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#############################################################
# #
# mle.wrappednormal function #
# Author: Claudio Agostinelli #
# Email: claudio.agostinelli@unitn.it #
# Date: 05 June 2017 #
# Copyright (C) 2017 Claudio Agostinelli #
# #
# Version 0.3 #
#############################################################
mle.wrappednormal <- function(x, mu=NULL, rho=NULL, sd=NULL, K=NULL, tol=1e-5, min.sd=1e-3, min.k=10, max.iter=100, verbose=FALSE, control.circular=list()) {
# Handling missing values
x <- na.omit(x)
if (length(x)==0) {
warning("No observations (at least after removing missing values)")
return(NULL)
}
if (is.circular(x)) {
datacircularp <- circularp(x)
} else if (is.circular(mu)) {
datacircularp <- circularp(mu)
} else {
datacircularp <- list(type="angles", units="radians", template="none", modulo="asis", zero=0, rotation="counter")
}
dc <- control.circular
if (is.null(dc$type))
dc$type <- datacircularp$type
if (is.null(dc$units))
dc$units <- datacircularp$units
if (is.null(dc$template))
dc$template <- datacircularp$template
if (is.null(dc$modulo))
dc$modulo <- datacircularp$modulo
if (is.null(dc$zero))
dc$zero <- datacircularp$zero
if (is.null(dc$rotation))
dc$rotation <- datacircularp$rotation
x <- conversion.circular(x, units="radians", zero=0, rotation="counter", modulo="2pi")
attr(x, "class") <- attr(x, "circularp") <- NULL
if (!is.null(mu)) {
mu <- conversion.circular(mu, units="radians", zero=0, rotation="counter", modulo="2pi")
attr(mu, "class") <- attr(mu, "circularp") <- NULL
}
res <- MlewrappednormalRad(x, mu, rho, sd, min.sd, K, min.k, tol, max.iter, verbose)
mu <- conversion.circular(circular(res[1]), dc$units, dc$type, dc$template, dc$modulo, dc$zero, dc$rotation)
result <- list()
result$call <- match.call()
result$mu <- mu
result$rho <- res[2]
result$sd <- res[3]
result$est.mu <- res[4]
result$est.rho <- res[5]
result$convergence <- TRUE
if (res[6] > max.iter) {
result$convergence <- FALSE
}
class(result) <- "mle.wrappednormal"
return(result)
}
MlewrappednormalRad <- function(x, mu=NULL, rho=NULL, sd=NULL, min.sd, K=NULL, min.k=10, tol, max.iter, verbose) {
n <- length(x)
sinr <- sum(sin(x))
cosr <- sum(cos(x))
est.mu <- FALSE
if (is.null(mu)) {
mu <- atan2(sinr, cosr)
est.mu <- TRUE
}
est.rho <- FALSE
if (is.null(sd)) {
if (is.null(rho)) {
sd <- sqrt(-2*log(sqrt(sinr^2 + cosr^2)/n))
if (is.na(sd) || sd < min.sd)
sd <- min.sd
est.rho <- TRUE
} else {
sd <- sqrt(-2*log(rho))
}
}
xdiff <- 1+tol
iter <- 0
if (is.null(K)) {
range <- max(mu, x) - min(mu, x)
K <- (range+6*sd)%/%(2*pi)+1
K <- max(min.k, K)
}
while (xdiff > tol & iter <= max.iter) {
iter <- iter + 1
mu.old <- mu
sd.old <- sd
z <- .Fortran("mlewrpno",
as.double(x),
as.double(mu),
as.double(sd),
as.integer(n),
as.integer(K),
as.integer(est.mu),
as.integer(est.rho),
w=double(n),
wk=double(n),
wm=double(n),
PACKAGE="circular"
)
w <- z$w
wk <- z$wk
wm <- z$wm
if (est.mu) {
mu <- sum(x)/n
if (any(wk!=0)) {
mu <- mu + 2*pi*sum(wk[wk!=0]/w[wk!=0])/n
}
}
if (est.rho) {
if (any(wm!=0)) {
sd <- sqrt(sum(wm[wm!=0]/w[wm!=0])/n)
} else {
sd <- min.sd
}
}
if (verbose) {
cat("mu: ", mu, "\n")
cat("rho: ", exp(-sd^2/2), "\n")
cat("sd: ", sd, "\n")
}
xdiff <- max(abs(mu - mu.old), abs(sd - sd.old))
}
rho <- exp(-sd^2/2)
result <- c(mu, rho, sd, est.mu, est.rho, iter)
return(result)
}
#############################################################
# #
# print.mle.wrappednormal function #
# Author: Claudio Agostinelli #
# E-mail: claudio@unive.it #
# Date: November, 19, 2003 #
# Version: 0.1-2 #
# #
# Copyright (C) 2003 Claudio Agostinelli #
# #
#############################################################
print.mle.wrappednormal <- function(x, digits = max(3, getOption("digits") - 3), ...) {
cat("\nCall:\n",deparse(x$call),"\n\n",sep="")
cat("mu: ")
cat(format(x$mu, digits=digits), "\n")
cat("\n")
cat("rho: ")
cat(format(x$rho, digits=digits), "\n")
cat("\n")
cat("sd: ")
cat(format(x$sd, digits=digits), "\n")
cat("\n")
if (!x$est.mu) cat("mu is known\n")
if (!x$est.rho) {
cat("rho and sd are known\n")
}
if (!x$convergence) cat("\nThe convergence is not achieved after the prescribed number of iterations \n")
invisible(x)
}
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