DORGRQ - generate an M-by-N real matrix Q with orthonormal
       rows,


SYNOPSIS

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

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

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


PURPOSE

       DORGRQ generates an M-by-N real matrix Q with  orthonormal
       rows,  which is defined as the last M rows of a product of
       K elementary reflectors of order N

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

       as returned by DGERQF.


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. N >= M.

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

       A       (input/output) DOUBLE PRECISION array, dimension
               (LDA,N)
               On entry, the (m-k+i)-th row must contain the vec­
               tor  which  defines the elementary reflector H(i),
               for i = 1,2,...,k, as returned by  DGERQF  in  the
               last k rows 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 DGERQF.

       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,M).  For optimum performance LWORK >=  M*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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