOTRS and PZPOTRS--Positive Definite Real Symmetric or Complex Hermitian Matrix Solve
PDPTSV...
PDPTSV--Positive Definite Symmetric Tridiagonal Matrix Factorization and Solve
PDPTTRF...
PDPTTRF--Positive Definite Symmetric Tridiagonal Matrix Factorization
PDPTTRS...
PDPTTRS--Positive Definite Symmetric Tridiagonal Matrix Solve
PDRCFT2...
PSRCFT2 and PDRCFT2--Real-to-Complex Fourier Transforms in Two Dimensions
PDRCFT3...
PSRCFT3 and PDRCFT3--Real-to-Complex Fourier Transforms in Three Dimensions
PDSPASB
PDSPASB--Assembles a General Sparse Matrix
PDSPGIS
PDSPGIS--Iterative Linear System Solver for a General Sparse Matrix
PDSPGPR
PDSPGPR--Preconditioner for a General Sparse Matrix
PDSPINIT
PDSPINIT--Initializes a General Sparse Matrix
PDSPINS
PDSPINS--Inserts Local Data into a General Sparse Matrix
PDSYEVX...
PDSYEVX--Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix
PDSYMM...
PDSYMM--Matrix-Matrix Product Where One Matrix is Real Symmetric
PDSYMV...
PDSYMV--Matrix-Vector Product for a Real Symmetric Matrix
PDSYR...
PDSYR--Rank-One Update of a Real Symmetric Matrix
PDSYRK...
PDSYRK--Rank-K Update of a Real Symmetric Matrix
PDSYR2...
PDSYR2--Rank-Two Update of a Real Symmetric Matrix
PDSYR2K...
PDSYR2K--Rank-2K Update of a Real Symmetric Matrix
PDSYTRD...
PDSYTRD--Reduce a Real Symmetric Matrix to Tridiagonal Form
PDTRAN...
PDTRAN--Matrix Transpose for a General Matrix
PDTRMM...
PDTRMM--Triangular Matrix-Matrix Product
PDTRMV...
PDTRMV--Matrix-Vector Product for a Triangular Matrix or Its Transpose
PDTRSM...
PDTRSM--Solution of Triangular System of Equations with Multiple Right-Hand Sides
PDTRSV...
PDTRSV--Solution of Triangular System of Equations with a Single Right-Hand Side
PDURNG...
PDURNG--Uniform Random Number Generator
PGEALL
PGEALL--Allocates Space for a Dense Vector
PGEASB
PGEASB--Assembles a Dense Vector
PGEFREE
PGEFREE--Deallocates Space for a Dense Vector
PGEINS
PGEINS--Inserts Local Data into a Dense Vector
POTRF...
POTRF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
POTRS...
POTRS--Positive Definite Real Symmetric or Complex Hermitian Matrix Solve
PSCFT2...
PSCFT2 and PDCFT2--Complex Fourier Transforms in Two Dimensions
PSCFT3...
PSCFT3 and PDCFT3--Complex Fourier Transforms in Three Dimensions
PSCRFT2...
PSCRFT2 and PDCRFT2--Complex-to-Real Fourier Transforms in Two Dimensions
PSCRFT3...
PSCRFT3 and PDCRFT3--Complex-to-Real Fourier Transforms in Three Dimensions
PSPALL
PSPALL--Allocates Space for a General Sparse Matrix
PSPASB
PSPASB--Assembles a General Sparse Matrix
PSPFREE
PSPFREE--Deallocates Space for a General Sparse Matrix
PSPGIS
PSPGIS--Iterative Linear System Solver for a General Sparse Matrix
PSPGPR
PSPGPR--Preconditioner for a General Sparse Matrix
PSPINS
PSPINS--Inserts Local Data into a General Sparse Matrix

PSRCFT2...
PSRCFT2 and PDRCFT2--Real-to-Complex Fourier Transforms in Two Dimensions
PSRCFT3...
PSRCFT3 and PDRCFT3--Real-to-Complex Fourier Transforms in Three Dimensions
PTSV...
PTSV--Positive Definite Symmetric Tridiagonal Matrix Factorization and Solve
PTTRF...
PTTRF--Positive Definite Symmetric Tridiagonal Matrix Factorization
PTTRS...
PTTRS--Positive Definite Symmetric Tridiagonal Matrix Solve
PZGEMM...
PDGEMM and PZGEMM--Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
PZGETRF...
PDGETRF and PZGETRF--General Matrix Factorization
PZGETRS...
PDGETRS and PZGETRS--General Matrix Solve
PZPOTRF...
PDPOTRF and PZPOTRF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
PZPOTRS...
PDPOTRS and PZPOTRS--Positive Definite Real Symmetric or Complex Hermitian Matrix Solve
SYEVX...
SYEVX--Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix
SYMM...
SYMM--Matrix-Matrix Product Where One Matrix is Real Symmetric
SYRK...
SYRK--Rank-K Update of a Real Symmetric Matrix
SYR2K...
SYR2K--Rank-2K Update of a Real Symmetric Matrix
SYTRD...
SYTRD--Reduce a Real Symmetric Matrix to Tridiagonal Form
TRAN...
TRAN--Matrix Transpose for a General Matrix
TRMM...
TRMM--Triangular Matrix-Matrix Product
TRSM...
TRSM--Solution of Triangular System of Equations with Multiple Right-Hand Sides
URNG...
URNG--Uniform Random Number Generator

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