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clarft(3) [debian man page]

clarft.f(3)							      LAPACK							       clarft.f(3)

NAME

       clarft.f -

SYNOPSIS

   Functions/Subroutines
       subroutine clarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
	   CLARFT

Function/Subroutine Documentation
   subroutine clarft (characterDIRECT, characterSTOREV, integerN, integerK, complex, dimension( ldv, * )V, integerLDV, complex, dimension( * )TAU,
       complex, dimension( ldt, * )T, integerLDT)
       CLARFT

       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**H

	    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**H * T * V

       Parameters:
	   DIRECT

		     DIRECT is 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

		     STOREV is CHARACTER*1
		     Specifies how the vectors which define the elementary
		     reflectors are stored (see also Further Details):
		     = 'C': columnwise
		     = 'R': rowwise

	   N

		     N is INTEGER
		     The order of the block reflector H. N >= 0.

	   K

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

	   V

		     V is COMPLEX array, dimension
					  (LDV,K) if STOREV = 'C'
					  (LDV,N) if STOREV = 'R'
		     The matrix V. See further details.

	   LDV

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

	   TAU

		     TAU is COMPLEX array, dimension (K)
		     TAU(i) must contain the scalar factor of the elementary
		     reflector H(i).

	   T

		     T is 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

		     LDT is INTEGER
		     The leading dimension of the array T. LDT >= K.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   April 2012

       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.

	     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 )

       Definition at line 164 of file clarft.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       clarft.f(3)

Check Out this Related Man Page

CLARFT(l)								 )								 CLARFT(l)

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.

       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  trian-
	       gular. 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 version 3.0						   15 June 2000 							 CLARFT(l)
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