dgelq2(3F)

NAME
     DGELQ2 - compute an LQ factorization of a real m by n matrix A

SYNOPSIS
     SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )

         INTEGER        INFO, LDA, M, N

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

PURPOSE
     DGELQ2 computes an LQ factorization of a real m by n matrix A:  A = L *
     Q.


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
             below the diagonal of the array contain the m by min(m,n) lower
             trapezoidal matrix L (L is lower triangular if m <= n); the
             elements above 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 (M)

     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(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n), and
     tau in TAU(i).