Billiard walk

R-proj/R/RcppExports.R

@@ -165,14 +165,14 @@ rotating <- function(P) {
 #' @param P A convex polytope (H- or V-representation or zonotope).
 #' @param random_walk Optional. A string that declares the random walk.
 #' @param walk_length Optional. The number of the steps for the random walk.
-#' @param radius Optional. The radius for the ball walk.
+#' @param parameters Optional. A list for the parameters of the methods:
 #'
 #' @section warning:
 #' Do not use this function.
 #'
 #' @return A numerical matrix that describes the rounded polytope and contains the round value.
-rounding <- function(P, random_walk = NULL, walk_length = NULL, radius = NULL) {
-    .Call(`_volesti_rounding`, P, random_walk, walk_length, radius)
+rounding <- function(P, random_walk = NULL, walk_length = NULL, parameters = NULL) {
+    .Call(`_volesti_rounding`, P, random_walk, walk_length, parameters)
 }
 
 #' Sample points from a convex Polytope (H-polytope, V-polytope or a zonotope) or use direct methods for uniform sampling from the unit or the canonical or an arbitrary \eqn{d}-dimensional simplex and the boundary or the interior of a \eqn{d}-dimensional hypersphere
@@ -183,16 +183,17 @@ rounding <- function(P, random_walk = NULL, walk_length = NULL, radius = NULL) {
 #' @param P A convex polytope. It is an object from class (a) Hpolytope or (b) Vpolytope or (c) Zonotope.
 #' @param N The number of points that the function is going to sample from the convex polytope. The default value is \eqn{100}.
 #' @param distribution Optional. A string that declares the target distribution: a) \code{'uniform'} for the uniform distribution or b) \code{'gaussian'} for the multidimensional spherical distribution. The default target distribution is uniform.
-#' @param random_walk Optional. A string that declares the random walk method: a) \code{'CDHR'} for Coordinate Directions Hit-and-Run, b) \code{'RDHR'} for Random Directions Hit-and-Run or c) \code{'BW'} for Ball Walk. The default walk is \code{'CDHR'}.
-#' @param walk_length Optional. The number of the steps for the random walk. The default value is \eqn{\lfloor 10 + d/10\rfloor}, where \eqn{d} implies the dimension of the polytope.
+#' @param random_walk Optional. A string that declares the random walk method: a) \code{'CDHR'} for Coordinate Directions Hit-and-Run, b) \code{'RDHR'} for Random Directions Hit-and-Run, c) \code{'BaW'} for Ball Walk or d) \code{'BiW'} for Billiard walk. The default walk is \code{'BiW'} for the uniform distribution or \code{'CDHR'} for the Normal distribution.
+#' @param walk_length Optional. The number of the steps for the random walk. The default value is \eqn{1} for \code{'BiW'} and \eqn{\lfloor 10 + d/10\rfloor} otherwise, where \eqn{d} is the dimension that the polytope lies.
 #' @param exact A boolean parameter. It should be used for the uniform sampling from the boundary or the interior of a hypersphere centered at the origin or from the unit or the canonical or an arbitrary simplex. The arbitrary simplex has to be given as a V-polytope. For the rest well known convex bodies the dimension has to be declared and the type of body as well as the radius of the hypersphere.
 #' @param body A string that declares the type of the body for the exact sampling: a) \code{'unit simplex'} for the unit simplex, b) \code{'canonical simplex'} for the canonical simplex, c) \code{'hypersphere'} for the boundary of a hypersphere centered at the origin, d) \code{'ball'} for the interior of a hypersphere centered at the origin.
-#' @param parameters A list for the parameters of the methods:
+#' @param parameters Optional. A list for the parameters of the methods:
 #' \itemize{
 #' \item{\code{variance} }{ The variance of the multidimensional spherical gaussian. The default value is 1.}
 #' \item{\code{dimension} }{ An integer that declares the dimension when exact sampling is enabled for a simplex or a hypersphere.}
 #' \item{\code{radius} }{ The radius of the \eqn{d}-dimensional hypersphere. The default value is \eqn{1}.}
 #' \item{\code{BW_rad} }{ The radius for the ball walk.}
+#' \item{\code{diameter} }{ The diameter of the polytope. It is used to set the maximum length of the trajectory in billiard walk.}
 #' }
 #' @param InnerPoint A \eqn{d}-dimensional numerical vector that defines a point in the interior of polytope P.
 #'
@@ -207,7 +208,7 @@ rounding <- function(P, random_walk = NULL, walk_length = NULL, radius = NULL) {
 #' @examples
 #' # uniform distribution from the 3d unit cube in V-representation using ball walk
 #' P = gen_cube(3, 'V')
-#' points = sample_points(P, random_walk = "BW", walk_length = 5)
+#' points = sample_points(P, random_walk = "BaW", walk_length = 5)
 #'
 #' # gaussian distribution from the 2d unit simplex in H-representation with variance = 2
 #' A = matrix(c(-1,0,0,-1,1,1), ncol=2, nrow=3, byrow=TRUE)
@@ -232,12 +233,12 @@ sample_points <- function(P = NULL, N = NULL, distribution = NULL, random_walk =
 #' For the volume approximation can be used two algorithms. Either SequenceOfBalls or CoolingGaussian. A H-polytope with \eqn{m} facets is described by a \eqn{m\times d} matrix \eqn{A} and a \eqn{m}-dimensional vector \eqn{b}, s.t.: \eqn{Ax\leq b}. A V-polytope is defined as the convex hull of \eqn{m} \eqn{d}-dimensional points which correspond to the vertices of P. A zonotope is desrcibed by the Minkowski sum of \eqn{m} \eqn{d}-dimensional segments.
 #'
 #' @param P A convex polytope. It is an object from class (a) Hpolytope or (b) Vpolytope or (c) Zonotope.
-#' @param walk_length Optional. The number of the steps for the random walk. The default value is \eqn{\lfloor 10 + d/10\rfloor} for SequenceOfBalls and \eqn{1} for CoolingGaussian.
-#' @param error Optional. Declare the upper bound for the approximation error. The default value is \eqn{1} for SequenceOfBalls and \eqn{0.1} for CoolingGaussian.
+#' @param walk_length Optional. The number of the steps for the random walk. The default value is \eqn{\lfloor 10 + d/10\rfloor} for SequenceOfBalls and \eqn{1} otherwise.
+#' @param error Optional. Declare the upper bound for the approximation error. The default value is \eqn{1} for SequenceOfBalls and \eqn{0.1} otherwise.
 #' @param inner_ball Optional. A \eqn{d+1} vector that contains an inner ball. The first \eqn{d} coordinates corresponds to the center and the last one to the radius of the ball. If it is not given then for H-polytopes the Chebychev ball is computed, for V-polytopes \eqn{d+1} vertices are picked randomly and the Chebychev ball of the defined simplex is computed. For a zonotope that is defined by the Minkowski sum of \eqn{m} segments we compute the maximal \eqn{r} s.t.: \eqn{re_i\in Z} for all \eqn{i=1,\dots ,d}, then the ball centered at the origin with radius \eqn{r/\sqrt{d}} is an inscribed ball.
 #' @param algo Optional. A string that declares which algorithm to use: a) \code{'SoB'} for SequenceOfBalls or b) \code{'CG'} for CoolingGaussian or c) \code{'CB'} for cooling bodies.
-#' @param random_walk Optional. A string that declares the random walk method: a) \code{'CDHR'} for Coordinate Directions Hit-and-Run, b) \code{'RDHR'} for Random Directions Hit-and-Run or c) \code{'BW'} for Ball Walk. The default walk is \code{'CDHR'}.
-#' @param rounding Optional. A boolean parameter for rounding. The default value is \code{FALSE}.
+#' @param random_walk Optional. A string that declares the random walk method: a) \code{'CDHR'} for Coordinate Directions Hit-and-Run, b) \code{'RDHR'} for Random Directions Hit-and-Run, c) \code{'BaW'} for Ball Walk, or \code{'BiW'} for Billiard walk. The default walk is \code{'CDHR'} for H-polytopes and \code{'BiW'} for the other representations.
+#' @param rounding Optional. A boolean parameter for rounding. The default value is \code{TRUE} for V-polytopes and \code{FALSE} otherwise.
 #' @param parameters Optional. A list for the parameters of the algorithms:
 #' \itemize{
 #' \item{\code{Window} }{ The length of the sliding window for CG algorithm. The default value is \eqn{500+4dimension^2}.}
@@ -254,6 +255,7 @@ sample_points <- function(P = NULL, N = NULL, distribution = NULL, random_walk =
 #'  \item{\code{prob} }{ The probability is used for the empirical confidence interval in ratio estimation of CB algorithm. The default value is \eqn{0.75}.}
 #'  \item{\code{hpoly} }{ A boolean parameter to use H-polytopes in MMC of CB algorithm. The default value is \code{FALSE}.}
 #'  \item{\code{minmaxW} }{ A boolean parameter to use the sliding window with a minmax values stopping criterion.}
+#'  \item{\code{diameter} }{ The diameter of the polytope. It is used to set the maximum length of the trajectory in billiard walk.}
 #' }
 #'
 #' @references \cite{I.Z.Emiris and V. Fisikopoulos,

R-proj/R/round_polytope.R

@@ -3,9 +3,13 @@
 #' Given a convex H or V polytope or a zonotope as input this functionbrings the polytope in well rounded position based on minimum volume enclosing ellipsoid of a pointset.
 #' 
 #' @param P A convex polytope. It is an object from class (a) Hpolytope or (b) Vpolytope or (c) Zonotope.
-#' @param random_walk Optional. A string that declares the random walk method: a) \code{'CDHR'} for Coordinate Directions Hit-and-Run, b) \code{'RDHR'} for Random Directions Hit-and-Run or c) \code{'BW'} for Ball Walk. The default walk is \code{'CDHR'}.
-#' @param walk_length Optional. The number of the steps for the random walk. The default value is \eqn{\lfloor 10 + d/10\rfloor}.
-#' @param radius Optional. The radius for the ball walk.
+#' @param random_walk Optional. A string that declares the random walk method: a) \code{'CDHR'} for Coordinate Directions Hit-and-Run, b) \code{'RDHR'} for Random Directions Hit-and-Run, c) \code{'BaW'} for Ball Walk or d) \code{'BiW'} for Billiard walk. The default walk is \code{'CDHR'} for H-polytope and \code{'BiW'} for the other representations.
+#' @param walk_length Optional. The number of the steps for the random walk. The default value is \eqn{1} for \code{'BiW'} and \eqn{\lfloor 10 + d/10\rfloor} otherwise.
+#' @param parameters Optional. A list for the parameters of the methods:
+#' \itemize{
+#'   \item{\code{BW_rad} }{ The radius for the ball walk.}
+#'   \item{\code{diameter} }{ The diameter of the polytope. It is used to set the maximum length of the trajectory in billiard walk.}
+#' }
 #' 
 #' @return A list with 2 elements: (a) a polytope of the same class as the input polytope class and (b) the element "round_value" which is the determinant of the square matrix of the linear transformation that was applied on the polytope that is given as input.
 #'
@@ -24,9 +28,9 @@
 #' Z = gen_rand_zonotope(2,6)
 #' ListZono = round_polytope(Z, random_walk = 'BW')
 #' @export
-round_polytope <- function(P, random_walk = NULL, walk_length = NULL, radius = NULL){
+round_polytope <- function(P, random_walk = NULL, walk_length = NULL, parameters = NULL){
 
-  ret_list = rounding(P, random_walk, walk_length, radius)
+  ret_list = rounding(P, random_walk, walk_length, parameters)
 
   #get the matrix that describes the polytope
   Mat = ret_list$Mat
@@ -41,8 +45,10 @@ round_polytope <- function(P, random_walk = NULL, walk_length = NULL, radius = N
     PP = list("P" = Vpolytope$new(A), "round_value" = ret_list$round_value)
   }else if (type == 3) {
     PP = list("P" = Zonotope$new(A), "round_value" = ret_list$round_value)
-  } else {
+  } else if(type == 1) {
     PP = list("P" = Hpolytope$new(A,b), "round_value" = ret_list$round_value)
+  } else {
+    PP = list("P" = VPolyintersectVPoly$new(V1 = t(Mat[,dim(P$V1)[1]]), V2 = t(Mat[,dim(P$V2)[1]])), "round_value" = ret_list$round_value)
   }
   return(PP)
 }