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


SYNOPSIS

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

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

           REAL           A( LDA, * ), TAU( * ), WORK( * )


PURPOSE

       SORGHR generates a  real  orthogonal  matrix  Q  which  is
       defined as the product of IHI-ILO elementary reflectors of
       order N, as returned by SGEHRD: 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  SGEHRD.  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) REAL array, dimension (LDA,N)
               On  entry, the vectors which define the elementary
               reflectors, as returned by SGEHRD.  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) REAL array, dimension (N-1)
               TAU(i) must contain the scalar factor of the  ele­
               mentary reflector H(i), as returned by SGEHRD.

       WORK    (workspace/output) REAL 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.

               If LWORK = -1, then a workspace query is  assumed;

               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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