# zunmbr (l) - Linux Manuals

## NAME

ZUNMBR - VECT = aqQaq, ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = aqLaq SIDE = aqRaq TRANS = aqNaq

## SYNOPSIS

SUBROUTINE ZUNMBR(
VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

CHARACTER SIDE, TRANS, VECT

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

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

## PURPOSE

If VECT = aqQaq, ZUNMBR overwrites the general complex M-by-N matrix C with
SIDE aqLaq     SIDE aqRaq TRANS = aqNaq: Q * C C * Q TRANS = aqCaq: Q**H * C C * Q**H
If VECT = aqPaq, ZUNMBR overwrites the general complex M-by-N matrix C with

SIDE aqLaq     SIDE aqRaq
TRANS = aqNaq: P * C C * P
TRANS = aqCaq: P**H * C C * P**H
Here Q and P**H are the unitary matrices determined by ZGEBRD when reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q and P**H are defined as products of elementary reflectors H(i) and G(i) respectively.
Let nq = m if SIDE = aqLaq and nq = n if SIDE = aqRaq. Thus nq is the order of the unitary matrix Q or P**H that is applied.
If VECT = aqQaq, A is assumed to have been an NQ-by-K matrix: if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).
If VECT = aqPaq, A is assumed to have been a K-by-NQ matrix: if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).

## ARGUMENTS

VECT (input) CHARACTER*1
= aqQaq: apply Q or Q**H;
= aqPaq: apply P or P**H.
SIDE (input) CHARACTER*1

= aqLaq: apply Q, Q**H, P or P**H from the Left;
= aqRaq: apply Q, Q**H, P or P**H from the Right.
TRANS (input) CHARACTER*1

= aqNaq: No transpose, apply Q or P;
= aqCaq: Conjugate transpose, apply Q**H or P**H.
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
If VECT = aqQaq, the number of columns in the original matrix reduced by ZGEBRD. If VECT = aqPaq, the number of rows in the original matrix reduced by ZGEBRD. K >= 0.
A (input) COMPLEX*16 array, dimension
(LDA,min(nq,K)) if VECT = aqQaq (LDA,nq) if VECT = aqPaq The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by ZGEBRD.
LDA (input) INTEGER
The leading dimension of the array A. If VECT = aqQaq, LDA >= max(1,nq); if VECT = aqPaq, LDA >= max(1,min(nq,K)).
TAU (input) COMPLEX*16 array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by ZGEBRD in the array argument TAUQ or TAUP.
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 or P*C or P**H*C or C*P or C*P**H.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If SIDE = aqLaq, LWORK >= max(1,N); if SIDE = aqRaq, LWORK >= max(1,M); if N = 0 or M = 0, LWORK >= 1. For optimum performance LWORK >= max(1,N*NB) if SIDE = aqLaq, and LWORK >= max(1,M*NB) if SIDE = aqRaq, where NB is the optimal blocksize. (NB = 0 if M = 0 or N = 0.) 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