The linear algebraic equation subroutines, provided in four areas, are described in this chapter.
This section describes the subroutines in each of the four linear algebraic equation areas:
| Note: | Some of the linear algebraic equations were designed in accordance with the Level 2 BLAS, Level 3 BLAS, and LAPACK de facto standard. If these subprograms do not comply with the standard as approved, IBM will consider updating them to do so. If IBM updates these subprograms, the updates could require modifications of the calling application program. For details on the Level 2 and 3 BLAS, see references [32] and [34]. For details on the LAPACK routines, see reference [8]. |
The dense linear algebraic equation subroutines provide solutions to linear
systems of equations for both real and complex general matrices and their
transposes, positive definite real symmetric and complex Hermitian matrices,
and triangular matrices. Some of these subroutines correspond to the Level 2
BLAS, Level 3 BLAS, and LAPACK routines described in references [32], [34], and [8].
Table 83. List of Dense Linear Algebraic Equation Subroutines
| Descriptive Name | Short- Precision Subroutine | Long- Precision Subroutine | Page |
|---|---|---|---|
| General Matrix Factorization |
SGEF CGEF SGETRF° CGETRF° |
DGEF ZGEF DGETRF° ZGETRF° DGEFP§ |
SGEF, DGEF, CGEF, and ZGEF--General Matrix Factorization SGETRF, DGETRF, CGETRF and ZGETRF--General Matrix Factorization |
| General Matrix, Its Transpose, or Its Conjugate Transpose Solve |
SGES CGES |
DGES ZGES | SGES, DGES, CGES, and ZGES--General Matrix, Its Transpose, or Its Conjugate Transpose Solve |
| General Matrix, Its Transpose, or Its Conjugate Transpose Multiple Right-Hand Side Solve |
SGESM CGESM SGETRS° CGETRS° |
DGESM ZGESM DGETRS° ZGETRS° |
SGESM, DGESM, CGESM, and ZGESM--General Matrix, Its Transpose, or Its Conjugate Transpose Multiple Right-Hand Side Solve SGETRS, DGETRS, CGETRS, and ZGETRS--General Matrix Multiple Right-Hand Side Solve |
| General Matrix Factorization, Condition Number Reciprocal, and Determinant | SGEFCD | DGEFCD | SGEFCD and DGEFCD--General Matrix Factorization, Condition Number Reciprocal, and Determinant |
| Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization |
SPPF SPOF CPOF |
DPPF DPOF ZPOF DPPFP§ | SPPF, DPPF, SPOF, DPOF, CPOF, and ZPOF--Positive Definite Real Symmetric or Complex Hermitian Matrix Factorization |
| Positive Definite Real Symmetric Matrix Solve | SPPS | DPPS | SPPS and DPPS--Positive Definite Real Symmetric Matrix Solve |
| Positive Definite Real Symmetric or Complex Hermitian Matrix Multiple Right-Hand Side Solve |
SPOSM CPOSM |
DPOSM ZPOSM | SPOSM, DPOSM, CPOSM, and ZPOSM--Positive Definite Real Symmetric or Complex Hermitian Matrix Multiple Right-Hand Side Solve |
| Positive Definite Real Symmetric Matrix Factorization, Condition Number Reciprocal, and Determinant |
SPPFCD SPOFCD |
DPPFCD DPOFCD | SPPFCD, DPPFCD, SPOFCD, and DPOFCD--Positive Definite Real Symmetric Matrix Factorization, Condition Number Reciprocal, and Determinant |
| General Matrix Inverse, Condition Number Reciprocal, and Determinant | SGEICD | DGEICD | SGEICD and DGEICD--General Matrix Inverse, Condition Number Reciprocal, and Determinant |
| Positive Definite Real Symmetric Matrix Inverse, Condition Number Reciprocal, and Determinant |
SPPICD SPOICD |
DPPICD DPOICD | SPPICD, DPPICD, SPOICD, and DPOICD--Positive Definite Real Symmetric Matrix Inverse, Condition Number Reciprocal, and Determinant |
| Solution of a Triangular System of Equations with a Single Right-Hand Side |
STRSVø CTRSVø STPSVø CTPSVø |
DTRSVø ZTRSVø DTPSVø ZTPSVø | STRSV, DTRSV, CTRSV, ZTRSV, STPSV, DTPSV, CTPSV, and ZTPSV--Solution of a Triangular System of Equations with a Single Right-Hand Side |
| Solution of Triangular Systems of Equations with Multiple Right-Hand Sides |
STRSM¢ CTRSM¢ |
DTRSM¢ ZTRSM¢ | STRSM, DTRSM, CTRSM, and ZTRSM--Solution of Triangular Systems of Equations with Multiple Right-Hand Sides |
| Triangular Matrix Inverse |
STRI STPI |
DTRI DTPI | STRI, DTRI, STPI, and DTPI--Triangular Matrix Inverse |
|
ø Level 2 BLAS ¢ Level 3 BLAS ° LAPACK § This subroutine is provided only for migration from
earlier releases of ESSL and is not intended for use is new programs.
Documentation for this subroutine is no longer provided.
| |||
The banded linear algebraic equation subroutines provide solutions to
linear systems of equations for real general band matrices, real positive
definite symmetric band matrices, real or complex general tridiagonal
matrices, real positive definite symmetric tridiagonal matrices, and real or
complex triangular band matrices.
Table 84. List of Banded Linear Algebraic Equation Subroutines
| Descriptive Name | Short- Precision Subroutine | Long- Precision Subroutine | Page |
|---|---|---|---|
| General Band Matrix Factorization | SGBF | DGBF | SGBF and DGBF--General Band Matrix Factorization |
| General Band Matrix Solve | SGBS | DGBS | SGBS and DGBS--General Band Matrix Solve |
| Positive Definite Symmetric Band Matrix Factorization |
SPBF SPBCHF |
DPBF DPBCHF | SPBF, DPBF, SPBCHF, and DPBCHF--Positive Definite Symmetric Band Matrix Factorization |
| Positive Definite Symmetric Band Matrix Solve |
SPBS SPBCHS |
DPBS DPBCHS | SPBS, DPBS, SPBCHS, and DPBCHS--Positive Definite Symmetric Band Matrix Solve |
| General Tridiagonal Matrix Factorization | SGTF | DGTF | SGTF and DGTF--General Tridiagonal Matrix Factorization |
| General Tridiagonal Matrix Solve | SGTS | DGTS | SGTS and DGTS--General Tridiagonal Matrix Solve |
| General Tridiagonal Matrix Combined Factorization and Solve with No Pivoting |
SGTNP CGTNP |
DGTNP ZGTNP | SGTNP, DGTNP, CGTNP, and ZGTNP--General Tridiagonal Matrix Combined Factorization and Solve with No Pivoting |
| General Tridiagonal Matrix Factorization with No Pivoting |
SGTNPF CGTNPF |
DGTNPF ZGTNPF | SGTNPF, DGTNPF, CGTNPF, and ZGTNPF--General Tridiagonal Matrix Factorization with No Pivoting |
| General Tridiagonal Matrix Solve with No Pivoting |
SGTNPS CGTNPS |
DGTNPS ZGTNPS | SGTNPS, DGTNPS, CGTNPS, and ZGTNPS--General Tridiagonal Matrix Solve with No Pivoting |
| Positive Definite Symmetric Tridiagonal Matrix Factorization | SPTF | DPTF | SPTF and DPTF--Positive Definite Symmetric Tridiagonal Matrix Factorization |
| Positive Definite Symmetric Tridiagonal Matrix Solve | SPTS | DPTS | SPTS and DPTS--Positive Definite Symmetric Tridiagonal Matrix Solve |
| Triangular Band Equation Solve |
STBSVø CTBSVø |
DTBSVø ZTBSVø | STBSV, DTBSV, CTBSV, and ZTBSV--Triangular Band Equation Solve |
|
ø Level 2 BLAS
| |||
The sparse linear algebraic equation subroutines provide direct and
iterative solutions to linear systems of equations both for general sparse
matrices and their transposes and for sparse symmetric matrices.
Table 85. List of Sparse Linear Algebraic Equation Subroutines
| Descriptive Name | Long- Precision Subroutine | Page |
|---|---|---|
| General Sparse Matrix Factorization Using Storage by Indices, Rows, or Columns | DGSF | DGSF--General Sparse Matrix Factorization Using Storage by Indices, Rows, or Columns |
| General Sparse Matrix or Its Transpose Solve Using Storage by Indices, Rows, or Columns | DGSS | DGSS--General Sparse Matrix or Its Transpose Solve Using Storage by Indices, Rows, or Columns |
| General Sparse Matrix or Its Transpose Factorization, Determinant, and Solve Using Skyline Storage Mode | DGKFS | DGKFS--General Sparse Matrix or Its Transpose Factorization, Determinant, and Solve Using Skyline Storage Mode |
| Symmetric Sparse Matrix Factorization, Determinant, and Solve Using Skyline Storage Mode | DSKFS | DSKFS--Symmetric Sparse Matrix Factorization, Determinant, and Solve Using Skyline Storage Mode |
| Iterative Linear System Solver for a General or Symmetric Sparse Matrix Stored by Rows | DSRIS | DSRIS--Iterative Linear System Solver for a General or Symmetric Sparse Matrix Stored by Rows |
| Sparse Positive Definite or Negative Definite Symmetric Matrix Iterative Solve Using Compressed-Matrix Storage Mode | DSMCG§ | DSMCG--Sparse Positive Definite or Negative Definite Symmetric Matrix Iterative Solve Using Compressed-Matrix Storage Mode |
| Sparse Positive Definite or Negative Definite Symmetric Matrix Iterative Solve Using Compressed-Diagonal Storage Mode | DSDCG | DSDCG--Sparse Positive Definite or Negative Definite Symmetric Matrix Iterative Solve Using Compressed-Diagonal Storage Mode |
| General Sparse Matrix Iterative Solve Using Compressed-Matrix Storage Mode | DSMGCG§ | DSMGCG--General Sparse Matrix Iterative Solve Using Compressed-Matrix Storage Mode |
| General Sparse Matrix Iterative Solve Using Compressed-Diagonal Storage Mode | DSDGCG | DSDGCG--General Sparse Matrix Iterative Solve Using Compressed-Diagonal Storage Mode |
|
§ These subroutines are provided only for migration from
earlier releases of ESSL and are not intended for use in new programs. Use
DSRIS instead.
| ||
The linear least squares subroutines provide least squares solutions to
linear systems of equations for real general matrices. Two methods are
provided: one that uses the singular value decomposition and another
that uses a QR decomposition with column pivoting.
Table 86. List of Linear Least Squares Subroutines
| Descriptive Name | Short- Precision Subroutine | Long- Precision Subroutine | Page |
|---|---|---|---|
| Singular Value Decomposition for a General Matrix | SGESVF | DGESVF | SGESVF and DGESVF--Singular Value Decomposition for a General Matrix |
| Linear Least Squares Solution for a General Matrix Using the Singular Value Decomposition | SGESVS | DGESVS | SGESVS and DGESVS--Linear Least Squares Solution for a General Matrix Using the Singular Value Decomposition |
| Linear Least Squares Solution for a General Matrix Using a QR Decomposition with Column Pivoting | SGELLS | DGELLS | SGELLS and DGELLS--Linear Least Squares Solution for a General Matrix Using a QR Decomposition with Column Pivoting |