RM <- function(C0,Cx,MM,SS,list_dist,a,iter,tol,n,alph){

CorrChol <- function(Cz,Cx,method){
V<-eigen(Cz)
if(any(V$values<0)){
C <- sdpt3r::nearcorr(Cz)
Cz <- C$X[[1]]}
return(Cz)
}
GN <- function(CovZ,Cx,MM,SS,list_dist,n,method){
m <- dim(CovZ)[1]
CovZ<-CorrChol(CovZ,Cx,method)
CholZ <- chol(CovZ)
W <- MASS::mvrnorm(n, rep(0,m), diag(m))
Z <- W%*%CholZ
U <- pnorm(as.matrix(Z))
X1<-sapply(1:m, FUN = function(i) list_dist[[i]](U[,i]))
Corr<-((t(X1)%*%X1)/n - MM)/SS
diag(Corr)<-1
return(Corr)
}
Cm <-C0
Ca <- C0
err <- 1:(iter+1)
er<-GN(C0,Cx,MM,SS,list_dist,n)- Cx
err[1] <- norm(er,'F')
e <- err[1]
for(i in 1:iter){
C1<-C0-(a*i^(-alph))*er
Cm<-Cm+C1
Cb<-Cm/(i+1)
er<-GN(Cb,Cx,MM,SS,list_dist,n)-Cx
err[i+1]<-norm(er,'F')
if(err[i+1]<e){
Ca <- Cb 
e <- err[i+1]}
if(norm(er,'F')<tol){
print('Convergence was reached')
print('Number of iterations:')
print(i)
err <- err[1:i+1]
Cb=CorrChol(Cb,Cx)
return(list(Cb,err))}
C0<-C1}
print('All iterations was reached')
Ca<-CorrChol(Ca,Cx)
return(list(Ca,err))}