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    1:       SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          SIDE
   10:       INTEGER            INCV, L, LDC, M, N
   11:       DOUBLE PRECISION   TAU
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  DLARZ applies a real elementary reflector H to a real M-by-N
   21: *  matrix C, from either the left or the right. H is represented in the
   22: *  form
   23: *
   24: *        H = I - tau * v * v'
   25: *
   26: *  where tau is a real scalar and v is a real vector.
   27: *
   28: *  If tau = 0, then H is taken to be the unit matrix.
   29: *
   30: *
   31: *  H is a product of k elementary reflectors as returned by DTZRZF.
   32: *
   33: *  Arguments
   34: *  =========
   35: *
   36: *  SIDE    (input) CHARACTER*1
   37: *          = 'L': form  H * C
   38: *          = 'R': form  C * H
   39: *
   40: *  M       (input) INTEGER
   41: *          The number of rows of the matrix C.
   42: *
   43: *  N       (input) INTEGER
   44: *          The number of columns of the matrix C.
   45: *
   46: *  L       (input) INTEGER
   47: *          The number of entries of the vector V containing
   48: *          the meaningful part of the Householder vectors.
   49: *          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
   50: *
   51: *  V       (input) DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV))
   52: *          The vector v in the representation of H as returned by
   53: *          DTZRZF. V is not used if TAU = 0.
   54: *
   55: *  INCV    (input) INTEGER
   56: *          The increment between elements of v. INCV <> 0.
   57: *
   58: *  TAU     (input) DOUBLE PRECISION
   59: *          The value tau in the representation of H.
   60: *
   61: *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
   62: *          On entry, the M-by-N matrix C.
   63: *          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
   64: *          or C * H if SIDE = 'R'.
   65: *
   66: *  LDC     (input) INTEGER
   67: *          The leading dimension of the array C. LDC >= max(1,M).
   68: *
   69: *  WORK    (workspace) DOUBLE PRECISION array, dimension
   70: *                         (N) if SIDE = 'L'
   71: *                      or (M) if SIDE = 'R'
   72: *
   73: *  Further Details
   74: *  ===============
   75: *
   76: *  Based on contributions by
   77: *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
   78: *
   79: *  =====================================================================
   80: *
   81: *     .. Parameters ..
   82:       DOUBLE PRECISION   ONE, ZERO
   83:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   84: *     ..
   85: *     .. External Subroutines ..
   86:       EXTERNAL           DAXPY, DCOPY, DGEMV, DGER
   87: *     ..
   88: *     .. External Functions ..
   89:       LOGICAL            LSAME
   90:       EXTERNAL           LSAME
   91: *     ..
   92: *     .. Executable Statements ..
   93: *
   94:       IF( LSAME( SIDE, 'L' ) ) THEN
   95: *
   96: *        Form  H * C
   97: *
   98:          IF( TAU.NE.ZERO ) THEN
   99: *
  100: *           w( 1:n ) = C( 1, 1:n )
  101: *
  102:             CALL DCOPY( N, C, LDC, WORK, 1 )
  103: *
  104: *           w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l )
  105: *
  106:             CALL DGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V,
  107:      $                  INCV, ONE, WORK, 1 )
  108: *
  109: *           C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
  110: *
  111:             CALL DAXPY( N, -TAU, WORK, 1, C, LDC )
  112: *
  113: *           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
  114: *                               tau * v( 1:l ) * w( 1:n )'
  115: *
  116:             CALL DGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
  117:      $                 LDC )
  118:          END IF
  119: *
  120:       ELSE
  121: *
  122: *        Form  C * H
  123: *
  124:          IF( TAU.NE.ZERO ) THEN
  125: *
  126: *           w( 1:m ) = C( 1:m, 1 )
  127: *
  128:             CALL DCOPY( M, C, 1, WORK, 1 )
  129: *
  130: *           w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
  131: *
  132:             CALL DGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
  133:      $                  V, INCV, ONE, WORK, 1 )
  134: *
  135: *           C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
  136: *
  137:             CALL DAXPY( M, -TAU, WORK, 1, C, 1 )
  138: *
  139: *           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
  140: *                               tau * w( 1:m ) * v( 1:l )'
  141: *
  142:             CALL DGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
  143:      $                 LDC )
  144: *
  145:          END IF
  146: *
  147:       END IF
  148: *
  149:       RETURN
  150: *
  151: *     End of DLARZ
  152: *
  153:       END