DGEQL2 - compute a QL factorization of a real m by n
matrix A
SYNOPSIS
SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )
INTEGER INFO, LDA, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK(
* )
PURPOSE
DGEQL2 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) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal 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).
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).
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