[22] | 1 | *> \brief \b SLARFG |
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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 SLARFG + dependencies |
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| 10 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarfg.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/slarfg.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/slarfg.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 SLARFG( 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 | * REAL ALPHA, TAU |
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| 26 | * .. |
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| 27 | * .. Array Arguments .. |
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| 28 | * REAL 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 | *> SLARFG 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 REAL |
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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 REAL 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 REAL |
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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 realOTHERauxiliary |
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| 105 | * |
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| 106 | * ===================================================================== |
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| 107 | SUBROUTINE SLARFG( 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 | REAL ALPHA, TAU |
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| 117 | * .. |
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| 118 | * .. Array Arguments .. |
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| 119 | REAL 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 | REAL ONE, ZERO |
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| 126 | PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+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 | REAL BETA, RSAFMN, SAFMIN, XNORM |
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| 131 | * .. |
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| 132 | * .. External Functions .. |
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| 133 | REAL SLAMCH, SLAPY2, SNRM2 |
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| 134 | EXTERNAL SLAMCH, SLAPY2, SNRM2 |
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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 SSCAL |
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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 = SNRM2( 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( SLAPY2( ALPHA, XNORM ), ALPHA ) |
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| 161 | SAFMIN = SLAMCH( 'S' ) / SLAMCH( '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 SSCAL( 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 = SNRM2( N-1, X, INCX ) |
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| 179 | BETA = -SIGN( SLAPY2( 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 SSCAL( 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 SLARFG |
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| 195 | * |
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| 196 | END |
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