[22] | 1 | *> \brief \b SORMR3 |
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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 SORMR3 + dependencies |
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| 10 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sormr3.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/sormr3.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/sormr3.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 SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
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| 22 | * WORK, INFO ) |
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| 23 | * |
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| 24 | * .. Scalar Arguments .. |
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| 25 | * CHARACTER SIDE, TRANS |
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| 26 | * INTEGER INFO, K, L, LDA, LDC, M, N |
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| 27 | * .. |
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| 28 | * .. Array Arguments .. |
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| 29 | * REAL A( LDA, * ), C( LDC, * ), TAU( * ), 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 | *> SORMR3 overwrites the general real m by n matrix C with |
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| 39 | *> |
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| 40 | *> Q * C if SIDE = 'L' and TRANS = 'N', or |
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| 41 | *> |
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| 42 | *> Q**T* C if SIDE = 'L' and TRANS = 'C', or |
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| 43 | *> |
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| 44 | *> C * Q if SIDE = 'R' and TRANS = 'N', or |
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| 45 | *> |
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| 46 | *> C * Q**T if SIDE = 'R' and TRANS = 'C', |
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| 47 | *> |
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| 48 | *> where Q is a real orthogonal matrix defined as the product of k |
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| 49 | *> elementary reflectors |
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| 50 | *> |
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| 51 | *> Q = H(1) H(2) . . . H(k) |
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| 52 | *> |
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| 53 | *> as returned by STZRZF. Q is of order m if SIDE = 'L' and of order n |
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| 54 | *> if SIDE = 'R'. |
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| 55 | *> \endverbatim |
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| 56 | * |
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| 57 | * Arguments: |
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| 58 | * ========== |
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| 59 | * |
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| 60 | *> \param[in] SIDE |
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| 61 | *> \verbatim |
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| 62 | *> SIDE is CHARACTER*1 |
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| 63 | *> = 'L': apply Q or Q**T from the Left |
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| 64 | *> = 'R': apply Q or Q**T from the Right |
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| 65 | *> \endverbatim |
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| 66 | *> |
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| 67 | *> \param[in] TRANS |
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| 68 | *> \verbatim |
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| 69 | *> TRANS is CHARACTER*1 |
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| 70 | *> = 'N': apply Q (No transpose) |
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| 71 | *> = 'T': apply Q**T (Transpose) |
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| 72 | *> \endverbatim |
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| 73 | *> |
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| 74 | *> \param[in] M |
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| 75 | *> \verbatim |
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| 76 | *> M is INTEGER |
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| 77 | *> The number of rows of the matrix C. M >= 0. |
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| 78 | *> \endverbatim |
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| 79 | *> |
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| 80 | *> \param[in] N |
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| 81 | *> \verbatim |
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| 82 | *> N is INTEGER |
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| 83 | *> The number of columns of the matrix C. N >= 0. |
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| 84 | *> \endverbatim |
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| 85 | *> |
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| 86 | *> \param[in] K |
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| 87 | *> \verbatim |
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| 88 | *> K is INTEGER |
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| 89 | *> The number of elementary reflectors whose product defines |
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| 90 | *> the matrix Q. |
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| 91 | *> If SIDE = 'L', M >= K >= 0; |
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| 92 | *> if SIDE = 'R', N >= K >= 0. |
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| 93 | *> \endverbatim |
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| 94 | *> |
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| 95 | *> \param[in] L |
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| 96 | *> \verbatim |
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| 97 | *> L is INTEGER |
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| 98 | *> The number of columns of the matrix A containing |
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| 99 | *> the meaningful part of the Householder reflectors. |
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| 100 | *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. |
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| 101 | *> \endverbatim |
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| 102 | *> |
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| 103 | *> \param[in] A |
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| 104 | *> \verbatim |
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| 105 | *> A is REAL array, dimension |
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| 106 | *> (LDA,M) if SIDE = 'L', |
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| 107 | *> (LDA,N) if SIDE = 'R' |
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| 108 | *> The i-th row must contain the vector which defines the |
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| 109 | *> elementary reflector H(i), for i = 1,2,...,k, as returned by |
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| 110 | *> STZRZF in the last k rows of its array argument A. |
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| 111 | *> A is modified by the routine but restored on exit. |
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| 112 | *> \endverbatim |
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| 113 | *> |
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| 114 | *> \param[in] LDA |
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| 115 | *> \verbatim |
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| 116 | *> LDA is INTEGER |
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| 117 | *> The leading dimension of the array A. LDA >= max(1,K). |
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| 118 | *> \endverbatim |
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| 119 | *> |
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| 120 | *> \param[in] TAU |
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| 121 | *> \verbatim |
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| 122 | *> TAU is REAL array, dimension (K) |
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| 123 | *> TAU(i) must contain the scalar factor of the elementary |
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| 124 | *> reflector H(i), as returned by STZRZF. |
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| 125 | *> \endverbatim |
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| 126 | *> |
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| 127 | *> \param[in,out] C |
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| 128 | *> \verbatim |
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| 129 | *> C is REAL array, dimension (LDC,N) |
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| 130 | *> On entry, the m-by-n matrix C. |
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| 131 | *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. |
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| 132 | *> \endverbatim |
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| 133 | *> |
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| 134 | *> \param[in] LDC |
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| 135 | *> \verbatim |
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| 136 | *> LDC is INTEGER |
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| 137 | *> The leading dimension of the array C. LDC >= max(1,M). |
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| 138 | *> \endverbatim |
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| 139 | *> |
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| 140 | *> \param[out] WORK |
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| 141 | *> \verbatim |
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| 142 | *> WORK is REAL array, dimension |
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| 143 | *> (N) if SIDE = 'L', |
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| 144 | *> (M) if SIDE = 'R' |
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| 145 | *> \endverbatim |
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| 146 | *> |
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| 147 | *> \param[out] INFO |
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| 148 | *> \verbatim |
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| 149 | *> INFO is INTEGER |
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| 150 | *> = 0: successful exit |
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| 151 | *> < 0: if INFO = -i, the i-th argument had an illegal value |
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| 152 | *> \endverbatim |
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| 153 | * |
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| 154 | * Authors: |
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| 155 | * ======== |
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| 156 | * |
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| 157 | *> \author Univ. of Tennessee |
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| 158 | *> \author Univ. of California Berkeley |
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| 159 | *> \author Univ. of Colorado Denver |
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| 160 | *> \author NAG Ltd. |
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| 161 | * |
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| 162 | *> \date November 2011 |
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| 163 | * |
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| 164 | *> \ingroup realOTHERcomputational |
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| 165 | * |
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| 166 | *> \par Contributors: |
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| 167 | * ================== |
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| 168 | *> |
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| 169 | *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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| 170 | * |
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| 171 | *> \par Further Details: |
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| 172 | * ===================== |
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| 173 | *> |
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| 174 | *> \verbatim |
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| 175 | *> \endverbatim |
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| 176 | *> |
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| 177 | * ===================================================================== |
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| 178 | SUBROUTINE SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
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| 179 | $ WORK, INFO ) |
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| 180 | * |
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| 181 | * -- LAPACK computational routine (version 3.4.0) -- |
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| 182 | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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| 183 | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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| 184 | * November 2011 |
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| 185 | * |
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| 186 | * .. Scalar Arguments .. |
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| 187 | CHARACTER SIDE, TRANS |
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| 188 | INTEGER INFO, K, L, LDA, LDC, M, N |
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| 189 | * .. |
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| 190 | * .. Array Arguments .. |
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| 191 | REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
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| 192 | * .. |
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| 193 | * |
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| 194 | * ===================================================================== |
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| 195 | * |
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| 196 | * .. Local Scalars .. |
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| 197 | LOGICAL LEFT, NOTRAN |
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| 198 | INTEGER I, I1, I2, I3, IC, JA, JC, MI, NI, NQ |
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| 199 | * .. |
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| 200 | * .. External Functions .. |
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| 201 | LOGICAL LSAME |
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| 202 | EXTERNAL LSAME |
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| 203 | * .. |
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| 204 | * .. External Subroutines .. |
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| 205 | EXTERNAL SLARZ, XERBLA |
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| 206 | * .. |
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| 207 | * .. Intrinsic Functions .. |
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| 208 | INTRINSIC MAX |
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| 209 | * .. |
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| 210 | * .. Executable Statements .. |
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| 211 | * |
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| 212 | * Test the input arguments |
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| 213 | * |
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| 214 | INFO = 0 |
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| 215 | LEFT = LSAME( SIDE, 'L' ) |
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| 216 | NOTRAN = LSAME( TRANS, 'N' ) |
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| 217 | * |
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| 218 | * NQ is the order of Q |
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| 219 | * |
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| 220 | IF( LEFT ) THEN |
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| 221 | NQ = M |
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| 222 | ELSE |
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| 223 | NQ = N |
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| 224 | END IF |
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| 225 | IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN |
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| 226 | INFO = -1 |
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| 227 | ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN |
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| 228 | INFO = -2 |
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| 229 | ELSE IF( M.LT.0 ) THEN |
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| 230 | INFO = -3 |
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| 231 | ELSE IF( N.LT.0 ) THEN |
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| 232 | INFO = -4 |
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| 233 | ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN |
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| 234 | INFO = -5 |
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| 235 | ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR. |
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| 236 | $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN |
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| 237 | INFO = -6 |
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| 238 | ELSE IF( LDA.LT.MAX( 1, K ) ) THEN |
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| 239 | INFO = -8 |
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| 240 | ELSE IF( LDC.LT.MAX( 1, M ) ) THEN |
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| 241 | INFO = -11 |
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| 242 | END IF |
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| 243 | IF( INFO.NE.0 ) THEN |
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| 244 | CALL XERBLA( 'SORMR3', -INFO ) |
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| 245 | RETURN |
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| 246 | END IF |
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| 247 | * |
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| 248 | * Quick return if possible |
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| 249 | * |
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| 250 | IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) |
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| 251 | $ RETURN |
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| 252 | * |
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| 253 | IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN |
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| 254 | I1 = 1 |
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| 255 | I2 = K |
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| 256 | I3 = 1 |
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| 257 | ELSE |
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| 258 | I1 = K |
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| 259 | I2 = 1 |
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| 260 | I3 = -1 |
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| 261 | END IF |
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| 262 | * |
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| 263 | IF( LEFT ) THEN |
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| 264 | NI = N |
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| 265 | JA = M - L + 1 |
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| 266 | JC = 1 |
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| 267 | ELSE |
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| 268 | MI = M |
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| 269 | JA = N - L + 1 |
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| 270 | IC = 1 |
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| 271 | END IF |
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| 272 | * |
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| 273 | DO 10 I = I1, I2, I3 |
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| 274 | IF( LEFT ) THEN |
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| 275 | * |
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| 276 | * H(i) or H(i)**T is applied to C(i:m,1:n) |
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| 277 | * |
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| 278 | MI = M - I + 1 |
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| 279 | IC = I |
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| 280 | ELSE |
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| 281 | * |
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| 282 | * H(i) or H(i)**T is applied to C(1:m,i:n) |
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| 283 | * |
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| 284 | NI = N - I + 1 |
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| 285 | JC = I |
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| 286 | END IF |
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| 287 | * |
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| 288 | * Apply H(i) or H(i)**T |
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| 289 | * |
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| 290 | CALL SLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ), |
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| 291 | $ C( IC, JC ), LDC, WORK ) |
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| 292 | * |
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| 293 | 10 CONTINUE |
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| 294 | * |
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| 295 | RETURN |
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| 296 | * |
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| 297 | * End of SORMR3 |
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| 298 | * |
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| 299 | END |
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