DORG2R - generate an m by n real matrix Q with orthonormal
       columns,


SYNOPSIS

       SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO )

           INTEGER        INFO, K, LDA, M, N

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


PURPOSE

       DORG2R  generates an m by n real matrix Q with orthonormal
       columns, which is defined as the  first  n  columns  of  a
       product of k elementary reflectors of order m

             Q  =  H(1) H(2) . . . H(k)

       as returned by DGEQRF.


ARGUMENTS

       M       (input) INTEGER
               The number of rows of the matrix Q. M >= 0.

       N       (input) INTEGER
               The  number  of columns of the matrix Q. M >= N >=
               0.

       K       (input) INTEGER
               The number of elementary reflectors whose  product
               defines the matrix Q. N >= K >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension
               (LDA,N)
               On entry, the i-th column must contain the  vector
               which defines the elementary reflector H(i), for i
               = 1,2,...,k, as returned by DGEQRF in the first  k
               columns  of its array argument A.  On exit, the m-
               by-n matrix Q.

       LDA     (input) INTEGER
               The  first  dimension  of  the  array  A.  LDA  >=
               max(1,M).

       TAU     (input) DOUBLE PRECISION array, dimension (K)
               TAU(i)  must contain the scalar factor of the ele­
               mentary reflector H(i), as returned by DGEQRF.

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

       INFO    (output) INTEGER
               = 0: successful exit

               gal value


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