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

Function/Subroutine Documentation

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 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


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:

December 2016

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 165 of file clarft.f.

Author

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Tue Nov 14 2017 Version 3.8.0