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Annotation of rpl/lapack/lapack/zlarfg.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )
        !             2: *
        !             3: *  -- LAPACK auxiliary routine (version 3.2) --
        !             4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             6: *     November 2006
        !             7: *
        !             8: *     .. Scalar Arguments ..
        !             9:       INTEGER            INCX, N
        !            10:       COMPLEX*16         ALPHA, TAU
        !            11: *     ..
        !            12: *     .. Array Arguments ..
        !            13:       COMPLEX*16         X( * )
        !            14: *     ..
        !            15: *
        !            16: *  Purpose
        !            17: *  =======
        !            18: *
        !            19: *  ZLARFG generates a complex elementary reflector H of order n, such
        !            20: *  that
        !            21: *
        !            22: *        H' * ( alpha ) = ( beta ),   H' * H = I.
        !            23: *             (   x   )   (   0  )
        !            24: *
        !            25: *  where alpha and beta are scalars, with beta real, and x is an
        !            26: *  (n-1)-element complex vector. H is represented in the form
        !            27: *
        !            28: *        H = I - tau * ( 1 ) * ( 1 v' ) ,
        !            29: *                      ( v )
        !            30: *
        !            31: *  where tau is a complex scalar and v is a complex (n-1)-element
        !            32: *  vector. Note that H is not hermitian.
        !            33: *
        !            34: *  If the elements of x are all zero and alpha is real, then tau = 0
        !            35: *  and H is taken to be the unit matrix.
        !            36: *
        !            37: *  Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .
        !            38: *
        !            39: *  Arguments
        !            40: *  =========
        !            41: *
        !            42: *  N       (input) INTEGER
        !            43: *          The order of the elementary reflector.
        !            44: *
        !            45: *  ALPHA   (input/output) COMPLEX*16
        !            46: *          On entry, the value alpha.
        !            47: *          On exit, it is overwritten with the value beta.
        !            48: *
        !            49: *  X       (input/output) COMPLEX*16 array, dimension
        !            50: *                         (1+(N-2)*abs(INCX))
        !            51: *          On entry, the vector x.
        !            52: *          On exit, it is overwritten with the vector v.
        !            53: *
        !            54: *  INCX    (input) INTEGER
        !            55: *          The increment between elements of X. INCX > 0.
        !            56: *
        !            57: *  TAU     (output) COMPLEX*16
        !            58: *          The value tau.
        !            59: *
        !            60: *  =====================================================================
        !            61: *
        !            62: *     .. Parameters ..
        !            63:       DOUBLE PRECISION   ONE, ZERO
        !            64:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
        !            65: *     ..
        !            66: *     .. Local Scalars ..
        !            67:       INTEGER            J, KNT
        !            68:       DOUBLE PRECISION   ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM
        !            69: *     ..
        !            70: *     .. External Functions ..
        !            71:       DOUBLE PRECISION   DLAMCH, DLAPY3, DZNRM2
        !            72:       COMPLEX*16         ZLADIV
        !            73:       EXTERNAL           DLAMCH, DLAPY3, DZNRM2, ZLADIV
        !            74: *     ..
        !            75: *     .. Intrinsic Functions ..
        !            76:       INTRINSIC          ABS, DBLE, DCMPLX, DIMAG, SIGN
        !            77: *     ..
        !            78: *     .. External Subroutines ..
        !            79:       EXTERNAL           ZDSCAL, ZSCAL
        !            80: *     ..
        !            81: *     .. Executable Statements ..
        !            82: *
        !            83:       IF( N.LE.0 ) THEN
        !            84:          TAU = ZERO
        !            85:          RETURN
        !            86:       END IF
        !            87: *
        !            88:       XNORM = DZNRM2( N-1, X, INCX )
        !            89:       ALPHR = DBLE( ALPHA )
        !            90:       ALPHI = DIMAG( ALPHA )
        !            91: *
        !            92:       IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN
        !            93: *
        !            94: *        H  =  I
        !            95: *
        !            96:          TAU = ZERO
        !            97:       ELSE
        !            98: *
        !            99: *        general case
        !           100: *
        !           101:          BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR )
        !           102:          SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' )
        !           103:          RSAFMN = ONE / SAFMIN
        !           104: *
        !           105:          KNT = 0
        !           106:          IF( ABS( BETA ).LT.SAFMIN ) THEN
        !           107: *
        !           108: *           XNORM, BETA may be inaccurate; scale X and recompute them
        !           109: *
        !           110:    10       CONTINUE
        !           111:             KNT = KNT + 1
        !           112:             CALL ZDSCAL( N-1, RSAFMN, X, INCX )
        !           113:             BETA = BETA*RSAFMN
        !           114:             ALPHI = ALPHI*RSAFMN
        !           115:             ALPHR = ALPHR*RSAFMN
        !           116:             IF( ABS( BETA ).LT.SAFMIN )
        !           117:      $         GO TO 10
        !           118: *
        !           119: *           New BETA is at most 1, at least SAFMIN
        !           120: *
        !           121:             XNORM = DZNRM2( N-1, X, INCX )
        !           122:             ALPHA = DCMPLX( ALPHR, ALPHI )
        !           123:             BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR )
        !           124:          END IF
        !           125:          TAU = DCMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA )
        !           126:          ALPHA = ZLADIV( DCMPLX( ONE ), ALPHA-BETA )
        !           127:          CALL ZSCAL( N-1, ALPHA, X, INCX )
        !           128: *
        !           129: *        If ALPHA is subnormal, it may lose relative accuracy
        !           130: *
        !           131:          DO 20 J = 1, KNT
        !           132:             BETA = BETA*SAFMIN
        !           133:  20      CONTINUE
        !           134:          ALPHA = BETA
        !           135:       END IF
        !           136: *
        !           137:       RETURN
        !           138: *
        !           139: *     End of ZLARFG
        !           140: *
        !           141:       END