CLARZB  - applie a complex block reflector H or its trans­
       pose H**H to a complex distributed M-by-N C from the  left
       or the right


SYNOPSIS

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

           CHARACTER      DIRECT, SIDE, STOREV, TRANS

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

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


PURPOSE

       CLARZB applies a complex block reflector H or  its  trans­
       pose  H**H to a complex distributed M-by-N C from the left
       or the right.  Currently, only STOREV = 'R' and  DIRECT  =
       'B' are supported.


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)
               = 'C': apply H' (Conjugate 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, not supported yet)
               = '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                        (not sup­
               ported yet)
               = '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

               block reflector).

       L       (input) INTEGER
               The  number  of columns of the matrix V containing
               the meaningful part of the Householder reflectors.
               If  SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L
               >= 0.

       V       (input) COMPLEX array, dimension (LDV,NV).
               If STOREV = 'C', NV = K; if STOREV = 'R', NV =  L.

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

       T       (input) COMPLEX 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) COMPLEX 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.  LDC  >=
               max(1,M).

       WORK    (workspace) COMPLEX 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).


FURTHER DETAILS

       Based on contributions by
         A.  Petitet,  Computer  Science  Dept.,  Univ. of Tenn.,
       Knoxville, USA


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