ZUNGBR(1) LAPACK routine (version 3.2) ZUNGBR(1)NAME
ZUNGBR - generates one of the complex unitary matrices Q or P**H deter‐
mined by ZGEBRD when reducing a complex matrix A to bidiagonal form
SYNOPSIS
SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
CHARACTER VECT
INTEGER INFO, K, LDA, LWORK, M, N
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
ZUNGBR generates one of the complex unitary matrices Q or P**H deter‐
mined 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 col‐
umns 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.
ARGUMENTS
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 ZGEBRD. 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 ZGEBRD. 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 (MAX(1,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 performance LWORK >= min(M,N)*NB, where NB is the opti‐
mal 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 routine (version 3.2) November 2008 ZUNGBR(1)
