*
************************************************************************
*
SUBROUTINE ESSYMV( UPLO, N, ALPHA, A, LDA, X, INCX,
$ BETA, Y, INCY )
* .. Scalar Arguments ..
REAL ALPHA, BETA
INTEGER INCX, INCY, LDA, N
CHARACTER*1 UPLO
* .. Array Arguments ..
DOUBLE PRECISION Y( * )
REAL A( LDA, * ), X( * )
* ..
*
* Purpose
* =======
*
* ESSYMV 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. Additional precision arithmetic is
* used in the computation.
*
* 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 - REAL .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - REAL 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 - REAL 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 - REAL .
* 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. At least REAL arithmetic is used in
* the computation of 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 20-July-1986.
* Sven Hammarling, Nag Central Office.
* Richard Hanson, Sandia National Labs.
*
*
* .. Parameters ..
REAL ONE , ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+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, DBLE
* ..
* .. 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( 'ESSYMV', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
$ RETURN
*
* 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 and set up the start points in X and Y if
* the increments are not both unity.
*
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
IF( BETA.NE.ONE )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
END IF
ELSE
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
IF( BETA.NE.ONE )THEN
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 = DBLE( ALPHA )*X( J )
TEMP2 = ZERO
DO 50, I = 1, J - 1
Y( I ) = Y( I ) + TEMP1*A( I, J )
TEMP2 = TEMP2 + A( I, J )*DBLE( X( I ) )
50 CONTINUE
Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2
60 CONTINUE
ELSE
IX = KX - INCX
DO 80, J = 1, N
TEMP1 = DBLE( ALPHA )*X( IX + INCX )
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 )*DBLE( X( IX ) )
IX = IX + INCX
IY = IY + INCY
70 CONTINUE
Y( IY ) = Y( IY ) + TEMP1*A( J, J ) + ALPHA*TEMP2
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 = DBLE( 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 + DBLE( 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 = DBLE( 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 + DBLE( 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 ESSYMV.
*
END