sgerqf(3)

NAME

SGERQF - compute an RQ factorization of a real M-by-N ma

trix A

SYNOPSIS

SUBROUTINE SGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
    INTEGER        INFO, LDA, LWORK, M, N
    REAL           A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

SGERQF computes an RQ factorization of a real M-by-N ma

trix 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) REAL 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 orthogonal 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) REAL array, dimension (min(M,N))

The scalar factors of the elementary reflectors

(see Further Details).

WORK (workspace/output) REAL 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 real scalar, and v is a real vector with
v(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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

SGERQF(3)