remotePARTS (version 1.0.4)

covar_taper: Tapered-spherical distance-based covariance function

Description

Tapered-spherical distance-based covariance function

Exponential distance-based covariance function

Exponential-power distance-based covariance function

Usage

covar_taper(d, theta, cor = NULL)
covar_exp(d, range)
covar_exppow(d, range, shape)

Value

a tapered-spherical transformation of d is returned.

the exponential covariance (v)

exponential-power covariance (v)

Arguments

d

a numeric vector or matrix of distances

theta

distance beyond which covariances are forced to 0.

cor

optional correlation parameter. If included, the covariance is subtracted from cor.

range

range parameter

shape

shape parameter

Details

covar_taper calculates covariance v as follows:

if d <= theta, then v = ((1 - (d/theta))^2) * (1 + (d/(2 * theta)))

if d > theta, then v = 0

covar_exp calculates covariance v as follows:

v = exp(-d/range)

covar_exppow calculates covariance v as follows:

v = exp(-(d/range)^2)

Note that covar_exppow(..., shape = 1) is equivalent to covar_exp() but is needed as a separate function for use with fitCor.

Examples

# simulate dummy data
map.width = 5 # square map width
coords = expand.grid(x = 1:map.width, y = 1:map.width) # coordinate matrix

# calculate distance
D = geosphere::distm(coords) # distance matrix

# visualize covariance matrix
image(covar_taper(D, theta = .5*max(D)))

# plot tapered covariance function
curve(covar_taper(x, theta = .5), from = 0, to = 1);abline(v = 0.5, lty = 2, col = "grey80")


# visualize covariance matrix
image(covar_exp(D, range = .2*max(D)))

# plot exponential function with different ranges
curve(covar_exp(x, range = .2), from = 0, to = 1)
curve(covar_exp(x, range = .1), from = 0, to = 1, col = "blue", add = TRUE)
legend("topright", legend = c("range = 0.2", "range = 0.1"), col = c("black", "blue"), lty = 1)


# visualize Exponential covariance matrix
image(covar_exppow(D, range = .2*max(D), shape = 1))

# visualize Exponential-power covariance matrix
image(covar_exppow(D, range = .2*max(D), shape = .5))

# plot exponential power function with different shapes
curve(covar_exppow(x, range = .2, shape = 1), from = 0, to = 1)
curve(covar_exppow(x, range = .2, shape = .5), from = 0, to = 1, col = "blue", add = TRUE)
legend("topright", legend = c("shape = 1.0", "shape = 0.5"), col = c("black", "blue"), lty = 1)