DORGQL - generate an M-by-N real matrix Q with orthonormal
       columns,


SYNOPSIS

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

           INTEGER        INFO, K, LDA, LWORK, M, N

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


PURPOSE

       DORGQL generates an M-by-N real matrix Q with  orthonormal
       columns, which is defined as the last N columns of a prod­
       uct of K elementary reflectors of order M

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

       as returned by DGEQLF.


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 (n-k+i)-th column must contain the
               vector  which  defines  the  elementary  reflector
               H(i),  for i = 1,2,...,k, as returned by DGEQLF in
               the last 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 DGEQLF.

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


       LWORK   (input) INTEGER
               The  dimension  of  the  array  WORK.   LWORK   >=
               max(1,N).   For optimum performance LWORK >= N*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 has an ille­
               gal value


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