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# given a markovchain object is it possible to reach goal state from
# a given state
#' @name is.accessible
#' @title Verify if a state j is reachable from state i.
#' @description This function verifies if a state is reachable from another, i.e.,
#' if there exists a path that leads to state j leaving from state i with
#' positive probability
#'
#' @param object A \code{markovchain} object.
#' @param from The name of state "i" (beginning state).
#' @param to The name of state "j" (ending state).
#'
#' @details It wraps an internal function named \code{reachabilityMatrix}.
#' @return A boolean value.
#'
#' @references James Montgomery, University of Madison
#'
#' @author Giorgio Spedicato, Ignacio Cordón
#' @seealso \code{is.irreducible}
#'
#' @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)
#' )
#' )
#' is.accessible(markovB, "a", "c")
#'
#' @exportMethod is.accessible
setGeneric("is.accessible", function(object, from, to) standardGeneric("is.accessible"))
setMethod("is.accessible", c("markovchain", "character", "character"),
function(object, from, to) {
# O(n²) procedure to see if to state is reachable starting at from state
return(.isAccessibleRcpp(object, from, to))
}
)
setMethod("is.accessible", c("markovchain", "missing", "missing"),
function(object, from, to) {
.reachabilityMatrixRcpp(object)
}
)
# a markov chain is irreducible if it is composed of only one communicating class
#' @name is.irreducible
#' @title Function to check if a Markov chain is irreducible (i.e. ergodic)
#' @description This function verifies whether a \code{markovchain} object transition matrix
#' is composed by only one communicating class.
#' @param object A \code{markovchain} object
#'
#' @details It is based on \code{.communicatingClasses} internal function.
#' @return A boolean values.
#'
#' @references Feres, Matlab listings for Markov Chains.
#' @author Giorgio Spedicato
#'
#' @seealso \code{\link{summary}}
#'
#' @examples
#' statesNames <- c("a", "b")
#' mcA <- new("markovchain", transitionMatrix = matrix(c(0.7,0.3,0.1,0.9),
#' byrow = TRUE, nrow = 2,
#' dimnames = list(statesNames, statesNames)
#' ))
#' is.irreducible(mcA)
#'
#' @exportMethod is.irreducible
setGeneric("is.irreducible", function(object) standardGeneric("is.irreducible"))
setMethod("is.irreducible", "markovchain", function(object) {
.isIrreducibleRcpp(object)
})
# what this function will do?
# It calculates the probability to go from given state
# to all other states in k steps
# k varies from 1 to n
#' @name firstPassage
#' @title First passage across states
#' @description This function compute the first passage probability in states
#'
#' @param object A \code{markovchain} object
#' @param state Initial state
#' @param n Number of rows on which compute the distribution
#'
#' @details Based on Feres' Matlab listings
#' @return A matrix of size 1:n x number of states showing the probability of the
#' first time of passage in states to be exactly the number in the row.
#'
#' @references Renaldo Feres, Notes for Math 450 Matlab listings for Markov chains
#'
#' @author Giorgio Spedicato
#' @seealso \code{\link{conditionalDistribution}}
#'
#' @examples
#' simpleMc <- new("markovchain", states = c("a", "b"),
#' transitionMatrix = matrix(c(0.4, 0.6, .3, .7),
#' nrow = 2, byrow = TRUE))
#' firstPassage(simpleMc, "b", 20)
#'
#' @export
firstPassage <- function(object, state, n) {
P <- object@transitionMatrix
stateNames <- states(object)
# row number
i <- which(stateNames == state)
outMatr <- .firstpassageKernelRcpp(P = P, i = i, n = n)
colnames(outMatr) <- stateNames
rownames(outMatr) <- 1:n
return(outMatr)
}
#' function to calculate first passage probabilities
#'
#' @description The function calculates first passage probability for a subset of
#' states given an initial state.
#'
#' @param object a markovchain-class object
#' @param state intital state of the process (charactervector)
#' @param set set of states A, first passage of which is to be calculated
#' @param n Number of rows on which compute the distribution
#'
#' @return A vector of size n showing the first time proabilities
#' @references
#' Renaldo Feres, Notes for Math 450 Matlab listings for Markov chains;
#' MIT OCW, course - 6.262, Discrete Stochastic Processes, course-notes, chap -05
#'
#' @author Vandit Jain
#'
#' @seealso \code{\link{firstPassage}}
#' @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)
#' ))
#' firstPassageMultiple(markovB,"a",c("b","c"),4)
#'
#' @export
firstPassageMultiple <- function(object,state,set, n){
# gets the transition matrix
P <- object@transitionMatrix
# character vector of states of the markovchain
stateNames <- states(object)
k <- -1
k <- which(stateNames == state)
if(k==-1)
stop("please provide a valid initial state")
# gets the set in numeric vector
setno <- rep(0,length(set))
for(i in 1:length(set))
{
setno[i] = which(set[i] == stateNames)
if(setno[i] == 0)
stop("please provide proper set of states")
}
# calls Rcpp implementation
outMatr <- .firstPassageMultipleRCpp(P,k,setno,n)
#sets column and row names of output
colnames(outMatr) <- "set"
rownames(outMatr) <- 1:n
return(outMatr)
}
#' @name communicatingClasses
#' @rdname structuralAnalysis
#' @aliases transientStates recurrentStates absorbingStates communicatingClasses
#' transientClasses recurrentClasses
#' @title Various function to perform structural analysis of DTMC
#' @description These functions return absorbing and transient states of the \code{markovchain} objects.
#'
#' @param object A \code{markovchain} object.
#'
#' @return
#' \describe{
#' \item{\code{period}}{returns a integer number corresponding to the periodicity of the Markov
#' chain (if it is irreducible)}
#' \item{\code{absorbingStates}}{returns a character vector with the names of the absorbing
#' states in the Markov chain}
#' \item{\code{communicatingClasses}}{returns a list in which each slot contains the names of
#' the states that are in that communicating class}
#' \item{\code{recurrentClasses}}{analogously to \code{communicatingClasses}, but with
#' recurrent classes}
#' \item{\code{transientClasses}}{analogously to \code{communicatingClasses}, but with
#' transient classes}
#' \item{\code{transientStates}}{returns a character vector with all the transient states
#' for the Markov chain}
#' \item{\code{recurrentStates}}{returns a character vector with all the recurrent states
#' for the Markov chain}
#' \item{\code{canonicForm}}{returns the Markov chain reordered by a permutation of states
#' so that we have blocks submatrices for each of the recurrent classes and a collection
#' of rows in the end for the transient states}
#' }
#'
#' @references Feres, Matlab listing for markov chain.
#'
#' @author Giorgio Alfredo Spedicato, Ignacio Cordón
#'
#' @seealso \code{\linkS4class{markovchain}}
#'
#' @examples
#' statesNames <- c("a", "b", "c")
#' mc <- 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))
#' )
#'
#' communicatingClasses(mc)
#' recurrentClasses(mc)
#' recurrentClasses(mc)
#' absorbingStates(mc)
#' transientStates(mc)
#' recurrentStates(mc)
#' canonicForm(mc)
#'
#' # periodicity analysis
#' A <- matrix(c(0, 1, 0, 0, 0.5, 0, 0.5, 0, 0, 0.5, 0, 0.5, 0, 0, 1, 0),
#' nrow = 4, ncol = 4, byrow = TRUE)
#' mcA <- new("markovchain", states = c("a", "b", "c", "d"),
#' transitionMatrix = A,
#' name = "A")
#'
#' is.irreducible(mcA) #true
#' period(mcA) #2
#'
#' # periodicity analysis
#' B <- matrix(c(0, 0, 1/2, 1/4, 1/4, 0, 0,
#' 0, 0, 1/3, 0, 2/3, 0, 0,
#' 0, 0, 0, 0, 0, 1/3, 2/3,
#' 0, 0, 0, 0, 0, 1/2, 1/2,
#' 0, 0, 0, 0, 0, 3/4, 1/4,
#' 1/2, 1/2, 0, 0, 0, 0, 0,
#' 1/4, 3/4, 0, 0, 0, 0, 0), byrow = TRUE, ncol = 7)
#' mcB <- new("markovchain", transitionMatrix = B)
#' period(mcB)
#'
#' @exportMethod communicatingClasses
setGeneric("communicatingClasses", function(object) standardGeneric("communicatingClasses"))
setMethod("communicatingClasses", "markovchain", function(object) {
return(.communicatingClassesRcpp(object))
})
# A communicating class will be a recurrent class if
# there is no outgoing edge from this class
# Recurrent classes are subset of communicating classes
#' @rdname structuralAnalysis
#'
#' @exportMethod recurrentClasses
setGeneric("recurrentClasses", function(object) standardGeneric("recurrentClasses"))
setMethod("recurrentClasses", "markovchain", function(object) {
return(.recurrentClassesRcpp(object))
})
# A communicating class will be a transient class iff
# there is an outgoing edge from this class to an state
# outside of the class
# Transient classes are subset of communicating classes
#' @rdname structuralAnalysis
#'
#' @exportMethod transientClasses
setGeneric("transientClasses", function(object) standardGeneric("transientClasses"))
setMethod("transientClasses", "markovchain", function(object) {
return(.transientClassesRcpp(object))
})
#' @rdname structuralAnalysis
#'
#' @exportMethod transientStates
setGeneric("transientStates", function(object) standardGeneric("transientStates"))
setMethod("transientStates", "markovchain", function(object) {
.transientStatesRcpp(object)
}
)
#' @rdname structuralAnalysis
#'
#' @exportMethod recurrentStates
setGeneric("recurrentStates", function(object) standardGeneric("recurrentStates"))
setMethod("recurrentStates", "markovchain", function(object) {
.recurrentStatesRcpp(object)
}
)
# generic function to extract absorbing states
#' @rdname structuralAnalysis
#'
#' @exportMethod absorbingStates
setGeneric("absorbingStates", function(object) standardGeneric("absorbingStates"))
setMethod("absorbingStates", "markovchain", function(object) {
.absorbingStatesRcpp(object)
}
)
#' @rdname structuralAnalysis
#'
#' @exportMethod canonicForm
setGeneric("canonicForm", function(object) standardGeneric("canonicForm"))
setMethod("canonicForm", "markovchain", function(object) {
.canonicFormRcpp(object)
}
)
#' @title Calculates committor of a markovchain object with respect to set A, B
#'
#' @description Returns the probability of hitting states rom set A before set B
#' with different initial states
#'
#' @usage committorAB(object,A,B,p)
#'
#' @param object a markovchain class object
#' @param A a set of states
#' @param B a set of states
#' @param p initial state (default value : 1)
#'
#' @details The function solves a system of linear equations to calculate probaility that the process hits
#' a state from set A before any state from set B
#'
#' @return Return a vector of probabilities in case initial state is not provided else returns a number
#'
#' @examples
#' transMatr <- matrix(c(0,0,0,1,0.5,
#' 0.5,0,0,0,0,
#' 0.5,0,0,0,0,
#' 0,0.2,0.4,0,0,
#' 0,0.8,0.6,0,0.5),
#' nrow = 5)
#' object <- new("markovchain", states=c("a","b","c","d","e"),transitionMatrix=transMatr)
#' committorAB(object,c(5),c(3))
#'
#' @export
committorAB <- function(object,A,B,p=1) {
if(!class(object) == "markovchain")
stop("please provide a valid markovchain object")
matrix <- object@transitionMatrix
noofstates <- length(object@states)
for(i in length(A))
{
if(A[i] <= 0 || A[i] > noofstates)
stop("please provide a valid set A")
}
for(i in length(B))
{
if(B[i] <= 0 || B[i] > noofstates)
stop("please provide a valid set B")
}
for(i in 1:noofstates)
{
if(i %in% A && i %in% B)
stop("intersection of set A and B in not null")
}
if(p <=0 || p > noofstates)
stop("please provide a valid initial state")
I <- diag(noofstates)
matrix <- matrix - I
A_size = length(A)
B_size = length(B)
# sets the matrix according to the provided states
for(i in 1:A_size)
{
for(j in 1:noofstates)
{
if(A[i]==j)
matrix[A[i],j] = 1
else
matrix[A[i],j] = 0
}
}
# sets the matrix according to the provided states
for(i in 1:B_size)
{
for(j in 1:noofstates)
{
if(B[i]==j)
matrix[B[i],j] = 1
else
matrix[B[i],j] = 0
}
}
# initialises b in the equation the system of equation AX =b
b <- rep(0,noofstates)
for(i in 1:A_size)
{
b[A[i]] = 1
}
# solve AX = b according using solve function from base package
out <- solve(matrix,b)
if(missing(p))
return(out)
else
return(out[p])
}
#' Expected Rewards for a markovchain
#'
#' @description Given a markovchain object and reward values for every state,
#' function calculates expected reward value after n steps.
#'
#' @usage expectedRewards(markovchain,n,rewards)
#'
#' @param markovchain the markovchain-class object
#' @param n no of steps of the process
#' @param rewards vector depicting rewards coressponding to states
#'
#' @details the function uses a dynamic programming approach to solve a
#' recursive equation described in reference.
#'
#' @return
#' returns a vector of expected rewards for different initial states
#'
#' @author Vandit Jain
#'
#' @references Stochastic Processes: Theory for Applications, Robert G. Gallager,
#' Cambridge University Press
#'
#' @examples
#' transMatr<-matrix(c(0.99,0.01,0.01,0.99),nrow=2,byrow=TRUE)
#' simpleMc<-new("markovchain", states=c("a","b"),
#' transitionMatrix=transMatr)
#' expectedRewards(simpleMc,1,c(0,1))
#' @export
expectedRewards <- function(markovchain, n, rewards) {
# gets the transition matrix
matrix <- markovchain@transitionMatrix
# Rcpp implementation of the function
out <- .expectedRewardsRCpp(matrix,n, rewards)
noofStates <- length(states(markovchain))
result <- rep(0,noofStates)
for(i in 1:noofStates)
result[i] = out[i]
#names(result) <- states(markovchain)
return(result)
}
#' Expected first passage Rewards for a set of states in a markovchain
#'
#' @description Given a markovchain object and reward values for every state,
#' function calculates expected reward value for a set A of states after n
#' steps.
#'
#' @usage expectedRewardsBeforeHittingA(markovchain, A, state, rewards, n)
#'
#' @param markovchain the markovchain-class object
#' @param A set of states for first passage expected reward
#' @param state initial state
#' @param rewards vector depicting rewards coressponding to states
#' @param n no of steps of the process
#'
#' @details The function returns the value of expected first passage
#' rewards given rewards coressponding to every state, an initial state
#' and number of steps.
#'
#' @return returns a expected reward (numerical value) as described above
#'
#' @author Sai Bhargav Yalamanchi, Vandit Jain
#'
#' @export
expectedRewardsBeforeHittingA <- function(markovchain, A, state, rewards, n) {
## gets the markovchain matrix
matrix <- markovchain@transitionMatrix
# gets the names of states
stateNames <- states(markovchain)
# no of states
S <- length(stateNames)
# vectors for states in S-A
SAno <- rep(0,S-length(A))
rewardsSA <- rep(0,S-length(A))
# for initialisation for set S-A
i=1
ini = -1
for(j in 1:length(stateNames))
{
if(!(stateNames[j] %in% A)){
SAno[i] = j
rewardsSA[i] = rewards[j]
if(stateNames[j] == state)
ini = i
i = i+1
}
}
## get the matrix coressponding to S-A
matrix <- matrix[SAno,SAno]
## cals the cpp implementation
out <- .expectedRewardsBeforeHittingARCpp(matrix, ini, rewardsSA, n)
return(out)
}
#' Mean First Passage Time for irreducible Markov chains
#'
#' @description Given an irreducible (ergodic) markovchain object, this function
#' calculates the expected number of steps to reach other states
#'
#' @param object the markovchain object
#' @param destination a character vector representing the states respect to
#' which we want to compute the mean first passage time. Empty by default
#'
#' @details For an ergodic Markov chain it computes:
#' \itemize{
#' \item If destination is empty, the average first time (in steps) that takes
#' the Markov chain to go from initial state i to j. (i, j) represents that
#' value in case the Markov chain is given row-wise, (j, i) in case it is given
#' col-wise.
#' \item If destination is not empty, the average time it takes us from the
#' remaining states to reach the states in \code{destination}
#' }
#'
#' @return a Matrix of the same size with the average first passage times if
#' destination is empty, a vector if destination is not
#'
#' @author Toni Giorgino, Ignacio Cordón
#'
#' @references C. M. Grinstead and J. L. Snell. Introduction to Probability.
#' American Mathematical Soc., 2012.
#'
#' @examples
#' m <- matrix(1 / 10 * c(6,3,1,
#' 2,3,5,
#' 4,1,5), ncol = 3, byrow = TRUE)
#' mc <- new("markovchain", states = c("s","c","r"), transitionMatrix = m)
#' meanFirstPassageTime(mc, "r")
#'
#'
#' # Grinstead and Snell's "Oz weather" worked out example
#' mOz <- matrix(c(2,1,1,
#' 2,0,2,
#' 1,1,2)/4, ncol = 3, byrow = TRUE)
#'
#' mcOz <- new("markovchain", states = c("s", "c", "r"), transitionMatrix = mOz)
#' meanFirstPassageTime(mcOz)
#'
#' @export meanFirstPassageTime
setGeneric("meanFirstPassageTime", function(object, destination) {
standardGeneric("meanFirstPassageTime")
})
setMethod("meanFirstPassageTime", signature("markovchain", "missing"),
function(object, destination) {
destination = character()
.meanFirstPassageTimeRcpp(object, destination)
}
)
setMethod("meanFirstPassageTime", signature("markovchain", "character"),
function(object, destination) {
states <- object@states
incorrectStates <- setdiff(destination, states)
if (length(incorrectStates) > 0)
stop("Some of the states you provided in destination do not match states from the markovchain")
result <- .meanFirstPassageTimeRcpp(object, destination)
asVector <- as.vector(result)
names(asVector) <- colnames(result)
asVector
}
)
#' Mean recurrence time
#'
#' @description Computes the expected time to return to a recurrent state
#' in case the Markov chain starts there
#'
#' @usage meanRecurrenceTime(object)
#'
#' @param object the markovchain object
#'
#' @return For a Markov chain it outputs is a named vector with the expected
#' time to first return to a state when the chain starts there.
#' States present in the vector are only the recurrent ones. If the matrix
#' is ergodic (i.e. irreducible), then all states are present in the output
#' and order is the same as states order for the Markov chain
#'
#' @author Ignacio Cordón
#'
#' @references C. M. Grinstead and J. L. Snell. Introduction to Probability.
#' American Mathematical Soc., 2012.
#'
#' @examples
#' m <- matrix(1 / 10 * c(6,3,1,
#' 2,3,5,
#' 4,1,5), ncol = 3, byrow = TRUE)
#' mc <- new("markovchain", states = c("s","c","r"), transitionMatrix = m)
#' meanRecurrenceTime(mc)
#'
#' @export meanRecurrenceTime
setGeneric("meanRecurrenceTime", function(object) {
standardGeneric("meanRecurrenceTime")
})
setMethod("meanRecurrenceTime", "markovchain", function(object) {
.meanRecurrenceTimeRcpp(object)
})
#' Mean absorption time
#'
#' @description Computes the expected number of steps to go from any of the
#' transient states to any of the recurrent states. The Markov chain should
#' have at least one transient state for this method to work
#'
#' @usage meanAbsorptionTime(object)
#'
#' @param object the markovchain object
#'
#' @return A named vector with the expected number of steps to go from a
#' transient state to any of the recurrent ones
#'
#' @author Ignacio Cordón
#'
#' @references C. M. Grinstead and J. L. Snell. Introduction to Probability.
#' American Mathematical Soc., 2012.
#'
#' @examples
#' m <- matrix(c(1/2, 1/2, 0,
#' 1/2, 1/2, 0,
#' 0, 1/2, 1/2), ncol = 3, byrow = TRUE)
#' mc <- new("markovchain", states = letters[1:3], transitionMatrix = m)
#' times <- meanAbsorptionTime(mc)
#'
#' @export meanAbsorptionTime
setGeneric("meanAbsorptionTime", function(object) {
standardGeneric("meanAbsorptionTime")
})
setMethod("meanAbsorptionTime", "markovchain", function(object) {
.meanAbsorptionTimeRcpp(object)
})
#' Absorption probabilities
#'
#' @description Computes the absorption probability from each transient
#' state to each recurrent one (i.e. the (i, j) entry or (j, i), in a
#' stochastic matrix by columns, represents the probability that the
#' first not transient state we can go from the transient state i is j
#' (and therefore we are going to be absorbed in the communicating
#' recurrent class of j)
#'
#' @usage absorptionProbabilities(object)
#'
#' @param object the markovchain object
#'
#' @return A named vector with the expected number of steps to go from a
#' transient state to any of the recurrent ones
#'
#' @author Ignacio Cordón
#'
#' @references C. M. Grinstead and J. L. Snell. Introduction to Probability.
#' American Mathematical Soc., 2012.
#'
#' @examples
#' m <- matrix(c(1/2, 1/2, 0,
#' 1/2, 1/2, 0,
#' 0, 1/2, 1/2), ncol = 3, byrow = TRUE)
#' mc <- new("markovchain", states = letters[1:3], transitionMatrix = m)
#' absorptionProbabilities(mc)
#'
#' @export absorptionProbabilities
setGeneric("absorptionProbabilities", function(object) {
standardGeneric("absorptionProbabilities")
})
setMethod("absorptionProbabilities", "markovchain", function(object) {
.absorptionProbabilitiesRcpp(object)
})
#' @title Check if a DTMC is regular
#'
#' @description Function to check wether a DTCM is regular
#
#' @details A Markov chain is regular if some of the powers of its matrix has all elements
#' strictly positive
#'
#' @param object a markovchain object
#'
#' @return A boolean value
#'
#' @author Ignacio Cordón
#' @references Matrix Analysis. Roger A.Horn, Charles R.Johnson. 2nd edition.
#' Corollary 8.5.8, Theorem 8.5.9
#'
#'
#' @examples
#' P <- matrix(c(0.5, 0.25, 0.25,
#' 0.5, 0, 0.5,
#' 0.25, 0.25, 0.5), nrow = 3)
#' colnames(P) <- rownames(P) <- c("R","N","S")
#' ciao <- as(P, "markovchain")
#' is.regular(ciao)
#'
#' @seealso \code{\link{is.irreducible}}
#'
#' @exportMethod is.regular
setGeneric("is.regular", function(object) standardGeneric("is.regular"))
setMethod("is.regular", "markovchain", function(object) {
.isRegularRcpp(object)
})
#' Hitting probabilities for markovchain
#'
#' @description Given a markovchain object,
#' this function calculates the probability of ever arriving from state i to j
#'
#' @usage hittingProbabilities(object)
#'
#' @param object the markovchain-class object
#'
#' @return a matrix of hitting probabilities
#'
#' @author Ignacio Cordón
#'
#' @references R. Vélez, T. Prieto, Procesos Estocásticos, Librería UNED, 2013
#'
#' @examples
#' M <- matlab::zeros(5, 5)
#' M[1,1] <- M[5,5] <- 1
#' M[2,1] <- M[2,3] <- 1/2
#' M[3,2] <- M[3,4] <- 1/2
#' M[4,2] <- M[4,5] <- 1/2
#'
#' mc <- new("markovchain", transitionMatrix = M)
#' hittingProbabilities(mc)
#'
#' @exportMethod hittingProbabilities
setGeneric("hittingProbabilities", function(object) standardGeneric("hittingProbabilities"))
setMethod("hittingProbabilities", "markovchain", function(object) {
.hittingProbabilitiesRcpp(object)
})
#' Mean num of visits for markovchain, starting at each state
#'
#' @description Given a markovchain object, this function calculates
#' a matrix where the element (i, j) represents the expect number of visits
#' to the state j if the chain starts at i (in a Markov chain by columns it
#' would be the element (j, i) instead)
#'
#' @usage meanNumVisits(object)
#'
#' @param object the markovchain-class object
#'
#' @return a matrix with the expect number of visits to each state
#'
#' @author Ignacio Cordón
#'
#' @references R. Vélez, T. Prieto, Procesos Estocásticos, Librería UNED, 2013
#'
#' @examples
#' M <- matlab::zeros(5, 5)
#' M[1,1] <- M[5,5] <- 1
#' M[2,1] <- M[2,3] <- 1/2
#' M[3,2] <- M[3,4] <- 1/2
#' M[4,2] <- M[4,5] <- 1/2
#'
#' mc <- new("markovchain", transitionMatrix = M)
#' meanNumVisits(mc)
#'
#' @exportMethod meanNumVisits
setGeneric("meanNumVisits", function(object) standardGeneric("meanNumVisits"))
setMethod("meanNumVisits", "markovchain", function(object) {
.minNumVisitsRcpp(object)
})
setMethod(
"steadyStates",
"markovchain",
function(object) {
.steadyStatesRcpp(object)
}
)
#' @exportMethod summary
setGeneric("summary")
# summary method for markovchain class
# lists: closed, transient classes, irreducibility, absorbint, transient states
setMethod("summary", signature(object = "markovchain"),
function(object){
# list of closed, recurrent and transient classes
outs <- .summaryKernelRcpp(object)
# display name of the markovchain object
cat(object@name," Markov chain that is composed by:", "\n")
# number of closed classes
check <- length(outs$closedClasses)
cat("Closed classes:","\n")
# display closed classes
if(check == 0) cat("NONE", "\n") else {
for(i in 1:check) cat(outs$closedClasses[[i]], "\n")
}
# number of recurrent classes
check <- length(outs$recurrentClasses)
cat("Recurrent classes:", "\n")
# display recurrent classes
if(check == 0) cat("NONE", "\n") else {
cat("{")
cat(outs$recurrentClasses[[1]], sep = ",")
cat("}")
if(check > 1) {
for(i in 2:check) {
cat(",{")
cat(outs$recurrentClasses[[i]], sep = ",")
cat("}")
}
}
cat("\n")
}
# number of transient classes
check <- length(outs$transientClasses)
cat("Transient classes:","\n")
# display transient classes
if(check == 0) cat("NONE", "\n") else {
cat("{")
cat(outs$transientClasses[[1]], sep = ",")
cat("}")
if(check > 1) {
for(i in 2:check) {
cat(",{")
cat(outs$transientClasses[[i]], sep = ",")
cat("}")
}
}
cat("\n")
}
# bool to say about irreducibility of markovchain
irreducibility <- is.irreducible(object)
if(irreducibility)
cat("The Markov chain is irreducible", "\n")
else cat("The Markov chain is not irreducible", "\n")
# display absorbing states
check <- absorbingStates(object)
if(length(check) == 0) check <- "NONE"
cat("The absorbing states are:", check )
cat("\n")
# return outs
# useful when user will assign the value returned
invisible(outs)
}
)
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