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



NAME
       DORGHR

SYNOPSIS
       SUBROUTINE DORGHR (N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO)



PURPOSE
            DORGHR generates a real orthogonal matrix Q which is defined as the
            product of IHI-ILO elementary reflectors of order N, as returned by
            DGEHRD:

            Q = H(ilo) H(ilo+1) . . . H(ihi-1).




ARGUMENTS
           N         (input)
                     N is INTEGER
                     The order of the matrix Q. N >= 0.

           ILO       (input)
                     ILO is INTEGER

           IHI       (input)
                     IHI is INTEGER

                     ILO and IHI must have the same values as in the previous call
                     of DGEHRD. Q is equal to the unit matrix except in the
                     submatrix Q(ilo+1:ihi,ilo+1:ihi).
                     1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

           A         (input/output)
                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the vectors which define the elementary reflectors,
                     as returned by DGEHRD.
                     On exit, the N-by-N orthogonal matrix Q.

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

           TAU       (input)
                     TAU is DOUBLE PRECISION array, dimension (N-1)
                     TAU(i) must contain the scalar factor of the elementary
                     reflector H(i), as returned by DGEHRD.

           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 >= IHI-ILO.
                     For optimum performance LWORK >= (IHI-ILO)*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                      DORGHR(3)