fdars (version 0.3.3)

kernel.polynomial: Polynomial Covariance Function

Description

Computes the polynomial covariance function: $$k(s, t) = \sigma^2 (s \cdot t + c)^p$$

Usage

kernel.polynomial(variance = 1, offset = 0, degree = 2)

Value

A covariance function object of class 'kernel_polynomial'.

Arguments

variance

Variance parameter \(\sigma^2\) (default 1).

offset

Offset parameter \(c\) (default 0).

degree

Polynomial degree \(p\) (default 2).

Details

The polynomial covariance function produces sample paths that are polynomial functions of degree at most degree. Setting degree = 1 and offset = 0 gives the linear kernel.

See Also

kernel.linear, make.gaussian.process

Examples

# Generate quadratic function samples
cov_func <- kernel.polynomial(degree = 2, offset = 1)
t <- seq(0, 1, length.out = 50)
fd <- make.gaussian.process(n = 10, t = t, cov = cov_func)
plot(fd)