man sgeql2 (Fonctions bibliothèques) - compute a QL factorization of a real m by n matrix A

NAME

SGEQL2 - compute a QL factorization of a real m by n matrix A

SYNOPSIS

SUBROUTINE SGEQL2(
M, N, A, LDA, TAU, WORK, INFO )
INTEGER INFO, LDA, M, N
REAL A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

SGEQL2 computes a QL factorization of a real m by n matrix A: A = Q * L.

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 lower triangle of the subarray A(m-n+1:m,1:n) contains the n by n lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix L; 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 (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(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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).