maxentropy
Maximum entropy sampling
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 Doptimal 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 dualgreedy approach. It uses a branchandbound strategy to calculate an optimal solution.
It is also possible to construct a completely new network, that means $nf=0$.
Usage
maxentropy(A,nf,ns,method="d",S.start=NULL,rtol=1e6,mattest=TRUE,etol=0,verbose=FALSE)
Arguments
 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:
"d"
=dualgreedy algorithm,"g"
=greedy algorithm,"dc"
=dualgreedy + interchange algorithm,"gc"
=greedy + interchange algorithm,"c"
=interchange algorithm + directly given initial solution. Otherwise this algorithm has to be started with an directly given 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
TRUE
a tes for for symmetry and positive definiteness of the matrix $A$ isperformed (default isTRUE
).  etol
 Tolerance for checking positve definiteness (default 0).
 verbose
 Logical, if
TRUE
some information is printed per iteration (default isFALSE
).
Details
$A[F]$ denotes the principal submatrix of $A$ having rows and columns indexed by $1..nf$.
Value

A object of class
 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.
monet
containing the following elements:
References
Ko, Lee, Queyranne, An exact algorithm for maximum entropy sampling, Operations Research 43 (1995), 684691.
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, 289294
See Also
Examples
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)