DGEQR2  -  compute  a  QR  factorization  of a real m by n
       matrix A


SYNOPSIS

       SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )

           INTEGER        INFO, LDA, M, N

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


PURPOSE

       DGEQR2 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 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) DOUBLE PRECISION array, dimension (N)

       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).


          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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