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NAME
     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( LWORK )



     #include <sunperf.h>

     void dorgrq(int m, int n, int k, double *da, int lda, double
               *tau, int *info) ;

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,  dimen-
               sion (LWORK)
               On exit, if INFO = 0, WORK(1) returns the  optimal
               LWORK.

     LWORK     (input) INTEGER
               The  dimension  of  the  array  WORK.   LWORK   >=
               max(1,M).   For optimum performance LWORK >= M*NB,
               where NB is the optimal blocksize.

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument has an ille-
               gal value

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