fdars (version 0.3.3)

make.gaussian.process: Generate Gaussian Process Samples

Description

Generates functional data samples from a Gaussian process with the specified mean and covariance functions.

Usage

make.gaussian.process(n, t, cov = kernel.gaussian(), mean = 0, seed = NULL)

Value

An fdata object containing the generated samples.

Arguments

n

Number of samples to generate.

t

Evaluation points (vector for 1D, list of two vectors for 2D).

cov

Covariance function (from kernel.gaussian, kernel.matern, etc.).

mean

Mean function. Can be a scalar (default 0), a vector of length equal to the number of evaluation points, or a function.

seed

Optional random seed for reproducibility.

Details

This function generates samples from a Gaussian process with the specified covariance structure. The samples are generated by computing the Cholesky decomposition of the covariance matrix and multiplying by standard normal random variables.

For 2D functional data, pass t as a list of two vectors representing the grid in each dimension.

See Also

kernel.gaussian, kernel.matern, kernel.exponential

Examples

# Generate smooth GP samples with Gaussian covariance
t <- seq(0, 1, length.out = 100)
fd <- make.gaussian.process(n = 20, t = t,
                            cov = kernel.gaussian(length_scale = 0.2),
                            seed = 42)
plot(fd)

# Generate rough GP samples with exponential covariance
fd_rough <- make.gaussian.process(n = 20, t = t,
                                  cov = kernel.exponential(length_scale = 0.1),
                                  seed = 42)
plot(fd_rough)

# Generate 2D GP samples (surfaces)
s <- seq(0, 1, length.out = 20)
t2 <- seq(0, 1, length.out = 20)
fd2d <- make.gaussian.process(n = 5, t = list(s, t2),
                              cov = kernel.gaussian(length_scale = 0.3),
                              seed = 42)
plot(fd2d)

# Generate GP with non-zero mean
mean_func <- function(t) sin(2 * pi * t)
fd_mean <- make.gaussian.process(n = 10, t = t,
                                 cov = kernel.gaussian(variance = 0.1),
                                 mean = mean_func, seed = 42)
plot(fd_mean)