| lp_norm {LambertW} | R Documentation |
Computes the \ell^p norm of an n-dimensional (real/complex) vector \mathbf{x} \in \mathbf{C}^n
≤ft|≤ft| \mathbf{x} \right|\right|_p = ≤ft( ∑_{i=1}^n ≤ft| x_i \right|^p \right)^{1/p}, p \in [0, ∞],
where ≤ft| x_i \right| is the absolute value of x_i. For p=2 this is Euclidean norm; for p=1 it is Manhattan norm. For p=0 it is defined as the number of non-zero elements in \mathbf{x}; for p = ∞ it is the maximum of the absolute values of \mathbf{x}.
The norm of \mathbf{x} equals 0 if and only if \mathbf{x} = \mathbf{0}.
lp_norm(x, p = 2)
x |
n-dimensional vector (possibly complex values) |
p |
which norm? Allowed values p ≥q 0 including |
Non-negative float, the norm of \mathbf{x}.
kRealVec <- c(3, 4) # Pythagoras lp_norm(kRealVec) # did not know Manhattan, lp_norm(kRealVec, p = 1) # so he just imagined running in circles. kComplexVec <- exp(1i * runif(20, -pi, pi)) plot(kComplexVec) sapply(kComplexVec, lp_norm)