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#' @importFrom stats rnorm
#' @importFrom stats cov
#' @importFrom stats pchisq
Iteration_GM <- function(num, full_id, G_all, M_all, evectors1, evectors2, evals1, evals2, pskat1, pskat2, acc, method) {
p1<-p2<-vector()
for (k in 1:num) {
r_star = rnorm(dim(full_id)[1], 0, 1)
r_star = cbind(full_id, r_star)
G_all_star = merge(r_star, G_all)
G_all_star = G_all_star[order(G_all_star$order),]
M_all_star = merge(r_star, M_all)
M_all_star = M_all_star[order(M_all_star$order),]
r_star1 = t(evectors1) %*% G_all_star$r_star
r_star2 = t(evectors2) %*% M_all_star$r_star
if (length(evals1)==1) { Q1_star = r_star1 * evals1 * r_star1
} else { Q1_star = t(r_star1) %*% diag(evals1) %*% r_star1 }
if (length(evals2)==1) { Q2_star = r_star2 * evals2 * r_star2
} else { Q2_star = t(r_star2) %*% diag(evals2) %*% r_star2 }
if (method=="davies"){
tmpout1_star<-davies(Q1_star, evals1, acc=acc)
tmpout2_star<-davies(Q2_star, evals2, acc=acc)
p1[k]<-tmpout1_star$Qq
p2[k]<-tmpout2_star$Qq
}
else if (method=="kuonen"){
p1[k]<-pchisqsum(Q1_star,rep(1,length(evals1)),evals1,lower.tail=F,method="sad")
p2[k]<-pchisqsum(Q2_star,rep(1,length(evals2)),evals2,lower.tail=F,method="sad")
}
}
p1[p1==0|p1<0] = 1e-4
p1[p1>1] = 1
p2[p2==0|p2<0] = 1e-4
p2[p2>1] = 1
p01_single = pskat1
p02_single = pskat2
T01 = -2*(log(pskat1) + log(pskat2))
E_T01 = 2*2
V_T01 = 2*2*2 + 2*cov(-2*log(p1),-2*log(p2))
v01 = 2*E_T01**2/V_T01
c01 = v01/E_T01
p01_dual = pchisq( c01*T01, df=v01, lower.tail=FALSE)
min0 = min(c(p01_single,p02_single,p01_dual))
p1_single = p1
p2_single = p2
T1 = -2*(log(p1) + log(p2))
E_T1 = 2*2
V_T1 = 2*2*2 + 2*cov(-2*log(p1),-2*log(p2))
v1 = 2*E_T1**2/V_T1
c1 = v1/E_T1
p1_dual = pchisq( c1*T1, df=v1, lower.tail=FALSE)
min_pert = apply(cbind(p1_single,p2_single,p1_dual),1,min)
pval_pert = sum(min_pert<min0)/(length(min_pert)+1)
if (is.na(pval_pert)) pval_pert=1
if (is.na(p01_dual)) p01_dual=1
c(pval_pert, p01_dual, p01_single,p02_single)
}
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