NAME¶

DGELQ2 - computes an LQ factorization of a real m by n matrix A

SYNOPSIS¶

SUBROUTINE DGELQ2(

M, N, A, LDA, TAU, WORK, INFO )

INTEGER INFO, LDA, M, N DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE¶

DGELQ2 computes an LQ factorization of a real m by n matrix A: A = L * 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) DOUBLE PRECISION array, dimension (LDA,N)

On entry, the m by n matrix A. On exit, the elements on and below the diagonal of the array contain the m by min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above 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 (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
Q = H(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).