dlarft.f man page

dlarft.f

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine dlarft (character DIRECT, character STOREV, integer N, integer K, double precision, dimension( ldv, * ) V, integer LDV, double precision, dimension( * ) TAU, double precision, dimension( ldt, * ) T, integer LDT)

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

Purpose:

DLARFT forms the triangular factor T of a real 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**T

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 * 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i).

T

T is DOUBLE PRECISION 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 dlarft.f.

Author

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Referenced By

The man page dlarft(3) is an alias of dlarft.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK