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CLARFT(3F)							    CLARFT(3F)

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

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

	 CHARACTER	DIRECT, STOREV

	 INTEGER	K, LDT, LDV, N

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

PURPOSE
     CLARFT forms the triangular factor T of a complex 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.

									Page 1

CLARFT(3F)							    CLARFT(3F)

     V	     (input/output) COMPLEX 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) COMPLEX array, dimension (K)
	     TAU(i) must contain the scalar factor of the elementary reflector
	     H(i).

     T	     (output) COMPLEX 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 )

									Page 2

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