# zlarft.f man page

zlarft.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine zlarft (characterDIRECT, characterSTOREV, integerN, integerK, complex*16, dimension( ldv, * )V, integerLDV, complex*16, dimension( * )TAU, complex*16, dimension( ldt, * )T, integerLDT)

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

**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
```

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

*T*

```
T is 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*

```
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 zlarft.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zlarft(3) is an alias of zlarft.f(3).