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# 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
################################################################################
# FUNCTION: DESCRIPTION:
# tsHessian Computes Two Sided Hessian matrix
################################################################################
tsHessian <-
function(x, fun, ...)
{
# Description:
# Computes two sided (TS) approximated Hessian
# Source:
# A function borrowed from Kevin Sheppard's Matlab garch toolbox
# as implemented by Alexios Ghalanos in his rgarch package
# Notes:
# optionally requires package Matrix (added as suggestion)
# FUNCTION:
# Settings:
n = length(x)
fx <- fun(x, ...)
eps = .Machine$double.eps
# Compute the stepsize:
h = eps^(1/3) *
apply( as.data.frame(x), 1, FUN = function(z) max(abs(z), 1.0e-2))
xh = x + h
h = xh - x
ee = diag(h) # Matrix(diag(h), sparse = TRUE)
# Compute forward and backward steps:
gp = vector(mode = "numeric", length = n)
for(i in 1:n) gp[i] <- fun(x + ee[, i], ...)
gm = vector(mode = "numeric", length = n)
for(i in 1:n) gm[i] <- fun(x - ee[, i], ...)
H = h %*% t(h)
Hm = H
Hp = H
# Compute double forward and backward steps:
for(i in 1:n){
for(j in i:n){
Hp[i, j] <- fun(x + ee[, i] + ee[, j], ...)
Hp[j, i] <- Hp[i, j]
Hm[i, j] <- fun(x - ee[, i] - ee[, j], ...)
Hm[j, i] <- Hm[i, j]
}
}
# Compute the Hessian:
for(i in 1:n){
for(j in i:n){
H[i, j] = ((Hp[i, j] - gp[i] - gp[j] + fx + fx - gm[i] - gm[j] +
Hm[i, j]) / H[i, j]) / 2
H[j, i] = H[i, j]
}
}
# Return Value:
return(H)
}
################################################################################
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