# larf - Man Page

larf: apply Householder reflector

## Synopsis

### Functions

subroutine clarf (side, m, n, v, incv, tau, c, ldc, work)
CLARF applies an elementary reflector to a general rectangular matrix.
subroutine dlarf (side, m, n, v, incv, tau, c, ldc, work)
DLARF applies an elementary reflector to a general rectangular matrix.
subroutine slarf (side, m, n, v, incv, tau, c, ldc, work)
SLARF applies an elementary reflector to a general rectangular matrix.
subroutine zlarf (side, m, n, v, incv, tau, c, ldc, work)
ZLARF applies an elementary reflector to a general rectangular matrix.

## Function Documentation

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

CLARF applies an elementary reflector to a general rectangular matrix.

Purpose:

``` CLARF 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.

To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
tau.```
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
(1 + (M-1)*abs(INCV)) if SIDE = 'L'
or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
The vector v in the representation of H. V is not used if
TAU = 0.```

INCV

```          INCV is INTEGER
The increment between elements of v. INCV <> 0.```

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'```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 127 of file clarf.f.

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

DLARF applies an elementary reflector to a general rectangular matrix.

Purpose:

``` DLARF 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.```
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
(1 + (M-1)*abs(INCV)) if SIDE = 'L'
or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
The vector v in the representation of H. V is not used if
TAU = 0.```

INCV

```          INCV is INTEGER
The increment between elements of v. INCV <> 0.```

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 >= max(1,M).```

WORK

```          WORK is DOUBLE PRECISION array, dimension
(N) if SIDE = 'L'
or (M) if SIDE = 'R'```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 123 of file dlarf.f.

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

SLARF applies an elementary reflector to a general rectangular matrix.

Purpose:

``` SLARF 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.```
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
(1 + (M-1)*abs(INCV)) if SIDE = 'L'
or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
The vector v in the representation of H. V is not used if
TAU = 0.```

INCV

```          INCV is INTEGER
The increment between elements of v. INCV <> 0.```

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 >= max(1,M).```

WORK

```          WORK is REAL array, dimension
(N) if SIDE = 'L'
or (M) if SIDE = 'R'```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 123 of file slarf.f.

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

ZLARF applies an elementary reflector to a general rectangular matrix.

Purpose:

``` ZLARF 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.

To apply H**H, supply conjg(tau) instead
tau.```
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
(1 + (M-1)*abs(INCV)) if SIDE = 'L'
or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
The vector v in the representation of H. V is not used if
TAU = 0.```

INCV

```          INCV is INTEGER
The increment between elements of v. INCV <> 0.```

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'```
Author

Univ. of Tennessee

Univ. of California Berkeley