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


SYNOPSIS

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

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

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


PURPOSE

       DORGQR 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/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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