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      1 *> \brief \b SLARF
      2 *
      3 *  =========== DOCUMENTATION ===========
      4 *
      5 * Online html documentation available at 
      6 *            http://www.netlib.org/lapack/explore-html/ 
      7 *
      8 *> \htmlonly
      9 *> Download SLARF + dependencies 
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     11 *> [TGZ]</a> 
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     13 *> [ZIP]</a> 
     14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarf.f"> 
     15 *> [TXT]</a>
     16 *> \endhtmlonly 
     17 *
     18 *  Definition:
     19 *  ===========
     20 *
     21 *       SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
     22 * 
     23 *       .. Scalar Arguments ..
     24 *       CHARACTER          SIDE
     25 *       INTEGER            INCV, LDC, M, N
     26 *       REAL               TAU
     27 *       ..
     28 *       .. Array Arguments ..
     29 *       REAL               C( LDC, * ), V( * ), WORK( * )
     30 *       ..
     31 *  
     32 *
     33 *> \par Purpose:
     34 *  =============
     35 *>
     36 *> \verbatim
     37 *>
     38 *> SLARF applies a real elementary reflector H to a real m by n matrix
     39 *> C, from either the left or the right. H is represented in the form
     40 *>
     41 *>       H = I - tau * v * v**T
     42 *>
     43 *> where tau is a real scalar and v is a real vector.
     44 *>
     45 *> If tau = 0, then H is taken to be the unit matrix.
     46 *> \endverbatim
     47 *
     48 *  Arguments:
     49 *  ==========
     50 *
     51 *> \param[in] SIDE
     52 *> \verbatim
     53 *>          SIDE is CHARACTER*1
     54 *>          = 'L': form  H * C
     55 *>          = 'R': form  C * H
     56 *> \endverbatim
     57 *>
     58 *> \param[in] M
     59 *> \verbatim
     60 *>          M is INTEGER
     61 *>          The number of rows of the matrix C.
     62 *> \endverbatim
     63 *>
     64 *> \param[in] N
     65 *> \verbatim
     66 *>          N is INTEGER
     67 *>          The number of columns of the matrix C.
     68 *> \endverbatim
     69 *>
     70 *> \param[in] V
     71 *> \verbatim
     72 *>          V is REAL array, dimension
     73 *>                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
     74 *>                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
     75 *>          The vector v in the representation of H. V is not used if
     76 *>          TAU = 0.
     77 *> \endverbatim
     78 *>
     79 *> \param[in] INCV
     80 *> \verbatim
     81 *>          INCV is INTEGER
     82 *>          The increment between elements of v. INCV <> 0.
     83 *> \endverbatim
     84 *>
     85 *> \param[in] TAU
     86 *> \verbatim
     87 *>          TAU is REAL
     88 *>          The value tau in the representation of H.
     89 *> \endverbatim
     90 *>
     91 *> \param[in,out] C
     92 *> \verbatim
     93 *>          C is REAL array, dimension (LDC,N)
     94 *>          On entry, the m by n matrix C.
     95 *>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
     96 *>          or C * H if SIDE = 'R'.
     97 *> \endverbatim
     98 *>
     99 *> \param[in] LDC
    100 *> \verbatim
    101 *>          LDC is INTEGER
    102 *>          The leading dimension of the array C. LDC >= max(1,M).
    103 *> \endverbatim
    104 *>
    105 *> \param[out] WORK
    106 *> \verbatim
    107 *>          WORK is REAL array, dimension
    108 *>                         (N) if SIDE = 'L'
    109 *>                      or (M) if SIDE = 'R'
    110 *> \endverbatim
    111 *
    112 *  Authors:
    113 *  ========
    114 *
    115 *> \author Univ. of Tennessee 
    116 *> \author Univ. of California Berkeley 
    117 *> \author Univ. of Colorado Denver 
    118 *> \author NAG Ltd. 
    119 *
    120 *> \date November 2011
    121 *
    122 *> \ingroup realOTHERauxiliary
    123 *
    124 *  =====================================================================
    125       SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
    126 *
    127 *  -- LAPACK auxiliary routine (version 3.4.0) --
    128 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    129 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    130 *     November 2011
    131 *
    132 *     .. Scalar Arguments ..
    133       CHARACTER          SIDE
    134       INTEGER            INCV, LDC, M, N
    135       REAL               TAU
    136 *     ..
    137 *     .. Array Arguments ..
    138       REAL               C( LDC, * ), V( * ), WORK( * )
    139 *     ..
    140 *
    141 *  =====================================================================
    142 *
    143 *     .. Parameters ..
    144       REAL               ONE, ZERO
    145       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
    146 *     ..
    147 *     .. Local Scalars ..
    148       LOGICAL            APPLYLEFT
    149       INTEGER            I, LASTV, LASTC
    150 *     ..
    151 *     .. External Subroutines ..
    152       EXTERNAL           SGEMV, SGER
    153 *     ..
    154 *     .. External Functions ..
    155       LOGICAL            LSAME
    156       INTEGER            ILASLR, ILASLC
    157       EXTERNAL           LSAME, ILASLR, ILASLC
    158 *     ..
    159 *     .. Executable Statements ..
    160 *
    161       APPLYLEFT = LSAME( SIDE, 'L' )
    162       LASTV = 0
    163       LASTC = 0
    164       IF( TAU.NE.ZERO ) THEN
    165 !     Set up variables for scanning V.  LASTV begins pointing to the end
    166 !     of V.
    167          IF( APPLYLEFT ) THEN
    168             LASTV = M
    169          ELSE
    170             LASTV = N
    171          END IF
    172          IF( INCV.GT.0 ) THEN
    173             I = 1 + (LASTV-1) * INCV
    174          ELSE
    175             I = 1
    176          END IF
    177 !     Look for the last non-zero row in V.
    178          DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )
    179             LASTV = LASTV - 1
    180             I = I - INCV
    181          END DO
    182          IF( APPLYLEFT ) THEN
    183 !     Scan for the last non-zero column in C(1:lastv,:).
    184             LASTC = ILASLC(LASTV, N, C, LDC)
    185          ELSE
    186 !     Scan for the last non-zero row in C(:,1:lastv).
    187             LASTC = ILASLR(M, LASTV, C, LDC)
    188          END IF
    189       END IF
    190 !     Note that lastc.eq.0 renders the BLAS operations null; no special
    191 !     case is needed at this level.
    192       IF( APPLYLEFT ) THEN
    193 *
    194 *        Form  H * C
    195 *
    196          IF( LASTV.GT.0 ) THEN
    197 *
    198 *           w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)
    199 *
    200             CALL SGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV,
    201      $           ZERO, WORK, 1 )
    202 *
    203 *           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T
    204 *
    205             CALL SGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
    206          END IF
    207       ELSE
    208 *
    209 *        Form  C * H
    210 *
    211          IF( LASTV.GT.0 ) THEN
    212 *
    213 *           w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
    214 *
    215             CALL SGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
    216      $           V, INCV, ZERO, WORK, 1 )
    217 *
    218 *           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T
    219 *
    220             CALL SGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
    221          END IF
    222       END IF
    223       RETURN
    224 *
    225 *     End of SLARF
    226 *
    227       END
    228