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#############################################################
# #
# Original Splus: Ulric Lund #
# E-mail: ulund@calpoly.edu #
# #
#############################################################
#############################################################
# #
# mle.wrappedcauchy function #
# Author: Claudio Agostinelli #
# Email: claudio@unive.it #
# Date: August, 10, 2006 #
# Copyright (C) 2006 Claudio Agostinelli #
# #
# Version 0.2-2 #
#############################################################
mle.wrappedcauchy <- function(x, mu=NULL, rho=NULL, tol = 1e-015, max.iter = 100, control.circular=list()) {
if (tol <= 0) stop("'tol' must be positive")
# 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 <- MlewrappedcauchyRad(x, mu, rho, tol, max.iter)
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$rho <- res[2]
result$est.mu <- res[3]
result$est.rho <- res[4]
result$convergence <- TRUE
if (!is.na(res[5]) && res[5] > max.iter) {
result$convergence <- FALSE
}
class(result) <- "mle.wrappedcauchy"
return(result)
}
MlewrappedcauchyRad <- function(x, mu, rho, tol, max.iter) {
n <- length(x)
est.mu <- FALSE
if (is.null(mu)) {
mu <- MeanCircularRad(x)
est.mu <- TRUE
}
est.rho <- FALSE
if (is.null(rho)) {
rho <- RhoCircularRad(x)
est.rho <- TRUE
}
if (rho < 0 | rho > 1) stop("'rho' must be between 0 and 1")
if (est.mu) {
if (est.rho) {
mu1.old <- (2 * rho * cos(mu))/(1 + rho^2)
mu2.old <- (2 * rho * sin(mu))/(1 + rho^2)
w.old <- 1/(1 - mu1.old * cos(x) - mu2.old * sin(x))
flag <- TRUE
iter <- 0
while (flag & iter <= max.iter) {
iter <- iter + 1
mu1.new <- sum(w.old * cos(x))/sum(w.old)
mu2.new <- sum(w.old * sin(x))/sum(w.old)
diff1 <- abs(mu1.new - mu1.old)
diff2 <- abs(mu2.new - mu2.old)
if ((diff1 < tol) && (diff2 < tol))
flag <- FALSE
else {
mu1.old <- mu1.new
mu2.old <- mu2.new
w.old <- 1/(1 - mu1.old * cos(x) - mu2.old * sin(x))
}
}
mu.const <- sqrt(mu1.new^2 + mu2.new^2)
mu <- atan2(mu2.new, mu1.new) %% (2 * pi)
rho <- (1 - sqrt(1 - mu.const^2))/mu.const
} else {
score <- function(x, data, rho) {
sum(sin(data-x)/(1+rho^2-2*rho*cos(data-x)))
}
res <- uniroot(f=score, lower=mu-pi/2, upper=mu+pi/2, data=x, rho=rho, tol=tol)
mu <- res$root
iter <- NA
}
} else {
if (est.rho) {
wt <- function(x, mu, rho) {
((1-rho^2)*(1+rho^2-2*rho*cos(x-mu)))^(-1)
}
diff <- 1+tol
iter <- 0
rho.old <- rho
while (diff >= tol & iter <= max.iter) {
iter <- iter + 1
w <- wt(x, mu, rho)
sumw <- sum(w)
sumwcos <- w%*%cos(x-mu)
rho <- (sumw - sqrt(sumw^2 - sumwcos^2))/sumwcos
diff <- abs(rho - rho.old)
##### cat("iter: ", iter, " rho: ", rho, "\n")
rho.old <- rho
}
}
}
result <- c(mu, rho, est.mu, est.rho, iter)
return(result)
}
#############################################################
# #
# print.mle.wrappednormal function #
# Author: Claudio Agostinelli #
# E-mail: claudio@unive.it #
# Date: May, 22, 2006 #
# Version: 0.2 #
# #
# Copyright (C) 2006 Claudio Agostinelli #
# #
#############################################################
print.mle.wrappedcauchy <- 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$rho, digits=digits), "\n")
cat("\n")
if (!x$est.mu) cat("mu is known\n")
if (!x$est.rho) cat("rho is known\n")
if (!x$convergence) cat("\n The convergence is not achieved after the prescribed number of iterations \n")
invisible(x)
}
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