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dorghr

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

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

          INTEGER        IHI, ILO, INFO, LDA, LWORK, N

          DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK(
                         LWORK )

 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) INTEGER
              The order of the matrix Q. N >= 0.

      ILO     (input) INTEGER
              IHI     (input) 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).  If N > 0, 1 <= ILO <= IHI
              <= N; otherwise ILO = 1 and IHI = N.

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

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

      WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK)
              On exit, if INFO = 0, WORK(1) returns the optimal
              LWORK.

      LWORK   (input) INTEGER
              The dimension of the array WORK. LWORK >= IHI-ILO.

              For optimum performance LWORK >= (IHI-ILO)*NB, where
              NB is the optimal blocksize.

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