DGEQR2(l) — LAPACK routine (version 2.0)

NAME

DGEQR2 - compute a QR factorization of a real m by n matrix A

SYNOPSIS

SUBROUTINE DGEQR2(
M, N, A, LDA, TAU, WORK, INFO )

INTEGER INFO, LDA, M, N

DOUBLE PRECISION A( LDA, ∗ ), TAU( ∗ ), WORK( ∗ )

PURPOSE

DGEQR2 computes a QR factorization of a real 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) DOUBLE PRECISION 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 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) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further Details).

WORK (workspace) DOUBLE PRECISION array, dimension (N)

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 real scalar, and v is a real 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).