Description Usage Arguments Details Value Author(s) References See Also Examples
Starting point is a network A[F] with nf points. Now one has to select ns points of a set of candidate sites to augment the existing network. The aim of maximum entropy sampling is to select a feasible D-optimal design that maximizes the logarithm of the determinant of all principal submatrices of A arising by this expansion.
This algorithm is based on the interlacing property of eigenvalues. It starts with an initial solution given directly or provided by the greedy or dual-greedy approach. It uses a branch-and-bound strategy to calculate an optimal solution.
It is also possible to construct a completely new network, that means nf=0.
1 | maxentropy(A,nf,ns,method="d",S.start=NULL,rtol=1e-6,mattest=TRUE,etol=0,verbose=FALSE)
|
A |
Spatial covariance matrix A. |
nf |
Number of stations are forced into every feasible solution. |
ns |
Number of stations have to be added to the existing network. |
method |
Method to determine the initial solution: |
S.start |
Vector that gives the ns indices contained in the initial solution of dimension dim(A)[1]-nf that should to be improved. |
rtol |
The algorithm terminates if the optimal solution is obtained with a tolerance of rtol. |
mattest |
Logical, if |
etol |
Tolerance for checking positve definiteness (default 0). |
verbose |
Logical, if |
A[F] denotes the principal submatrix of A having rows and columns indexed by 1..nf.
A object of class monet
containing the following elements:
S |
Vector containing the indices of the added sites in the initial solution or 0 for the other sites. |
det.start |
Determinant of the principal submatrix indexed by the initial solution. |
det |
Determinant of the principal submatrix indexed by the optimal solution. |
maxcount |
Maximum of active subproblems. |
iter |
Number of iterations. |
C. Gebhardt
Ko, Lee, Queyranne, An exact algorithm for maximum entropy sampling, Operations Research 43 (1995), 684-691.
Gebhardt, C.: Bayessche Methoden in der geostatistischen Versuchsplanung. PhD Thesis, Univ. Klagenfurt, Austria, 2003
O.P. Baume, A. Gebhardt, C. Gebhardt, G.B.M. Heuvelink and J. Pilz: Network optimization algorithms and scenarios in the context of automatic mapping. Computers & Geosciences 37 (2011) 3, 289-294
greedy
, dualgreedy
, interchange
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | x <- c(0.97900601,0.82658702,0.53105628,0.91420190,0.35304969,
0.14768239,0.58000004,0.60690101,0.36289026,0.82022147,
0.95290664,0.07928365,0.04833764,0.55631735,0.06427738,
0.31216689,0.43851418,0.34433556,0.77699357,0.84097327)
y <- c(0.36545512,0.72144122,0.95688671,0.25422154,0.48199229,
0.43874199,0.90166634,0.60898628,0.82634713,0.29670695,
0.86879093,0.45277452,0.09386800,0.04788365,0.20557817,
0.61149264,0.94643855,0.78219937,0.53946353,0.70946842)
A <- outer(x, x, "-")^2 + outer(y, y, "-")^2
A <- (2 - A)/10
diag(A) <- 0
diag(A) <- 1/20 + apply(A, 2, sum)
S.entrp<-c(0,7,0,9,0,11,0,13,14,0,0,0,0,0,0)
maxentropy(A,5,5,S.start=S.entrp)
maxentropy(A,5,5,method="g")
maxentropy(A,5,5)
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