      SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )
*
*  -- LAPACK routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            I
      DOUBLE PRECISION   DLAM, RHO
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   D( 2 ), DELTA( 2 ), Z( 2 )
*     ..
*
*  Purpose
*  =======
*
*  This subroutine computes the I-th eigenvalue of a symmetric rank-one
*  modification of a 2-by-2 diagonal matrix
*
*             diag( D )  +  RHO *  Z * transpose(Z) .
*
*  The diagonal elements in the array D are assumed to satisfy
*
*             D(i) < D(j)  for  i < j .
*
*  We also assume RHO > 0 and that the Euclidean norm of the vector
*  Z is one.
*
*  Arguments
*  =========
*
*  I      (input) INTEGER
*         The index of the eigenvalue to be computed.  I = 1 or I = 2.
*
*  D      (input) DOUBLE PRECISION array, dimension (2)
*         The original eigenvalues.  We assume D(1) < D(2).
*
*  Z      (input) DOUBLE PRECISION array, dimension (2)
*         The components of the updating vector.
*
*  DELTA  (output) DOUBLE PRECISION array, dimension (2)
*         The vector DELTA contains the information necessary
*         to construct the eigenvectors.
*
*  RHO    (input) DOUBLE PRECISION
*         The scalar in the symmetric updating formula.
*
*  DLAM   (output) DOUBLE PRECISION
*         The computed lambda_I, the I-th updated eigenvalue.
*
*  Further Details
*  ===============
*
*  Based on contributions by
*     Ren-Cang Li, Computer Science Division, University of California
*     at Berkeley, USA
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE, TWO, FOUR
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
     $                   FOUR = 4.0D0 )
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION   B, C, DEL, TAU, TEMP, W
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, SQRT
*     ..
*     .. Executable Statements ..
*
      DEL = D( 2 ) - D( 1 )
      IF( I.EQ.1 ) THEN
         W = ONE + TWO*RHO*( Z( 2 )*Z( 2 )-Z( 1 )*Z( 1 ) ) / DEL
         IF( W.GT.ZERO ) THEN
            B = DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) )
            C = RHO*Z( 1 )*Z( 1 )*DEL
*
*           B > ZERO, always
*
            TAU = TWO*C / ( B+SQRT( ABS( B*B-FOUR*C ) ) )
            DLAM = D( 1 ) + TAU
            DELTA( 1 ) = -Z( 1 ) / TAU
            DELTA( 2 ) = Z( 2 ) / ( DEL-TAU )
         ELSE
            B = -DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) )
            C = RHO*Z( 2 )*Z( 2 )*DEL
            IF( B.GT.ZERO ) THEN
               TAU = -TWO*C / ( B+SQRT( B*B+FOUR*C ) )
            ELSE
               TAU = ( B-SQRT( B*B+FOUR*C ) ) / TWO
            END IF
            DLAM = D( 2 ) + TAU
            DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU )
            DELTA( 2 ) = -Z( 2 ) / TAU
         END IF
         TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) )
         DELTA( 1 ) = DELTA( 1 ) / TEMP
         DELTA( 2 ) = DELTA( 2 ) / TEMP
      ELSE
*
*     Now I=2
*
         B = -DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) )
         C = RHO*Z( 2 )*Z( 2 )*DEL
         IF( B.GT.ZERO ) THEN
            TAU = ( B+SQRT( B*B+FOUR*C ) ) / TWO
         ELSE
            TAU = TWO*C / ( -B+SQRT( B*B+FOUR*C ) )
         END IF
         DLAM = D( 2 ) + TAU
         DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU )
         DELTA( 2 ) = -Z( 2 ) / TAU
         TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) )
         DELTA( 1 ) = DELTA( 1 ) / TEMP
         DELTA( 2 ) = DELTA( 2 ) / TEMP
      END IF
      RETURN
*
*     End OF DLAED5
*
      END
