cor_lagr_askey: Calculate Lagrangian correlation of the Askey form

In mcgf: Markov Chain Gaussian Fields Simulation and Parameter Estimation

Calculate Lagrangian correlation of the Askey form

Description

Calculate Lagrangian correlation of the Askey form

Usage

cor_lagr_askey(v1, v2, k = 2, h1, h2, u)

Arguments

v1	Prevailing wind, u-component.
v2	Prevailing wind, v-component.
k	Scale parameter of \|\boldsymbol v\|, k>0. Default is 2.
h1	Horizontal distance matrix or array.
h2	Vertical distance matrix or array, same dimension as h1.
u	Time lag, same dimension as h1.

Details

The Lagrangian correlation function of the Askey form with parameters \boldsymbol v = (v_1, v_2)^\top\in\mathbb{R}^2 has the form

C(\mathbf{h}, u)=\left(1-\dfrac{1}{k\|\boldsymbol v\|} \left\|\mathbf{h}-u\boldsymbol v\right\|\right)^{3/2}_+,

where \|\cdot\| is the Euclidean distance, x_+=\max(x,0), \mathbf{h} = (\mathrm{h}_1, \mathrm{h}_2)^\top\in\mathbb{R}^2, and k > 0 is the scale parameter controlling the magnitude of asymmetry in correlation.

Value

Correlations of the same dimension as h1.

References

Askey, R. (1973). Radial characteristic functions, Tech. Report No. 1262, Math. Research Center, University of Wisconsin-Madison.

See Also

Other correlation functions: cor_cauchy(), cor_exp(), cor_fs(), cor_lagr_exp(), cor_lagr_tri(), cor_sep(), cor_stat(), cor_stat_rs()

Examples

h1 <- matrix(c(0, -5, 5, 0), nrow = 2)
h2 <- matrix(c(0, -8, 8, 0), nrow = 2)
u <- matrix(0.1, nrow = 2, ncol = 2)
cor_lagr_askey(v1 = 5, v2 = 10, h1 = h1, h2 = h2, u = u)

h1 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3))
h2 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3))
u <- array(rep(-c(1, 2, 3), each = 4), dim = c(2, 2, 3))
cor_lagr_askey(v1 = 10, v2 = 10, h1 = h1, h2 = h2, u = u)

mcgf documentation built on June 29, 2024, 9:09 a.m.