# fnorm: Function Norm

### Description

The `fnorm` function calculates several different types of function norms for depending on the argument `p`.

### Usage

 `1` ```fnorm(f, g, x1, x2, p = 2, npoints = 100) ```

### Arguments

 `f, g` functions given by name or string. `x1, x2` endpoints of the interval. `p` Numeric scalar or Inf, -Inf; default is 2. `npoints` number of points to be considered in the interval.

### Details

`fnorm` returns a scalar that gives some measure of the distance of two functions `f` and `g` on the interval `[x1, x2]`.

It takes `npoints` equidistant points in the interval, computes the function values for `f` and `g` and applies `Norm` to their difference.

Especially `p=Inf` returns the maximum norm, while `fnorm(f, g, x1, x2, p = 1, npoints) / npoints` would return some estimate of the mean distance.

### Value

Numeric scalar (or `Inf`), or `NA` if one of these functions returns `NA`.

### Note

Another kind of ‘mean’ distance could be calculated by integrating the difference `f-g` and dividing through the length of the interval.

`Norm`

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```xp <- seq(-1, 1, length.out = 6) yp <- runge(xp) p5 <- polyfit(xp, yp, 5) f5 <- function(x) polyval(p5, x) fnorm(runge, f5, -1, 1, p = Inf) #=> 0.4303246 fnorm(runge, f5, -1, 1, p = Inf, npoints = 1000) #=> 0.4326690 # Compute mean distance using fnorm: fnorm(runge, f5, -1, 1, p = 1, 1000) / 1000 #=> 0.1094193 # Compute mean distance by integration: fn <- function(x) abs(runge(x) - f5(x)) integrate(fn, -1, 1)\$value / 2 #=> 0.1095285 ```

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