\(\sqrt{sill/L}\sum_l z_l(\langle x, u_l\rangle)\) over L bands with spectral line processes \(z_l(t) = \sqrt{2/M}\sum_m \cos(r_{lm} t + \phi_{lm})\), frequencies from the radial spectral law of the covariance (Matheron 1973; Mantoglou and Wilson 1982; Emery and Lantuejoul 2006). 2-D: directions \(\pi(l + U)/L\), models exponential, gaussian, matern, geometric anisotropy; 3-D: Fibonacci directions under a uniform random rotation (Shoemake 1992 quaternion), gaussian and exponential. Philox streams: 0 offset, then 3l + 1 radii, 3l + 2 phases, 3l + 3 extra normals; identical to the Python arm.
Usage
TurningBands(
coords,
cov_model = "exponential",
sill = 1,
range_ = 1,
nu = 0.5,
n_bands = 64L,
n_waves = 50L,
angle = 0,
ratio = 1,
seed = 1L
)References
Matheron, G. (1973). The intrinsic random functions and their applications. Advances in Applied Probability 5, 439-468.
Mantoglou, A. and Wilson, J. L. (1982). The turning bands method for simulation of random fields using line generation by a spectral method. Water Resources Research 18, 1379-1394.
Emery, X. and Lantuejoul, C. (2006). TBSIM: a computer program for conditional simulation of three-dimensional Gaussian random fields via the turning bands method. Computers and Geosciences 32, 1615-1628.
Shoemake, K. (1992). Uniform random rotations. Graphics Gems III, 124-132.