NAME
ZSYMM - perform one of the matrix-matrix operations C := alpha*A*B +
beta*C,
SYNOPSIS
SUBROUTINE ZSYMM ( SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C,
LDC )
CHARACTER*1 SIDE, UPLO
INTEGER M, N, LDA, LDB, LDC
COMPLEX*16 ALPHA, BETA
COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )
PURPOSE
ZSYMM performs one of the matrix-matrix operations
or
C := alpha*B*A + beta*C,
where alpha and beta are scalars, A is a symmetric matrix and B and C
are m by n matrices.
PARAMETERS
SIDE - CHARACTER*1.
On entry, SIDE specifies whether the symmetric matrix A
appears on the left or right in the operation as follows:
SIDE = ’L’ or ’l’ C := alpha*A*B + beta*C,
SIDE = ’R’ or ’r’ 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 symmetric matrix A is to be
referenced as follows:
UPLO = ’U’ or ’u’ Only the upper triangular part of the
symmetric matrix is to be referenced.
UPLO = ’L’ or ’l’ Only the lower triangular part of the
symmetric 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 = ’L’ or ’l’ and is n otherwise. Before entry
with SIDE = ’L’ or ’l’, the m by m part of the array A
must contain the symmetric matrix, such that when UPLO = ’U’
or ’u’, the leading m by m upper triangular part of the array A
must contain the upper triangular part of the symmetric matrix
and the strictly lower triangular part of A is not
referenced, and when UPLO = ’L’ or ’l’, the leading m by m
lower triangular part of the array A must contain the
lower triangular part of the symmetric matrix and the
strictly upper triangular part of A is not referenced. Before
entry with SIDE = ’R’ or ’r’, the n by n part of the array
A must contain the symmetric matrix, such that when UPLO =
’U’ or ’u’, the leading n by n upper triangular part of the
array A must contain the upper triangular part of the
symmetric matrix and the strictly lower triangular part of A
is not referenced, and when UPLO = ’L’ or ’l’, the leading n
by n lower triangular part of the array A must contain the
lower triangular part of the symmetric matrix and the
strictly upper triangular part of A is not referenced.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared in
the calling (sub) program. When SIDE = ’L’ or ’l’ 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.
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.