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NAME
     dlarfb - apply 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 )



     #include <sunperf.h>

     void dlarfb(char side, char trans, char direct, char storev,
               int  m,  int  n, int k, double *v, int ldv, double
               *t, int ldt, double *dc, int ldc)

     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).

     V         (input) DOUBLE PRECISION array, dimension
               (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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