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) 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 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.

VECT

          VECT is 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

          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 SGEBRD.


          If VECT = 'P', the number of rows in the original K-by-N


          matrix reduced by SGEBRD.


          K >= 0.

A

          A is 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

          LDA is INTEGER


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

TAU

          TAU is REAL 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 SGEBRD in its array argument TAUQ or TAUP.

WORK

          WORK is REAL 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