zgeql2 (l) - Linux Manuals

NAME

ZGEQL2 - computes a QL factorization of a complex m by n matrix A

SYNOPSIS

SUBROUTINE ZGEQL2(
M, N, A, LDA, TAU, WORK, INFO )

INTEGER INFO, LDA, M, N

COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

ZGEQL2 computes a QL factorization of a complex 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) COMPLEX*16 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 unitary 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) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further Details).
WORK (workspace) COMPLEX*16 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
H(k) . . . H(2) H(1), where k min(m,n).
Each H(i) has the form

H(i) I - tau vaq
where tau is a complex scalar, and v is a complex 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).