DGEQLF(l) ) DGEQLF(l)NAME
DGEQLF - compute a QL factorization of a real M-by-N matrix A
SYNOPSIS
SUBROUTINE DGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
DGEQLF 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) DOUBLE PRECISION 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 opti‐
mum performance LWORK >= N*NB, where NB is the optimal block‐
size.
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
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).
LAPACK version 3.0 15 June 2000 DGEQLF(l)