Guide and Reference

List of Parallel ESSL Subroutines (Message Passing and HPF)

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:

The message passing 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. The HPF subroutines were designed to be consistent with the proposals for the Fortran 90 BLAS and the Fortran 90 LAPACK. (See references [30] and [31].) If these subroutines do not comply with any eventual proposal for HPF interfaces to the PBLAS and ScaLAPACK, IBM will consider updating them to do so. If IBM updates these subroutines, the update could require modifications of the calling application program.

Table 2. List of Level 2 PBLAS

Descriptive Name	Long- Precision Subprogram	Page
Matrix-Vector Product for a General Matrix or Its Transpose	PDGEMV GEMM	PDGEMV--Matrix-Vector Product for a General Matrix or Its Transpose  GEMM--Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
Matrix-Vector Product for a Real Symmetric Matrix	PDSYMV SYMM	PDSYMV--Matrix-Vector Product for a Real Symmetric Matrix  SYMM--Matrix-Matrix Product Where One Matrix is Real Symmetric
Rank-One Update of a General Matrix	PDGER GEMM	PDGER--Rank-One Update of a General Matrix  GEMM--Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
Rank-One Update of a Real Symmetric Matrix	PDSYR SYRK	PDSYR--Rank-One Update of a Real Symmetric Matrix  SYRK--Rank-K Update of a Real Symmetric Matrix
Rank-Two Update of a Real Symmetric Matrix	PDSYR2 SYR2K	PDSYR2--Rank-Two Update of a Real Symmetric Matrix  SYR2K--Rank-2K Update of a Real Symmetric Matrix
Matrix-Vector Product for a Triangular Matrix or Its Transpose	PDTRMV TRMM	PDTRMV--Matrix-Vector Product for a Triangular Matrix or Its Transpose  TRMM--Triangular Matrix-Matrix Product
Solution of Triangular System of Equations with a Single Right-Hand Side	PDTRSV TRSM	PDTRSM--Solution of Triangular System of Equations with Multiple Right-Hand Sides  TRSM--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:

The message passing 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. The HPF subroutines were designed to be consistent with the proposals for the Fortran 90 BLAS and the Fortran 90 LAPACK. (See references [30] and [31].) If these subroutines do not comply with any eventual proposal for HPF interfaces to the PBLAS and ScaLAPACK, 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 GEMM	PDGEMM and PZGEMM--Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose  GEMM--Matrix-Matrix Product for a General Matrix, Its Transpose, or Its Conjugate Transpose
Matrix-Matrix Product Where One Matrix is Real Symmetric	PDSYMM SYMM	PDSYMM--Matrix-Matrix Product Where One Matrix is Real Symmetric  SYMM--Matrix-Matrix Product Where One Matrix is Real Symmetric
Triangular Matrix-Matrix Product	PDTRMM TRMM	PDTRMM--Triangular Matrix-Matrix Product  TRMM--Triangular Matrix-Matrix Product
Solution of Triangular System of Equations with Multiple Right-Hand Sides	PDTRSM TRSM	PDTRSM--Solution of Triangular System of Equations with Multiple Right-Hand Sides  TRSM--Solution of Triangular System of Equations with Multiple Right-Hand Sides
Rank-K Update of a Real Symmetric Matrix	PDSYRK SYRK	PDSYRK--Rank-K Update of a Real Symmetric Matrix  SYRK--Rank-K Update of a Real Symmetric Matrix
Rank-2K Update of a Real Symmetric Matrix	PDSYR2K SYR2K	PDSYR2K--Rank-2K Update of a Real Symmetric Matrix  SYR2K--Rank-2K Update of a Real Symmetric Matrix
Matrix Transpose for a General Matrix	PDTRAN TRAN	PDTRAN--Matrix Transpose for a General Matrix  TRAN--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 message passing dense and banded linear algebraic equations subroutines were designed in accordance with the proposed ScaLAPACK standard. (However, PDDTTRS does not support General Tridiagonal Matrix Transpose Solve. For details, see PDGTTRS and PDDTTRS--General Tridiagonal Matrix Solve.) 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. The HPF dense and banded linear algebraic equations subroutines were designed to be consistent with the proposals for the Fortran 90 BLAS and the Fortran 90 LAPACK. (See references [30] and [31].) If these subroutines do not comply with any eventual proposal for HPF interfaces to the PBLAS and ScaLAPACK, 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.

Table 4. List of Dense Linear Algebraic Equation Subroutines

Descriptive Name	Long- Precision Subroutine	Page
General Matrix Factorization	PDGETRF PZGETRF GETRF	PDGETRF and PZGETRF--General Matrix Factorization  GETRF--General Matrix Factorization
General Matrix Solve	PDGETRS PZGETRS GETRS	PDGETRS and PZGETRS--General Matrix Solve  GETRS--General Matrix Solve
Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization	PDPOTRF PZPOTRF POTRF	PDPOTRF and PZPOTRF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization  POTRF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization
Positive Definite Real Symmetric or Complex Hermitian Matrix Solve	PDPOTRS PZPOTRS POTRS	PDPOTRS and PZPOTRS--Positive Definite Real Symmetric or Complex Hermitian Matrix Solve  POTRS--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 PBSV	PDPBSV--Positive Definite Symmetric Band Matrix Factorization and Solve  PBSV--Positive Definite Symmetric Band Matrix Factorization and Solve
Positive Definite Symmetric Band Matrix Factorization	PDPBTRF PBTRF	PDPBTRF--Positive Definite Symmetric Band Matrix Factorization  PBTRF--Positive Definite Symmetric Band Matrix Factorization
Positive Definite Symmetric Band Matrix Solve	PDPBTRS PBTRS	PDPBTRS--Positive Definite Symmetric Band Matrix Solve  PBTRS--Positive Definite Symmetric Band Matrix Solve
General Tridiagonal Matrix Factorization and Solve	PDGTSV GTSV	PDGTSV and PDDTSV--General Tridiagonal Matrix Factorization and Solve  GTSV and DTSV--General Tridiagonal Matrix Factorization and Solve
General Tridiagonal Matrix Factorization	PDGTTRF GTTRF	PDGTTRF and PDDTTRF--General Tridiagonal Matrix Factorization  GTTRF and DTTRF--General Tridiagonal Matrix Factorization
General Tridiagonal Matrix Solve	PDGTTRS GTTRS	PDGTTRS and PDDTTRS--General Tridiagonal Matrix Solve  GTTRS and DTTRS--General Tridiagonal Matrix Solve
Diagonally-Dominant General Tridiagonal Matrix Factorization and Solve	PDDTSV DTSV	PDGTSV and PDDTSV--General Tridiagonal Matrix Factorization and Solve  GTSV and DTSV--General Tridiagonal Matrix Factorization and Solve
Diagonally-Dominant General Tridiagonal Matrix Factorization	PDDTTRF DTTRF	PDGTTRF and PDDTTRF--General Tridiagonal Matrix Factorization  GTTRF and DTTRF--General Tridiagonal Matrix Factorization
Diagonally-Dominant General Tridiagonal Matrix Solve	PDDTTRS DTTRS	PDGTTRS and PDDTTRS--General Tridiagonal Matrix Solve  GTTRS and DTTRS--General Tridiagonal Matrix Solve
Positive Definite Symmetric Tridiagonal Matrix Factorization and Solve	PDPTSV PTSV	PDPTSV--Positive Definite Symmetric Tridiagonal Matrix Factorization and Solve  PTSV--Positive Definite Symmetric Tridiagonal Matrix Factorization and Solve
Positive Definite Symmetric Tridiagonal Matrix Factorization	PDPTTRF PTTRF	PDPTTRF--Positive Definite Symmetric Tridiagonal Matrix Factorization  PTTRF--Positive Definite Symmetric Tridiagonal Matrix Factorization
Positive Definite Symmetric Tridiagonal Matrix Solve	PDPTTRS PTTRS	PDPTTRS--Positive Definite Symmetric Tridiagonal Matrix Solve  PTTRS--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 eigensystem analysis and singular value analysis subroutines include a subset of the ScaLAPACK subroutines. See references [19] and [20].

Note:

The message passing 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. The HPF subroutines were designed to be consistent with the proposals for the Fortran 90 BLAS and the Fortran 90 LAPACK. (See references [30] and [31].) If these subroutines do not comply with any eventual proposal for HPF interfaces to the PBLAS and ScaLAPACK, 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 Matrix	PDSYEVX SYEVX	PDSYEVX--Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix  SYEVX--Selected Eigenvalues and, Optionally, the Eigenvectors of a Real Symmetric Matrix
Reduce a Real Symmetric Matrix to Tridiagonal Form	PDSYTRD SYTRD	PDSYTRD--Reduce a Real Symmetric Matrix to Tridiagonal Form  SYTRD--Reduce a Real Symmetric Matrix to Tridiagonal Form
Reduce a General Matrix to Upper Hessenberg Form	PDGEHRD GEHRD	PDGEHRD--Reduce a General Matrix to Upper Hessenberg Form  GEHRD--Reduce a General Matrix to Upper Hessenberg Form
Reduce a General Matrix to Bidiagonal Form	PDGEBRD GEBRD	PDGEBRD--Reduce a General Matrix to Bidiagonal Form  GEBRD--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 FFT	PDCFT2 FFT	PSCFT2 and PDCFT2--Complex Fourier Transforms in Two Dimensions  FFT--Fourier Transforms in Two Dimensions
Real-to-Complex Fourier Transforms in Two Dimensions	PSRCFT2 FFT	PDRCFT2 FFT	PSRCFT2 and PDRCFT2--Real-to-Complex Fourier Transforms in Two Dimensions  FFT--Fourier Transforms in Two Dimensions
Complex-to-Real Fourier Transforms in Two Dimensions	PSCRFT2 FFT	PDCRFT2 FFT	PSCRFT2 and PDCRFT2--Complex-to-Real Fourier Transforms in Two Dimensions  FFT--Fourier Transforms in Two Dimensions
Complex Fourier Transforms in Three Dimensions	PSCFT3 FFT	PDCFT3 FFT	PSCFT3 and PDCFT3--Complex Fourier Transforms in Three Dimensions  FFT--Fourier Transforms in Three Dimensions
Real-to-Complex Fourier Transforms in Three Dimensions	PSRCFT3 FFT	PDRCFT3 FFT	PSRCFT3 and PDRCFT3--Real-to-Complex Fourier Transforms in Three Dimensions  FFT--Fourier Transforms in Three Dimensions
Complex-to-Real Fourier Transforms in Three Dimensions	PSCRFT3 FFT	PDCRFT3 FFT	PSCRFT3 and PDCRFT3--Complex-to-Real Fourier Transforms in Three Dimensions  FFT--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 URNG	PDURNG--Uniform Random Number Generator  URNG--Uniform Random Number Generator

Utilities

The message passing utility subroutines perform general service functions that support Parallel ESSL, rather than mathematical computations.

Table 11. List of Utility Subroutines

Descriptive Name	Integer Subroutine	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