SUBROUTINE DSYMV ( UPLO, N, ALPHA, A, LDA, X, INCX, & BETA, Y, INCY ) ! .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, LDA, N CHARACTER*1 UPLO ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) ! .. ! ! Purpose ! ======= ! ! DSYMV performs the matrix-vector operation ! ! y := alpha*A*x + beta*y, ! ! where alpha and beta are scalars, x and y are n element vectors and ! A is an n by n symmetric matrix. ! ! Parameters ! ========== ! ! UPLO - CHARACTER*1. ! On entry, UPLO specifies whether the upper or lower ! triangular part of the array A is to be referenced as ! follows: ! ! UPLO = 'U' or 'u' Only the upper triangular part of A ! is to be referenced. ! ! UPLO = 'L' or 'l' Only the lower triangular part of A ! is to be referenced. ! ! Unchanged on exit. ! ! N - INTEGER. ! On entry, N specifies the order of the matrix A. ! 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, n ). ! Before entry with 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. ! Before entry with 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. LDA must be at least ! max( 1, n ). ! Unchanged on exit. ! ! X - DOUBLE PRECISION array of dimension at least ! ( 1 + ( n - 1 )*abs( INCX ) ). ! Before entry, the incremented array X must contain the n ! element vector x. ! Unchanged on exit. ! ! INCX - INTEGER. ! On entry, INCX specifies the increment for the elements of ! X. INCX must not be zero. ! Unchanged on exit. ! ! BETA - DOUBLE PRECISION. ! On entry, BETA specifies the scalar beta. When BETA is ! supplied as zero then Y need not be set on input. ! Unchanged on exit. ! ! Y - DOUBLE PRECISION array of dimension at least ! ( 1 + ( n - 1 )*abs( INCY ) ). ! Before entry, the incremented array Y must contain the n ! element vector y. On exit, Y is overwritten by the updated ! vector y. ! ! INCY - INTEGER. ! On entry, INCY specifies the increment for the elements of ! Y. INCY must not be zero. ! Unchanged on exit. ! ! ! Level 2 Blas routine. ! ! -- Written on 22-October-1986. ! Jack Dongarra, Argonne National Lab. ! Jeremy Du Croz, Nag Central Office. ! Sven Hammarling, Nag Central Office. ! Richard Hanson, Sandia National Labs. ! ! ! .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) ! .. Local Scalars .. DOUBLE PRECISION TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY ! .. External Functions .. ! LOGICAL LSAME ! EXTERNAL LSAME ! .. External Subroutines .. ! EXTERNAL XERBLA ! .. Intrinsic Functions .. INTRINSIC MAX ! .. ! .. Executable Statements .. ! ! Test the input parameters. ! 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( LDA.LT.MAX( 1, N ) )THEN INFO = 5 ELSE IF( INCX.EQ.0 )THEN INFO = 7 ELSE IF( INCY.EQ.0 )THEN INFO = 10 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSYMV ', INFO ) RETURN END IF ! ! Quick return if possible. ! IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) & RETURN ! ! Set up the start points in X and Y. ! 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 ! ! Start the operations. In this version the elements of A are ! accessed sequentially with one pass through the triangular part ! of A. ! ! First form y := beta*y. ! IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) & RETURN IF( LSAME( UPLO, 'U' ) )THEN ! ! Form y when A is stored in upper triangle. ! IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO DO 50, I = 1, J - 1 Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO IX = KX IY = KY DO 70, I = 1, J - 1 Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF ELSE ! ! Form y when A is stored in lower triangle. ! IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*A( J, J ) DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*A( J, J ) IX = JX IY = JY DO 110, I = J + 1, N IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( I, J ) TEMP2 = TEMP2 + A( I, J )*X( IX ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF ! RETURN ! ! End of DSYMV . ! END SUBROUTINE DSYMV