Last chance! 50% off unlimited learning
Sale ends in
fnorm function calculates several different types of function
norms for depending on the argument p.fnorm(f, g, x1, x2, p = 2, npoints = 100)Inf), or NA if one of these functions
returns NA.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 vnorm 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.
vnormxp <- 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 #=> 0.1095285Run the code above in your browser using DataLab