DOPGTR  -  generate  a  real  orthogonal matrix Q which is
       defined as the product of n-1 elementary  reflectors  H(i)
       of order n, as returned by DSPTRD using packed storage


SYNOPSIS

       SUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, LDQ, N

           DOUBLE         PRECISION  AP( * ), Q( LDQ, * ), TAU( *
                          ), WORK( * )


PURPOSE

       DOPGTR generates a  real  orthogonal  matrix  Q  which  is
       defined  as  the product of n-1 elementary reflectors H(i)
       of order n, as returned by DSPTRD using packed storage: 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  triangular  packed storage used in
               previous call to DSPTRD; = 'L':  Lower  triangular
               packed storage used in previous call to DSPTRD.

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

       AP      (input) DOUBLE PRECISION array, dimension
               (N*(N+1)/2)
               The vectors which define  the  elementary  reflec­
               tors, as returned by DSPTRD.

       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 DSPTRD.

       Q       (output) DOUBLE PRECISION array, dimension (LDQ,N)
               The N-by-N orthogonal matrix Q.

       LDQ     (input) INTEGER
               The  leading  dimension  of  the  array  Q. LDQ >=
               max(1,N).

       WORK    (workspace) DOUBLE PRECISION array, dimension
               (N-1)

       INFO    (output) INTEGER
               = 0:  successful exit

               gal value


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