zgerqf(3)

NAME

ZGERQF - compute an RQ factorization of a complex M-by-N

matrix A

SYNOPSIS

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

PURPOSE

ZGERQF computes an RQ factorization of a complex M-by-N

matrix A: A = R * Q.

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 upper triangle of the subarray A(1:m,n-m+1:n) contains the

M-by-M upper triangular matrix R; if m >= n, the elements on and

above the (m-n)-th subdiagonal contain the M-by-N upper trape

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

resent 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,M). For optimum performance LWORK >= M*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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is

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

LAPACK version 3.0 15 June 2000

ZGERQF(3)