poisson.cov {fields} R Documentation

## Poisson spherical covariance function

### Description

Given two sets of locations in lon/lat computes the cross covariance matrix for the Poisson covariance among all pairings.

### Usage

```poisson.cov(x1, x2, eta = .2)
```

### Arguments

 `x1` Matrix of first set of locations where each row gives the coordinates of a particular point. First column is longitudes and the second column is latitudes. `x2` Matrix of second set of locations where each row gives the coordinates of a particular point. If this is missing x1 is used. `eta` Range (or scale) parameter. Should be in the interval [0,1]

### Details

This covariance is one of the few closed form covariances for the sphere and also know as the Poisson kernel. If x1 and x2 are matrices where nrow(x1)=m and nrow(x2)=n then this function should return a mXn matrix where the (i,j) element is the covariance between the locations x1[i,] and x2[j,]. The covariance is found as

(1-eta**2)/(1 - 2 * eta * D.ij + eta**2)**(1.5)

where D.ij is the great circle distance between x1[i,] and x2[j,].

### Value

If nrow(x1)=m and nrow(x2)=n then the returned cross covariance matrix, will be mXn.

Krig, rdist.earth

### Examples

```# plot of covariance

x<- make.surface.grid( list( x=seq( -180,180,,40), y= seq( -85,85,,40)))
x0<- matrix( c(0,0), ncol=2)
look<- poisson.cov( x,x0, eta=.5)
image.plot(as.surface(x,look))
```

[Package fields version 3.3.1 Index]