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NAME
     dgeqrf - compute a QR factorization of a real M-by-N  matrix
     A

SYNOPSIS
     SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

     INTEGER INFO, LDA, LWORK, M, N

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



     #include <sunperf.h>

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

PURPOSE
     DGEQRF computes a QR factorization of a real  M-by-N  matrix
     A:  A = Q * R.


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

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

     A         (input/output) DOUBLE PRECISION  array,  dimension
               (LDA,N)
               On entry, the M-by-N matrix A.  On exit, the  ele-
               ments  on and above the diagonal of the array con-
               tain the min(M,N)-by-N upper trapezoidal matrix  R
               (R  is  upper  triangular if m >= n); the elements
               below the diagonal, with the array TAU,  represent
               the  orthogonal  matrix Q as a product of min(m,n)
               elementary reflectors (see Further Details).

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

     TAU       (output)   DOUBLE   PRECISION   array,   dimension
               (min(M,N))
               The scalar factors of  the  elementary  reflectors
               (see Further Details).

     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,N).   For optimum performance LWORK >= N*NB,
               where NB is the optimal blocksize.

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

FURTHER DETAILS
     The matrix Q is  represented  as  a  product  of  elementary
     reflectors

        Q = H(1) H(2) . . . H(k), where k = min(m,n).

     Each H(i) has the form

        H(i) = I - tau * v * v'

     where tau is a real scalar, and v is a real vector with
     v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is  stored  on  exit  in
     A(i+1:m,i), and tau in TAU(i).

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