SORGTR  -  generate  a  real  orthogonal matrix Q which is
       defined as the product of  n-1  elementary  reflectors  of
       order N, as returned by SSYTRD


SYNOPSIS

       SUBROUTINE SORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO
                          )

           CHARACTER      UPLO

           INTEGER        INFO, LDA, LWORK, N

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


PURPOSE

       SORGTR generates a  real  orthogonal  matrix  Q  which  is
       defined  as  the  product  of n-1 elementary reflectors of
       order N, as returned by SSYTRD: if UPLO = 'U', Q =  H(n-1)
       . . . H(2) H(1),

       if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).


ARGUMENTS

       UPLO    (input) CHARACTER*1
               =  'U':  Upper  triangle  of A contains elementary
               reflectors from SSYTRD; = 'L': Lower triangle of A
               contains elementary reflectors from SSYTRD.

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

       A       (input/output) REAL array, dimension (LDA,N)
               On  entry, the vectors which define the elementary
               reflectors, as returned by SSYTRD.  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 SSYTRD.

       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   >=
               max(1,N-1).   For  optimum  performance  LWORK  >=
               (N-1)*NB, where NB is the optimal blocksize.

               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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