CXML
        	    
LAPACK version 3.0
slarft(3)

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

SYNTAX
  SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )

      CHARACTER	     DIRECT, STOREV

      INTEGER	     K, LDT, LDV, N

      REAL	     T( LDT, * ), TAU( * ), V( LDV, * )

DESCRIPTION
  SLARFT 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
	  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 elementary 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) REAL 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) REAL array, dimension (K)
	  TAU(i) must contain the scalar factor of the elementary reflector
	  H(i).

  T	  (output) REAL 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 )