R: Vector Norm

Norm {pracma} | R Documentation

## Vector Norm

### Description

The `Norm` function calculates several different types of vector norms for `x`, depending on the argument `p`.

### Usage

    Norm(x, p = 2)

### Arguments

`x` | Numeric vector; matrices not allowed.
`p` | Numeric scalar or Inf, -Inf; default is 2

### Details

`Norm` returns a scalar that gives some measure of the magnitude of the elements of `x`. It is called the p-norm for values -Inf ≤ p ≤ Inf, defining Hilbert spaces on R^n.

`Norm(x)` is the Euclidean length of a vecor `x`; same as `Norm(x, 2)`.
`Norm(x, p)` for finite p is defined as `sum(abs(A)^p)^(1/p)`.
`Norm(x, Inf)` returns `max(abs(x))`, while `Norm(x, -Inf)` returns `min(abs(x))`.

### Value

Numeric scalar (or `Inf`), or `NA` if an element of `x` is `NA`.

### Note

In Matlab/Octave this is called `norm`; R's `norm` function `norm(x, "F")` (‘Frobenius Norm’) is the same as `Norm(x)`.

### See Also

`norm` of a matrix

### Examples

    Norm(c(3, 4))          #=> 5  Pythagoras triple
    Norm(c(1, 1, 1), p=2)  #   sqrt(3)
    Norm(1:10, p = 1)      #   sum(1:10)
    Norm(1:10, p = 0)      #   Inf
    Norm(1:10, p = Inf)    #   max(1:10)
    Norm(1:10, p = -Inf)   #   min(1:10)

[Package pracma version 2.0.4 Index]