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DGEQR2(1) LAPACK routine (version 3.2) DGEQR2(1)

NAME

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

SYNOPSIS

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

The number of rows of the matrix A. M >= 0.
The number of columns of the matrix A. N >= 0.
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).
The scalar factors of the elementary reflectors (see Further Details).
= 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).

November 2008 LAPACK routine (version 3.2)