DORGBR(l) ) DORGBR(l)
DORGBR - generate one of the real orthogonal matrices Q or P**T determined by DGEBRD when
reducing a real matrix A to bidiagonal form
SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, K, LDA, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
DORGBR generates one of the real orthogonal matrices Q or P**T determined by DGEBRD when
reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and P**T 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 DORGBR returns the first n columns of Q, where m
>= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an M-by-M matrix.
If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is of order N:
if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m rows of P**T, where n
>= m >= k;
if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as an N-by-N matrix.
VECT (input) CHARACTER*1
Specifies whether the matrix Q or the matrix P**T is required, as defined in the
transformation applied by DGEBRD:
= 'Q': generate Q;
= 'P': generate P**T.
M (input) INTEGER
The number of rows of the matrix Q or P**T to be returned. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q or P**T 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 DGE-
BRD. If VECT = 'P', the number of rows in the original K-by-N matrix reduced by
DGEBRD. K >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors, as returned by DGE-
BRD. On exit, the M-by-N matrix Q or P**T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (input) DOUBLE PRECISION 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**T, as
returned by DGEBRD in its array argument TAUQ or TAUP.
WORK (workspace/output) DOUBLE PRECISION 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 perfor-
mance 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 version 3.0 15 June 2000 DORGBR(l)