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


SYNOPSIS

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

           CHARACTER      UPLO

           INTEGER        INFO, LDA, LWORK, N

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


PURPOSE

       DORGTR  generates  a  real  orthogonal  matrix  Q which is
       defined as the product of  n-1  elementary  reflectors  of
       order  N, as returned by DSYTRD: 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 DSYTRD; = 'L': Lower triangle of A
               contains elementary reflectors from DSYTRD.

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

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

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

               The  dimension  of  the  array  WORK.   LWORK   >=
               max(1,N-1).   For  optimum  performance  LWORK  >=
               (N-1)*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) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value


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