[136] | 1 | *> \brief \b CLARF
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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 CLARF + dependencies
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| 10 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clarf.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/clarf.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/clarf.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 CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
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| 22 | *
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| 23 | * .. Scalar Arguments ..
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| 24 | * CHARACTER SIDE
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| 25 | * INTEGER INCV, LDC, M, N
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| 26 | * COMPLEX TAU
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| 27 | * ..
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| 28 | * .. Array Arguments ..
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| 29 | * COMPLEX C( LDC, * ), V( * ), WORK( * )
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| 30 | * ..
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| 31 | *
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| 32 | *
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| 33 | *> \par Purpose:
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| 34 | * =============
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| 35 | *>
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| 36 | *> \verbatim
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| 37 | *>
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| 38 | *> CLARF applies a complex elementary reflector H to a complex M-by-N
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| 39 | *> matrix C, from either the left or the right. H is represented in the
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| 40 | *> form
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| 41 | *>
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| 42 | *> H = I - tau * v * v**H
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| 43 | *>
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| 44 | *> where tau is a complex scalar and v is a complex vector.
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| 45 | *>
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| 46 | *> If tau = 0, then H is taken to be the unit matrix.
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| 47 | *>
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| 48 | *> To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
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| 49 | *> tau.
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| 50 | *> \endverbatim
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| 51 | *
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| 52 | * Arguments:
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| 53 | * ==========
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| 54 | *
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| 55 | *> \param[in] SIDE
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| 56 | *> \verbatim
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| 57 | *> SIDE is CHARACTER*1
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| 58 | *> = 'L': form H * C
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| 59 | *> = 'R': form C * H
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| 60 | *> \endverbatim
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| 61 | *>
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| 62 | *> \param[in] M
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| 63 | *> \verbatim
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| 64 | *> M is INTEGER
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| 65 | *> The number of rows of the matrix C.
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| 66 | *> \endverbatim
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| 67 | *>
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| 68 | *> \param[in] N
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| 69 | *> \verbatim
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| 70 | *> N is INTEGER
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| 71 | *> The number of columns of the matrix C.
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| 72 | *> \endverbatim
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| 73 | *>
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| 74 | *> \param[in] V
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| 75 | *> \verbatim
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| 76 | *> V is COMPLEX array, dimension
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| 77 | *> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
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| 78 | *> or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
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| 79 | *> The vector v in the representation of H. V is not used if
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| 80 | *> TAU = 0.
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| 81 | *> \endverbatim
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| 82 | *>
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| 83 | *> \param[in] INCV
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| 84 | *> \verbatim
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| 85 | *> INCV is INTEGER
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| 86 | *> The increment between elements of v. INCV <> 0.
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| 87 | *> \endverbatim
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| 88 | *>
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| 89 | *> \param[in] TAU
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| 90 | *> \verbatim
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| 91 | *> TAU is COMPLEX
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| 92 | *> The value tau in the representation of H.
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| 93 | *> \endverbatim
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| 94 | *>
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| 95 | *> \param[in,out] C
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| 96 | *> \verbatim
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| 97 | *> C is COMPLEX array, dimension (LDC,N)
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| 98 | *> On entry, the M-by-N matrix C.
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| 99 | *> On exit, C is overwritten by the matrix H * C if SIDE = 'L',
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| 100 | *> or C * H if SIDE = 'R'.
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| 101 | *> \endverbatim
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| 102 | *>
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| 103 | *> \param[in] LDC
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| 104 | *> \verbatim
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| 105 | *> LDC is INTEGER
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| 106 | *> The leading dimension of the array C. LDC >= max(1,M).
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| 107 | *> \endverbatim
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| 108 | *>
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| 109 | *> \param[out] WORK
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| 110 | *> \verbatim
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| 111 | *> WORK is COMPLEX array, dimension
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| 112 | *> (N) if SIDE = 'L'
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| 113 | *> or (M) if SIDE = 'R'
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| 114 | *> \endverbatim
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| 115 | *
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| 116 | * Authors:
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| 117 | * ========
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| 118 | *
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| 119 | *> \author Univ. of Tennessee
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| 120 | *> \author Univ. of California Berkeley
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| 121 | *> \author Univ. of Colorado Denver
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| 122 | *> \author NAG Ltd.
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| 123 | *
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| 124 | *> \date November 2011
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| 125 | *
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| 126 | *> \ingroup complexOTHERauxiliary
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| 127 | *
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| 128 | * =====================================================================
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| 129 | SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
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| 130 | *
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| 131 | * -- LAPACK auxiliary routine (version 3.4.0) --
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| 132 | * -- LAPACK is a software package provided by Univ. of Tennessee, --
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| 133 | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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| 134 | * November 2011
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| 135 | *
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| 136 | * .. Scalar Arguments ..
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| 137 | CHARACTER SIDE
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| 138 | INTEGER INCV, LDC, M, N
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| 139 | COMPLEX TAU
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| 140 | * ..
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| 141 | * .. Array Arguments ..
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| 142 | COMPLEX C( LDC, * ), V( * ), WORK( * )
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| 143 | * ..
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| 144 | *
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| 145 | * =====================================================================
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| 146 | *
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| 147 | * .. Parameters ..
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| 148 | COMPLEX ONE, ZERO
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| 149 | PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
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| 150 | $ ZERO = ( 0.0E+0, 0.0E+0 ) )
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| 151 | * ..
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| 152 | * .. Local Scalars ..
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| 153 | LOGICAL APPLYLEFT
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| 154 | INTEGER I, LASTV, LASTC
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| 155 | * ..
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| 156 | * .. External Subroutines ..
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| 157 | EXTERNAL CGEMV, CGERC
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| 158 | * ..
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| 159 | * .. External Functions ..
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| 160 | LOGICAL LSAME
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| 161 | INTEGER ILACLR, ILACLC
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| 162 | EXTERNAL LSAME, ILACLR, ILACLC
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| 163 | * ..
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| 164 | * .. Executable Statements ..
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| 165 | *
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| 166 | APPLYLEFT = LSAME( SIDE, 'L' )
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| 167 | LASTV = 0
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| 168 | LASTC = 0
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| 169 | IF( TAU.NE.ZERO ) THEN
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| 170 | ! Set up variables for scanning V. LASTV begins pointing to the end
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| 171 | ! of V.
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| 172 | IF( APPLYLEFT ) THEN
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| 173 | LASTV = M
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| 174 | ELSE
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| 175 | LASTV = N
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| 176 | END IF
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| 177 | IF( INCV.GT.0 ) THEN
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| 178 | I = 1 + (LASTV-1) * INCV
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| 179 | ELSE
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| 180 | I = 1
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| 181 | END IF
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| 182 | ! Look for the last non-zero row in V.
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| 183 | DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )
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| 184 | LASTV = LASTV - 1
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| 185 | I = I - INCV
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| 186 | END DO
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| 187 | IF( APPLYLEFT ) THEN
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| 188 | ! Scan for the last non-zero column in C(1:lastv,:).
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| 189 | LASTC = ILACLC(LASTV, N, C, LDC)
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| 190 | ELSE
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| 191 | ! Scan for the last non-zero row in C(:,1:lastv).
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| 192 | LASTC = ILACLR(M, LASTV, C, LDC)
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| 193 | END IF
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| 194 | END IF
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| 195 | ! Note that lastc.eq.0 renders the BLAS operations null; no special
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| 196 | ! case is needed at this level.
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| 197 | IF( APPLYLEFT ) THEN
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| 198 | *
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| 199 | * Form H * C
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| 200 | *
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| 201 | IF( LASTV.GT.0 ) THEN
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| 202 | *
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| 203 | * w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)
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| 204 | *
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| 205 | CALL CGEMV( 'Conjugate transpose', LASTV, LASTC, ONE,
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| 206 | $ C, LDC, V, INCV, ZERO, WORK, 1 )
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| 207 | *
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| 208 | * C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H
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| 209 | *
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| 210 | CALL CGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
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| 211 | END IF
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| 212 | ELSE
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| 213 | *
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| 214 | * Form C * H
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| 215 | *
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| 216 | IF( LASTV.GT.0 ) THEN
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| 217 | *
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| 218 | * w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
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| 219 | *
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| 220 | CALL CGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
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| 221 | $ V, INCV, ZERO, WORK, 1 )
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| 222 | *
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| 223 | * C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H
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| 224 | *
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| 225 | CALL CGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
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| 226 | END IF
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| 227 | END IF
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| 228 | RETURN
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| 229 | *
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| 230 | * End of CLARF
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| 231 | *
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| 232 | END
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