ZGERQF - compute an RQ factorization of a complex M-by-N
matrix A
SYNOPSIS
SUBROUTINE ZGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
ZGERQF computes an RQ factorization of a complex M-by-N
matrix A: A = R * 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, if m <=
n, the upper triangle of the subarray A(1:m,n-
m+1:n) contains the M-by-M upper triangular matrix
R; if m >= n, the elements on and above the (m-
n)-th subdiagonal contain the M-by-N upper trape
zoidal matrix R; the remaining elements, with the
array TAU, represent the unitary matrix Q as a
product of min(m,n) 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
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(1)' H(2)' . . . H(k)', 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-
k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau
in TAU(i).
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