https://github.com/cran/kappalab
Tip revision: a332a7e86fee6eab7a1737fe089ffa558c0c5692 authored by Ivan Kojadinovic on 04 May 2012, 00:00:00 UTC
version 0.4-6
version 0.4-6
Tip revision: a332a7e
ls.ranking.capa.ident.R
##############################################################################
#
# Copyright 2005 Michel Grabisch, Ivan Kojadinovic, and Patrick Meyer
#
# 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".
#
# As a counterpart to the access to the source code and rights to copy,
# 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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#
##############################################################################
## Least squares ranking capacity identification
##############################################################################
ls.ranking.capa.ident <- function(n, k, C, rk, d,
A.Shapley.preorder = NULL,
A.Shapley.interval = NULL,
A.interaction.preorder = NULL,
A.interaction.interval = NULL,
A.inter.additive.partition = NULL,
sigf = 5,
maxiter = 20,
epsilon = 1e-6) {
## check n and k
if (!(as.integer(n) == n && k %in% 1:n))## check n and k
stop("wrong arguments")
## number of alternatives
n.var.alt <- dim(C)[1]
## check C
if (!(is.matrix(C) && dim(C)[2] == n))
stop("wrong criteria matrix")
## check rk
if (!(is.matrix(rk) && dim(rk)[2] == 2))
stop("wrong criteria matrix")
Integral <- "Choquet"
## 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 linked to the capacity
n.var.a <- binom.sum(n,k) - 1
## total number of variables
n.var <- n.var.a + n.var.alt
## number of monotonicity constraints
n.con <- n*2^(n-1)
## infinity value
infty <- 1000
## k power set in natural order
subsets <- .C("k_power_set",
as.integer(n),
as.integer(k),
subsets = integer(n.var.a+1),
PACKAGE="kappalab")$subsets
## monotonicity constraints
A <- .C("monotonicity_constraints",
as.integer(n),
as.integer(k),
as.integer(subsets),
A = integer(n.var.a * n.con),
PACKAGE="kappalab")$A
A <- matrix(A,n.con,n.var.a,byrow=TRUE)
A <- cbind(A,matrix(0,n.con,n.var.alt))
## add the normalization constraint sum a(T) = 1
A <- rbind(c(rep(1,n.var.a),numeric(n.var.alt)),A)
b <- c(1,rep(epsilon,n.con))
r <- c(0,rep(1,n.con))
## a part of the objectif matrix R'R
obj <- .C("k_additive_objectif",
as.integer(n),
as.integer(k),
as.integer(subsets),
as.integer(Integral == "Choquet"),
as.double(t(C)),
as.integer(n.var.alt),
R = double(n.var.alt * n.var.a),
l = double(n.var.a),
u = double(n.var.a),
PACKAGE="kappalab")
Rmat <- cbind(matrix(obj$R,n.var.alt,n.var.a,byrow=TRUE),
diag(-1,n.var.alt,n.var.alt))
Dmat <- t(Rmat) %*% Rmat
## constraints relative to the order on the prototypes
for (i in 1:dim(rk)[1]){
proto.constraint <- numeric(n.var.alt)
proto.constraint[which(rownames(C)==rk[i,2])]=-1
proto.constraint[which(rownames(C)==rk[i,1])] = 1
A <- rbind(A, c(numeric(n.var.a), proto.constraint))
b <- c(b, d)
r <- c(r, infty - (-infty) - d)
}
## add the constraints relative to the preorder of the criteria
if (!is.null(A.Shapley.preorder)) {
for (i in 1:dim(A.Shapley.preorder)[1]) {
spc <- Shapley.preorder.constraint(n,k,subsets,
A.Shapley.preorder[i,1],
A.Shapley.preorder[i,2],
A.Shapley.preorder[i,3])
spc$A <- c(spc$A, numeric(n.var.alt))
A <- rbind(A, spc$A)
b <- c(b,spc$b)
r <- c(r,spc$r)
}
}
## add the constraints relative to the absolute 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])
sic$A <- c(sic$A,numeric(n.var.alt))
A <- rbind(A,sic$A)
b <- c(b,sic$b)
r <- c(r,sic$r)
}
}
## add the constraints relative to the preorder of the interactions
if (!is.null(A.interaction.preorder)) {
for (i in 1:dim(A.interaction.preorder)[1]) {
ipc <- interaction.preorder.constraint(n,k,subsets,
A.interaction.preorder[i,1],
A.interaction.preorder[i,2],
A.interaction.preorder[i,3],
A.interaction.preorder[i,4],
A.interaction.preorder[i,5])
ipc$A <- c(ipc$A,numeric(n.var.alt))
A <- rbind(A,ipc$A)
b <- c(b,ipc$b)
r <- c(r,ipc$r)
}
}
## 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])
iic$A <- c(iic$A, numeric(n.var.alt))
A <- rbind(A,iic$A)
b <- c(b,iic$b)
r <- c(r,iic$r)
}
}
## add the constraints relative to the inter-addtive partition
if (!is.null(A.inter.additive.partition)) {
iapc <- inter.additive.partition.constraint(n,k,subsets,
A.inter.additive.partition)
zeros <- matrix(numeric(n.var.alt * dim(iapc$A)[1]),dim(iapc$A)[1],n.var.alt)
iapc$A <- cbind(iapc$A, zeros)
A <- rbind(A,iapc$A)
b <- c(b,iapc$b)
r <- c(r,iapc$r)
}
## the global scores on the alternatives can vary between
## -infinity and +infinity
l<-c(obj$l,rep(-infty,n.var.alt))
u<-c(obj$u,rep(+infty,n.var.alt))
## ipop quadratic program solver
qp <- ipop(matrix(0,n.var,1),
Dmat,
A,
matrix(b),
matrix(l),
matrix(u),
matrix(r),
sigf,
maxiter,
verb=0)
## solution
Choquet.C <- numeric(dim(C)[1])
for (i in 1:(dim(C)[1]))
Choquet.C[i] <- Choquet.integral(Mobius.capacity(c(0,qp@primal[1:n.var.a]),n,k),C[i,])
rk.C <- as.matrix(rank(round(Choquet.C,4), ties.method="min"))
rownames(rk.C) <- rownames(C)
colnames(rk.C) <- "rank"
return(list(solution = Mobius.capacity(c(0,qp@primal[1:n.var.a]),n,k),
glob.eval = qp@primal[(n.var.a+1):(n.var.a+n.var.alt)],
how = qp@how,
rk.C = rk.C,
Choquet.C = Choquet.C))
}
##############################################################################