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diff --git a/eigen/lapack/zlarfg.f b/eigen/lapack/zlarfg.f new file mode 100644 index 0000000..a90ae9f --- /dev/null +++ b/eigen/lapack/zlarfg.f @@ -0,0 +1,203 @@ +*> \brief \b ZLARFG +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLARFG + dependencies +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfg.f"> +*> [TGZ]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfg.f"> +*> [ZIP]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfg.f"> +*> [TXT]</a> +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) +* +* .. Scalar Arguments .. +* INTEGER INCX, N +* COMPLEX*16 ALPHA, TAU +* .. +* .. Array Arguments .. +* COMPLEX*16 X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLARFG generates a complex elementary reflector H of order n, such +*> that +*> +*> H**H * ( alpha ) = ( beta ), H**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**H ) , +*> ( 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 . +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the elementary reflector. +*> \endverbatim +*> +*> \param[in,out] ALPHA +*> \verbatim +*> ALPHA is COMPLEX*16 +*> On entry, the value alpha. +*> On exit, it is overwritten with the value beta. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX*16 array, dimension +*> (1+(N-2)*abs(INCX)) +*> On entry, the vector x. +*> On exit, it is overwritten with the vector v. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The increment between elements of X. INCX > 0. +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is COMPLEX*16 +*> The value tau. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX, N + COMPLEX*16 ALPHA, TAU +* .. +* .. Array Arguments .. + COMPLEX*16 X( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER J, KNT + DOUBLE PRECISION ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM +* .. +* .. External Functions .. + DOUBLE PRECISION DLAMCH, DLAPY3, DZNRM2 + COMPLEX*16 ZLADIV + EXTERNAL DLAMCH, DLAPY3, DZNRM2, ZLADIV +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, DCMPLX, DIMAG, SIGN +* .. +* .. External Subroutines .. + EXTERNAL ZDSCAL, ZSCAL +* .. +* .. Executable Statements .. +* + IF( N.LE.0 ) THEN + TAU = ZERO + RETURN + END IF +* + XNORM = DZNRM2( N-1, X, INCX ) + ALPHR = DBLE( ALPHA ) + ALPHI = DIMAG( ALPHA ) +* + IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN +* +* H = I +* + TAU = ZERO + ELSE +* +* general case +* + BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) + SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) + RSAFMN = ONE / SAFMIN +* + KNT = 0 + IF( ABS( BETA ).LT.SAFMIN ) THEN +* +* XNORM, BETA may be inaccurate; scale X and recompute them +* + 10 CONTINUE + KNT = KNT + 1 + CALL ZDSCAL( 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 = DZNRM2( N-1, X, INCX ) + ALPHA = DCMPLX( ALPHR, ALPHI ) + BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) + END IF + TAU = DCMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA ) + ALPHA = ZLADIV( DCMPLX( ONE ), ALPHA-BETA ) + CALL ZSCAL( N-1, ALPHA, X, INCX ) +* +* If ALPHA is subnormal, it may lose relative accuracy +* + DO 20 J = 1, KNT + BETA = BETA*SAFMIN + 20 CONTINUE + ALPHA = BETA + END IF +* + RETURN +* +* End of ZLARFG +* + END |