NAME

cunmhr - overwrite the general complex M-by-N matrix C with   SIDE = ’L’ SIDE = ’R’ TRANS = ’N’

SYNOPSIS

SUBROUTINE CUNMHR(
SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

CHARACTER SIDE, TRANS

INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N

COMPLEX A( LDA, ∗ ), C( LDC, ∗ ), TAU( ∗ ), WORK( LWORK )

PURPOSE

CUNMHR overwrites the general complex M-by-N matrix C with TRANS = ’C’:      Q∗∗H ∗ C       C ∗ Q∗∗H
 
where Q is a complex unitary matrix of order nq, with nq = m if SIDE = ’L’ and nq = n if SIDE = ’R’. Q is defined as the product of IHI-ILO elementary reflectors, as returned by CGEHRD:
 
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
 

ARGUMENTS

SIDE    (input) CHARACTER∗1
= ’L’: apply Q or Q∗∗H from the Left;
= ’R’: apply Q or Q∗∗H from the Right.

TRANS   (input) CHARACTER∗1
= ’N’: apply Q  (No transpose)
= ’C’: apply Q∗∗H (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.

ILO     (input) INTEGER
IHI     (input) INTEGER ILO and IHI must have the same values as in the previous call of CGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). If SIDE = ’L’, then 1 <= ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI = 0, if M = 0; if SIDE = ’R’, then 1 <= ILO <= IHI <= N, if N > 0, and ILO = 1 and IHI = 0, if N = 0.

A       (input) COMPLEX array, dimension
(LDA,M) if SIDE = ’L’ (LDA,N) if SIDE = ’R’ The vectors which define the elementary reflectors, as returned by CGEHRD.

LDA     (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M) if SIDE = ’L’; LDA >= max(1,N) if SIDE = ’R’.

TAU     (input) COMPLEX array, dimension
(M-1) if SIDE = ’L’ (N-1) if SIDE = ’R’ TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEHRD.

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 Q∗∗H∗C or C∗Q∗∗H or C∗Q.

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

WORK    (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK. If SIDE = ’L’, LWORK >= max(1,N); if SIDE = ’R’, LWORK >= max(1,M). For optimum performance LWORK >= N∗NB if SIDE = ’L’, and LWORK >= M∗NB if SIDE = ’R’, where NB is the optimal blocksize.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

SunSoft, Inc.  —  Last change: 27 Jun 1995