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.

VECT

          VECT is 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

          M is INTEGER


          The number of rows of the matrix Q or P**T to be returned.


          M >= 0.

N

          N is 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

          K is 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

          A is 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

          LDA is INTEGER


          The leading dimension of the array A. LDA >= max(1,M).

TAU

          TAU is 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

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is 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

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

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April 2012