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+#' evaluates the number of occurances of predicted next click vs total number of starting pattern occurances
+#' in a given clickstream. The predicted next click can be from a markov chain of any order.
+#' @export
+#' @param mc a markovchain object (this should have been built from a set of training data) 
+#' @param startPattern the starting pattern we want to predict next click on, and evaluate observed occurances in test data. 
+#' @param testCLS clickstream object with test data 
+#' @examples
+#' training <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
+#'               "User2,i,c,i,c,c,c,d",
+#'               "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
+#'               "User4,c,c,p,c,d")
+#' 
+#' test <- c("User1,h,h,h,h,c,c,p,p,h,c,p,p,c,p,p,o",
+#'           "User2,i,c,i,c,c,c,d",
+#'           "User4,c,c,c,c,d,c,c,c,c")
+#' 
+#' csf <- tempfile()
+#' writeLines(training, csf)
+#' trainingCLS <- readClickstreams(csf, header = TRUE)
+#' 
+#' csf <- tempfile()
+#' writeLines(test, csf)
+#' testCLS <- readClickstreams(csf, header = TRUE)
+#' 
+#' mc <- fitMarkovChain(trainingCLS, order = 1)
+#' startPattern <- new("Pattern", sequence = c("c","c")) 
+#' res <- mcEvaluate(mc, startPattern, testCLS)
+#' res
+
+mcEvaluate = function(mc, startPattern, testCLS){
+  setClass(
+    "Result",
+    representation(
+      totalclicks = "numeric",
+      observed = "numeric",
+      expected = "numeric",
+      residual = "numeric",
+      residualSquared = "numeric",
+      component = "numeric",
+      predictedNextClick = "character",
+      patternSequence = "character",
+      probability = "numeric"
+    )
+  )
+  patternMatch <- function(p,s) {
+    gg <- gregexpr(paste0("(?=",p,")"),s,perl=TRUE)[[1]]
+    if (length(gg)==1 && gg==-1) 0 else length(gg)
+  }
+  pred <- predict(mc, startPattern)
+  expec <- pred@probability
+  predicted <- as.character(pred@sequence)
+  vec_totalPages <- NULL
+  vec_observed <- NULL
+  for (i in testCLS){
+    
+    clicks <- paste(i, collapse = ",")
+    pattern <- paste(startPattern@sequence, collapse = ",")
+    pattern <- as.character(pattern)
+    patternchar <- paste(pattern, ",", sep = "")
+    totalPages <- patternMatch(patternchar, clicks)
+    vec_totalPages <- append(vec_totalPages, totalPages)
+    expectedSeq <- paste(pattern, predicted, sep = ",")
+    obs <- patternMatch(expectedSeq, clicks)
+    vec_observed <- append(vec_observed, obs)
+  }
+  TotalExpectded <- sum(vec_totalPages) * expec
+  observed = sum(vec_observed)
+  expected = TotalExpectded
+  residual = observed-expected
+  residualSquared = residual^2
+  component = residualSquared/expected
+  result = new(
+    "Result", expected = expected, observed = observed, residual = residual,
+    residualSquared = residualSquared, component = component,
+    predictedNextClick = predicted, patternSequence = pattern, totalclicks = sum(vec_totalPages),
+    probability = expec
+  )
+  return(result)
+}
+
+getNOrderPatterns = function(trainingCLS, order){
+  secondOrder = function(patternlist = NULL){
+    if (is.null(patternlist)){
+      vec<-unlist(trainingCLS)
+      dedupe <- vec[which(!duplicated(vec))]
+    }
+    else{
+      dedupe <- patternlist
+    }
+    listPatterns <- list()
+    OuterlistPatterns <- list()
+    for (a in dedupe){
+      value <- a[[1]]
+      vecPatternsList <- list()
+      for(b in dedupe){
+        vecPattern <- append(value,b)
+        vecPatternsList <- list.append(vecPatternsList, vecPattern)
+      }
+      OuterlistPatterns <- list.append(OuterlistPatterns, vecPatternsList)
+    }
+    OuterlistPatterns <- unlist(OuterlistPatterns, recursive = FALSE)
+  }
+  for(i in 2:order){
+    if(i>2){
+      patternlist <- secondOrder(patternlist=patternlist)
+    }
+    else{
+      patternlist <- secondOrder()
+    }
+  }
+  return(patternlist)
+}
+
+#' evaluates all next page clicks in a clickstream training data set against the test data. Handles higher order by cycling through every possible pattern permutation (uses getNOrderPatterns function to get patterns). Produces a report of observed and expected values in a matrix
+#'
+#' @export
+#' @param mc a markovchain object that corresponds to a list of clusters
+#' @param trainingCLS clickstream object with training data (this should be the data used to build the markov chain object)
+#' @param testCLS clickstream object with test data 
+#' @param mc the markov chain against which to compare the clickstream data
+#' @examples
+#' training <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p",
+#'               "User2,i,c,i,c,c,c,d")
+#' 
+#' test <- c("User1,h,c,c,p,c,h,c,d,p,c,d,p",
+#'              "User2,i,c,i,p,c,c,d")
+#' 
+#' csf <- tempfile()
+#' writeLines(training, csf)
+#' trainingCLS <- readClickstreams(csf, header = TRUE)
+#' 
+#' csf <- tempfile()
+#' writeLines(test, csf)
+#' testCLS <- readClickstreams(csf, header = TRUE)
+#' 
+#' mc <- fitMarkovChain(trainingCLS, order = 2)
+#' mcEvaluateAll(mc, testCLS, trainingCLS)
+
+
+mcEvaluateAll = function(mc, testCLS, trainingCLS, includeChiSquare = TRUE, returnChiSquareOnly = FALSE){
+  results <- data.frame( "totalclicks" = character(), "observed" = character(), "expected" = character(), "residual" = character(), "residualSquared" = character(), "component" = numeric(), "predictedNextClick" = character(), "patternSequence" = character(), "probability" = character(),  stringsAsFactors=FALSE)
+  if(mc@order==1){
+    vec<-unlist(trainingCLS)
+    dedupe <- vec[which(!duplicated(vec))]
+  }
+  else{
+    dedupe <-getNOrderPatterns(trainingCLS, order = mc@order)
+  }
+  for (d in dedupe){
+    if(mc@order==1){
+      value <- d[[1]]
+    }
+    else{
+      value <- d
+    }
+    startPattern <- new("Pattern", sequence = c(value)) 
+    res <- mcEvaluate(mc, startPattern, testCLS)
+    if (res@totalclicks != 0 && res@expected > 0){
+      vec_results <- c(res@totalclicks, res@observed, res@expected, res@residual, res@residualSquared, res@component, res@patternSequence, res@predictedNextClick,res@probability)
+      results[nrow(results) + 1, ] <- c(res@totalclicks, res@observed, res@expected, res@residual, res@residualSquared, res@component, res@predictedNextClick, res@patternSequence, res@probability)
+    }
+  }   
+  ChiSquare <- sum(as.numeric(results$component))
+  if (includeChiSquare == TRUE){
+    results[nrow(results) + 1, ] <- c(0, 0, 0, 0, "variance:", ChiSquare, 0, 0, 0)
+  }
+  if (returnChiSquareOnly == TRUE){
+    results <- ChiSquare
+  }
+  return(results)
+}
+
+
+#' evaluates all next page clicks in a clickstream training data set against the test data on the basis of a set of pre-computed Markov chains and corresponding clusters. Handles higher order by cycling through every possible pattern permutation (uses getNOrderPatterns function to get patterns). Produces and produces a report of observed and expected values in a matrix
+#'
+#' @export
+#' @param markovchains a list of pre-computed markovchain objects that correspond to a list of clusters
+#' @param clusters a clist of clusters
+#' @param trainingCLS clickstream object with training data (this should be the data used to build the markov chains objects)
+#' @param testCLS clickstream object with test data 
+#' @param mc the markov chain against which to compare the clickstream data
+#' @examples
+#' training <- c("User1,h,c,c,p,c,h,c,h,o,p,p,c,p,p,o",
+#'               "User2,i,c,i,c,c,c,o,o,o,i,d",
+#'               "User3,h,i,c,i,c,o,i,p,c,c,p,c,c,i,d",
+#'               "User4,c,c,p,c,d,o,i,h,o,o")
+#' 
+#' test <- c("User1,h,c,c,p,p,h,o,i,c,p,p,c,p,p,o",
+#'           "User2,i,c,i,c,c,c,d",
+#'           "User4,c,c,c,c,d")
+#' 
+#' csf <- tempfile()
+#' writeLines(training, csf)
+#' trainingCLS <- readClickstreams(csf, header = TRUE)
+#' 
+#' csf <- tempfile()
+#' writeLines(test, csf)
+#' testCLS <- readClickstreams(csf, header = TRUE)
+#' 
+#' clusters <- clusterClickstreams(trainingCLS, centers = 2, order = 1)
+#' markovchains <- fitMarkovChains(clusters, order = 2)
+#' mcEvaluateAllClusters(markovchains, clusters, testCLS, trainingCLS)
+
+mcEvaluateAllClusters = function(markovchains, clusters, testCLS, trainingCLS, includeChiSquare = TRUE, returnChiSquareOnly = FALSE){
+  results <- data.frame( "totalclicks" = character(), "observed" = character(), "expected" = character(), "residual" = character(), "residualSquared" = character(), "component" = numeric(), "predictedNextClick" = character(), "patternSequence" = character(), "probability" = character(),  stringsAsFactors=FALSE)
+  if(markovchains[[1]]@order==1){
+    vec<-unlist(trainingCLS)
+    dedupe <- vec[which(!duplicated(vec))]
+  }
+  else{
+    dedupe <-getNOrderPatterns(trainingCLS, order = markovchains[[1]]@order)
+  }   
+  for (d in dedupe){
+    if(markovchains[[1]]@order==1){
+      value <- d[[1]]
+    }
+    else{
+      value <- d
+    }
+    startPattern <- new("Pattern", sequence = c(value)) 
+    mc <- getOptimalMarkovChain(startPattern,markovchains,clusters)
+    res <- mcEvaluate(mc, startPattern, testCLS)
+    if (res@totalclicks != 0){
+      vec_results <- c(res@totalclicks, res@observed, res@expected, res@residual, res@residualSquared, res@component, res@patternSequence, res@predictedNextClick,res@probability)
+      results[nrow(results) + 1, ] <- c(res@totalclicks, res@observed, res@expected, res@residual, res@residualSquared, res@component, res@predictedNextClick, res@patternSequence, res@probability)
+    }
+  }
+  ChiSquare <- sum(as.numeric(results$component))
+  if (includeChiSquare == TRUE){
+    results[nrow(results) + 1, ] <- c(0, 0, 0, 0, "variance:", ChiSquare, 0, 0, 0)
+  }
+  if (returnChiSquareOnly == TRUE){
+    results <- ChiSquare
+  }
+  return(results)
+}
+
+
+getSequenceTotal = function(startPattern, nextSequence, testCLS){
+  setClass(
+    "Result",
+    representation(
+      totalclicks = "numeric",
+      observed = "numeric",
+      nextSequence = "character",
+      startPattern = "character"
+    )
+  )
+  patternMatch <- function(p,s) {
+    gg <- gregexpr(paste0("(?=",p,")"),s,perl=TRUE)[[1]]
+    if (length(gg)==1 && gg==-1) 0 else length(gg)
+  }
+  nextseq <- nextSequence
+  vec_totalPages <- NULL
+  vec_observed <- NULL
+  for (i in testCLS){
+    clicks <- paste(i, collapse = ",")
+    clicks <- paste(clicks, ",", sep = "")
+    pattern <- paste(startPattern@sequence, collapse = ",")
+    pattern <- as.character(pattern)
+    patternchar <- paste(pattern, ",", sep = "")
+    totalPages <- patternMatch(patternchar, clicks)    
+    vec_totalPages <- append(vec_totalPages, totalPages)
+    expectedSeq <- paste(pattern, nextseq, sep = ",")
+    obs <- patternMatch(expectedSeq, clicks)
+    vec_observed <- append(vec_observed, obs)
+  }
+  result = new(
+    "Result",  observed = sum(vec_observed),
+    nextSequence = nextseq, startPattern = pattern, totalclicks = sum(vec_totalPages)
+  )
+  return(result)
+}
+
+getSequenceMatrix = function(mc, testCLS){
+  empiricalMatrix <- mc
+  cols <- colnames(empiricalMatrix)
+  rows <- rownames(empiricalMatrix)
+  for (c in rows){
+    for(r in cols){
+      value <- empiricalMatrix[[c,r]]
+      startPattern <- new("Pattern", sequence = c(c))
+      nextSequence <- r
+      value <- getSequenceTotal(startPattern, nextSequence, testCLS)
+      empiricalMatrix[[c,r]] <- value@observed
+    }
+  }
+  return(empiricalMatrix)
+}
+
+
+#' calculates the Chi-Square Statistic, p-value, and degrees of freedom, for a transition matrix compared with observed state changes. 
+#' 
+#'
+#' @export
+#' @param cls The clickstream
+#' @param mc the markov chain against which to compare the clickstream data
+#' @examples
+#' clickstreams <- c("User1,h,c,c,p,c,h,c,p,p,c,p,p,o",
+#'                  "User2,i,c,i,c,c,c,d",
+#'                  "User3,h,i,c,i,c,p,c,c,p,c,c,i,d",
+#'                  "User4,c,c,p,c,d")
+#'
+#' csf <- tempfile()
+#' writeLines(clickstreams, csf)
+#' cls <- readClickstreams(csf, header = TRUE)
+#' mc <- fitMarkovChain(cls)
+#' chiSquareTest(cls,mc, verbose = TRUE)
+
+chiSquareTest <- function(cls, mc, printValues = TRUE) {
+  object <- as.data.frame(t(mc@transitions[[1]]))
+  data <- cls
+  data <- getSequenceMatrix(object, data)
+  data <- data[match(rownames(data),names(object)),]
+  data <- data[,match(colnames(data),names(object))]
+  cols <- colSums(data)
+  statistic <- 0
+  for (i in 1:length(object)) {
+    for (j in 1:length(object)) {
+      if (data[i, j]>0&object[i, j]>0) statistic <- statistic + data[i, j]*log(data[i, j]/(cols[i]*object[i, j]))
+    }
+  }
+  statistic <- statistic * 2
+  null_elements <- sum(object == 0)
+  dof <- length(object) * (length(object) - 1) - null_elements
+  p.value <- 1 - pchisq(q = statistic,df = dof)
+  if(printValues==TRUE){
+    cat("Test data:\n");print(data);cat("Transition matrix: \n");print(object);print("...")
+    cat("Chi-Square Statistic:",statistic,"\n")
+    cat("degrees of freedom:",dof,"\n")
+    cat("The p-value:",p.value,"\n")  
+  }
+  out <- list(statistic = statistic, dof = dof,pvalue = p.value)
+  return(out)
+}