sphere {assist} | R Documentation |

## 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)
```

### 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. |

### 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.

### 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).

### Author(s)

Chunlei Ke chunlei_ke@yahoo.com and Yuedong Wang yuedong@pstat.ucsb.edu

### 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

### Examples

```
## Not run:
x<- seq(0, 2*pi, len=10)
y<- seq(-pi/2, pi/2, len=10)
s.ker<- sphere(cbind(x, y), order=3)
## End(Not run)
```

*assist*version 3.1.9 Index]