ZUNGBR(l) ) ZUNGBR(l)
ZUNGBR - generate one of the complex unitary matrices Q or P**H determined by ZGEBRD when
reducing a complex matrix A to bidiagonal form
SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, K, LDA, LWORK, M, N
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
ZUNGBR generates one of the complex unitary matrices Q or P**H 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) or G(i) respectively.
If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of order M:
if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n columns of Q, where m
>= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an M-by-M matrix.
If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H is of order N:
if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m rows of P**H, where n
>= m >= k;
if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as an N-by-N matrix.
VECT (input) CHARACTER*1
Specifies whether the matrix Q or the matrix P**H is required, as defined in the
transformation applied by ZGEBRD:
= 'Q': generate Q;
= 'P': generate P**H.
M (input) INTEGER
The number of rows of the matrix Q or P**H to be returned. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q or P**H to be returned. N >= 0. If VECT =
'Q', M >= N >= min(M,K); if VECT = 'P', N >= M >= min(N,K).
K (input) INTEGER
If VECT = 'Q', the number of columns in the original M-by-K matrix reduced by ZGE-
BRD. If VECT = 'P', the number of rows in the original K-by-N matrix reduced by
ZGEBRD. K >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors, as returned by ZGE-
BRD. On exit, the M-by-N matrix Q or P**H.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= M.
TAU (input) COMPLEX*16 array, dimension
(min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P' TAU(i) must contain the scalar
factor of the elementary reflector H(i) or G(i), which determines Q or P**H, as
returned by ZGEBRD in its array argument TAUQ or TAUP.
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. LWORK >= max(1,min(M,N)). For optimum perfor-
mance LWORK >= min(M,N)*NB, 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
LAPACK version 3.0 15 June 2000 ZUNGBR(l)