https://github.com/cran/kappalab
Tip revision: c35c3217a80758cae846a0c1336934ca8aee9b2b authored by Ivan Kojadinovic on 23 September 2006, 00:00:00 UTC
version 0.3-0
version 0.3-0
Tip revision: c35c321
min.dist.capa.ident.R
##############################################################################
#
# Copyright ゥ 2005 Michel Grabisch and Ivan Kojadinovic
#
# Ivan.Kojadinovic@polytech.univ-nantes.fr
#
# This software is a package for the statistical system GNU R:
# http://www.r-project.org
#
# This software is governed by the CeCILL license under French law and
# abiding by the rules of distribution of free software. You can use,
# modify and/ or redistribute the software under the terms of the CeCILL
# license as circulated by CEA, CNRS and INRIA at the following URL
# "http://www.cecill.info".
#
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# modify and redistribute granted by the license, users are provided only
# with a limited warranty and the software's author, the holder of the
# economic rights, and the successive licensors have only limited
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#
##############################################################################
## Minimum distance capacity identification
##############################################################################
## Constructs a Mobius.capacity object by means of a quadratic program
mini.dist.capa.ident <- function(a, k, distance = "Choquet.coefficients",
A.Choquet.preorder = NULL,
A.Shapley.preorder = NULL,
A.Shapley.interval = NULL,
A.interaction.preorder = NULL,
A.interaction.interval = NULL,
A.inter.additive.partition = NULL,
epsilon = 1e-6) {
## check a
if (!("Mobius.game" %in% is(a)))
stop("Object a is not of class Mobius.game")
## number of elements (criteria)
n <- a@n
## check k
if (!(k %in% 1:n))
stop("wrong arguments")
# check distance
if (!(distance %in% c("Choquet.coefficients","binary.alternatives","global.scores")))
stop("wrong distance type")
## check A.Choquet.preorder
if (!((is.matrix(A.Choquet.preorder)
&& dim(A.Choquet.preorder)[2] == 2*n+1)
|| is.null(A.Choquet.preorder)))
stop("wrong Choquet preorder constraint matrix")
## check A.Shapley.preorder
if (!((is.matrix(A.Shapley.preorder) && dim(A.Shapley.preorder)[2] == 3)
|| is.null(A.Shapley.preorder)))
stop("wrong Shapley preorder constraint matrix")
## check A.Shapley.interval
if (!((is.matrix(A.Shapley.interval) && dim(A.Shapley.interval)[2] == 3)
|| is.null(A.Shapley.interval)))
stop("wrong Shapley interval constraint matrix")
## check A.interaction.preorder
if (!((is.matrix(A.interaction.preorder)
&& dim(A.interaction.preorder)[2] == 5)
|| is.null(A.interaction.preorder)))
stop("wrong interaction preorder constraint matrix")
## check A.interaction.interval
if (!((is.matrix(A.interaction.interval)
&& dim(A.interaction.interval)[2] == 4)
|| is.null(A.interaction.interval)))
stop("wrong interaction interval constraint matrix")
## check A.inter.additive.partition
if (!((is.numeric(A.inter.additive.partition)
&& sum(levels(factor(A.inter.additive.partition))
== 1:max(A.inter.additive.partition))
== max(A.inter.additive.partition))
|| is.null(A.inter.additive.partition)))
stop("wrong inter-additive partition")
## check epsilon
if (!(is.positive(epsilon) && epsilon <= 1e-3))
stop("wrong epsilon value")
## number of variables
n.var <- binom.sum(n,k) - 1
## size of the vector representing a
s.a <- binom.sum(n,a@k) - 1
## 2^n - 1
pow.n <- 2^n - 1
## number of monotonicity constraints
n.con <- n*2^(n-1)
## k power set or a@k power set in natural order
power.set <- .C("k_power_set",
as.integer(n),
as.integer(max(k,a@k)),
subsets = integer(max(n.var+1,s.a+1)),
PACKAGE="kappalab")$subsets
subsets <- power.set[1:(n.var+1)]
subsets.a <- power.set[1:(s.a+1)]
## monotonicity constraints
M <- .C("monotonicity_constraints",
as.integer(n),
as.integer(k),
as.integer(subsets),
M = integer(n.var * n.con),
PACKAGE="kappalab")$M
M <- matrix(M,n.con,n.var,byrow=TRUE)
## objective function
if (distance == "Choquet.coefficients") {
cat("Distance used: Choquet.coefficients \n\n")
D.Shapley <- .C("objective_function_Choquet_coefficients",
as.integer(n),
D = double(n.con),
PACKAGE="kappalab")$D
Dmat <- t(M) %*% diag(D.Shapley) %*% M
## forming the second part of the objective function (dvec)
M.a <- .C("monotonicity_constraints",
as.integer(n),
as.integer(a@k),
as.integer(subsets.a),
M = integer(s.a * n.con),
PACKAGE="kappalab")$M
M.a <- matrix(M.a,n.con,s.a,byrow=TRUE)
## linear part of the objective function
dvec <- a@data[-1] %*% t(M.a) %*% diag(D.Shapley) %*% M
} else if (distance == "binary.alternatives") {
cat("Distance used: binary.alternatives \n\n")
B <- .C("objective_function_binary_alternatives",
as.integer(n),
as.integer(k),
as.integer(subsets),
B = integer(n.var * pow.n),
PACKAGE="kappalab")$B
B <- matrix(B,pow.n,n.var,byrow=TRUE)
Dmat <- t(B) %*% B
dvec <- zeta(a)@data[-1] %*% B
} else { # distance = "global.scores"
cat("Distance used: global.scores \n\n")
Q <- .C("objective_function_global_scores",
as.integer(n),
as.integer(max(a@k,k)),
as.integer(k),
as.integer(power.set),
Q = double(max(s.a,n.var) * n.var),
PACKAGE="kappalab")$Q
Q <- matrix(Q,max(s.a,n.var),n.var,byrow=TRUE)
Dmat <- Q[1:n.var,]
dvec <- a@data[-1] %*% Q[1:s.a,]
}
## the constraint matrix
A <- M
## add the normalization constraint sum a(T) = 1
A <- rbind(rep(1,n.var),A)
bvec <- c(1,rep(epsilon,n.con))
meq <- 1
## add the constraints relative to the preorder of the alternatives
if (!is.null(A.Choquet.preorder)) {
for (i in 1:dim(A.Choquet.preorder)[1]) {
cpc <- Choquet.preorder.constraint(n,k,subsets,
A.Choquet.preorder[i,][1:n],
A.Choquet.preorder[i,][(n+1):(2*n)],
A.Choquet.preorder[i,2*n+1])
A <- rbind(A,cpc$A)
bvec <- c(bvec,cpc$b)
}
}
## add the constraints relative to the preorder of the criteria
if (!is.null(A.Shapley.preorder)) {
for (i in 1:dim(A.Shapley.preorder)[1]) {
spc <- Shapley.preorder.constraint(n,k,subsets,
A.Shapley.preorder[i,1],
A.Shapley.preorder[i,2],
A.Shapley.preorder[i,3])
A <- rbind(A,spc$A)
bvec <- c(bvec,spc$b)
}
}
## add the constraints relative to the importance of the criteria
if (!is.null(A.Shapley.interval)) {
for (i in 1:dim(A.Shapley.interval)[1]) {
sic <- Shapley.interval.constraint(n,k,subsets,
A.Shapley.interval[i,1],
A.Shapley.interval[i,2],
A.Shapley.interval[i,3])
## Sh(i) >= a
A <- rbind(A,sic$A)
bvec <- c(bvec,sic$b)
## - Sh(i) >= -b
A <- rbind(A,-sic$A)
bvec <- c(bvec,-(sic$b + sic$r))
}
}
## add the constraints relative to the preorder of the interactions
if (!is.null(A.interaction.preorder)) {
for (i in 1:dim(A.interaction.preorder)[1]) {
ipc <- interaction.preorder.constraint(n,k,subsets,
A.interaction.preorder[i,1],
A.interaction.preorder[i,2],
A.interaction.preorder[i,3],
A.interaction.preorder[i,4],
A.interaction.preorder[i,5])
A <- rbind(A,ipc$A)
bvec <- c(bvec,ipc$b)
}
}
## add the constraints relative to the magnitude of the interaction
if (!is.null(A.interaction.interval)) {
for (i in 1:dim(A.interaction.interval)[1]) {
iic <- interaction.interval.constraint(n,k,subsets,
A.interaction.interval[i,1],
A.interaction.interval[i,2],
A.interaction.interval[i,3],
A.interaction.interval[i,4])
## I(ij) >= a
A <- rbind(A,iic$A)
bvec <- c(bvec,iic$b)
## I(ij) <= b
A <- rbind(A,-iic$A)
bvec <- c(bvec,-(iic$b+iic$r))
}
}
## add the constraints relative to the inter-addtive partition
if (!is.null(A.inter.additive.partition)) {
iapc <- inter.additive.partition.constraint(n,k,subsets,
A.inter.additive.partition)
A <- rbind(iapc$A,A)
bvec <- c(iapc$b,bvec)
meq <- meq + length(iapc$b)
}
## quadprog
qp <- solve.QP(Dmat, dvec , t(A), bvec, meq = meq)
return(list(solution = Mobius.capacity(c(0,qp$solution),n,k),
value = qp$value, iterations = qp$iterations,
iact = qp$iact))
}
##############################################################################