Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  generates  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).

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 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 routine (version 3.2)               April 2011                            ZUNGBR(3lapack)
```