# 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>
#   info@rmetrics.org
#   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:               PARAMETER ESTIMATION:    
#  .garchRCDAGradient      Computes R coded CDA matrix of contributions 
#				                   to the Gradient
################################################################################


.garchRCDAGradient <- 
    function(par, .params, .series, eps = 1.0e-4)
{   
    # A function implemented by Diethelm Wuertz

    # Description:
    #   Compute R coded CDA (central difference approximated) Gradient
    
    # Reference:
    #   http://status.sph.umich.edu/computing/manuals/sas8/stat/chap46/sect26.htm
    
    # FUNCTION:
    
    # Starttime
    .StartGradient <- Sys.time()
    
    # Algorithm
    algorithm = .params$control$algorithm[1]
    .trace = FALSE
 
    # Compute matrix of contributions to the Gradient:
    eps = eps * par
    n = length(llh.grad)
    K = length(par)
    G = matrix(0, nrow = n, ncol = K)
    for (i in 1:K) {
        x1 = x2 = par
        x1[i] = x1[i] + eps[i]
        x2[i] = x2[i] - eps[i]
        .garchLLH(x1, .trace)
        llh.grad1 <- llh.grad
        .garchLLH(x2, .trace)
        llh.grad2 <- llh.grad
        G[,i] = ( 
             llh.grad1 - 
             llh.grad2 ) / 
                 (2*eps[i])
    } 
    rownames(G) = c(1:n)
    colnames(G) = names(par)
    time = Sys.time() - .StartGradient
    
    # Attribute Exdecution time
    attr(G, "time") = time
    
    # Return Value: 
    G
}

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