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# zungbr

```
NAME
ZUNGBR - generate one of the 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( LWORK )

PURPOSE
ZUNGBR generates one of the 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).

K       (input) INTEGER
K >= 0.  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.

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 elemen-
tary 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) 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.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
```