 ZLARZ(3) applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right

## SYNOPSIS

SUBROUTINE ZLARZ(
SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )

CHARACTER SIDE

INTEGER INCV, L, LDC, M, N

COMPLEX*16 TAU

COMPLEX*16 C( LDC, * ), V( * ), WORK( * )

## PURPOSE

ZLARZ 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'
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' (the conjugate transpose of H), supply conjg(tau) instead tau.
H is a product of k elementary reflectors as returned by ZTZRZF.

## 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.
L (input) INTEGER
The number of entries of the vector V containing the meaningful part of the Householder vectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
V (input) COMPLEX*16 array, dimension (1+(L-1)*abs(INCV))
The vector v in the representation of H as returned by ZTZRZF. V is not used if TAU = 0.
INCV (input) INTEGER
The increment between elements of v. INCV <> 0.
TAU (input) COMPLEX*16
The value tau in the representation of H.
C (input/output) 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 (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace) COMPLEX*16 array, dimension
(N) if SIDE = 'L' or (M) if SIDE = 'R'

## FURTHER DETAILS

Based on contributions by

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA