[136] | 1 | *> \brief \b DLARFG
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| 2 | *
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| 3 | * =========== DOCUMENTATION ===========
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| 4 | *
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| 5 | * Online html documentation available at
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| 6 | * http://www.netlib.org/lapack/explore-html/
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| 7 | *
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| 8 | *> \htmlonly
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| 9 | *> Download DLARFG + dependencies
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| 10 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfg.f">
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| 11 | *> [TGZ]</a>
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| 12 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfg.f">
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| 13 | *> [ZIP]</a>
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| 14 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfg.f">
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| 15 | *> [TXT]</a>
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| 16 | *> \endhtmlonly
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| 17 | *
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| 18 | * Definition:
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| 19 | * ===========
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| 20 | *
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| 21 | * SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
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| 22 | *
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| 23 | * .. Scalar Arguments ..
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| 24 | * INTEGER INCX, N
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| 25 | * DOUBLE PRECISION ALPHA, TAU
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| 26 | * ..
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| 27 | * .. Array Arguments ..
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| 28 | * DOUBLE PRECISION X( * )
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| 29 | * ..
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| 30 | *
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| 31 | *
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| 32 | *> \par Purpose:
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| 33 | * =============
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| 34 | *>
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| 35 | *> \verbatim
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| 36 | *>
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| 37 | *> DLARFG generates a real elementary reflector H of order n, such
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| 38 | *> that
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| 39 | *>
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| 40 | *> H * ( alpha ) = ( beta ), H**T * H = I.
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| 41 | *> ( x ) ( 0 )
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| 42 | *>
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| 43 | *> where alpha and beta are scalars, and x is an (n-1)-element real
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| 44 | *> vector. H is represented in the form
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| 45 | *>
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| 46 | *> H = I - tau * ( 1 ) * ( 1 v**T ) ,
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| 47 | *> ( v )
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| 48 | *>
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| 49 | *> where tau is a real scalar and v is a real (n-1)-element
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| 50 | *> vector.
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| 51 | *>
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| 52 | *> If the elements of x are all zero, then tau = 0 and H is taken to be
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| 53 | *> the unit matrix.
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| 54 | *>
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| 55 | *> Otherwise 1 <= tau <= 2.
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| 56 | *> \endverbatim
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| 57 | *
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| 58 | * Arguments:
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| 59 | * ==========
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| 60 | *
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| 61 | *> \param[in] N
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| 62 | *> \verbatim
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| 63 | *> N is INTEGER
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| 64 | *> The order of the elementary reflector.
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| 65 | *> \endverbatim
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| 66 | *>
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| 67 | *> \param[in,out] ALPHA
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| 68 | *> \verbatim
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| 69 | *> ALPHA is DOUBLE PRECISION
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| 70 | *> On entry, the value alpha.
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| 71 | *> On exit, it is overwritten with the value beta.
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| 72 | *> \endverbatim
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| 73 | *>
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| 74 | *> \param[in,out] X
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| 75 | *> \verbatim
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| 76 | *> X is DOUBLE PRECISION array, dimension
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| 77 | *> (1+(N-2)*abs(INCX))
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| 78 | *> On entry, the vector x.
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| 79 | *> On exit, it is overwritten with the vector v.
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| 80 | *> \endverbatim
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| 81 | *>
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| 82 | *> \param[in] INCX
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| 83 | *> \verbatim
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| 84 | *> INCX is INTEGER
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| 85 | *> The increment between elements of X. INCX > 0.
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| 86 | *> \endverbatim
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| 87 | *>
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| 88 | *> \param[out] TAU
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| 89 | *> \verbatim
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| 90 | *> TAU is DOUBLE PRECISION
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| 91 | *> The value tau.
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| 92 | *> \endverbatim
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| 93 | *
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| 94 | * Authors:
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| 95 | * ========
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| 96 | *
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| 97 | *> \author Univ. of Tennessee
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| 98 | *> \author Univ. of California Berkeley
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| 99 | *> \author Univ. of Colorado Denver
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| 100 | *> \author NAG Ltd.
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| 101 | *
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| 102 | *> \date November 2011
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| 103 | *
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| 104 | *> \ingroup doubleOTHERauxiliary
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| 105 | *
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| 106 | * =====================================================================
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| 107 | SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
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| 108 | *
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| 109 | * -- LAPACK auxiliary routine (version 3.4.0) --
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| 110 | * -- LAPACK is a software package provided by Univ. of Tennessee, --
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| 111 | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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| 112 | * November 2011
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| 113 | *
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| 114 | * .. Scalar Arguments ..
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| 115 | INTEGER INCX, N
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| 116 | DOUBLE PRECISION ALPHA, TAU
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| 117 | * ..
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| 118 | * .. Array Arguments ..
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| 119 | DOUBLE PRECISION X( * )
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| 120 | * ..
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| 121 | *
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| 122 | * =====================================================================
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| 123 | *
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| 124 | * .. Parameters ..
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| 125 | DOUBLE PRECISION ONE, ZERO
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| 126 | PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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| 127 | * ..
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| 128 | * .. Local Scalars ..
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| 129 | INTEGER J, KNT
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| 130 | DOUBLE PRECISION BETA, RSAFMN, SAFMIN, XNORM
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| 131 | * ..
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| 132 | * .. External Functions ..
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| 133 | DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2
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| 134 | EXTERNAL DLAMCH, DLAPY2, DNRM2
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| 135 | * ..
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| 136 | * .. Intrinsic Functions ..
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| 137 | INTRINSIC ABS, SIGN
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| 138 | * ..
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| 139 | * .. External Subroutines ..
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| 140 | EXTERNAL DSCAL
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| 141 | * ..
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| 142 | * .. Executable Statements ..
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| 143 | *
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| 144 | IF( N.LE.1 ) THEN
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| 145 | TAU = ZERO
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| 146 | RETURN
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| 147 | END IF
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| 148 | *
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| 149 | XNORM = DNRM2( N-1, X, INCX )
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| 150 | *
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| 151 | IF( XNORM.EQ.ZERO ) THEN
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| 152 | *
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| 153 | * H = I
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| 154 | *
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| 155 | TAU = ZERO
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| 156 | ELSE
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| 157 | *
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| 158 | * general case
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| 159 | *
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| 160 | BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA )
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| 161 | SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' )
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| 162 | KNT = 0
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| 163 | IF( ABS( BETA ).LT.SAFMIN ) THEN
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| 164 | *
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| 165 | * XNORM, BETA may be inaccurate; scale X and recompute them
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| 166 | *
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| 167 | RSAFMN = ONE / SAFMIN
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| 168 | 10 CONTINUE
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| 169 | KNT = KNT + 1
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| 170 | CALL DSCAL( N-1, RSAFMN, X, INCX )
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| 171 | BETA = BETA*RSAFMN
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| 172 | ALPHA = ALPHA*RSAFMN
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| 173 | IF( ABS( BETA ).LT.SAFMIN )
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| 174 | $ GO TO 10
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| 175 | *
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| 176 | * New BETA is at most 1, at least SAFMIN
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| 177 | *
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| 178 | XNORM = DNRM2( N-1, X, INCX )
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| 179 | BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA )
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| 180 | END IF
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| 181 | TAU = ( BETA-ALPHA ) / BETA
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| 182 | CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )
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| 183 | *
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| 184 | * If ALPHA is subnormal, it may lose relative accuracy
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| 185 | *
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| 186 | DO 20 J = 1, KNT
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| 187 | BETA = BETA*SAFMIN
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| 188 | 20 CONTINUE
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| 189 | ALPHA = BETA
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| 190 | END IF
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| 191 | *
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| 192 | RETURN
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| 193 | *
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| 194 | * End of DLARFG
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| 195 | *
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| 196 | END
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