Parallel Engineering and Scientific Subroutine Library for AIX Version 2 Release 3: Guide and Reference

List of Parallel ESSL Subroutines

This section provides an overview of the subroutines in each of the areas of Parallel ESSL.

Level 2 PBLAS

The Level 2 PBLAS include a subset of the standard set of distributed memory parallel versions of the Level 2 BLAS.

Note:: These subroutines were designed in accordance with the proposed Level 2 PBLAS standard. (See references [14], [15], and [17].) If these subroutines do not comply with the standard as approved, IBM will consider updating them to do so.
If IBM updates these subroutines, the update could require modifications of the calling application program.

Descriptive Name	Long-Precision Subprogram	Page
Matrix-Vector Product for a General Matrix or Its Transpose	PDGEMV PZGEMV	PDGEMV and PZGEMV--Matrix-Vector Product for a General Matrix or Its Transpose
Matrix-Vector Product for a Real Symmetric or a Complex Hermitian Matrix	PDSYMV PZHEMV	PDSYMV and PZHEMV--Matrix-Vector Product for a Real Symmetric or a Complex Hermitian Matrix
Rank-One Update of a General Matrix	PDGER PZGERC PZGERU	PDGER, PZGERC, and PZGERU--Rank-One Update of a General Matrix
Rank-One Update of a Real Symmetric or a Complex Hermitian Matrix	PDSYR PZHER	PDSYR and PZHER--Rank-One Update of a Real Symmetric or a Complex Hermitian Matrix
Rank-Two Update of a Real Symmetric or a Complex Hermitian Matrix	PDSYR2 PZHER2	PDSYR2 and PZHER2--Rank-Two Update of a Real Symmetric or a Complex Hermitian Matrix
Matrix-Vector Product for a Triangular Matrix or Its Transpose	PDTRMV PZTRMV	PDTRMV and PZTRMV--Matrix-Vector Product for a Triangular Matrix or Its Transpose
Solution of Triangular System of Equations with a Single Right-Hand Side	PDTRSV PZTRSV	PDTRSM and PZTRSM--Solution of Triangular System of Equations with Multiple Right-Hand Sides

Level 3 PBLAS

The Level 3 PBLAS include a subset of the standard set of distributed memory parallel versions of the Level 3 BLAS.

Note:: These subroutines were designed in accordance with the proposed Level 3 PBLAS standard. (See references [14], [15], and [17].) If these subroutines do not comply with the standard as approved, IBM will consider updating them to do so.
If IBM updates these subroutines, the update could require modifications of the calling application program.

Table 3. List of Level 3 PBLAS

Descriptive Name	Long-Precision Subprogram	Page
Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose	PDGEMM PZGEMM	PDGEMM and PZGEMM--Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian	PDSYMM PZSYMM PZHEMM	PDSYMM, PZSYMM, and PZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian
Triangular Matrix-Matrix Product	PDTRMM PZTRMM	PDTRMM and PZTRMM--Triangular Matrix-Matrix Product
Solution of Triangular System of Equations with Multiple Right-Hand Sides	PDTRSM PZTRSM	PDTRSM and PZTRSM--Solution of Triangular System of Equations with Multiple Right-Hand Sides
Rank-K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix	PDSYRK PZSYRK PZHERK	PDSYRK, PZSYRK, and PZHERK--Rank-K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
Rank-2K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix	PDSYR2K PZSYR2K PZHER2K	PDSYR2K, PZSYR2K, and PZHER2K--Rank-2K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
Matrix Transpose for a General Matrix	PDTRAN PZTRANC PZTRANU	PDTRAN, PZTRANC, and PZTRANU--Matrix Transpose for a General Matrix

Linear Algebraic Equations

These subroutines consist of dense, banded, and sparse subroutines, and include a subset of the ScaLAPACK subroutines.

Note:: The dense and banded linear algebraic equations subroutines were designed in accordance with the proposed ScaLAPACK standard. See references [10], [16], [18], [27], and [28]. If these subroutines do not comply with the standard as approved, IBM will consider updating them to do so.
If IBM updates these subroutines, the update could require modifications of the calling application program.

Dense Linear Algebraic Equations

The dense linear algebraic equation subroutines provide:

Solutions to linear systems of equations for real and complex general matrices, and their transposes, and for positive definite real symmetric and complex Hermitian matrices.
Least squares solutions to linear systems of equations for real |and complex general matrices.

Table 4. List of Dense Linear Algebraic Equation Subroutines

Descriptive Name	Long-Precision Subroutine	Page
General Matrix Factorization and Solve	PDGESV PZGESV	PDGESV and PZGESV--General Matrix Factorization and Solve
General Matrix Factorization	PDGETRF PZGETRF	PDGETRF and PZGETRF--General Matrix Factorization
General Matrix Solve	PDGETRS PZGETRS	PDGETRS and PZGETRS--General Matrix Solve
General Matrix Inverse	PDGETRI PZGETRI	PDGETRI and PZGETRI--General Matrix Inverse
Estimate the Reciprocal of the Condition Number of a General Matrix	PDGECON PZGECON	PDGECON and PZGECON--Estimate the Reciprocal of the Condition Number of a General Matrix
General Matrix QR Factorization	PDGEQRF PZGEQRF	PDGEQRF and PZGEQRF--General Matrix QR Factorization
General Matrix Least Squares Solution	PDGELS PZGELS	PDGELS and PZGELS--General Matrix Least Squares Solution
Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization and Solve	PDPOSV PZPOSV	PDPOSV and PZPOSV--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization and Solve
Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization	PDPOTRF PZPOTRF	PDPOTRF and PZPOTRF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
Positive Definite Real Symmetric or Complex Hermitian Matrix Solve	PDPOTRS PZPOTRS	PDPOTRS and PZPOTRS--Positive Definite Real Symmetric or Complex Hermitian Matrix Solve

Banded Linear Algebraic Equations

The banded linear algebraic equation subroutines provide solutions to linear systems of equations for real positive definite symmetric band matrices, real general tridiagonal matrices, diagonally-dominant real general tridiagonal matrices, and real positive definite symmetric tridiagonal matrices.

Table 5. List of Banded Linear Algebraic Equation Subroutines

Descriptive Name	Long- Precision Subroutine	Page
Positive Definite Symmetric Band Matrix Factorization and Solve	PDPBSV	PDPBSV--Positive Definite Symmetric Band Matrix Factorization and Solve
Positive Definite Symmetric Band Matrix Factorization	PDPBTRF	PDPBTRF--Positive Definite Symmetric Band Matrix Factorization
Positive Definite Symmetric Band Matrix Solve	PDPBTRS	PDPBTRS--Positive Definite Symmetric Band Matrix Solve
General Tridiagonal Matrix Factorization and Solve	PDGTSV	PDGTSV and PDDTSV--General Tridiagonal Matrix Factorization and Solve
General Tridiagonal Matrix Factorization	PDGTTRF	PDGTTRF and PDDTTRF--General Tridiagonal Matrix Factorization
General Tridiagonal Matrix Solve	PDGTTRS	PDGTTRS and PDDTTRS--General Tridiagonal Matrix Solve
Diagonally-Dominant General Tridiagonal Matrix Factorization and Solve	PDDTSV	PDGTSV and PDDTSV--General Tridiagonal Matrix Factorization and Solve
Diagonally-Dominant General Tridiagonal Matrix Factorization	PDDTTRF	PDGTTRF and PDDTTRF--General Tridiagonal Matrix Factorization
Diagonally-Dominant General Tridiagonal Matrix Solve	PDDTTRS	PDGTTRS and PDDTTRS--General Tridiagonal Matrix Solve
Positive Definite Symmetric Tridiagonal Matrix Factorization and Solve	PDPTSV	PDPTSV--Positive Definite Symmetric Tridiagonal Matrix Factorization and Solve
Positive Definite Symmetric Tridiagonal Matrix Factorization	PDPTTRF	PDPTTRF--Positive Definite Symmetric Tridiagonal Matrix Factorization
Positive Definite Symmetric Tridiagonal Matrix Solve	PDPTTRS	PDPTTRS--Positive Definite Symmetric Tridiagonal Matrix Solve

Fortran 90 Sparse Linear Algebraic Equation Subroutines

The Fortran 90 sparse linear algebraic equation subroutines provide solutions to linear systems of equations for a real general sparse matrix. The sparse utility subroutines provided in Parallel ESSL must be used in conjunction with the sparse linear algebraic equation subroutines.

Table 6. List of Fortran 90 Sparse Linear Algebraic Equation Subroutines

Descriptive Name	Long-Precision Subroutine	Page
Allocates Space for an Array Descriptor for a General Sparse Matrix	PADALL	PADALL--Allocates Space for an Array Descriptor for a General Sparse Matrix
Allocates Space for a General Sparse Matrix	PSPALL	PSPALL--Allocates Space for a General Sparse Matrix
Allocates Space for a Dense Vector	PGEALL	PGEALL--Allocates Space for a Dense Vector
Inserts Local Data into a General Sparse Matrix	PSPINS	PSPINS--Inserts Local Data into a General Sparse Matrix
Inserts Local Data into a Dense Vector	PGEINS	PGEINS--Inserts Local Data into a Dense Vector
Assembles a General Sparse Matrix	PSPASB	PSPASB--Assembles a General Sparse Matrix
Assembles a Dense Vector	PGEASB	PGEASB--Assembles a Dense Vector
Preconditioner for a General Sparse Matrix	PSPGPR	PSPGPR--Preconditioner for a General Sparse Matrix
Iterative Linear System Solver for a General Sparse Matrix	PSPGIS	PSPGIS--Iterative Linear System Solver for a General Sparse Matrix
Deallocates Space for a Dense Vector	PGEFREE	PGEFREE--Deallocates Space for a Dense Vector
Deallocates Space for a General Sparse Matrix	PSPFREE	PSPFREE--Deallocates Space for a General Sparse Matrix
Deallocates Space for an Array Descriptor for a General Sparse Matrix	PADFREE	PADFREE--Deallocates Space for an Array Descriptor for a General Sparse Matrix

Fortran 77 Sparse Linear Algebraic Equation Subroutines

The Fortran 77 sparse linear algebraic equation subroutines provide solutions to linear systems of equations for a real general sparse matrix. The sparse utility subroutines provided in Parallel ESSL must be used in conjunction with the sparse linear algebraic equation subroutines.

Table 7. List of The Fortran 77 Sparse Linear Algebraic Equation Subroutines

Descriptive Name	Long-Precision Subroutine	Page
Initializes an Array Descriptor for a General Sparse Matrix	PADINIT	PADINIT--Initializes an Array Descriptor for a General Sparse Matrix
Initializes a General Sparse Matrix	PDSPINIT	PDSPINIT--Initializes a General Sparse Matrix
Inserts Local Data into a General Sparse Matrix	PDSPINS	PDSPINS--Inserts Local Data into a General Sparse Matrix
Inserts Local Data into a Dense Vector	PDGEINS	PDGEINS--Inserts Local Data into a Dense Vector
Assembles a General Sparse Matrix	PDSPASB	PDSPASB--Assembles a General Sparse Matrix
Assembles a Dense Vector	PDGEASB	PDGEASB--Assembles a Dense Vector
Preconditioner for a General Sparse Matrix	PDSPGPR	PDSPGPR--Preconditioner for a General Sparse Matrix
Iterative Linear System Solver for a General Sparse Matrix	PDSPGIS	PDSPGIS--Iterative Linear System Solver for a General Sparse Matrix

Eigensystem Analysis and Singular Value Analysis

The eigensystems analysis and singular value analysis subroutines provide solutions to the algebraic eigensystem analysis problem for real symmetric matrices and complex Hermitian matrices and the real symmetric |and complex Hermitian positive definite generalized eigensystem analysis problem. In addition, subroutines to reduce real symmetric and complex Hermitian matrices, real symmetric |and complex Hermitian positive definite generalized eigenproblems, and real general matrices to condensed form are provided. These subroutines include a subset of the ScaLAPACK subroutines. See references [19] and [20].

Note:: These subroutines were designed in accordance with the proposed ScaLAPACK standard. If these subroutines do not comply with the standard as approved, IBM will consider updating them to do so.
If IBM updates these subroutines, the update could require modifications of the calling application program.

Table 8. List of Eigensystem Analysis and Singular Value Analysis Subroutines

Descriptive Name	Long-Precision Subroutine	Page
Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric or Complex Hermitian Matrix	PDSYEVX PZHEEVX	PDSYEVX and PZHEEVX--Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric or Complex Hermitian Matrix
Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric or Complex Hermitian Positive Definite Generalized Eigenproblem	PDSYGVX PZHEGVX	PDSYGVX and PZHEGVX--Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric or Complex Hermitian Positive Definite Generalized Eigenproblem
Reduce a Real Symmetric or Complex Hermitian Matrix to Tridiagonal Form	PDSYTRD PZHETRD	PDSYTRD and PZHETRD--Reduce a Real Symmetric or Complex Hermitian Matrix to Tridiagonal Form
Reduce a Real Symmetric or Complex Hermitian Positive Definite Generalized Eigenproblem to Standard Form	PDSYGST PZHEGST	PDSYGST and PZHEGST--Reduce a Real Symmetric or Complex Hermitian Positive Definite Generalized Eigenproblem to Standard Form
Reduce a General Matrix to Upper Hessenberg Form	PDGEHRD	PDGEHRD--Reduce a General Matrix to Upper Hessenberg Form
Reduce a General Matrix to Bidiagonal Form	PDGEBRD	PDGEBRD--Reduce a General Matrix to Bidiagonal Form

Fourier Transforms

The Fourier transform subroutines perform mixed-radix transforms in two and three dimensions. See references [1] and [3].

Table 9. List of Fourier Transform Subroutines

Descriptive Name	Short- Precision Subroutine	Long- Precision Subroutine	Page
Complex Fourier Transforms in Two Dimensions	PSCFT2	PDCFT2	PSCFT2 and PDCFT2--Complex Fourier Transforms in Two Dimensions
Real-to-Complex Fourier Transforms in Two Dimensions	PSRCFT2	PDRCFT2	PSRCFT2 and PDRCFT2--Real-to-Complex Fourier Transforms in Two Dimensions
Complex-to-Real Fourier Transforms in Two Dimensions	PSCRFT2	PDCRFT2	PSCRFT2 and PDCRFT2--Complex-to-Real Fourier Transforms in Two Dimensions
Complex Fourier Transforms in Three Dimensions	PSCFT3	PDCFT3	PSCFT3 and PDCFT3--Complex Fourier Transforms in Three Dimensions
Real-to-Complex Fourier Transforms in Three Dimensions	PSRCFT3	PDRCFT3	PSRCFT3 and PDRCFT3--Real-to-Complex Fourier Transforms in Three Dimensions
Complex-to-Real Fourier Transforms in Three Dimensions	PSCRFT3	PDCRFT3	PSCRFT3 and PDCRFT3--Complex-to-Real Fourier Transforms in Three Dimensions

Random Number Generation

The random number generation subroutine generates uniformly distributed random numbers.

Table 10. List of Random Number Generation Subroutines

Descriptive Name	Long-Precision Subroutine	Page
Uniform Random Number Generator	PDURNG	PDURNG--Uniform Random Number Generator

Utilities

The utility subroutines perform general service functions that support Parallel ESSL.

Table 11. List of Utility Subroutines

Descriptive Name	Subprogram	Page
Determine the Level of Parallel ESSL Installed on Your System	IPESSL	IPESSL--Determine the Level of Parallel ESSL Installed on Your System
Compute the Number of Rows or Columns of a Block-Cyclically Distributed Matrix Contained in a Process	NUMROC	NUMROC--Compute the Number of Rows or Columns of a Block-Cyclically Distributed Matrix Contained in a Process
General Matrix Norm	PDLANGE PZLANGE	PDLANGE and PZLANGE--General Matrix Norm

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