ZUNGBR - generate one of the complex unitary matrices Q or
P**H determined 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 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.
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).
If VECT = 'Q', the number of columns in the origi
nal 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 ele
mentary reflector H(i) or G(i), which determines Q
or P**H, as returned by ZGEBRD in its array argu
ment 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 performance 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 ille
gal value
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