ZGELQF(l) ) ZGELQF(l)NAME
ZGELQF - compute an LQ factorization of a complex M-by-N matrix A
SYNOPSIS
SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L
* Q.
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, the elements on and
below the diagonal of the array contain the m-by-min(m,n) lower
trapezoidal matrix L (L is lower triangular if m <= n); the
elements above the diagonal, with the array TAU, represent the
unitary matrix Q as a product of elementary reflectors (see
Further Details). LDA (input) INTEGER The leading dimen‐
sion 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/output) COMPLEX*16 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,M). For opti‐
mum performance LWORK >= M*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 complex scalar, and v is a complex vector with v(1:i-1)
= 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and
tau in TAU(i).
LAPACK version 3.0 15 June 2000 ZGELQF(l)