| vgram.matrix {fields} | R Documentation |
Computes a variogram for an image taking into account different directions and returning summary information about the differences in each of these directions.
vgram.matrix(dat, R=5, dx = 1,dy = 1 ) plot.vgram.matrix(x,...)
dat |
A matrix spacing of rows and columns are assumed to have the same distance. |
R |
Maximum radius for finding variogram differences assuming that the grid points are spaced one unit a part. Default is go out to a radius of 5. |
dx |
The spacing of grid points on the X axis. This is used to calculate the correct distance between grid points. If dx is not equal to dy then the collapse argument must be FALSE. |
dy |
The spacing of grid points on the Y axis. See additional notes for dx. |
x |
Returned list from vgram.matrix |
... |
Arguments for image.plot |
For the "full" case the statistics can summarize departures from isotropy by separating the variogram differences according to orientation. For small R this runs efficiently because the differences are found by sub-setting the image matrix.
For example, suppose that a row of the ind matrix is (2,3). The variogram value associated with this row is the mean of the differences (1/2)*(X(i,j)- X( i+2,j+3))**2 for all i and j. (Here X(.,.) are the values for the spatial field.) In this example d= sqrt(13) and there will be another entry with the same distance but corresponding to the direction (3,2). plot.vgram.matrix attempts to organize all the different directions into a coherent image plot.
A list with the following components: d, a vector of distances for
the differences,
and vgram, the variogram values. This is the traditional variogram
ignoring direction.
d.full, a vector of distances for all possible shifts up distance R,
ind, a two column matrix giving the x and y increment used to compute
the shifts, and vgram.full, the variogram at each of these
separations. Also computed is vgram.robust, Cressie's version of a robust
variogram statistic.
Also returned is the component N the number of differences found for each
separation csae.
# variogram for Lennon image. data(lennon) out<-vgram.matrix( lennon) plot( out$d, out$vgram, xlab="separation distance", ylab="variogram") # image plot of vgram values by direction. # look at different directions out<-vgram.matrix( lennon, R=8) plot( out$d, out$vgram) # add in different orientations points( out$d.full, out$vgram.full, col="red") #image plot of variogram values for different directions. set.panel(1,1) plot.vgram.matrix( out) # John Lennon appears remarkably isotropic!