zgeqlf(3)

NAME

ZGEQLF - compute a QL factorization of a complex M-by-N

matrix A

SYNOPSIS

SUBROUTINE ZGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
    INTEGER        INFO, LDA, LWORK, M, N
    COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

ZGEQLF computes a QL factorization of a complex M-by-N ma

trix 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 subarray A(m-n+1:m,1:n) contains the

N-by-N lower triangular matrix L; if m <= n, the elements on and

below the (n-m)-th superdiagonal contain the M-by-N lower trape

zoidal matrix L; the remaining elements, with the array TAU, rep

resent the unitary matrix Q as a product of elementary reflectors

(see Further Details). LDA (input) INTEGER The leading di

mension 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/output) COMPLEX*16 array, dimension

(LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal

LWORK.

LWORK (input) INTEGER

The dimension of the array WORK. LWORK >=

max(1,N). For optimum performance LWORK >= N*NB, where NB is the

optimal blocksize.

If LWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the WORK array,

returns this value as the first entry of the WORK array, and no

error message related to LWORK is issued by XERBLA.

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 re

flectors

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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on

exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).

LAPACK version 3.0 15 June 2000

ZGEQLF(3)