minkowski {fastmatrix}

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)

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.

Value

The vector p-norm, a non-negative number.

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