CUNGBR(l) ) CUNGBR(l)NAME
CUNGBR - generate one of the complex unitary matrices Q or P**H deter‐
mined 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 deter‐
mined 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 col‐
umns 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 (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 opti‐
mal 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 version 3.0 15 June 2000 CUNGBR(l)
