*DECK DSYMM
SUBROUTINE DSYMM (SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA,
$ C, LDC)
C***BEGIN PROLOGUE DSYMM
C***PURPOSE Perform one of the matrix-matrix operations.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B6
C***TYPE DOUBLE PRECISION (SSYMM-S, DSYMM-D, CSYMM-C)
C***KEYWORDS LEVEL 3 BLAS, LINEAR ALGEBRA
C***AUTHOR Dongarra, J., (ANL)
C Duff, I., (AERE)
C Du Croz, J., (NAG)
C Hammarling, S. (NAG)
C***DESCRIPTION
C
C DSYMM performs one of the matrix-matrix operations
C
C C := alpha*A*B + beta*C,
C
C or
C
C C := alpha*B*A + beta*C,
C
C where alpha and beta are scalars, A is a symmetric matrix and B and
C C are m by n matrices.
C
C Parameters
C ==========
C
C SIDE - CHARACTER*1.
C On entry, SIDE specifies whether the symmetric matrix A
C appears on the left or right in the operation as follows:
C
C SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
C
C SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
C
C Unchanged on exit.
C
C UPLO - CHARACTER*1.
C On entry, UPLO specifies whether the upper or lower
C triangular part of the symmetric matrix A is to be
C referenced as follows:
C
C UPLO = 'U' or 'u' Only the upper triangular part of the
C symmetric matrix is to be referenced.
C
C UPLO = 'L' or 'l' Only the lower triangular part of the
C symmetric matrix is to be referenced.
C
C Unchanged on exit.
C
C M - INTEGER.
C On entry, M specifies the number of rows of the matrix C.
C M must be at least zero.
C Unchanged on exit.
C
C N - INTEGER.
C On entry, N specifies the number of columns of the matrix C.
C N must be at least zero.
C Unchanged on exit.
C
C ALPHA - DOUBLE PRECISION.
C On entry, ALPHA specifies the scalar alpha.
C Unchanged on exit.
C
C A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
C m when SIDE = 'L' or 'l' and is n otherwise.
C Before entry with SIDE = 'L' or 'l', the m by m part of
C the array A must contain the symmetric matrix, such that
C when UPLO = 'U' or 'u', the leading m by m upper triangular
C part of the array A must contain the upper triangular part
C of the symmetric matrix and the strictly lower triangular
C part of A is not referenced, and when UPLO = 'L' or 'l',
C the leading m by m lower triangular part of the array A
C must contain the lower triangular part of the symmetric
C matrix and the strictly upper triangular part of A is not
C referenced.
C Before entry with SIDE = 'R' or 'r', the n by n part of
C the array A must contain the symmetric matrix, such that
C when UPLO = 'U' or 'u', the leading n by n upper triangular
C part of the array A must contain the upper triangular part
C of the symmetric matrix and the strictly lower triangular
C part of A is not referenced, and when UPLO = 'L' or 'l',
C the leading n by n lower triangular part of the array A
C must contain the lower triangular part of the symmetric
C matrix and the strictly upper triangular part of A is not
C referenced.
C Unchanged on exit.
C
C LDA - INTEGER.
C On entry, LDA specifies the first dimension of A as declared
C in the calling (sub) program. When SIDE = 'L' or 'l' then
C LDA must be at least max( 1, m ), otherwise LDA must be at
C least max( 1, n ).
C Unchanged on exit.
C
C B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
C Before entry, the leading m by n part of the array B must
C contain the matrix B.
C Unchanged on exit.
C
C LDB - INTEGER.
C On entry, LDB specifies the first dimension of B as declared
C in the calling (sub) program. LDB must be at least
C max( 1, m ).
C Unchanged on exit.
C
C BETA - DOUBLE PRECISION.
C On entry, BETA specifies the scalar beta. When BETA is
C supplied as zero then C need not be set on input.
C Unchanged on exit.
C
C C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
C Before entry, the leading m by n part of the array C must
C contain the matrix C, except when beta is zero, in which
C case C need not be set on entry.
C On exit, the array C is overwritten by the m by n updated
C matrix.
C
C LDC - INTEGER.
C On entry, LDC specifies the first dimension of C as declared
C in the calling (sub) program. LDC must be at least
C max( 1, m ).
C Unchanged on exit.
C
C***REFERENCES Dongarra, J., Du Croz, J., Duff, I., and Hammarling, S.
C A set of level 3 basic linear algebra subprograms.
C ACM TOMS, Vol. 16, No. 1, pp. 1-17, March 1990.
C***ROUTINES CALLED LSAME, XERBLA
C***REVISION HISTORY (YYMMDD)
C 890208 DATE WRITTEN
C 910605 Modified to meet SLATEC prologue standards. Only comment
C lines were modified. (BKS)
C***END PROLOGUE DSYMM
C .. Scalar Arguments ..
CHARACTER*1 SIDE, UPLO
INTEGER M, N, LDA, LDB, LDC
DOUBLE PRECISION ALPHA, BETA
C .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX
C .. Local Scalars ..
LOGICAL UPPER
INTEGER I, INFO, J, K, NROWA
DOUBLE PRECISION TEMP1, TEMP2
C .. Parameters ..
DOUBLE PRECISION ONE , ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
C***FIRST EXECUTABLE STATEMENT DSYMM
C
C Set NROWA as the number of rows of A.
C
IF( LSAME( SIDE, 'L' ) )THEN
NROWA = M
ELSE
NROWA = N
END IF
UPPER = LSAME( UPLO, 'U' )
C
C Test the input parameters.
C
INFO = 0
IF( ( .NOT.LSAME( SIDE, 'L' ) ).AND.
$ ( .NOT.LSAME( SIDE, 'R' ) ) )THEN
INFO = 1
ELSE IF( ( .NOT.UPPER ).AND.
$ ( .NOT.LSAME( UPLO, 'L' ) ) )THEN
INFO = 2
ELSE IF( M .LT.0 )THEN
INFO = 3
ELSE IF( N .LT.0 )THEN
INFO = 4
ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
INFO = 7
ELSE IF( LDB.LT.MAX( 1, M ) )THEN
INFO = 9
ELSE IF( LDC.LT.MAX( 1, M ) )THEN
INFO = 12
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'DSYMM ', INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
$ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
$ RETURN
C
C And when alpha.eq.zero.
C
IF( ALPHA.EQ.ZERO )THEN
IF( BETA.EQ.ZERO )THEN
DO 20, J = 1, N
DO 10, I = 1, M
C( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
ELSE
DO 40, J = 1, N
DO 30, I = 1, M
C( I, J ) = BETA*C( I, J )
30 CONTINUE
40 CONTINUE
END IF
RETURN
END IF
C
C Start the operations.
C
IF( LSAME( SIDE, 'L' ) )THEN
C
C Form C := alpha*A*B + beta*C.
C
IF( UPPER )THEN
DO 70, J = 1, N
DO 60, I = 1, M
TEMP1 = ALPHA*B( I, J )
TEMP2 = ZERO
DO 50, K = 1, I - 1
C( K, J ) = C( K, J ) + TEMP1 *A( K, I )
TEMP2 = TEMP2 + B( K, J )*A( K, I )
50 CONTINUE
IF( BETA.EQ.ZERO )THEN
C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2
ELSE
C( I, J ) = BETA *C( I, J ) +
$ TEMP1*A( I, I ) + ALPHA*TEMP2
END IF
60 CONTINUE
70 CONTINUE
ELSE
DO 100, J = 1, N
DO 90, I = M, 1, -1
TEMP1 = ALPHA*B( I, J )
TEMP2 = ZERO
DO 80, K = I + 1, M
C( K, J ) = C( K, J ) + TEMP1 *A( K, I )
TEMP2 = TEMP2 + B( K, J )*A( K, I )
80 CONTINUE
IF( BETA.EQ.ZERO )THEN
C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2
ELSE
C( I, J ) = BETA *C( I, J ) +
$ TEMP1*A( I, I ) + ALPHA*TEMP2
END IF
90 CONTINUE
100 CONTINUE
END IF
ELSE
C
C Form C := alpha*B*A + beta*C.
C
DO 170, J = 1, N
TEMP1 = ALPHA*A( J, J )
IF( BETA.EQ.ZERO )THEN
DO 110, I = 1, M
C( I, J ) = TEMP1*B( I, J )
110 CONTINUE
ELSE
DO 120, I = 1, M
C( I, J ) = BETA*C( I, J ) + TEMP1*B( I, J )
120 CONTINUE
END IF
DO 140, K = 1, J - 1
IF( UPPER )THEN
TEMP1 = ALPHA*A( K, J )
ELSE
TEMP1 = ALPHA*A( J, K )
END IF
DO 130, I = 1, M
C( I, J ) = C( I, J ) + TEMP1*B( I, K )
130 CONTINUE
140 CONTINUE
DO 160, K = J + 1, N
IF( UPPER )THEN
TEMP1 = ALPHA*A( J, K )
ELSE
TEMP1 = ALPHA*A( K, J )
END IF
DO 150, I = 1, M
C( I, J ) = C( I, J ) + TEMP1*B( I, K )
150 CONTINUE
160 CONTINUE
170 CONTINUE
END IF
C
RETURN
C
C End of DSYMM .
C
END