Generates n realizations of a zero-mean Gaussian process. The function also
accepts user-defined covariance functions (without "nugget" effect, see
cov), The implemented defaults with scale parameter \(\phi\), order
\(o\) and nugget effect variance \(\sigma^2\) are:
squared exponential covariance \(Cov(x(t), x(t')) = \exp(-(t-t')^2)/\phi) + \sigma^2 \delta_{t}(t')\).
Wiener process covariance \(Cov(x(t), x(t')) = \min(t',t)/\phi + \sigma^2 \delta_{t}(t')\),
Matèrn process covariance \(Cov(x(t), x(t')) = \tfrac{2^{1-o}}{\Gamma(o)} (\tfrac{\sqrt{2o}|t-t'|}{\phi})^o \text{Bessel}_o(\tfrac{\sqrt{2o}|t-t'|}{s}) + \sigma^2 \delta_{t}(t')\)
tf_rgp(
n,
arg = 51L,
cov = c("squareexp", "wiener", "matern"),
scale = diff(range(arg))/10,
nugget = scale/200,
order = 1.5
)an tfd-vector of length n
how many realizations to draw
vector of evaluation points (arg of the return object). Defaults
to (0, 0.02, 0.04, ..., 1). If given as a single integer (don't forget
the L...), creates a regular grid of that length over (0,1).
type of covariance function to use. Implemented defaults are
"squareexp", "wiener", "matern", see Description. Can also be any
vectorized function returning \(Cov(x(t), x(t'))\) without nugget
effect for pairs of inputs t and t'.
scale parameter (see Description). Defaults to the width of the domain divided by 10.
nugget effect for additional white noise / unstructured
variability. Defaults to scale/200 (so: very little white noise).
order of the Matèrn covariance (if used, must be >0), defaults
to 1.5. The higher, the smoother the process. Evaluation of the covariance
function becomes numerically unstable for large (>20) order, use
"squareexp".
Other tidyfun RNG functions:
tf_jiggle()