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196 lines
4.8 KiB
196 lines
4.8 KiB
*> \brief \b SLARFG |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download SLARFG + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarfg.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarfg.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarfg.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INCX, N |
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* REAL ALPHA, TAU |
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* .. |
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* .. Array Arguments .. |
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* REAL X( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> SLARFG generates a real elementary reflector H of order n, such |
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*> that |
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*> |
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*> H * ( alpha ) = ( beta ), H**T * H = I. |
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*> ( x ) ( 0 ) |
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*> |
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*> where alpha and beta are scalars, and x is an (n-1)-element real |
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*> vector. H is represented in the form |
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*> |
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*> H = I - tau * ( 1 ) * ( 1 v**T ) , |
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*> ( v ) |
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*> |
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*> where tau is a real scalar and v is a real (n-1)-element |
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*> vector. |
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*> |
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*> If the elements of x are all zero, then tau = 0 and H is taken to be |
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*> the unit matrix. |
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*> |
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*> Otherwise 1 <= tau <= 2. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the elementary reflector. |
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*> \endverbatim |
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*> |
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*> \param[in,out] ALPHA |
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*> \verbatim |
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*> ALPHA is REAL |
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*> On entry, the value alpha. |
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*> On exit, it is overwritten with the value beta. |
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*> \endverbatim |
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*> |
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*> \param[in,out] X |
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*> \verbatim |
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*> X is REAL array, dimension |
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*> (1+(N-2)*abs(INCX)) |
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*> On entry, the vector x. |
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*> On exit, it is overwritten with the vector v. |
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*> \endverbatim |
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*> |
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*> \param[in] INCX |
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*> \verbatim |
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*> INCX is INTEGER |
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*> The increment between elements of X. INCX > 0. |
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*> \endverbatim |
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*> |
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*> \param[out] TAU |
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*> \verbatim |
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*> TAU is REAL |
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*> The value tau. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup realOTHERauxiliary |
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* |
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* ===================================================================== |
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SUBROUTINE SLARFG( N, ALPHA, X, INCX, TAU ) |
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* |
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* -- LAPACK auxiliary routine (version 3.4.0) -- |
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* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2011 |
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* |
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* .. Scalar Arguments .. |
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INTEGER INCX, N |
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REAL ALPHA, TAU |
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* .. |
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* .. Array Arguments .. |
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REAL X( * ) |
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* .. |
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* |
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* ===================================================================== |
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* |
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* .. Parameters .. |
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REAL ONE, ZERO |
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) |
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* .. |
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* .. Local Scalars .. |
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INTEGER J, KNT |
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REAL BETA, RSAFMN, SAFMIN, XNORM |
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* .. |
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* .. External Functions .. |
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REAL SLAMCH, SLAPY2, SNRM2 |
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EXTERNAL SLAMCH, SLAPY2, SNRM2 |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC ABS, SIGN |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL SSCAL |
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* .. |
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* .. Executable Statements .. |
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* |
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IF( N.LE.1 ) THEN |
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TAU = ZERO |
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RETURN |
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END IF |
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* |
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XNORM = SNRM2( N-1, X, INCX ) |
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* |
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IF( XNORM.EQ.ZERO ) THEN |
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* |
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* H = I |
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* |
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TAU = ZERO |
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ELSE |
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* |
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* general case |
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* |
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BETA = -SIGN( SLAPY2( ALPHA, XNORM ), ALPHA ) |
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SAFMIN = SLAMCH( 'S' ) / SLAMCH( 'E' ) |
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KNT = 0 |
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IF( ABS( BETA ).LT.SAFMIN ) THEN |
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* |
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* XNORM, BETA may be inaccurate; scale X and recompute them |
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* |
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RSAFMN = ONE / SAFMIN |
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10 CONTINUE |
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KNT = KNT + 1 |
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CALL SSCAL( N-1, RSAFMN, X, INCX ) |
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BETA = BETA*RSAFMN |
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ALPHA = ALPHA*RSAFMN |
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IF( ABS( BETA ).LT.SAFMIN ) |
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$ GO TO 10 |
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* |
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* New BETA is at most 1, at least SAFMIN |
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* |
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XNORM = SNRM2( N-1, X, INCX ) |
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BETA = -SIGN( SLAPY2( ALPHA, XNORM ), ALPHA ) |
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END IF |
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TAU = ( BETA-ALPHA ) / BETA |
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CALL SSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX ) |
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* |
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* If ALPHA is subnormal, it may lose relative accuracy |
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* |
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DO 20 J = 1, KNT |
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BETA = BETA*SAFMIN |
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20 CONTINUE |
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ALPHA = BETA |
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END IF |
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* |
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RETURN |
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* |
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* End of SLARFG |
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* |
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END
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