dlasq6.f

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*> \brief \b DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
*                          DNM1, DNM2 )
*
*       .. Scalar Arguments ..
*       INTEGER            I0, N0, PP
*       DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   Z( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLASQ6 computes one dqd (shift equal to zero) transform in
*> ping-pong form, with protection against underflow and overflow.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] I0
*> \verbatim
*>          I0 is INTEGER
*>        First index.
*> \endverbatim
*>
*> \param[in] N0
*> \verbatim
*>          N0 is INTEGER
*>        Last index.
*> \endverbatim
*>
*> \param[in] Z
*> \verbatim
*>          Z is DOUBLE PRECISION array, dimension ( 4*N )
*>        Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
*>        an extra argument.
*> \endverbatim
*>
*> \param[in] PP
*> \verbatim
*>          PP is INTEGER
*>        PP=0 for ping, PP=1 for pong.
*> \endverbatim
*>
*> \param[out] DMIN
*> \verbatim
*>          DMIN is DOUBLE PRECISION
*>        Minimum value of d.
*> \endverbatim
*>
*> \param[out] DMIN1
*> \verbatim
*>          DMIN1 is DOUBLE PRECISION
*>        Minimum value of d, excluding D( N0 ).
*> \endverbatim
*>
*> \param[out] DMIN2
*> \verbatim
*>          DMIN2 is DOUBLE PRECISION
*>        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
*> \endverbatim
*>
*> \param[out] DN
*> \verbatim
*>          DN is DOUBLE PRECISION
*>        d(N0), the last value of d.
*> \endverbatim
*>
*> \param[out] DNM1
*> \verbatim
*>          DNM1 is DOUBLE PRECISION
*>        d(N0-1).
*> \endverbatim
*>
*> \param[out] DNM2
*> \verbatim
*>          DNM2 is DOUBLE PRECISION
*>        d(N0-2).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup lasq6
*
*  =====================================================================
      SUBROUTINE dlasq6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
     $                   DNM1, DNM2 )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            I0, N0, PP
      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   Z( * )
*     ..
*
*  =====================================================================
*
*     .. Parameter ..
      DOUBLE PRECISION   ZERO
      parameter( zero = 0.0d0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J4, J4P2
      DOUBLE PRECISION   D, EMIN, SAFMIN, TEMP
*     ..
*     .. External Function ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           dlamch
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          min
*     ..
*     .. Executable Statements ..
*
      IF( ( n0-i0-1 ).LE.0 )
     $   RETURN
*
      safmin = dlamch( 'Safe minimum' )
      j4 = 4*i0 + pp - 3
      emin = z( j4+4 )
      d = z( j4 )
      dmin = d
*
      IF( pp.EQ.0 ) THEN
         DO 10 j4 = 4*i0, 4*( n0-3 ), 4
            z( j4-2 ) = d + z( j4-1 )
            IF( z( j4-2 ).EQ.zero ) THEN
               z( j4 ) = zero
               d = z( j4+1 )
               dmin = d
               emin = zero
            ELSE IF( safmin*z( j4+1 ).LT.z( j4-2 ) .AND.
     $               safmin*z( j4-2 ).LT.z( j4+1 ) ) THEN
               temp = z( j4+1 ) / z( j4-2 )
               z( j4 ) = z( j4-1 )*temp
               d = d*temp
            ELSE
               z( j4 ) = z( j4+1 )*( z( j4-1 ) / z( j4-2 ) )
               d = z( j4+1 )*( d / z( j4-2 ) )
            END IF
            dmin = min( dmin, d )
            emin = min( emin, z( j4 ) )
   10    CONTINUE
      ELSE
         DO 20 j4 = 4*i0, 4*( n0-3 ), 4
            z( j4-3 ) = d + z( j4 )
            IF( z( j4-3 ).EQ.zero ) THEN
               z( j4-1 ) = zero
               d = z( j4+2 )
               dmin = d
               emin = zero
            ELSE IF( safmin*z( j4+2 ).LT.z( j4-3 ) .AND.
     $               safmin*z( j4-3 ).LT.z( j4+2 ) ) THEN
               temp = z( j4+2 ) / z( j4-3 )
               z( j4-1 ) = z( j4 )*temp
               d = d*temp
            ELSE
               z( j4-1 ) = z( j4+2 )*( z( j4 ) / z( j4-3 ) )
               d = z( j4+2 )*( d / z( j4-3 ) )
            END IF
            dmin = min( dmin, d )
            emin = min( emin, z( j4-1 ) )
   20    CONTINUE
      END IF
*
*     Unroll last two steps.
*
      dnm2 = d
      dmin2 = dmin
      j4 = 4*( n0-2 ) - pp
      j4p2 = j4 + 2*pp - 1
      z( j4-2 ) = dnm2 + z( j4p2 )
      IF( z( j4-2 ).EQ.zero ) THEN
         z( j4 ) = zero
         dnm1 = z( j4p2+2 )
         dmin = dnm1
         emin = zero
      ELSE IF( safmin*z( j4p2+2 ).LT.z( j4-2 ) .AND.
     $         safmin*z( j4-2 ).LT.z( j4p2+2 ) ) THEN
         temp = z( j4p2+2 ) / z( j4-2 )
         z( j4 ) = z( j4p2 )*temp
         dnm1 = dnm2*temp
      ELSE
         z( j4 ) = z( j4p2+2 )*( z( j4p2 ) / z( j4-2 ) )
         dnm1 = z( j4p2+2 )*( dnm2 / z( j4-2 ) )
      END IF
      dmin = min( dmin, dnm1 )
*
      dmin1 = dmin
      j4 = j4 + 4
      j4p2 = j4 + 2*pp - 1
      z( j4-2 ) = dnm1 + z( j4p2 )
      IF( z( j4-2 ).EQ.zero ) THEN
         z( j4 ) = zero
         dn = z( j4p2+2 )
         dmin = dn
         emin = zero
      ELSE IF( safmin*z( j4p2+2 ).LT.z( j4-2 ) .AND.
     $         safmin*z( j4-2 ).LT.z( j4p2+2 ) ) THEN
         temp = z( j4p2+2 ) / z( j4-2 )
         z( j4 ) = z( j4p2 )*temp
         dn = dnm1*temp
      ELSE
         z( j4 ) = z( j4p2+2 )*( z( j4p2 ) / z( j4-2 ) )
         dn = z( j4p2+2 )*( dnm1 / z( j4-2 ) )
      END IF
      dmin = min( dmin, dn )
*
      z( j4+2 ) = dn
      z( 4*n0-pp ) = emin
      RETURN
*
*     End of DLASQ6
*
      END