R: Computes the p-norm of a vector

minkowski {fastmatrix} | R Documentation

## Computes the p-norm of a vector

### Description

Computes a `p`-norm of vector `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

[Package fastmatrix version 0.4-1 Index]