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 ele
ments on and below the diagonal of the array con
tain 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 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/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 optimum performance LWORK >= M*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.
= 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).
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).
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