# zhemm (l) - Linux Man Pages

## NAME

ZHEMM - performs one of the matrix-matrix operations C := alpha*A*B + beta*C,

## SYNOPSIS

SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)

DOUBLE COMPLEX ALPHA,BETA

INTEGER LDA,LDB,LDC,M,N

CHARACTER SIDE,UPLO

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

## PURPOSE

ZHEMM performs one of the matrix-matrix operations

or

C := alpha*B*A beta*C,

where alpha and beta are scalars, A is an hermitian matrix and B and C are m by n matrices.

## ARGUMENTS

SIDE - CHARACTER*1.
On entry, SIDE specifies whether the hermitian matrix A appears on the left or right in the operation as follows:

SIDE = aqLaq or aqlaq C := alpha*A*B + beta*C,

SIDE = aqRaq or aqraq C := alpha*B*A + beta*C,

Unchanged on exit.

UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower triangular part of the hermitian matrix A is to be referenced as follows:

UPLO = aqUaq or aquaq Only the upper triangular part of the hermitian matrix is to be referenced.

UPLO = aqLaq or aqlaq Only the lower triangular part of the hermitian matrix is to be referenced.

Unchanged on exit.

M - INTEGER.
On entry, M specifies the number of rows 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 C. N 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
m when SIDE = aqLaq or aqlaq and is n otherwise. Before entry with SIDE = aqLaq or aqlaq, the m by m part of the array A must contain the hermitian matrix, such that when UPLO = aqUaq or aquaq, the leading m by m upper triangular part of the array A must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of A is not referenced, and when UPLO = aqLaq or aqlaq, the leading m by m lower triangular part of the array A must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of A is not referenced. Before entry with SIDE = aqRaq or aqraq, the n by n part of the array A must contain the hermitian matrix, such that when UPLO = aqUaq or aquaq, the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of A is not referenced, and when UPLO = aqLaq or aqlaq, the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero. Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = aqLaq or aqlaq then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ). Unchanged on exit.
B - COMPLEX*16 array of DIMENSION ( LDB, n ).
Before entry, the leading m by n 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. LDB must be at least max( 1, m ). 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 updated matrix.
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.