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# dlarf

```
NAME
DLARF - apply a real elementary reflector H to a real m by n
matrix C, from either the left or the right

SYNOPSIS
SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )

CHARACTER     SIDE

INTEGER       INCV, LDC, M, N

DOUBLE        PRECISION TAU

DOUBLE        PRECISION C( LDC, * ), V( * ), WORK( * )

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'

where tau is a real scalar and v is a real vector.

If tau = 0, then H is taken to be the unit matrix.

ARGUMENTS
SIDE    (input) CHARACTER*1
= 'L': form  H * C
= 'R': form  C * H

M       (input) INTEGER
The number of rows of the matrix C.

N       (input) INTEGER
The number of columns of the matrix C.

V       (input) 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    (input) INTEGER
The increment between elements of v. INCV <> 0.

TAU     (input) DOUBLE PRECISION
The value tau in the representation of H.

C       (input/output) 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     (input) INTEGER
The leading dimension of the array C. LDC >=
max(1,M).

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