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R/depth.R
In DepthProc: Statistical Depth Functions for Multivariate Analysis
#'@title Depth calculation
#'
#' @details Calculate depth functions.
#'
#'@export
#'
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param method Character string which determines the depth function. \code{method} can be "Projection" (the default), "Mahalanobis", "Euclidean" or "Tukey". For details see \code{\link{depth}.}
#' @param name name for this data set - it will be used on plots.
#' @param threads number of threads used in parallel computations. Default value -1 means that all possible cores will be used.
#' @param ... parameters specific to method - see \code{\link{depthEuclid}}
#'
#' @details
#'
#' {the Mahalanobis depth} \deqn{ {D}_{MAH}(y,{X}^{n})=\frac{1}{1+{{(y-\bar{x})}^{T}}{{S}^{-1}}(y-\bar{x})}, } where \eqn{ S } denotes the sample covariance matrix \eqn{ {X}^{n} } .
#'
#' #' A symmetric projection depth \eqn{ D\left( x,X \right) } of a point \eqn{ x\in {{{R}}^{d}} } , \eqn{ d\ge 1 } is defined as \eqn{ D\left( x,X \right)_{PRO}={{\left[ 1+su{{p}_{\left\| u \right\|=1}}\frac{\left| {{u}^{T}}x-Med\left( {{u}^{T}}X \right) \right|}{MAD\left( {{u}^{T}}X \right)} \right]}^{-1}}, } where Med denotes the univariate median, \eqn{ MAD\left( Z \right) } = \eqn{ Med\left( \left| Z-Med\left( Z \right) \right| \right) } . Its sample version denoted by \eqn{ D\left( x,{X}^{n} \right) } or \eqn{ D\left( x,{X}^{n} \right) } is obtained by replacing \eqn{ F } by its empirical counterpart \eqn{ {{F}_{n}} } calculated from the sample \eqn{ {X}^{n} } .
#'
#' Next interesting depth is the weighted \eqn{ {L}^{p} } depth. The weighted \eqn{ {L}^{p} } depth \eqn{ D({x},F) } of a point \eqn{ {x}\in {R}^{d} } , \eqn{ d\ge 1 } generated by \eqn{ d } dimensional random vector \eqn{ {X} } with distribution \eqn{ F } , is defined as \eqn{ D({x},F)=\frac{1}{1+Ew({{\left\| x-X \right\|}_{p}})}, } where \eqn{ w } is a suitable weight function on \eqn{ [0,\infty ) } , and \eqn{ {{\left\| \cdot \right\|}_{p}} } stands for the \eqn{ {L}^{p} } norm (when p=2 we have usual Euclidean norm). We assume that \eqn{ w } is non-decreasing and continuous on \eqn{ [0,\infty ) } with \eqn{ w(\infty -)=\infty } , and for \eqn{ a,b\in {{{R}}^{d}} } satisfying \eqn{ w(\left\| a+b \right\|)\le w(\left\| a \right\|)+w(\left\| b \right\|) } . Examples of the weight functions are: \eqn{ w(x)=a+bx } , \eqn{ a,b>0 } or \eqn{ w(x)={x}^{\alpha } } . The empirical version of the weighted \eqn{ {L}^{p} } depth is obtained by replacing distribution \eqn{ F } of \eqn{ {X} } in \eqn{ Ew({{\left\| {x}-{X} \right\|}_{p}})=\int{w({{\left\| x-t \right\|}_{p}})}dF(t) } by its empirical counterpart calculated from the sample \eqn{ {{{X}}^{n}} } ....
#'
#'
#' The Projection and Tukey's depths are calculated using an approximate algorithm. Calculations of Mahalanobis, Euclidean and \eqn{ L^p } depths are exact. Returns the depth of multivariate point u with respect to data set X.
#'
#'
#' @references
#'
#' Liu, R.Y., Parelius, J.M. and Singh, K. (1999), Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion), Ann. Statist., 27, 783-858.
#'
#' Mosler K (2013). Depth statistics. In C Becker, R Fried, K S (eds.), Robustness and Complex Data Structures, Festschrift in Honour of Ursula Gather, pp. 17-34. Springer.
#'
#' Rousseeuw, P.J. and Struyf, A. (1998), Computing location depth and regression depth in higher dimensions, Stat. Comput., 8, 193-203.
#'
#' Zuo, Y. and Serfling, R. (2000), General Notions of Statistical Depth Functions, Ann. Statist., 28, no. 2, 461-482.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#' @seealso \code{\link{depthContour}} and \code{\link{depthPersp}} for depth graphics.
#'
#' @examples
#' require(robustbase)
#'
#' ## Calculation of Projection depth
#' data(starsCYG, package = "robustbase")
#' depth(t(colMeans(starsCYG)), starsCYG)
#'
#' #Aslo for matrices
#' depth(starsCYG, starsCYG)
#'
#' ## Projection depth applied to a large bivariate data set
#' x = matrix(rnorm(9999), nc = 3)
#' depth(x, x)
#'
#' @keywords
#' multivariate
#' nonparametric
#' robust
#' depth function
#'
#'
depth = function(u, X, method="Projection", name = "X", threads = -1,...)
{
if(is.data.frame(u)) u = as.matrix(u)
if(is.vector(u)) u = matrix(u,ncol = dim(X)[2])
if(missing(X) && method == "MBD") return(depthMBD(u,...))
if(missing(X)) X = u
if(is.data.frame(X)) X = as.matrix(X)
if(is.vector(X)) X = matrix(X,ncol = 1)
###################################
if (method=="Mahalanobis")
{
return(depthMah(u, X, name = name, threads = threads, ...))
}
####################################
if (method=="Euclidean")
{
return(depthEuclid(u, X, name = name))
}
####################################
if(method == "Projection")
{
return(depthProjection(u, X, name = name, threads = threads, ...))
}
#######################################################################
if (method=="Tukey")
{
return(depthTukey(u, X, name = name, ...))
}
########################################################
if (method=="LP")
{
return(depthLP(u, X, name = name, threads = threads,...))
}
if(method=="Local")
{
return(depthLocal(u, X, name = name, ...))
}
if(method == "MBD") return(depthMBD(u, X,...))
}
############################################
############################################
############################################
#'@title Euclidean Depth
#'@export
#'
#'@description Computes the euclidean depth of a point or vectors of points with respect to a multivariate data set.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param name name for this data set - it will be used on plots from depthproc.
#' @param \dots currently not supported.
#'
#'
#'@details
#'
#' Calculation of Euclidean depth is exact.
#'
#' Returns the depth of multivariate point \code{u} with respect to data set \code{X}.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#'
#' @examples
#' x <- matrix(rnorm(9999), nc = 3)
#' depthEuclid(x, x)
#'
#'
#'
#' @keywords
#' multivariate
#' nonparametric
#' depth function
depthEuclid = function(u, X, name = "X",...)
{
if(missing(X)) X = u
n = dim(u)[1]
center = colMeans(X)
center = matrix(rep(center,n),nrow=n,byrow=TRUE)
depth=1/(1+(rowSums((u-center)^2)))
new("DepthEuclid", depth, u = u, X = X, method = "Euclidean", name = name)
}
############################################
############################################
############################################
#'@title Mahalanobis Depth
#'@export
#'@description Computes the mahalanobis depth of a point or vectors of points with respect to a multivariate data set.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param name name for this data set - it will be used on plots.
#' @param threads number of threads used in parallel computations. Default value -1 means that all possible cores will be used.
#' @param cov custom covariance matrix passed. If NULL standard calculations will be based on standard covariance estimator.
#' @param mean custom mean vector. If null mean average will be used.
#' @param \dots currently not supported.
#'
#'@details
#'
#' Calculation of Mahalanobis depth is exact.
#'
#' Returns the depth of multivariate point \code{u} with respect to data set \code{X}.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#'
#' @examples
#' x <- matrix(rnorm(9999), nc = 3)
#' depthMah(x, x)
#'
#'
#'
#' @keywords
#' multivariate
#' nonparametric
#' depth function
depthMah = function(u, X, name = "X", cov = NULL, mean = NULL, threads = -1, ...)
{
if(missing(X)) X = u
if(!is.null(mean)) mean = matrix(mean, ncol = length(mean))
depth = depthMahCPP(u,X, cov, mean, threads)
new("DepthMahalanobis", depth, u = u, X = X, method = "Mahalanobis", name = name)
}
############################################
############################################
############################################
#'@title Projection Depth
#'@export
#'@description Computes the Projection depth of a point or vectors of points with respect to a multivariate data set.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param ndir number of directions used in computations
#' @param threads number of threads used in parallel computations. Default value -1 means that all possible cores will be used.
#' @param name name for this data set - it will be used on plots from depthproc.
#' @param \dots currently not supported.
#'
#'@details
#'
#' Irrespective of dimension, Projection and Tukey's depth is obtained by approximate calculation.
#'
#' Returns the depth of multivariate point \code{u} with respect to data set \code{X}.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#'
#' @examples
#' x = matrix(rnorm(3000), nc = 3)
#' a = depthProjection(x, x, ndir = 2000)
#'
#'
#' @keywords
#' multivariate
#' nonparametric
#' depth function
depthProjection = function(u, X, ndir = 1000, name = "X", threads = -1,...)
{
if(missing(X)) X = u
depth = depthProjCPP(u, X, ndir, threads)
new("DepthProjection", depth, u = u, X = X, method = "Projection", name = name)
}
############################################
############################################
############################################
#'@title Tukey Depth
#'@export
#'@description Computes the Tukey depth of a point or vectors of points with respect to a multivariate data set.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param ndir number of directions used in computations
#' @param threads number of threads used in parallel computations. Default value -1 means that all possible cores will be used.
#' @param name name for this data set - it will be used on plots from depthproc.
#' @param exact if TRUE exact alhorithm will be used . Currently it works only for 2 dimensional data set.
#' @param \dots currently not supported.
#'
#'@details
#'
#' Irrespective of dimension, Projection and Tukey's depth is obtained by approximate calculation.
#'
#' Returns the depth of multivariate point \code{u} with respect to data set \code{X}.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#'
#' @examples
#' \dontrun{
#' x = matrix(rnorm(3000), nc = 3)
#' depthTukey(x, ndir = 2000)
#' }
#'
#' # Exact algorithm in 2d
#' x = matrix(rnorm(2000), nc = 2)
#' depthTukey(x, exact = TRUE)
#'
#' @keywords
#' multivariate
#' nonparametric
#' depth function
depthTukey = function(u, X, ndir = 1000, name = "X", threads = -1, exact = FALSE,...)
{
if(missing(X)) X = u
tukey1d = function(u,X)
{
Xecdf = ecdf(X)
uecdf = Xecdf(u)
uecdf2 = 1-uecdf
min.ecdf = uecdf>uecdf2
depth = uecdf
depth[min.ecdf]=uecdf2[min.ecdf]
depth
}
if (ncol(X)==1)
{
depth= tukey1d(u,X)
} else if(ncol(X) == 2 && exact)
{
depth = depthTukeyCPP(u,X, exact,threads)
} else # czyli jesli wymiar d>2
{
proj = t(runifsphere(ndir, ncol(X)))
xut = X%*%proj
uut = u%*%proj
OD = matrix(nrow=nrow(uut),ncol=ncol(uut))
for (i in 1:ndir)
{
OD[,i]=tukey1d(uut[,i],xut[,i])
}
depth = apply(OD,1,min)
}
new("DepthTukey", depth, u = u, X = X, method = "Tukey", name = name)
}
#'@title LP Depth
#'@export
#'@description Computes the LP depth of a point or vectors of points with respect to a multivariate data set.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param pdim dimension used in calculating depth function.
#' @param la slope the weighing function.
#' @param lb intercept in the weighing function.
#' @param name name for this data set - it will be used on plots from depthproc.
#' @param threads number of threads used in parallel computations. Default value -1 means that all possible cores will be used.
#' @param func the weighing function. Currently it is not supported.
#' @param \dots currently not supported.
#'
#'@details
#'
#' Returns the depth of multivariate point \code{u} with respect to data set \code{X}.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#'
#' @examples
#' x = matrix(rnorm(3000), ncol = 3)
#'
#' #Same results
#' depthLP(x, x, ndir = 2000, pdim = 2)
#'
#' @keywords
#' multivariate
#' nonparametric
#' depth function
#'
depthLP = function(u, X, pdim = 2, la = 1, lb = 1, name = "X", threads = -1, func = NULL,...)
{
if(missing(X)) X = u
if(is.null(func)) depth = depthLPCPP(u, X, pdim, la, lb, threads = threads)
#norm = function(xi, z, p = 1) sum(abs(z-xi)^p)^(1/p)
new("DepthLP", depth, u = u, X = X, method = "LP", name = name)
}
#'@title Modified band depth
#'@export
#'@description Computes the modified band depth.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param name for this data set - it will be used on plots from depthproc.
#' @param \dots currently not supported.
#'
#'@examples
#'
#' x = matrix(rnorm(600), nc = 20)
#' depthMBD(x)
#'
depthMBD = function(u, X, name = "X",...)
{
if(missing(X))
{
X = u
depth = modBandDepth(u)
} else
{
depth = modBandDepthRef(u,X)
}
new("DepthMBD", as.numeric(depth), u = u, X = X, method = "MBD", name = name)
}
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#'@title Depth calculation
#'
#' @details Calculate depth functions.
#'
#'@export
#'
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param method Character string which determines the depth function. \code{method} can be "Projection" (the default), "Mahalanobis", "Euclidean" or "Tukey". For details see \code{\link{depth}.}
#' @param name name for this data set - it will be used on plots.
#' @param threads number of threads used in parallel computations. Default value -1 means that all possible cores will be used.
#' @param ... parameters specific to method - see \code{\link{depthEuclid}}
#'
#' @details
#'
#' {the Mahalanobis depth} \deqn{ {D}_{MAH}(y,{X}^{n})=\frac{1}{1+{{(y-\bar{x})}^{T}}{{S}^{-1}}(y-\bar{x})}, } where \eqn{ S } denotes the sample covariance matrix \eqn{ {X}^{n} } .
#'
#' #' A symmetric projection depth \eqn{ D\left( x,X \right) } of a point \eqn{ x\in {{{R}}^{d}} } , \eqn{ d\ge 1 } is defined as \eqn{ D\left( x,X \right)_{PRO}={{\left[ 1+su{{p}_{\left\| u \right\|=1}}\frac{\left| {{u}^{T}}x-Med\left( {{u}^{T}}X \right) \right|}{MAD\left( {{u}^{T}}X \right)} \right]}^{-1}}, } where Med denotes the univariate median, \eqn{ MAD\left( Z \right) } = \eqn{ Med\left( \left| Z-Med\left( Z \right) \right| \right) } . Its sample version denoted by \eqn{ D\left( x,{X}^{n} \right) } or \eqn{ D\left( x,{X}^{n} \right) } is obtained by replacing \eqn{ F } by its empirical counterpart \eqn{ {{F}_{n}} } calculated from the sample \eqn{ {X}^{n} } .
#'
#' Next interesting depth is the weighted \eqn{ {L}^{p} } depth. The weighted \eqn{ {L}^{p} } depth \eqn{ D({x},F) } of a point \eqn{ {x}\in {R}^{d} } , \eqn{ d\ge 1 } generated by \eqn{ d } dimensional random vector \eqn{ {X} } with distribution \eqn{ F } , is defined as \eqn{ D({x},F)=\frac{1}{1+Ew({{\left\| x-X \right\|}_{p}})}, } where \eqn{ w } is a suitable weight function on \eqn{ [0,\infty ) } , and \eqn{ {{\left\| \cdot \right\|}_{p}} } stands for the \eqn{ {L}^{p} } norm (when p=2 we have usual Euclidean norm). We assume that \eqn{ w } is non-decreasing and continuous on \eqn{ [0,\infty ) } with \eqn{ w(\infty -)=\infty } , and for \eqn{ a,b\in {{{R}}^{d}} } satisfying \eqn{ w(\left\| a+b \right\|)\le w(\left\| a \right\|)+w(\left\| b \right\|) } . Examples of the weight functions are: \eqn{ w(x)=a+bx } , \eqn{ a,b>0 } or \eqn{ w(x)={x}^{\alpha } } . The empirical version of the weighted \eqn{ {L}^{p} } depth is obtained by replacing distribution \eqn{ F } of \eqn{ {X} } in \eqn{ Ew({{\left\| {x}-{X} \right\|}_{p}})=\int{w({{\left\| x-t \right\|}_{p}})}dF(t) } by its empirical counterpart calculated from the sample \eqn{ {{{X}}^{n}} } ....
#'
#'
#' The Projection and Tukey's depths are calculated using an approximate algorithm. Calculations of Mahalanobis, Euclidean and \eqn{ L^p } depths are exact. Returns the depth of multivariate point u with respect to data set X.
#'
#'
#' @references
#'
#' Liu, R.Y., Parelius, J.M. and Singh, K. (1999), Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion), Ann. Statist., 27, 783-858.
#'
#' Mosler K (2013). Depth statistics. In C Becker, R Fried, K S (eds.), Robustness and Complex Data Structures, Festschrift in Honour of Ursula Gather, pp. 17-34. Springer.
#'
#' Rousseeuw, P.J. and Struyf, A. (1998), Computing location depth and regression depth in higher dimensions, Stat. Comput., 8, 193-203.
#'
#' Zuo, Y. and Serfling, R. (2000), General Notions of Statistical Depth Functions, Ann. Statist., 28, no. 2, 461-482.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#' @seealso \code{\link{depthContour}} and \code{\link{depthPersp}} for depth graphics.
#'
#' @examples
#' require(robustbase)
#'
#' ## Calculation of Projection depth
#' data(starsCYG, package = "robustbase")
#' depth(t(colMeans(starsCYG)), starsCYG)
#'
#' #Aslo for matrices
#' depth(starsCYG, starsCYG)
#'
#' ## Projection depth applied to a large bivariate data set
#' x = matrix(rnorm(9999), nc = 3)
#' depth(x, x)
#'
#' @keywords
#' multivariate
#' nonparametric
#' robust
#' depth function
#'
#'
depth = function(u, X, method="Projection", name = "X", threads = -1,...)
{
if(is.data.frame(u)) u = as.matrix(u)
if(is.vector(u)) u = matrix(u,ncol = dim(X)[2])
if(missing(X) && method == "MBD") return(depthMBD(u,...))
if(missing(X)) X = u
if(is.data.frame(X)) X = as.matrix(X)
if(is.vector(X)) X = matrix(X,ncol = 1)
###################################
if (method=="Mahalanobis")
{
return(depthMah(u, X, name = name, threads = threads, ...))
}
####################################
if (method=="Euclidean")
{
return(depthEuclid(u, X, name = name))
}
####################################
if(method == "Projection")
{
return(depthProjection(u, X, name = name, threads = threads, ...))
}
#######################################################################
if (method=="Tukey")
{
return(depthTukey(u, X, name = name, ...))
}
########################################################
if (method=="LP")
{
return(depthLP(u, X, name = name, threads = threads,...))
}
if(method=="Local")
{
return(depthLocal(u, X, name = name, ...))
}
if(method == "MBD") return(depthMBD(u, X,...))
}
############################################
############################################
############################################
#'@title Euclidean Depth
#'@export
#'
#'@description Computes the euclidean depth of a point or vectors of points with respect to a multivariate data set.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param name name for this data set - it will be used on plots from depthproc.
#' @param \dots currently not supported.
#'
#'
#'@details
#'
#' Calculation of Euclidean depth is exact.
#'
#' Returns the depth of multivariate point \code{u} with respect to data set \code{X}.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#'
#' @examples
#' x <- matrix(rnorm(9999), nc = 3)
#' depthEuclid(x, x)
#'
#'
#'
#' @keywords
#' multivariate
#' nonparametric
#' depth function
depthEuclid = function(u, X, name = "X",...)
{
if(missing(X)) X = u
n = dim(u)[1]
center = colMeans(X)
center = matrix(rep(center,n),nrow=n,byrow=TRUE)
depth=1/(1+(rowSums((u-center)^2)))
new("DepthEuclid", depth, u = u, X = X, method = "Euclidean", name = name)
}
############################################
############################################
############################################
#'@title Mahalanobis Depth
#'@export
#'@description Computes the mahalanobis depth of a point or vectors of points with respect to a multivariate data set.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param name name for this data set - it will be used on plots.
#' @param threads number of threads used in parallel computations. Default value -1 means that all possible cores will be used.
#' @param cov custom covariance matrix passed. If NULL standard calculations will be based on standard covariance estimator.
#' @param mean custom mean vector. If null mean average will be used.
#' @param \dots currently not supported.
#'
#'@details
#'
#' Calculation of Mahalanobis depth is exact.
#'
#' Returns the depth of multivariate point \code{u} with respect to data set \code{X}.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#'
#' @examples
#' x <- matrix(rnorm(9999), nc = 3)
#' depthMah(x, x)
#'
#'
#'
#' @keywords
#' multivariate
#' nonparametric
#' depth function
depthMah = function(u, X, name = "X", cov = NULL, mean = NULL, threads = -1, ...)
{
if(missing(X)) X = u
if(!is.null(mean)) mean = matrix(mean, ncol = length(mean))
depth = depthMahCPP(u,X, cov, mean, threads)
new("DepthMahalanobis", depth, u = u, X = X, method = "Mahalanobis", name = name)
}
############################################
############################################
############################################
#'@title Projection Depth
#'@export
#'@description Computes the Projection depth of a point or vectors of points with respect to a multivariate data set.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param ndir number of directions used in computations
#' @param threads number of threads used in parallel computations. Default value -1 means that all possible cores will be used.
#' @param name name for this data set - it will be used on plots from depthproc.
#' @param \dots currently not supported.
#'
#'@details
#'
#' Irrespective of dimension, Projection and Tukey's depth is obtained by approximate calculation.
#'
#' Returns the depth of multivariate point \code{u} with respect to data set \code{X}.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#'
#' @examples
#' x = matrix(rnorm(3000), nc = 3)
#' a = depthProjection(x, x, ndir = 2000)
#'
#'
#' @keywords
#' multivariate
#' nonparametric
#' depth function
depthProjection = function(u, X, ndir = 1000, name = "X", threads = -1,...)
{
if(missing(X)) X = u
depth = depthProjCPP(u, X, ndir, threads)
new("DepthProjection", depth, u = u, X = X, method = "Projection", name = name)
}
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#'@title Tukey Depth
#'@export
#'@description Computes the Tukey depth of a point or vectors of points with respect to a multivariate data set.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param ndir number of directions used in computations
#' @param threads number of threads used in parallel computations. Default value -1 means that all possible cores will be used.
#' @param name name for this data set - it will be used on plots from depthproc.
#' @param exact if TRUE exact alhorithm will be used . Currently it works only for 2 dimensional data set.
#' @param \dots currently not supported.
#'
#'@details
#'
#' Irrespective of dimension, Projection and Tukey's depth is obtained by approximate calculation.
#'
#' Returns the depth of multivariate point \code{u} with respect to data set \code{X}.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#'
#' @examples
#' \dontrun{
#' x = matrix(rnorm(3000), nc = 3)
#' depthTukey(x, ndir = 2000)
#' }
#'
#' # Exact algorithm in 2d
#' x = matrix(rnorm(2000), nc = 2)
#' depthTukey(x, exact = TRUE)
#'
#' @keywords
#' multivariate
#' nonparametric
#' depth function
depthTukey = function(u, X, ndir = 1000, name = "X", threads = -1, exact = FALSE,...)
{
if(missing(X)) X = u
tukey1d = function(u,X)
{
Xecdf = ecdf(X)
uecdf = Xecdf(u)
uecdf2 = 1-uecdf
min.ecdf = uecdf>uecdf2
depth = uecdf
depth[min.ecdf]=uecdf2[min.ecdf]
depth
}
if (ncol(X)==1)
{
depth= tukey1d(u,X)
} else if(ncol(X) == 2 && exact)
{
depth = depthTukeyCPP(u,X, exact,threads)
} else # czyli jesli wymiar d>2
{
proj = t(runifsphere(ndir, ncol(X)))
xut = X%*%proj
uut = u%*%proj
OD = matrix(nrow=nrow(uut),ncol=ncol(uut))
for (i in 1:ndir)
{
OD[,i]=tukey1d(uut[,i],xut[,i])
}
depth = apply(OD,1,min)
}
new("DepthTukey", depth, u = u, X = X, method = "Tukey", name = name)
}
#'@title LP Depth
#'@export
#'@description Computes the LP depth of a point or vectors of points with respect to a multivariate data set.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param pdim dimension used in calculating depth function.
#' @param la slope the weighing function.
#' @param lb intercept in the weighing function.
#' @param name name for this data set - it will be used on plots from depthproc.
#' @param threads number of threads used in parallel computations. Default value -1 means that all possible cores will be used.
#' @param func the weighing function. Currently it is not supported.
#' @param \dots currently not supported.
#'
#'@details
#'
#' Returns the depth of multivariate point \code{u} with respect to data set \code{X}.
#'
#' @author Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.
#'
#'
#' @examples
#' x = matrix(rnorm(3000), ncol = 3)
#'
#' #Same results
#' depthLP(x, x, ndir = 2000, pdim = 2)
#'
#' @keywords
#' multivariate
#' nonparametric
#' depth function
#'
depthLP = function(u, X, pdim = 2, la = 1, lb = 1, name = "X", threads = -1, func = NULL,...)
{
if(missing(X)) X = u
if(is.null(func)) depth = depthLPCPP(u, X, pdim, la, lb, threads = threads)
#norm = function(xi, z, p = 1) sum(abs(z-xi)^p)^(1/p)
new("DepthLP", depth, u = u, X = X, method = "LP", name = name)
}
#'@title Modified band depth
#'@export
#'@description Computes the modified band depth.
#'
#' @param u Numerical vector or matrix whose depth is to be calculated. Dimension has to be the same as that of the observations.
#' @param X The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations).
#' @param name for this data set - it will be used on plots from depthproc.
#' @param \dots currently not supported.
#'
#'@examples
#'
#' x = matrix(rnorm(600), nc = 20)
#' depthMBD(x)
#'
depthMBD = function(u, X, name = "X",...)
{
if(missing(X))
{
X = u
depth = modBandDepth(u)
} else
{
depth = modBandDepthRef(u,X)
}
new("DepthMBD", as.numeric(depth), u = u, X = X, method = "MBD", name = name)
}
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