[R-sig-Geo] Non-symmetric variogram map in gstat

[Edzer J. Pebesma]

David, you may also notice that the map produced does not have a cell 
centre or cell 'crossing' at (0,0). Of course you'd assume enough 
cleverness that this would be enforced automatically, but too bad. Try

 v <- variogram(Ni ~ 1, jura.pred, cutoff=1.8, width=0.18, map=T)

(making sure that the cutoff is a multiple of the width) and you'll see 
something symmetric.

Best wishes,
--
Edzer

David Rossiter wrote:
> I've found a quite puzzling behaviour in gstat's variogram method, with
> the map=T argument. I believe the result should be a symmetric map
> because all the semivariances are squared differences. This is indeed
> the case if I try an example from the Meuse set:
>
>   
>> library(gstat)
>> data(meuse)
>> coordinates(meuse) <- ~x + y
>> class(meuse)
>>     
> [1] "SpatialPointsDataFrame"
> attr(,"package")
> [1] "sp"
>   
>> v <- variogram(log(lead) ~ 1, meuse, cutoff=1000, width=200, map=T)
>> plot(v)
>> # symmetric plot as expected, confirm by looking at array
>> v$map at data$var1
>>     
>   [1] 0.241586 0.875118 1.329685 0.978228 0.877734 0.854946 0.628017
> 0.356488  0.323171 0.299103 0.389137
> ...
> [111] 0.387982 0.302654 0.319343 0.356488 0.630622 0.862242 0.877734
> 0.978228  1.329685 0.875118 0.241586
>   
>> # and the number of pairs:
>> v$map at data$np.var1
>>     
>   [1]   2  10  13  36  44  63  86 137 141 122 123   3   7  26  53  60
> 92 123  150 156 123  87   4  12  41  61
>  ...
> [105]  92  61  53  26   7   3 122 122 143 137  87  64  44  36  13  10
> 2
>
> BUT ... when I try with the Jura dataset I get non-symmetric results:
>
>   
>> data(jura)
>> coordinates(jura.pred) <- ~Xloc + Yloc
>> class(jura.pred)
>>     
> [1] "SpatialPointsDataFrame"
> attr(,"package")
> [1] "sp"
>   
>> v <- variogram(Ni ~ 1, jura.pred, cutoff=1.2, width=0.18, map=T)
>> plot(v)
>>     
> # not symmetric! Confirm with array:
>   
>> v$map at data$var1
>>     
>   [1]  89.5503  59.3319  88.4276  79.4282  75.1518 147.6931  55.4805
> 43.6888   70.5159  86.9107  59.5392
> ...
> [188] 105.4008  48.2219  72.3849  35.7244  66.7842  62.4743  72.9742
> 72.6469   70.9808
>   
>> # and the number of pairs
>> v$map at data$np.var1
>>     
>   [1]  42  78  54  97 124  39 159  82  92  62  79  70  93  68 114  78
> 177  86   92  72  59  82 192  95 192  79
> ...
> [183]  73 135  72  72  97 101  76 137  39 111 105 132  94  31
>
> Clearly both the number of pairs and the resulting average semivariance
> are not symmetric!
>
> Both of the objects are converted to SpatialPointsDataFrames. I can see
> no obvious reason for this discrepency.
>
> D G Rossiter
> Senior University Lecturer
> Department of Earth Systems Analysis (DESA)
> International Institute for Geo-Information Science and Earth
> Observation (ITC)
> mailto:rossiter at itc.nl,  Internet: http://www.itc.nl/personal/rossiter
>
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