% Generated by roxygen2: do not edit by hand % Please edit documentation in R/NICER.R name{NICER} alias{NICER} title{New Incremental Cell Enumeration (in) R} usage{ NICER(A, b, initial = c(0, 0), verb = TRUE, epsbound = 1,
epstol = 1e-07)
} description{ Modified version of the algorithm of Rada and Cerny (2018).
The main modifications include preprocessing as hyperplanes are added to determine which new cells are created, thereby reducing the number of calls to the witness function to solve LPs, and treatment of degenerate configurations as well as those in "general position." When the hyperplanes are in general position the number of cells (polytopes) is determined by the elegant formula of Zazlavsky (1975) \deqn{m = {n \choose d} - n + 1}. In degenerate cases, i.e. when hyperplanes are not in general position, the number of cells is more complicated as considered by Alexanderson and Wetzel (1981). The function \code{polycount} is provided to check agreement with their results in an effort to aid in the selection of tolerances for the \code{witness} function. Current version is intended for use with \eqn{d = 2}, but the algorithm is adaptable to \eqn{d > 2}.
} details{ @param A is a n by m matrix of hyperplane slope coefficients
@param b is an n vector of hyperplane intercept coefficients @param initial origin for the interior point vectors \code{w} @param epsbound is a scalar tolerance controlling how close the witness point
can be to an edge of the polytope
@param epstol is a scalar tolerance for the LP convergence @param verb controls verbosity of Mosek solution
@return A list with components:
\itemize{
item SignVector a n by m matrix of signs determining position of cell relative
to each hyperplane.
item w a d by m matrix of interior points for the m cells }
@references Alexanderson, G.L and J.E. Wetzel, (1981) Arrangements of planes in space,
Discrete Math, 34, 219–240.
Rada, M. and M. Cerny (2018) A new algorithm for the enumeration of cells
of hyperplane arrangements and a comparison with Avis and Fukada's reverse search, SIAM J. of Discrete Math, 32, 455-473.
Zaslavsky, T. (1975) Facing up to arrangements: Face-Count Formulas for
Partitions of Space by Hyperplanes, Memoirs of the AMS, Number 154.
@export
}