dgeqlf(3)

NAME

DGEQLF - compute a QL factorization of a real M-by-N ma

trix A

SYNOPSIS

SUBROUTINE DGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
    INTEGER        INFO, LDA, LWORK, M, N
    DOUBLE          PRECISION A( LDA, * ), TAU( * ), WORK(
* )

PURPOSE

DGEQLF 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(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 orthogonal matrix Q as a product of elementary reflec

tors (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/output) DOUBLE PRECISION array, dimen

sion (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 real scalar, and v is a real 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

DGEQLF(3)