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NAME
     dlarft - form the  triangular  factor  T  of  a  real  block
     reflector  H  of order n, which is defined as a product of k
     elementary reflectors

SYNOPSIS
     SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT
               )

     CHARACTER DIRECT, STOREV

     INTEGER K, LDT, LDV, N

     DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )



     #include <sunperf.h>

     void dlarft(char direct, char storev, int n, int  k,  double
               *v, int ldv, double *tau, double *t, int ldt) ;

PURPOSE
     DLARFT forms the triangular factor T of a real block reflec-
     tor H of order n, which is defined as a product of k elemen-
     tary reflectors.

     If DIRECT = 'F', H = H(1) H(2) . . . H(k)  and  T  is  upper
     triangular;

     If DIRECT = 'B', H = H(k) . . . H(2) H(1)  and  T  is  lower
     triangular.

     If STOREV = 'C', the vector  which  defines  the  elementary
     reflector  H(i) is stored in the i-th column of the array V,
     and

        H  =  I - V * T * V'

     If STOREV = 'R', the vector  which  defines  the  elementary
     reflector H(i) is stored in the i-th row of the array V, and

        H  =  I - V' * T * V


ARGUMENTS
     DIRECT    (input) CHARACTER*1
               Specifies  the  order  in  which  the   elementary
               reflectors   are  multiplied  to  form  the  block
               reflector:
               = 'F': H = H(1) H(2) . . . H(k) (Forward)
               = 'B': H = H(k) . . . H(2) H(1) (Backward)

     STOREV    (input) CHARACTER*1
               Specifies how the vectors which define the elemen-
               tary  reflectors  are  stored  (see  also  Further
               Details):
               = 'R': rowwise

     N         (input) INTEGER
               The order of the block reflector H. N >= 0.

     K         (input) INTEGER
               The order of the triangular factor T (= the number
               of elementary reflectors). K >= 1.

     V         (input/output) DOUBLE PRECISION array, dimension
               (LDV,K) if STOREV = 'C' (LDV,N) if  STOREV  =  'R'
               The matrix V. See further details.

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

     TAU       (input) DOUBLE PRECISION array, dimension (K)
               TAU(i) must contain the scalar factor of the  ele-
               mentary reflector H(i).

     T         (output) DOUBLE PRECISION array, dimension (LDT,K)
               The k by  k  triangular  factor  T  of  the  block
               reflector.   If  DIRECT = 'F', T is upper triangu-
               lar; if DIRECT = 'B', T is lower  triangular.  The
               rest of the array is not used.

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

FURTHER DETAILS
     The shape of the matrix V and the  storage  of  the  vectors
     which  define  the H(i) is best illustrated by the following
     example with n = 5 and k = 3. The elements equal  to  1  are
     not  stored;  the  corresponding array elements are modified
     but restored on exit. The rest of the array is not used.

     DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':

                  V = (  1       )                 V = (  1 v1 v1 v1 v1 )
                      ( v1  1    )                     (     1 v2 v2 v2 )
                      ( v1 v2  1 )                     (        1 v3 v3 )
                      ( v1 v2 v3 )
                      ( v1 v2 v3 )

     DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':

                  V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
                      ( v1 v2 v3 )                     ( v2 v2 v2  1    )
                      (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
                      (     1 v3 )
                      (        1 )

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