[R-sig-Geo] gstat now uses Lapack / failing cokriging

[Edzer Pebesma]

On 17/11/15 18:14, Bruin, Sytze de wrote:
> Hi Edzer, thanks for your prompt reply. I tried reproducing your matrix r but got a different result, i.e. a valid covariance matrix. The cross-covariances are different. Using the same example as above, my code is as follows:
> 
> library(sp)
> library(gstat)
> 
> # some data
> x <- c(215, 330, 410, 470, 545)
> y <- c(230, 310, 330, 340, 365)
> fc <- c(0.211, 0.251, 0.281, 0.262, 0.242)
> por <- c(0.438, 0.457, 0.419, 0.430, 0.468)
> Allier <- data.frame(x, y, fc, por)
> coordinates(Allier) = ~x+y
> 
> # gstat object for co-kriging using linear model of co-regionalization
> g <- gstat(id=c("fc"), formula=fc~1, data=Allier,
>             model=vgm(0.00247, "Sph", 480, 0.00166))
> g <- gstat(g, id="por", formula=por~1, data=Allier,
>             model=vgm(0.00239, "Sph", 480, 0.00118))
> g <- gstat(g, id=c("fc", "por"),
>             model=vgm(0.00151, "Sph", 480, -0.00124))
> 
> 
> dists <- spDists(Allier)
> r11 <- variogramLine(g$model$fc, dist_vector = dists, covariance = T)
> r12 <- variogramLine(g$model$fc.por, dist_vector = dists, covariance = T)
> r22 <- variogramLine(g$model$por, dist_vector = dists, covariance = T)
> r <- cbind(r11, r12)
> r <- rbind(r, cbind(r12, r22))
> 
>> r
>               [,1]         [,2]         [,3]         [,4]         [,5]         [,6]         [,7]
>  [1,] 0.0041300000 0.0014193874 0.0008959951 0.0005655821 0.0002240733 0.0002700000 0.0008677227
>  [2,] 0.0014193874 0.0041300000 0.0018397575 0.0013976206 0.0008790828 0.0008677227 0.0002700000
>  [3,] 0.0008959951 0.0018397575 0.0041300000 0.0020030001 0.0014238096 0.0005477541 0.0011247100
>  [4,] 0.0005655821 0.0013976206 0.0020030001 0.0041300000 0.0018652970 0.0003457607 0.0008544158
>  [5,] 0.0002240733 0.0008790828 0.0014238096 0.0018652970 0.0041300000 0.0001369841 0.0005374150
>  [6,] 0.0002700000 0.0008677227 0.0005477541 0.0003457607 0.0001369841 0.0035700000 0.0013734154
>  [7,] 0.0008677227 0.0002700000 0.0011247100 0.0008544158 0.0005374150 0.0013734154 0.0035700000
>  [8,] 0.0005477541 0.0011247100 0.0002700000 0.0012245061 0.0008704261 0.0008669750 0.0017801702
>  [9,] 0.0003457607 0.0008544158 0.0012245061 0.0002700000 0.0011403233 0.0005472637 0.0013523535
> [10,] 0.0001369841 0.0005374150 0.0008704261 0.0011403233 0.0002700000 0.0002168159 0.0008506105
>               [,8]         [,9]        [,10]
>  [1,] 0.0005477541 0.0003457607 0.0001369841
>  [2,] 0.0011247100 0.0008544158 0.0005374150
>  [3,] 0.0002700000 0.0012245061 0.0008704261
>  [4,] 0.0012245061 0.0002700000 0.0011403233
>  [5,] 0.0008704261 0.0011403233 0.0002700000
>  [6,] 0.0008669750 0.0005472637 0.0002168159
>  [7,] 0.0017801702 0.0013523535 0.0008506105
>  [8,] 0.0035700000 0.0019381256 0.0013776943
>  [9,] 0.0019381256 0.0035700000 0.0018048825
> [10,] 0.0013776943 0.0018048825 0.0035700000
> 
>> eigen(r)$values
>  [1] 0.0124609506 0.0055040132 0.0046425761 0.0035980843 0.0031064016 0.0028989486 0.0028042439
>  [8] 0.0018107335 0.0010254131 0.0006486352
> 
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> 

Building upon your earlier example,

predict(g, SpatialPoints(data.frame(x=450, y=350)), debug = 32)

gives you the generalized covariance matrix that is used for the
cokriging, which I looked at. gstat computes generalized covariances as
C(0)-gamma(h) with C(0) = max(0, sum of the positive sill values),
instead of the sill of all sill values. If one of the sill components is
negative, this matters.

I looked in the Ver Hoef & Cressie 1993 paper, but couldn't find out
which one is right. Maybe Gerard can also take a look at it; the fix
would be trivial.

-- 
Edzer Pebesma
Institute for Geoinformatics (ifgi),  University of Münster,
Heisenbergstraße 2, 48149 Münster, Germany; +49 251 83 33081
Journal of Statistical Software:   http://www.jstatsoft.org/
Computers & Geosciences:   http://elsevier.com/locate/cageo/
Spatial Statistics Society http://www.spatialstatistics.info

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