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UPsystematicpi2<-function(pik)
{
n=sum(pik)
n=.as_int(n)
pik1 = pik[pik > 0 & pik < 1]
N = length(pik1)
Vk = cumsum(pik1)
Vk1=Vk%%1
if(Vk1[N]!=0) Vk1[N]=0
r = c(sort(Vk1), 1)
cent = (r[1:N] + r[2:(N + 1)])/2
p = r[2:(N + 1)] - r[1:N]
A = matrix(c(0, Vk), nrow = N + 1, ncol = N) -
t(matrix(cent,nrow = N, ncol = N + 1))
A = A%%1
M = matrix(as.integer(A[1:N, ] > A[2:(N + 1), ]), N, N)
pi21 = M %*% diag(p) %*% t(M)
pi2 = pik %*% t(pik)
pi2[pik > 0 & pik < 1, pik > 0 & pik < 1] = pi21
pi2
}
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