## Function Zgeqrf

(

**zgeqrf** < m > < n > < a > < lda > < tau > < work > < lwork > < info > )

-- LAPACK routine (version 3.0) --

Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,

Courant Institute, Argonne National Lab, and Rice University

June 30, 1999

Purpose

=======

ZGEQRF computes a QR factorization of a complex M-by-N matrix 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 elements 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) 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/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 illegal value

Further Details

===============

The matrix Q is represented as a product of elementary reflectors

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).