[R-sig-Geo] gstat fails with valid (?) LMC

[Tom Gottfried]

Dear list(en)ers,

by the way I discovered the following behaviour: fitting the LMC as in 
the example below and then using it for prediction raises an error 
telling the coefficient matrix is not positive definite. However, 
cauchy-schwartz inequalities are met (which should suffice for the 2 by 
2 coefficient matrix [1]). Sorry if this is only due to me having not 
done my homework, but isn't positive *semi*-definiteness of the 
coefficient matrix a sufficient condition for a valid LMC? Setting 
nocheck=1 does not end up with negative prediction variances in this 
example, too.

Thanks for any hint that can adjust me on this topic!
Tom

library(gstat)
data(meuse)
coordinates(meuse) <- ~x+y
data(meuse.grid)
coordinates(meuse.grid) <- ~x+y

g <- gstat(NULL, "z", zinc~1, meuse)
g <- gstat(g, "dist", I(dist*1000)~1, meuse)
variog.g <- variogram(g)
g <- fit.lmc(variog.g, g, vgm(100000, "Gau", 500, 1000))

predict(g, newdata=meuse.grid)
   # raises error ("coefficient matrix not positive definite") but ...

all(abs(g$model$z.dist$psill)<=sqrt(g$model$z$psill*g$model$dist$psill))
   # ... shows that cauchy-schwartz inequalities are met ...
all(abs(g$model$z.dist$psill)<sqrt(g$model$z$psill*g$model$dist$psill))
   # though the coefficient matrix seems to be "only" positive
   #semi-definite, no negative variances occur:
g <- gstat(NULL, "z", zinc~1, meuse, set=list(nocheck=1))
g <- gstat(g, "dist", I(dist*1000)~1, meuse)
variog.g <- variogram(g)
g <- fit.lmc(variog.g, g, vgm(100000, "Gau", 500, 1000))
pred <- predict(g, newdata=meuse.grid)
any(c(pred$z.var, pred$dist.var)<0)

[1]
@article{goovaerts_controversial_1994,
	title = {On a controversial method for modeling a coregionalization},
	volume = {26},
	doi = {10.1007/BF02082763},
	number = {2},
	journal = {Mathematical Geology},
	author = {Goovaerts, P.},
	year = {1994},
	pages = {197--204}
}

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