CUNGBR - generate one of the complex unitary matrices Q or
P**H determined by CGEBRD when reducing a complex matrix A
to bidiagonal form
SYNOPSIS
SUBROUTINE CUNGBR( VECT, M, N, K, A, LDA, TAU, WORK,
LWORK, INFO )
CHARACTER VECT
INTEGER INFO, K, LDA, LWORK, M, N
COMPLEX A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
CUNGBR generates one of the complex unitary matrices Q or
P**H determined by CGEBRD 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 CUNGBR returns the
first n columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR 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 CUNGBR 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 CUNGBR
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 CGEBRD:
= '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 CGEBRD. If VECT =
'P', the number of rows in the original K-by-N
matrix reduced by CGEBRD. K >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the vectors which define the elementary
reflectors, as returned by CGEBRD. 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 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 CGEBRD in its array argu
ment TAUQ or TAUP.
WORK (workspace/output) COMPLEX 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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