SYNOPSIS
 SUBROUTINE DGEQL2(
 M, N, A, LDA, TAU, WORK, INFO )
 INTEGER INFO, LDA, M, N
 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
DGEQL2 computes a QL factorization of a real m by n matrix A: A = Q * L.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, if m >= n, the lower triangle of the subarray A(mn+1:m,1:n) contains the n by n lower triangular matrix L; if m <= n, the elements on and below the (nm)th superdiagonal contain the m by n lower trapezoidal matrix L; the remaining elements, 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 ith argument had an illegal value
FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectorsQ = 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(mk+i+1:m) = 0 and v(mk+i) = 1; v(1:mk+i1) is stored on exit in A(1:mk+i1,nk+i), and tau in TAU(i).