clarft-f(3)

clarft.f –

Synopsis

Functions/Subroutines

subroutine clarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
CLARFT forms the triangular factor T of a block reflector H = I – vtvH

Function/Subroutine Documentation

subroutine clarft (characterDIRECT, characterSTOREV, integerN, integerK, complex, dimension( ldv, * )V, integerLDV, complex, dimension( * )TAU, complex, dimension( ldt, * )T, integerLDT)

CLARFT forms the triangular factor T of a block reflector H = I – vtvH

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

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

 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 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:

September 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

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