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Annotation of rpl/lapack/lapack/zlarfg.f, revision 1.1.1.1

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