[22] | 1 | *> \brief \b SLARZ |
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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 SLARZ + dependencies |
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| 10 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarz.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/slarz.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/slarz.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 SLARZ( SIDE, M, N, L, 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, L, LDC, M, N |
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| 26 | * REAL TAU |
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| 27 | * .. |
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| 28 | * .. Array Arguments .. |
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| 29 | * REAL 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 | *> SLARZ applies a real elementary reflector H to a real 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**T |
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| 43 | *> |
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| 44 | *> where tau is a real scalar and v is a real 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 | *> |
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| 49 | *> H is a product of k elementary reflectors as returned by STZRZF. |
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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] L |
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| 75 | *> \verbatim |
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| 76 | *> L is INTEGER |
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| 77 | *> The number of entries of the vector V containing |
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| 78 | *> the meaningful part of the Householder vectors. |
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| 79 | *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. |
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| 80 | *> \endverbatim |
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| 81 | *> |
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| 82 | *> \param[in] V |
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| 83 | *> \verbatim |
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| 84 | *> V is REAL array, dimension (1+(L-1)*abs(INCV)) |
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| 85 | *> The vector v in the representation of H as returned by |
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| 86 | *> STZRZF. V is not used if TAU = 0. |
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| 87 | *> \endverbatim |
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| 88 | *> |
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| 89 | *> \param[in] INCV |
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| 90 | *> \verbatim |
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| 91 | *> INCV is INTEGER |
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| 92 | *> The increment between elements of v. INCV <> 0. |
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| 93 | *> \endverbatim |
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| 94 | *> |
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| 95 | *> \param[in] TAU |
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| 96 | *> \verbatim |
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| 97 | *> TAU is REAL |
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| 98 | *> The value tau in the representation of H. |
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| 99 | *> \endverbatim |
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| 100 | *> |
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| 101 | *> \param[in,out] C |
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| 102 | *> \verbatim |
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| 103 | *> C is REAL array, dimension (LDC,N) |
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| 104 | *> On entry, the M-by-N matrix C. |
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| 105 | *> On exit, C is overwritten by the matrix H * C if SIDE = 'L', |
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| 106 | *> or C * H if SIDE = 'R'. |
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| 107 | *> \endverbatim |
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| 108 | *> |
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| 109 | *> \param[in] LDC |
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| 110 | *> \verbatim |
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| 111 | *> LDC is INTEGER |
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| 112 | *> The leading dimension of the array C. LDC >= max(1,M). |
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| 113 | *> \endverbatim |
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| 114 | *> |
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| 115 | *> \param[out] WORK |
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| 116 | *> \verbatim |
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| 117 | *> WORK is REAL array, dimension |
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| 118 | *> (N) if SIDE = 'L' |
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| 119 | *> or (M) if SIDE = 'R' |
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| 120 | *> \endverbatim |
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| 121 | * |
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| 122 | * Authors: |
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| 123 | * ======== |
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| 124 | * |
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| 125 | *> \author Univ. of Tennessee |
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| 126 | *> \author Univ. of California Berkeley |
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| 127 | *> \author Univ. of Colorado Denver |
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| 128 | *> \author NAG Ltd. |
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| 129 | * |
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| 130 | *> \date November 2011 |
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| 131 | * |
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| 132 | *> \ingroup realOTHERcomputational |
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| 133 | * |
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| 134 | *> \par Contributors: |
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| 135 | * ================== |
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| 136 | *> |
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| 137 | *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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| 138 | * |
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| 139 | *> \par Further Details: |
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| 140 | * ===================== |
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| 141 | *> |
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| 142 | *> \verbatim |
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| 143 | *> \endverbatim |
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| 144 | *> |
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| 145 | * ===================================================================== |
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| 146 | SUBROUTINE SLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK ) |
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| 147 | * |
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| 148 | * -- LAPACK computational routine (version 3.4.0) -- |
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| 149 | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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| 150 | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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| 151 | * November 2011 |
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| 152 | * |
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| 153 | * .. Scalar Arguments .. |
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| 154 | CHARACTER SIDE |
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| 155 | INTEGER INCV, L, LDC, M, N |
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| 156 | REAL TAU |
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| 157 | * .. |
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| 158 | * .. Array Arguments .. |
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| 159 | REAL C( LDC, * ), V( * ), WORK( * ) |
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| 160 | * .. |
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| 161 | * |
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| 162 | * ===================================================================== |
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| 163 | * |
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| 164 | * .. Parameters .. |
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| 165 | REAL ONE, ZERO |
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| 166 | PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) |
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| 167 | * .. |
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| 168 | * .. External Subroutines .. |
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| 169 | EXTERNAL SAXPY, SCOPY, SGEMV, SGER |
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| 170 | * .. |
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| 171 | * .. External Functions .. |
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| 172 | LOGICAL LSAME |
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| 173 | EXTERNAL LSAME |
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| 174 | * .. |
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| 175 | * .. Executable Statements .. |
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| 176 | * |
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| 177 | IF( LSAME( SIDE, 'L' ) ) THEN |
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| 178 | * |
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| 179 | * Form H * C |
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| 180 | * |
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| 181 | IF( TAU.NE.ZERO ) THEN |
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| 182 | * |
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| 183 | * w( 1:n ) = C( 1, 1:n ) |
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| 184 | * |
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| 185 | CALL SCOPY( N, C, LDC, WORK, 1 ) |
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| 186 | * |
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| 187 | * w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l ) |
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| 188 | * |
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| 189 | CALL SGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V, |
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| 190 | $ INCV, ONE, WORK, 1 ) |
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| 191 | * |
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| 192 | * C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n ) |
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| 193 | * |
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| 194 | CALL SAXPY( N, -TAU, WORK, 1, C, LDC ) |
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| 195 | * |
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| 196 | * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... |
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| 197 | * tau * v( 1:l ) * w( 1:n )**T |
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| 198 | * |
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| 199 | CALL SGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ), |
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| 200 | $ LDC ) |
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| 201 | END IF |
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| 202 | * |
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| 203 | ELSE |
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| 204 | * |
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| 205 | * Form C * H |
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| 206 | * |
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| 207 | IF( TAU.NE.ZERO ) THEN |
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| 208 | * |
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| 209 | * w( 1:m ) = C( 1:m, 1 ) |
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| 210 | * |
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| 211 | CALL SCOPY( M, C, 1, WORK, 1 ) |
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| 212 | * |
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| 213 | * w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l ) |
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| 214 | * |
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| 215 | CALL SGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC, |
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| 216 | $ V, INCV, ONE, WORK, 1 ) |
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| 217 | * |
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| 218 | * C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m ) |
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| 219 | * |
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| 220 | CALL SAXPY( M, -TAU, WORK, 1, C, 1 ) |
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| 221 | * |
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| 222 | * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ... |
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| 223 | * tau * w( 1:m ) * v( 1:l )**T |
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| 224 | * |
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| 225 | CALL SGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ), |
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| 226 | $ LDC ) |
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| 227 | * |
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| 228 | END IF |
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| 229 | * |
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| 230 | END IF |
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| 231 | * |
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| 232 | RETURN |
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| 233 | * |
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| 234 | * End of SLARZ |
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| 235 | * |
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| 236 | END |
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