interchange: Interchange algorithm for maximum entropy sampling

In edesign: Maximum Entropy Sampling

Description

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.

The interchange algorithm improves a feasible initial solution directly given or obtained by the greedy or dual greedy algorithm for maximum entropy sampling.

It is also possible to improve the initial solution for the construction of a completely new network, that means nf=0, but in this case the interchange algorithm fails for ns=1.

Usage

interchange(A, nf, ns, S.start, etol=0, mattest = TRUE)

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.
S.start	Vector that gives the ns indices contained in the initial solution of the dimension dim(A)[1]-nf that should to be improved.
etol	Tolerance for checking positve definiteness (default 0)
mattest	Toggles testing matrix A for symmetry and positive definiteness (default T)

Details

A[F] denotes the principal submatrix of A having rows and columns indexed by 1..nf.

Value

A object of class monet containing the following elements:

S.start	Vector containing the indices of the added sites in the initial solution or 0 for the other sites.
S	Vector containing the indices of the added sites in the solution or 0 for the other sites.
det	Determinant of the principal submatrix indexed by the initial solution.

Author(s)

C. Gebhardt

References

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

See Also

greedy, dualgreedy

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.c<-c(0,7,0,9,0,11,0,13,14,0,0,0,0,0,0)
interchange(A,5,5,S.c)
interchange(A,5,5,greedy(A,5,5)$S)
interchange(A,5,5,dualgreedy(A,5,5)$S)

Example output

  Entropy based monitoring network

method:  interchange 

determinant of selected cov. matrix:  134444.815798555 
total number of given locations:     20 
total number of fixed locations:     5 
total number of locations to select: 5 
total number of eligible locations:  15 
fixed locations:     1  ...  5 
eligible locations:  6  ...  20 
indices of additionally selected locations:
[1]  8  9 16 18 19

  Entropy based monitoring network

method:  interchange 

determinant of selected cov. matrix:  134444.815798555 
total number of given locations:     20 
total number of fixed locations:     5 
total number of locations to select: 5 
total number of eligible locations:  15 
fixed locations:     1  ...  5 
eligible locations:  6  ...  20 
indices of additionally selected locations:
[1]  8  9 16 18 19

  Entropy based monitoring network

method:  interchange 

determinant of selected cov. matrix:  134444.815798555 
total number of given locations:     20 
total number of fixed locations:     5 
total number of locations to select: 5 
total number of eligible locations:  15 
fixed locations:     1  ...  5 
eligible locations:  6  ...  20 
indices of additionally selected locations:
[1]  8  9 16 18 19

edesign documentation built on May 2, 2019, 8:24 a.m.