Revision 2b28322cd75357fc6c5547746b38a5c7d71f576a authored by Edzer J. Pebesma on 02 June 2005, 13:54:10 UTC, committed by cran-robot on 02 June 2005, 13:54:10 UTC
1 parent e5a07f3
merge.Rout.save
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> # illustrates the use of merge, for merging parameters accross variables:
> # Z1=m+e1(s)
> # Z2=m+e2(s)
> # Z1 and Z2 each have a different variogram, but share the parameter m
> # see documentation of gstat() function
> library(gstat)
Loading required package: lattice
> d1 = data.frame(x=c(0,2),y=c(0,0),z=c(0,1))
> d2 = data.frame(x=c(0,2),y=c(2,2),z=c(4,5))
> g = gstat(NULL,"d1", z~1,~x+y,d1,model=vgm(1, "Exp", 1))
> g = gstat(g,"d2", z~1,~x+y,d2,model=vgm(1, "Exp", 1), merge=c("d1","d2"))
> g = gstat(g, c("d1", "d2"), model = vgm(0.5, "Exp", 1))
> predict.gstat(g, data.frame(x=1,y=1), debug = 32)
Intrinsic Correlation found. Good.
[using ordinary cokriging]
we're at location X: 1 Y: 1 Z: 0
zero block size
we're at point X: 1 Y: 1 Z: 0
# X:
Matrix: 4 by 1
row 0: 1
row 1: 1
row 2: 1
row 3: 1
[using generalized covariances: max_val - semivariance()]
# Covariances (x_i, x_j) matrix C (lower triangle only):
Matrix: 4 by 4
row 0: 1 0 0 0
row 1: 0.135335283 1 0 0
row 2: 0.0676676416 0.0295528733 1 0
row 3: 0.0295528733 0.0676676416 0.135335283 1
# X'C-1 X:
Matrix: 1 by 1
row 0: 3.24528918
# beta:
Vector: dim: 1
2.5
# Cov(beta), (X'C-1 X)-1:
Matrix: 1 by 1
row 0: 0.30813895
# Corr(beta):
Matrix: 1 by 1
row 0: 1
# X0 (X values at prediction location x0):
Matrix: 1 by 2
row 0: 1 1
# BLUE(mu), E(y(x0)) = X0'beta:
Vector: dim: 2
2.5 2.5
# Covariances (x_i, x_0), C0:
Matrix: 4 by 2
row 0: 0.243116734 0.121558367
row 1: 0.243116734 0.121558367
row 2: 0.121558367 0.243116734
row 3: 0.121558367 0.243116734
# C-1 C0:
Matrix: 4 by 2
row 0: 0.206482174 0.089386867
row 1: 0.206482174 0.089386867
row 2: 0.089386867 0.206482174
row 3: 0.089386867 0.206482174
# [a] Cov_ij(B,B) or Cov_ij(0,0):
Matrix: 2 by 2
row 0: 1 0.5
row 1: 0.5 1
# [c] (x0-X'C-1 c0)'(X'C-1 X)-1(x0-X'C-1 c0):
Matrix: 2 by 2
row 0: 0.0513599204 0.0513599204
row 1: 0.0513599204 0.0513599204
# [b] c0'C-1 c0:
Matrix: 2 by 2
row 0: 0.122129987 0.0936621582
row 1: 0.0936621582 0.122129987
# Best Linear Unbiased Predictor:
Vector: dim: 2
2.03161877 2.96838123
# MSPE ([a]-[b]+[c]):
Matrix: 2 by 2
row 0: 0.929229934 0.457697762
row 1: 0.457697762 0.929229934
# kriging weights:
Matrix: 4 by 2
row 0: 0.308547653 0.191452347
row 1: 0.308547653 0.191452347
row 2: 0.191452347 0.308547653
row 3: 0.191452347 0.308547653
x y d1.pred d1.var d2.pred d2.var cov.d1.d2
1 1 1 2.031619 0.92923 2.968381 0.92923 0.4576978
>
> # Z1 and Z2 share a regression slope:
> g = gstat(NULL,"d1", z~x,~x+y,d1,model=vgm(1, "Exp", 1))
> g = gstat(g,"d2", z~x,~x+y,d2,model=vgm(1, "Exp", 1),
+ merge=list(c("d1",2,"d2",2)))
> g = gstat(g, c("d1", "d2"), model = vgm(0.5, "Exp", 1))
> predict.gstat(g, data.frame(x=1,y=1), debug = 32)
Intrinsic Correlation found. Good.
[using universal cokriging]
we're at location X: 1 Y: 1 Z: 0
zero block size
we're at point X: 1 Y: 1 Z: 0
# X:
Matrix: 4 by 3
row 0: 1 0 0
row 1: 1 2 0
row 2: 0 0 1
row 3: 0 2 1
[using generalized covariances: max_val - semivariance()]
# Covariances (x_i, x_j) matrix C (lower triangle only):
Matrix: 4 by 4
row 0: 1 0 0 0
row 1: 0.135335283 1 0 0
row 2: 0.0676676416 0.0295528733 1 0
row 3: 0.0295528733 0.0676676416 0.135335283 1
# X'C-1 X:
Matrix: 3 by 3
row 0: 1.77460693 1.62264459 -0.151962334
row 1: 1.62264459 7.67605004 1.62264459
row 2: -0.151962334 1.62264459 1.77460693
# beta:
Vector: dim: 3
2.10985743e-16 0.5 4
# Cov(beta), (X'C-1 X)-1:
Matrix: 3 by 3
row 0: 0.793362513 -0.225694871 0.274305129
row 1: -0.225694871 0.225694871 -0.225694871
row 2: 0.274305129 -0.225694871 0.793362513
# Corr(beta):
Matrix: 3 by 3
row 0: 1 -0.533365606 0.34575005
row 1: -0.533365606 1 -0.533365606
row 2: 0.34575005 -0.533365606 1
# X0 (X values at prediction location x0):
Matrix: 3 by 2
row 0: 1 0
row 1: 1 1
row 2: 0 1
# BLUE(mu), E(y(x0)) = X0'beta:
Vector: dim: 2
0.5 4.5
# Covariances (x_i, x_0), C0:
Matrix: 4 by 2
row 0: 0.243116734 0.121558367
row 1: 0.243116734 0.121558367
row 2: 0.121558367 0.243116734
row 3: 0.121558367 0.243116734
# C-1 C0:
Matrix: 4 by 2
row 0: 0.206482174 0.089386867
row 1: 0.206482174 0.089386867
row 2: 0.089386867 0.206482174
row 3: 0.089386867 0.206482174
# [a] Cov_ij(B,B) or Cov_ij(0,0):
Matrix: 2 by 2
row 0: 1 0.5
row 1: 0.5 1
# [c] (x0-X'C-1 c0)'(X'C-1 X)-1(x0-X'C-1 c0):
Matrix: 2 by 2
row 0: 0.20356416 -0.100844319
row 1: -0.100844319 0.20356416
# [b] c0'C-1 c0:
Matrix: 2 by 2
row 0: 0.122129987 0.0936621582
row 1: 0.0936621582 0.122129987
# Best Linear Unbiased Predictor:
Vector: dim: 2
0.5 4.5
# MSPE ([a]-[b]+[c]):
Matrix: 2 by 2
row 0: 1.08143417 0.305493523
row 1: 0.305493523 1.08143417
# kriging weights:
Matrix: 4 by 2
row 0: 0.5 4.16333634e-17
row 1: 0.5 -1.38777878e-17
row 2: -5.55111512e-17 0.5
row 3: 2.77555756e-17 0.5
x y d1.pred d1.var d2.pred d2.var cov.d1.d2
1 1 1 0.5 1.081434 4.5 1.081434 0.3054935
>
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