# sgerq2 (l) - Linux Manuals

## NAME

SGERQ2 - computes an RQ factorization of a real m by n matrix A

## SYNOPSIS

SUBROUTINE SGERQ2(
M, N, A, LDA, TAU, WORK, INFO )

INTEGER INFO, LDA, M, N

REAL A( LDA, * ), TAU( * ), WORK( * )

## PURPOSE

SGERQ2 computes an RQ factorization of a real 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) 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 trapezoidal matrix R; the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of elementary 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) REAL array, dimension (M)
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
H(1) H(2) . . . H(k), where k min(m,n).
Each H(i) has the form

H(i) I - tau vaq
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).