SGEQLF(l) ) SGEQLF(l)
SGEQLF - compute a QL factorization of a real M-by-N matrix A
SUBROUTINE SGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
REAL A( LDA, * ), TAU( * ), WORK( * )
SGEQLF computes a QL factorization of a real M-by-N matrix A: A = Q * L.
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 sub-
array 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 trape-
zoidal matrix L; the remaining elements, with the array TAU, represent the orthog-
onal 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.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the
optimal size of the WORK array, returns this value as the first entry of the WORK
array, and no error message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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).
LAPACK version 3.0 15 June 2000 SGEQLF(l)