fastmatrix (version 0.5-7721)

minkowski: Computes the p-norm of a vector

Description

Computes a \(p\)-norm of vector \(\bold{x}\). The norm can be the one (\(p = 1\)) norm, Euclidean (\(p = 2\)) norm, the infinity (\(p\) = Inf) norm. The underlying C or Fortran code is inspired on ideas of BLAS Level 1.

Usage

minkowski(x, p = 2)

Value

The vector \(p\)-norm, a non-negative number.

Arguments

x

a numeric vector.

p

a number, specifying the type of norm desired. Possible values include real number greater or equal to 1, or Inf, Default value is \(p = 2\).

Details

Method of minkowski for \(p\) = Inf calls idamax BLAS function. For other values, C or Fortran subroutines using unrolled cycles are called.

Examples

# a tiny example
x <- rnorm(1000)
minkowski(x, p = 1)
minkowski(x, p = 1.5)
minkowski(x, p = 2)
minkowski(x, p = Inf)

x <- x / minkowski(x)
minkowski(x, p = 2) # equal to 1