---
name: "clarfb"
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/clarfb.f"
---

# clarfb(3)

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

## NAME

SRC/clarfb.f

## SYNOPSIS

### Functions/Subroutines

subroutine **clarfb** (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)\
 **CLARFB** applies a block reflector or its conjugate-transpose to a general rectangular matrix.

## Function/Subroutine Documentation

### subroutine clarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, complex, dimension( ldv, \* ) v, integer ldv, complex, dimension( ldt, \* ) t, integer ldt, complex, dimension( ldc, \* ) c, integer ldc, complex, dimension( ldwork, \* ) work, integer ldwork)

**CLARFB** applies a block reflector or its conjugate-transpose to a general rectangular matrix.

**Purpose:**

```
!>
!> CLARFB applies a complex block reflector H or its transpose H**H to a
!> complex M-by-N matrix C, from either the left or the right.
!>
```

**Parameters**

*SIDE*

```
!>          SIDE is CHARACTER*1
!>          = 'L': apply H or H**H from the Left
!>          = 'R': apply H or H**H from the Right
!>
```

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          = 'N': apply H (No transpose)
!>          = 'C': apply H**H (Conjugate transpose)
!>
```

*DIRECT*

```
!>          DIRECT is CHARACTER*1
!>          Indicates how H is formed from a product of elementary
!>          reflectors
!>          = 'F': H = H(1) H(2) . . . H(k) (Forward)
!>          = 'B': H = H(k) . . . H(2) H(1) (Backward)
!>
```

*STOREV*

```
!>          STOREV is CHARACTER*1
!>          Indicates how the vectors which define the elementary
!>          reflectors are stored:
!>          = 'C': Columnwise
!>          = 'R': Rowwise
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix C.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix C.
!>
```

*K*

```
!>          K is INTEGER
!>          The order of the matrix T (= the number of elementary
!>          reflectors whose product defines the block reflector).
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0.
!>
```

*V*

```
!>          V is COMPLEX array, dimension
!>                                (LDV,K) if STOREV = 'C'
!>                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
!>                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
!>          The matrix V. See Further Details.
!>
```

*LDV*

```
!>          LDV is INTEGER
!>          The leading dimension of the array V.
!>          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
!>          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
!>          if STOREV = 'R', LDV >= K.
!>
```

*T*

```
!>          T is COMPLEX array, dimension (LDT,K)
!>          The triangular K-by-K matrix T in the representation of the
!>          block reflector.
!>
```

*LDT*

```
!>          LDT is INTEGER
!>          The leading dimension of the array T. LDT >= K.
!>
```

*C*

```
!>          C is COMPLEX array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C.
!>          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
!>
```

*LDC*

```
!>          LDC is INTEGER
!>          The leading dimension of the array C. LDC >= max(1,M).
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (LDWORK,K)
!>
```

*LDWORK*

```
!>          LDWORK is INTEGER
!>          The leading dimension of the array WORK.
!>          If SIDE = 'L', LDWORK >= max(1,N);
!>          if SIDE = 'R', LDWORK >= max(1,M).
!>
```

**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 triangular part of V (including its diagonal) is not
!>  referenced.
!>
!>  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 **194** of file **clarfb.f**.

## Author

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