SORGBR - generate one of the real orthogonal matrices Q or
P**T determined by SGEBRD when reducing a real matrix A to
bidiagonal form
SYNOPSIS
SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK,
LWORK, INFO )
CHARACTER VECT
INTEGER INFO, K, LDA, LWORK, M, N
REAL A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
SORGBR generates one of the real orthogonal matrices Q or
P**T determined by SGEBRD 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 SORGBR returns the
first n columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR 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 SORGBR 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 SORGBR
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 SGEBRD:
= '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 SGEBRD. If VECT =
'P', the number of rows in the original K-by-N
matrix reduced by SGEBRD. K >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the vectors which define the elementary
reflectors, as returned by SGEBRD. 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) REAL 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 SGEBRD in its array argu
ment TAUQ or TAUP.
WORK (workspace/output) REAL 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
Man(1) output converted with
man2html