# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General 
# Public License along with this library; if not, write to the 
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston, 
# MA  02111-1307  USA

# Copyrights (C)
# for this R-port: 
#   1999 - 2008, Diethelm Wuertz, Rmetrics Foundation, GPL
#   Diethelm Wuertz <wuertz@itp.phys.ethz.ch>
#   www.rmetrics.org
# for the code accessed (or partly included) from other R-ports:
#   see R's copyright and license files
# for the code accessed (or partly included) from contributed R-ports
# and other sources
#   see Rmetrics's copyright file


################################################################################
# FUNCTION:             DESCRIPTION:  
#  dgh                   Returns density for generalized hyperbolic DF
#  pgh                   Returns probability for generalized hyperbolic DF
#  qgh                   Returns quantiles for generalized hyperbolic DF
#  rgh                   Returns random variates for generalized hyperbolic DF
################################################################################


dgh = 
function(x, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = 1, log = FALSE)
{   # A function implemented by Diethelm Wuertz
    
    # Description:
    #   Returns density for the generalized hyperbolic distribution

    # FUNCTION:
    
    # Checks:
    if (alpha <= 0) stop("alpha must be greater than zero")  
    if (delta <= 0) stop("delta must be greater than zero")
    if (abs(beta) >= alpha) stop("abs value of beta must be less than alpha")

    # Density:
    arg = delta*sqrt(alpha^2-beta^2)
    a = (lambda/2)*log(alpha^2-beta^2) - (
        log(sqrt(2*pi)) + (lambda-0.5)*log(alpha) + lambda*log(delta) +
        log(besselK(arg, lambda, expon.scaled = TRUE)) - arg )      
    f = ((lambda-0.5)/2)*log(delta^2+(x - mu)^2)
    
    # Use exponential scaled form to prevent from overflows:
    arg = alpha * sqrt(delta^2+(x-mu)^2)
    k = log(besselK(arg, lambda-0.5, expon.scaled = TRUE)) - arg
    e = beta*(x-mu)  
    
    # Put all together:
    ans = a + f + k + e
    if(!log) ans = exp(ans)
    
    # Return Value:  
    ans
}


# ------------------------------------------------------------------------------

    
pgh = 
function(q, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = 1) 
{   # A function implemented by Diethelm Wuertz

    # Description:
    #   Returns probability for the generalized hyperbolic distribution
  
    # FUNCTION:
    
    # Checks:
    if (alpha <= 0) stop("alpha must be greater than zero")  
    if (delta <= 0) stop("delta must be greater than zero")
    if (abs(beta) >= alpha) stop("abs value of beta must be less than alpha")
    
    # Probability:
    ans = NULL
    for (Q in q) {
        Integral = integrate(dgh, -Inf, Q, stop.on.error = FALSE, 
            alpha = alpha, beta = beta, delta = delta, mu = mu, 
            lambda = lambda)
        ans = c(ans, as.numeric(unlist(Integral)[1]))
    }
       
    # Return Value: 
    ans
}
    
 
# ------------------------------------------------------------------------------

    
qgh = 
function (p, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = 1) 
{   # A function implemented by Diethelm Wuertz

    # Description:
    #   Returns quantiles for the generalized hyperbolic distribution
 
    # FUNCTION:
    
    # Checks:
    if (alpha <= 0) stop("alpha must be greater than zero")  
    if (delta <= 0) stop("delta must be greater than zero")
    if (abs(beta) >= alpha) stop("abs value of beta must be less than alpha")
    
    # Internal Function:
    .froot <- 
    function(x, alpha, beta, delta, mu, lambda, p) 
    {
        pgh(q = x, alpha = alpha, beta = beta, delta = delta, 
            mu = mu, lambda = lambda) - p
    }
    
    # Quantiles:
    result = NULL
    for (pp in p) {
        lower = -1
        upper = +1
        counter = 0
        iteration = NA
        while (is.na(iteration)) {
            iteration = .unirootNA(f = .froot, interval = c(lower, 
                upper), alpha = alpha, beta = beta, delta = delta, 
                mu = mu, lambda = lambda, p = pp)
            counter = counter + 1
            lower = lower - 2^counter
            upper = upper + 2^counter
        }
        result = c(result, iteration)
    }
    
    # Return Value:
    result
}


# ------------------------------------------------------------------------------


rgh = 
function (n, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = 1)
{   # A function implemented by Diethelm Wuertz
    
    # Description:
    #   Returns random variates for the generalized hyperbolic distribution

    # FUNCTION:
    
    # Checks:
    if (alpha <= 0) stop("alpha must be greater than zero")  
    if (delta <= 0) stop("delta must be greater than zero")
    if (abs(beta) >= alpha) stop("abs value of beta must be less than alpha")
    
    # Settings:
    theta = c(lambda, alpha, beta, delta, mu)
    
    # Random Numbers:
    ans = .rghyp(n, theta)
    
    # Attributes:
    attr(ans, "control") = c(dist = "gh", alpha = alpha, beta = beta, 
    delta = delta, mu = mu, lambda = lambda)
    
    # Return Value:
    ans 
}


################################################################################