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