ZUNMBR(1) LAPACK routine (version 3.2) ZUNMBR(1)NAME
ZUNMBR - VECT = 'Q', ZUNMBR overwrites the general complex M-by-N
matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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 = 'Q', ZUNMBR 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
If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * C C * P
TRANS = 'C': 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 = 'L' and nq = n if SIDE = 'R'. Thus nq is the order
of the unitary matrix Q or P**H that is applied.
If VECT = 'Q', 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 = 'P', 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
= 'Q': apply Q or Q**H;
= 'P': apply P or P**H.
SIDE (input) CHARACTER*1
= 'L': apply Q, Q**H, P or P**H from the Left;
= 'R': apply Q, Q**H, P or P**H from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q or P;
= 'C': 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 = 'Q', the number of columns in the original matrix
reduced by ZGEBRD. If VECT = 'P', 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 = 'Q' (LDA,nq) if VECT = 'P' 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 = 'Q', LDA >=
max(1,nq); if VECT = 'P', 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 reflec‐
tor 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 = 'L', LWORK >=
max(1,N); if SIDE = 'R', LWORK >= max(1,M); if N = 0 or M = 0,
LWORK >= 1. For optimum performance LWORK >= max(1,N*NB) if
SIDE = 'L', and LWORK >= max(1,M*NB) if SIDE = 'R', 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 calcu‐
lates 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
LAPACK routine (version 3.2) November 2008 ZUNMBR(1)