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

SUBROUTINE ZUNMHR(

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

ZUNMHR 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 ZGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

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 ZGEHRD. 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*16 array, dimension

(LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by ZGEHRD.

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*16 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 ZGEHRD.

C (input/output) COMPLEX*16 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*16 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 illegal value