SORGBR(l) ) SORGBR(l)NAME
SORGBR - generate one of the real orthogonal matrices Q or P**T deter‐
mined 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 deter‐
mined 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) 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 SORGBR returns the first n col‐
umns 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).
K (input) INTEGER
If VECT = 'Q', the number of columns in the original 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 elementary reflector H(i) or
G(i), which determines Q or P**T, as returned by SGEBRD in its
array argument 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 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 SORGBR(l)
