DLARZT(l)								 )								 DLARZT(l)

NAME

       DLARZT - 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 DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )

	   CHARACTER	  DIRECT, STOREV

	   INTEGER	  K, LDT, LDV, N

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

PURPOSE

       DLARZT  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

       Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

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, not supported yet)
	       = '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) 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 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 triangular; if DIRECT = 'B', T is lower  trian-
	       gular. The rest of the array is not used.

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

FURTHER DETAILS

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

       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_____
	      ( v1 v2 v3 )			  /		      ( v1 v2 v3 )			( v1 v1 v1 v1 v1 . . . . 1 )
	  V = ( v1 v2 v3 )			( v2 v2 v2 v2 v2 . . . 1   )
	      ( v1 v2 v3 )			( v3 v3 v3 v3 v3 . . 1	   )
	      ( v1 v2 v3 )
		 .  .  .
		 .  .  .
		 1  .  .
		    1  .
		       1

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

							     ______V_____
		 1					    /			   .  1 			  ( 1 . . . . v1 v1 v1 v1 v1 )
		 .  .  1			( . 1 . . . v2 v2 v2 v2 v2 )
		 .  .  .			( . . 1 . . v3 v3 v3 v3 v3 )
		 .  .  .
	      ( v1 v2 v3 )
	      ( v1 v2 v3 )
	  V = ( v1 v2 v3 )
	      ( v1 v2 v3 )
	      ( v1 v2 v3 )

LAPACK version 3.0						   15 June 2000 							 DLARZT(l)