fastmatrix (version 0.5-7721)

matrix.norm: Compute the norm of a rectangular matrix

Description

Computes a matrix norm of x using LAPACK. The norm can be the one ("1") norm, the infinity ("inf") norm, the Frobenius norm, the maximum modulus ("maximum") among elements of a matrix, as determined by the value of type.

Usage

matrix.norm(x, type = "Frobenius")

Value

The matrix norm, a non-negative number.

Arguments

x

a numeric matrix.

type

character string, specifying the type of matrix norm to be computed. A character indicating the type of norm desired.

"1"

specifies the one norm, (maximum absolute column sum);

"Inf"

specifies the infinity norm (maximum absolute row sum);

"Frobenius"

specifies the Frobenius norm (the Euclidean norm of x treated as if it were a vector);

"maximum"

specifies the maximum modulus of all the elements in x.

Details

As function norm in package base, method of matrix.norm calls the LAPACK function DLANGE.

Note that the 1-, Inf- and maximum norm is faster to calculate than the Frobenius one.

Examples

# a tiny example
x <- matrix(c(1, 1, 1,
              1, 2, 1,
              1, 3, 1,
              1, 1,-1,
              1, 2,-1,
              1, 3,-1), ncol = 3, byrow = TRUE)
matrix.norm(x, type = "Frobenius")
matrix.norm(x, type = "1")
matrix.norm(x, type = "Inf")

# an example not that small
n <- 1000
x <- .5 * diag(n) + 0.5 * matrix(1, nrow = n, ncol = n)
matrix.norm(x, type = "Frobenius")
matrix.norm(x, type = "1")
matrix.norm(x, type = "Inf")
matrix.norm(x, type = "maximum") # equal to 1