---
name: "larfx"
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/larfx"
---

# larfx(3)

larfx: apply Householder reflector, unrolled

## NAME

larfx - larfx: apply Householder reflector, unrolled

## SYNOPSIS

### Functions

subroutine **clarfx** (side, m, n, v, tau, c, ldc, work)\
 **CLARFX** applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.  subroutine **dlarfx** (side, m, n, v, tau, c, ldc, work)\
 **DLARFX** applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.  subroutine **slarfx** (side, m, n, v, tau, c, ldc, work)\
 **SLARFX** applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.  subroutine **zlarfx** (side, m, n, v, tau, c, ldc, work)\
 **ZLARFX** applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

## Detailed Description

## Function Documentation

### subroutine clarfx (character side, integer m, integer n, complex, dimension( \* ) v, complex tau, complex, dimension( ldc, \* ) c, integer ldc, complex, dimension( \* ) work)

**CLARFX** applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

**Purpose:**

```
!>
!> CLARFX applies a complex elementary reflector H to a complex m by n
!> matrix C, from either the left or the right. H is represented in the
!> form
!>
!>       H = I - tau * v * v**H
!>
!> where tau is a complex scalar and v is a complex vector.
!>
!> If tau = 0, then H is taken to be the unit matrix
!>
!> This version uses inline code if H has order < 11.
!>
```

**Parameters**

*SIDE*

```
!>          SIDE is CHARACTER*1
!>          = 'L': form  H * C
!>          = 'R': form  C * H
!>
```

*M*

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

*N*

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

*V*

```
!>          V is COMPLEX array, dimension (M) if SIDE = 'L'
!>                                        or (N) if SIDE = 'R'
!>          The vector v in the representation of H.
!>
```

*TAU*

```
!>          TAU is COMPLEX
!>          The value tau in the representation of H.
!>
```

*C*

```
!>          C is COMPLEX array, dimension (LDC,N)
!>          On entry, the m by n matrix C.
!>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
!>          or C * H if SIDE = 'R'.
!>
```

*LDC*

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

*WORK*

```
!>          WORK is COMPLEX array, dimension (N) if SIDE = 'L'
!>                                            or (M) if SIDE = 'R'
!>          WORK is not referenced if H has order < 11.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **118** of file **clarfx.f**.

### subroutine dlarfx (character side, integer m, integer n, double precision, dimension( \* ) v, double precision tau, double precision, dimension( ldc, \* ) c, integer ldc, double precision, dimension( \* ) work)

**DLARFX** applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

**Purpose:**

```
!>
!> DLARFX applies a real elementary reflector H to a real m by n
!> matrix C, from either the left or the right. H is represented in the
!> form
!>
!>       H = I - tau * v * v**T
!>
!> where tau is a real scalar and v is a real vector.
!>
!> If tau = 0, then H is taken to be the unit matrix
!>
!> This version uses inline code if H has order < 11.
!>
```

**Parameters**

*SIDE*

```
!>          SIDE is CHARACTER*1
!>          = 'L': form  H * C
!>          = 'R': form  C * H
!>
```

*M*

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

*N*

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

*V*

```
!>          V is DOUBLE PRECISION array, dimension (M) if SIDE = 'L'
!>                                     or (N) if SIDE = 'R'
!>          The vector v in the representation of H.
!>
```

*TAU*

```
!>          TAU is DOUBLE PRECISION
!>          The value tau in the representation of H.
!>
```

*C*

```
!>          C is DOUBLE PRECISION array, dimension (LDC,N)
!>          On entry, the m by n matrix C.
!>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
!>          or C * H if SIDE = 'R'.
!>
```

*LDC*

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

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension
!>                      (N) if SIDE = 'L'
!>                      or (M) if SIDE = 'R'
!>          WORK is not referenced if H has order < 11.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **119** of file **dlarfx.f**.

### subroutine slarfx (character side, integer m, integer n, real, dimension( \* ) v, real tau, real, dimension( ldc, \* ) c, integer ldc, real, dimension( \* ) work)

**SLARFX** applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

**Purpose:**

```
!>
!> SLARFX applies a real elementary reflector H to a real m by n
!> matrix C, from either the left or the right. H is represented in the
!> form
!>
!>       H = I - tau * v * v**T
!>
!> where tau is a real scalar and v is a real vector.
!>
!> If tau = 0, then H is taken to be the unit matrix
!>
!> This version uses inline code if H has order < 11.
!>
```

**Parameters**

*SIDE*

```
!>          SIDE is CHARACTER*1
!>          = 'L': form  H * C
!>          = 'R': form  C * H
!>
```

*M*

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

*N*

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

*V*

```
!>          V is REAL array, dimension (M) if SIDE = 'L'
!>                                     or (N) if SIDE = 'R'
!>          The vector v in the representation of H.
!>
```

*TAU*

```
!>          TAU is REAL
!>          The value tau in the representation of H.
!>
```

*C*

```
!>          C is REAL array, dimension (LDC,N)
!>          On entry, the m by n matrix C.
!>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
!>          or C * H if SIDE = 'R'.
!>
```

*LDC*

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

*WORK*

```
!>          WORK is REAL array, dimension
!>                      (N) if SIDE = 'L'
!>                      or (M) if SIDE = 'R'
!>          WORK is not referenced if H has order < 11.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **119** of file **slarfx.f**.

### subroutine zlarfx (character side, integer m, integer n, complex\*16, dimension( \* ) v, complex\*16 tau, complex\*16, dimension( ldc, \* ) c, integer ldc, complex\*16, dimension( \* ) work)

**ZLARFX** applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10.

**Purpose:**

```
!>
!> ZLARFX applies a complex elementary reflector H to a complex m by n
!> matrix C, from either the left or the right. H is represented in the
!> form
!>
!>       H = I - tau * v * v**H
!>
!> where tau is a complex scalar and v is a complex vector.
!>
!> If tau = 0, then H is taken to be the unit matrix
!>
!> This version uses inline code if H has order < 11.
!>
```

**Parameters**

*SIDE*

```
!>          SIDE is CHARACTER*1
!>          = 'L': form  H * C
!>          = 'R': form  C * H
!>
```

*M*

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

*N*

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

*V*

```
!>          V is COMPLEX*16 array, dimension (M) if SIDE = 'L'
!>                                        or (N) if SIDE = 'R'
!>          The vector v in the representation of H.
!>
```

*TAU*

```
!>          TAU is COMPLEX*16
!>          The value tau in the representation of H.
!>
```

*C*

```
!>          C is COMPLEX*16 array, dimension (LDC,N)
!>          On entry, the m by n matrix C.
!>          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
!>          or C * H if SIDE = 'R'.
!>
```

*LDC*

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

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (N) if SIDE = 'L'
!>                                            or (M) if SIDE = 'R'
!>          WORK is not referenced if H has order < 11.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **118** of file **zlarfx.f**.

## Author

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