sgeqlf(l) — SunSoft Performance Library

NAME

sgeqlf - compute a QL factorization of a real M-by-N matrix A

SYNOPSIS

SUBROUTINE SGEQLF(
M, N, A, LDA, TAU, WORK, LWORK, INFO )

INTEGER INFO, LDA, LWORK, M, N

REAL A( LDA, ∗ ), TAU( ∗ ), WORK( LWORK )

PURPOSE

SGEQLF 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/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N∗NB, where NB is the optimal blocksize.

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).