# zgemm (l) - Linux Manuals

## zgemm: performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C,

## NAME

ZGEMM - performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C,## SYNOPSIS

- SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)

- DOUBLE COMPLEX ALPHA,BETA

- INTEGER K,LDA,LDB,LDC,M,N

- CHARACTER TRANSA,TRANSB

- DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)

## PURPOSE

ZGEMM performs one of the matrix-matrix operations
where op( X ) is one of

op(

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.

## ARGUMENTS

TRANSA - CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows:

TRANSA = aqNaq or aqnaq, op( A ) = A.

TRANSA = aqTaq or aqtaq, op( A ) = Aaq.

TRANSA = aqCaq or aqcaq, op( A ) = conjg( Aaq ).

Unchanged on exit.

TRANSB - CHARACTER*1. On entry, TRANSB specifies the form of op( B ) to be used in the matrix multiplication as follows:

TRANSB = aqNaq or aqnaq, op( B ) = B.

TRANSB = aqTaq or aqtaq, op( B ) = Baq.

TRANSB = aqCaq or aqcaq, op( B ) = conjg( Baq ).

Unchanged on exit.

- M - INTEGER.
- On entry, M specifies the number of rows of the matrix op( A ) and of the matrix C. M must be at least zero. Unchanged on exit.
- N - INTEGER.
- 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 zero. Unchanged on exit.
- K - INTEGER.
- 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 zero. Unchanged on exit.
- ALPHA - COMPLEX*16 .
- On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
- A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
- k when TRANSA = aqNaq or aqnaq, and is m otherwise. Before entry with TRANSA = aqNaq or aqnaq, 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 - INTEGER.
- On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANSA = aqNaq or aqnaq then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ). Unchanged on exit.
- B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
- n when TRANSB = aqNaq or aqnaq, and is k otherwise. Before entry with TRANSB = aqNaq or aqnaq, 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 - INTEGER.
- On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANSB = aqNaq or aqnaq then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ). Unchanged on exit.
- BETA - COMPLEX*16 .
- On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. Unchanged on exit.
- C - COMPLEX*16 array of DIMENSION ( LDC, n ).
- Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, 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 - INTEGER.
- 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.

## FURTHER DETAILS

Level 3 Blas routine.
-- Written on 8-February-1989.

Jack Dongarra, Argonne National Laboratory.

Iain Duff, AERE Harwell.

Jeremy Du Croz, Numerical Algorithms Group Ltd.

Sven Hammarling, Numerical Algorithms Group Ltd.