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

SUBROUTINE DSYMM

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

CHARACTER*1 SIDE, UPLO

INTEGER M, N, LDA, LDB, LDC

DOUBLE PRECISION ALPHA, BETA

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

DSYMM 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.

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 - DOUBLE PRECISION.

On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

A - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION.

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 - DOUBLE PRECISION 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.