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# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program 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 General Public License for more details.
#
# A copy of the GNU General Public License is available at
# http://www.r-project.org/Licenses/
charStable <- function(theta, tau, pm = 0)
{
# pm is the type parametrization as described by Nolan(2009)
# It takes the value 0 or 1
# const can fixe parameters. It is NULL for no constraint or
# a matrix in which case the constraint is theta[const[,1]]=const[,2]
a <- theta[1]
b <- theta[2]
g <- theta[3]
d <- theta[4]
if(pm == 0)
{
if(a == 1)
{
if(g == 0)
{
the_car <- exp(complex(imaginary = d*tau))
}
else
{
re_p <- -g * abs(tau)
im_p <- d * tau
im_p[tau!=0] <- im_p[tau != 0] + re_p[tau != 0]*2/pi*b*sign(tau[tau != 0])*log(g*abs(tau[tau != 0]))
the_car <- exp(complex(real = re_p, imaginary = im_p))
}
}
else
{
if(g == 0)
{
the_car <- exp(complex(imaginary = d*tau))
}
else
{
phi <- tan(pi*a/2)
re_p <- -g^a*abs(tau)^a
im_p <- d*tau*1i
im_p[tau != 0] <- im_p[tau != 0] + re_p*( b*phi*sign(tau[tau != 0])*(abs(g*tau[tau != 0])^(1-a) - 1) )
the_car <- exp(complex(real = re_p, imaginary = im_p))
}
}
}
if(pm == 1)
{
if(a == 1)
{
re_p <- -g*abs(tau)
im_p <- d*tau
im_p[tau!=0] <- im_p[tau != 0]+re_p*(b*2/pi*sign(tau[tau != 0])*log(abs(tau[tau!=0])))
the_car <- exp(complex(real = re_p, imaginary = im_p))
}
else
{
phi <- tan(pi*a/2)
re_p <- -g^a*abs(tau)^a
im_p <- re_p*(-phi*b*sign(tau)) + d*tau
the_car <- exp(complex(real = re_p, imaginary = im_p))
}
}
return(the_car)
}
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