---
name: "clarft"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/clarft.f"
---

# clarft(3)

Part of [clarft.f(3)](/clarft.f/3.md).

## NAME

SRC/clarft.f

## SYNOPSIS

### Functions/Subroutines

recursive subroutine **clarft** (direct, storev, n, k, v, ldv, tau, t, ldt)\
 **CLARFT** forms the triangular factor T of a block reflector H = I - vtvH

## Function/Subroutine Documentation

### recursive subroutine clarft (character direct, character storev, integer n, integer k, complex, dimension( ldv, \* ) v, integer ldv, complex, dimension( \* ) tau, complex, dimension( ldt, \* ) t, integer ldt)

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

**Purpose:**

```
!>
!> CLARFT 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 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 array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i).
!>
```

*T*

```
!>          T is COMPLEX 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.

**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 **162** of file **clarft.f**.

## Author

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