DLARFB  - applie a real block reflector H or its transpose
       H' to a real m by n matrix C, from either the left or  the
       right


SYNOPSIS

       SUBROUTINE DLARFB( SIDE,  TRANS,  DIRECT, STOREV, M, N, K,
                          V, LDV, T, LDT, C, LDC, WORK, LDWORK )

           CHARACTER      DIRECT, SIDE, STOREV, TRANS

           INTEGER        K, LDC, LDT, LDV, LDWORK, M, N

           DOUBLE         PRECISION C( LDC, * ), T( LDT, * ),  V(
                          LDV, * ), WORK( LDWORK, * )


PURPOSE

       DLARFB  applies  a real block reflector H or its transpose
       H' to a real m by n matrix C, from either the left or  the
       right.


ARGUMENTS

       SIDE    (input) CHARACTER*1
               = 'L': apply H or H' from the Left
               = 'R': apply H or H' from the Right

       TRANS   (input) CHARACTER*1
               = 'N': apply H (No transpose)
               = 'T': apply H' (Transpose)

       DIRECT  (input) CHARACTER*1
               Indicates  how  H is formed from a product of ele­
               mentary reflectors = 'F': H = H(1) H(2) . . . H(k)
               (Forward)
               = 'B': H = H(k) . . . H(2) H(1) (Backward)

       STOREV  (input) CHARACTER*1
               Indicates how the vectors which define the elemen­
               tary reflectors are stored:
               = 'C': Columnwise
               = 'R': Rowwise

       M       (input) INTEGER
               The number of rows of the matrix C.

       N       (input) INTEGER
               The number of columns of the matrix C.

       K       (input) INTEGER
               The order of the matrix T (= the number of elemen­
               tary  reflectors  whose  product defines the block
               reflector).

               (LDV,K) if STOREV = 'C' (LDV,M) if  STOREV  =  'R'
               and  SIDE = 'L' (LDV,N) if STOREV = 'R' and SIDE =
               'R' The matrix V. See further details.

       LDV     (input) INTEGER
               The leading dimension of the array V.  If STOREV =
               'C'  and  SIDE = 'L', LDV >= max(1,M); if STOREV =
               'C' and SIDE = 'R', LDV >= max(1,N); if  STOREV  =
               'R', LDV >= K.

       T       (input) DOUBLE PRECISION array, dimension (LDT,K)
               The  triangular k by k matrix T in the representa­
               tion of the block reflector.

       LDT     (input) INTEGER
               The leading dimension of the array T. LDT >= K.

       C       (input/output) DOUBLE PRECISION array, dimension
               (LDC,N)
               On  entry,  the  m  by  n matrix C.  On exit, C is
               overwritten by H*C or H'*C or C*H or C*H'.

       LDC     (input) INTEGER
               The leading dimension  of  the  array  C.  LDA  >=
               max(1,M).

       WORK    (workspace) DOUBLE PRECISION array, dimension
               (LDWORK,K)

       LDWORK  (input) INTEGER
               The leading dimension of the array WORK.  If  SIDE
               =  'L',  LDWORK >= max(1,N); if SIDE = 'R', LDWORK
               >= max(1,M).


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