dlartg.f

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      SUBROUTINE dlartg( F, G, CS, SN, R )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     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