Running 'autoKrige.cv.R' [167s]
  Running 'automap.R' [180s]
Running the tests in 'tests/autoKrige.cv.R' failed.
Complete output:
  > library(automap)
  > library(sp)
  > library(sf)
  Linking to GEOS 3.11.2, GDAL 3.8.2, PROJ 9.3.1; sf_use_s2() is TRUE
  > 
  > data(meuse)
  > coordinates(meuse) = ~x+y
  > data(meuse.grid)
  > gridded(meuse.grid) = ~x+y
  > 
  > kr.cv = autoKrige.cv(log(zinc)~1, meuse, model = c("Exp"))
  > kr_dist.cv = autoKrige.cv(log(zinc)~sqrt(dist), meuse, 
  +        model = c("Exp"))
  > kr_dist_ffreq.cv = autoKrige.cv(log(zinc)~sqrt(dist)+ffreq, 
  +        meuse, model = c("Exp"))
  > 
  > summary(kr.cv)
              [,1]     
  mean_error  0.002008 
  me_mean     0.0003412
  MAE         0.2918   
  MSE         0.1549   
  MSNE        0.8555   
  cor_obspred 0.8374   
  cor_predres 0.04027  
  RMSE        0.3936   
  RMSE_sd     0.5452   
  URMSE       0.3936   
  iqr         0.4275   
  > summary(kr_dist.cv)
              [,1]      
  mean_error  -0.003065 
  me_mean     -0.0005207
  MAE         0.2707    
  MSE         0.143     
  MSNE        1.071     
  cor_obspred 0.8509    
  cor_predres -0.02513  
  RMSE        0.3781    
  RMSE_sd     0.5238    
  URMSE       0.3781    
  iqr         0.4035    
  > summary(kr_dist_ffreq.cv)
              [,1]      
  mean_error  -0.0008806
  me_mean     -0.0001496
  MAE         0.2345    
  MSE         0.1032    
  MSNE        1.083     
  cor_obspred 0.8949    
  cor_predres -0.02777  
  RMSE        0.3213    
  RMSE_sd     0.4451    
  URMSE       0.3213    
  iqr         0.3629    
  > 
  > compare.cv(kr.cv, kr_dist.cv, kr_dist_ffreq.cv)
                  kr.cv kr_dist.cv kr_dist_ffreq.cv
  mean_error   0.002008  -0.003065       -0.0008806
  me_mean     0.0003412 -0.0005207       -0.0001496
  MAE            0.2918     0.2707           0.2345
  MSE            0.1549      0.143           0.1032
  MSNE           0.8555      1.071            1.083
  cor_obspred    0.8374     0.8509           0.8949
  cor_predres   0.04027   -0.02513         -0.02777
  RMSE           0.3936     0.3781           0.3213
  RMSE_sd        0.5452     0.5238           0.4451
  URMSE          0.3936     0.3781           0.3213
  iqr            0.4275     0.4035           0.3629
  > 
  > 
  > meuse = as(meuse, "sf")
  > meuse.grid = as(meuse.grid, "sf")
  > kr.cv.sf = autoKrige.cv(log(zinc)~1, meuse, model = c("Exp"))
  > kr_dist.cv.sf = autoKrige.cv(log(zinc)~sqrt(dist), meuse, 
  +                           model = c("Exp"))
  > kr_dist_ffreq.cv.sf = autoKrige.cv(log(zinc)~sqrt(dist)+ffreq, 
  +                                 meuse, model = c("Exp"))
  > 
  > summary(kr.cv.sf)
              [,1]     
  mean_error  0.002008 
  me_mean     0.0003412
  MAE         0.2918   
  MSE         0.1549   
  MSNE        0.8555   
  cor_obspred 0.8374   
  cor_predres 0.04027  
  RMSE        0.3936   
  RMSE_sd     0.5452   
  URMSE       0.3936   
  iqr         0.4275   
  > summary(kr_dist.cv.sf)
              [,1]      
  mean_error  -0.003065 
  me_mean     -0.0005207
  MAE         0.2707    
  MSE         0.143     
  MSNE        1.071     
  cor_obspred 0.8509    
  cor_predres -0.02513  
  RMSE        0.3781    
  RMSE_sd     0.5238    
  URMSE       0.3781    
  iqr         0.4035    
  > summary(kr_dist_ffreq.cv.sf)
              [,1]      
  mean_error  -0.0008806
  me_mean     -0.0001496
  MAE         0.2345    
  MSE         0.1032    
  MSNE        1.083     
  cor_obspred 0.8949    
  cor_predres -0.02777  
  RMSE        0.3213    
  RMSE_sd     0.4451    
  URMSE       0.3213    
  iqr         0.3629    
  > 
  > compare.cv(kr.cv, kr_dist.cv, kr_dist_ffreq.cv, kr.cv.sf, kr_dist.cv.sf, kr_dist_ffreq.cv.sf)
                  kr.cv kr_dist.cv kr_dist_ffreq.cv  kr.cv.sf kr_dist.cv.sf
  mean_error   0.002008  -0.003065       -0.0008806  0.002008     -0.003065
  me_mean     0.0003412 -0.0005207       -0.0001496 0.0003412    -0.0005207
  MAE            0.2918     0.2707           0.2345    0.2918        0.2707
  MSE            0.1549      0.143           0.1032    0.1549         0.143
  MSNE           0.8555      1.071            1.083    0.8555         1.071
  cor_obspred    0.8374     0.8509           0.8949    0.8374        0.8509
  cor_predres   0.04027   -0.02513         -0.02777   0.04027      -0.02513
  RMSE           0.3936     0.3781           0.3213    0.3936        0.3781
  RMSE_sd        0.5452     0.5238           0.4451    0.5452        0.5238
  URMSE          0.3936     0.3781           0.3213    0.3936        0.3781
  iqr            0.4275     0.4035           0.3629    0.4275        0.4035
              kr_dist_ffreq.cv.sf
  mean_error           -0.0008806
  me_mean              -0.0001496
  MAE                      0.2345
  MSE                      0.1032
  MSNE                      1.083
  cor_obspred              0.8949
  cor_predres            -0.02777
  RMSE                     0.3213
  RMSE_sd                  0.4451
  URMSE                    0.3213
  iqr                      0.3629
  > 
  > proc.time()
     user  system elapsed 
    13.14    0.54   14.23 
Running the tests in 'tests/automap.R' failed.
Complete output:
  > options(digits=6)
  > 
  > library(automap)
  > library(sp)
  > library(sf)
  Linking to GEOS 3.11.2, GDAL 3.8.2, PROJ 9.3.1; sf_use_s2() is TRUE
  > 
  > 
  > # Data preparation
  > data(meuse)
  > coordinates(meuse) =~ x+y
  > data(meuse.grid)
  > gridded(meuse.grid) =~ x+y
  > 
  > # Fitting some variograms
  > variogram = autofitVariogram(zinc ~ soil + ffreq + dist, meuse, 
  +     miscFitOptions = list(min.np.bin = 500))
  > variogram
  $exp_var
      np     dist   gamma dir.hor dir.ver   id
  1  500  174.036 38065.2       0       0 var1
  2  711  337.604 50150.7       0       0 var1
  3  830  502.048 50347.6       0       0 var1
  4 1349  713.215 61255.3       0       0 var1
  5 1314  961.272 70311.9       0       0 var1
  6 1139 1213.412 75870.3       0       0 var1
  7 1355 1506.551 72043.9       0       0 var1
  
  $var_model
    model    psill   range kappa
  1   Nug  5294.22    0.00   0.0
  2   Ste 91418.10 1781.65   0.2
  
  $sserr
  [1] 130690
  
  attr(,"class")
  [1] "autofitVariogram" "list"            
  > 
  > # ...and diable the merging, note the difference between the two plots
  > variogram = autofitVariogram(zinc ~ soil + ffreq + dist, meuse, 
  +     miscFitOptions = list(min.np.bin = 500, merge.small.bins = FALSE))
  > variogram
  $exp_var
       np      dist   gamma dir.hor dir.ver   id
  1    17   59.3347 23959.6       0       0 var1
  2    36   86.0145 16671.6       0       0 var1
  3   114  131.0287 33270.3       0       0 var1
  4   149  176.1885 52846.3       0       0 var1
  5   184  226.7565 34555.3       0       0 var1
  6   711  337.6036 50150.7       0       0 var1
  7   830  502.0477 50347.6       0       0 var1
  8  1349  713.2149 61255.3       0       0 var1
  9  1314  961.2718 70311.9       0       0 var1
  10 1139 1213.4116 75870.3       0       0 var1
  11 1355 1506.5505 72043.9       0       0 var1
  
  $var_model
    model    psill   range kappa
  1   Nug  2454.94   0.000   0.0
  2   Ste 68746.15 482.025   0.3
  
  $sserr
  [1] 2044182
  
  attr(,"class")
  [1] "autofitVariogram" "list"            
  > 
  > # Ordinary kriging
  > kriging_result = autoKrige(zinc~1, meuse, meuse.grid)
  [using ordinary kriging]
  > summary(kriging_result)
  krige_output:
  Object of class SpatialPixelsDataFrame
  Coordinates:
       min    max
  x 178440 181560
  y 329600 333760
  Is projected: NA 
  proj4string : [NA]
  Number of points: 3103
  Grid attributes:
    cellcentre.offset cellsize cells.dim
  x            178460       40        78
  y            329620       40       104
  Data attributes:
     var1.pred       var1.var        var1.stdev 
   Min.   : 106   Min.   : 40440   Min.   :201  
   1st Qu.: 207   1st Qu.: 49617   1st Qu.:223  
   Median : 309   Median : 55256   Median :235  
   Mean   : 406   Mean   : 62453   Mean   :247  
   3rd Qu.: 555   3rd Qu.: 69014   3rd Qu.:263  
   Max.   :1620   Max.   :142357   Max.   :377  
  
  exp_var:
       np      dist    gamma dir.hor dir.ver   id
  1    17   59.3347  46207.0       0       0 var1
  2    36   86.0145  32203.6       0       0 var1
  3   114  131.0287  53862.7       0       0 var1
  4   149  176.1885  87068.5       0       0 var1
  5   184  226.7565  62486.3       0       0 var1
  6   711  337.6036 104453.8       0       0 var1
  7   830  502.0477 127330.5       0       0 var1
  8  1349  713.2149 150556.5       0       0 var1
  9  1314  961.2718 165153.6       0       0 var1
  10 1139 1213.4116 165496.0       0       0 var1
  11 1355 1506.5505 149245.9       0       0 var1
  
  var_model:
    model    psill   range kappa
  1   Nug  31957.6   0.000   0.0
  2   Ste 133556.2 485.511   1.1
  Sums of squares betw. var. model and sample var.[1] 4235991
  > pos = posPredictionInterval(kriging_result, 95, 75)
  > summary(pos)
  Upper and lower boundary and the position relative to value:Object of class SpatialPixelsDataFrame
  Coordinates:
       min    max
  x 178440 181560
  y 329600 333760
  Is projected: NA 
  proj4string : [NA]
  Number of points: 3103
  Grid attributes:
    cellcentre.offset cellsize cells.dim
  x            178460       40        78
  y            329620       40       104
  Data attributes:
       upper          lower                       position   
   Min.   : 554   Min.   :-448.1   higher             : 717  
   1st Qu.: 673   1st Qu.:-272.2   not distinguishable:2386  
   Median : 812   Median :-156.6                             
   Mean   : 891   Mean   : -78.9                             
   3rd Qu.:1052   3rd Qu.:  50.6                             
   Max.   :2066   Max.   :1174.5                             
  
  $p
  [1] 95
  
  $value
  [1] 75
  
  > 
  > kriging_result = autoKrige(zinc~1, meuse, meuse.grid, fix.values = c(0.2,NA,NA))
  [using ordinary kriging]
  > summary(kriging_result)
  krige_output:
  Object of class SpatialPixelsDataFrame
  Coordinates:
       min    max
  x 178440 181560
  y 329600 333760
  Is projected: NA 
  proj4string : [NA]
  Number of points: 3103
  Grid attributes:
    cellcentre.offset cellsize cells.dim
  x            178460       40        78
  y            329620       40       104
  Data attributes:
     var1.pred       var1.var        var1.stdev   
   Min.   : 120   Min.   :  3295   Min.   : 57.4  
   1st Qu.: 201   1st Qu.: 40754   1st Qu.:201.9  
   Median : 298   Median : 52570   Median :229.3  
   Mean   : 404   Mean   : 58013   Mean   :235.4  
   3rd Qu.: 552   3rd Qu.: 71374   3rd Qu.:267.2  
   Max.   :1801   Max.   :141490   Max.   :376.2  
  
  exp_var:
       np      dist    gamma dir.hor dir.ver   id
  1    17   59.3347  46207.0       0       0 var1
  2    36   86.0145  32203.6       0       0 var1
  3   114  131.0287  53862.7       0       0 var1
  4   149  176.1885  87068.5       0       0 var1
  5   184  226.7565  62486.3       0       0 var1
  6   711  337.6036 104453.8       0       0 var1
  7   830  502.0477 127330.5       0       0 var1
  8  1349  713.2149 150556.5       0       0 var1
  9  1314  961.2718 165153.6       0       0 var1
  10 1139 1213.4116 165496.0       0       0 var1
  11 1355 1506.5505 149245.9       0       0 var1
  
  var_model:
    model    psill   range kappa
  1   Nug      0.2   0.000   0.0
  2   Ste 173889.1 567.423   0.4
  Sums of squares betw. var. model and sample var.[1] 4751276
  > pos = posPredictionInterval(kriging_result, 95, 75)
  > summary(pos)
  Upper and lower boundary and the position relative to value:Object of class SpatialPixelsDataFrame
  Coordinates:
       min    max
  x 178440 181560
  y 329600 333760
  Is projected: NA 
  proj4string : [NA]
  Number of points: 3103
  Grid attributes:
    cellcentre.offset cellsize cells.dim
  x            178460       40        78
  y            329620       40       104
  Data attributes:
       upper          lower                       position   
   Min.   : 292   Min.   :-465.4   higher             : 759  
   1st Qu.: 655   1st Qu.:-260.3   not distinguishable:2344  
   Median : 788   Median :-130.9                             
   Mean   : 865   Mean   : -57.8                             
   3rd Qu.:1028   3rd Qu.:  70.0                             
   Max.   :2109   Max.   :1575.5                             
  
  $p
  [1] 95
  
  $value
  [1] 75
  
  > 
  > # Universal kriging
  > kriging_result = autoKrige(zinc~soil+ffreq+dist, meuse, meuse.grid)
  [using universal kriging]
  > summary(kriging_result)
  krige_output:
  Object of class SpatialPixelsDataFrame
  Coordinates:
       min    max
  x 178440 181560
  y 329600 333760
  Is projected: NA 
  proj4string : [NA]
  Number of points: 3103
  Grid attributes:
    cellcentre.offset cellsize cells.dim
  x            178460       40        78
  y            329620       40       104
  Data attributes:
     var1.pred       var1.var       var1.stdev   
   Min.   :-181   Min.   : 9538   Min.   : 97.7  
   1st Qu.: 114   1st Qu.:29049   1st Qu.:170.4  
   Median : 259   Median :34707   Median :186.3  
   Mean   : 345   Mean   :36358   Mean   :188.7  
   3rd Qu.: 521   3rd Qu.:42945   3rd Qu.:207.2  
   Max.   :1728   Max.   :67434   Max.   :259.7  
  
  exp_var:
       np      dist   gamma dir.hor dir.ver   id
  1    17   59.3347 23959.6       0       0 var1
  2    36   86.0145 16671.6       0       0 var1
  3   114  131.0287 33270.3       0       0 var1
  4   149  176.1885 52846.3       0       0 var1
  5   184  226.7565 34555.3       0       0 var1
  6   711  337.6036 50150.7       0       0 var1
  7   830  502.0477 50347.6       0       0 var1
  8  1349  713.2149 61255.3       0       0 var1
  9  1314  961.2718 70311.9       0       0 var1
  10 1139 1213.4116 75870.3       0       0 var1
  11 1355 1506.5505 72043.9       0       0 var1
  
  var_model:
    model    psill   range kappa
  1   Nug  2454.94   0.000   0.0
  2   Ste 68746.15 482.025   0.3
  Sums of squares betw. var. model and sample var.[1] 2044182
  > pos = posPredictionInterval(kriging_result, 95, 75)
  > summary(pos)
  Upper and lower boundary and the position relative to value:Object of class SpatialPixelsDataFrame
  Coordinates:
       min    max
  x 178440 181560
  y 329600 333760
  Is projected: NA 
  proj4string : [NA]
  Number of points: 3103
  Grid attributes:
    cellcentre.offset cellsize cells.dim
  x            178460       40        78
  y            329620       40       104
  Data attributes:
       upper          lower                       position   
   Min.   : 166   Min.   :-662.8   higher             : 933  
   1st Qu.: 481   1st Qu.:-249.0   not distinguishable:2170  
   Median : 610   Median : -90.7                             
   Mean   : 715   Mean   : -25.1                             
   3rd Qu.: 912   3rd Qu.: 140.1                             
   Max.   :1970   Max.   :1485.5                             
  
  $p
  [1] 95
  
  $value
  [1] 75
  
  > 
  > # Block kriging
  > kriging_result = autoKrige(zinc~soil+ffreq+dist, meuse, meuse.grid, block = c(400,400))
  [using universal kriging]
  > summary(kriging_result)
  krige_output:
  Object of class SpatialPixelsDataFrame
  Coordinates:
       min    max
  x 178440 181560
  y 329600 333760
  Is projected: NA 
  proj4string : [NA]
  Number of points: 3103
  Grid attributes:
    cellcentre.offset cellsize cells.dim
  x            178460       40        78
  y            329620       40       104
  Data attributes:
     var1.pred       var1.var       var1.stdev   
   Min.   :-190   Min.   : 2251   Min.   : 47.4  
   1st Qu.: 112   1st Qu.: 4680   1st Qu.: 68.4  
   Median : 283   Median : 6688   Median : 81.8  
   Mean   : 348   Mean   : 8516   Mean   : 88.6  
   3rd Qu.: 536   3rd Qu.:10855   3rd Qu.:104.2  
   Max.   :1338   Max.   :29401   Max.   :171.5  
  
  exp_var:
       np      dist   gamma dir.hor dir.ver   id
  1    17   59.3347 23959.6       0       0 var1
  2    36   86.0145 16671.6       0       0 var1
  3   114  131.0287 33270.3       0       0 var1
  4   149  176.1885 52846.3       0       0 var1
  5   184  226.7565 34555.3       0       0 var1
  6   711  337.6036 50150.7       0       0 var1
  7   830  502.0477 50347.6       0       0 var1
  8  1349  713.2149 61255.3       0       0 var1
  9  1314  961.2718 70311.9       0       0 var1
  10 1139 1213.4116 75870.3       0       0 var1
  11 1355 1506.5505 72043.9       0       0 var1
  
  var_model:
    model    psill   range kappa
  1   Nug  2454.94   0.000   0.0
  2   Ste 68746.15 482.025   0.3
  Sums of squares betw. var. model and sample var.[1] 2044182
  > pos = posPredictionInterval(kriging_result, 95, 75)
  > summary(pos)
  Upper and lower boundary and the position relative to value:Object of class SpatialPixelsDataFrame
  Coordinates:
       min    max
  x 178440 181560
  y 329600 333760
  Is projected: NA 
  proj4string : [NA]
  Number of points: 3103
  Grid attributes:
    cellcentre.offset cellsize cells.dim
  x            178460       40        78
  y            329620       40       104
  Data attributes:
       upper          lower                       position   
   Min.   :  24   Min.   :-490.6   higher             :1790  
   1st Qu.: 277   1st Qu.: -47.5   lower              : 107  
   Median : 433   Median : 131.8   not distinguishable:1206  
   Mean   : 522   Mean   : 174.4                             
   3rd Qu.: 733   3rd Qu.: 359.4                             
   Max.   :1480   Max.   :1196.4                             
  
  $p
  [1] 95
  
  $value
  [1] 75
  
  > 
  > # Kriging with power model
  > kriging_result = autoKrige(zinc~soil+ffreq+dist, meuse, meuse.grid, model = "Pow")
  [using universal kriging]
  Warning message:
  In getModel(initial_sill - initial_nugget, m, initial_range, kappa = 0,  :
    Using the power model is at your own risk, read the docs of autofitVariogram for more details.
  > 
  > 
  > 
  > # Testing with sf objects
  > meuse = as(meuse, "sf")
  > meuse.grid = as(meuse.grid, "sf")
  > 
  > # Fitting some variograms
  > variogram = autofitVariogram(zinc ~ soil + ffreq + dist, meuse, 
  +                              miscFitOptions = list(min.np.bin = 500))
  > variogram
  $exp_var
      np     dist   gamma dir.hor dir.ver   id
  1  500  174.036 38065.2       0       0 var1
  2  711  337.604 50150.7       0       0 var1
  3  830  502.048 50347.6       0       0 var1
  4 1349  713.215 61255.3       0       0 var1
  5 1314  961.272 70311.9       0       0 var1
  6 1139 1213.412 75870.3       0       0 var1
  7 1355 1506.551 72043.9       0       0 var1
  
  $var_model
    model    psill   range kappa
  1   Nug  5294.22    0.00   0.0
  2   Ste 91418.10 1781.65   0.2
  
  $sserr
  [1] 130690
  
  attr(,"class")
  [1] "autofitVariogram" "list"            
  > 
  > # ...and diable the merging, note the difference between the two plots
  > variogram = autofitVariogram(zinc ~ soil + ffreq + dist, meuse, 
  +                              miscFitOptions = list(min.np.bin = 500, merge.small.bins = FALSE))
  > variogram
  $exp_var
       np      dist   gamma dir.hor dir.ver   id
  1    17   59.3347 23959.6       0       0 var1
  2    36   86.0145 16671.6       0       0 var1
  3   114  131.0287 33270.3       0       0 var1
  4   149  176.1885 52846.3       0       0 var1
  5   184  226.7565 34555.3       0       0 var1
  6   711  337.6036 50150.7       0       0 var1
  7   830  502.0477 50347.6       0       0 var1
  8  1349  713.2149 61255.3       0       0 var1
  9  1314  961.2718 70311.9       0       0 var1
  10 1139 1213.4116 75870.3       0       0 var1
  11 1355 1506.5505 72043.9       0       0 var1
  
  $var_model
    model    psill   range kappa
  1   Nug  2454.94   0.000   0.0
  2   Ste 68746.15 482.025   0.3
  
  $sserr
  [1] 2044182
  
  attr(,"class")
  [1] "autofitVariogram" "list"            
  > 
  > # Ordinary kriging
  > kriging_result = autoKrige(zinc~1, meuse, meuse.grid)
  [using ordinary kriging]
  > summary(kriging_result)
  krige_output:
     var1.pred       var1.var         geometry      var1.stdev 
   Min.   : 106   Min.   : 40440   POINT  :3103   Min.   :201  
   1st Qu.: 207   1st Qu.: 49617   epsg:NA:   0   1st Qu.:223  
   Median : 309   Median : 55256                  Median :235  
   Mean   : 406   Mean   : 62453                  Mean   :247  
   3rd Qu.: 555   3rd Qu.: 69014                  3rd Qu.:263  
   Max.   :1620   Max.   :142357                  Max.   :377  
  
  exp_var:
       np      dist    gamma dir.hor dir.ver   id
  1    17   59.3347  46207.0       0       0 var1
  2    36   86.0145  32203.6       0       0 var1
  3   114  131.0287  53862.7       0       0 var1
  4   149  176.1885  87068.5       0       0 var1
  5   184  226.7565  62486.3       0       0 var1
  6   711  337.6036 104453.8       0       0 var1
  7   830  502.0477 127330.5       0       0 var1
  8  1349  713.2149 150556.5       0       0 var1
  9  1314  961.2718 165153.6       0       0 var1
  10 1139 1213.4116 165496.0       0       0 var1
  11 1355 1506.5505 149245.9       0       0 var1
  
  var_model:
    model    psill   range kappa
  1   Nug  31957.6   0.000   0.0
  2   Ste 133556.2 485.511   1.1
  Sums of squares betw. var. model and sample var.[1] 4235991
  > pos = posPredictionInterval(kriging_result, 95, 75)
  > summary(pos)
  Upper and lower boundary and the position relative to value:     upper          lower                       position       geometry   
   Min.   : 554   Min.   :-448.1   higher             : 717   POINT  :3103  
   1st Qu.: 673   1st Qu.:-272.2   not distinguishable:2386   epsg:NA:   0  
   Median : 812   Median :-156.6                                            
   Mean   : 891   Mean   : -78.9                                            
   3rd Qu.:1052   3rd Qu.:  50.6                                            
   Max.   :2066   Max.   :1174.5                                            
  
  $p
  [1] 95
  
  $value
  [1] 75
  
  > 
  > kriging_result = autoKrige(zinc~1, meuse, meuse.grid, fix.values = c(0.2,NA,NA))
  [using ordinary kriging]
  > summary(kriging_result)
  krige_output:
     var1.pred       var1.var         geometry      var1.stdev   
   Min.   : 120   Min.   :  3295   POINT  :3103   Min.   : 57.4  
   1st Qu.: 201   1st Qu.: 40754   epsg:NA:   0   1st Qu.:201.9  
   Median : 298   Median : 52570                  Median :229.3  
   Mean   : 404   Mean   : 58013                  Mean   :235.4  
   3rd Qu.: 552   3rd Qu.: 71374                  3rd Qu.:267.2  
   Max.   :1801   Max.   :141490                  Max.   :376.2  
  
  exp_var:
       np      dist    gamma dir.hor dir.ver   id
  1    17   59.3347  46207.0       0       0 var1
  2    36   86.0145  32203.6       0       0 var1
  3   114  131.0287  53862.7       0       0 var1
  4   149  176.1885  87068.5       0       0 var1
  5   184  226.7565  62486.3       0       0 var1
  6   711  337.6036 104453.8       0       0 var1
  7   830  502.0477 127330.5       0       0 var1
  8  1349  713.2149 150556.5       0       0 var1
  9  1314  961.2718 165153.6       0       0 var1
  10 1139 1213.4116 165496.0       0       0 var1
  11 1355 1506.5505 149245.9       0       0 var1
  
  var_model:
    model    psill   range kappa
  1   Nug      0.2   0.000   0.0
  2   Ste 173889.1 567.423   0.4
  Sums of squares betw. var. model and sample var.[1] 4751276
  > pos = posPredictionInterval(kriging_result, 95, 75)
  > summary(pos)
  Upper and lower boundary and the position relative to value:     upper          lower                       position       geometry   
   Min.   : 292   Min.   :-465.4   higher             : 759   POINT  :3103  
   1st Qu.: 655   1st Qu.:-260.3   not distinguishable:2344   epsg:NA:   0  
   Median : 788   Median :-130.9                                            
   Mean   : 865   Mean   : -57.8                                            
   3rd Qu.:1028   3rd Qu.:  70.0                                            
   Max.   :2109   Max.   :1575.5                                            
  
  $p
  [1] 95
  
  $value
  [1] 75
  
  > 
  > # Universal kriging
  > kriging_result = autoKrige(zinc~soil+ffreq+dist, meuse, meuse.grid)
  [using universal kriging]
  > summary(kriging_result)
  krige_output:
     var1.pred       var1.var        geometry      var1.stdev   
   Min.   :-181   Min.   : 9538   POINT  :3103   Min.   : 97.7  
   1st Qu.: 114   1st Qu.:29049   epsg:NA:   0   1st Qu.:170.4  
   Median : 259   Median :34707                  Median :186.3  
   Mean   : 345   Mean   :36358                  Mean   :188.7  
   3rd Qu.: 521   3rd Qu.:42945                  3rd Qu.:207.2  
   Max.   :1728   Max.   :67434                  Max.   :259.7  
  
  exp_var:
       np      dist   gamma dir.hor dir.ver   id
  1    17   59.3347 23959.6       0       0 var1
  2    36   86.0145 16671.6       0       0 var1
  3   114  131.0287 33270.3       0       0 var1
  4   149  176.1885 52846.3       0       0 var1
  5   184  226.7565 34555.3       0       0 var1
  6   711  337.6036 50150.7       0       0 var1
  7   830  502.0477 50347.6       0       0 var1
  8  1349  713.2149 61255.3       0       0 var1
  9  1314  961.2718 70311.9       0       0 var1
  10 1139 1213.4116 75870.3       0       0 var1
  11 1355 1506.5505 72043.9       0       0 var1
  
  var_model:
    model    psill   range kappa
  1   Nug  2454.94   0.000   0.0
  2   Ste 68746.15 482.025   0.3
  Sums of squares betw. var. model and sample var.[1] 2044182
  > pos = posPredictionInterval(kriging_result, 95, 75)
  > summary(pos)
  Upper and lower boundary and the position relative to value:     upper          lower                       position       geometry   
   Min.   : 166   Min.   :-662.8   higher             : 933   POINT  :3103  
   1st Qu.: 481   1st Qu.:-249.0   not distinguishable:2170   epsg:NA:   0  
   Median : 610   Median : -90.7                                            
   Mean   : 715   Mean   : -25.1                                            
   3rd Qu.: 912   3rd Qu.: 140.1                                            
   Max.   :1970   Max.   :1485.5                                            
  
  $p
  [1] 95
  
  $value
  [1] 75
  
  > 
  > # Block kriging
  > kriging_result = autoKrige(zinc~soil+ffreq+dist, meuse, meuse.grid, block = c(400,400))
  [using universal kriging]
  > summary(kriging_result)
  krige_output:
     var1.pred       var1.var        geometry      var1.stdev   
   Min.   :-190   Min.   : 2251   POINT  :3103   Min.   : 47.4  
   1st Qu.: 112   1st Qu.: 4680   epsg:NA:   0   1st Qu.: 68.4  
   Median : 283   Median : 6688                  Median : 81.8  
   Mean   : 348   Mean   : 8516                  Mean   : 88.6  
   3rd Qu.: 536   3rd Qu.:10855                  3rd Qu.:104.2  
   Max.   :1338   Max.   :29401                  Max.   :171.5  
  
  exp_var:
       np      dist   gamma dir.hor dir.ver   id
  1    17   59.3347 23959.6       0       0 var1
  2    36   86.0145 16671.6       0       0 var1
  3   114  131.0287 33270.3       0       0 var1
  4   149  176.1885 52846.3       0       0 var1
  5   184  226.7565 34555.3       0       0 var1
  6   711  337.6036 50150.7       0       0 var1
  7   830  502.0477 50347.6       0       0 var1
  8  1349  713.2149 61255.3       0       0 var1
  9  1314  961.2718 70311.9       0       0 var1
  10 1139 1213.4116 75870.3       0       0 var1
  11 1355 1506.5505 72043.9       0       0 var1
  
  var_model:
    model    psill   range kappa
  1   Nug  2454.94   0.000   0.0
  2   Ste 68746.15 482.025   0.3
  Sums of squares betw. var. model and sample var.[1] 2044182
  > pos = posPredictionInterval(kriging_result, 95, 75)
  > summary(pos)
  Upper and lower boundary and the position relative to value:     upper          lower                       position       geometry   
   Min.   :  24   Min.   :-490.6   higher             :1790   POINT  :3103  
   1st Qu.: 277   1st Qu.: -47.5   lower              : 107   epsg:NA:   0  
   Median : 433   Median : 131.8   not distinguishable:1206                 
   Mean   : 522   Mean   : 174.4                                            
   3rd Qu.: 733   3rd Qu.: 359.4                                            
   Max.   :1480   Max.   :1196.4                                            
  
  $p
  [1] 95
  
  $value
  [1] 75
  
  > 
  > # Kriging with power model
  > kriging_result = autoKrige(zinc~soil+ffreq+dist, meuse, meuse.grid, model = "Pow")
  [using universal kriging]
  Warning message:
  In getModel(initial_sill - initial_nugget, m, initial_range, kappa = 0,  :
    Using the power model is at your own risk, read the docs of autofitVariogram for more details.
  > 
  > 
  > proc.time()
     user  system elapsed 
    25.45    0.40   25.87