CGERQF(l) ) CGERQF(l)
CGERQF - compute an RQ factorization of a complex M-by-N matrix A
SUBROUTINE CGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
COMPLEX A( LDA, * ), TAU( * ), WORK( * )
CGERQF computes an RQ factorization of a complex M-by-N matrix A: A = R * Q.
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 array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, if m <= n, the upper triangle of the sub-
array 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 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further Details).
WORK (workspace/output) COMPLEX 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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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).
LAPACK version 3.0 15 June 2000 CGERQF(l)