Guide and Reference

Matrix Operations

The matrix operation subroutines are described in this chapter.

Overview of the Matrix Operation Subroutines

Some of the matrix operation subroutines were designed in accordance with the Level 3 BLAS de facto 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 updates could require modifications of the calling application program. For details on the Level 3 BLAS, see reference [32]. The matrix operation subroutines also include the commonly used matrix operations: addition, subtraction, multiplication, and transposition (Table 71).

Table 71. List of Matrix Operation Subroutines

Descriptive Name	Short- Precision Subroutine	Long- Precision Subroutine	Page
Matrix Addition for General Matrices or Their Transposes	SGEADD CGEADD	DGEADD ZGEADD	SGEADD, DGEADD, CGEADD, and ZGEADD--Matrix Addition for General Matrices or Their Transposes
Matrix Subtraction for General Matrices or Their Transposes	SGESUB CGESUB	DGESUB ZGESUB	SGESUB, DGESUB, CGESUB, and ZGESUB--Matrix Subtraction for General Matrices or Their Transposes
Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes	SGEMUL CGEMUL	DGEMUL ZGEMUL DGEMLP§	SGEMUL, DGEMUL, CGEMUL, and ZGEMUL--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes
Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes Using Winograd's Variation of Strassen's Algorithm	SGEMMS CGEMMS	DGEMMS ZGEMMS	SGEMMS, DGEMMS, CGEMMS, and ZGEMMS--Matrix Multiplication for General Matrices, Their Transposes, or Conjugate Transposes Using Winograd's Variation of Strassen's Algorithm
Combined Matrix Multiplication and Addition for General Matrices, Their Transposes, or Conjugate Transposes	SGEMM¢ CGEMM¢	DGEMM¢ ZGEMM¢	SGEMM, DGEMM, CGEMM, and ZGEMM--Combined Matrix Multiplication and Addition for General Matrices, Their Transposes, or Conjugate Transposes
Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian	SSYMM¢ CSYMM¢ CHEMM¢	DSYMM¢ ZSYMM¢ ZHEMM¢	SSYMM, DSYMM, CSYMM, ZSYMM, CHEMM, and ZHEMM--Matrix-Matrix Product Where One Matrix is Real or Complex Symmetric or Complex Hermitian
Triangular Matrix-Matrix Product	STRMM¢ CTRMM¢	DTRMM¢ ZTRMM¢	STRMM, DTRMM, CTRMM, and ZTRMM--Triangular Matrix-Matrix Product
Rank-K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix	SSYRK¢ CSYRK¢ CHERK¢	DSYRK¢ ZSYRK¢ ZHERK¢	SSYRK, DSYRK, CSYRK, ZSYRK, CHERK, and ZHERK--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	SSYR2K¢ CSYR2K¢ CHER2K¢	DSYR2K¢ ZSYR2K¢ ZHER2K¢	SSYR2K, DSYR2K, CSYR2K, ZSYR2K, CHER2K, and ZHER2K--Rank-2K Update of a Real or Complex Symmetric or a Complex Hermitian Matrix
General Matrix Transpose (In-Place)	SGETMI CGETMI	DGETMI ZGETMI	SGETMI, DGETMI, CGETMI, and ZGETMI--General Matrix Transpose (In-Place)
General Matrix Transpose (Out-of-Place)	SGETMO CGETMO	DGETMO ZGETMO	SGETMO, DGETMO, CGETMO, and ZGETMO--General Matrix Transpose (Out-of-Place)
¢ Level 3 BLAS § This subroutine is provided only for migration from earlier releases of ESSL and is not intended for use in new programs. Documentation for this subroutine is no longer provided.