I am trying to achieve parallel Kriging in R on several variables using a loop. Here is a reproducible example using data meuse and a code for parallel kriging that I found here. In the code below, each kriging is overwritten, but that's not the issue, since I can't even run the first kriging.

    names <- colnames(meuse)[3:6]
    coordinates(meuse) = ~x+y
    gridded(meuse.grid) = ~x+y
    m <- vgm(.59, "Sph", 874, .04)
    no_cores <- 7
    # ordinary kriging:
    for (i in 1:length(names)) {
      parts <- split(x = 1:length(meuse.grid), f = 1:no_cores)
cl <- makeCluster(no_cores)          
clusterExport(cl = cl, varlist = c("meuse", "meuse.grid", "m", "parts"), envir = .GlobalEnv)
          clusterEvalQ(cl = cl, expr = c(library('sp'), library('gstat')))
          parallelX <- parLapply(cl = cl, X = 1:no_cores, fun = function(x) krige(formula = log(get(names[i]))~1, locations = meuse, newdata = meuse.grid[parts[[x]],], model = m))
          # Merge all the predictions    
          mergeParallelX <- maptools::spRbind(parallelX[[1]], parallelX[[2]])
          mergeParallelX <- maptools::spRbind(mergeParallelX, parallelX[[3]])
          mergeParallelX <- maptools::spRbind(mergeParallelX, parallelX[[4]])
          mergeParallelX <- maptools::spRbind(mergeParallelX, parallelX[[5]])
          mergeParallelX <- maptools::spRbind(mergeParallelX, parallelX[[6]])
          mergeParallelX <- maptools::spRbind(mergeParallelX, parallelX[[7]])
          # Create SpatialPixelsDataFrame from mergeParallelX
          mergeParallelX <- SpatialPixelsDataFrame(points = mergeParallelX, data = mergeParallelX@data)

I keep having issues which are, I think, related to the dynamic formula. I tried a lot of other functions, such as paste, paste0, as.formula, objects, etc. Nothing works, I can't paste the variable names into looped parallel kriging, no matter how I code the dynamic formula. Maybe that's because of how the parallel function is coded?

Any idea about a dynamic formula that works with the above code?

  • What does "not working" mean here? Is this really only a Q about how to dynamically construct a formula?
    – Spacedman
    Jul 11, 2022 at 14:44
  • Thanks, I didn't know about the vocabulary I had to use for this issue. So, the answer is yes and no, apparently a formula constructed dynamically don't work with the package parallel. For example the structure you gave below doesn't work. I will edit the question and the title to reflect on this issue.
    – ePoQ
    Jul 12, 2022 at 9:14
  • As written you are trying to do n_cores replications of kriging of each of the columns? Because your loop over the columns is outside the cluster creation and execution. This seems a bit off. Normally you'd throw all the replicated work inside the cluster and let the cluster's n_cores specification optimise the number of cores working. That then puts i in side the cluster loop. Also as written you're only going to return the value from the last column's kriging.
    – Spacedman
    Jul 12, 2022 at 9:37
  • As a matter of fact, I have a double loop to record all kringing, and I use detectCores for setting the number of clusters. I wrote the code this way in the Q to have a simple and reproducible example. What doesn't work is the dynamic formula here, but if you have a suggestion for a better structure I am ears. That's the first time I try parallel computing so I am quite a newbie here.
    – ePoQ
    Jul 12, 2022 at 9:45
  • And yes, since Kriging predictions are independent of each other, I am just trying to speed up the processing time by making all my cores work at the same time for each variable successively, rather than allocating different variables to different cores.
    – ePoQ
    Jul 12, 2022 at 9:56

1 Answer 1


Guessing that your problem is constructing a formula dynamically, you can build one as character and convert to a formula with as.formula:

So this:

> k1 = krige(log(copper)~1, meuse, meuse.grid, model = m)
[using ordinary kriging]

is the same as:

> k2 = krige(as.formula("log(copper)~1"), meuse, meuse.grid, model = m)
[using ordinary kriging]

which you can construct

> names
[1] "cadmium" "copper"  "lead"    "zinc"   
> i
[1] 2
> k3 = krige(as.formula(paste0("log(",names[i],")~1")), meuse, meuse.grid, model = m)
[using ordinary kriging]

And then:

> identical(k1, k2)
[1] TRUE
> identical(k1, k3)
[1] TRUE
> identical(k2, k3)
[1] TRUE
  • I just edited the question/title. as.formula(paste0("log(",names[i],")~1")) doesn't work either with the package parallel
    – ePoQ
    Jul 12, 2022 at 9:24

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