How to extract specific values with point coordinates from Kriging interpolations made in R?

Question

By using R version 3.4.2 and the library "geoR", I made kriging interpolations for different variables (bellow I give an example of my process). I also made a matrix with the coordinates for 305 trees with distinct marks (species, DBH, Height) that are within the same space for the interpolations, as seen in the image attached (https://i.sstatic.net/LIppE.jpg). I've been looking for ways to extract the nearest value from each variable for each tree and save the corresponding values in a data.frame or matrix, but haven't been successful, and I can't find specific answers to this.

One thing I've been looking at is trying to convert the Kriging result into a Raster (.tif) and proceed from there. But Kriging interpolations are made out of vector data, so is it even posible?

I'm doing this so that I can latter use the data for spatial point patern analysis.

#Kriging####:
PG<-read.csv("PGF.csv", header=T, stringsAsFactors=FALSE)
library("geoR")
x<-(PG$x)
y<-(PG$y)

#Grid
loci<-expand.grid(x=seq(-5, 65, length=100), y=seq(-5, 85, length=100))
names(loci)<-c("x", "y")

mix<-cbind(rep(1,10000), loci$x, loci$y, loci$x*loci$y)

#Model
pH1.mod<-lm(pH1~y*x, data=PG, x=T)
pH1.kg<-cbind(pH1.mod$x[,3], pH1.mod$x[,2], pH1.mod$residuals)
#Transform to geographic data
pH1.geo<-as.geodata(pH1.kg)
#Variogram
pH1.vario<-variog(pH1.geo, max.dist=35)
pH1.vario.mod<-eyefit(pH1.vario)
#Cross validation
pH1.valcruz<-xvalid(pH1.geo, model=pH1.vario.mod)
#Kriging
pH1.krig<-krige.conv(pH1.geo, loc=loci, krige=krige.control(obj.model=pH1.vario.mod[[1]]))
#Predictive model
pH1a.yhat<-mix %*% pH1.mod$coefficients + pH1.krig$predict
#Exchange Kriging prediction values
pH1.krig$predict<-pH1.yhat
#Image
image(pH1.krig2)
contour(pH1.krig2, add=TRUE)

#Tree matrix####:

CoA<-read.csv("CoAr.csv", header=T)
#Data
xa<-(CoA$X)
ya<-(CoA$Y)
points(xa,ya, col=4)

TreeDF<-(cbind.data.frame(xa, ya, CoA$Species, CoA$DBH, CoA$Height, stringsAsFactors = TRUE))
m<-(cbind(xa, ya, 1:305)) 
as.matrix(m)

I tried to find the value of a point in space (trees [1:305]) through the minimum distance to a predicted value using the following code, (I suggest not running this since it takes too long):

for(i in 1:2){print(c(2:10000)[as.matrix(dist(rbind(m[i,], as.matrix(pH1.krig2$predict))))[i,2:10000]==min(as.matrix(dist(rbind(m[i,],as.matrix(pH1.krig2$predict))))[i,2:10000])])}

Answer 1

Use extract() function from raster package:

library(raster)

r <- SpatialPointsDataFrame(loci, data.frame(predict = pH1.krig$predict))
gridded(r) <- T
r <- as(r,'RasterLayer')

pts <- SpatialPointsDataFrame(CoA[,c('X','Y')],CoA)

extract(r, pts)