 CUNGBR(3) generates 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).
K (input) INTEGER
If VECT = 'Q', the number of columns in the original 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 elementary reflector H(i) or G(i), which determines Q or P**H, as returned by CGEBRD in its array argument TAUQ or TAUP.
WORK (workspace/output) COMPLEX 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