cunmhr(3)

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( * )

PURPOSE

CUNMHR overwrites the general complex M-by-N matrix C with

SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q 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.

If LWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the WORK array,

returns this value as the first entry of the WORK array, and no

error message related to LWORK is issued by XERBLA.

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value

LAPACK version 3.0 15 June 2000

CUNMHR(3)