QR factorization — dgeqrf • bigalgebra

DGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

dgeqrf(
  M = NULL,
  N = NULL,
  A,
  LDA = NULL,
  TAU = NULL,
  WORK = NULL,
  LWORK = NULL
)

Arguments

M	an integer. The number of rows of the matrix A. M >= 0.
N	an integer. The number of columns of the matrix A. N >= 0.
A	the M-by-N big matrix A.
LDA	an integer. The leading dimension of the array A. LDA >= max(1,M).
TAU	a min(M,N) matrix. The scalar factors of the elementary reflectors.
WORK	a (MAX(1,LWORK)) matrix. On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK	an integer. The dimension of th array WORK.

Value

M-by-N big matrix A. The elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors.

Examples

if (FALSE) {
#' hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
h9 <- hilbert(9); h9
qr(h9)$rank           #--> only 7
qrh9 <- qr(h9, tol = 1e-10)
qrh9$rank 
C <- as.big.matrix(h9)
dgeqrf(A=C)

# The big.matrix file backings will be deleted when garbage collected.
rm(C)
gc()
}