# clarf.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index

clarf.f

## SYNOPSIS

### Functions/Subroutines

subroutine clarf (SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.

## Function/Subroutine 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

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 130 of file clarf.f.

## Author

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