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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