*DECK DSYR2 SUBROUTINE DSYR2 (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA) C***BEGIN PROLOGUE DSYR2 C***PURPOSE Perform the symmetric rank 2 operation. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B4 C***TYPE DOUBLE PRECISION (SSYR2-S, DSYR2-D, CSYR2-C) C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA C***AUTHOR Dongarra, J. J., (ANL) C Du Croz, J., (NAG) C Hammarling, S., (NAG) C Hanson, R. J., (SNLA) C***DESCRIPTION C C DSYR2 performs the symmetric rank 2 operation C C A := alpha*x*y' + alpha*y*x' + A, C C where alpha is a scalar, x and y are n element vectors and A is an n C by n symmetric matrix. C C Parameters C ========== C C UPLO - CHARACTER*1. C On entry, UPLO specifies whether the upper or lower C triangular part of the array A is to be referenced as C follows: C C UPLO = 'U' or 'u' Only the upper triangular part of A C is to be referenced. C C UPLO = 'L' or 'l' Only the lower triangular part of A C is to be referenced. C C Unchanged on exit. C C N - INTEGER. C On entry, N specifies the order of the matrix A. 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 X - DOUBLE PRECISION array of dimension at least C ( 1 + ( n - 1)*abs( INCX)). C Before entry, the incremented array X must contain the n C element vector x. C Unchanged on exit. C C INCX - INTEGER. C On entry, INCX specifies the increment for the elements of C X. INCX must not be zero. C Unchanged on exit. C C Y - DOUBLE PRECISION array of dimension at least C ( 1 + ( n - 1 )*abs( INCY ) ). C Before entry, the incremented array Y must contain the n C element vector y. C Unchanged on exit. C C INCY - INTEGER. C On entry, INCY specifies the increment for the elements of C Y. INCY must not be zero. C Unchanged on exit. C C A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). C Before entry with UPLO = 'U' or 'u', the leading n by n C upper triangular part of the array A must contain the upper C triangular part of the symmetric matrix and the strictly C lower triangular part of A is not referenced. On exit, the C upper triangular part of the array A is overwritten by the C upper triangular part of the updated matrix. C Before entry with UPLO = 'L' or 'l', the leading n by n C lower triangular part of the array A must contain the lower C triangular part of the symmetric matrix and the strictly C upper triangular part of A is not referenced. On exit, the C lower triangular part of the array A is overwritten by the C lower triangular part of the updated matrix. C C LDA - INTEGER. C On entry, LDA specifies the first dimension of A as declared C in the calling (sub) program. LDA must be at least C max( 1, n ). C Unchanged on exit. C C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and C Hanson, R. J. An extended set of Fortran basic linear C algebra subprograms. ACM TOMS, Vol. 14, No. 1, C pp. 1-17, March 1988. C***ROUTINES CALLED LSAME, XERBLA C***REVISION HISTORY (YYMMDD) C 861022 DATE WRITTEN C 910605 Modified to meet SLATEC prologue standards. Only comment C lines were modified. (BKS) C***END PROLOGUE DSYR2 C .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO C .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) C .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) C .. Local Scalars .. DOUBLE PRECISION TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY C .. External Functions .. LOGICAL LSAME EXTERNAL LSAME C .. External Subroutines .. EXTERNAL XERBLA C .. Intrinsic Functions .. INTRINSIC MAX C***FIRST EXECUTABLE STATEMENT DSYR2 C C Test the input parameters. C INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. $ .NOT.LSAME( UPLO, 'L' ) )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, N ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSYR2 ', INFO ) RETURN END IF C C Quick return if possible. C IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN C C Set up the start points in X and Y if the increments are not both C unity. C IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF JX = KX JY = KY END IF C C Start the operations. In this version the elements of A are C accessed sequentially with one pass through the triangular part C of A. C IF( LSAME( UPLO, 'U' ) )THEN C C Form A when A is stored in the upper triangle. C IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) DO 10, I = 1, J A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 10 CONTINUE END IF 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = KX IY = KY DO 30, I = 1, J A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE END IF JX = JX + INCX JY = JY + INCY 40 CONTINUE END IF ELSE C C Form A when A is stored in the lower triangle. C IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) DO 50, I = J, N A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2 50 CONTINUE END IF 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = JX IY = JY DO 70, I = J, N A( I, J ) = A( I, J ) + X( IX )*TEMP1 $ + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF END IF C RETURN C C End of DSYR2 . C END