超出数据网格的外推

我有一个(x,y,z)值的网格,我想要一个函数,当给定(x,y)点位于网格之外时,它可以近似z值。

我已经尝试使用Akima包(代码块3)解决这个问题,但我似乎无法让interp函数与linear=FALSE选项一起工作,这是外推到网格之外所需的。

数据:

# Grid data
x <- seq(0,1,length.out=6)
y <- seq(0,1,length.out=6)
z <- outer(x,y,function(x,y){sqrt(x^2+y^3)})

可视化数据(这不是问题的关键):

## Visualize the data - Not important for question ##
  jet.colors <- colorRampPalette( c("Royal Blue", "Lime Green") )
  nbcol <- 100
  color <- jet.colors(nbcol)
  nrz <- nrow(z)
  ncz <- ncol(z)
  zfacet <- z[-1, -1] + z[-1, -ncz] + z[-nrz, -1] + z[-nrz, -ncz]
  facetcol <- cut(zfacet, nbcol)
  pmat <- persp(x, y, z, d = 1,r = 4,
                ticktype="detailed", 
                col = color[facetcol], 
                main = "Title",
                xlab="x value", 
                ylab = "y value", 
                zlab= "z value",
                scale=FALSE,
                expand=0.6, 
                theta=-40, 
                phi=25)
## End visualization ##

我尝试使用Akima包解决问题

library(akima)

# Vectorize the grid:
zz <- as.vector(z)
# create all combinations of x and y
xy <- expand.grid(x,y)

# What we want:
sqrt(0.7^2 + 0.7^3) # c(0.7, 0.7) = 0.9126883
sqrt(0.7^2 + 1.2^3) # c(0.7, 1.2) = 1.489295

# We get a result for the first point inside the grid,
# but not for the second one outside the grid.
# This is expected behaviour when linear=TRUE:
interp(xy[,1], xy[,2], zz, xo = c(0.7), yo= c(0.7, 1.2), linear=TRUE)
# = (0.929506, NA)

# When LINEAR = FALSE we get z= 0, 0!!
interp(xy[,1], xy[,2], zz, xo = c(0.7), yo= c(0.7, 1.2), linear=FALSE, extrap = TRUE)
# = (0, 0)

# Dropping extrap=TRUE we see that both are actually NA in this case
interp(xy[,1], xy[,2], zz, xo = c(0.7), yo= c(0.7, 1.2), linear=FALSE)
# = (NA, NA)
# What is going on?

使用R 3.1.3和akima_0.5-11。