NAME

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( LWORK )

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) 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.
 

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).

K       (input) INTEGER
If VECT = ’Q’, the number of columns in the original 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 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 performance LWORK >= min(M,N)∗NB, where NB is the optimal blocksize.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

  —  LAPACK version 2.0  —  08 October 1994