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DLARFT(1)	    LAPACK auxiliary routine (version 3.2)	     DLARFT(1)

NAME
       DLARFT  -  forms 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 )

	   IMPLICIT	  NONE

	   CHARACTER	  DIRECT, STOREV

	   INTEGER	  K, LDT, LDV, N

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

PURPOSE
       DLARFT forms the triangular factor T of a real  block  reflector	 H  of
       order  n, which is defined as a product of k elementary 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 mul‐
	       tiplied 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 elementary reflec‐
	       tors 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  elemen‐
	       tary 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 elementary reflec‐
	       tor 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 triangular; 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 )

 LAPACK auxiliary routine (versioNovember 2008			     DLARFT(1)
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