Generalised P-Norm

Calculate the p-norm of any function between given limits.

generalPNorm(fun, p, lower, upper, range = NULL)

Arguments

fun

function to calculate the p-norm of.

p

the pth norm to calculate

lower

lower bound for the integral

upper

upper bound for the integral

range

if discrete then range of the function to sum over

Value

Returns a numeric value for the p norm of a function evaluated between given limits.

Details

The p-norm of a continuous function \(f\) is given by, $$(\int_S |f|^p d\mu)^{1/p}$$ where \(S\) is the function support. And for a discrete function by $$\sum_i (x_{i + 1} - x_i) * |f(x_i)|^p$$ where \(i\) is over a given range.

The p-norm is calculated numerically using the integrate function and therefore results are approximate only.

Examples

generalPNorm(Exponential$new()$pdf, 2, 0, 10)
#> Results from numeric calculations are approximate only. Better results may be available.
#> [1] 0.7071068