[SOLVED] Kriging with gstat : "Covariance matrix singular at location" with predict

Kriging with gstat : "Covariance matrix singular at location" with predict

I am trying to do an estimation by kriging with gstat, but can never achieve it because of an issue with the covariance matrix. I never have estimates on the locations I want, because they are all skipped. I have the following warning message, for each location :

1: In predict.gstat(g, newdata = newdata, block = block, nsim = nsim,  : 
Covariance matrix singular at location [-8.07794,48.0158,0]: skipping...

And all estimates are NA.

So far I've browsed many related StackOverflow threads, but none resolved my problems (https://gis.stackexchange.com/questions/222192/r-gstat-krige-covariance-matrix-singular-at-location-5-88-47-4-0-skipping ; https://gis.stackexchange.com/questions/200722/gstat-krige-error-covariance-matrix-singular-at-location-917300-3-6109e06-0 ; https://gis.stackexchange.com/questions/262993/r-gstat-predict-error?rq=1)

I checked that :

there is actually a spatial structure in my dataset (see bubble plot with code below)
there are no duplicate locations
the variogram model is not singular and has a good fit to the experimental variogram (see plot with code below)
I also tried several values of range, sill, nugget and all the models in the gstat library
The covariance matrix is positive definite and has positive eigen values. It is singular according to gstat, but not to is.singular.matrix function
There were enough pair of points to do the experimental variogram

How to overcome this problem? What tips to avoid a singular covariance matrix? I also welcome any "best practice" for kriging.

Code (requires forSO.Rdata : https://www.dropbox.com/s/5vfj2gw9rkt365r/forSO.Rdata?dl=0 ) :

library(ggplot2)
library(gstat)

#Attached Rdata
load("forSO.Rdata")

#The observations
str(abun)

#Spatial structure
abun %>% as.data.frame %>% 
  ggplot(aes(lon, lat)) +
  geom_point(aes(colour=prop_species_cells), alpha=3/4) + 
  coord_equal() + theme_bw()

#Number of pair of points
cvgm <- variogram(prop_species_cells ~1, data=abun, width=3,  cutoff=300)
plot(cvgm$dist,cvgm$np)

#Fit a model covariogram
efitted = fit.variogram(cvgm, vgm(model="Mat", range=100, nugget=1), fit.method=7, fit.sills=TRUE, fit.ranges=TRUE)
plot(cvgm,efitted)

#No warning, and the model is non singular
attr(efitted, "singular")

#Covariance matrix (only on a small set of points, I have more than 25000 points) : positive-definite, postiive eigen values and not singular
hex_pointsDegTiny=hex_pointsDeg
hex_pointsDegTiny@coords=hex_pointsDegTiny@coords[1:10,]
dists <- spDists(hex_pointsDegTiny)
covarianceMatrix=variogramLine(efitted, maxdist = max(cvgm$dist), n = 10*max(cvgm$dist), dir = c(1,0,0), dist_vector = dists, covariance = TRUE)
eigen(covarianceMatrix)$values
is.positive.definite(covarianceMatrix)
is.singular.matrix(covarianceMatrix)

# No duplicate locations
zerodist(hex_pointsDegTiny)

# Impossible to krig
OK_fit <- gstat(id = "OK_fit", formula = prop_species_cells ~ 1, data = abun, model = efitted)
dist <- predict(OK_fit, newdata = hex_pointsDegTiny)
dist@data

Solution

Actually, there were duplicate locations in abun dataset (zerodist(abun)), they were not to be seeked into the grid on which I wanted to krig estimates. After getting rid of the duplicates, kriging worked fine.