DGERQF(l) ) DGERQF(l)NAME
DGERQF - compute an RQ factorization of a real M-by-N matrix A
SYNOPSIS
SUBROUTINE DGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
DGERQF computes an RQ factorization of a real 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) DOUBLE PRECISION 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 trapezoidal
matrix R; the remaining elements, with the array TAU, represent
the orthogonal 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) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) DOUBLE PRECISION 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(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 real scalar, and v is a real vector with
v(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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 DGERQF(l)
