norm {base} | R Documentation |
Computes a matrix norm of x
using LAPACK. The norm can be
the one ("O"
) norm, the infinity ("I"
) norm, the
Frobenius ("F"
) norm, the maximum modulus ("M"
) among
elements of a matrix, or the “spectral” or "2"
-norm, as
determined by the value of type
.
norm(x, type = c("O", "I", "F", "M", "2"))
x |
numeric matrix; note that packages such as Matrix
define more |
type |
character string, specifying the type of matrix norm to be computed. A character indicating the type of norm desired.
The default is |
The base method of norm()
calls the LAPACK function
dlange
.
Note that the 1-, Inf- and "M"
norm is faster to calculate than
the Frobenius one.
Unsuccessful results from the underlying LAPACK code will result in an error giving a positive error code: these can only be interpreted by detailed study of the FORTRAN code.
The matrix norm, a non-negative number.
Except for norm = "2"
, the LAPACK routine DLANGE
.
LAPACK is from https://netlib.org/lapack/.
Anderson, E., et al (1994). LAPACK User's Guide, 2nd edition, SIAM, Philadelphia.
rcond
for the (reciprocal) condition number.
(x1 <- cbind(1, 1:10))
norm(x1)
norm(x1, "I")
norm(x1, "M")
stopifnot(all.equal(norm(x1, "F"),
sqrt(sum(x1^2))))
hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, `+`) }
h9 <- hilbert(9)
## all 5 types of norm:
(nTyp <- eval(formals(base::norm)$type))
sapply(nTyp, norm, x = h9)