# the inverse function
lsfi_from_lsmi <- function( lsmi, num_intervals ) {
lsfi <- lsmi[1]
if (length(num_intervals) > 1) {
for (i in 2:length(num_intervals)) {
lsfi <- lsfi + prod(num_intervals[1:(i-1)]) * (lsmi[i]-1)
}
}
return(lsfi)
}
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