GP.simulate.curves.fast: Simulate multiple curves on d-dimensional Euclidean space based on Gaussian processes via modified exponential squared kernel.

Description

Simulate multiple curves on d-dimensional Euclidean space based on Gaussian processes via modified exponential squared kernel.

Usage

GP.simulate.curves.fast(
  n,
  x,
  poly_degree,
  a,
  b,
  center = NULL,
  scale = NULL,
  max_range = 6
)

Value

A list of variables representing the simulated curve:

f: A matrix of real numbers for the multiple simulated curves.
x: A matrix of real numbers for the grid points where rows are observations and columns are coordinates.
work_x: A matrix of real numbers for the standardized grid points for the simulated curve. It has the same dimension as "x".

Arguments

n: An integer number to specify the number of curves to simulate
x: A matrix of real numbers as grid points where rows are observations and columns are coordinates.
poly_degree: An integer number to specify the highest degree of Hermite polynomials. The default value is 10L.
a: A positive real number to specify the concentration parameter in the standard modified exponential squared kernel. The larger value the more the GP concentrates around the center. The default value is 0.01.
b: A positive real number to specify the smoothness parameter in the standard modified exponential squared kernel. The smaller value the smoother the GP is. The default value is 1.0.
center: A vector of real numbers specifying the centroid parameters in the modified exponential squared kernel. The default value is NULL and set to the center of the grid points: apply(x,2,mean).
scale: A vector of positive numbers specifying the scale parameters in the modified exponential squared kernel. The default value is NULL and set to values such that grid points in a range of (-max_range,max_range) in each dimension.
max_range: A positive real number indicating the maximum range of the grid points to specify the scale parameter. The default value is NULL and set to 6.

Author

Jian Kang <jiankang@umich.edu>

Examples

Run this code

library(BayesGPfit)
library(lattice)
set.seed(1224)
dat = list()
dat$x = GP.generate.grids(d=1,num_grids = 100)
curves = GP.simulate.curves.fast(n = 10, dat$x,a=0.01,b=0.5,poly_degree=20L)
GP.plot.curves(curves,main="Simulated Curves")

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