Nothing
R/RandomMass.R
In ibelief: Belief Function Implementation
Defines functions
bin2dec
RandomSSF
RandomConsonant
Sample
RandomMass
Documented in
RandomMass
##' Generating masses
##'
##' Different ways to generate masses
##'
##' @export
##'
##' @param nbFocalElement The number of focal elements
##' @param ThetaSize The length of the discernment frame \eqn{\Theta}
##' @param nbMass The number of masses to generate
##' @param Type Which kind of mass to generate:
##'
##' Type=1 for focal elements can be everywhere
##'
##' Type=2 for focal elements can not be on the emptyset
##'
##' Type=3 for no dogmatic mass : one focal element is on \eqn{\Theta} (ignorance)
##'
##' Type=4 for no dogmatic mass : one focal element is on \eqn{\Theta} (ignorance) and no focal elements are on the emptyset
##'
##' Type=5 for all the focal elements are the singletons
##'
##' Type=6 for all the focal elements are the singletons and on \eqn{\Theta} (ignorance)
##'
##' Type=7 for all the focal elements are the singletons and on \eqn{\Theta} (ignorance), but not on all the singletons
##'
##' Type=8 On only one defined singleton, on \eqn{\Theta} (ignorance), and others
##'
##' Type=9 On one defined singleton, on other singletons and on \eqn{\Theta} (ignorance)
##'
##' Type=10 On one focal element contain a defined singleton, on other focal elements and on \eqn{\Theta} (ignorance)
##'
##' Type=11 On one focal element contain a defined singleton, on other focal elements (not emptyset) and on
##' \eqn{\Theta} (ignorance)
##'
##' Type=12 For consonant bba with nested focal elements, all of them contain a defined singleton. If parameter singleton is set to 0, the defined singleton can be any one of the element in the discernment framework. Note that the defined singleton may not be one of the focal elements.
##'
##' Type=13 For non-dogmatic consonant bba with nested focal elements, all of them contain a defined singleton. Different from Type 12, the mass given to \eqn{\Theta} must be positive (non-dogmatic). If parameter singleton is set to 0, the defined sigleton can be any one of the element in the discernment framework. Note that the defined singleton is one of the focal elements.
##'
##' Type=14 For non-dogmatic consonant bba with nested focal elements, all of them contain a defined singleton. The focal elements must contain the defined sigleton and \eqn{\Theta}. If parameter singleton is set to 0, the defined sigleton can be any one of the element in the discernment framework. Note that the difined singleton may not be the focal elements.
##'
##' Type=15 Random SSFs with Include and \eqn{\Theta} as focal elements. Generally, parameter Include shoud have the same length as nbMass. If the lenght of parameter Include is 1, all the random masses have the same focal elements. If Include is missing, then the focal element (except \eqn{\Theta}) could be randomly set to be any subset of \eqn{\Theta} except the empty set and the total ignorance.
##' @param singleton The singleton element (with only one element) in the focal sets. It should be given a number from 1 to \eqn{ThetaSize} if Type is from 5 to 11.
##' @param Include The natrual id of the focal element (not \eqn{\Theta}) of SSFs
##' @return The generated mass matrix. Each column represents a piece of mass
##' @examples
##'
##' RandomMass(nbFocalElement=3, ThetaSize=3, nbMass=4, Type=1)
##' RandomMass(nbFocalElement=3, ThetaSize=4, nbMass=4, Type=3)
##' RandomMass(nbFocalElement=4, ThetaSize=4, nbMass=4, Type=5,singleton=2)
##' RandomMass(nbFocalElement=4, ThetaSize=4, nbMass=4, Type=10,singleton=2)
##' RandomMass(nbFocalElement=4, ThetaSize=4, nbMass=4, Type=13,singleton=2)
##' RandomMass(nbFocalElement=2, ThetaSize=4, nbMass=4, Type=14,singleton=2)
##' RandomMass(ThetaSize=4, nbMass=4, Type=15, Include=2)
##'
RandomMass <- function(nbFocalElement, ThetaSize, nbMass, Type, singleton, Include) {
# depending program
# new Sample function. To avoid the problem by the function base::sample
# if there is only one element, i, for Sample, base::sample will think that the data set to Sample is 1:i
# for example, base::sample(5, 1) will return a random integer from 1 to 5
# this may bring some problem when using base::sample(setdiff(..), ..), when the results of setdiff(..) is only one element
indice <- function(ThetaSize, nbFocalElement, Type, singleton) {
Type = Type
# the empty set is 1; the Theta is 2^K
nb = 2^ThetaSize
if (Type == 1) {
# focal elements can be everywhere
ind = Sample(1:nb)
} else if (Type == 2) {
# focal elements can not be on the emptyset
ind = Sample(2:nb)
} else if (Type == 3) {
# no dogmatic mass : one focal element is on Theta (ignorance)
ind = c(nb, Sample(1:(nb - 1)))
} else if (Type == 4) {
# no dogmatic mass : one focal element is on Theta (ignorance) and no focal elements are on the emptyset
ind = c(nb, Sample(2:(nb - 1)))
} else if (Type == 5) {
# all the focal elements are the singletons
if (nbFocalElement == ThetaSize) {
ind = 1 + 2^(1:ThetaSize - 1)
} else {
stop("Accident: in RandomMass - indice: nbFocalElement and ThetaSize are not the same\n")
}
} else if (Type == 6) {
# all the focal elements are the singletons and on Theta (ignorance)
if (nbFocalElement == ThetaSize + 1) {
ind = c(1 + 2^(1:ThetaSize - 1), nb)
} else {
stop("Accident: in RandomMass - indice: nbFocalElement and ThetaSize+1 are not the same\n")
}
} else if (Type == 7) {
# all the focal elements are the singletons and on Theta (ignorance), but not on all the singletons
indtmp = Sample(1:ThetaSize)
ind = 1 + 2^(indtmp[1:(nbFocalElement - 1)] - 1)
ind = c(ind, nb)
} else if (Type == 8) {
# On only one defined singleton, on Theta (ignorance), and others
# check the number of input arguments
if (!missing(singleton)) {
indRest = Sample(setdiff(1:nb, c(nb, 1 + 2^(singleton - 1))), nbFocalElement - 2)
ind = c(nb, 1 + 2^(singleton - 1), indRest)
} else {
stop("Accident: in RandomMass - indice: the defined singleton is not given\n")
}
} else if (Type == 9) {
# On one defined singleton, on other singletons and on Theta (ignorance)
# check the number of input arguments
if (!missing(singleton)) {
indRest = Sample(setdiff(1 + 2^(1:ThetaSize - 1), 1 + 2^(singleton - 1)), nbFocalElement - 2)
ind = c(1 + 2^(singleton - 1), indRest, nb)
} else {
stop("Accident: in RandomMass - indice: the defined singleton is not given\n")
}
} else if (Type == 10) {
# On one focal element contain a defined singleton, on other focal elements and on Theta (ignorance)
# check the number of input arguments
if (!missing(singleton)) {
myF = t(sapply(1:nb, function(x) {
dec2bin(x - 1, ThetaSize)
}))
indSing = which(myF[, singleton] == 1)
Alea = Sample(setdiff(indSing, nb), 1)
indRest = Sample(setdiff(1:(nb - 1), Alea), nbFocalElement - 2)
ind = c(nb, Alea, indRest)
} else {
stop("Accident: in RandomMass - indice: the defined singleton is not given\n")
}
} else if (Type == 11) {
# idem 10 without emptyset (On one focal element contain a defined singleton, on other focal elements and on Theta (ignorance))
# check the number of input arguments
if (!missing(singleton)) {
if (nbFocalElement != 2^ThetaSize) {
myF = t(sapply(1:nb, function(x) {
dec2bin(x - 1, ThetaSize)
}))
indSing = which(myF[, singleton] == 1)
Alea = Sample(setdiff(indSing, nb), 1)
indRest = Sample(setdiff(2:(nb - 1), Alea), nbFocalElement - 2)
ind = c(nb, Alea, indRest)
} else {
stop("Accident: in RandomMass - indice: The number of focal element must be < 2^ThetaSize\n")
}
} else {
stop("Accident: in RandomMass - indice: the defined singleton is not given\n")
}
}
return(ind)
}
if (Type == 15 || nbFocalElement < 2^ThetaSize + 1) {
if (Type %in% 1:11){
MassOut = matrix(0, 2^ThetaSize, nbMass)
for (i in 1:nbMass) {
ind = indice(ThetaSize, nbFocalElement, Type, singleton)
indFocalElement = ind[1:nbFocalElement]
randMass = diff(c(0, sort(runif(nbFocalElement - 1)), 1))
MassOut[indFocalElement, i] = randMass
}
}else if (Type == 12){
MassOut = RandomConsonant(nbFocalElement, ThetaSize, nbMass, singleton, nondogmatic = FALSE, con_sig = FALSE)
}else if (Type == 13){
MassOut = RandomConsonant(nbFocalElement, ThetaSize, nbMass, singleton, nondogmatic = TRUE, con_sig = FALSE)
}else if (Type == 14){
MassOut = RandomConsonant(nbFocalElement, ThetaSize, nbMass, singleton, nondogmatic = TRUE, con_sig = TRUE)
}else if (Type == 15){
MassOut = RandomSSF(ThetaSize = ThetaSize, nbMass = nbMass, Include = Include)
}else {
stop("Accident: in RandomMass - indice: choose of Type: incorrect\n")
}
} else {
stop("Accident: in RandomMass nbFocalElement > 2^ThetaSize\n")
}
return(MassOut)
}
Sample <- function(x, size, replace = FALSE, prob = NULL) {
if (missing(size))
size <- length(x)
x[sample.int(length(x), size, replace, prob)]
}
RandomConsonant <- function(nbFocalElement, ThetaSize, nbMass, singleton, nondogmatic = TRUE, con_sig = FALSE) {
## generated nested bba
## the parameters are the same as that in RandomMass in ibelief Package
## singleton = 0, random singleton, could be any one in the discernment framework
## con_sig, if contains the singleton element as a focal element
## For SSF with only singleton and Theta, run like: RandomMass(2, ThetaSize, nbMass, singleton, TRUE, TRUE)
indice <- function(ThetaSize, singleton) {
nb = 2^ThetaSize
ind = rep(0, ThetaSize)
if(singleton == 0){
singleton = Sample(1:ThetaSize, 1)
}
ind[1] = 2^(singleton - 1) + 1
temp = rep(0, ThetaSize)
temp[singleton] = 1
for (i in 2:ThetaSize) {
id_cond = which(temp == 0)
id_push = Sample(id_cond, 1)
# cat(id_push, '\n')
temp[id_push] = 1
ind[i] = bin2dec(temp) + 1
}
# cat(ind, '\n')
return(ind)
}
if (nbFocalElement <= ThetaSize) {
MassOut = matrix(0, 2^ThetaSize, nbMass)
for (i in 1:nbMass) {
ind = indice(ThetaSize = ThetaSize, singleton = singleton)
# cat("here-")
# cat(ind, "\n")
if(nondogmatic){
if(con_sig){
indFocalElement = c(Sample(ind[2: (ThetaSize - 1)], nbFocalElement - 2), ind[1], 2^ThetaSize)
}else{
indFocalElement = c(Sample(ind[1: (ThetaSize - 1)], nbFocalElement - 1), 2^ThetaSize)
}
}else{
indFocalElement = Sample(ind, nbFocalElement)
}
# cat(indFocalElement, '\n')
randMass = diff(c(0, sort(runif(nbFocalElement - 1)), 1))
MassOut[indFocalElement, i] = randMass
}
} else {
stop("Accident: in RandomMass for nested bbas, nbFocalElement > ThetaSize\n")
}
return(MassOut)
}
RandomSSF <- function(ThetaSize, nbMass, Include){
# Include is the focal element of SSF except Theta
nf = 2^ThetaSize
if(missing(Include)){
Include = sample(2:(nf-1), nbMass, replace = TRUE)
}
if(length(Include) == 1){
Include = rep(Include, nbMass)
}
MassOut = matrix(0, nf, nbMass);
for(i in 1:nbMass){
MassOut[c(Include[i], nf) ,i] = runif(2);
}
MassOut = MassOut / (matrix(1, nf, 1) %*% colSums(MassOut))
return(MassOut)
}
bin2dec <- function(x) {
return(sum(2^(1:length(x) - 1) * x))
}
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Defines functions bin2dec RandomSSF RandomConsonant Sample RandomMass
Documented in RandomMass
##' Generating masses
##'
##' Different ways to generate masses
##'
##' @export
##'
##' @param nbFocalElement The number of focal elements
##' @param ThetaSize The length of the discernment frame \eqn{\Theta}
##' @param nbMass The number of masses to generate
##' @param Type Which kind of mass to generate:
##'
##' Type=1 for focal elements can be everywhere
##'
##' Type=2 for focal elements can not be on the emptyset
##'
##' Type=3 for no dogmatic mass : one focal element is on \eqn{\Theta} (ignorance)
##'
##' Type=4 for no dogmatic mass : one focal element is on \eqn{\Theta} (ignorance) and no focal elements are on the emptyset
##'
##' Type=5 for all the focal elements are the singletons
##'
##' Type=6 for all the focal elements are the singletons and on \eqn{\Theta} (ignorance)
##'
##' Type=7 for all the focal elements are the singletons and on \eqn{\Theta} (ignorance), but not on all the singletons
##'
##' Type=8 On only one defined singleton, on \eqn{\Theta} (ignorance), and others
##'
##' Type=9 On one defined singleton, on other singletons and on \eqn{\Theta} (ignorance)
##'
##' Type=10 On one focal element contain a defined singleton, on other focal elements and on \eqn{\Theta} (ignorance)
##'
##' Type=11 On one focal element contain a defined singleton, on other focal elements (not emptyset) and on
##' \eqn{\Theta} (ignorance)
##'
##' Type=12 For consonant bba with nested focal elements, all of them contain a defined singleton. If parameter singleton is set to 0, the defined singleton can be any one of the element in the discernment framework. Note that the defined singleton may not be one of the focal elements.
##'
##' Type=13 For non-dogmatic consonant bba with nested focal elements, all of them contain a defined singleton. Different from Type 12, the mass given to \eqn{\Theta} must be positive (non-dogmatic). If parameter singleton is set to 0, the defined sigleton can be any one of the element in the discernment framework. Note that the defined singleton is one of the focal elements.
##'
##' Type=14 For non-dogmatic consonant bba with nested focal elements, all of them contain a defined singleton. The focal elements must contain the defined sigleton and \eqn{\Theta}. If parameter singleton is set to 0, the defined sigleton can be any one of the element in the discernment framework. Note that the difined singleton may not be the focal elements.
##'
##' Type=15 Random SSFs with Include and \eqn{\Theta} as focal elements. Generally, parameter Include shoud have the same length as nbMass. If the lenght of parameter Include is 1, all the random masses have the same focal elements. If Include is missing, then the focal element (except \eqn{\Theta}) could be randomly set to be any subset of \eqn{\Theta} except the empty set and the total ignorance.
##' @param singleton The singleton element (with only one element) in the focal sets. It should be given a number from 1 to \eqn{ThetaSize} if Type is from 5 to 11.
##' @param Include The natrual id of the focal element (not \eqn{\Theta}) of SSFs
##' @return The generated mass matrix. Each column represents a piece of mass
##' @examples
##'
##' RandomMass(nbFocalElement=3, ThetaSize=3, nbMass=4, Type=1)
##' RandomMass(nbFocalElement=3, ThetaSize=4, nbMass=4, Type=3)
##' RandomMass(nbFocalElement=4, ThetaSize=4, nbMass=4, Type=5,singleton=2)
##' RandomMass(nbFocalElement=4, ThetaSize=4, nbMass=4, Type=10,singleton=2)
##' RandomMass(nbFocalElement=4, ThetaSize=4, nbMass=4, Type=13,singleton=2)
##' RandomMass(nbFocalElement=2, ThetaSize=4, nbMass=4, Type=14,singleton=2)
##' RandomMass(ThetaSize=4, nbMass=4, Type=15, Include=2)
##'
RandomMass <- function(nbFocalElement, ThetaSize, nbMass, Type, singleton, Include) {
# depending program
# new Sample function. To avoid the problem by the function base::sample
# if there is only one element, i, for Sample, base::sample will think that the data set to Sample is 1:i
# for example, base::sample(5, 1) will return a random integer from 1 to 5
# this may bring some problem when using base::sample(setdiff(..), ..), when the results of setdiff(..) is only one element
indice <- function(ThetaSize, nbFocalElement, Type, singleton) {
Type = Type
# the empty set is 1; the Theta is 2^K
nb = 2^ThetaSize
if (Type == 1) {
# focal elements can be everywhere
ind = Sample(1:nb)
} else if (Type == 2) {
# focal elements can not be on the emptyset
ind = Sample(2:nb)
} else if (Type == 3) {
# no dogmatic mass : one focal element is on Theta (ignorance)
ind = c(nb, Sample(1:(nb - 1)))
} else if (Type == 4) {
# no dogmatic mass : one focal element is on Theta (ignorance) and no focal elements are on the emptyset
ind = c(nb, Sample(2:(nb - 1)))
} else if (Type == 5) {
# all the focal elements are the singletons
if (nbFocalElement == ThetaSize) {
ind = 1 + 2^(1:ThetaSize - 1)
} else {
stop("Accident: in RandomMass - indice: nbFocalElement and ThetaSize are not the same\n")
}
} else if (Type == 6) {
# all the focal elements are the singletons and on Theta (ignorance)
if (nbFocalElement == ThetaSize + 1) {
ind = c(1 + 2^(1:ThetaSize - 1), nb)
} else {
stop("Accident: in RandomMass - indice: nbFocalElement and ThetaSize+1 are not the same\n")
}
} else if (Type == 7) {
# all the focal elements are the singletons and on Theta (ignorance), but not on all the singletons
indtmp = Sample(1:ThetaSize)
ind = 1 + 2^(indtmp[1:(nbFocalElement - 1)] - 1)
ind = c(ind, nb)
} else if (Type == 8) {
# On only one defined singleton, on Theta (ignorance), and others
# check the number of input arguments
if (!missing(singleton)) {
indRest = Sample(setdiff(1:nb, c(nb, 1 + 2^(singleton - 1))), nbFocalElement - 2)
ind = c(nb, 1 + 2^(singleton - 1), indRest)
} else {
stop("Accident: in RandomMass - indice: the defined singleton is not given\n")
}
} else if (Type == 9) {
# On one defined singleton, on other singletons and on Theta (ignorance)
# check the number of input arguments
if (!missing(singleton)) {
indRest = Sample(setdiff(1 + 2^(1:ThetaSize - 1), 1 + 2^(singleton - 1)), nbFocalElement - 2)
ind = c(1 + 2^(singleton - 1), indRest, nb)
} else {
stop("Accident: in RandomMass - indice: the defined singleton is not given\n")
}
} else if (Type == 10) {
# On one focal element contain a defined singleton, on other focal elements and on Theta (ignorance)
# check the number of input arguments
if (!missing(singleton)) {
myF = t(sapply(1:nb, function(x) {
dec2bin(x - 1, ThetaSize)
}))
indSing = which(myF[, singleton] == 1)
Alea = Sample(setdiff(indSing, nb), 1)
indRest = Sample(setdiff(1:(nb - 1), Alea), nbFocalElement - 2)
ind = c(nb, Alea, indRest)
} else {
stop("Accident: in RandomMass - indice: the defined singleton is not given\n")
}
} else if (Type == 11) {
# idem 10 without emptyset (On one focal element contain a defined singleton, on other focal elements and on Theta (ignorance))
# check the number of input arguments
if (!missing(singleton)) {
if (nbFocalElement != 2^ThetaSize) {
myF = t(sapply(1:nb, function(x) {
dec2bin(x - 1, ThetaSize)
}))
indSing = which(myF[, singleton] == 1)
Alea = Sample(setdiff(indSing, nb), 1)
indRest = Sample(setdiff(2:(nb - 1), Alea), nbFocalElement - 2)
ind = c(nb, Alea, indRest)
} else {
stop("Accident: in RandomMass - indice: The number of focal element must be < 2^ThetaSize\n")
}
} else {
stop("Accident: in RandomMass - indice: the defined singleton is not given\n")
}
}
return(ind)
}
if (Type == 15 || nbFocalElement < 2^ThetaSize + 1) {
if (Type %in% 1:11){
MassOut = matrix(0, 2^ThetaSize, nbMass)
for (i in 1:nbMass) {
ind = indice(ThetaSize, nbFocalElement, Type, singleton)
indFocalElement = ind[1:nbFocalElement]
randMass = diff(c(0, sort(runif(nbFocalElement - 1)), 1))
MassOut[indFocalElement, i] = randMass
}
}else if (Type == 12){
MassOut = RandomConsonant(nbFocalElement, ThetaSize, nbMass, singleton, nondogmatic = FALSE, con_sig = FALSE)
}else if (Type == 13){
MassOut = RandomConsonant(nbFocalElement, ThetaSize, nbMass, singleton, nondogmatic = TRUE, con_sig = FALSE)
}else if (Type == 14){
MassOut = RandomConsonant(nbFocalElement, ThetaSize, nbMass, singleton, nondogmatic = TRUE, con_sig = TRUE)
}else if (Type == 15){
MassOut = RandomSSF(ThetaSize = ThetaSize, nbMass = nbMass, Include = Include)
}else {
stop("Accident: in RandomMass - indice: choose of Type: incorrect\n")
}
} else {
stop("Accident: in RandomMass nbFocalElement > 2^ThetaSize\n")
}
return(MassOut)
}
Sample <- function(x, size, replace = FALSE, prob = NULL) {
if (missing(size))
size <- length(x)
x[sample.int(length(x), size, replace, prob)]
}
RandomConsonant <- function(nbFocalElement, ThetaSize, nbMass, singleton, nondogmatic = TRUE, con_sig = FALSE) {
## generated nested bba
## the parameters are the same as that in RandomMass in ibelief Package
## singleton = 0, random singleton, could be any one in the discernment framework
## con_sig, if contains the singleton element as a focal element
## For SSF with only singleton and Theta, run like: RandomMass(2, ThetaSize, nbMass, singleton, TRUE, TRUE)
indice <- function(ThetaSize, singleton) {
nb = 2^ThetaSize
ind = rep(0, ThetaSize)
if(singleton == 0){
singleton = Sample(1:ThetaSize, 1)
}
ind[1] = 2^(singleton - 1) + 1
temp = rep(0, ThetaSize)
temp[singleton] = 1
for (i in 2:ThetaSize) {
id_cond = which(temp == 0)
id_push = Sample(id_cond, 1)
# cat(id_push, '\n')
temp[id_push] = 1
ind[i] = bin2dec(temp) + 1
}
# cat(ind, '\n')
return(ind)
}
if (nbFocalElement <= ThetaSize) {
MassOut = matrix(0, 2^ThetaSize, nbMass)
for (i in 1:nbMass) {
ind = indice(ThetaSize = ThetaSize, singleton = singleton)
# cat("here-")
# cat(ind, "\n")
if(nondogmatic){
if(con_sig){
indFocalElement = c(Sample(ind[2: (ThetaSize - 1)], nbFocalElement - 2), ind[1], 2^ThetaSize)
}else{
indFocalElement = c(Sample(ind[1: (ThetaSize - 1)], nbFocalElement - 1), 2^ThetaSize)
}
}else{
indFocalElement = Sample(ind, nbFocalElement)
}
# cat(indFocalElement, '\n')
randMass = diff(c(0, sort(runif(nbFocalElement - 1)), 1))
MassOut[indFocalElement, i] = randMass
}
} else {
stop("Accident: in RandomMass for nested bbas, nbFocalElement > ThetaSize\n")
}
return(MassOut)
}
RandomSSF <- function(ThetaSize, nbMass, Include){
# Include is the focal element of SSF except Theta
nf = 2^ThetaSize
if(missing(Include)){
Include = sample(2:(nf-1), nbMass, replace = TRUE)
}
if(length(Include) == 1){
Include = rep(Include, nbMass)
}
MassOut = matrix(0, nf, nbMass);
for(i in 1:nbMass){
MassOut[c(Include[i], nf) ,i] = runif(2);
}
MassOut = MassOut / (matrix(1, nf, 1) %*% colSums(MassOut))
return(MassOut)
}
bin2dec <- function(x) {
return(sum(2^(1:length(x) - 1) * x))
}
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