      SUBROUTINE DLARTG( F, G, CS, SN, R )
*
*  -- LAPACK auxiliary routine (version 2.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     September 30, 1994
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   CS, F, G, R, SN
*     ..
*
*  Purpose
*  =======
*
*  DLARTG generate a plane rotation so that
*
*     [  CS  SN  ]  .  [ F ]  =  [ R ]   where CS**2 + SN**2 = 1.
*     [ -SN  CS  ]     [ G ]     [ 0 ]
*
*  This is a slower, more accurate version of the BLAS1 routine DROTG,
*  with the following other differences:
*     F and G are unchanged on return.
*     If G=0, then CS=1 and SN=0.
*     If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any
*        floating point operations (saves work in DBDSQR when
*        there are zeros on the diagonal).
*
*  If F exceeds G in magnitude, CS will be positive.
*
*  Arguments
*  =========
*
*  F       (input) DOUBLE PRECISION
*          The first component of vector to be rotated.
*
*  G       (input) DOUBLE PRECISION
*          The second component of vector to be rotated.
*
*  CS      (output) DOUBLE PRECISION
*          The cosine of the rotation.
*
*  SN      (output) DOUBLE PRECISION
*          The sine of the rotation.
*
*  R       (output) DOUBLE PRECISION
*          The nonzero component of the rotated vector.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D0 )
      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D0 )
      DOUBLE PRECISION   TWO
      PARAMETER          ( TWO = 2.0D0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            FIRST
      INTEGER            COUNT, I
      DOUBLE PRECISION   EPS, F1, G1, SAFMIN, SAFMN2, SAFMX2, SCALE
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           DLAMCH
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, INT, LOG, MAX, SQRT
*     ..
*     .. Save statement ..
      SAVE               FIRST, SAFMX2, SAFMIN, SAFMN2
*     ..
*     .. Data statements ..
      DATA               FIRST / .TRUE. /
*     ..
*     .. Executable Statements ..
*
      IF( FIRST ) THEN
         FIRST = .FALSE.
         SAFMIN = DLAMCH( 'S' )
         EPS = DLAMCH( 'E' )
         SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
     $            LOG( DLAMCH( 'B' ) ) / TWO )
         SAFMX2 = ONE / SAFMN2
      END IF
      IF( G.EQ.ZERO ) THEN
         CS = ONE
         SN = ZERO
         R = F
      ELSE IF( F.EQ.ZERO ) THEN
         CS = ZERO
         SN = ONE
         R = G
      ELSE
         F1 = F
         G1 = G
         SCALE = MAX( ABS( F1 ), ABS( G1 ) )
         IF( SCALE.GE.SAFMX2 ) THEN
            COUNT = 0
   10       CONTINUE
            COUNT = COUNT + 1
            F1 = F1*SAFMN2
            G1 = G1*SAFMN2
            SCALE = MAX( ABS( F1 ), ABS( G1 ) )
            IF( SCALE.GE.SAFMX2 )
     $         GO TO 10
            R = SQRT( F1**2+G1**2 )
            CS = F1 / R
            SN = G1 / R
            DO 20 I = 1, COUNT
               R = R*SAFMX2
   20       CONTINUE
         ELSE IF( SCALE.LE.SAFMN2 ) THEN
            COUNT = 0
   30       CONTINUE
            COUNT = COUNT + 1
            F1 = F1*SAFMX2
            G1 = G1*SAFMX2
            SCALE = MAX( ABS( F1 ), ABS( G1 ) )
            IF( SCALE.LE.SAFMN2 )
     $         GO TO 30
            R = SQRT( F1**2+G1**2 )
            CS = F1 / R
            SN = G1 / R
            DO 40 I = 1, COUNT
               R = R*SAFMN2
   40       CONTINUE
         ELSE
            R = SQRT( F1**2+G1**2 )
            CS = F1 / R
            SN = G1 / R
         END IF
         IF( ABS( F ).GT.ABS( G ) .AND. CS.LT.ZERO ) THEN
            CS = -CS
            SN = -SN
            R = -R
         END IF
      END IF
      RETURN
*
*     End of DLARTG
*
      END
