R/classesAndMethods.R
In spedygiorgio/markovchain: Easy Handling Discrete Time Markov Chains
Defines functions
.getMode
.mc2igraph
.mc2matrix
.markovchain2sparseMatrix
.sparseMatrix2markovchain
.etm2Mc
.msmest2Mc
.msm2Mc
.table2Mc
.df2Mc
.whichColProb
.mc2Df
.matrix2Mc
.checkMatrix
getColorVector
.getNet
.showInt
#' @title Markov Chain class
#' @name markovchain-class
#' @aliases markovchain-class *,markovchain,markovchain-method
#' *,markovchain,matrix-method *,markovchain,numeric-method
#' *,matrix,markovchain-method *,numeric,markovchain-method
#' ==,markovchain,markovchain-method !=,markovchain,markovchain-method
#' absorbingStates,markovchain-method transientStates,markovchain-method
#' recurrentStates,markovchain-method transientClasses,markovchain-method
#' recurrentClasses,markovchain-method communicatingClasses,markovchain-method
#' steadyStates,markovchain-method meanNumVisits,markovchain-method
#' is.regular,markovchain-method is.irreducible,markovchain-method
#' is.accessible,markovchain,character,character-method
#' is.accessible,markovchain,missing,missing-method
#' absorptionProbabilities,markovchain-method
#' meanFirstPassageTime,markovchain,character-method
#' meanFirstPassageTime,markovchain,missing-method
#' meanAbsorptionTime,markovchain-method
#' meanRecurrenceTime,markovchain-method
#' conditionalDistribution,markovchain-method hittingProbabilities,markovchain-method
#' canonicForm,markovchain-method coerce,data.frame,markovchain-method
#' coerce,markovchain,data.frame-method coerce,table,markovchain-method
#' coerce,markovchain,igraph-method coerce,markovchain,matrix-method
#' coerce,markovchain,sparseMatrix-method coerce,sparseMatrix,markovchain-method
#' coerce,matrix,markovchain-method coerce,msm,markovchain-method
#' coerce,msm.est,markovchain-method coerce,etm,markovchain-method
#' dim,markovchain-method initialize,markovchain-method
#' names<-,markovchain-method plot,markovchain,missing-method
#' predict,markovchain-method print,markovchain-method
#' show,markovchain-method summary,markovchain-method
#' sort,markovchain-method t,markovchain-method
#' [,markovchain,ANY,ANY,ANY-method ^,markovchain,numeric-method
#' @description The S4 class that describes \code{markovchain} objects.
#'
#' @param states Name of the states. Must be the same of \code{colnames} and \code{rownames} of the transition matrix
#' @param byrow TRUE or FALSE indicating whether the supplied matrix
#' is either stochastic by rows or by columns
#' @param transitionMatrix Square transition matrix
#' @param name Optional character name of the Markov chain
#'
#' @section Creation of objects:
#'
#' Objects can be created by calls of the form \code{new("markovchain", states, byrow, transitionMatrix, ...)}.
#'
#' @section Methods:
#'
#' \describe{
#' \item{*}{\code{signature(e1 = "markovchain", e2 = "markovchain")}: multiply two \code{markovchain} objects}
#' \item{*}{\code{signature(e1 = "markovchain", e2 = "matrix")}: markovchain by matrix multiplication}
#' \item{*}{\code{signature(e1 = "markovchain", e2 = "numeric")}: markovchain by numeric vector multiplication }
#' \item{*}{\code{signature(e1 = "matrix", e2 = "markovchain")}: matrix by markov chain}
#' \item{*}{\code{signature(e1 = "numeric", e2 = "markovchain")}: numeric vector by \code{markovchain} multiplication }
#' \item{[}{\code{signature(x = "markovchain", i = "ANY", j = "ANY", drop = "ANY")}: ... }
#' \item{^}{\code{signature(e1 = "markovchain", e2 = "numeric")}: power of a \code{markovchain} object}
#' \item{==}{\code{signature(e1 = "markovchain", e2 = "markovchain")}: equality of two \code{markovchain} object}
#' \item{!=}{\code{signature(e1 = "markovchain", e2 = "markovchain")}: non-equality of two \code{markovchain} object}
#' \item{absorbingStates}{\code{signature(object = "markovchain")}: method to get absorbing states }
#' \item{canonicForm}{\code{signature(object = "markovchain")}: return a \code{markovchain} object into canonic form }
#' \item{coerce}{\code{signature(from = "markovchain", to = "data.frame")}: coerce method from markovchain to \code{data.frame}}
#' \item{conditionalDistribution}{\code{signature(object = "markovchain")}: returns the conditional probability of subsequent states given a state}
#' \item{coerce}{\code{signature(from = "data.frame", to = "markovchain")}: coerce method from \code{data.frame} to \code{markovchain}}
#' \item{coerce}{\code{signature(from = "table", to = "markovchain")}: coerce method from \code{table} to \code{markovchain} }
#' \item{coerce}{\code{signature(from = "msm", to = "markovchain")}: coerce method from \code{msm} to \code{markovchain} }
#' \item{coerce}{\code{signature(from = "msm.est", to = "markovchain")}: coerce method from \code{msm.est} (but only from a Probability Matrix) to \code{markovchain} }
#' \item{coerce}{\code{signature(from = "etm", to = "markovchain")}: coerce method from \code{etm} to \code{markovchain} }
#' \item{coerce}{\code{signature(from = "sparseMatrix", to = "markovchain")}: coerce method from \code{sparseMatrix} to \code{markovchain} }
#' \item{coerce}{\code{signature(from = "markovchain", to = "igraph")}: coercing to \code{igraph} objects }
#' \item{coerce}{\code{signature(from = "markovchain", to = "matrix")}: coercing to \code{matrix} objects }
#' \item{coerce}{\code{signature(from = "markovchain", to = "sparseMatrix")}: coercing to \code{sparseMatrix} objects }
#' \item{coerce}{\code{signature(from = "matrix", to = "markovchain")}: coercing to \code{markovchain} objects from \code{matrix} one }
#' \item{dim}{\code{signature(x = "markovchain")}: method to get the size}
#' \item{names}{\code{signature(x = "markovchain")}: method to get the names of states}
#' \item{names<-}{\code{signature(x = "markovchain", value = "character")}: method to set the names of states}
#' \item{initialize}{\code{signature(.Object = "markovchain")}: initialize method }
#' \item{plot}{\code{signature(x = "markovchain", y = "missing")}: plot method for \code{markovchain} objects }
#' \item{predict}{\code{signature(object = "markovchain")}: predict method }
#' \item{print}{\code{signature(x = "markovchain")}: print method. }
#' \item{show}{\code{signature(object = "markovchain")}: show method. }
#' \item{sort}{\code{signature(x = "markovchain", decreasing=FALSE)}: sorting the transition matrix. }
#' \item{states}{\code{signature(object = "markovchain")}: returns the names of states (as \code{names}. }
#' \item{steadyStates}{\code{signature(object = "markovchain")}: method to get the steady vector. }
#' \item{summary}{\code{signature(object = "markovchain")}: method to summarize structure of the markov chain }
#' \item{transientStates}{\code{signature(object = "markovchain")}: method to get the transient states. }
#' \item{t}{\code{signature(x = "markovchain")}: transpose matrix }
#' \item{transitionProbability}{\code{signature(object = "markovchain")}: transition probability }
#' }
#'
#' @references
#' A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
#'
#' @author Giorgio Spedicato
#' @note
#' \enumerate{
#' \item \code{markovchain} object are backed by S4 Classes.
#' \item Validation method is used to assess whether either columns or rows totals to one.
#' Rounding is used up to \code{.Machine$double.eps * 100}. If state names are not properly
#' defined for a probability \code{matrix}, coercing to \code{markovhcain} object leads
#' to overriding states name with artificial "s1", "s2", ... sequence. In addition, operator
#' overloading has been applied for \eqn{+,*,^,==,!=} operators.
#' }
#'
#' @seealso \code{\link{markovchainSequence}},\code{\link{markovchainFit}}
#'
#' @examples
#' #show markovchain definition
#' showClass("markovchain")
#' #create a simple Markov chain
#' transMatr<-matrix(c(0.4,0.6,.3,.7),nrow=2,byrow=TRUE)
#' simpleMc<-new("markovchain", states=c("a","b"),
#' transitionMatrix=transMatr,
#' name="simpleMc")
#' #power
#' simpleMc^4
#' #some methods
#' steadyStates(simpleMc)
#' absorbingStates(simpleMc)
#' simpleMc[2,1]
#' t(simpleMc)
#' is.irreducible(simpleMc)
#' #conditional distributions
#' conditionalDistribution(simpleMc, "b")
#' #example for predict method
#' sequence<-c("a", "b", "a", "a", "a", "a", "b", "a", "b", "a", "b", "a", "a", "b", "b", "b", "a")
#' mcFit<-markovchainFit(data=sequence)
#' predict(mcFit$estimate, newdata="b",n.ahead=3)
#' #direct conversion
#' myMc<-as(transMatr, "markovchain")
#'
#' #example of summary
#' summary(simpleMc)
#' \dontrun{plot(simpleMc)}
#'
#' @keywords classes
#'
#' @export
setClass(
# Class name
"markovchain",
# Define the slots
slots = list(states = "character", byrow = "logical",
transitionMatrix = "matrix", name = "character"),
# Set the default values for the slots
prototype = list(
states = c("a", "b"),
byrow = TRUE,
transitionMatrix = matrix(
data = c(0, 1, 1, 0),
nrow = 2,
byrow = TRUE,
dimnames = list(c("a", "b"), c("a", "b"))),
name = "Unnamed Markov chain")
)
# Initializing method for markovchain objects
setMethod(
"initialize",
signature(.Object = "markovchain"),
function (.Object, states, byrow, transitionMatrix, name, ...) {
# Put the standard markovchain
if (missing(transitionMatrix)) {
transitionMatrix <- matrix(
data = c(0, 1, 1, 0),
nrow = 2,
byrow = TRUE,
dimnames = list(c("a", "b"), c("a", "b")))
}
rowNames <- rownames(transitionMatrix)
colNames <- colnames(transitionMatrix)
# Check names of transition matrix
# if all names are missing it initializes them to "1", "2", ....
if (all(is.null(rowNames), is.null(colNames)) == TRUE) {
if (missing(states)) {
numRows <- nrow(transitionMatrix)
stateNames <- as.character(seq(1:numRows))
} else {
stateNames <- states
}
rownames(transitionMatrix) <- stateNames
colnames(transitionMatrix) <- stateNames
# Fix when rownames null
} else if (is.null(rowNames)) {
rownames(transitionMatrix) <- colNames
# Fix when colnames null
} else if (is.null(colNames)) {
colnames(transitionMatrix) <- rowNames
# Fix when different
} else if (! setequal(rowNames, colNames)) {
colnames(transitionMatrix) <- rowNames
}
if (missing(states))
states <- rownames(transitionMatrix)
if (missing(byrow))
byrow <- TRUE
if (missing(name))
name <- "Unnamed Markov chain"
callNextMethod(
.Object,
states = states,
byrow = byrow,
transitionMatrix = transitionMatrix,
name = name,
...
)
}
)
#' @title Non homogeneus discrete time Markov Chains class
#' @name markovchainList-class
#' @aliases [[,markovchainList-method dim,markovchainList-method
#' predict,markovchainList-method print,markovchainList-method
#' show,markovchainList-method
#' @description A class to handle non homogeneous discrete Markov chains
#'
#' @param markovchains Object of class \code{"list"}: a list of markovchains
#' @param name Object of class \code{"character"}: optional name of the class
#'
#' @section Objects from the Class:
#'
#' A \code{markovchainlist} is a list of \code{markovchain} objects. They can
#' be used to model non homogeneous discrete time Markov Chains, when
#' transition probabilities (and possible states) change by time.
#' @section Methods:
#' \describe{
#' \item{[[}{\code{signature(x = "markovchainList")}: extract the
#' i-th \code{markovchain} }
#' \item{dim}{\code{signature(x = "markovchainList")}: number
#' of \code{markovchain} underlying the matrix }
#' \item{predict}{\code{signature(object = "markovchainList")}: predict
#' from a \code{markovchainList} }
#' \item{print}{\code{signature(x = "markovchainList")}: prints the list
#' of markovchains }
#' \item{show}{\code{signature(object = "markovchainList")}: same as \code{print} }
#' }
#'
#' @references
#' A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
#'
#' @author Giorgio Spedicato
#'
#' @note
#' The class consists in a list of \code{markovchain} objects.
#' It is aimed at working with non homogeneous Markov chains.
#'
#' @seealso \code{\linkS4class{markovchain}}
#' @examples
#' showClass("markovchainList")
#' #define a markovchainList
#' statesNames=c("a","b")
#'
#' mcA<-new("markovchain",name="MCA",
#' transitionMatrix=matrix(c(0.7,0.3,0.1,0.9),
#' byrow=TRUE, nrow=2,
#' dimnames=list(statesNames,statesNames))
#' )
#'
#' mcB<-new("markovchain", states=c("a","b","c"), name="MCB",
#' transitionMatrix=matrix(c(0.2,0.5,0.3,0,1,0,0.1,0.8,0.1),
#' nrow=3, byrow=TRUE))
#'
#' mcC<-new("markovchain", states=c("a","b","c","d"), name="MCC",
#' transitionMatrix=matrix(c(0.25,0.75,0,0,0.4,0.6,
#' 0,0,0,0,0.1,0.9,0,0,0.7,0.3),
#' nrow=4, byrow=TRUE)
#' )
#' mcList<-new("markovchainList",markovchains=list(mcA, mcB, mcC),
#' name="Non - homogeneous Markov Chain")
#'
#' @keywords classes
#'
#' @export
setClass(
"markovchainList",
slots = list(
markovchains = "list",
name = "character")
)
# Verifies whether a markovchainList object is valid or not
# A markovchainList is valid iff all the slots are markovchain objects
# Returns true if the markovchainList is valid, the indexes of the
# wrong slots otherwise
setValidity(
"markovchainList",
function(object) {
check <- FALSE
markovchains <- object@markovchains
classes <- sapply(markovchains, class)
nonMarkovchain <- which(classes != "markovchain")
errors <- sapply(nonMarkovchain, function(i) {
paste(i, "-th element class is not 'markovchain'")
})
if (length(errors) == 0) TRUE else errors
}
)
# generic method to print out states
#' @name states
#'
#' @title Defined states of a transition matrix
#'
#' @description This method returns the states of a transition matrix.
#'
#' @param object A discrete \code{markovchain} object
#' @return The character vector corresponding to states slot.
#'
#' @references A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
#'
#' @author Giorgio Spedicato
#'
#' @seealso \code{\linkS4class{markovchain}}
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
#' byrow = TRUE, dimnames=list(statesNames,statesNames)),
#' name = "A markovchain Object"
#' )
#' states(markovB)
#' names(markovB)
#'
#' @rdname states
#'
#' @export
setGeneric("states", function(object) standardGeneric("states"))
#' @rdname states
#' @title states
setMethod(
"states",
"markovchain",
function(object) {
object@states
}
)
#' @title Returns the states for a Markov chain object
#'
#' @param x object we want to return states for
#'
#' @rdname names
setMethod(
"names",
"markovchain",
function(x) {
x@states
}
)
#' @title Method to retrieve name of markovchain object
#'
#' @name name
#'
#' @description This method returns the name of a markovchain object
#'
#' @param object A markovchain object
#' @rdname getName
#' @author Giorgio Spedicato, Deepak Yadav
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
#' byrow = TRUE, dimnames=list(statesNames,statesNames)),
#' name = "A markovchain Object"
#' )
#' name(markovB)
#'
#' @export
setGeneric("name", function(object) standardGeneric("name"))
#' @rdname getName
setMethod(
"name",
"markovchain",
function(object) {
object@name
})
#' @title Method to set name of markovchain object
#'
#' @name name<-
#'
#' @description This method modifies the existing name of markovchain object
#'
#' @param object A markovchain object
#' @param value New name of markovchain object
#' @rdname setName
#' @author Giorgio Spedicato, Deepak Yadav
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
#' byrow = TRUE, dimnames=list(statesNames,statesNames)),
#' name = "A markovchain Object"
#' )
#' name(markovB) <- "dangerous mc"
#'
#' @export
setGeneric("name<-", function(object, value) standardGeneric("name<-"))
#' @rdname setName
setMethod(
"name<-",
"markovchain",
function(object, value) {
object@name <- value
object
}
)
setMethod(
"names<-",
"markovchain",
function(x, value) {
rownames(x@transitionMatrix) <- value
colnames(x@transitionMatrix) <- value
x@states <- value
x
}
)
#' @exportMethod dim
setGeneric("dim")
# Generic methods to get the dim of a markovchain and markovchainList
setMethod(
"dim",
"markovchain",
function(x) {
nrow(x@transitionMatrix)
}
)
setMethod(
"dim",
"markovchainList",
function(x) {
length(x@markovchains)
}
)
# method to set the validity of a markovchain object
setValidity(
"markovchain",
function(object) {
errors <- character()
transitionMatrix <- object@transitionMatrix
states <- object@states
if (length(setdiff(states, unique(states))) > 0) {
msg <- "Error! States must be unique!"
errors <- c(errors, msg)
}
# Performs a set of checks. If any error arises, it ends up concatenated to errors
# Check all values of transition matrix belongs to [0, 1]
maybeProbabilities <- sapply(as.numeric(transitionMatrix), .isProbability)
if (any(maybeProbabilities) == FALSE) {
msg <- "Error! Some elements of transitionMatrix are not probabilities"
errors <- c(errors, msg)
}
# Check whether matrix is square matrix or not
if (nrow(transitionMatrix) != ncol(transitionMatrix)) {
msg <- "Error! transitionMatrix is not a square matrix"
errors <- c(errors, msg)
}
if (!.checkMatrix(transitionMatrix, object@byrow)) {
msg <- paste(
paste("Error!",
ifelse(object@byrow, "Rows", "Cols")),
"of transition matrix do not sum to one"
)
errors <- c(errors, msg)
}
# Check whether column names or rows names equal to state names or not
if (! setequal(colnames(transitionMatrix), states)) {
msg <- "Error! Colnames of transitionMatrix do not match states"
errors <- c(errors, msg)
}
if (! setequal(rownames(transitionMatrix), states)) {
msg <- "Error! Rownames of transitionMatrix do not match states"
errors <- c(errors, msg)
}
if (length(errors) > 0) errors else TRUE
}
)
# generic method to extract transition probability
# from state t0 to state t1
#' @name transitionProbability
#' @title Function to get the transition probabilities from initial
#' to subsequent states.
#' @description This is a convenience function to get transition probabilities.
#'
#' @param object A \code{markovchain} object.
#' @param t0 Initial state.
#' @param t1 Subsequent state.
#'
#' @references A First Course in Probability (8th Edition),
#' Sheldon Ross, Prentice Hall 2010
#'
#' @return Numeric Vector
#'
#' @author Giorgio Spedicato
#' @seealso \code{\linkS4class{markovchain}}
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
#' byrow = TRUE, dimnames=list(statesNames,statesNames)),
#' name = "A markovchain Object"
#' )
#' transitionProbability(markovB,"b", "c")
#' @rdname transitionProbability
#'
#' @exportMethod transitionProbability
setGeneric("transitionProbability", function(object, t0, t1) standardGeneric("transitionProbability"))
#' @rdname transitionProbability
setMethod("transitionProbability", "markovchain",
function(object, t0, t1) {
fromState <- which(object@states == t0)
toState <- which(object@states == t1)
out <- ifelse(object@byrow == TRUE, object@transitionMatrix[fromState, toState] ,
object@transitionMatrix[toState, fromState])
return(out)
}
)
# print, plot and show methods
.showInt <- function(object, verbose = TRUE) {
# find the direction
if (object@byrow == TRUE) {
direction <- "(by rows)"
} else {
direction <- "(by cols)"
}
if (verbose == TRUE) {
cat(object@name, "\n A ", dim(object), "- dimensional discrete Markov Chain defined by the following states: \n",
paste(states(object), collapse=", "), "\n The transition matrix ",
direction, " is defined as follows: \n")
}
print(object@transitionMatrix)
cat("\n")
}
#' @exportMethod show
setGeneric("show")
# show methods for markovchain and markovchain list objects
setMethod("show", "markovchain",
function(object){
.showInt(object)
}
)
setMethod("show", "markovchainList",
function(object) {
cat(object@name, " list of Markov chain(s)", "\n")
for(i in 1:length(object@markovchains)) {
cat("Markovchain ",i,"\n")
show(object@markovchains[[i]])
}
}
)
#' @exportMethod print
setGeneric("print")
# print methods
setMethod("print", "markovchainList", function(x) show(x))
setMethod("print", "markovchain",
function(x){
object <- x
.showInt(object, verbose = FALSE)
}
)
.getNet <- function(object, round = FALSE) {
# function to get the absorbency matrix to plot and export to igraph
#
# Args:
# object: a markovchain object
# round: boolean to round
#
# Returns:
#
# a graph adjacency
if (object@byrow == FALSE) {
object <- t(object)
}
matr <- object@transitionMatrix*100
if(round == TRUE) {
matr <- round(matr, 2)
}
net <- graph.adjacency(adjmatrix = matr, weighted = TRUE, mode = "directed")
return(net)
}
getColorVector <- function(object){
list <- .communicatingClassesRcpp(object)
sections <- length(list)
colorList <- grDevices::colors()
colorList <- sample(colorList,sections)
colorvector <- rep("white",length(object@states))
for(i in 1:length(list)){
part <- list[[i]]
for(j in 1:length(part)){
colorvector[match(part[j],object@states)] <- colorList[i]
}
}
return(colorvector)
}
#' @exportMethod plot
setGeneric("plot")
# Plot methods for markovchain objects
# plot method from stat5
setMethod("plot", signature(x = "markovchain", y = "missing"),
function(x, y, package = "igraph", ...) {
switch(package,
diagram = {
if (requireNamespace("diagram", quietly = TRUE)) {
.plotdiagram(object = x, ...)
} else {
netMc <- .getNet(object = x, round = TRUE)
edgeLabel <- round(E(netMc)$weight / 100, 2)
plot.igraph(x = netMc, edge.label = edgeLabel, ...)
}
},
DiagrammeR = {
if (requireNamespace("DiagrammeR", quietly = TRUE)) {
.plotDiagrammeR(object = x, ...)
} else {
netMc <- .getNet(object = x, round = TRUE)
edgeLabel <- round(E(netMc)$weight / 100, 2)
plot.igraph(x = netMc, edge.label = edgeLabel, ...)
}
},
{
netMc <- .getNet(object = x,round = TRUE)
edgeLabel <- round(E(netMc)$weight / 100, 2)
plot.igraph(x = netMc, edge.label = edgeLabel, ...)
})
}
)
##################################################AS METHODS#########################
.checkMatrix <- function(matr, byrow = TRUE, verbose = FALSE) {
# firstly, check size
if (ncol(matr) != nrow(matr)) {
if(verbose) stop("Error! Not a rectangular matrix")
return(FALSE)
}
# secondly, check is stochastic
isStochastic <- .isStochasticMatrix(matr, byrow)
if (!isStochastic) {
if (verbose)
stop("Error! Either rows or cols should sum to 1")
return(FALSE)
}
# if all test are passed
return(TRUE)
}
# Internal function to return a markovchain object given a matrix
.matrix2Mc <- function(from) {
# whether given matrix is a transition matrix or not
# if it is then how probabilities are stored
# row-wise or columnwise
byrow <- TRUE
checkByRows <- .checkMatrix(from, byrow = byrow)
if(!checkByRows) {
byrow <- FALSE
checkByCols <- .checkMatrix(from, byrow = byrow)
if(!checkByCols) {
#error could be either in rows or in cols
if (any(colSums(from) != 1)) cat("columns sums not equal to one are:", which(colSums(from) != 1),"\n")
if (any(rowSums(from) != 1)) cat("row sums not equal to one are:", which(rowSums(from) != 1),"\n")
stop("Error! Not a transition matrix")
}
}
# extract states names
if(byrow) {
namesCandidate <- rownames(from)
} else {
namesCandidate <- colnames(from)
}
# if states names is not there create it s1, s2, s3, ....
if(is.null(namesCandidate)) {
namesCandidate <- paste("s", 1:nrow(from), sep = "")
}
# create markovchain object
out <- new("markovchain", transitionMatrix = from, states = namesCandidate, byrow = byrow)
invisible(out)
}
#' @exportMethod coerce
NULL
# coerce matrix to markovchain object using internal method
# example: as("some matrix", "markovchain")
setAs(from = "matrix", to = "markovchain", def = .matrix2Mc)
# Function to transform a markovchain into a data.frame
# Args:
# from: a markovchain object
#
# returns:
# a data.frame
.mc2Df <- function(from) {
# number of rows or columns
nr <- nrow(from@transitionMatrix)
for(i in 1:nr){
for(j in 1:nr){
t0 <- from@states[i]
t1 <- from@states[j]
prob <- transitionProbability(object = from, t0 = t0, t1 = t1)
#cope with the new default of R 4.0 (5-3-2020)
rowDf <- data.frame(t0 = t0, t1 = t1, prob = prob,stringsAsFactors = TRUE )
# go to else part if first row of data frame is generated
if(exists("outDf")) {
outDf <- rbind(outDf, rowDf)
} else {
outDf <- rowDf
}
}
}
return(outDf)
}
# method to convert(coerce) from markovchain to data.frame
setAs(from = "markovchain", to = "data.frame", def = .mc2Df)
# method to find the column which stores transition probability
.whichColProb <- function(df) {
# column number which stores transition probability
out <- 0
# check for validity of data frame
if(ncol(df) > 3) {
warning("Warning! More than three columns. Only the first three will be used")
}
if(ncol(df) < 3) {
stop("Error! Three columns needed")
}
for(i in 1:ncol(df)) {
# when found the first numeric and probability col
if((is(df[, i], "numeric")) & (all(sapply(df[, i], .isProbability) == TRUE))) {
out <- i
break
}
}
return(out)
}
# Function to convert from a data.frame containing initial, ending
# and probability columns to a proper markovchain object
#
# Args:
# from: a data.frame
#
# Returns:
# A markovchain object
.df2Mc <- function(from) {
statesNames <- unique(from[, 1])
colProb <- .whichColProb(from) # what is the use
# transition matrix
prMatr <- zeros(length(statesNames))
rownames(prMatr) <- statesNames
colnames(prMatr) <- statesNames
for(i in 1:nrow(from)) {
idRow <- which(statesNames == from[i, 1]) # assume first col from
idCol <- which(statesNames == from[i, 2]) # assume second col to
prMatr[idRow, idCol] <- from[i, 3] # assume third col t-probability
}
out <- new("markovchain", transitionMatrix = prMatr)
return(out)
}
# method to convert(coerce) data frame to markovchain object
setAs(from = "data.frame", to = "markovchain", def = .df2Mc)
# example
# data <- data.frame(from = c("a", "a", "b", "b", "b", "b"),
# to = c("a", "b", "b", "b", "b", "a"))
#
# from <- table(data)
# .table2Mc(from)
.table2Mc <- function(from) {
# check whether table has square dimension or not
if(dim(from)[1] != dim(from)[2]) {
stop("Error! Table is not squared")
}
# rows ond columns name should be same
if(!setequal(rownames(from),colnames(from))) {
stop("Error! Rows not equal to coulumns")
}
temp <- unclass(as.matrix(from))
# make same sequence of col / row
fromMatr <- temp[, order(rownames(temp))]
# obtain transition matrix
outMatr <- fromMatr / rowSums(fromMatr)
out <- new("markovchain", states = rownames(temp),
transitionMatrix = outMatr, byrow=TRUE)
return(out)
}
# coerce table to markovchain object
setAs(from = "table", to = "markovchain", def = .table2Mc)
# function from msm to markovchain
# msm is a package. Use this package to create msm object.
# see how to create msm object using ?msm
.msm2Mc <- function(from) {
if(requireNamespace(package='msm', quietly = TRUE)) {
temp <- msm::pmatrix.msm(from)
prMatr <- unclass(as.matrix(temp))
out <- new("markovchain", transitionMatrix = prMatr)
} else {
out <- NULL
print("msm unavailable")
}
return(out)
}
# coerce msm object to markovchain object
setClass("msm")
setAs(from = "msm", to = "markovchain", def = .msm2Mc)
# function for msm.est to mc. Assume a probability matrix given
.msmest2Mc <- function(from) {
if (is.matrix(from)) {
# central estimate
pMatr <- from
}
if (is.list(from)) {
# central estimate
pMatr <- from[[1]]
}
out <- new("markovchain", transitionMatrix = as(pMatr, "matrix"))
return(out)
}
# coerce ms.est to markovchain object
setClass("msm.est")
setAs(from = "msm.est", to = "markovchain", def = .msmest2Mc)
# function from etm to markovchain
.etm2Mc<-function(from) {
# data frame consists of 'from' and 'to' column
df <- from$trans
# name of states
elements <- from$state.names
# number of unique states
nelements <- length(elements)
# temporary t-matrix
prMatr <- zeros(nelements)
dimnames(prMatr) <- list(elements, elements)
# populate t-matrix
for(i in 1:dim(df)[1]) {
r <- df[i, ] # each row one by one
stateFrom <- r$from
stateTo <- r$to
prMatr[stateFrom, stateTo] <- prMatr[stateFrom, stateTo] + 1
}
# convert freq-matrix to trans-matrix
rsums <- rowSums(prMatr)
prMatr <- prMatr / rsums
# take care of rows with all entries 0
if(any(rsums == 0)) {
indicesToBeSanitized <- which(rsums == 0)
for(i in indicesToBeSanitized) {
for(j in 1:nelements) {
prMatr[i, j] <- 1 / nelements
}
}
}
# create markovchain object
out <- new("markovchain", transitionMatrix = prMatr)
return(out)
}
# coerce etm object to markovchain object
setClass("etm")
setAs(from = "etm", to = "markovchain", def = .etm2Mc)
#sparse matrix from Matrix package
.sparseMatrix2markovchain<-function(from){
temp<-as(from,"matrix")
out <- as(temp, "markovchain")
return(out)
}
.markovchain2sparseMatrix<-function(from){
temp<-as(from,"matrix")
out <- as(temp, "sparseMatrix")
return(out)
}
setAs(from = "sparseMatrix", to = "markovchain", def = .sparseMatrix2markovchain)
setAs(from = "markovchain", to = "sparseMatrix", def = .markovchain2sparseMatrix)
# functions and methods to return a matrix
.mc2matrix <- function(from) {
out <- from@transitionMatrix
return(out)
}
# coerce markovchain object to matrix(transition)
setAs(from = "markovchain", to = "matrix", def = .mc2matrix)
# functions and methods to return a matrix
.mc2igraph <- function(from) {
# convert the markovchain to data.frame
temp <- .mc2Df(from=from)
# convert the data frame to igraph graph
# need to set only non zero weights
out <- graph.data.frame(d=temp[temp$prob>0,])
return(out)
}
# coerce markovchain object to igraph
setClass("igraph")
setAs(from = "markovchain", to = "igraph", def = .mc2igraph)
#' @exportMethod t
setGeneric("t")
# transposing method for markovchain objects
setMethod("t", "markovchain",
function(x) {
out <- new("markovchain", byrow = !x@byrow,
transitionMatrix = t(x@transitionMatrix))
return(out)
}
)
#' @exportMethod *
setGeneric("*")
# function to multiplicate two markov chains
#
# Args:
# e1: first markovchain
# e2: second markov chain
#
# Returns:
# if feasible, a markovchain where the transition matrix is e1*e2
setMethod("*", c("markovchain", "markovchain"),
function(e1, e2) {
# compare states of markovchains
if(!setequal(e1@states, e2@states)) {
warning("Warning! Different states")
}
# dimension must be equal
if(!setequal(dim(e1@transitionMatrix), dim(e2@transitionMatrix))) {
stop("Error! Different size")
}
# both must be either row wise or col wise
if(!(e1@byrow == e2@byrow)) {
stop("Error! Both transition matrix should be defined either by row or by column")
}
newStates <- e1@states
newTransMatr <- e1@transitionMatrix %*% e2@transitionMatrix
byRow <- e1@byrow
# multiplicated matrix takes the first matrix's name
mcName <- e1@name
out<-new("markovchain", states = newStates, transitionMatrix = newTransMatr,
byrow = byRow, name = mcName)
return(out)
}
)
# methods implemented for multiplication of markovchain object with
# matrix, 1-D vector, and vice-versa
setMethod("*", c("matrix", "markovchain"),
function(e1, e2) {
out <- e1 %*% e2@transitionMatrix
return(out)
}
)
setMethod("*", c("markovchain", "matrix"),
function(e1, e2) {
out <- e1@transitionMatrix %*% e2
return(out)
}
)
setMethod("*", c("numeric", "markovchain"),
function(e1, e2) {
if(length(e1) != dim(e2)) {
stop("Error! Uncompatible dimensions")
} else {
out <- e1 %*% e2@transitionMatrix
}
return(out)
}
)
setMethod("*", c("markovchain", "numeric"),
function(e1, e2) {
if(length(e2) != dim(e1)) {
stop("Error! Uncompatible dimensions")
} else {
out <- e1@transitionMatrix %*% e2
}
return(out)
}
)
#' @exportMethod ==
setGeneric("==")
# compare two markovchain object
setMethod("==", c("markovchain", "markovchain"),
function(e1, e2) {
out <- .approxEqualMatricesRcpp(e1@transitionMatrix, e2@transitionMatrix)
return(out)
}
)
#' @exportMethod !=
setGeneric("!=")
setMethod("!=", c("markovchain", "markovchain"),
function(e1, e2) {
out <- FALSE
out <- !(e1 == e2)
return(out)
}
)
#'@exportMethod ^
setGeneric("^")
# markovchain raise to some power
# this method is O(n³ log(m)) where n = {num cols (= rows) of e1} and m = e2
setMethod("^", c("markovchain", "numeric"),
function(e1, e2) {
out <- new("markovchain", states = e1@states, byrow = e1@byrow,
transitionMatrix = e1@transitionMatrix %^% e2,
name = paste(e1@name, "^", e2, sep = "")
)
return(out)
}
)
#' @exportMethod [
setGeneric("[")
# methods to directly access transition matrix elements
setMethod("[", signature(x = "markovchain", i = "ANY", j = "ANY"),
function(x, i, j) {
out <- x@transitionMatrix[i, j]
return(out)
}
)
#' @exportMethod [[
setGeneric("[[")
# methods to directly access markovchain objects composing a markovchainList object
setMethod("[[", signature(x = "markovchainList", i = "ANY"),
function(x, i) {
out <- x@markovchains[[i]]
return(out)
}
)
# transition probabilty vector from a given state
#' @title \code{conditionalDistribution} of a Markov Chain
#'
#' @name conditionalDistribution
#'
#' @description It extracts the conditional distribution of the subsequent state,
#' given current state.
#'
#' @param object A \code{markovchain} object.
#' @param state Subsequent state.
#'
#' @author Giorgio Spedicato, Deepak Yadav
#'
#' @return A named probability vector
#' @references A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
#'
#' @seealso \code{\linkS4class{markovchain}}
#'
#' @examples
#' # define a markov chain
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1),nrow = 3,
#' byrow = TRUE, dimnames = list(statesNames, statesNames)))
#'
#' conditionalDistribution(markovB, "b")
#'
#' @exportMethod conditionalDistribution
setGeneric("conditionalDistribution", function(object, state) standardGeneric("conditionalDistribution"))
setMethod("conditionalDistribution", "markovchain",
function(object, state) {
# get the states names
stateNames <- states(object)
# number of unique states
out <- numeric(length(stateNames))
# states are assumed to be sorted
index2Take <- which(stateNames == state)
if(object@byrow == TRUE) {
out <- object@transitionMatrix[index2Take, ]
} else {
out <- object@transitionMatrix[, index2Take]
}
# names the output and returs it
names(out) <- stateNames
return(out)
}
)
# Function to get the mode of a probability vector
#
# Args:
# probVector: the probability vector
# ties: specifies if ties are to be sampled, otherwise more than one element is returned
#
# Returns:
# the name of the model element
.getMode <- function(probVector, ties = "random") {
maxIndex <- which(probVector == max(probVector))
temp <- probVector[maxIndex] # index of maximum probabilty
if((ties == "random") & (length(temp) > 1)) {
out <- sample(temp, 1)
} else {
out <- temp
}
return(names(out))
}
#' @exportMethod predict
setGeneric("predict")
# predict method for markovchain objects
# given initial state return a vector of next n.ahead states
setMethod("predict", "markovchain",
function(object, newdata, n.ahead = 1) {
# identify the last state
lastState <- newdata[length(newdata)]
out <- character()
for(i in 1:n.ahead) {
# cyclically determine the most probable subsequent state from the conditional distribution
newState <- .getMode(probVector = conditionalDistribution(object, lastState), ties = "random")
out <- c(out, newState)
lastState <- newState
}
return(out)
}
)
# predict method for markovchainList objects
setMethod("predict", "markovchainList",
function(object, newdata, n.ahead = 1, continue = FALSE) {
# object a markovchainList
# newdata = the actual data
# n.ahead = how much ahead
# continue = veryfy if that lasts
# allocate output
out <- character()
actualPos <- length(newdata)
lastState <- newdata[actualPos] # take last position
for(i in 1:n.ahead) {
newPos <- actualPos + i - 1
if(newPos <= dim(object)) {
newState <- predict(object = object[[newPos]], newdata = lastState, n.ahead = 1)
out <- c(out, newState)
lastState <- newState
} else {
if(continue == TRUE) {
newState <- predict(object = object[[dim(object)]], newdata = lastState, n.ahead = 1)
out <- c(out, newState)
lastState <- newState
} else break;
}
}
return(out)
}
)
#sort method for markovchain objects
setGeneric("sort", function(x, decreasing=FALSE, ...) standardGeneric("sort"))
setMethod("sort", signature(x="markovchain"), function(x, decreasing = FALSE) {
#get matrix and state names 2 be sorted
matr2besorted<-x@transitionMatrix
if (x@byrow)
states2besorted <- rownames(matr2besorted)
else
states2besorted <- colnames(matr2besorted)
#sorting
sort_index<-order(states2besorted,decreasing = decreasing)
#reallocating
matr_sorted<-matr2besorted[sort_index,sort_index]
states_sorted<-states2besorted[sort_index]
out<-x
out@transitionMatrix<-matr_sorted
out@states<-states_sorted
return(out)
}
)
# method to get stationary states
#' @name steadyStates
#' @title Stationary states of a \code{markovchain} object
#'
#' @description This method returns the stationary vector in matricial form of a markovchain object.
#' @param object A discrete \code{markovchain} object
#'
#' @return A matrix corresponding to the stationary states
#'
#' @references A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
#' @author Giorgio Spedicato
#' @seealso \code{\linkS4class{markovchain}}
#'
#' @note The steady states are identified starting from which eigenvectors correspond
#' to identity eigenvalues and then normalizing them to sum up to unity. When negative values are found
#' in the matrix, the eigenvalues extraction is performed on the recurrent classes submatrix.
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
#' byrow = TRUE, dimnames=list(statesNames,statesNames)),
#' name = "A markovchain Object"
#' )
#' steadyStates(markovB)
#'
#' @rdname steadyStates
#' @exportMethod steadyStates
setGeneric("steadyStates", function(object) standardGeneric("steadyStates"))
spedygiorgio/markovchain documentation built on Feb. 29, 2024, 3:01 p.m.
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Defines functions .getMode .mc2igraph .mc2matrix .markovchain2sparseMatrix .sparseMatrix2markovchain .etm2Mc .msmest2Mc .msm2Mc .table2Mc .df2Mc .whichColProb .mc2Df .matrix2Mc .checkMatrix getColorVector .getNet .showInt
#' @title Markov Chain class
#' @name markovchain-class
#' @aliases markovchain-class *,markovchain,markovchain-method
#' *,markovchain,matrix-method *,markovchain,numeric-method
#' *,matrix,markovchain-method *,numeric,markovchain-method
#' ==,markovchain,markovchain-method !=,markovchain,markovchain-method
#' absorbingStates,markovchain-method transientStates,markovchain-method
#' recurrentStates,markovchain-method transientClasses,markovchain-method
#' recurrentClasses,markovchain-method communicatingClasses,markovchain-method
#' steadyStates,markovchain-method meanNumVisits,markovchain-method
#' is.regular,markovchain-method is.irreducible,markovchain-method
#' is.accessible,markovchain,character,character-method
#' is.accessible,markovchain,missing,missing-method
#' absorptionProbabilities,markovchain-method
#' meanFirstPassageTime,markovchain,character-method
#' meanFirstPassageTime,markovchain,missing-method
#' meanAbsorptionTime,markovchain-method
#' meanRecurrenceTime,markovchain-method
#' conditionalDistribution,markovchain-method hittingProbabilities,markovchain-method
#' canonicForm,markovchain-method coerce,data.frame,markovchain-method
#' coerce,markovchain,data.frame-method coerce,table,markovchain-method
#' coerce,markovchain,igraph-method coerce,markovchain,matrix-method
#' coerce,markovchain,sparseMatrix-method coerce,sparseMatrix,markovchain-method
#' coerce,matrix,markovchain-method coerce,msm,markovchain-method
#' coerce,msm.est,markovchain-method coerce,etm,markovchain-method
#' dim,markovchain-method initialize,markovchain-method
#' names<-,markovchain-method plot,markovchain,missing-method
#' predict,markovchain-method print,markovchain-method
#' show,markovchain-method summary,markovchain-method
#' sort,markovchain-method t,markovchain-method
#' [,markovchain,ANY,ANY,ANY-method ^,markovchain,numeric-method
#' @description The S4 class that describes \code{markovchain} objects.
#'
#' @param states Name of the states. Must be the same of \code{colnames} and \code{rownames} of the transition matrix
#' @param byrow TRUE or FALSE indicating whether the supplied matrix
#' is either stochastic by rows or by columns
#' @param transitionMatrix Square transition matrix
#' @param name Optional character name of the Markov chain
#'
#' @section Creation of objects:
#'
#' Objects can be created by calls of the form \code{new("markovchain", states, byrow, transitionMatrix, ...)}.
#'
#' @section Methods:
#'
#' \describe{
#' \item{*}{\code{signature(e1 = "markovchain", e2 = "markovchain")}: multiply two \code{markovchain} objects}
#' \item{*}{\code{signature(e1 = "markovchain", e2 = "matrix")}: markovchain by matrix multiplication}
#' \item{*}{\code{signature(e1 = "markovchain", e2 = "numeric")}: markovchain by numeric vector multiplication }
#' \item{*}{\code{signature(e1 = "matrix", e2 = "markovchain")}: matrix by markov chain}
#' \item{*}{\code{signature(e1 = "numeric", e2 = "markovchain")}: numeric vector by \code{markovchain} multiplication }
#' \item{[}{\code{signature(x = "markovchain", i = "ANY", j = "ANY", drop = "ANY")}: ... }
#' \item{^}{\code{signature(e1 = "markovchain", e2 = "numeric")}: power of a \code{markovchain} object}
#' \item{==}{\code{signature(e1 = "markovchain", e2 = "markovchain")}: equality of two \code{markovchain} object}
#' \item{!=}{\code{signature(e1 = "markovchain", e2 = "markovchain")}: non-equality of two \code{markovchain} object}
#' \item{absorbingStates}{\code{signature(object = "markovchain")}: method to get absorbing states }
#' \item{canonicForm}{\code{signature(object = "markovchain")}: return a \code{markovchain} object into canonic form }
#' \item{coerce}{\code{signature(from = "markovchain", to = "data.frame")}: coerce method from markovchain to \code{data.frame}}
#' \item{conditionalDistribution}{\code{signature(object = "markovchain")}: returns the conditional probability of subsequent states given a state}
#' \item{coerce}{\code{signature(from = "data.frame", to = "markovchain")}: coerce method from \code{data.frame} to \code{markovchain}}
#' \item{coerce}{\code{signature(from = "table", to = "markovchain")}: coerce method from \code{table} to \code{markovchain} }
#' \item{coerce}{\code{signature(from = "msm", to = "markovchain")}: coerce method from \code{msm} to \code{markovchain} }
#' \item{coerce}{\code{signature(from = "msm.est", to = "markovchain")}: coerce method from \code{msm.est} (but only from a Probability Matrix) to \code{markovchain} }
#' \item{coerce}{\code{signature(from = "etm", to = "markovchain")}: coerce method from \code{etm} to \code{markovchain} }
#' \item{coerce}{\code{signature(from = "sparseMatrix", to = "markovchain")}: coerce method from \code{sparseMatrix} to \code{markovchain} }
#' \item{coerce}{\code{signature(from = "markovchain", to = "igraph")}: coercing to \code{igraph} objects }
#' \item{coerce}{\code{signature(from = "markovchain", to = "matrix")}: coercing to \code{matrix} objects }
#' \item{coerce}{\code{signature(from = "markovchain", to = "sparseMatrix")}: coercing to \code{sparseMatrix} objects }
#' \item{coerce}{\code{signature(from = "matrix", to = "markovchain")}: coercing to \code{markovchain} objects from \code{matrix} one }
#' \item{dim}{\code{signature(x = "markovchain")}: method to get the size}
#' \item{names}{\code{signature(x = "markovchain")}: method to get the names of states}
#' \item{names<-}{\code{signature(x = "markovchain", value = "character")}: method to set the names of states}
#' \item{initialize}{\code{signature(.Object = "markovchain")}: initialize method }
#' \item{plot}{\code{signature(x = "markovchain", y = "missing")}: plot method for \code{markovchain} objects }
#' \item{predict}{\code{signature(object = "markovchain")}: predict method }
#' \item{print}{\code{signature(x = "markovchain")}: print method. }
#' \item{show}{\code{signature(object = "markovchain")}: show method. }
#' \item{sort}{\code{signature(x = "markovchain", decreasing=FALSE)}: sorting the transition matrix. }
#' \item{states}{\code{signature(object = "markovchain")}: returns the names of states (as \code{names}. }
#' \item{steadyStates}{\code{signature(object = "markovchain")}: method to get the steady vector. }
#' \item{summary}{\code{signature(object = "markovchain")}: method to summarize structure of the markov chain }
#' \item{transientStates}{\code{signature(object = "markovchain")}: method to get the transient states. }
#' \item{t}{\code{signature(x = "markovchain")}: transpose matrix }
#' \item{transitionProbability}{\code{signature(object = "markovchain")}: transition probability }
#' }
#'
#' @references
#' A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
#'
#' @author Giorgio Spedicato
#' @note
#' \enumerate{
#' \item \code{markovchain} object are backed by S4 Classes.
#' \item Validation method is used to assess whether either columns or rows totals to one.
#' Rounding is used up to \code{.Machine$double.eps * 100}. If state names are not properly
#' defined for a probability \code{matrix}, coercing to \code{markovhcain} object leads
#' to overriding states name with artificial "s1", "s2", ... sequence. In addition, operator
#' overloading has been applied for \eqn{+,*,^,==,!=} operators.
#' }
#'
#' @seealso \code{\link{markovchainSequence}},\code{\link{markovchainFit}}
#'
#' @examples
#' #show markovchain definition
#' showClass("markovchain")
#' #create a simple Markov chain
#' transMatr<-matrix(c(0.4,0.6,.3,.7),nrow=2,byrow=TRUE)
#' simpleMc<-new("markovchain", states=c("a","b"),
#' transitionMatrix=transMatr,
#' name="simpleMc")
#' #power
#' simpleMc^4
#' #some methods
#' steadyStates(simpleMc)
#' absorbingStates(simpleMc)
#' simpleMc[2,1]
#' t(simpleMc)
#' is.irreducible(simpleMc)
#' #conditional distributions
#' conditionalDistribution(simpleMc, "b")
#' #example for predict method
#' sequence<-c("a", "b", "a", "a", "a", "a", "b", "a", "b", "a", "b", "a", "a", "b", "b", "b", "a")
#' mcFit<-markovchainFit(data=sequence)
#' predict(mcFit$estimate, newdata="b",n.ahead=3)
#' #direct conversion
#' myMc<-as(transMatr, "markovchain")
#'
#' #example of summary
#' summary(simpleMc)
#' \dontrun{plot(simpleMc)}
#'
#' @keywords classes
#'
#' @export
setClass(
# Class name
"markovchain",
# Define the slots
slots = list(states = "character", byrow = "logical",
transitionMatrix = "matrix", name = "character"),
# Set the default values for the slots
prototype = list(
states = c("a", "b"),
byrow = TRUE,
transitionMatrix = matrix(
data = c(0, 1, 1, 0),
nrow = 2,
byrow = TRUE,
dimnames = list(c("a", "b"), c("a", "b"))),
name = "Unnamed Markov chain")
)
# Initializing method for markovchain objects
setMethod(
"initialize",
signature(.Object = "markovchain"),
function (.Object, states, byrow, transitionMatrix, name, ...) {
# Put the standard markovchain
if (missing(transitionMatrix)) {
transitionMatrix <- matrix(
data = c(0, 1, 1, 0),
nrow = 2,
byrow = TRUE,
dimnames = list(c("a", "b"), c("a", "b")))
}
rowNames <- rownames(transitionMatrix)
colNames <- colnames(transitionMatrix)
# Check names of transition matrix
# if all names are missing it initializes them to "1", "2", ....
if (all(is.null(rowNames), is.null(colNames)) == TRUE) {
if (missing(states)) {
numRows <- nrow(transitionMatrix)
stateNames <- as.character(seq(1:numRows))
} else {
stateNames <- states
}
rownames(transitionMatrix) <- stateNames
colnames(transitionMatrix) <- stateNames
# Fix when rownames null
} else if (is.null(rowNames)) {
rownames(transitionMatrix) <- colNames
# Fix when colnames null
} else if (is.null(colNames)) {
colnames(transitionMatrix) <- rowNames
# Fix when different
} else if (! setequal(rowNames, colNames)) {
colnames(transitionMatrix) <- rowNames
}
if (missing(states))
states <- rownames(transitionMatrix)
if (missing(byrow))
byrow <- TRUE
if (missing(name))
name <- "Unnamed Markov chain"
callNextMethod(
.Object,
states = states,
byrow = byrow,
transitionMatrix = transitionMatrix,
name = name,
...
)
}
)
#' @title Non homogeneus discrete time Markov Chains class
#' @name markovchainList-class
#' @aliases [[,markovchainList-method dim,markovchainList-method
#' predict,markovchainList-method print,markovchainList-method
#' show,markovchainList-method
#' @description A class to handle non homogeneous discrete Markov chains
#'
#' @param markovchains Object of class \code{"list"}: a list of markovchains
#' @param name Object of class \code{"character"}: optional name of the class
#'
#' @section Objects from the Class:
#'
#' A \code{markovchainlist} is a list of \code{markovchain} objects. They can
#' be used to model non homogeneous discrete time Markov Chains, when
#' transition probabilities (and possible states) change by time.
#' @section Methods:
#' \describe{
#' \item{[[}{\code{signature(x = "markovchainList")}: extract the
#' i-th \code{markovchain} }
#' \item{dim}{\code{signature(x = "markovchainList")}: number
#' of \code{markovchain} underlying the matrix }
#' \item{predict}{\code{signature(object = "markovchainList")}: predict
#' from a \code{markovchainList} }
#' \item{print}{\code{signature(x = "markovchainList")}: prints the list
#' of markovchains }
#' \item{show}{\code{signature(object = "markovchainList")}: same as \code{print} }
#' }
#'
#' @references
#' A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
#'
#' @author Giorgio Spedicato
#'
#' @note
#' The class consists in a list of \code{markovchain} objects.
#' It is aimed at working with non homogeneous Markov chains.
#'
#' @seealso \code{\linkS4class{markovchain}}
#' @examples
#' showClass("markovchainList")
#' #define a markovchainList
#' statesNames=c("a","b")
#'
#' mcA<-new("markovchain",name="MCA",
#' transitionMatrix=matrix(c(0.7,0.3,0.1,0.9),
#' byrow=TRUE, nrow=2,
#' dimnames=list(statesNames,statesNames))
#' )
#'
#' mcB<-new("markovchain", states=c("a","b","c"), name="MCB",
#' transitionMatrix=matrix(c(0.2,0.5,0.3,0,1,0,0.1,0.8,0.1),
#' nrow=3, byrow=TRUE))
#'
#' mcC<-new("markovchain", states=c("a","b","c","d"), name="MCC",
#' transitionMatrix=matrix(c(0.25,0.75,0,0,0.4,0.6,
#' 0,0,0,0,0.1,0.9,0,0,0.7,0.3),
#' nrow=4, byrow=TRUE)
#' )
#' mcList<-new("markovchainList",markovchains=list(mcA, mcB, mcC),
#' name="Non - homogeneous Markov Chain")
#'
#' @keywords classes
#'
#' @export
setClass(
"markovchainList",
slots = list(
markovchains = "list",
name = "character")
)
# Verifies whether a markovchainList object is valid or not
# A markovchainList is valid iff all the slots are markovchain objects
# Returns true if the markovchainList is valid, the indexes of the
# wrong slots otherwise
setValidity(
"markovchainList",
function(object) {
check <- FALSE
markovchains <- object@markovchains
classes <- sapply(markovchains, class)
nonMarkovchain <- which(classes != "markovchain")
errors <- sapply(nonMarkovchain, function(i) {
paste(i, "-th element class is not 'markovchain'")
})
if (length(errors) == 0) TRUE else errors
}
)
# generic method to print out states
#' @name states
#'
#' @title Defined states of a transition matrix
#'
#' @description This method returns the states of a transition matrix.
#'
#' @param object A discrete \code{markovchain} object
#' @return The character vector corresponding to states slot.
#'
#' @references A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
#'
#' @author Giorgio Spedicato
#'
#' @seealso \code{\linkS4class{markovchain}}
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
#' byrow = TRUE, dimnames=list(statesNames,statesNames)),
#' name = "A markovchain Object"
#' )
#' states(markovB)
#' names(markovB)
#'
#' @rdname states
#'
#' @export
setGeneric("states", function(object) standardGeneric("states"))
#' @rdname states
#' @title states
setMethod(
"states",
"markovchain",
function(object) {
object@states
}
)
#' @title Returns the states for a Markov chain object
#'
#' @param x object we want to return states for
#'
#' @rdname names
setMethod(
"names",
"markovchain",
function(x) {
x@states
}
)
#' @title Method to retrieve name of markovchain object
#'
#' @name name
#'
#' @description This method returns the name of a markovchain object
#'
#' @param object A markovchain object
#' @rdname getName
#' @author Giorgio Spedicato, Deepak Yadav
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
#' byrow = TRUE, dimnames=list(statesNames,statesNames)),
#' name = "A markovchain Object"
#' )
#' name(markovB)
#'
#' @export
setGeneric("name", function(object) standardGeneric("name"))
#' @rdname getName
setMethod(
"name",
"markovchain",
function(object) {
object@name
})
#' @title Method to set name of markovchain object
#'
#' @name name<-
#'
#' @description This method modifies the existing name of markovchain object
#'
#' @param object A markovchain object
#' @param value New name of markovchain object
#' @rdname setName
#' @author Giorgio Spedicato, Deepak Yadav
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
#' byrow = TRUE, dimnames=list(statesNames,statesNames)),
#' name = "A markovchain Object"
#' )
#' name(markovB) <- "dangerous mc"
#'
#' @export
setGeneric("name<-", function(object, value) standardGeneric("name<-"))
#' @rdname setName
setMethod(
"name<-",
"markovchain",
function(object, value) {
object@name <- value
object
}
)
setMethod(
"names<-",
"markovchain",
function(x, value) {
rownames(x@transitionMatrix) <- value
colnames(x@transitionMatrix) <- value
x@states <- value
x
}
)
#' @exportMethod dim
setGeneric("dim")
# Generic methods to get the dim of a markovchain and markovchainList
setMethod(
"dim",
"markovchain",
function(x) {
nrow(x@transitionMatrix)
}
)
setMethod(
"dim",
"markovchainList",
function(x) {
length(x@markovchains)
}
)
# method to set the validity of a markovchain object
setValidity(
"markovchain",
function(object) {
errors <- character()
transitionMatrix <- object@transitionMatrix
states <- object@states
if (length(setdiff(states, unique(states))) > 0) {
msg <- "Error! States must be unique!"
errors <- c(errors, msg)
}
# Performs a set of checks. If any error arises, it ends up concatenated to errors
# Check all values of transition matrix belongs to [0, 1]
maybeProbabilities <- sapply(as.numeric(transitionMatrix), .isProbability)
if (any(maybeProbabilities) == FALSE) {
msg <- "Error! Some elements of transitionMatrix are not probabilities"
errors <- c(errors, msg)
}
# Check whether matrix is square matrix or not
if (nrow(transitionMatrix) != ncol(transitionMatrix)) {
msg <- "Error! transitionMatrix is not a square matrix"
errors <- c(errors, msg)
}
if (!.checkMatrix(transitionMatrix, object@byrow)) {
msg <- paste(
paste("Error!",
ifelse(object@byrow, "Rows", "Cols")),
"of transition matrix do not sum to one"
)
errors <- c(errors, msg)
}
# Check whether column names or rows names equal to state names or not
if (! setequal(colnames(transitionMatrix), states)) {
msg <- "Error! Colnames of transitionMatrix do not match states"
errors <- c(errors, msg)
}
if (! setequal(rownames(transitionMatrix), states)) {
msg <- "Error! Rownames of transitionMatrix do not match states"
errors <- c(errors, msg)
}
if (length(errors) > 0) errors else TRUE
}
)
# generic method to extract transition probability
# from state t0 to state t1
#' @name transitionProbability
#' @title Function to get the transition probabilities from initial
#' to subsequent states.
#' @description This is a convenience function to get transition probabilities.
#'
#' @param object A \code{markovchain} object.
#' @param t0 Initial state.
#' @param t1 Subsequent state.
#'
#' @references A First Course in Probability (8th Edition),
#' Sheldon Ross, Prentice Hall 2010
#'
#' @return Numeric Vector
#'
#' @author Giorgio Spedicato
#' @seealso \code{\linkS4class{markovchain}}
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
#' byrow = TRUE, dimnames=list(statesNames,statesNames)),
#' name = "A markovchain Object"
#' )
#' transitionProbability(markovB,"b", "c")
#' @rdname transitionProbability
#'
#' @exportMethod transitionProbability
setGeneric("transitionProbability", function(object, t0, t1) standardGeneric("transitionProbability"))
#' @rdname transitionProbability
setMethod("transitionProbability", "markovchain",
function(object, t0, t1) {
fromState <- which(object@states == t0)
toState <- which(object@states == t1)
out <- ifelse(object@byrow == TRUE, object@transitionMatrix[fromState, toState] ,
object@transitionMatrix[toState, fromState])
return(out)
}
)
# print, plot and show methods
.showInt <- function(object, verbose = TRUE) {
# find the direction
if (object@byrow == TRUE) {
direction <- "(by rows)"
} else {
direction <- "(by cols)"
}
if (verbose == TRUE) {
cat(object@name, "\n A ", dim(object), "- dimensional discrete Markov Chain defined by the following states: \n",
paste(states(object), collapse=", "), "\n The transition matrix ",
direction, " is defined as follows: \n")
}
print(object@transitionMatrix)
cat("\n")
}
#' @exportMethod show
setGeneric("show")
# show methods for markovchain and markovchain list objects
setMethod("show", "markovchain",
function(object){
.showInt(object)
}
)
setMethod("show", "markovchainList",
function(object) {
cat(object@name, " list of Markov chain(s)", "\n")
for(i in 1:length(object@markovchains)) {
cat("Markovchain ",i,"\n")
show(object@markovchains[[i]])
}
}
)
#' @exportMethod print
setGeneric("print")
# print methods
setMethod("print", "markovchainList", function(x) show(x))
setMethod("print", "markovchain",
function(x){
object <- x
.showInt(object, verbose = FALSE)
}
)
.getNet <- function(object, round = FALSE) {
# function to get the absorbency matrix to plot and export to igraph
#
# Args:
# object: a markovchain object
# round: boolean to round
#
# Returns:
#
# a graph adjacency
if (object@byrow == FALSE) {
object <- t(object)
}
matr <- object@transitionMatrix*100
if(round == TRUE) {
matr <- round(matr, 2)
}
net <- graph.adjacency(adjmatrix = matr, weighted = TRUE, mode = "directed")
return(net)
}
getColorVector <- function(object){
list <- .communicatingClassesRcpp(object)
sections <- length(list)
colorList <- grDevices::colors()
colorList <- sample(colorList,sections)
colorvector <- rep("white",length(object@states))
for(i in 1:length(list)){
part <- list[[i]]
for(j in 1:length(part)){
colorvector[match(part[j],object@states)] <- colorList[i]
}
}
return(colorvector)
}
#' @exportMethod plot
setGeneric("plot")
# Plot methods for markovchain objects
# plot method from stat5
setMethod("plot", signature(x = "markovchain", y = "missing"),
function(x, y, package = "igraph", ...) {
switch(package,
diagram = {
if (requireNamespace("diagram", quietly = TRUE)) {
.plotdiagram(object = x, ...)
} else {
netMc <- .getNet(object = x, round = TRUE)
edgeLabel <- round(E(netMc)$weight / 100, 2)
plot.igraph(x = netMc, edge.label = edgeLabel, ...)
}
},
DiagrammeR = {
if (requireNamespace("DiagrammeR", quietly = TRUE)) {
.plotDiagrammeR(object = x, ...)
} else {
netMc <- .getNet(object = x, round = TRUE)
edgeLabel <- round(E(netMc)$weight / 100, 2)
plot.igraph(x = netMc, edge.label = edgeLabel, ...)
}
},
{
netMc <- .getNet(object = x,round = TRUE)
edgeLabel <- round(E(netMc)$weight / 100, 2)
plot.igraph(x = netMc, edge.label = edgeLabel, ...)
})
}
)
##################################################AS METHODS#########################
.checkMatrix <- function(matr, byrow = TRUE, verbose = FALSE) {
# firstly, check size
if (ncol(matr) != nrow(matr)) {
if(verbose) stop("Error! Not a rectangular matrix")
return(FALSE)
}
# secondly, check is stochastic
isStochastic <- .isStochasticMatrix(matr, byrow)
if (!isStochastic) {
if (verbose)
stop("Error! Either rows or cols should sum to 1")
return(FALSE)
}
# if all test are passed
return(TRUE)
}
# Internal function to return a markovchain object given a matrix
.matrix2Mc <- function(from) {
# whether given matrix is a transition matrix or not
# if it is then how probabilities are stored
# row-wise or columnwise
byrow <- TRUE
checkByRows <- .checkMatrix(from, byrow = byrow)
if(!checkByRows) {
byrow <- FALSE
checkByCols <- .checkMatrix(from, byrow = byrow)
if(!checkByCols) {
#error could be either in rows or in cols
if (any(colSums(from) != 1)) cat("columns sums not equal to one are:", which(colSums(from) != 1),"\n")
if (any(rowSums(from) != 1)) cat("row sums not equal to one are:", which(rowSums(from) != 1),"\n")
stop("Error! Not a transition matrix")
}
}
# extract states names
if(byrow) {
namesCandidate <- rownames(from)
} else {
namesCandidate <- colnames(from)
}
# if states names is not there create it s1, s2, s3, ....
if(is.null(namesCandidate)) {
namesCandidate <- paste("s", 1:nrow(from), sep = "")
}
# create markovchain object
out <- new("markovchain", transitionMatrix = from, states = namesCandidate, byrow = byrow)
invisible(out)
}
#' @exportMethod coerce
NULL
# coerce matrix to markovchain object using internal method
# example: as("some matrix", "markovchain")
setAs(from = "matrix", to = "markovchain", def = .matrix2Mc)
# Function to transform a markovchain into a data.frame
# Args:
# from: a markovchain object
#
# returns:
# a data.frame
.mc2Df <- function(from) {
# number of rows or columns
nr <- nrow(from@transitionMatrix)
for(i in 1:nr){
for(j in 1:nr){
t0 <- from@states[i]
t1 <- from@states[j]
prob <- transitionProbability(object = from, t0 = t0, t1 = t1)
#cope with the new default of R 4.0 (5-3-2020)
rowDf <- data.frame(t0 = t0, t1 = t1, prob = prob,stringsAsFactors = TRUE )
# go to else part if first row of data frame is generated
if(exists("outDf")) {
outDf <- rbind(outDf, rowDf)
} else {
outDf <- rowDf
}
}
}
return(outDf)
}
# method to convert(coerce) from markovchain to data.frame
setAs(from = "markovchain", to = "data.frame", def = .mc2Df)
# method to find the column which stores transition probability
.whichColProb <- function(df) {
# column number which stores transition probability
out <- 0
# check for validity of data frame
if(ncol(df) > 3) {
warning("Warning! More than three columns. Only the first three will be used")
}
if(ncol(df) < 3) {
stop("Error! Three columns needed")
}
for(i in 1:ncol(df)) {
# when found the first numeric and probability col
if((is(df[, i], "numeric")) & (all(sapply(df[, i], .isProbability) == TRUE))) {
out <- i
break
}
}
return(out)
}
# Function to convert from a data.frame containing initial, ending
# and probability columns to a proper markovchain object
#
# Args:
# from: a data.frame
#
# Returns:
# A markovchain object
.df2Mc <- function(from) {
statesNames <- unique(from[, 1])
colProb <- .whichColProb(from) # what is the use
# transition matrix
prMatr <- zeros(length(statesNames))
rownames(prMatr) <- statesNames
colnames(prMatr) <- statesNames
for(i in 1:nrow(from)) {
idRow <- which(statesNames == from[i, 1]) # assume first col from
idCol <- which(statesNames == from[i, 2]) # assume second col to
prMatr[idRow, idCol] <- from[i, 3] # assume third col t-probability
}
out <- new("markovchain", transitionMatrix = prMatr)
return(out)
}
# method to convert(coerce) data frame to markovchain object
setAs(from = "data.frame", to = "markovchain", def = .df2Mc)
# example
# data <- data.frame(from = c("a", "a", "b", "b", "b", "b"),
# to = c("a", "b", "b", "b", "b", "a"))
#
# from <- table(data)
# .table2Mc(from)
.table2Mc <- function(from) {
# check whether table has square dimension or not
if(dim(from)[1] != dim(from)[2]) {
stop("Error! Table is not squared")
}
# rows ond columns name should be same
if(!setequal(rownames(from),colnames(from))) {
stop("Error! Rows not equal to coulumns")
}
temp <- unclass(as.matrix(from))
# make same sequence of col / row
fromMatr <- temp[, order(rownames(temp))]
# obtain transition matrix
outMatr <- fromMatr / rowSums(fromMatr)
out <- new("markovchain", states = rownames(temp),
transitionMatrix = outMatr, byrow=TRUE)
return(out)
}
# coerce table to markovchain object
setAs(from = "table", to = "markovchain", def = .table2Mc)
# function from msm to markovchain
# msm is a package. Use this package to create msm object.
# see how to create msm object using ?msm
.msm2Mc <- function(from) {
if(requireNamespace(package='msm', quietly = TRUE)) {
temp <- msm::pmatrix.msm(from)
prMatr <- unclass(as.matrix(temp))
out <- new("markovchain", transitionMatrix = prMatr)
} else {
out <- NULL
print("msm unavailable")
}
return(out)
}
# coerce msm object to markovchain object
setClass("msm")
setAs(from = "msm", to = "markovchain", def = .msm2Mc)
# function for msm.est to mc. Assume a probability matrix given
.msmest2Mc <- function(from) {
if (is.matrix(from)) {
# central estimate
pMatr <- from
}
if (is.list(from)) {
# central estimate
pMatr <- from[[1]]
}
out <- new("markovchain", transitionMatrix = as(pMatr, "matrix"))
return(out)
}
# coerce ms.est to markovchain object
setClass("msm.est")
setAs(from = "msm.est", to = "markovchain", def = .msmest2Mc)
# function from etm to markovchain
.etm2Mc<-function(from) {
# data frame consists of 'from' and 'to' column
df <- from$trans
# name of states
elements <- from$state.names
# number of unique states
nelements <- length(elements)
# temporary t-matrix
prMatr <- zeros(nelements)
dimnames(prMatr) <- list(elements, elements)
# populate t-matrix
for(i in 1:dim(df)[1]) {
r <- df[i, ] # each row one by one
stateFrom <- r$from
stateTo <- r$to
prMatr[stateFrom, stateTo] <- prMatr[stateFrom, stateTo] + 1
}
# convert freq-matrix to trans-matrix
rsums <- rowSums(prMatr)
prMatr <- prMatr / rsums
# take care of rows with all entries 0
if(any(rsums == 0)) {
indicesToBeSanitized <- which(rsums == 0)
for(i in indicesToBeSanitized) {
for(j in 1:nelements) {
prMatr[i, j] <- 1 / nelements
}
}
}
# create markovchain object
out <- new("markovchain", transitionMatrix = prMatr)
return(out)
}
# coerce etm object to markovchain object
setClass("etm")
setAs(from = "etm", to = "markovchain", def = .etm2Mc)
#sparse matrix from Matrix package
.sparseMatrix2markovchain<-function(from){
temp<-as(from,"matrix")
out <- as(temp, "markovchain")
return(out)
}
.markovchain2sparseMatrix<-function(from){
temp<-as(from,"matrix")
out <- as(temp, "sparseMatrix")
return(out)
}
setAs(from = "sparseMatrix", to = "markovchain", def = .sparseMatrix2markovchain)
setAs(from = "markovchain", to = "sparseMatrix", def = .markovchain2sparseMatrix)
# functions and methods to return a matrix
.mc2matrix <- function(from) {
out <- from@transitionMatrix
return(out)
}
# coerce markovchain object to matrix(transition)
setAs(from = "markovchain", to = "matrix", def = .mc2matrix)
# functions and methods to return a matrix
.mc2igraph <- function(from) {
# convert the markovchain to data.frame
temp <- .mc2Df(from=from)
# convert the data frame to igraph graph
# need to set only non zero weights
out <- graph.data.frame(d=temp[temp$prob>0,])
return(out)
}
# coerce markovchain object to igraph
setClass("igraph")
setAs(from = "markovchain", to = "igraph", def = .mc2igraph)
#' @exportMethod t
setGeneric("t")
# transposing method for markovchain objects
setMethod("t", "markovchain",
function(x) {
out <- new("markovchain", byrow = !x@byrow,
transitionMatrix = t(x@transitionMatrix))
return(out)
}
)
#' @exportMethod *
setGeneric("*")
# function to multiplicate two markov chains
#
# Args:
# e1: first markovchain
# e2: second markov chain
#
# Returns:
# if feasible, a markovchain where the transition matrix is e1*e2
setMethod("*", c("markovchain", "markovchain"),
function(e1, e2) {
# compare states of markovchains
if(!setequal(e1@states, e2@states)) {
warning("Warning! Different states")
}
# dimension must be equal
if(!setequal(dim(e1@transitionMatrix), dim(e2@transitionMatrix))) {
stop("Error! Different size")
}
# both must be either row wise or col wise
if(!(e1@byrow == e2@byrow)) {
stop("Error! Both transition matrix should be defined either by row or by column")
}
newStates <- e1@states
newTransMatr <- e1@transitionMatrix %*% e2@transitionMatrix
byRow <- e1@byrow
# multiplicated matrix takes the first matrix's name
mcName <- e1@name
out<-new("markovchain", states = newStates, transitionMatrix = newTransMatr,
byrow = byRow, name = mcName)
return(out)
}
)
# methods implemented for multiplication of markovchain object with
# matrix, 1-D vector, and vice-versa
setMethod("*", c("matrix", "markovchain"),
function(e1, e2) {
out <- e1 %*% e2@transitionMatrix
return(out)
}
)
setMethod("*", c("markovchain", "matrix"),
function(e1, e2) {
out <- e1@transitionMatrix %*% e2
return(out)
}
)
setMethod("*", c("numeric", "markovchain"),
function(e1, e2) {
if(length(e1) != dim(e2)) {
stop("Error! Uncompatible dimensions")
} else {
out <- e1 %*% e2@transitionMatrix
}
return(out)
}
)
setMethod("*", c("markovchain", "numeric"),
function(e1, e2) {
if(length(e2) != dim(e1)) {
stop("Error! Uncompatible dimensions")
} else {
out <- e1@transitionMatrix %*% e2
}
return(out)
}
)
#' @exportMethod ==
setGeneric("==")
# compare two markovchain object
setMethod("==", c("markovchain", "markovchain"),
function(e1, e2) {
out <- .approxEqualMatricesRcpp(e1@transitionMatrix, e2@transitionMatrix)
return(out)
}
)
#' @exportMethod !=
setGeneric("!=")
setMethod("!=", c("markovchain", "markovchain"),
function(e1, e2) {
out <- FALSE
out <- !(e1 == e2)
return(out)
}
)
#'@exportMethod ^
setGeneric("^")
# markovchain raise to some power
# this method is O(n³ log(m)) where n = {num cols (= rows) of e1} and m = e2
setMethod("^", c("markovchain", "numeric"),
function(e1, e2) {
out <- new("markovchain", states = e1@states, byrow = e1@byrow,
transitionMatrix = e1@transitionMatrix %^% e2,
name = paste(e1@name, "^", e2, sep = "")
)
return(out)
}
)
#' @exportMethod [
setGeneric("[")
# methods to directly access transition matrix elements
setMethod("[", signature(x = "markovchain", i = "ANY", j = "ANY"),
function(x, i, j) {
out <- x@transitionMatrix[i, j]
return(out)
}
)
#' @exportMethod [[
setGeneric("[[")
# methods to directly access markovchain objects composing a markovchainList object
setMethod("[[", signature(x = "markovchainList", i = "ANY"),
function(x, i) {
out <- x@markovchains[[i]]
return(out)
}
)
# transition probabilty vector from a given state
#' @title \code{conditionalDistribution} of a Markov Chain
#'
#' @name conditionalDistribution
#'
#' @description It extracts the conditional distribution of the subsequent state,
#' given current state.
#'
#' @param object A \code{markovchain} object.
#' @param state Subsequent state.
#'
#' @author Giorgio Spedicato, Deepak Yadav
#'
#' @return A named probability vector
#' @references A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
#'
#' @seealso \code{\linkS4class{markovchain}}
#'
#' @examples
#' # define a markov chain
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1),nrow = 3,
#' byrow = TRUE, dimnames = list(statesNames, statesNames)))
#'
#' conditionalDistribution(markovB, "b")
#'
#' @exportMethod conditionalDistribution
setGeneric("conditionalDistribution", function(object, state) standardGeneric("conditionalDistribution"))
setMethod("conditionalDistribution", "markovchain",
function(object, state) {
# get the states names
stateNames <- states(object)
# number of unique states
out <- numeric(length(stateNames))
# states are assumed to be sorted
index2Take <- which(stateNames == state)
if(object@byrow == TRUE) {
out <- object@transitionMatrix[index2Take, ]
} else {
out <- object@transitionMatrix[, index2Take]
}
# names the output and returs it
names(out) <- stateNames
return(out)
}
)
# Function to get the mode of a probability vector
#
# Args:
# probVector: the probability vector
# ties: specifies if ties are to be sampled, otherwise more than one element is returned
#
# Returns:
# the name of the model element
.getMode <- function(probVector, ties = "random") {
maxIndex <- which(probVector == max(probVector))
temp <- probVector[maxIndex] # index of maximum probabilty
if((ties == "random") & (length(temp) > 1)) {
out <- sample(temp, 1)
} else {
out <- temp
}
return(names(out))
}
#' @exportMethod predict
setGeneric("predict")
# predict method for markovchain objects
# given initial state return a vector of next n.ahead states
setMethod("predict", "markovchain",
function(object, newdata, n.ahead = 1) {
# identify the last state
lastState <- newdata[length(newdata)]
out <- character()
for(i in 1:n.ahead) {
# cyclically determine the most probable subsequent state from the conditional distribution
newState <- .getMode(probVector = conditionalDistribution(object, lastState), ties = "random")
out <- c(out, newState)
lastState <- newState
}
return(out)
}
)
# predict method for markovchainList objects
setMethod("predict", "markovchainList",
function(object, newdata, n.ahead = 1, continue = FALSE) {
# object a markovchainList
# newdata = the actual data
# n.ahead = how much ahead
# continue = veryfy if that lasts
# allocate output
out <- character()
actualPos <- length(newdata)
lastState <- newdata[actualPos] # take last position
for(i in 1:n.ahead) {
newPos <- actualPos + i - 1
if(newPos <= dim(object)) {
newState <- predict(object = object[[newPos]], newdata = lastState, n.ahead = 1)
out <- c(out, newState)
lastState <- newState
} else {
if(continue == TRUE) {
newState <- predict(object = object[[dim(object)]], newdata = lastState, n.ahead = 1)
out <- c(out, newState)
lastState <- newState
} else break;
}
}
return(out)
}
)
#sort method for markovchain objects
setGeneric("sort", function(x, decreasing=FALSE, ...) standardGeneric("sort"))
setMethod("sort", signature(x="markovchain"), function(x, decreasing = FALSE) {
#get matrix and state names 2 be sorted
matr2besorted<-x@transitionMatrix
if (x@byrow)
states2besorted <- rownames(matr2besorted)
else
states2besorted <- colnames(matr2besorted)
#sorting
sort_index<-order(states2besorted,decreasing = decreasing)
#reallocating
matr_sorted<-matr2besorted[sort_index,sort_index]
states_sorted<-states2besorted[sort_index]
out<-x
out@transitionMatrix<-matr_sorted
out@states<-states_sorted
return(out)
}
)
# method to get stationary states
#' @name steadyStates
#' @title Stationary states of a \code{markovchain} object
#'
#' @description This method returns the stationary vector in matricial form of a markovchain object.
#' @param object A discrete \code{markovchain} object
#'
#' @return A matrix corresponding to the stationary states
#'
#' @references A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010
#' @author Giorgio Spedicato
#' @seealso \code{\linkS4class{markovchain}}
#'
#' @note The steady states are identified starting from which eigenvectors correspond
#' to identity eigenvalues and then normalizing them to sum up to unity. When negative values are found
#' in the matrix, the eigenvalues extraction is performed on the recurrent classes submatrix.
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' markovB <- new("markovchain", states = statesNames, transitionMatrix =
#' matrix(c(0.2, 0.5, 0.3, 0, 1, 0, 0.1, 0.8, 0.1), nrow = 3,
#' byrow = TRUE, dimnames=list(statesNames,statesNames)),
#' name = "A markovchain Object"
#' )
#' steadyStates(markovB)
#'
#' @rdname steadyStates
#' @exportMethod steadyStates
setGeneric("steadyStates", function(object) standardGeneric("steadyStates"))
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