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*AIX Version 4.3 Base Operating System and Extensions Technical Reference, Volume 2*

## SGEMM, DGEMM, CGEMM, or ZGEMM Subroutine

### Purpose

Performs matrix-matrix operations on general matrices.

### Library

BLAS Library (**libblas.a**)

### FORTRAN Syntax

**SUBROUTINE SGEMM(***TRANSA***, ***TRANSB***, ***M***, ***N***, ***K***,**
*ALPHA***, ***A***, ***LDA***, ***B***, ***LDB***, ***BETA***, ***C***, ***LDC***)**
**CHARACTER*1** *TRANSA***,***TRANSB*
**INTEGER** *M***,***N***,***K***,***LDA***,***LDB***,***LDC*
**REAL** *ALPHA***,***BETA*
**REAL** *A***(***LDA***,*), ***B***(***LDB***,*), ***C***(***LDC***,*)**

**SUBROUTINE** **DGEMM(***TRANSA***, ***TRANSB***, ***M***, ***N***, ***K***,**
*ALPHA***, ***A***, ***LDA***, ***B***, ***LDB***, ***BETA***, ***C***, ***LDC***)**
**CHARACTER*1** *TRANSA***,***TRANSB*
**INTEGER** *M***,***N***,***K***,***LDA***,***LDB***,***LDC*
**DOUBLE PRECISION** *ALPHA***,***BETA*
**DOUBLE PRECISION** *A***(***LDA***,*), ***B***(***LDB***,*), ***C***(***LDC***,*)**

**SUBROUTINE** **CGEMM(***TRANSA***, ***TRANSB***, ***M***, ***N***, ***K***,**
*ALPHA***, ***A***, ***LDA***, ***B***, ***LDB***, ***BETA***, ***C***, ***LDC***)**
**CHARACTER*1** *TRANSA***,***TRANSB*
**INTEGER** *M***,***N***,***K***,***LDA***,***LDB***,***LDC*
**COMPLEX** *ALPHA***,***BETA*
**COMPLEX** *A***(***LDA***,*), ***B***(***LDB***,*), ***C***(***LDC***,*)**

**SUBROUTINE** **ZGEMM(***TRANSA***, ***TRANSB***, ***M***, ***N***, ***K***,**
*ALPHA***, ***A***, ***LDA***, ***B***, ***LDB***, ***BETA***, ***C***, ***LDC***)**
**CHARACTER*1** *TRANSA***,***TRANSB*
**INTEGER** *M***,***N***,***K***,***LDA***,***LDB***,***LDC*
**COMPLEX*16** *ALPHA***,***BETA*
**COMPLEX*16** *A***(***LDA***,*), ***B***(***LDB***,*), ***C***(***LDC***,*)**

### Description

The **SGEMM**, **DGEMM**, **CGEMM**, or **ZGEMM** subroutine performs one of the matrix-matrix operations:

`C`` := alpha * op( ``A`` ) * op( ``B`` ) + beta * ``C`

where op( X ) is one of op( X ) = X or op( X ) = X',alpha and beta are scalars, and *A*, *B* and *C* are matrices, with op( *A* ) an *M* by *K* matrix, op( *B* ) a *K* by *N* matrix and *C* an *M* by *N* matrix.

### Parameters

*TRANSA* |
On entry, *TRANSA* specifies the form of op( *A* ) to be used in the matrix multiplication as follows:
*TRANSA* = 'N' or 'n' |
op( *A *) =* A* |
*TRANSA* = 'T' or 't' |
op( *A* ) = *A'* |
*TRANSA *= 'C' or 'c' |
op(* A *) =* A'* |
Unchanged on exit. |

*TRANSB* |
On entry, *TRANSB* specifies the form of op( *B* ) to be used in the matrix multiplication as follows:
*TRANSB* = 'N' or 'n' |
op(* B* ) = *B* |
*TRANSB* = 'T' or 't' |
op( B ) = B' |
*TRANSB* = 'C' or 'c' |
op(* B *) = *B*' |
Unchanged on exit. |

*M* |
On entry, *M *specifies the number of rows of the matrix op( *A* ) and of the matrix *C; M* must be at least 0; unchanged on exit. |

*N* |
On entry, *N* specifies the number of columns of the matrix op(* B* ) and the number of columns of the matrix *C*; *N* must be at least 0; unchanged on exit. |

*K* |
On entry, *K* specifies the number of columns of the matrix op( *A* ) and the number of rows of the matrix op(* B* );* K* must be at least 0; unchanged on exit. |

*ALPHA* |
On entry, *ALPHA* specifies the scalar alpha; unchanged on exit. |

*A* |
An array of dimension (* LDA*, *KA* ), where *KA* is *K* when *TRANSA* = 'N' or 'n', and is *M* otherwise; on entry with *TRANSA* = 'N' or 'n', the leading *M* by *K* part of the array *A* must contain the matrix *A*, otherwise the leading *K* by *M* part of the array *A* must contain the matrix *A*; unchanged on exit. |

*LDA* |
On entry, *LDA* specifies the first dimension of *A* as declared in the calling (sub) program. When *TRANSA* = 'N' or 'n' then* LDA* must be at least max( 1, *M* ), otherwise* LDA* must be at least max( 1, *K* ); unchanged on exit. |

*B* |
An array of dimension ( *LDB*, *KB* ) where *KB* is *N* when *TRANSB* = 'N' or 'n', and is *K* otherwise; on entry with *TRANSB* = 'N' or 'n', the leading *K* by *N* part of the array *B* must contain the matrix* B*, otherwise the leading *N* by *K* part of the array *B* must contain the matrix* B*; unchanged on exit. |

*LDB* |
On entry, *LDB* specifies the first dimension of *B* as declared in the calling (sub) program. When *TRANSB* = 'N' or 'n' then *LDB* must be at least max( 1, *K* ), otherwise *LDB* must be at least max( 1, *N* ); unchanged on exit. |

*BETA* |
On entry, *BETA* specifies the scalar beta. When *BETA* is supplied as 0 then* C* need not be set on input; unchanged on exit. |

*C* |
An array of dimension ( *LDC*, *N* ); on entry, the leading *M* by *N* part of the array *C* must contain the matrix *C*, except when beta is 0, in which case* C* need not be set on entry; on exit, the array *C* is overwritten by the *M* by *N* matrix ( alpha * op( *A* ) * op(* B* ) + beta * *C* ). |

*LDC* |
On entry, *LDC* specifies the first dimension of *C* as declared in the calling (sub) program; *LDC* must be at least max( 1, *M* ); unchanged on exit. |

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