R/not.R
In rbaranowski/not: Narrowest-Over-Threshold Change-Point Detection
Defines functions
not.default
not
Documented in
not
not.default
#' @title Narrowest-Over-Threshold Change-Point Detection
#' @description Implements the Narrowest-Over-Threshold approach for general multiple change-point
#' detection in one-dimensional data following 'deterministic signal + noise' model. Scenarios that are currently implemented are: piecewise-constant signal, piecewise-constant signal with a heavy tailed noise, piecewise-linear signal, piecewise-quadratic signal, piecewise-constant signal and with piecewise-constant standard deviation of the noise. The main routines of the package are \code{\link{not}} and \code{\link{features}}.
#' @references R. Baranowski, Y. Chen, and P. Fryzlewicz (2019). Narrowest-Over-Threshold Change-Point Detection. (\url{http://stats.lse.ac.uk/fryzlewicz/not/not.pdf})
#' @docType package
#' @useDynLib not, .registration = TRUE
#' @name not-package
#' @importFrom graphics plot lines title
#' @importFrom stats cov lm.fit logLik predict residuals sd mad quantile runif ts.plot var
#' @importFrom splines bs
NULL
#' @title Narrowest-Over-Threshold Change-Point Detection
#' @description Identifies potential locations of the change-points in the data following 'deterministic signal + noise' model (see details below) in a number of different scenarios.
#' The object returned by this routine can be further passed to the \code{\link{features}} function, which finds the final estimate of the change-points based on a chosen stopping criterion.
#' It can be also passed to \code{\link{plot}}, \code{\link{predict}} and \code{\link{residuals}} routines.
#' @details The data points provided in \code{x} are assumed to follow
#' \deqn{Y_{t} = f_{t}+\sigma_{t}\varepsilon_{t},}{Y_t= f_t + sigma_t varepsilon_t,}
#' for \eqn{t=1,\ldots,n}{t=1,...,n}, where \eqn{n}{n} is the number of observations in \code{x}, the signal \eqn{f_{t}}{f_t} and the standard deviation \eqn{\sigma_{t}}{sigma_{t}}
#' are non-stochastic with structural breaks at unknown locations in time \eqn{t}{t}. Currently, thefollowing scenarios for \eqn{f_{t}}{f_t} and \eqn{\sigma_{t}}{sigma_t} are implemented:
#' \itemize{
#' \item Piecewise-constant signal with a Gaussian noise and constant standard deviation.
#'
#' Use \code{contrast="pcwsConstMean"} here.
#' \item Piecewise-constant mean with a heavy-tailed noise and constant standard deviation.
#'
#' Use \code{contrast="pcwsConstMeanHT"} here.
#' \item Piecewise-linear continuous signal with Gaussian noise and constant standard deviation.
#'
#' Use \code{contrast="pcwsLinContMean"} here.
#' \item Piecewise-linear signal with Gaussian noise and constant standard deviation.
#'
#' Use \code{contrast="pcwsLinMean"} here.
#' \item Piecewise-quadratic signal with Gaussian noise and constant standard deviation.
#'
#' Use \code{contrast="pcwsQuadMean"} here.
#' \item Piecewise-constant signal and piecewise-constant standard deviation of the Gaussian noise.
#'
#' Use \code{contrast="pcwsConstMeanVar"} here.
#' }
#' @param x A numeric vector with data points.
#' @param M A number of intervals drawn in the procedure.
#' @param method Choice of "not" (recommended) and "max". If \code{method="not"}, the Narrowest-Over-Threshold intervals are used in the algorithm.
#' If \code{method="max"}, the intervals corresponding to the largest contrast function are used. For an explanation, see the references.
#' @param contrast A type of the contrast function used in the NOT algorithm.
#' Choice of \code{"pcwsConstMean"}, \code{"pcwsConstMeanHT"}, \code{"pcwsLinContMean"}, \code{"pcwsLinMean"}, \code{"pcwsQuadMean"}, \code{"pcwsConstMeanVar"}.
#' For the explanation, see details below.
#' @param rand.intervals A logical variable. If \code{rand.intervals=TRUE} intervals used in the procedure are drawn uniformly using the \code{\link{random.intervals}} routine.
#' If \code{rand.intervals=FALSE}, the intervals need to be passed using the \code{intervals} argument.
#' @param parallel A logical variable. If TRUE some of computations are run in parallel using OpenMP framework. Currently this option is not supported on Windows.
#' @param augmented A logical variable. if TRUE, the entire data are considered when the NOT segmentation tree is constructed (see the solution path algorithm in the references).
#' @param intervals A 2-column matrix with the intervals considered in the algorithm, with start- and end- points of the intervals in, respectively, the first and the second column.
#' The intervals are used only if \code{rand.intervals=FALSE}.
#' @param ... Not in use.
#' @rdname not
#' @export
#' @examples
#' # **** Piecewisce-constant mean with Gaussian noise.
#' # *** signal
#' pcws.const.sig <- c(rep(0, 100), rep(1,100))
#' # *** data vector
#' x <- pcws.const.sig + rnorm(100)
#' # *** identify potential locations of the change-points
#' w <- not(x, contrast = "pcwsConstMean")
#' # *** some examples of how the w object can be used
#' plot(w)
#' plot(residuals(w))
#' plot(predict(w))
#' # *** this is how to extract the change-points
#' fo <- features(w)
#' fo$cpt
#'
#' # **** Piecewisce-constant mean with a heavy-tailed noise.
#' # *** data vector, signal the same as in the previous example, but heavy tails
#' x <- pcws.const.sig + rt(100, 3)
#' # *** identify potential locations of the change-points,
#' # using a contrast taylored to heavy-tailed data
#' w <- not(x, contrast = "pcwsConstMeanHT")
#' plot(w)
#'
#' # **** Piecewisce-constant mean and piecewise-constant variance
#' # *** signal's standard deviation
#' pcws.const.sd <- c(rep(2, 50), rep(1,150))
#' # *** data vector with pcws-const mean and variance
#' x <- pcws.const.sig + pcws.const.sd * rnorm(100)
#' # *** identify potential locations of the change-points in this model
#' w <- not(x, contrast = "pcwsConstMeanVar")
#' # *** extracting locations of the change-points
#' fo <- features(w)
#' fo$cpt
#'
#' # **** Piecewisce-linear coninuous mean
#' # *** signal with a change in slope
#' pcws.lin.cont.sig <- cumsum(c(rep(-1/50, 100), rep(1/50,100)))
#' # *** data vector
#' x <- pcws.lin.cont.sig + rnorm(100)
#' # *** identify potential locations of the change-points in the slope coefficient
#' w <- not(x, contrast = "pcwsLinContMean")
#' # *** ploting the results
#' plot(w)
#' # *** location(s) of the change-points
#' fo <- features(w)
#' fo$cpt
#'
#' # **** Piecewisce-linear mean with jumps
#' # *** signal with a change in slope and jumpe
#' pcws.lin.sig <- pcws.lin.cont.sig + pcws.const.sig
#' # *** data vector
#' x <- pcws.lin.sig + rnorm(100)
#' # *** identify potential locations of the change-points in the slope coefficient and the intercept
#' w <- not(x, contrast = "pcwsLinMean")
#' # *** ploting the results
#' plot(w)
#' # *** location(s) of the change-points
#' fo <- features(w)
#' fo$cpt
#'
#' # **** Piecewisce-quadratic mean with jumps
#' # *** Piecewise-quadratic signal
#' pcws.quad.sig <- 2*c((1:50)^2 /1000, rep(2, 100), 1:50 / 50 )
#' # *** data vector
#' x <- pcws.quad.sig + rnorm(100)
#' # *** identify potential locations of the change-points in the slope coefficient and the intercept
#' w <- not(x, contrast = "pcwsQuadMean")
#' # *** ploting the results
#' plot(w)
#' # *** location(s) of the change-points
#' fo <- features(w)
#' fo$cpt
not <- function(x, ...) UseMethod("not")
#' @method not default
#' @export
#' @rdname not
#' @return An object of class "not", which contains the following fields:
#' \item{x}{The input vector.}
#' \item{n}{The length of \code{x}.}
#' \item{contrast}{A scenario for the change-points.}
#' \item{contrasts}{A 5-column matrix with the values of the contrast function, where 's' and 'e' denote start-
#' end points of the intervals in which change-points candidates 'arg.max' have been found; 'length' shows the length of the intervals drawn,
#' column 'max.contrast' contains corresponding value of the contrast statistic.}
#' \item{solution.path}{A list with the solution path of the NOT algorithm (see the references) containing three fields of the same length: \code{cpt} - a list with consecutive solutions, i.e. s the sets of change-point candidates,
#' \code{th} - a vector of thresholds corresponding to the solutions, \code{n.cpt} - a vector with the number of change-points for each solution.}
#' @references R. Baranowski, Y. Chen, and P. Fryzlewicz (2019). Narrowest-Over-Threshold Change-Point Detection. (\url{http://stats.lse.ac.uk/fryzlewicz/not/not.pdf})
not.default <- function(x,
M=10000,
method = c("not", "max"),
contrast = c("pcwsConstMean",
"pcwsConstMeanHT",
"pcwsLinContMean",
"pcwsLinMean",
"pcwsQuadMean",
"pcwsConstMeanVar"),
rand.intervals = TRUE,
parallel = FALSE,
augmented = FALSE,
intervals,
...){
results <- list()
#veryfing the input parameters - x
results$x <- as.numeric(x)
storage.mode(results$x) <- "double"
results$n <- length(results$x)
if(results$n < 2) stop("Data vector x should contain at least two elements.")
if(any(is.na(results$x))) stop("Data vector x vector cannot contain NA's")
if(var(x) <= sqrt(.Machine$double.eps)) stop("Data vector x is essentially a constant vector, change-point detection is not needed")
#veryfing the input parameters - M
M <- as.integer(M)
if(any(is.na(M))) stop("M cannot be NA")
if(length(M)> 1) stop("M should be a single integer.")
if(M<0) stop("M should be an integer > 0.")
#veryfing the input parameters - method
method <- match.arg(method, c("not", "max"))
#veryfing the input parameters - contrast
results$contrast <- match.arg(contrast,
c("pcwsConstMean",
"pcwsConstMeanHT",
"pcwsLinContMean",
"pcwsLinMean",
"pcwsQuadMean",
"pcwsConstMeanVar"))
#veryfing the input parameters - rand.intervals
rand.intervals <- as.logical(rand.intervals[1])
#veryfing the input parameters - parallel
parallel <- as.integer(parallel[1])
if(parallel != 0 ) parallel <- as.integer(1)
if(.Platform$OS.type != "unix")
if(parallel == 1) {
warning("Running computations in parallel on non-unix systems is currently not supported. Using a single core.")
parallel <- as.integer(0)
}
#veryfing the input parameters - augmented
augmented <- as.logical(augmented[1])
#drawing the intervals over which the contrast function will be computed
if(rand.intervals){
intervals <- matrix(random.intervals(results$n,M, ...), ncol=2)
} else if(missing(intervals)){
stop("intervals need to be specified when rand.intervals==FALSE")
}else{
intervals <- matrix(as.integer(intervals), ncol=2)
M <- nrow(intervals)
if(any(intervals[,1] > intervals[,2])) stop("intervals[,2] must be > than intervals[,1]")
if(any(intervals < 1 || intervals > length(x))) stop("endpoints in intervals must be between 1 and length(x)")
}
#making sure that not_r_wrapper gets the right type
storage.mode(intervals) <- "integer"
#choosing the way the contrast functions are aggregated
if(method == "not") method <- as.integer(0)
else if(method == "max") method <- as.integer(1)
#should we additionally compute the contrast function while constructing the segmenation tree?
if(augmented == FALSE) augmented <- as.integer(0)
else augmented <- as.integer(1)
#picking the correct type of the contrast function
if(results$contrast == "pcwsConstMean") contrast <- as.integer(0)
else if (results$contrast == "pcwsLinContMean") contrast <- as.integer(1)
else if (results$contrast == "pcwsLinMean") contrast <- as.integer(2)
else if (results$contrast == "pcwsQuadMean") contrast <- as.integer(3)
else if (results$contrast == "pcwsConstMeanVar") contrast <- as.integer(4)
else if (results$contrast == "pcwsConstMeanHT") contrast <- as.integer(5)
#calling the C code
tmp <- .Call("not_r_wrapper", results$x, intervals, method, contrast, parallel, augmented)
#combining the results with the info on how the method has been run
results <- c(results, tmp)
class(results) <- "not"
return(results)
}
rbaranowski/not documentation built on March 22, 2022, 1:18 p.m.
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Defines functions not.default not
Documented in not not.default
#' @title Narrowest-Over-Threshold Change-Point Detection
#' @description Implements the Narrowest-Over-Threshold approach for general multiple change-point
#' detection in one-dimensional data following 'deterministic signal + noise' model. Scenarios that are currently implemented are: piecewise-constant signal, piecewise-constant signal with a heavy tailed noise, piecewise-linear signal, piecewise-quadratic signal, piecewise-constant signal and with piecewise-constant standard deviation of the noise. The main routines of the package are \code{\link{not}} and \code{\link{features}}.
#' @references R. Baranowski, Y. Chen, and P. Fryzlewicz (2019). Narrowest-Over-Threshold Change-Point Detection. (\url{http://stats.lse.ac.uk/fryzlewicz/not/not.pdf})
#' @docType package
#' @useDynLib not, .registration = TRUE
#' @name not-package
#' @importFrom graphics plot lines title
#' @importFrom stats cov lm.fit logLik predict residuals sd mad quantile runif ts.plot var
#' @importFrom splines bs
NULL
#' @title Narrowest-Over-Threshold Change-Point Detection
#' @description Identifies potential locations of the change-points in the data following 'deterministic signal + noise' model (see details below) in a number of different scenarios.
#' The object returned by this routine can be further passed to the \code{\link{features}} function, which finds the final estimate of the change-points based on a chosen stopping criterion.
#' It can be also passed to \code{\link{plot}}, \code{\link{predict}} and \code{\link{residuals}} routines.
#' @details The data points provided in \code{x} are assumed to follow
#' \deqn{Y_{t} = f_{t}+\sigma_{t}\varepsilon_{t},}{Y_t= f_t + sigma_t varepsilon_t,}
#' for \eqn{t=1,\ldots,n}{t=1,...,n}, where \eqn{n}{n} is the number of observations in \code{x}, the signal \eqn{f_{t}}{f_t} and the standard deviation \eqn{\sigma_{t}}{sigma_{t}}
#' are non-stochastic with structural breaks at unknown locations in time \eqn{t}{t}. Currently, thefollowing scenarios for \eqn{f_{t}}{f_t} and \eqn{\sigma_{t}}{sigma_t} are implemented:
#' \itemize{
#' \item Piecewise-constant signal with a Gaussian noise and constant standard deviation.
#'
#' Use \code{contrast="pcwsConstMean"} here.
#' \item Piecewise-constant mean with a heavy-tailed noise and constant standard deviation.
#'
#' Use \code{contrast="pcwsConstMeanHT"} here.
#' \item Piecewise-linear continuous signal with Gaussian noise and constant standard deviation.
#'
#' Use \code{contrast="pcwsLinContMean"} here.
#' \item Piecewise-linear signal with Gaussian noise and constant standard deviation.
#'
#' Use \code{contrast="pcwsLinMean"} here.
#' \item Piecewise-quadratic signal with Gaussian noise and constant standard deviation.
#'
#' Use \code{contrast="pcwsQuadMean"} here.
#' \item Piecewise-constant signal and piecewise-constant standard deviation of the Gaussian noise.
#'
#' Use \code{contrast="pcwsConstMeanVar"} here.
#' }
#' @param x A numeric vector with data points.
#' @param M A number of intervals drawn in the procedure.
#' @param method Choice of "not" (recommended) and "max". If \code{method="not"}, the Narrowest-Over-Threshold intervals are used in the algorithm.
#' If \code{method="max"}, the intervals corresponding to the largest contrast function are used. For an explanation, see the references.
#' @param contrast A type of the contrast function used in the NOT algorithm.
#' Choice of \code{"pcwsConstMean"}, \code{"pcwsConstMeanHT"}, \code{"pcwsLinContMean"}, \code{"pcwsLinMean"}, \code{"pcwsQuadMean"}, \code{"pcwsConstMeanVar"}.
#' For the explanation, see details below.
#' @param rand.intervals A logical variable. If \code{rand.intervals=TRUE} intervals used in the procedure are drawn uniformly using the \code{\link{random.intervals}} routine.
#' If \code{rand.intervals=FALSE}, the intervals need to be passed using the \code{intervals} argument.
#' @param parallel A logical variable. If TRUE some of computations are run in parallel using OpenMP framework. Currently this option is not supported on Windows.
#' @param augmented A logical variable. if TRUE, the entire data are considered when the NOT segmentation tree is constructed (see the solution path algorithm in the references).
#' @param intervals A 2-column matrix with the intervals considered in the algorithm, with start- and end- points of the intervals in, respectively, the first and the second column.
#' The intervals are used only if \code{rand.intervals=FALSE}.
#' @param ... Not in use.
#' @rdname not
#' @export
#' @examples
#' # **** Piecewisce-constant mean with Gaussian noise.
#' # *** signal
#' pcws.const.sig <- c(rep(0, 100), rep(1,100))
#' # *** data vector
#' x <- pcws.const.sig + rnorm(100)
#' # *** identify potential locations of the change-points
#' w <- not(x, contrast = "pcwsConstMean")
#' # *** some examples of how the w object can be used
#' plot(w)
#' plot(residuals(w))
#' plot(predict(w))
#' # *** this is how to extract the change-points
#' fo <- features(w)
#' fo$cpt
#'
#' # **** Piecewisce-constant mean with a heavy-tailed noise.
#' # *** data vector, signal the same as in the previous example, but heavy tails
#' x <- pcws.const.sig + rt(100, 3)
#' # *** identify potential locations of the change-points,
#' # using a contrast taylored to heavy-tailed data
#' w <- not(x, contrast = "pcwsConstMeanHT")
#' plot(w)
#'
#' # **** Piecewisce-constant mean and piecewise-constant variance
#' # *** signal's standard deviation
#' pcws.const.sd <- c(rep(2, 50), rep(1,150))
#' # *** data vector with pcws-const mean and variance
#' x <- pcws.const.sig + pcws.const.sd * rnorm(100)
#' # *** identify potential locations of the change-points in this model
#' w <- not(x, contrast = "pcwsConstMeanVar")
#' # *** extracting locations of the change-points
#' fo <- features(w)
#' fo$cpt
#'
#' # **** Piecewisce-linear coninuous mean
#' # *** signal with a change in slope
#' pcws.lin.cont.sig <- cumsum(c(rep(-1/50, 100), rep(1/50,100)))
#' # *** data vector
#' x <- pcws.lin.cont.sig + rnorm(100)
#' # *** identify potential locations of the change-points in the slope coefficient
#' w <- not(x, contrast = "pcwsLinContMean")
#' # *** ploting the results
#' plot(w)
#' # *** location(s) of the change-points
#' fo <- features(w)
#' fo$cpt
#'
#' # **** Piecewisce-linear mean with jumps
#' # *** signal with a change in slope and jumpe
#' pcws.lin.sig <- pcws.lin.cont.sig + pcws.const.sig
#' # *** data vector
#' x <- pcws.lin.sig + rnorm(100)
#' # *** identify potential locations of the change-points in the slope coefficient and the intercept
#' w <- not(x, contrast = "pcwsLinMean")
#' # *** ploting the results
#' plot(w)
#' # *** location(s) of the change-points
#' fo <- features(w)
#' fo$cpt
#'
#' # **** Piecewisce-quadratic mean with jumps
#' # *** Piecewise-quadratic signal
#' pcws.quad.sig <- 2*c((1:50)^2 /1000, rep(2, 100), 1:50 / 50 )
#' # *** data vector
#' x <- pcws.quad.sig + rnorm(100)
#' # *** identify potential locations of the change-points in the slope coefficient and the intercept
#' w <- not(x, contrast = "pcwsQuadMean")
#' # *** ploting the results
#' plot(w)
#' # *** location(s) of the change-points
#' fo <- features(w)
#' fo$cpt
not <- function(x, ...) UseMethod("not")
#' @method not default
#' @export
#' @rdname not
#' @return An object of class "not", which contains the following fields:
#' \item{x}{The input vector.}
#' \item{n}{The length of \code{x}.}
#' \item{contrast}{A scenario for the change-points.}
#' \item{contrasts}{A 5-column matrix with the values of the contrast function, where 's' and 'e' denote start-
#' end points of the intervals in which change-points candidates 'arg.max' have been found; 'length' shows the length of the intervals drawn,
#' column 'max.contrast' contains corresponding value of the contrast statistic.}
#' \item{solution.path}{A list with the solution path of the NOT algorithm (see the references) containing three fields of the same length: \code{cpt} - a list with consecutive solutions, i.e. s the sets of change-point candidates,
#' \code{th} - a vector of thresholds corresponding to the solutions, \code{n.cpt} - a vector with the number of change-points for each solution.}
#' @references R. Baranowski, Y. Chen, and P. Fryzlewicz (2019). Narrowest-Over-Threshold Change-Point Detection. (\url{http://stats.lse.ac.uk/fryzlewicz/not/not.pdf})
not.default <- function(x,
M=10000,
method = c("not", "max"),
contrast = c("pcwsConstMean",
"pcwsConstMeanHT",
"pcwsLinContMean",
"pcwsLinMean",
"pcwsQuadMean",
"pcwsConstMeanVar"),
rand.intervals = TRUE,
parallel = FALSE,
augmented = FALSE,
intervals,
...){
results <- list()
#veryfing the input parameters - x
results$x <- as.numeric(x)
storage.mode(results$x) <- "double"
results$n <- length(results$x)
if(results$n < 2) stop("Data vector x should contain at least two elements.")
if(any(is.na(results$x))) stop("Data vector x vector cannot contain NA's")
if(var(x) <= sqrt(.Machine$double.eps)) stop("Data vector x is essentially a constant vector, change-point detection is not needed")
#veryfing the input parameters - M
M <- as.integer(M)
if(any(is.na(M))) stop("M cannot be NA")
if(length(M)> 1) stop("M should be a single integer.")
if(M<0) stop("M should be an integer > 0.")
#veryfing the input parameters - method
method <- match.arg(method, c("not", "max"))
#veryfing the input parameters - contrast
results$contrast <- match.arg(contrast,
c("pcwsConstMean",
"pcwsConstMeanHT",
"pcwsLinContMean",
"pcwsLinMean",
"pcwsQuadMean",
"pcwsConstMeanVar"))
#veryfing the input parameters - rand.intervals
rand.intervals <- as.logical(rand.intervals[1])
#veryfing the input parameters - parallel
parallel <- as.integer(parallel[1])
if(parallel != 0 ) parallel <- as.integer(1)
if(.Platform$OS.type != "unix")
if(parallel == 1) {
warning("Running computations in parallel on non-unix systems is currently not supported. Using a single core.")
parallel <- as.integer(0)
}
#veryfing the input parameters - augmented
augmented <- as.logical(augmented[1])
#drawing the intervals over which the contrast function will be computed
if(rand.intervals){
intervals <- matrix(random.intervals(results$n,M, ...), ncol=2)
} else if(missing(intervals)){
stop("intervals need to be specified when rand.intervals==FALSE")
}else{
intervals <- matrix(as.integer(intervals), ncol=2)
M <- nrow(intervals)
if(any(intervals[,1] > intervals[,2])) stop("intervals[,2] must be > than intervals[,1]")
if(any(intervals < 1 || intervals > length(x))) stop("endpoints in intervals must be between 1 and length(x)")
}
#making sure that not_r_wrapper gets the right type
storage.mode(intervals) <- "integer"
#choosing the way the contrast functions are aggregated
if(method == "not") method <- as.integer(0)
else if(method == "max") method <- as.integer(1)
#should we additionally compute the contrast function while constructing the segmenation tree?
if(augmented == FALSE) augmented <- as.integer(0)
else augmented <- as.integer(1)
#picking the correct type of the contrast function
if(results$contrast == "pcwsConstMean") contrast <- as.integer(0)
else if (results$contrast == "pcwsLinContMean") contrast <- as.integer(1)
else if (results$contrast == "pcwsLinMean") contrast <- as.integer(2)
else if (results$contrast == "pcwsQuadMean") contrast <- as.integer(3)
else if (results$contrast == "pcwsConstMeanVar") contrast <- as.integer(4)
else if (results$contrast == "pcwsConstMeanHT") contrast <- as.integer(5)
#calling the C code
tmp <- .Call("not_r_wrapper", results$x, intervals, method, contrast, parallel, augmented)
#combining the results with the info on how the method has been run
results <- c(results, tmp)
class(results) <- "not"
return(results)
}
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