clarft.f File Reference

Functions/Subroutines
subroutine	clarft (direct, storev, n, k, v, ldv, tau, t, ldt)
	CLARFT

Function/Subroutine Documentation

clarft()

subroutine clarft	(	character	direct,
		character	storev,
		integer	n,
		integer	k,
		complex, dimension( ldv, * )	v,
		integer	ldv,
		complex, dimension( * )	tau,
		complex, dimension( ldt, * )	t,
		integer	ldt
	)

CLARFT

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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

[in]	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)
[in]	STOREV	STOREV is CHARACTER*1 Specifies how the vectors which define the elementary reflectors are stored (see also Further Details): = 'C': columnwise = 'R': rowwise
[in]	N	N is INTEGER The order of the block reflector H. N >= 0.
[in]	K	K is INTEGER The order of the triangular factor T (= the number of elementary reflectors). K >= 1.
[in]	V	V is COMPLEX array, dimension (LDV,K) if STOREV = 'C' (LDV,N) if STOREV = 'R' The matrix V. See further details.
[in]	LDV	LDV is INTEGER The leading dimension of the array V. If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
[in]	TAU	TAU is COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i).
[out]	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.
[in]	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 )