fields (version 5.02)

smooth.2d: Kernel smoother for irregular 2-d data

Description

An approximate Nadaraya Watson kernel smoother is obtained by first discretizing the locations to a grid and then using convolutions to find and to apply the kernel weights. The main advantage of this function is a smoother that avoids explicit looping.

Usage

smooth.2d(Y, ind = NULL, weight.obj = NULL, setup = FALSE, grid = NULL,
    x = NULL, nrow = 64, ncol = 64, surface = TRUE, cov.function =
gauss.cov, Mwidth = NULL, Nwidth = NULL, ...)

Value

Either a matrix of smoothed values or a surface object. The surface object also has a component 'ind' that gives the subscripts of the image matrix where the data is present.

Details

The irregular locations are first discretized to a regular grid ( using as.image) then a 2d- FFT is used to compute a Nadaraya-Watson type kernel estimator. Here we take advantage of two features. The kernel estimator is a convolution and by padding the regular by zeroes where data is not obsevred one can sum the kernel over irregular sets of locations. A second convolutions to find the normalization of the kernel weights.

The kernel function is specified by an function that should evaluate with the kernel for two matrices of locations. Assume that the kernel has the form: K( u-v) for two locations u and v. The function given as the argument to cov.function should have the call myfun( x1,x2) where x1 and x2 are matrices of 2-d locations if nrow(x1)=m and nrow( x2)=n then this function should return a mXn matrix where the (i,j) element is K( x1[i,]- x2[j,]). Optional arguments that are included in the ... arguments are passed to this function when it is used. The default kernel is the Gaussian and the argument theta is the bandwidth. It is easy to write other other kernels, just use Exp.cov.simple as a template.

Examples

# Normal kernel smooth of the precip data with bandwidth of .5 ( degree) 
#  
look<- smooth.2d( RMprecip$y,  x=RMprecip$x, theta=.25)

# finer resolution used in computing the smooth 
look3<-smooth.2d( RMprecip$y, x=RMprecip$x, theta=.25, nrow=256, 
ncol=256,Nwidth=32,
Mwidth=32) 
# if the width arguments were omitted the padding would create a  
# 512X 512 matrix with the data filled in the upper 256X256 part. 
# with a bandwidth of .25 degrees the normal kernel is essentially zero  
# beyond 32 grid points from its center ( about 6 standard deviations) 
#
# take a look:

#set.panel(2,1)
#image( look3, zlim=c(-8,12))
#points( RMprecip$x, pch=".")  
#image( look, zlim =c(-8,12))
#points( RMprecip$x, pch=".")  


# bandwidth changed to .25, exponential kernel   
look2<- smooth.2d( RMprecip$y, x=RMprecip$x, cov.function=Exp.cov,theta=.25)
#