# cunmr3 (l) - Linux Man Pages

## NAME

CUNMR3 - overwrites the general complex m by n matrix C with Q * C if SIDE = aqLaq and TRANS = aqNaq, or Qaq* C if SIDE = aqLaq and TRANS = aqCaq, or C * Q if SIDE = aqRaq and TRANS = aqNaq, or C * Qaq if SIDE = aqRaq and TRANS = aqCaq,

## SYNOPSIS

SUBROUTINE CUNMR3(
SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO )

CHARACTER SIDE, TRANS

INTEGER INFO, K, L, LDA, LDC, M, N

COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

## PURPOSE

CUNMR3 overwrites the general complex m by n matrix C with where Q is a complex unitary matrix defined as the product of k elementary reflectors

H(1) H(2) . . . H(k)
as returned by CTZRZF. Q is of order m if SIDE = aqLaq and of order n if SIDE = aqRaq.

## ARGUMENTS

SIDE (input) CHARACTER*1
= aqLaq: apply Q or Qaq from the Left
= aqRaq: apply Q or Qaq from the Right
TRANS (input) CHARACTER*1

= aqNaq: apply Q (No transpose)
= aqCaq: apply Qaq (Conjugate transpose)
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the matrix Q. If SIDE = aqLaq, M >= K >= 0; if SIDE = aqRaq, N >= K >= 0.
L (input) INTEGER
The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = aqLaq, M >= L >= 0, if SIDE = aqRaq, N >= L >= 0.
A (input) COMPLEX array, dimension
(LDA,M) if SIDE = aqLaq, (LDA,N) if SIDE = aqRaq The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CTZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,K).
TAU (input) COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CTZRZF.
C (input/output) COMPLEX array, dimension (LDC,N)
On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Qaq*C or C*Qaq or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace) COMPLEX array, dimension
(N) if SIDE = aqLaq, (M) if SIDE = aqRaq
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

## FURTHER DETAILS

Based on contributions by

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