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(
                          * )


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  subma­
               trix  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) 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  ele­
               mentary reflector H(i), as returned by DGEHRD.

       WORK     (workspace/output)  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,


               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) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value


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