#' @name prediction
#'
#' @title Function to create prediction objects
#'
#' @description
#' Every classifier evaluation using ROCR starts with creating a
#' \code{prediction} object. This function is used to transform the input data
#' (which can be in vector, matrix, data frame, or list form) into a
#' standardized format.
#'
#' @details
#' \code{predictions} and \code{labels} can simply be vectors of the same
#' length. However, in the case of cross-validation data, different
#' cross-validation runs can be provided as the *columns* of a matrix or
#' data frame, or as the entries of a list. In the case of a matrix or
#' data frame, all cross-validation runs must have the same length, whereas
#' in the case of a list, the lengths can vary across the cross-validation
#' runs. Internally, as described in section 'Value', all of these input
#' formats are converted to list representation.
#'
#' Since scoring classifiers give relative tendencies towards a negative
#' (low scores) or positive (high scores) class, it has to be declared
#' which class label denotes the negative, and which the positive class.
#' Ideally, labels should be supplied as ordered factor(s), the lower
#' level corresponding to the negative class, the upper level to the
#' positive class. If the labels are factors (unordered), numeric,
#' logical or characters, ordering of the labels is inferred from
#' R's built-in \code{<} relation (e.g. 0 < 1, -1 < 1, 'a' < 'b',
#' FALSE < TRUE). Use \code{label.ordering} to override this default
#' ordering. Please note that the ordering can be locale-dependent
#' e.g. for character labels '-1' and '1'.
#'
#' Currently, ROCR supports only binary classification (extensions toward
#' multiclass classification are scheduled for the next release,
#' however). If there are more than two distinct label symbols, execution
#' stops with an error message. If all predictions use the same two
#' symbols that are used for the labels, categorical predictions are
#' assumed. If there are more than two predicted values, but all numeric,
#' continuous predictions are assumed (i.e. a scoring
#' classifier). Otherwise, if more than two symbols occur in the
#' predictions, and not all of them are numeric, execution stops with an
#' error message.
#'
#' @param predictions A vector, matrix, list, or data frame containing the
#'   predictions.
#' @param labels A vector, matrix, list, or data frame containing the true class
#'   labels. Must have the same dimensions as \code{predictions}.
#' @param label.ordering The default ordering (cf.details)  of the classes can
#'   be changed by supplying a vector containing the negative and the positive
#'   class label.
#'
#' @return An S4 object of class \code{prediction}.
#'
#' @references
#' A detailed list of references can be found on the ROCR homepage at
#' \url{http://rocr.bioinf.mpi-sb.mpg.de}.
#'
#' @author
#' Tobias Sing \email{tobias.sing@gmail.com}, Oliver Sander
#' \email{osander@gmail.com}
#'
#' @seealso
#' \code{\link{prediction-class}},
#' \code{\link{performance}},
#' \code{\link{performance-class}},
#' \code{\link{plot.performance}}
#'
#' @export
#'
#' @examples
#' # create a simple prediction object
#' library(ROCR)
#' data(ROCR.simple)
#' pred <- prediction(ROCR.simple$predictions,ROCR.simple$labels)
#' pred
prediction <- function(predictions, labels, label.ordering=NULL) {

  ## bring 'predictions' and 'labels' into list format,
  ## each list entry representing one x-validation run

  ## convert predictions into canonical list format
  if (is.data.frame(predictions)) {
    names(predictions) <- c()
    predictions <- as.list(predictions)
  } else if (is.matrix(predictions)) {
    predictions <- as.list(data.frame(predictions))
    names(predictions) <- c()
  } else if (is.vector(predictions) && !is.list(predictions)) {
    predictions <- list(predictions)
  } else if (!is.list(predictions)) {
    stop("Format of predictions is invalid. It couldn't be coerced to a list.",
         call. = FALSE)
  }
  ## if predictions is a list -> keep unaltered
  if(any(vapply(predictions,anyNA,logical(1)))){
    stop("'predictions' contains NA.", call. = FALSE)
  }

  ## convert labels into canonical list format
  if (is.data.frame(labels)) {
    names(labels) <- c()
    labels <- as.list( labels)
  } else if (is.matrix(labels)) {
    labels <- as.list( data.frame( labels))
    names(labels) <- c()
  } else if ((is.vector(labels) ||
              is.ordered(labels) ||
              is.factor(labels)) &&
             !is.list(labels)) {
    labels <- list( labels)
  } else if (!is.list(labels)) {
    stop("Format of labels is invalid. It couldn't be coerced to a list.",
         call. = FALSE)
  }
  ## if labels is a list -> keep unaltered

  ## Length consistency checks
  if (length(predictions) != length(labels))
    stop(paste("Number of cross-validation runs must be equal",
               "for predictions and labels."))
  if (! all(sapply(predictions, length) == sapply(labels, length)))
    stop(paste("Number of predictions in each run must be equal",
               "to the number of labels for each run."))

  ## only keep prediction/label pairs that are finite numbers
  for (i in 1:length(predictions)) {
    finite.bool <- is.finite( predictions[[i]] )
    predictions[[i]] <- predictions[[i]][ finite.bool ]
    labels[[i]] <- labels[[i]][ finite.bool ]
  }

  ## abort if 'labels' format is inconsistent across
  ## different cross-validation runs
  label.format=""  ## one of 'normal','factor','ordered'
  if (all(sapply( labels, is.factor)) &&
      !any(sapply(labels, is.ordered))) {
    label.format <- "factor"
  } else if (all(sapply( labels, is.ordered))) {
    label.format <- "ordered"
  } else if (all(sapply( labels, is.character)) ||
             all(sapply( labels, is.numeric)) ||
             all(sapply( labels, is.logical))) {
    label.format <- "normal"
  } else {
    stop(paste("Inconsistent label data type across different",
               "cross-validation runs."))
  }

  ## abort if levels are not consistent across different
  ## cross-validation runs
  if (! all(sapply(labels, levels)==levels(labels[[1]])) ) {
    stop(paste("Inconsistent factor levels across different",
               "cross-validation runs."))
  }

  ## convert 'labels' into ordered factors, aborting if the number
  ## of classes is not equal to 2.
  levels <- c()
  if ( label.format == "ordered" ) {
    if (!is.null(label.ordering)) {
      stop(paste("'labels' is already ordered. No additional",
                 "'label.ordering' must be supplied."))
    } else {
      levels <- levels(labels[[1]])
    }
  } else {
    if ( is.null( label.ordering )) {
      if ( label.format == "factor" ) levels <- sort(levels(labels[[1]]))
      else levels <- sort( unique( unlist( labels)))
    } else {
      ## if (!setequal( levels, label.ordering)) {
      if (!setequal( unique(unlist(labels)), label.ordering )) {
        stop("Label ordering does not match class labels.")
      }
      levels <- label.ordering
    }
    for (i in 1:length(labels)) {
      if (is.factor(labels))
        labels[[i]] <- ordered(as.character(labels[[i]]),
                               levels=levels)
      else labels[[i]] <- ordered( labels[[i]], levels=levels)
    }

  }

  if (length(levels) != 2) {
    message <- paste("Number of classes is not equal to 2.\n",
                     "ROCR currently supports only evaluation of ",
                     "binary classification tasks.",sep="")
    stop(message)
  }

  ## determine whether predictions are continuous or categorical
  ## (in the latter case stop; scheduled for the next ROCR version)
  if (!is.numeric( unlist( predictions ))) {
    stop("Currently, only continuous predictions are supported by ROCR.")
  }

  ## compute cutoff/fp/tp data

  cutoffs <- list()
  fp <- list()
  tp <- list()
  fn <- list()
  tn <- list()
  n.pos <- list()
  n.neg <- list()
  n.pos.pred <- list()
  n.neg.pred <- list()
  for (i in 1:length(predictions)) {
    n.pos <- c( n.pos, sum( labels[[i]] == levels[2] ))
    n.neg <- c( n.neg, sum( labels[[i]] == levels[1] ))
    ans <- .compute.unnormalized.roc.curve( predictions[[i]], labels[[i]] )
    cutoffs <- c( cutoffs, list( ans$cutoffs ))
    fp <- c( fp, list( ans$fp ))
    tp <- c( tp, list( ans$tp ))
    fn <- c( fn, list( n.pos[[i]] - tp[[i]] ))
    tn <- c( tn, list( n.neg[[i]] - fp[[i]] ))
    n.pos.pred <- c(n.pos.pred, list(tp[[i]] + fp[[i]]) )
    n.neg.pred <- c(n.neg.pred, list(tn[[i]] + fn[[i]]) )
  }


  return( new("prediction", predictions=predictions,
              labels=labels,
              cutoffs=cutoffs,
              fp=fp,
              tp=tp,
              fn=fn,
              tn=tn,
              n.pos=n.pos,
              n.neg=n.neg,
              n.pos.pred=n.pos.pred,
              n.neg.pred=n.neg.pred))
}


## fast fp/tp computation based on cumulative summing
.compute.unnormalized.roc.curve <- function( predictions, labels ) {
  ## determine the labels that are used for the pos. resp. neg. class :
  pos.label <- levels(labels)[2]
  neg.label <- levels(labels)[1]

  pred.order <- order(predictions, decreasing=TRUE)
  predictions.sorted <- predictions[pred.order]
  tp <- cumsum(labels[pred.order]==pos.label)
  fp <- cumsum(labels[pred.order]==neg.label)

  ## remove fp & tp for duplicated predictions
  ## as duplicated keeps the first occurrence, but we want the last, two
  ## rev are used.
  ## Highest cutoff (Infinity) corresponds to tp=0, fp=0
  dups <- rev(duplicated(rev(predictions.sorted)))
  tp <- c(0, tp[!dups])
  fp <- c(0, fp[!dups])
  cutoffs <- c(Inf, predictions.sorted[!dups])

  return(list( cutoffs=cutoffs, fp=fp, tp=tp ))
}