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) respectively.If VECT = 'Q', A is assumed to have been an MbyK 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(m1) and DORGBR returns Q as an MbyM matrix.
If VECT = 'P', A is assumed to have been a KbyN 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(n1) . . . G(2) G(1) and DORGBR returns P**T as an NbyN 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 MbyK matrix reduced by DGEBRD. If VECT = 'P', the number of rows in the original KbyN 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 MbyN 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 (MAX(1,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 ith argument had an illegal value