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#' Trigonometric solution for asymmetric cusp distribution
#'
#' The simplified trigonometric solution for \eqn{x^2=-y^3-beta*x*y}
#'
#'
#' @param x Array of x dimension
#' @param beta the skew parameter
#'
#' @return Array of y
#'
#' @keywords analytic
#'
#' @export
#'
#' @examples
#' x <- seq(-100,100,by=0.1)
#' y <- ecd.solve_cusp_asym(x, beta=0.5)
### <======================================================================>
"ecd.solve_cusp_asym" <- function(x, beta)
{
if (length(beta)!=1) {
stop("Asym cusp requires beta to be length-one numeric!")
}
if (beta==0) {
return(-abs(x)^(2/3)) # revert to std cusp
}
# handle beta < 0
if (beta < 0) {
y <- ecd.solve_cusp_asym(-x, -beta)
return(y)
}
# handle beta > 0
x0 <- -(4*beta^3)/27
V <- abs(x/x0)^(1/2)
W <- 2*abs(beta*x/3)^(1/2)
ifelse( x>=0, {
-W*sinh(1/3*asinh(V))
},
ifelse( x<x0, {
A <- suppressWarnings(acosh(V))
-W*cosh(1/3*A)
}, {
A <- suppressWarnings(acos(V))
-W*cos(1/3*A)
})
)
}
### <---------------------------------------------------------------------->
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