
ZGEQL2(l) ) ZGEQL2(l)
NAME
ZGEQL2  compute a QL factorization of a complex m by n matrix A
SYNOPSIS
SUBROUTINE ZGEQL2( M, N, A, LDA, TAU, WORK, INFO )
INTEGER INFO, LDA, M, N
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
ZGEQL2 computes a QL factorization of a complex 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) COMPLEX*16 array, dimension (LDA,N)
On entry, the m by n matrix A. On exit, if m >= n, the lower triangle of the sub
array 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 trape
zoidal matrix L; the remaining elements, with the array TAU, represent the unitary
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) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further Details).
WORK (workspace) COMPLEX*16 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 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 complex scalar, and v is a complex vector with v(mk+i+1:m) = 0 and v(m
k+i) = 1; v(1:mk+i1) is stored on exit in A(1:mk+i1,nk+i), and tau in TAU(i).
LAPACK version 3.0 15 June 2000 ZGEQL2(l) 
