# R/gen_cross.R In volesti: Volume Approximation and Sampling of Convex Polytopes

#### Documented in gen_cross

```#' Generator function for cross polytopes
#'
#' This function generates the \eqn{d}-dimensional cross polytope in H- or V-representation.
#'
#' @param dimension The dimension of the cross polytope.
#' @param representation A string to declare the representation. It has to be \code{'H'} for H-representation or \code{'V'} for V-representation. Default valus is 'H'.
#'
#' @return A polytope class representing a cross polytope in H- or V-representation.
#' @examples
#' # generate a 10-dimensional cross polytope in H-representation
#' P = gen_cross(5, 'H')
#'
#' # generate a 15-dimension cross polytope in V-representation
#' P = gen_cross(15, 'V')
#' @export
gen_cross <- function(dimension, representation = 'H') {

kind_gen = 2
m_gen = 0
if (representation == 'V') {
Vpoly_gen = TRUE
} else if (representation == 'H') {
Vpoly_gen = FALSE
} else {
stop('Not a known representation.')
}

Mat = poly_gen(kind_gen, Vpoly_gen, FALSE, dimension, m_gen)

# first column is the vector b
b = Mat[, 1]
Mat = Mat[, -c(1), drop = FALSE]

if (Vpoly_gen) {
P = Vpolytope(V = Mat, volume = 2^dimension / prod(1:dimension))
} else {
P = Hpolytope(A = -Mat, b = b, volume = 2^dimension / prod(1:dimension))
}

return(P)
}
```

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volesti documentation built on Sept. 19, 2023, 5:08 p.m.