SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU ) * * -- LAPACK auxiliary routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INCX, N COMPLEX ALPHA, TAU * .. * .. Array Arguments .. COMPLEX X( * ) * .. * * Purpose * ======= * * CLARFG generates a complex elementary reflector H of order n, such * that * * H' * ( alpha ) = ( beta ), H' * H = I. * ( x ) ( 0 ) * * where alpha and beta are scalars, with beta real, and x is an * (n-1)-element complex vector. H is represented in the form * * H = I - tau * ( 1 ) * ( 1 v' ) , * ( v ) * * where tau is a complex scalar and v is a complex (n-1)-element * vector. Note that H is not hermitian. * * If the elements of x are all zero and alpha is real, then tau = 0 * and H is taken to be the unit matrix. * * Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . * * Arguments * ========= * * N (input) INTEGER * The order of the elementary reflector. * * ALPHA (input/output) COMPLEX * On entry, the value alpha. * On exit, it is overwritten with the value beta. * * X (input/output) COMPLEX array, dimension * (1+(N-2)*abs(INCX)) * On entry, the vector x. * On exit, it is overwritten with the vector v. * * INCX (input) INTEGER * The increment between elements of X. INCX > 0. * * TAU (output) COMPLEX * The value tau. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER J, KNT REAL ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM * .. * .. External Functions .. REAL SCNRM2, SLAMCH, SLAPY3 COMPLEX CLADIV EXTERNAL SCNRM2, SLAMCH, SLAPY3, CLADIV * .. * .. Intrinsic Functions .. INTRINSIC ABS, AIMAG, CMPLX, REAL, SIGN * .. * .. External Subroutines .. EXTERNAL CSCAL, CSSCAL * .. * .. Executable Statements .. * IF( N.LE.0 ) THEN TAU = ZERO RETURN END IF * XNORM = SCNRM2( N-1, X, INCX ) ALPHR = REAL( ALPHA ) ALPHI = AIMAG( ALPHA ) * IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN * * H = I * TAU = ZERO ELSE * * general case * BETA = -SIGN( SLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) SAFMIN = SLAMCH( 'S' ) / SLAMCH( 'E' ) RSAFMN = ONE / SAFMIN * IF( ABS( BETA ).LT.SAFMIN ) THEN * * XNORM, BETA may be inaccurate; scale X and recompute them * KNT = 0 10 CONTINUE KNT = KNT + 1 CALL CSSCAL( N-1, RSAFMN, X, INCX ) BETA = BETA*RSAFMN ALPHI = ALPHI*RSAFMN ALPHR = ALPHR*RSAFMN IF( ABS( BETA ).LT.SAFMIN ) \$ GO TO 10 * * New BETA is at most 1, at least SAFMIN * XNORM = SCNRM2( N-1, X, INCX ) ALPHA = CMPLX( ALPHR, ALPHI ) BETA = -SIGN( SLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) TAU = CMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA ) ALPHA = CLADIV( CMPLX( ONE ), ALPHA-BETA ) CALL CSCAL( N-1, ALPHA, X, INCX ) * * If ALPHA is subnormal, it may lose relative accuracy * ALPHA = BETA DO 20 J = 1, KNT ALPHA = ALPHA*SAFMIN 20 CONTINUE ELSE TAU = CMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA ) ALPHA = CLADIV( CMPLX( ONE ), ALPHA-BETA ) CALL CSCAL( N-1, ALPHA, X, INCX ) ALPHA = BETA END IF END IF * RETURN * * End of CLARFG * END