DORGBR - generate one of the real orthogonal matrices Q or
P**T determined by DGEBRD when reducing a real matrix A to
bidiagonal form
SYNOPSIS
SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK,
LWORK, INFO )
CHARACTER VECT
INTEGER INFO, K, LDA, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK(
* )
PURPOSE
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) respec
tively.
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.
ARGUMENTS
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).
If VECT = 'Q', the number of columns in the origi
nal M-by-K matrix reduced by DGEBRD. 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 DGEBRD. 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 ele
mentary reflector H(i) or G(i), which determines Q
or P**T, as returned by DGEBRD in its array argu
ment 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 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 ille
gal value
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