# SLARFT (3) - Linux Manuals

slarft.f -

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine slarft (characterDIRECT, characterSTOREV, integerN, integerK, real, dimension( ldv, * )V, integerLDV, real, dimension( * )TAU, real, dimension( ldt, * )T, integerLDT)

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

Purpose:

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

T

```          T is REAL 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 slarft.f.

## Author

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