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ciEMoFI=function (x, alpha, eps = 1e-04, expmethod = "PadeRBS")
{
JVector = function(h, i) {
J = rep(0, h)
J[i] = 1
J
}
JMatrix = function(h, i, j) {
J = matrix(0, h, h)
J[i, j] = 1
J
}
signif_level = alpha
Q = x$par
h = nrow(Q)
te = x$te
tmabs = x$tm
QUseable = matrix(0, h, h)
for (i in 1:h) {
for (j in 1:h) {
if (Q[i, j] > eps && j != i)
QUseable[i, j] = 1
}
}
VQ = matrix(0, sum(sum(QUseable)), 2)
Points = length(VQ[, 1])
counter = 1
for (i in 1:h) {
for (j in 1:h) {
if (QUseable[i, j] == 1) {
VQ[counter, 1] = i
VQ[counter, 2] = j
counter = counter + 1
}
}
}
Hess = matrix(0, Points, Points)
LowerPart1 = matrix(0, h, h)
LowerPart2 = matrix(0, 2 * h, 2 * h)
ExpQ = expm(Q * te, method = expmethod)
Ceta=list()
MatrixExponentialeta=list()
for(i in 1:Points){
alpha = VQ[i, 1]
beta = VQ[i, 2]
UpperParteta = JVector(h, alpha) %*% t(JVector(h,beta)) - JVector(h, alpha) %*% t(JVector(h, alpha))
Ceta[[i]] = rbind(cbind(Q, UpperParteta), cbind(LowerPart1, Q))
MatrixExponentialeta[[i]] = expm(Ceta[[i]] * te, method = expmethod)
}
for (i in 1:Points) {
alpha = VQ[i, 1]
beta = VQ[i, 2]
for (j in 1:Points) {
mu = VQ[j, 1]
nu = VQ[j, 2]
UpperPartxi = rbind(cbind(JVector(h, mu) %*% t(JVector(h, nu)) - JVector(h, mu) %*% t(JVector(h,mu)),
LowerPart1), cbind(LowerPart1, JVector(h,mu) %*% t(JVector(h, nu)) - JVector(h, mu) %*% t(JVector(h, mu))))
Cxi = rbind(cbind(Ceta[[i]], UpperPartxi), cbind(LowerPart2, Ceta[[i]]))
MatrixExponentialxi = expm(Cxi * te, method = expmethod)
for (s in 1:h) {
for (r in 1:h) {
if (tmabs[s, r] > 0) {
Hess[i, j] = Hess[i, j] + tmabs[s, r] * ExpQ[s, r]^(-1) *( MatrixExponentialxi[s,r+3*h]
-ExpQ[s, r]^(-1) * MatrixExponentialeta[[i]][s, h+ r])*MatrixExponentialeta[[j]][s,h+r]
}
}
}
}
}
CVmat = -solve((Hess + t(Hess))/2)
SEvec = sqrt(diag(CVmat))
SEmat = matrix(0, nrow(tmabs), nrow(tmabs))
for (k in 1:length(VQ[, 1])) {
SEmat[VQ[k, 1], VQ[k, 2]] = SEvec[k]
}
diagse = vector(length = nrow(tmabs))
for (i in unique(VQ[, 1])) {
elem = VQ[which(VQ[, 1] == i), 2]
if (length(elem) == 1) {
diagse[i] = SEmat[i, elem]
}
else {
combs = combn(elem, 2)
CVsum = 0
for (k in 1:ncol(combs)) {
par1 = intersect(which(VQ[, 1] == i), which(VQ[,2] == combs[1, k]))
par2 = intersect(which(VQ[, 1] == i), which(VQ[,2] == combs[2, k]))
CVsum = CVsum + CVmat[par1, par2]
}
diagse[i] = sqrt(sum(SEmat[i, elem]^2) + 2 * CVsum)
}
}
diag(SEmat) = diagse
lowermat = Q - qnorm(1 - signif_level/2) * SEmat
lowermat[which(SEmat == 0)] = NA
lowermat[which(diag(Q) == 0), ] = 0
uppermat = Q + qnorm(1 - signif_level/2) * SEmat
uppermat[which(SEmat == 0)] = NA
uppermat[which(diag(Q) == 0), ] = 0
limits = list(lower = lowermat, upper = uppermat, FI=Hess, CVmat=CVmat)
limits
}
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