ZUNGBR - generate one of the complex unitary matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form

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( * )

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.

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 (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