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    1:       SUBROUTINE ZLARZ( 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:       COMPLEX*16         TAU
   12: *     ..
   13: *     .. Array Arguments ..
   14:       COMPLEX*16         C( LDC, * ), V( * ), WORK( * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  ZLARZ applies a complex elementary reflector H to a complex
   21: *  M-by-N matrix C, from either the left or the right. H is represented
   22: *  in the form
   23: *
   24: *        H = I - tau * v * v'
   25: *
   26: *  where tau is a complex scalar and v is a complex vector.
   27: *
   28: *  If tau = 0, then H is taken to be the unit matrix.
   29: *
   30: *  To apply H' (the conjugate transpose of H), supply conjg(tau) instead
   31: *  tau.
   32: *
   33: *  H is a product of k elementary reflectors as returned by ZTZRZF.
   34: *
   35: *  Arguments
   36: *  =========
   37: *
   38: *  SIDE    (input) CHARACTER*1
   39: *          = 'L': form  H * C
   40: *          = 'R': form  C * H
   41: *
   42: *  M       (input) INTEGER
   43: *          The number of rows of the matrix C.
   44: *
   45: *  N       (input) INTEGER
   46: *          The number of columns of the matrix C.
   47: *
   48: *  L       (input) INTEGER
   49: *          The number of entries of the vector V containing
   50: *          the meaningful part of the Householder vectors.
   51: *          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
   52: *
   53: *  V       (input) COMPLEX*16 array, dimension (1+(L-1)*abs(INCV))
   54: *          The vector v in the representation of H as returned by
   55: *          ZTZRZF. V is not used if TAU = 0.
   56: *
   57: *  INCV    (input) INTEGER
   58: *          The increment between elements of v. INCV <> 0.
   59: *
   60: *  TAU     (input) COMPLEX*16
   61: *          The value tau in the representation of H.
   62: *
   63: *  C       (input/output) COMPLEX*16 array, dimension (LDC,N)
   64: *          On entry, the M-by-N matrix C.
   65: *          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
   66: *          or C * H if SIDE = 'R'.
   67: *
   68: *  LDC     (input) INTEGER
   69: *          The leading dimension of the array C. LDC >= max(1,M).
   70: *
   71: *  WORK    (workspace) COMPLEX*16 array, dimension
   72: *                         (N) if SIDE = 'L'
   73: *                      or (M) if SIDE = 'R'
   74: *
   75: *  Further Details
   76: *  ===============
   77: *
   78: *  Based on contributions by
   79: *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
   80: *
   81: *  =====================================================================
   82: *
   83: *     .. Parameters ..
   84:       COMPLEX*16         ONE, ZERO
   85:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
   86:      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
   87: *     ..
   88: *     .. External Subroutines ..
   89:       EXTERNAL           ZAXPY, ZCOPY, ZGEMV, ZGERC, ZGERU, ZLACGV
   90: *     ..
   91: *     .. External Functions ..
   92:       LOGICAL            LSAME
   93:       EXTERNAL           LSAME
   94: *     ..
   95: *     .. Executable Statements ..
   96: *
   97:       IF( LSAME( SIDE, 'L' ) ) THEN
   98: *
   99: *        Form  H * C
  100: *
  101:          IF( TAU.NE.ZERO ) THEN
  102: *
  103: *           w( 1:n ) = conjg( C( 1, 1:n ) )
  104: *
  105:             CALL ZCOPY( N, C, LDC, WORK, 1 )
  106:             CALL ZLACGV( N, WORK, 1 )
  107: *
  108: *           w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l ) )
  109: *
  110:             CALL ZGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ),
  111:      $                  LDC, V, INCV, ONE, WORK, 1 )
  112:             CALL ZLACGV( N, WORK, 1 )
  113: *
  114: *           C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
  115: *
  116:             CALL ZAXPY( N, -TAU, WORK, 1, C, LDC )
  117: *
  118: *           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
  119: *                               tau * v( 1:l ) * conjg( w( 1:n )' )
  120: *
  121:             CALL ZGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
  122:      $                  LDC )
  123:          END IF
  124: *
  125:       ELSE
  126: *
  127: *        Form  C * H
  128: *
  129:          IF( TAU.NE.ZERO ) THEN
  130: *
  131: *           w( 1:m ) = C( 1:m, 1 )
  132: *
  133:             CALL ZCOPY( M, C, 1, WORK, 1 )
  134: *
  135: *           w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
  136: *
  137:             CALL ZGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
  138:      $                  V, INCV, ONE, WORK, 1 )
  139: *
  140: *           C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
  141: *
  142:             CALL ZAXPY( M, -TAU, WORK, 1, C, 1 )
  143: *
  144: *           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
  145: *                               tau * w( 1:m ) * v( 1:l )'
  146: *
  147:             CALL ZGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
  148:      $                  LDC )
  149: *
  150:          END IF
  151: *
  152:       END IF
  153: *
  154:       RETURN
  155: *
  156: *     End of ZLARZ
  157: *
  158:       END