DORGBR(3)      LAPACK routine of NEC Numeric Library Collection      DORGBR(3)



NAME
       DORGBR

SYNOPSIS
       SUBROUTINE DORGBR (VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)



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 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)
                     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         (input)
                     M is INTEGER
                     The number of rows of the matrix Q or P**T to be returned.
                     M >= 0.

           N         (input)
                     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         (input)
                     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         (input/output)
                     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       (input)
                     LDA is INTEGER
                     The leading dimension of the array A. LDA >= max(1,M).

           TAU       (input)
                     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      (output)
                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     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      (output)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value



LAPACK routine                  31 October 2017                      DORGBR(3)