clartg.f

          SUBROUTINE CLARTG( F, G, CS, SN, R )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          REAL               CS
          COMPLEX            F, G, R, SN
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CLARTG generates a plane rotation so that
    *
    *     [  CS  SN  ]     [ F ]     [ R ]
    *     [  __      ]  .  [   ]  =  [   ]   where CS**2 + |SN|**2 = 1.
    *     [ -SN  CS  ]     [ G ]     [ 0 ]
    *
    *  This is a faster version of the BLAS1 routine CROTG, except for
    *  the following differences:
    *     F and G are unchanged on return.
    *     If G=0, then CS=1 and SN=0.
    *     If F=0, then CS=0 and SN is chosen so that R is real.
    *
    *  Arguments
    *  =========
    *
    *  F       (input) COMPLEX
    *          The first component of vector to be rotated.
    *
    *  G       (input) COMPLEX
    *          The second component of vector to be rotated.
    *
    *  CS      (output) REAL
    *          The cosine of the rotation.
    *
    *  SN      (output) COMPLEX
    *          The sine of the rotation.
    *
    *  R       (output) COMPLEX
    *          The nonzero component of the rotated vector.
    *
    *  Further Details
    *  ======= =======
    *
    *  3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel
    *
    *  This version has a few statements commented out for thread safety
    *  (machine parameters are computed on each entry). 10 feb 03, SJH.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               TWO, ONE, ZERO
          PARAMETER          ( TWO = 2.0E+0, ONE = 1.0E+0, ZERO = 0.0E+0 )
          COMPLEX            CZERO
          PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
    *     LOGICAL            FIRST
          INTEGER            COUNT, I
          REAL               D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN,
         $                   SAFMN2, SAFMX2, SCALE
          COMPLEX            FF, FS, GS
    *     ..
    *     .. External Functions ..
          REAL               SLAMCH, SLAPY2
          EXTERNAL           SLAMCH, SLAPY2
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, AIMAG, CMPLX, CONJG, INT, LOG, MAX, REAL,
         $                   SQRT
    *     ..
    *     .. Statement Functions ..
          REAL               ABS1, ABSSQ
    *     ..
    *     .. Save statement ..
    *     SAVE               FIRST, SAFMX2, SAFMIN, SAFMN2
    *     ..
    *     .. Data statements ..
    *     DATA               FIRST / .TRUE. /
    *     ..
    *     .. Statement Function definitions ..
          ABS1( FF ) = MAX( ABS( REAL( FF ) ), ABS( AIMAG( FF ) ) )
          ABSSQ( FF ) = REAL( FF )**2 + AIMAG( FF )**2
    *     ..
    *     .. Executable Statements ..
    *
    *     IF( FIRST ) THEN
             SAFMIN = SLAMCH( 'S' )
             EPS = SLAMCH( 'E' )
             SAFMN2 = SLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
         $            LOG( SLAMCH( 'B' ) ) / TWO )
             SAFMX2 = ONE / SAFMN2
    *        FIRST = .FALSE.
    *     END IF
          SCALE = MAX( ABS1( F ), ABS1( G ) )
          FS = F
          GS = G
          COUNT = 0
          IF( SCALE.GE.SAFMX2 ) THEN
       10    CONTINUE
             COUNT = COUNT + 1
             FS = FS*SAFMN2
             GS = GS*SAFMN2
             SCALE = SCALE*SAFMN2
             IF( SCALE.GE.SAFMX2 )
         $      GO TO 10
          ELSE IF( SCALE.LE.SAFMN2 ) THEN
             IF( G.EQ.CZERO ) THEN
                CS = ONE
                SN = CZERO
                R = F
                RETURN
             END IF
       20    CONTINUE
             COUNT = COUNT - 1
             FS = FS*SAFMX2
             GS = GS*SAFMX2
             SCALE = SCALE*SAFMX2
             IF( SCALE.LE.SAFMN2 )
         $      GO TO 20
          END IF
          F2 = ABSSQ( FS )
          G2 = ABSSQ( GS )
          IF( F2.LE.MAX( G2, ONE )*SAFMIN ) THEN
    *
    *        This is a rare case: F is very small.
    *
             IF( F.EQ.CZERO ) THEN
                CS = ZERO
                R = SLAPY2( REAL( G ), AIMAG( G ) )
    *           Do complex/real division explicitly with two real divisions
                D = SLAPY2( REAL( GS ), AIMAG( GS ) )
                SN = CMPLX( REAL( GS ) / D, -AIMAG( GS ) / D )
                RETURN
             END IF
             F2S = SLAPY2( REAL( FS ), AIMAG( FS ) )
    *        G2 and G2S are accurate
    *        G2 is at least SAFMIN, and G2S is at least SAFMN2
             G2S = SQRT( G2 )
    *        Error in CS from underflow in F2S is at most
    *        UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS
    *        If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN,
    *        and so CS .lt. sqrt(SAFMIN)
    *        If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN
    *        and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS)
    *        Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S
             CS = F2S / G2S
    *        Make sure abs(FF) = 1
    *        Do complex/real division explicitly with 2 real divisions
             IF( ABS1( F ).GT.ONE ) THEN
                D = SLAPY2( REAL( F ), AIMAG( F ) )
                FF = CMPLX( REAL( F ) / D, AIMAG( F ) / D )
             ELSE
                DR = SAFMX2*REAL( F )
                DI = SAFMX2*AIMAG( F )
                D = SLAPY2( DR, DI )
                FF = CMPLX( DR / D, DI / D )
             END IF
             SN = FF*CMPLX( REAL( GS ) / G2S, -AIMAG( GS ) / G2S )
             R = CS*F + SN*G
          ELSE
    *
    *        This is the most common case.
    *        Neither F2 nor F2/G2 are less than SAFMIN
    *        F2S cannot overflow, and it is accurate
    *
             F2S = SQRT( ONE+G2 / F2 )
    *        Do the F2S(real)*FS(complex) multiply with two real multiplies
             R = CMPLX( F2S*REAL( FS ), F2S*AIMAG( FS ) )
             CS = ONE / F2S
             D = F2 + G2
    *        Do complex/real division explicitly with two real divisions
             SN = CMPLX( REAL( R ) / D, AIMAG( R ) / D )
             SN = SN*CONJG( GS )
             IF( COUNT.NE.0 ) THEN
                IF( COUNT.GT.0 ) THEN
                   DO 30 I = 1, COUNT
                      R = R*SAFMX2
       30          CONTINUE
                ELSE
                   DO 40 I = 1, -COUNT
                      R = R*SAFMN2
       40          CONTINUE
                END IF
             END IF
          END IF
          RETURN
    *
    *     End of CLARTG
    *
          END