| cor_lagr_askey {mcgf} | R Documentation |
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 |
h1 |
Horizontal distance matrix or array. |
h2 |
Vertical distance matrix or array, same dimension as |
u |
Time lag, same dimension as |
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)