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


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