assist (version 3.1.9)

sphere: Calculate Pseudo Reproducing Kernels for Spherical Splines

Description

Return a matrix evaluating reproducing kernels for splines on a sphere.

Usage

sphere(x, y=x, order=2)

Value

a matrix with the numbers of row and column equal to the lengths of x and y respectively. The [i, j] element is the reproducing kernel evaluated at \((x[i,], y[j,])\)

(or \(((x[[1]][i], x[[2]][i]), (y[[1]][j], y[[2]][j]))\) for lists).

Arguments

x

a matrix of two columns or a list of two components, representing observed latitude and longitude respectively.

y

a matrix of two columns or a list of two components, representing latitude and longitude respectively. Default is the same as x.

order

an optional integer sepcifying the order of the spherical spline. Available are 2, 3, 4, 5 and 6, with a default 2.

Author

Chunlei Ke and Yuedong Wang

Details

The kernel for sperical splines is a series inconvenient to compute. This pseudo kernel is based on a topological equivalence as described in Wahba (1981), for which cases the closed form can be derived.

References

Wahba, G. (1981). Spline Interprolation and Smoothing on the Sphere. SIAM J. Sci. Stat.Comput., Vol. 2, No. 1, March 1981.

Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol. 59.

See Also

periodic

Examples

if (FALSE) {
x<- seq(0, 2*pi, len=10)
y<- seq(-pi/2, pi/2, len=10)
s.ker<- sphere(cbind(x, y), order=3)
}