# dlarft (l) - Linux Man Pages

## NAME

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

## SYNOPSIS

SUBROUTINE DLARFT(
DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )

IMPLICIT NONE

CHARACTER DIRECT, STOREV

INTEGER K, LDT, LDV, N

DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )

## 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 = aqFaq, H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = aqBaq, H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = aqCaq, the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and

I - V Vaq
If STOREV = aqRaq, the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and

I - Vaq V

## ARGUMENTS

DIRECT (input) CHARACTER*1
Specifies the order in which the elementary reflectors are multiplied to form the block reflector:
= aqFaq: H = H(1) H(2) . . . H(k) (Forward)
= aqBaq: 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):
= aqRaq: 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) DOUBLE PRECISION array, dimension
(LDV,K) if STOREV = aqCaq (LDV,N) if STOREV = aqRaq The matrix V. See further details.
LDV (input) INTEGER
The leading dimension of the array V. If STOREV = aqCaq, LDV >= max(1,N); if STOREV = aqRaq, LDV >= K.
TAU (input) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflector H(i).
T (output) DOUBLE PRECISION array, dimension (LDT,K)
The k by k triangular factor T of the block reflector. If DIRECT = aqFaq, T is upper triangular; if DIRECT = aqBaq, T is lower triangular. 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 = aqFaq and STOREV = aqCaq: DIRECT = aqFaq and STOREV = aqRaq:
1 v1 v1 v1 v1 )
v1                             1 v2 v2 v2 )
v1 v2                             1 v3 v3 )
v1 v2 v3 )

v1 v2 v3 )
DIRECT = aqBaq and STOREV = aqCaq: DIRECT = aqBaq and STOREV = aqRaq:
v1 v2 v3                 v1 v1        )
v1 v2 v3                     v2 v2 v2     )
1 v2 v3                     v3 v3 v3 v3  )
1 v3 )

)