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dgeqr2 examples
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Man Page Details
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NAME
       DGEQR2 - 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  elements  on  and
               above the diagonal of the array contain 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 dimen-
               sion 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 illegal 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).

