Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  - forms the triangular factor T of a complex block reflector H of order n, which
is defined as a product of k elementary reflectors

```

#### SYNOPSIS

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

CHARACTER      DIRECT, STOREV

INTEGER        K, LDT, LDV, N

COMPLEX*16     T( LDT, * ), TAU( * ), V( LDV, * )

```

#### PURPOSE

```       ZLARFT 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

```

#### ARGUMENTS

```        DIRECT  (input) 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  (input) CHARACTER*1
Specifies how the vectors which define the elementary
= 'R': 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) COMPLEX*16 array, dimension
(LDV,K) if STOREV = 'C'
(LDV,N) if STOREV = 'R'
The matrix V. See further details.

LDV     (input) INTEGER
The leading dimension of the array V.
If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.

TAU     (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i).

T       (output) COMPLEX*16 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     (input) INTEGER
The leading dimension of the array T. LDT >= K.

```

#### FURTHERDETAILS

```        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 = '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 )

LAPACK auxiliary routine (version 3.3.1)   April 2011                            ZLARFT(3lapack)
```