zgeqrf(3)

NAME

ZGEQRF - compute a QR factorization of a complex M-by-N

matrix A

SYNOPSIS

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

PURPOSE

ZGEQRF computes a QR factorization of a complex M-by-N ma

trix A: A = Q * R.

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, the ele

ments on and above the diagonal of the array contain the

min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular

if m >= n); the elements below the diagonal, with the array TAU,

represent the unitary matrix Q as a product of min(m,n) elemen

tary 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/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(1) H(2) . . . H(k), 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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in

A(i+1:m,i), and tau in TAU(i).

LAPACK version 3.0 15 June 2000

ZGEQRF(3)